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THE JOURNAL OF FINANCE • VOL. LXXVIII, NO. 6 • DECEMBER 2023

Global Pricing of Carbon-Transition Risk
PATRICK BOLTON and MARCIN KACPERCZYK*
ABSTRACT
The energy transition away from fossil fuels exposes companies to carbon-transition
risk. Estimating the market-based premium associated with carbon-transition risk
in a cross section of 14,400 firms in 77 countries, we find higher stock returns associated with higher levels and growth rates of carbon emissions in all sectors and most
countries. Carbon premia related to emissions growth are greater for firms located
in countries with lower economic development, larger energy sectors, and less inclusive political systems. Premia related to emission levels are higher in countries with
stricter domestic climate policies. The latter have increased with investor awareness
about climate change risk.

PUBLIC OPINION, GOVERNMENTS, BUSINESS LEADERS, and institutional
investors all over the world are awakening to the urgency of combatting climate change.1 This growing concern about climate change may crystalize into
a faster and perhaps more disorderly transition away from fossil fuels to
* Patrick Bolton is with Columbia University; Imperial College; CEPR; and NBER. Marcin
Kacperczyk is with Imperial College and CEPR. We thank Lucian Bebchuk; John Cochrane; Harrison Hong; Paul Hsu; Louis Kaplow; Paymon Khorrami; Christian Leuz; Pedro Matos; Stefan Nagel
(the editor); Kunal Sachdeva; Zacharias Sautner; two referees; and the associate editor for many
helpful suggestions. We are also grateful to seminar participants at the Bank for International
Settlements, Bank of England, Bank of Italy, Bank of Japan, Blackrock, Danmarks Nationalbank
Climate Conference, Florida State University, Harvard Law School, HEC Montreal, Imperial College, INSEAD, Mayo Finance Seminar, McGill, NBER LTAM Meetings, NBIM, Rice University,
University of Alberta, University of Cyprus, University of Geneva Climate Conference, University
of Miami, UNPRI, Virtual Seminar on Climate Economics, and the World Bank for their comments. We are grateful to Trucost for giving us access to their corporate carbon emissions data,
and to Adrian Lam and Jingyu Zhang for their very helpful research assistance. Some of the ideas
in this paper have been reported in the working draft, “Carbon Premium around the World.” This
project has received funding from the European Research Council (ERC) under the ERC Advanced
Grant program (grant agreement No. 885552 Investors and Climate Change). We have read The
Journal of Finance’s disclosure policy and have no conflicts of interest to disclose.
Correspondence: Marcin Kacperczyk, Imperial College, London Business School, London, SW7
2AZ, UK, e-mail: m.kacperczyk@imperial.ac.uk

This is an open access article under the terms of the Creative Commons AttributionNonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.
1 Some of the most notable actions include the national and pan-national initiatives, such as
Conference of the Parties (COP), Nationally Declared Contributions (NDCs) supported by the
United Nations, or the G20 Taskforce for Climate-related Financial Disclosure (TCFD).
DOI: 10.1111/jofi.13272
© 2023 The Authors. The Journal of Finance published by Wiley Periodicals LLC on behalf of
American Finance Association.

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renewable energy. By now, over 100 countries have committed to carbon net
neutrality targets, representing nearly 50% of the world’s gross domestic product (GDP). In addition, several multilateral agreements and other commitments to reduce carbon emissions have been reached.2 This, in turn, means
greater carbon-transition risk for companies, especially those that rely more
on fossil fuel production or consumption. From an individual firm’s perspective, transition risk reflects the uncertain rate of adjustment toward carbon
neutrality. From investors’ perspective, the risk also embodies evolving beliefs
about the transition to cleaner energy. Hence, transition risk is the amalgamation of a wide range of shocks, including changes in climate policy, reputational
impacts, shifts in market preferences and norms, and technological innovation.
In this paper, we take a (forward-looking) global financial market perspective
to evaluate the economic importance investors attach to this transition risk by
looking at stock prices of a large set of global companies with different degrees
of exposure to this risk.
The economics literature on climate change following Nordhaus (1991) has
framed the issue of mitigation of climate change as a public goods problem that
requires a global Pigouvian carbon tax to internalize the externality of carbon
emissions. The tax should be set equal to the social cost of carbon (SCC) to
achieve efficiency, where the SCC is given by the discounted, expected, and
physical harm from a warming climate caused by the accumulation of carbon
particles in the atmosphere. This literature does not address the transition
risk that firms relying on fossil energy face as the economy adjusts to a renewable energy base. In contrast, the finance literature on climate change is
more directly concerned with the pricing of climate change risk, in particular,
transition risk. But this literature is still in its infancy, and we currently only
have patchy evidence on the pricing of carbon-transition risk, and especially
on the various sources of this risk. Accordingly, in this study we attempt a
more systematic, a more wide-ranging analysis than has been done to date on
the pricing of transition risk. We explore how corporate carbon emissions together with country characteristics that reflect the country’s likely progress in
the energy transition affect stock returns of over 14,400 listed companies in 77
countries over a period ranging from 2005 to 2018. This is essentially the universe of all listed companies globally for which it is possible to obtain carbon
emissions data and represents 80% of the market value of all public firms.
As is well known, cross-country studies are beset by endogeneity and identification challenges, as country-level variation can be driven by many different
sources. In this study, we can to some extent overcome these challenges by exploiting rich country-, industry-, and firm-level variation in carbon emissions
and other characteristics to identify the different sources of transition risk
relating to technological shifts, social norms, and energy policies. This granularity of firm-level observations can be combined with various fixed effects
2 Some of the prominent examples include China’s commitment to carbon net neutrality by
2060, and Japan’s and the United Kingdom’s commitments by 2050. See Bolton and Kacperczyk
(2021b) for more details on net zero commitments.

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to better understand what is driving transition risk. To our knowledge, this
is the first study in economics on transition risk with such a large panel data
structure.
The first contribution of our paper is to shed light on the distribution of corporate carbon emissions across all countries in our sample. In most studies
on global carbon emissions, the unit of analysis is the country and little information is provided about the breakdown of emissions across companies within
each country. According to Fortune magazine, in 2017 the 500 largest companies in the world generated $30 trillion in revenues.3 This represents 37.5%
of world GDP, which was around $80 trillion in 2017 according to the Central
Intelligence Agency’s CIA World Factbook. It is thus natural to view climate
change mitigation not just through the lens of the largest emitting countries,
but also through the lens of the largest emitting companies.
As a second contribution of our paper, we estimate the size of a global carbontransition risk premium by relating lagged firm-level emissions to individual
stock returns. Given the lack of concern about climate change until recently,
a plausible null hypothesis is that we should not find higher stock returns
for companies with higher carbon emissions over our sample period, with the
exception perhaps of Europe (and to some extent the United States, Japan, and
a few other OECD countries). A reasonable alternative hypothesis, however, is
that investors do pay attention to climate risk and that a carbon premium is
to be found in the parts of the world responsible for the highest fraction of
carbon emissions, that is, in the largest and most developed economies. It is in
these economies that emission reductions are most urgent and therefore where
transition risk is highest.
A few general striking results emerge from our analysis. The first general
finding is that the carbon premium is positively related to both the level of
emissions and the year-to-year growth in emissions, controlling for characteristics that predict returns. Given that the carbon transition is in essence transitory, carbon transition risk a priori ought to be reflected in both the levels
and rates of change in emissions. We also find that the premium is related to
both direct emissions from production (scope 1) and indirect emissions from
firms in the supply chain (scope 2 & scope 3). All the results are statistically
and economically highly significant. As an example, a one-standard-deviation
increase in cross-sectional scope 1 emissions is associated with a 1.1% increase
in annualized stock returns. A comparable result for changes in emissions is
2.2%. In general, the magnitude of the effect is stronger when we account for
underlying differences across industries, which underscores the importance of
industry adjustment in any study of carbon-transition risk. It is also stronger
for indirect scope 3 emissions.
Our findings bring out the fact that a firm’s exposure to carbon-transition
risk is proportional to the level of its emissions. This is a very robust finding,
which goes against the near exclusive focus of attention on emission intensity (the ratio of carbon emissions over sales, assets, or kWh) by practitioners
3 https://fortune.com/global500/2018/.

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and other climate finance studies. There are two reasons why asset managers
have focused on emission intensity. First, from a portfolio diversification perspective, the emission intensity measure allows for a portfolio construction approach that is independent of the size of the portfolio. Second, emission intensity treats firms of different sizes the same way. Firms are evaluated on their
carbon efficiency per unit of sales. By that metric, a large firm can be seen
as more environmentally friendly than a small firm, even though its climate
impact in terms of the size of its carbon emissions is much larger.
To be sure, the Financial Times-Statista ranking of Europe’s Climate Leaders ranks which companies performed best in terms of improving their carbon
intensity. As the 2022 Financial Times article listing the best performers explains: “The 400 companies listed below are those that achieved the greatest
reduction in their Scope 1 and 2 greenhouse gas (GHG) emissions intensity
over a 5-year period (2015–20) this time.”4 Two problematic examples from
this list (among others) are Fortum, with a reported 29.8% reduction in emission intensity, but an increase in total emissions of 157.2%; and Axereal, with
a 23.8% reduction in emission intensity, but an increase in total emissions of
236.2%. The list of climate leaders also includes companies with huge GHG
emissions, for example, Engie with 40.9 million tons of CO2e for 2020, or Holcim Group with 117 million tons of CO2e. These examples vividly illustrate the
difficulty with carbon intensity as a measure of carbon-transition risk.
Given the limited and fast disappearing carbon budget (consistent with
maintaining a temperature rise below 1.5° C with 83% probability),5 any improvement in carbon efficiency is, of course, desirable. Yet, the overriding objective for the world is to achieve carbon neutrality and bring net emissions down
to zero. The fact that all net zero pledges are in terms of absolute emission reduction targets is telling. What the world needs and aims for is first a reduction
in carbon emission levels, and second only an improvement in carbon efficiency.
It is therefore to be expected that investor exposure to carbon-transition risk
would be proportional to the level of emissions. The size of emissions is also
the core focus of institutional investor initiatives to reduce carbon emissions,
such as Climate Action 100+, which aims “to ensure [that] the world’s largest
corporate GHG emitters take necessary action on climate change.”6
Interestingly, the levels of and growth in emissions affect the carbon premium independently, which we interpret as reflecting both a long-run and
short-run component in carbon transition. Given that emissions are highly
persistent over time, the level of emissions picks up the long-run exposure
to transition risk, whereas changes reflect a company’s short-run drift away
from (or into) greater future emissions. Changes in emissions could also reflect
4 Neville Hawcock, “Special Report: Europe’s Climate Leaders 2022,” Financial Times, April 8,

2022, https://www.ft.com/climate-leaders-europe-2022.
5 See Intergovernmental Panel on Climate Change (IPCC) “Climate Change 2021, The Physical
Science Basis, Summary for Policy Makers,” https://www.ipcc.ch/report/sixthassessment-reportworking-group-i.
6 See https://www.climateaction100.org/.

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changes in earnings, but we control for this effect by adding the company’s
return on equity and sales growth to our independent variables.
To provide additional robustness to our estimation of the carbon premium,
and to partially address the possibility that stock returns are noisy, we also
relate carbon emissions to firms’ book-to-market ratios. We find that a onestandard-deviation increase in cross-sectional direct emissions is associated
with 13% higher book-to-market ratios, again controlling for a host of fixed
effects and firm characteristics. These results corroborate our return-based
findings. In particular, the economic magnitude of these findings is within the
range of our return estimates. This adds further evidence against the interpretation that the carbon premium is driven by unexpected return components.
A second general finding is a positive and significant carbon premium in
most areas of the world. It is present in North America, Europe, and Asia, but
with different magnitudes. It is less present in the Southern Hemisphere region, but this is an economically and socially more diverse group of countries.
Our cross-country results also suggest that financial markets are not fully integrated globally. A simple categorization of countries based on their level of
economic development does not explain the variation in carbon premium across
countries. However, at a more granular level, we find that the short-term carbon premium is generally higher among firms that are headquartered in countries with more modest economic development. It is higher in countries with
lower GDP per capita, countries whose economic output relies more on the
manufacturing sector, and in countries with less developed healthcare sectors.
Yet, the same characteristics cannot explain the cross-country variation in the
long-term carbon premium. These results stand in contrast to the common
view that carbon transition is exclusively a problem for developed countries.
As a third general contribution of our paper, we study the different sources
of this carbon-transition risk. The main premise of our tests is that in partially
segmented markets, the local country environment can amplify or mitigate the
average premium. Since country-level evidence is possibly subject to omitted
variables bias, we exploit firm-level variation in carbon emissions in conjunction with a variety of firm-level controls and fixed effects to better identify each
economic channel. Our identification approach is similar to the one effectively
used by Rajan and Zingales (1998) in their study of the link between financial
development and economic growth.
We identify several country-level characteristics that matter significantly.
We group these characteristics into two broad categories, respectively, political or social factors, and energy factors. Regarding political factors, we find
that both “voice” and “rule of law” significantly affect the short-run carbon
premium associated with the growth in emissions. More democratic countries
(with stronger rules of law) tend to have lower carbon premia, other things
equal. Further, we find that the long-term carbon premium is larger in countries with tighter climate policies. This finding suggests that investors perceive climate policies to be permanent and unlikely to be reversed. Notably,
when we separate domestic policies from international agreements, we find
that only the former are economically significant, and the latter have a very

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small effect. This result underscores the importance of political coordination
costs associated with climate policies, a problem that has beset the international community in recent years.
When we consider country-level variations in the energy mix, we find that
the carbon premium is lower in countries with a higher share of renewable
energy, and higher in countries with greater dependence on the energy sector.
The energy mix effect is reflected in the short-term premium, which suggests
that any technological shocks are perceived as transitory, or alternatively as
a factor that is hard to estimate in the long run. Interestingly, we find that a
country’s energy consumption is not a significant predictor of the carbon premium, which underscores the importance of distinguishing between the production and consumption sides of energy.
Finally, we also find that in the countries that have been exposed to greater
damages from climate disasters (such as floods, wild fires, and droughts) there
is no significantly different carbon premium. This result suggests that the carbon premium does not reflect physical climate risks, nor that physical risk is
positively correlated with transition risk, or that (consistent with the findings
of Hong, Li, and Xu (2019)) transition risk may be more salient to investors in
countries experiencing rising physical risk.
The sociopolitical and energy-related channels mostly reflect the cash flow
effects related to transition risk. Of equal importance may be discount rate
effects that reflect investors’ perceptions about carbon-transition risk. To assess the importance of the latter, we consider natural time period breaks in
our sample period. Given that climate change has become a major issue for
investors only recently, we explore how the carbon premium has changed in
recent years. We compare the estimated premia for the 2 years leading up to
the Paris agreement in 2015 and following the agreement. Several striking results emerge from this analysis. First, when we pool all countries together, we
find that there was no significant premium right before the Paris agreement,
but a highly significant and large premium after the agreement. This result
is consistent with the view that the Paris agreement has changed investors’
awareness regarding the urgency of climate change. Second, the change in the
carbon premium is mostly related to long-term risks, which, given our previous results, suggests that the Paris agreement led investors to update their beliefs about the long-term impact of climate policy tightness rather than on the
short-term impact of technological shocks or changes in the political environment. Finally, when we break down the change in the carbon premium around
the Paris agreement by continent, we find that the premium has sharply
risen in Asia, and less so in North America and Europe. In effect, Asia is entirely responsible for the rise in the global carbon premium around the Paris
agreement.
A difficult question to answer is how changes in carbon-transition risk get
impounded into asset prices. From an equilibrium perspective, our results imply the existence of a transition stage during which prices of assets with low
emissions are bid up while prices of assets with high emissions are bid down
in response to changing investor beliefs. The different repricing phases are

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difficult to pin down since individual asset prices may transition at different
times and at different speeds. Still, we provide some evidence that such repricing has indeed taken place. We show that the rise in the use of renewable
technology coincides with the decrease in stock prices of oil majors. Similar
findings can be observed for countries that rely more on natural resources.
These repricing effects are economically large and underscore the importance
of the energy transition to a new equilibrium.
I. Related Literature
We are obviously not the first to undertake a cross-country analysis in sustainable finance. The closest analysis to ours is by Görgen et al. (2021), who
construct a carbon risk factor using stock return differences between a group
of “brown” and “green” firms around the world. Their paper is mostly focused
on the pricing properties of the factor and not on transition risk itself. It does
not relate stock returns to any of the mechanisms that are central to our paper, such as short-term versus long-term risk, or technology, social, and policy
risk. Also related in terms of general subject matter are the studies by Dyck
et al. (2019) and Gibson et al. (2022), both of which explore how environmental,
social, and governance (ESG)-motivated investing varies around the world. Notably, neither of these studies addresses the pricing of carbon-transition risk,
which is the focus of our paper.
Next to this cross-country literature there is, of course, a growing countrylevel climate finance literature, mostly focused on the United States. In an
early theoretical contribution, Heinkel, Kraus, and Zechner (2001) have shown
how divestment from companies with high emissions can give rise to higher
stock returns. An early study by Matsumura, Prakash, and Vera-Munoz (2014)
finds that higher emissions are associated with lower firm values. Similarly,
Chava (2014) finds that firms with higher carbon emissions have a higher cost
of capital. More recently, Ilhan, Sautner, and Vilkov (2021) have found that
carbon emission risk is reflected in out-of-the-money put option prices. Hsu,
Li, and Tsou (2023) derive and test a model showing that highly polluting
firms are more exposed to environmental regulation risk and command higher
average returns. Engle et al. (2020) have constructed an index of climate news
through textual analysis of the Wall Street Journal and other media and show
how a dynamic portfolio strategy can be implemented that hedges risk with
respect to climate change news. Monasterolo and De Angelis (2020) explore
whether investors demand higher risk premia for carbon-intensive assets following the COP21 agreement. Garvey, Iyer, and Nash (2018) study the effect
of changes in direct emissions on stock returns, and Bolton and Kacperczyk
(2021a) find that there is a significantly positive effect of carbon emissions on
U.S. firms’ stock returns for both direct and indirect carbon emissions. Among
all these studies, the last one is most closely related given its focus on carbon
pricing and the use of similar data sources. Nevertheless, that paper is mostly
focused on carbon pricing and the response of portfolio managers to transition
risk. More fundamentally, because it is solely based on U.S. data, that paper is

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silent on the mechanisms driving transition risk, which is the central focus of
this paper.
Other related studies have explored the asset pricing consequences of
greater material risks linked to climate events and global warming. Bansal,
Kiku, and Ochoa (2016) reveal the asset pricing implications of rising temperatures using an equilibrium framework with an endogenous temperature
process embodied in a standard long-run risk model. Hong, Wang, and Yang
(2023) propose an asset pricing model in which natural disaster mitigation
costs are priced in the cross section of firms. Hong, Li, and Xu (2019) find that
the rising drought risk caused by climate change is not efficiently priced by
stock markets.
The remainder of the paper is organized as follows: Section II outlines
the conceptual framework for our empirical tests, Section III describes the
data and provides summary statistics, Section IV discusses the results, and
Section V concludes.
II. Conceptual Framework
We begin by outlining a conceptual framework that could account for the
presence of carbon-transition risk for investors in a global economy on the way
to decarbonization in the next couple of decades. The basic concept of carbontransition risk is meant to capture investor uncertainty with respect to all the
changes companies will be faced with along the expected pathway to carbon
net neutrality. The net zero targets that many countries and companies have
embraced are anchored around the current scientific consensus on the need
to eliminate global carbon emissions by 2050 to avoid increases in average
temperatures of more than 1.5 C relative to preindustrial levels that would
pose a threat to human existence.
We illustrate the formal link between global emissions and temperature
changes in Figure 1. This Intergovernmental Panel on Climate Change (IPCC)
graph provides simulations of various scenarios relating the changes in emissions and projected temperature outcomes. As is illustrated, to stay within a
1.5 C limit, global emissions would need to go down to zero by 2050, from the
level of 420 Gt of CO2 as of 2018. Since then, the problem has become even
more dire, as the latest IPCC report warns that additional carbon emissions as
of 2020 should not exceed a cumulative total of 300Gt of CO2 . Achieving this
goal involves a complete transition of the corporate sector from brown to green
energy. Such a radical transition will come with new risks, which we define
as carbon-transition risk. Importantly, this risk will materialize irrespective of
the physical damages due to future changes in climate.
This carbon-transition risk should be understood in the context of a nonstationary climate that is evolving in response to the accumulation of carbon
emissions in the atmosphere. Because the underlying economy and climate
are nonstationary, carbon-transition risk is also a nonstationary risk. Even if
there is no unexpected change in a company’s emissions, the carbon premium
can change with time simply because the underlying economy is nonstationary.

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Figure 1. Global emissions and projected average annual global temperature. (Color
figure can be viewed at wileyonlinelibrary.com)

Also, the marginal effect of emissions is different depending on how close we
are to a potentially cataclysmic tipping point.
The closer we get to exhausting the carbon budget, the worse any marginal
emissions will be. The transition to a net zero economy involves a finite time
frame. Thus, for the same level of emissions, coming closer to the end date
(say, 2050) is going to be riskier for a given company because of the increasing
pressure to eliminate emissions. That is why the premium is likely to be rising
over time even if a company’s level of emissions does not change. Of course, this
does not necessarily mean that the carbon premium will rise steadily over time.
A more plausible scenario could be an abrupt unexpected downward repricing
of brown assets or upward repricing of green assets.
From an asset pricing perspective, we can split carbon-transition risk into
two separate sources: risks tied to cash flows and risks associated with changes
in discount rates. The cash flow channel concerns all the risks related to the
cost of decarbonization, stranded assets, and technological shocks. Further,
these adjustment costs and the speed at which they materialize are affected by
the degree of climate policy tightness, which itself is uncertain. Another amplifying effect works through capital expenditures, which are required to refit
the economy for renewable energy use. The rate at which these capital expenditures are made over the next decades is difficult to predict. Even if one can
predict the relative vulnerabilities of certain industries, cash flow outcomes
as well as investors’ beliefs for individual firms are far from certain. Take the
auto industry for example. All car manufacturers are now scrambling to switch
to electric vehicles (EVs). Except for Tesla and new EV entrants, their market
values have taken a beating (another way of saying that there is a carbon

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premium on their stocks). Which of these companies will successfully transition to 100% EVs is difficult to say.
There are no models for the energy transition that can be readily applied
to capture carbon-transition risk. However, equilibrium models in which technological risk is priced, as in Kogan and Papanikolaou (2014) and Hsu, Li,
and Tsou (2023), are helpful reference points to guide the analysis of carbontransition risk. In addition, the asset pricing model of Hong, Wang, and Yang
(2023), which links natural disaster mitigation costs to asset prices in the
cross section of firms could be applied to determine the impact on firm valuation of expected future carbon-transition costs. Other helpful related frameworks are the equilibrium models with uncertainty about policy changes of
Pastor and Veronesi (2013). The basic prediction from these models is that
risk-averse investors require compensation for holding assets that are exposed
to carbon-transition risk, so that the equilibrium firms with greater exposure
to carbon-transition risk offer higher expected returns. Note that the same prediction would obtain if investors simply developed a distaste for brown companies. These investors would require compensation for holding their noses, so to
speak, so that brown companies would also offer higher returns even if there
is no divestment in equilibrium.
The carbon premium can also be affected by changes in discount rates and
investor expectations about carbon-transition risk. An important aspect of investor preferences and expectations is how the prevailing socioeconomic environment shapes investors’ attitudes and outlooks toward climate change. In
a society that values protection of the environment and combatting climate
change, one should expect that investors will demand greater premia for holding assets associated with high carbon emissions. The role of social preferences
works in a way similar to specialized and incomplete information in the equilibrium models of Merton (1987), Pastor, Stambaugh, and Taylor (2021), or
Pedersen, Fitzgibbons, and Pomorski (2021), which generate higher risk premia driven by limitations imposed on investors’ effective investment opportunity sets. This discount rate channel is different from the categorical divestment channel, as in the “sin stock” literature (Hong and Kacperczyk (2009)).
The main difference is that it involves an intensive margin adjustment, with
investors demanding higher compensation for holding assets with greater exposure to carbon-transition risk, rather than an extensive margin adjustment
by a fraction of categorical divestors. Of course, both discount rate channel and
divestment channels could be present in practice. Our findings of a significant
carbon premium in all sectors, not just in the coal, oil, and gas sector, suggest that the discount rate channel is an important factor and that carbon risk
premia are not just caused by divestment.
Each of these different channels is a plausible driver of carbon-transition
risk. Determining their relative importance is largely an empirical question.
Also, determining the size of the premium associated with carbon-transition
risk is an empirical matter. Our empirical analysis aims to provide a quantitative assessment of each channel. Following Bolton and Kacperczyk (2021a),
we use firm-level carbon emissions as proxies for the relative exposure of a

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Figure 2. Decarbonization pathways conditional on period-specific emissions. (Color
figure can be viewed at wileyonlinelibrary.com)

company to carbon-transition risk. We distinguish between the level of emissions, which indicates the firm’s distance from a net zero emission target (a
measure of long-term risk), and the growth rate of emissions, which indicates
the rate at which a company is decarbonizing (a measure of short-term risk).
Firms that keep increasing their emissions may be seen as riskier due to their
growing future decarbonization challenge. In this respect, carbon emissions
are a state variable that investors care about, and increasingly so, just as investors care about vulnerabilities such as supply bottlenecks and commodity
price changes. In our empirical tests, we use the cross-sectional variation in
both measures to characterize differences in corporate exposures to carbontransition risk. Interestingly, we find that long-term and short-term carbontransition risk are not highly correlated at the firm level.
Carbon emissions are plausibly a time-dependent state variable. The same
level of emissions in year t does not reflect the same conditions as in year t−1
or year t+1. The reason is that any year that passes brings a firm closer to the
net zero target deadline. If the level of emissions in year t remains the same as
in year t−1, this means that the firm faces a steeper decarbonization challenge
in year t than it did in year t−1, as Figure 2 below illustrates. Therefore, investors’ perceptions of carbon transition risk evolve as they update their information about a firm’s year-to-year decarbonization progress. The most recent
carbon emissions data reflect investors’ best assessment of the decarbonization effort their firm faces going forward. Given that the underlying context
evolves over time, this means that the information contained in the emissions
of year t−1 is superseded by those of year t as they are gradually revealed. We
illustrate this logic in Figure 2 below.
The figure displays the level of emissions E in years t−1 and t. The level
of emissions sets the pathway to net zero by year T. When investors observe
the new level of emissions for year t, the information contained in the previous year’s emissions Et−1 is obsolete because it no longer informs investors
about the transition risk reflected in the new pathway starting in year t. This

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Global Pricing of Carbon

The Journal of Finance®

observation suggests that the news effect of the emissions in any given year
should dissipate over time, as investors gradually learn about the likely new
yearly emission numbers. Therefore, any carbon premium we may identify is
likely to be linked to a transitory firm-level state variable. This firm-level state
variable can be transitory even if yearly emissions are highly persistent. As the
figure shows, the level Et is almost the same as the level Et−1 , yet the pathway
gets steeper as time passes. What investors care about is the transition risk
embedded in the pathway to net zero going forward; the slope of this pathway
changes even if the level of emissions remains unchanged. The level of emissions, of course, can itself change, but, as we show, this change is quite volatile
and hard to predict. As a result, there is a lot of news content in the latest
emission numbers.
The strength of our empirical analysis is its global reach. Given that firms in
different countries may face different carbon transition paths, it is natural to
explore whether such variation in geographic location matters for asset prices.
From the perspective of investors pricing transition risk, what matters is the
ability to share risk with other investors as well as across different assets. Under the hypothesis of fully integrated markets and a global representative investor, one should expect the pricing of transition risk not to vary much across
different locations. On the other hand, under (partially) segmented markets,
one would expect to see clear differences in pricing across different locations.
This heterogeneity could result from different policy regimes, different technological progress, or different perceptions of the threat of climate change. Thus,
our empirical tests should shed useful light on the degree of market integration
in pricing carbon risk.
In the rest of the paper, we build on the broad notions above and test them
empirically using a large cross section of publicly listed firms from around the
world.
III. Data and Sample
Our primary database matches two data sets: Trucost, which provides annual information on firm-level carbon and other GHG emissions, and FactSet,
which assembles data on stock returns and corporate balance sheets. We performed the matching using ISIN as a main identifier. In some instances, in
which the ISIN was not available to create a perfect match, we relied on matching based on company names.7 Finally, when there were multiple subsidiaries
of a given company, we used the primary location as a matching entity. The ultimate matching produced 14,468 unique companies out of 16,222 companies
available in Trucost. They represent 77 countries. Among the companies we
were not able to match, more than twothirds are not listed, and the remaining
ones are small and are not available through Factset. The top three countries
in terms of missing data are China, Japan, and the United States. Our sample
7 After standardizing the company names in FactSet and Trucost, we choose companies whose

names have a similarity score of one, based on the standardized company names.

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3688

3689

covers more than 98% of publicly listed companies (in terms of their market
capitalization) for which we have emissions data, representing 80% to 85% of
the market value of all publicly listed firms available in Factset. Since Trucost
sample firms fairly uniformly across different industries, our sample ought
to cover as a first approximation the value-weighted emissions of the Factset
universe. We augment these data with country-level variables from the World
Bank, Germanwatch (the provider of the global climate policy index and the
climate risk index [CRI]), Morgan Stanley (for the MSCI world index data),
and IBES (for analyst earnings growth forecasts).
A. Data on Corporate Carbon Emissions
The Trucost EDX firm-level carbon emissions database follows the Greenhouse Gas Protocol that sets the standards for measuring corporate emissions.8 The Greenhouse Gas Protocol distinguishes between three different
sources of emissions: Scope 1 emissions, which cover direct emissions over 1
year from establishments that are owned or controlled by the company; these
include all emissions from fossil fuel used in production. Scope 2 emissions
come from the generation of purchased heat, steam, and electricity consumed
by the company. Scope 3 emissions are caused by the operations and products of the company but occur from sources not owned or controlled by the
company; these include emissions from the production of purchased materials,
product use, waste disposal, and outsourced activities. The Greenhouse Gas
Protocol provides detailed guidance on how to identify a company’s most important sources of scope 3 emissions and how to calculate them. For purchased
goods and services, this basically involves measuring inputs, or “activity data,”
and applying emission factors to these purchased inputs that convert activity
data into emissions data. Trucost upstream scope 3 data are constructed using
an input-output model that provides the fraction of expenditures from one sector across all other sectors of the economy. This model is extended to include
sector-level emission factors, so that an upstream scope 3 emission estimate
can be determined from each firm’s expenditures across all sectors from which
it obtains its inputs.9
The Trucost database reports all three scopes of carbon emissions in units
of tons of CO2 emitted in a year. We first provide basic summary statistics on
carbon emissions across our 77 countries aggregated up from the firm-level
emissions reported by Trucost. Table I reports the country-level distribution of
firms in our sample and various measures of emissions broken down into scope
1, scope 2, and scope 3. We consider the average total yearly emissions in tons
of CO2 equivalent per firm in each country (S1TOT, S2TOT, and S3TOT), the
(winsorized at 2.5%) yearly percentage rate of change in emissions (S1CHG,
8 See https://ghgprotocol.org.
9 Downstream scope 3 emissions, caused by the use of sold products, can also be estimated and
are increasingly reported by companies. Trucost has only recently started assembling these data;
given its much shorter time span, we did not include these data in our study.

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Global Pricing of Carbon

Table I

Country

UAE
Argentina
Austria
Australia
Bangladesh
Belgium
Bulgaria
Bahrain
Brazil
Botswana
Canada
Switzerland
Côte d’ivoire
Chile
China
Colombia
Czech Republic
Germany
Denmark
Estonia
Egypt
Spain
Finland
France
UK

AE
AR
AT
AU
BD
BE
BG
BH
BR
BW
CA
CH
CI
CL
CN
CO
CZ
DE
DK
EE
EG
ES
FI
FR
GB

1,748
550
3,741
37,405
254
3,883
123
198
10,249
68
25,479
12,638
154
3,991
73,490
1,141
446
19,023
4,310
116
2,855
7,140
4,049
20,256
68,153

0.2
0.06
0.42
4.21
0.03
0.44
0.01
0.02
1.15
0.01
2.87
1.42
0.02
0.45
8.28
0.13
0.05
2.14
0.49
0.01
0.32
0.8
0.46
2.28
7.68

S1TOT

S2TOT

S3TOT S1CHG S2CHG S3CHG

TOTS1

TOTS2

TOTS3

(Continued)

34 382,822 45,424 133,220 10.93% 16.32% 11.05%
13,000,000
1,106,904
3,338,979
6 1,977,235 259,067 1,032,782 11.18% 38.18% 10.24%
9,816,885
1,137,898
4,831,946
42 1,543,117 175,280 1,478,427 10.00% 16.37% 7.56%
34,500,000
4,073,719 33,900,000
471 580,313 225,151 390,624 14.38% 20.19% 11.88% 141,000,000 51,700,000 91,500,000
5 112,458 23,661 145,789 16.66% 25.97% 14.83%
490,572
106,452
624,504
52 1,611,505 398,625 1,586,838 5.88% 11.12% 6.28%
35,200,000
9,368,517 39,000,000
3
49,815 11,011
44,659 34.85% 6.04% 14.60%
1,010,125
85,163
303,958
3
1,986
5,858
28,640 7.04% 8.84% 9.21%
5,696
16,924
83,299
126 1,846,871 200,604 2,147,921 11.05% 16.74% 9.09% 119,000,000 12,700,000 145,000,000
2
3,986 16,534
38,093 12.15% 21.45% 21.82%
6,650
28,041
64,964
399 1,179,827 194,523 794,471 13.80% 18.99% 11.30% 226,000,000 35,700,000 147,000,000
172 1,751,558 219,020 1,848,782 5.40% 9.95% 5.63% 142,000,000 18,500,000 144,000,000
2
10,867 13,642 102,418 5.46% 6.50% 6.45%
18,779
25,697
181,503
37 2,520,658 150,335 526,513 9.99% 17.85% 9.09%
61,800,000
3,816,032 13,500,000
1,660 4,009,318 258,028 1,121,424 17.16% 24.86% 16.47% 2,910,000,000 232,000,000 841,000,000
13 2,638,497 153,165 1,602,004 16.65% 23.03% 13.89%
24,900,000
1,460,375 14,600,000
5
80,966 84,133 106,096 3.29% 8.69% −2.05%
298,304
276,486
311,847
253 4,126,920 584,281 3,403,940 7.12% 13.69% 7.24% 458,000,000 70,800,000 397,000,000
48 1,830,641 81,427 715,844 6.29% 8.37% 5.98%
48,000,000
2,101,215 19,200,000
2 1,324,801 23,427
72,707 10.45% 18.91% 5.49%
2,649,601
46,855
145,415
30 1,300,763 71,534 347,754 4.98% 10.42% 5.58%
22,200,000
1,285,661
6,255,982
84 3,733,641 254,727 2,095,625 9.14% 15.39% 6.55% 153,000,000 11,100,000 89,400,000
42 1,401,658 320,239 1,548,562 2.96% 10.18% 3.74%
34,300,000
7,964,368 37,800,000
248 3,537,015 457,697 2,902,571 7.12% 11.09% 6.26% 411,000,000 57,400,000 355,000,000
660 1,037,499 263,688 1,350,755 7.47% 8.86% 6.25% 436,000,000 110,000,000 560,000,000

Frequency Percentage. # co.

The Journal of Finance®

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Code

S1TOT (S2TOT; S3TOT) measures the firm-level average (by country) of scope 1(scope 2; scope 3) carbon emissions measured in tons of CO2e.
S1CHG (S2CHG; S3CHG) measures the percentage growth rate in carbon emissions of scope 1 (scope 2; scope 3) (winsorized at 2.5%). TOTS1
(TOTS2; TOTS3) is a sum of S1TOT (S2TOT; S3TOT) within a country in a given year (averaged across all years).

Carbon Emissions by Country: 2005 to 2018

3690

0.03
0.22
3.25
0.01
0.05
1
0.2
0.64
3.78
0.01
0.75
0.01
0.02
14.07
0.06
5.83
0.01
0.01
0.05
0.01
0.01
0.15
0.01
0.47
1.42
0.13
0.63
0.64

S1TOT

S2TOT

S3TOT

S1CHG S2CHG S3CHG

TOTS1

TOTS2

TOTS3

(Continued)

2
3,583
3,103
68,338
0.63%
3.23%
2.96%
6,882
5,945
133,928
23 4,208,318 155,010 938,891 13.98% 18.93%
7.11% 47,800,000
2,284,545
11,200,000
830 1,963,473 177,584 524,083 14.95% 28.14% 14.69% 383,000,000 45,200,000 119,000,000
2 839,807 101,136 745,120 −6.99% −1.29% 12.21% 1,503,091
194,606
1,321,002
3 2,033,690 348,850 2,292,191
8.91% 22.72%
0.16% 6,100,691
1,046,018
6,871,986
130 982,778 88,318 416,476 12.58% 14.81% 10.12% 62,100,000
5,377,655
28,000,000
20 1,013,523 88,576 854,927
5.99%
9.48%
5.64% 12,700,000
1,108,046
10,300,000
92 207,414 49,185 289,135 12.32% 15.74%
9.46% 9,144,490
1,943,727
10,900,000
518 3,452,714 141,930 1,006,817 13.04% 19.06% 12.24% 831,000,000 34,700,000 248,000,000
3
1,257
1,412
26,849 32.91% 28.11% 28.32%
3,156
3,806
67,937
107 4,129,000 307,340 2,549,945
6.26% 11.40%
5.64% 169,000,000 14,300,000 118,000,000
2
335
1,422
11,711
1.05% 16.31% 12.74%
671
2,843
23,423
4
1,325
6,190
30,871 −7.52%
0.47%
6.09%
4,338
17,295
102,857
2,258 1,312,299 231,427 1,511,355
4.90% 10.72%
5.22% 980,000,000 204,000,000 1,250,000,000
8 103,831
8,819
75,464 24.97% 27.08% 14.38%
799,872
58,883
458,581
843 1,243,235 166,251 1,001,098 10.34% 14.19%
9.15% 397,000,000 60,700,000 344,000,000
1
1,153
1,005
21,863 19.74% 18.64% 13.32%
1,153
1,005
21,863
2
3,788 11,484
34,112 10.68% 13.73% 19.42%
5,696
17,485
54,787
4
11,715 29,408
42,644 10.17% 23.04%
6.94%
28,522
89,216
136,662
1
1,590
4,595
18,366 23.73% 20.36% 21.61%
1,590
4,595
18,366
3
1,035
1,368
8,149 −33.03% −36.01% −24.82%
2,263
2,823
17,197
13 1,690,454 67,664 307,399
6.16%
8.18%
5.86% 15,400,000
582,425
2,563,349
3
925
1,368
9,340 45.24% 67.68% 27.90%
2,115
3,259
22,106
65 630,508 322,220 1,146,013 10.20% 15.58%
9.50% 23,000,000 10,100,000
36,900,000
188 1,289,048 58,716 364,614 12.85% 18.36%
9.32% 108,000,000
6,093,201
32,100,000
16 1,556,752 68,555 299,827
1.31%
5.69%
0.65% 23,600,000
1,024,925
4,236,235
63 5,563,867 702,550 2,898,875
5.06%
7.38%
4.50% 188,000,000 23,700,000
97,700,000
97 1,269,294 294,583 1,627,966 10.02% 13.26%
9.33% 49,000,000
9,238,739
56,700,000

Frequency Percentage. # co.

Ghana
235
Greece
1,929
Hong Kong
28,827
Croatia
128
Hungary
474
Indonesia
8,865
Ireland
1,749
Israel
5,688
India
33,514
Iceland
81
Italy
6,656
Jamaica
68
Jordan
196
Japan
124,903
Kenya
524
Korea
51,738
Kazakhstan
45
Lebanon
85
Sri Lanka
452
Lithuania
58
Luxembourg
54
Morocco
1,352
Mauritius
114
Mexico
4,157
Malaysia
12,596
Nigeria
1,182
Netherlands
5,579
Norway
5,680

Country

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GH
GR
HK
HR
HU
ID
IE
IL
IN
IS
IT
JM
JO
JP
KE
KW
KZ
LB
LK
LT
LU
MA
MU
MX
MY
NG
NL
NO

Code

Table I—Continued

Global Pricing of Carbon

Country

0.34
0.05
0.06
0.63
0.36
0.64
0.15
0.14
0.03
0.02
0.22
0.12
1.3
1.11
0.02
0.65
0.02
0.53
4.63
0.01
19.76
0.09
1.68
0.01
100

S1TOT

S2TOT

S3TOT S1CHG S2CHGS3CHG

TOTS1

TOTS2

TOTS3

50
393,267
32,502 239,998
5.67% 9.68% 8.79%
8,036,961
707,115
5,067,580
8
369,577
60,682 106,543
6.60% 16.64% 8.10%
2,686,115
433,197
755,255
5 1,023,906 213,257 201,341 15.87% 18.77% 10.71%
3,617,539
755,370
721,199
72 1,077,980
87,818 518,201 17.10% 26.63% 12.56%
49,100,000
4,010,504
23,100,000
51
750,597
40,021 217,645 12.02% 14.41% 9.61%
25,900,000
1,223,456
6,959,005
60 2,368,805 158,750 619,717 12.22% 18.37% 10.16%
94,300,000
6,032,271
22,200,000
17 3,179,836 233,808 1,365,071
2.71% 12.34% 3.92%
26,400,000
1,974,726
11,800,000
23
611,145
45,424 210,790
7.31% 12.18% 6.43%
10,900,000
812,774
3,752,829
4
886,381
56,688 680,844 14.92% 9.79% 8.08%
3,381,664
202,319
2,430,224
3
272,240
23,975 196,896 23.17% 18.38% 19.48%
601,691
55,795
452,004
26 10,100,000 816,962 6,098,643 16.11% 19.48% 9.72% 147,000,000
10,800,000
72,600,000
98 2,345,866 1,002,530 1,190,067 −10.47% 8.66% 4.26%
66,100,000
22,600,000
43,600,000
174
228,060
74,868 703,569
7.48% 11.15% 7.68%
17,000,000
6,014,555
53,200,000
145
864,602 122,194 1,143,235 12.55% 18.94% 10.64%
55,800,000
8,285,673
74,100,000
3
13,270
26,995
71,210
1.05% 21.79% 5.40%
37,469
78,045
203,048
106 2,089,681 167,475 674,012 14.69% 23.17% 13.21%
88,800,000
6,770,391
31,000,000
2
239
235
5,106 −6.55% 0.70%−1.53%
477
469
10,212
58 1,697,617 130,762 768,350 15.98% 18.69% 8.58%
55,000,000
4,237,040
23,400,000
684
530,858 134,310 531,483 10.24% 17.23% 7.74% 135,000,000
41,300,000 147,000,000
1
842
1,470
4,194 34.73% 71.91% 4.62%
842
1,470
4,194
3,013 2,012,926 323,727 1,733,058
7.87% 13.84% 8.24% 2,330,000,000 403,000,000 2,100,000,000
15
479,322
43,086 343,905 12.19% 18.35% 14.68%
6,087,639
552,733
4,260,247
148 1,074,195 444,228 423,650 10.53% 17.41% 6.08%
95,900,000
41,400,000
40,100,000
2
15,480
14,546 138,070 −6.75% 1.28% 8.77%
48,346
45,915
457,559
14,468 1,874,065 246,606 1,301,047
9.73% 15.35% 8.86%11,813,099,883 1,615,895,170 7,990,066,031

FrequencyPercentage. # co.

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NZ New Zealand
3,011
OM Oman
488
PE Peru
544
PH Philippines
5,583
PK Pakistan
3,169
PL Poland
5,672
PT Portugal
1,351
QA Qatar
1,222
RO Romania
250
RS Serbia
168
RU Russia
1,925
SA Saudi Arabia
1,088
SE Sweden
11,560
SG Singapore
9,881
SI Slovenia
220
TH Thailand
5,767
TN Tunisia
140
TR Turkey
4,706
TW Taiwan
41,061
UG Uganda
88
US USA
175,377
VN Vietnam
820
ZA South Africa 14,883
ZW Zimbabwe
56
Total
887,429

Code

Table I—Continued

3692

3693

S2CHG, and S3CHG), and the total yearly emissions by country (TOTS1,
TOTS2, and TOTS3).
The largest country by number of observations is obviously the United
States, but remarkably it only represents around 19.8% of total observations,
with Japan a close second with 14% of observations, and China as third with
around 8.2% of observations. Importantly for our analysis, Table I highlights
that the majority of the listed firms in our sample is not concentrated in these
three large economies. In aggregate, the entire population of countries in our
sample produces a staggering 11.81 billion tons of scope 1, 1.62 billion tons of
scope 2, and 7.99 billion tons of scope 3 emissions per year. The three biggest
contributors in terms of total carbon emissions produced are China producing
2.91 billion tons of scope 1 emissions per year, followed by the United States
with 2.33 billion, and Japan contributing 980 million. The same three countries
also dominate scope 2 and scope 3 emissions, except that the ranking changes,
with the United States producing 2.1 billion of scope 3 emissions, followed by
Japan with 1.25 billion, and China with 841 million tons of CO2 .
The global production of emissions does not necessarily reflect the contribution of each firm to the total, as the relative sizes of countries vary. In fact,
the top three countries in terms of scope 1 emissions per firm are Russia, the
Netherlands, and Greece, with their respective emission levels of 10.1 million,
5.6 million, and 4.2 million tons of CO2 per year. An average Russian firm also
leads the rankings in terms of scope 3 emissions with 6.1 million tons of CO2 ,
followed by Germany and France, with respective numbers of 3.4 and 2.9 million tons of CO2 . A slightly different picture can be painted when we compare
firm-level emission intensities. The most intense countries in terms of scope
1 emissions include Estonia, Morocco, and Peru. Among the largest countries,
Russia, India, and China score relatively high, while France, Japan, and the
United Kingdom score relatively low.
Another striking observation is that carbon emissions are growing in most
countries throughout our sample period. The country with the highest growth
rate in scope 1 emissions is Mauritius, with an average yearly growth rate of
45%. The second largest is Bulgaria, with a 35% growth rate, and the third,
fourth, and fifth largest are, respectively, Iceland, Kenya, and Lithuania. All
these five countries have witnessed rapid GDP growth over our sample period. Among the largest economies, the ones with the highest growth rate in
emissions are China with nearly 18%, the Russian Federation with 16%, the
United States with 7.9%, and Germany with 7.1% growth rates. Among the
countries with the lowest growth rates in scope 1 emissions are, remarkably,
Saudi Arabia with a negative 10.5% growth rate (this may reflect the fact that
a lot of companies have gone public over our sample period, lowering the average per-company scope 1 emissions), Luxembourg with a negative 33% growth
rate, and Jordan with a minus 7.5% growth rate. When it comes to the growth
rate in scope 3 emissions, some of these rankings are reversed, reflecting the
fact that some countries increasingly rely on imports whose production generates high emissions. Thus, Saudi Arabia has a 4.3% growth rate in scope 3
emissions.

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Global Pricing of Carbon

The Journal of Finance®

Figure 3. Total annual carbon emissions by country. (Color figure can be viewed at wileyonlinelibrary.com)

Figure 4. Average annual total carbon emissions per firm. (Color figure can be viewed at
wileyonlinelibrary.com)

In Figures 3 and 4, we further represent the detailed cross-country variation in total emissions over two equal-length time periods, which classify
countries into four categories by their performance in these metrics. The
left panel of each figure represents scope 1 emissions, the middle panel
scope 2 emissions, and the right panel scope 3 emissions. As can be seen in

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3694

3695

Figure 3, the countries with the highest total average yearly emissions are
first, the countries with the highest GDP, second the countries with the largest
populations, and third the largest commodity exporting countries. Important
exceptions are Sweden, which has the lowest emissions among developed countries, Iceland, and the Czech Republic. Importantly for our analysis, there is
considerable cross-country variation in total emissions. To the extent that the
carbon premium reflects concerns about the level of emissions, we expect to see
considerable variation in the premium across countries.
We further show how the performance of countries has changed from the
first half period of our sample from 2005 to 2011, to the second half period
from 2012 to 2018. The most noteworthy changes are the deterioration in total
emission performance of Latin America, the Russian Federation, Turkey, and
Australia.
Interestingly, however, there is little correlation between a country’s levels
of total emissions and average per-firm emissions, as can be seen in Figure 4,
which represents the cross-country variation in average per-firm emissions.
Among the worst performers in the world in per-firm emissions are the United
States, Saudi Arabia, Argentina, Colombia, China, the Russian Federation,
India, Japan, and the European Union (excluding the United Kingdom).
In Table II, Panel A, we report summary statistics on per-firm carbon emissions in units of tons of CO2 emitted in a year, normalized using the natural
log scale. Thus, the log of total scope 1 emissions of the average firm in our
sample (LOGS1TOT) is 10.32, with a standard deviation of 2.95. Note that
the median number is the largest for scope 3 emissions (LOGS3TOT), indicating that most companies in our sample are significantly exposed to indirect
emissions. To mitigate the impact of outliers, we have winsorized all growth
measures at the 2.5% level. In Panel B, we report the correlations between
the total emissions variable and the emission percentage change variable for
the three different categories of emissions. Interestingly, the correlation coefficients are quite low, indicating that the emission change variable reflects a
different type of variation in the data.
In Panel C, we study the autocorrelation patterns of both levels and rates
of change of emissions. Formally, we estimate the regression model of annual
emissions measures with their respective 1-year lags only (in columns (1) to
(3)), and year-month- and firm-fixed effects (in columns (4) to (6)). We double
the cluster standard errors by firm and year. The results indicate a significant persistence of emission levels, even after controlling for fixed effects, and
almost no persistence in the rates of change measure. These results provide
additional empirical support for emission levels as a metric of long-term transition risk and emission changes as a metric of short-term transition risk.
Finally, Panel D provides summary statistics on stock returns and several
control variables we use in our subsequent tests. The dependent variable,
RETi, t , in our cross-sectional return regressions is the monthly return of an
individual stock i in month t. We use the following control variables in our
cross-sectional regressions: LOGSIZEi,t , which is given by the natural logarithm of firm i’s market capitalization (price times shares outstanding) at the

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Global Pricing of Carbon

Table II

Mean
10.317
10.173
11.966
9.73%
15.35%
8.86%

Log (Carbon Emissions Scope 1 (tons CO2e)) (LOGS1TOT)
Log (Carbon Emissions Scope 2 (tons CO2e)) (LOGS2TOT)
Log (Carbon Emissions Scope 3 (tons CO2e)) (LOGS3TOT)
Growth Rate in Carbon Emissions Scope 1 (winsorized at 2.5%) (S1CHG)
Growth Rate in Carbon Emissions Scope 2 (winsorized at 2.5%) (S2CHG)
Growth Rate in Carbon Emissions Scope 3 (winsorized at 2.5%) (S2CHG)

10.135
10.233
12.021
3.34%
5.83%
5.44%

Median

(Continued)

2.951
2.265
2.219
41.34%
49.01%
25.74%

Standard Deviation

The Journal of Finance®

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Variable

Panel A: Carbon Emissions

This tables reports summary statistics (averages, medians, and standard deviations) for the variables used in regressions. The sample period is from
2005 to 2018. Panels A and B report the emission variables and their pairwise correlations. Panel C shows the results from the autocorrelation results
for the levels and changes in emissions measured at an annual frequency. Columns (1) to (3) include no fixed effects, while columns (4) to (6) include
year- and firm-fixed effects. Standard errors (in parentheses) are double clustered by firm and year. Panel D reports summary statistics of the control
variables. RET is the monthly stock return; LOGSIZE is the natural logarithm of market capitalization (in $ million); B/M is the book value of equity
divided by market value of equity; ROE is the return on equity; LEVERAGE is the book value of leverage defined as the book value of debt divided by
the book value of assets; MOM is the cumulative stock return over the 1 year period; INVEST/A is the CAPEX divided by book value of assets; HHI
is the Herfindahl index of the business segments of a company with weights proportional to revenues; LOGPPE is the natural logarithm of plant,
property, and equipment (in $ million); VOLAT is the monthly stock return volatility calculated over the 1 year period; MSCIi,t is an indicator variable
equal to 1 if a stock i is part of MSCI World Index in year t, and 0 otherwise. SALESGR is the annual percentage change in firm revenues. LTG is the
mean consensus forecast of long-term earnings growth. GDPPC is a country’s GDP per capita. MANUFPERC is the percentage of a country’s output
that is attributed to the manufacturing sector. HEALTHEXPPC is the value of expenses on health per capita. ELRENEW is a country’s percentage
contribution of renewable energy to the total energy production. ENINT is a country’s energy intensity. ENUSEPC is a country’s energy consumption
per capita. Rule of law, RULELAW, captures perceptions of the extent to which agents have confidence in and abide by the rules of society, and in
particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence. The measure
is standardized between −2.5 and 2.5. VOICE reflects perceptions of the extent to which a country’s citizens are able to participate in selecting their
government, as well as freedom of expression, freedom of association, and a free media. The measure is standardized between −2.5 and 2.5. GINI is
a country’s Gini inequality index as a percentage. INTPOLICY is a country’s tightness of climate international policies. DOMPOLICY is a country’s
tightness of climate domestic policies. CRI is a country’s index of physical climate risk. ***1% significance; **5% significance; *10% significance.

Summary Statistics

3696

0.222***
(0.027)
No
No
64,568
0.962

0.981***
(0.002)

0.462***
(0.069)
No
No
64,575
0.936

0.962***
(0.005)

(2)
LOGS2TOT

1
0.503
−0.004
0.045
−0.046

S2CHG

0.973***
(0.005)
0.386***
(0.067)
No
No
64,635
0.973

(3)
LOGS3TOT

3.809***
(0.313)
Yes
Yes
61,357
0.975

0.640***
(0.030)

(4)
LOGS1TOT

1
0.736
0.808

LOGS1TOT

Panel C: Autocorrelations

1
−0.045
−0.061
−0.059

S3CHG

4.076***
(0.301)
Yes
Yes
61,366
0.956

0.613***
(0.029)

(5)
LOGS2TOT

1
0.824

LOGS2TOT

(Continued)

0.647***
(0.027)
4.349***
(0.332)
Yes
Yes
61,426
0.983

(6)
LOGS3TOT

1

LOGS3TOT

3697

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Year-fixed effects
Firm-fixed effects
Observations
R-squared

Constant

LOGS3TOTt-12

LOGS2TOTt-12

LOGS1TOTt-12

(1)
LOGS1TOT

1
0.485
0.555
0.040
−0.020
−0.047

S1CHG
S2CHG
S3CHG
LOGS1TOT
LOGS2TOT
LOGS3TOT

Variables

S1CHG

Variables

Panel B: Carbon Emissions: Cross-Correlations

Table II—Continued

Global Pricing of Carbon

Year-fixed effects
Firm-fixed effects
Observations
R-squared

Constant

S3CHGt-12
0.127***
(0.018)
No
No
52,173
0.000

−0.009
(0.012)

(2)
S2CHG

0.088**
(0.029)
0.062***
(0.019)
No
No
52,232
0.009

(3)
S3CHG

0.086***
(0.001)
Yes
Yes
47,912
0.162

−0.120***
(0.017)

(4)
S1CHG

0.143***
(0.002)
Yes
Yes
47,914
0.164

−0.135***
(0.014)

(5)
S2CHG

(Continued)

−0.068**
(0.029)
0.074***
(0.002)
Yes
Yes
47,974
0.241

(6)
S3CHG

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0.077***
(0.011)
No
No
52,175
0.000

0.016
(0.014)

S1CHGt-12

S2CHGt-12

(1)
S1CHG

Variables

Table II—Continued

3698

1.076
11.105
0.572
0.227
0.136
0.049
0.798
7.748
11.094
0.090
0.337
0.095
12.80
36,540.75
15.93
4,235.74
5.33
5.19
4,476.64
1.15
0.73
36.96
0.49
0.53
46.84

Mean
0.054
9.644
0.440
0.209
0.089
0.035
0.985
7.684
10.870
0.079
0
0.062
11.55
44,508
12.99
4,099.47
3.83
5.20
3,921.90
1.53
1.03
35.40
0.58
0.51
44.83

Median

10.229
5.212
0.510
0.175
0.383
0.048
0.252
3.313
16.076
0.051
0.473
0.240
11.48
19,253
7.43
3,025.87
5.71
1.66
2,186.91
0.77
0.85
6.32
0.29
0.27
25.86

Standard Deviation

3699

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RET (%)
LOGSIZE
B/M (winsorized at 2.5%)
LEVERAGE (winsorized at 2.5%)
MOM (winsorized at 2.5%)
INVEST/A (winsorized at 2.5%)
HHI
LOGPPE
ROE (winsorized at 2.5%)
VOLAT (winsorized at 2.5%)
MSCI
SALESGR (winsorized at 2.5%)
LTG (winsorized at 1%)
GDPPC
MANUFPERC (%)
HLTHEXPPC
ELRENEW (%)
ENINT
ENUSEPC
RULELAW
VOICE
GINI (%)
INTPOLICY
DOMPOLICY
CRI

Variables

Panel D: Regression Controls

Table II—Continued

Global Pricing of Carbon

The Journal of Finance®

end of year t; B/Mi,t , which is firm i’s book value divided by its market cap
at the end of year t; LEVERAGEi,t , which is the ratio of debt to book value of
assets; momentum, MOMi,t , which is given by the average of the most recent 12
months’ returns on stock i, leading up to and including month t−1; capital expenditures INVEST/Ai,t , which we measure as the firm’s capital expenditures
divided by the book value of its assets; a measure of the firm’s specialization,
HHIi,t , which is the Herfindahl concentration index of the firm with respect to
its different business segments, based on each segment’s revenues; the firm’s
stock of physical capital, LOGPPEi,t , which is given by the natural logarithm,
of the firm’s property, plant, and equipment; the firm’s earnings performance
ROEi,t , which is given by the ratio of firm i’s net yearly income divided by the
value of its equity; the firm’s idiosyncratic risk, VOLATi,t , which is the standard deviation of returns based on the past 12 month’s returns; and, MSCIi,t ,
which is an indicator variable equal to 1 if a stock i is part of the MSCI World
index in year t, and 0 otherwise. SALESGRi,t is the annual growth rate in firm
sales, LTGi,t is the analyst forecasts of the long-term earnings growth for firm
i at time t, averaged across all analysts. To mitigate the impact of outliers, we
have winsorized B/M, LEVERAGE, INVEST/A, ROE, MOM, and VOLAT at
the 2.5% level, and LTG at the 1% level.
In Panel D, we also summarize all the relevant variables that we use in
our cross-sectional analysis. These include measures related to technological progress, energy intensity, socioeconomic development, policy environment,
and physical risk. We define each one explicitly in their respective tests in Section V. The average firm’s monthly stock return equals 1.08%, with a standard
deviation of 10.23%. The average firm has a market capitalization of $66 billion, significantly larger than the size of the median firm in our sample, which
is $15 billion. The average book-to-market ratio is 0.57, and average book leverage is 23%. The average return on equity equals 11.1%, slightly more than the
median of 10.87%.
Table III provides summary statistics by year for the total number of firms in
our sample in any given year, and the level and percentage change in emissions
for all three scope categories. Note the large increase in coverage after 2015,
when the number of firms jumps from 5,427 in 2015 to 11,961 in 2016. This
is because Trucost has been able to substantially expand the set of firms for
which it collects data on carbon emissions from 2016 onward. For most of our
empirical tests, we rely on cross-sectional variation in the data, so that we are
less exposed to a possible structural break in the data in 2016. Moreover, many
of our results hold when we restrict our sample to legacy firms, that is, those
present in the sample prior to 2016.
We also report the distribution of firms by industry in Table IA.I, using the
six-digit Global Industry Classification (GIC6). Our global database should reflect a greater proportion of firms in manufacturing and agriculture than is
the case in developed economies. This is indeed what is reflected in Table IV,
with 580 companies in the machinery industry; 530 in the chemicals industry;
520 in the electronic equipment, instruments, and components industry; 506
in metals and mining; and 440 food products companies. In the services sector,

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3700

Table III

Number of Firms

3,232
3,532
3,689
3,736
3,949
4,098
4,221
4,253
4,912
5,323
5,427
11,961
12,817
8,781

2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018

2,391,417
2,367,787
2,488,889
2,541,971
2,285,281
2,407,166
2,563,380
2,402,493
2,211,603
2,118,666
2,009,876
1,038,161
1,046,853
1,136,396

S1TOT
246,612
264,064
290,500
330,705
311,700
308,070
322,518
317,779
297,793
292,460
276,453
143,425
167,407
148,745

S2TOT
1,822,093
1,705,187
1,800,563
1,679,148
1,643,489
1,633,414
1,825,353
1,791,769
1,619,450
1,432,881
1,228,497
693,127
759,076
729,199

S3TOT
–
16.18%
18.89%
9.34%
3.24%
14.26%
9.51%
8.71%
7.06%
6.88%
3.87%
5.95%
13.60%
10.53%

S1CHG
–
18.59%
22.94%
18.13%
8.47%
18.14%
15.73%
10.60%
8.43%
20.46%
2.48%
11.13%
26.03%
12.24%

S2CHG
–
9.83%
15.94%
−0.16%
10.02%
8.34%
14.51%
3.31%
4.06%
4.90%
−1.76%
10.81%
19.03%
6.21%

S3CHG
917000000
894000000
934000000
955000000
870000000
904000000
937000000
868000000
878000000
895000000
860000000
1130000000
1230000000
1050000000

TOTS1

106000000
115000000
125000000
146000000
136000000
130000000
136000000
133000000
135000000
142000000
137000000
183000000
221000000
142000000

TOTS2

828000000
749000000
766000000
728000000
720000000
689000000
761000000
748000000
743000000
694000000
604000000
902000000
1050000000
663000000

TOTS3

3701

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Year

The table reports the annual averages across all countries of all emission variables over the period 2005 till 2018.

Carbon Emissions by Year

Global Pricing of Carbon

Table IV

(2)
LOGS2TOT
0.265***
(0.023)
0.108**
(0.040)
0.011***
(0.001)
0.326
(0.226)
1.079**
(0.396)
−0.763***
(0.087)
0.469***
(0.014)
0.226***
(0.045)
3.850***
(0.263)
Yes
Yes
No
886,895
0.531

(1)
LOGS1TOT

−0.085**
(0.039)
−0.093
(0.061)
0.010***
(0.002)
0.533**
(0.221)
5.021***
(0.698)
−2.038***
(0.145)
0.782***
(0.026)
0.119*
(0.059)
6.359***
(0.383)
Yes
Yes
No
886,751
0.544
0.210***
(0.016)
−0.007
(0.037)
0.014***
(0.001)
−0.363*
(0.170)
−1.882***
(0.300)
−1.232***
(0.118)
0.534***
(0.014)
0.203***
(0.041)
6.456***
(0.240)
Yes
Yes
No
887,429
0.621

(3)
LOGS3TOT
0.329***
(0.020)
0.371***
(0.044)
0.008***
(0.001)
0.669***
(0.099)
−1.136***
(0.371)
−1.216***
(0.074)
0.428***
(0.015)
0.176***
(0.040)
3.902***
(0.215)
Yes
Yes
Yes
874,592
0.779

(4)
LOGS1TOT
0.472***
(0.027)
0.451***
(0.051)
0.008***
(0.001)
0.671***
(0.127)
−1.928***
(0.322)
−0.660***
(0.059)
0.336***
(0.016)
0.256***
(0.049)
2.415***
(0.260)
Yes
Yes
Yes
874,736
0.715

(5)
LOGS2TOT

(Continued)

0.453***
(0.023)
0.381***
(0.047)
0.009***
(0.001)
0.370***
(0.097)
−3.089***
(0.287)
−0.722***
(0.062)
0.346***
(0.016)
0.218***
(0.042)
4.555***
(0.212)
Yes
Yes
Yes
875,270
0.793

(6)
LOGS3TOT

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Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Constant

MSCI

LOGPPE

HHI

INVEST/A

LEVERAGE

ROE

B/M

LOGSIZE

Variables

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variables are carbon emission levels (Panel A) and the growth in emissions (Panel B). All
variables are defined in Tables I and II. We report the results of the pooled regression with standard errors (in parentheses) double clustered at the
firm and year levels. All regressions include year-month-fixed effects and country-fixed effects. In columns (4) to (6), we additionally include Trucost
industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Predictors of Carbon Emissions

3702

0.025***
(0.002)
−0.060***
(0.009)
−0.002***
(0.000)
0.060***
(0.015)
0.594***
(0.073)
0.007
(0.008)
−0.021***
(0.003)
−0.033***
(0.005)
0.004
(0.024)
Yes
Yes
No
765,387
0.036

(1)
S1CHG
0.029***
(0.005)
−0.061***
(0.009)
−0.002***
(0.000)
0.064***
(0.012)
0.589***
(0.098)
−0.022
(0.012)
−0.021***
(0.002)
−0.041***
(0.005)
0.037
(0.059)
Yes
Yes
No
765,397
0.044

(2)
S2CHG
0.025***
(0.002)
−0.066***
(0.006)
−0.001***
(0.000)
0.049***
(0.011)
0.372***
(0.069)
0.019***
(0.005)
−0.020***
(0.002)
−0.030***
(0.005)
−0.025
(0.026)
Yes
Yes
No
765,949
0.119

(3)
S3CHG
0.025***
(0.002)
−0.067***
(0.009)
−0.001***
(0.000)
0.060***
(0.012)
0.451***
(0.085)
0.011*
(0.005)
−0.023***
(0.003)
−0.033***
(0.005)
0.020
(0.024)
Yes
Yes
Yes
755,257
0.047

(4)
S1CHG
0.027***
(0.005)
−0.069***
(0.009)
−0.002***
(0.000)
0.063***
(0.012)
0.525***
(0.063)
−0.017
(0.014)
−0.022***
(0.002)
−0.040***
(0.005)
0.071
(0.062)
Yes
Yes
Yes
755,267
0.055

(5)
S2CHG

0.025***
(0.003)
−0.070***
(0.007)
−0.001***
(0.000)
0.043***
(0.008)
0.317***
(0.052)
0.020***
(0.004)
−0.021***
(0.002)
−0.029***
(0.004)
−0.015
(0.031)
Yes
Yes
Yes
755,819
0.131

(6)
S3CHG

3703

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Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Constant

MSCI

LOGPPE

HHI

INVEST/A

LEVERAGE

ROE

B/M

LOGSIZE

Variables

Panel B: Growth in Emissions

Table IV—Continued

Global Pricing of Carbon

The Journal of Finance®

the largest represented industries are banking, with 679 banks and real estate, with 619 companies (some of which are also engaged in construction and
development).
Finally, we report summary statistics on the main determinants of carbon
emissions in Table IV. We regress in turn the log of total firm-level emissions
and the percentage change in total emissions on the following firm-level characteristics: LOGSIZE, B/M, ROE, LEVERAGE, INVEST/A, HHI, LOGPPE,
and MSCI. To allow for systematic differences in correlations across countries
and over time, we include year-month-fixed effects and country-fixed effects,
so that our identification comes from within-country variation across firms.
In columns (4) to (6), we further include industry-fixed effects (following the
classification of Trucost10 ) to account for possible differences across industries.
The results are also robust to using GIC6 codes, though these are less desirable
because they may capture companies with different emission profiles.
In Panel A, we show considerable variation across industries in the effect of
these variables on emissions (e.g., the R-square increases from 0.696 to 0.779
when we add industry-fixed effects to the regression for LOGS1TOT). Accordingly, we focus on the regressions with industry-fixed effects and note that
total emissions significantly increase with the size of the firm (in particular,
if it is a constituent of the MSCI world index), its book-to-market ratio, its
leverage, and its tangible capital stock (PPE). This is altogether not surprising to the extent that emissions are generated by economic activity, which is
proportional to the size of the firm. Somewhat surprising is the strong effect
of leverage. One possible explanation is that firms with higher emissions may
anticipate a future drop in profitability due to transition risk and, as a result,
take more leverage. Interestingly, investment has a strong negative effect on
emissions, suggesting that new capital vintages are more carbon efficient. Industry specialization (a high Herfindahl index [HHI]) also has a negative effect
on emissions, perhaps because nonspecialized conglomerates tend to be larger.
Alternatively, conglomeration can reflect a firm’s response to potential costs of
high emissions in a particular sector.
IV. Results
We organize our discussion into three subsections. The first subsection reports results on the pricing of carbon-transition risk throughout the world, the
second reports results related to specific drivers of carbon-transition risk, and
the third subsection briefly discusses how carbon-transition risk may be gradually priced in as the underlying economy is transitioning away from fossil
fuels.

10 These roughly correspond to a three-digit SIC classification.

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3704

3705

A. Pricing Carbon-Transition Risk throughout the World
In this section, we present our main findings on the pricing of carbontransition risk. We begin by reporting findings for the full sample of firms. We
then proceed to show how the carbon premium is distributed across geographic
locations.
A.1. Empirical Specification
Our analysis of carbon-transition risk centers on two different crosssectional regression models relating individual companies’ stock returns
to carbon emissions. Rather than a factor-based model, we take a firm
characteristic–based approach along the lines of Daniel and Titman (1997).
This approach is particularly well suited given the rich cross-sectional variation in firm characteristics in our sample.11 As shown in Bolton and Kacperczyk (2021a), the following characteristics are particularly relevant when using carbon emissions as the main sorting variable: firm size, book-to-market,
leverage, capital expenditures over assets, property plant and equipment, return on equity, sales growth, sectoral diversification, and a measure of stock
price momentum and volatility. This characteristic–based approach also allows us to take full advantage of fixed effects along time, country, and industry dimensions. Further, we can better account for potential dependence of
residuals by using a clustering methodology. Finally, the advantage of taking
a characteristic-based approach is that we do not need to take a stance on the
underlying asset pricing model. One basic conceptual difficulty with the choice
of asset pricing model in the context of a complex pricing problem such as climate change risk, is that such a model has not yet been formulated. However,
since we do not take a risk-factor approach, we cannot explore the presence of a
“carbon alpha” or of any mispricing of carbon-transition risk. Our aim is more
limited: to provide a comprehensive picture of the cross-sectional variation in
stock-level returns throughout the world. Stated differently, our approach is to
identify a company’s “carbon beta.”
We begin by linking companies’ monthly stock returns to their corresponding total emissions and other characteristics, all lagged by 1 month. This regression model reflects the long-run, structural, firm-level impact of emissions
on stock returns. Taking absolute carbon neutrality as a benchmark, one can
think of this measure as a rough proxy for the quantity of risk a firm is exposed
to at a given point in time. Specifically, we estimate the following model:


(1)
RETi,t = a0 + a1 T OT Emissions i,t−1 + a2Controlsi,t−1 + μt + εi,t ,
where RETi,t measures the stock return of company i in month t and
TOT Emissions is a generic term standing for LOGS1TOT, LOGS2TOT,
11 The risk factor-based approach has been a popular method for measuring risk premia in a
single country, but in a fully global study such as this one, this approach is problematic because
of the difficulties in specifying appropriate factor-mimicking portfolios for a large number of countries with limited data, and because of cross-country comparability issues.

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Global Pricing of Carbon

The Journal of Finance®

and LOGS3TOT. The vector of firm-level controls includes the firm-specific
variables LOGSIZE, B/M, LEVERAGE, MOM, INVEST/ASSETS, HHI,
LOGPPE, ROE, and VOLAT.
Second, we relate companies’ growth in annual total emissions to their
monthly stock returns by estimating the following cross-sectional regression
model:


(2)
RETi,t = a0 + a1 Total Emissions i,t−1 + a2Controlsi,t−1 +μt +i,t .
The percentage change in total emissions (S1CHG, S2CHG, and S3CHG)
captures the short-run impact of emissions on stock returns. In particular,
changes in total emissions reflect the extent to which companies load up on,
or decrease, their material risk with respect to carbon emissions. From a transition perspective, this measure captures the position of a firm on a long-term
path toward carbon neutrality. In this respect, it is complementary to the longterm objective captured by the level of emissions.
We estimate these two cross-sectional regressions using pooled OLS. In both
models, we also include country-fixed effects, as well as year-month-fixed effects. Hence, our identification is cross-sectional in nature. In some tests, we
also include the same set of industry-fixed effects as in Table IV to capture
within-industry variation across firms. In all the model specifications, we double cluster standard errors at the firm and year levels, which allows us to account for any cross-firm correlation in the residuals as well as capture the fact
that some control variables, including emissions, are measured at an annual
frequency. Our coefficient of interest is a1 .
A.2. Evidence from the United States and China
We begin our analysis by comparing the results for our regression models in
the two economies with the largest emissions, China and the United States.
We report the results in Table V. These two economies differ in fundamental
ways, and one would expect the carbon premium to reflect basic differences in
the level of economic and financial development and in the legal and political
regimes. Yet, we find that the results for scope 1 emissions are surprisingly
similar, which suggests that firm-level variation in emissions may be more relevant for transition risk than are the differences between the two countries.
Specifically, once one controls for industry and time as well as a battery of firm
characteristics, firm-level differences in LOGS1TOT generate a highly significant carbon premium of similar size both in China (.069) and in the United
States (.071), or equivalently an annualized value of 1.18% and 0.95% per
one-standard-deviation change in total emission levels in each country, respectively.12 Using a slightly shorter period (from 2005 to 2017), Bolton and Kacperczyk (2021a) find that the premium for U.S. companies is slightly lower. Here
12 Throughout the paper, whenever we refer to a one-standard-deviation movement, we calcu-

late standard deviations of a given variable, taking into account the impact of all other controls in

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3706

Table V

−0.115
(0.129)
0.535
(0.347)
−0.453
(0.266)
0.296
(0.328)
0.407
(2.422)
0.013
(0.117)
0.011
(0.043)
0.005*
(0.003)
3.793
(3.655)
0.548
(0.944)
Yes
Yes
143,367
0.224

0.071***
(0.021)

(1)

−0.134
(0.135)
0.522
(0.340)
−0.456
(0.257)
0.305
(0.327)
0.507
(2.420)
−0.037
(0.093)
0.014
(0.045)
0.005*
(0.003)
3.635
(3.597)
0.704
(1.000)
Yes
Yes
143,340
0.224

0.075*
(0.036)

(2)
United States

0.126**
(0.044)
−0.159
(0.138)
0.496
(0.345)
−0.467*
(0.261)
0.307
(0.328)
0.734
(2.343)
0.001
(0.108)
0.000
(0.044)
0.005
(0.003)
3.715
(3.636)
0.195
(1.003)
Yes
Yes
143,461
0.224

(3)

−0.338***
(0.096)
1.003**
(0.395)
−0.113
(0.198)
1.014*
(0.517)
−0.403
(0.786)
0.610
(0.431)
0.058
(0.079)
0.026*
(0.013)
−2.932
(1.966)
2.882*
(1.585)
Yes
Yes
60,210
0.301

0.069**
(0.030)

(4)

−0.369***
(0.111)
0.963**
(0.373)
−0.121
(0.186)
1.005*
(0.511)
−0.150
(0.866)
0.561
(0.418)
0.038
(0.066)
0.025*
(0.012)
−2.983
(1.941)
2.727
(1.613)
Yes
Yes
60,210
0.301

0.147*
(0.073)

(5)
China

(Continued)

0.208*
(0.106)
−0.387***
(0.114)
0.944**
(0.363)
−0.194
(0.172)
0.993*
(0.501)
−0.062
(0.869)
0.563
(0.413)
0.003
(0.054)
0.023*
(0.012)
−2.829
(1.911)
2.251
(1.814)
Yes
Yes
60,210
0.301

(6)

3707

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Year/month-fixed effects
Industry-fixed effects
Observations
R-squared

Constant

VOLAT

ROE

LOGPPE

HHI

INVEST/A

MOM

LEVERAGE

B/M

LOGSIZE

LOGS3TOT

LOGS2TOT

LOGS1TOT

Dependent Variable: RET

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is RET, measured monthly. The main independent variables are carbon emission
levels (Panel A) and the growth in emissions (Panel B). All variables are defined in Tables I and II. We report the results of the pooled regression with
standard errors (in parentheses) double clustered at the firm and year level. All regressions include year-month-fixed effects, country-fixed effects,
and industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: United States and China

Global Pricing of Carbon

−0.145
(0.103)
0.560
(0.343)
−0.593**
(0.250)
0.209
(0.331)
−0.283
(2.425)
−0.114
(0.096)
0.074
(0.048)
0.007**
(0.003)
2.678
(3.904)
1.335
(0.753)
Yes
Yes
141,035
0.227

0.679***
(0.159)

(1)

−0.130
(0.103)
0.538
(0.343)
−0.567**
(0.251)
0.238
(0.335)
−0.086
(2.374)
−0.081
(0.100)
0.061
(0.046)
0.006**
(0.003)
2.842
(3.895)
1.264
(0.765)
Yes
Yes
140,974
0.227

0.294*
(0.137)

(2)
United States

1.254**
(0.467)
−0.163
(0.103)
0.603*
(0.320)
−0.598**
(0.253)
0.151
(0.320)
−0.556
(2.453)
−0.125
(0.096)
0.089
(0.051)
0.007**
(0.003)
2.622
(3.998)
1.354
(0.777)
Yes
Yes
141,106
0.227

(3)

−0.315***
(0.092)
0.969**
(0.386)
−0.047
(0.226)
0.872
(0.509)
−0.987
(0.785)
0.539
(0.425)
0.091
(0.083)
0.027*
(0.013)
−2.699
(1.964)
3.050*
(1.604)
Yes
Yes
58,980
0.303

0.759**
(0.256)

(4)

−0.307***
(0.090)
0.903**
(0.361)
−0.002
(0.218)
0.876
(0.493)
−1.312
(0.754)
0.534
(0.414)
0.085
(0.083)
0.026*
(0.013)
−2.833
(2.031)
3.031*
(1.586)
Yes
Yes
58,980
0.302

0.587**
(0.193)

(5)
China

1.899***
(0.504)
−0.337***
(0.098)
1.031**
(0.382)
−0.104
(0.237)
0.717
(0.450)
−1.401
(0.793)
0.426
(0.395)
0.103
(0.093)
0.026*
(0.013)
−2.934
(2.018)
3.198*
(1.608)
Yes
Yes
58,980
0.304

(6)

The Journal of Finance®

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Year/month-fixed effects
Industry-fixed effects
Observations
R-squared

Constant

VOLAT

ROE

LOGPPE

HHI

INVEST/A

MOM

LEVERAGE

B/M

LOGSIZE

S3CHG

S2CHG

S1CHG

Dependent Variable: RET

Panel B: Growth in Emissions

Table V—Continued

3708

3709

we find a higher premium estimated over the time interval between 2005 and
2018. This higher premium is in line with the findings of Bolton and Kacperczyk (2021a) that the carbon premium is rising over time, especially after the
Paris agreement of 2015.
The finding of a firm-level carbon premium for listed Chinese companies is
novel and surprising. Although China in many ways has been a pioneer in the
promotion of renewable energy, it does not stand out for its ESG institutional
investor constituency, nor for its institutional investors’ focus on carbon emissions. Yet, financial markets in China do price in a carbon premium at the firm
level, both when it comes to direct emissions as well as indirect emissions.
The magnitude of the premium is slightly lower relative to that in the United
States. The quantitative similarities in the results across the two economies
are slightly weaker for the carbon premium associated with the growth in
emissions, as can be seen in Panel B. Still, for both countries, the premium
is highly statistically significant, though the magnitudes of the premium for
China are 10% to 20% higher. The latter finding could be due to the fact that
a smaller fraction of companies in China disclose their emissions and to the
generally higher growth rate in emissions of Chinese companies.
A.3. Unconditional Results
We next turn to the estimation of the model for the full sample of 77 countries. Relative to our previous specification, we also include country-fixed effects to account for country-specific variation in the data. We report the results
in Table VI. In columns (1) to (3), the estimates are for regressions without
industry adjustment; in columns (4) to (6), we include industry-fixed effects.
In Panel A, we report the results for the level of carbon emissions. Throughout all specifications, we find a positive and mostly statistically significant
effect of total emissions on individual stock returns, consistent with the hypothesis that higher-emission firms are riskier. Interestingly, when we do not
control for industry, the economic significance of the carbon premium at the
firm level for total scope 1 emissions is much smaller. One possibility is that
some firms (or industries) with high emissions have experienced unexpectedly
low returns. One example could be the recent devaluation of the energy sector
following the decline in commodity prices. For that reason, it seems natural
to focus on within-industry variations in carbon emissions. Indeed, when we
add an industry-fixed effect, the premium is large and highly significant. A
one-standard-deviation increase in LOGS1TOT across firms, equal to 1.4, is
associated with a return premium of 1.06% per year. These results indicate
that variations in stock returns across industries swamp variations in firmlevel emissions within a given industry. In our untabulated results, we have
also included country-fixed effects interacted with year-month-fixed effects,
and industry-fixed effects interacted with year-month-fixed effects, to account
the model, including fixed effects. This is equivalent to calculating the standard deviation of the
residual from the predictive model of each emission measure in the model.

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Global Pricing of Carbon

Table VI

−0.149***
(0.041)
0.519**
(0.217)
−0.426**
(0.180)
1.028**
(0.365)
−0.741
(1.102)
0.010
(0.119)
−0.002
(0.018)
0.014***
(0.004)

0.027
(0.021)

(1)

−0.180***
(0.042)
0.512**
(0.215)
−0.431**
(0.167)
1.035**
(0.366)
−0.693
(1.157)
0.028
(0.117)
−0.024
(0.022)
0.013***
(0.004)

0.093***
(0.029)

(2)

0.112***
(0.031)
−0.180***
(0.043)
0.522**
(0.216)
−0.362**
(0.165)
1.035**
(0.364)
−0.392
(1.215)
0.097
(0.114)
−0.039
(0.023)
0.012***
(0.004)

(3)

−0.185***
(0.041)
0.630**
(0.218)
−0.373**
(0.158)
1.021**
(0.370)
−0.435
(1.064)
0.055
(0.125)
0.009
(0.017)
0.013***
(0.004)

0.063***
(0.015)

(4)

−0.222***
(0.042)
0.608**
(0.212)
−0.402**
(0.146)
1.030**
(0.370)
−0.275
(1.090)
0.056
(0.121)
−0.001
(0.017)
0.013***
(0.004)

0.113***
(0.027)

(5)

(Continued)

0.164***
(0.035)
−0.244***
(0.044)
0.597**
(0.213)
−0.386**
(0.150)
1.033**
(0.369)
0.006
(1.103)
0.102
(0.127)
−0.020
(0.018)
0.013***
(0.004)

(6)

The Journal of Finance®

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ROE

LOGPPE

HHI

INVEST/A

MOM

LEVERAGE

B/M

LOGSIZE

LOGS3TOT

LOGS2TOT

LOGS1TOT

Dependent Variable: RET

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A)
and the growth in emissions (Panel B). Panel C includes both levels and changes of respective emissions. In Panels D and E, we consider different
(monthly) lag structures for the measures of emissions. All variables are defined in Tables I and II. We report the results of the pooled regression
with standard errors (in parentheses) double clustered at the firm and year level. All regressions include year-month-fixed effects and country-fixed
effects. In columns (4) to (6), we additionally include industry-fixed effects. Panels D and E only include specifications with the full set of fixed effects.
***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: Full Sample

3710

−0.156***
(0.041)
0.506**
(0.217)

0.437***
(0.086)

(1)

0.129
(3.539)
Yes
Yes
No
746,499
0.150

(1)
0.009
(3.522)
Yes
Yes
No
747,139
0.150

−0.052
(3.482)
Yes
Yes
No
746,642
0.150

−0.153***
(0.040)
0.500**
(0.216)

0.250***
(0.067)

(2)

1.157***
(0.278)
−0.170***
(0.041)
0.537**
(0.217)

(3)

Panel B: Growth in Emissions

(3)

(2)

−0.170***
(0.039)
0.640**
(0.221)

0.453***
(0.088)

(4)

0.359
(3.203)
Yes
Yes
Yes
736,711
0.151

(4)

−0.166***
(0.039)
0.633**
(0.220)

0.255***
(0.069)

(5)

0.309
(3.182)
Yes
Yes
Yes
736,854
0.151

(5)

(Continued)

1.175***
(0.288)
−0.183***
(0.040)
0.672**
(0.220)

(6)

0.334
(3.201)
Yes
Yes
Yes
737,351
0.151

(6)

3711

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B/M

LOGSIZE

S3CHG

S2CHG

S1CHG

Dependent Variable: RET

Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

VOLAT

Dependent Variable: RET

Panel A: Levels

Table VI—Continued

Global Pricing of Carbon

(2)
−0.444**
(0.173)
0.974**
(0.363)
−0.870
(1.194)
−0.036
(0.128)
0.025
(0.020)
0.014***
(0.004)
−0.059
(3.619)
Yes
Yes
No
735,362
0.151

(1)
−0.459**
(0.179)
0.958**
(0.362)
−1.000
(1.180)
−0.046
(0.127)
0.029
(0.021)
0.014***
(0.004)
−0.146
(3.602)
Yes
Yes
No
735,359
0.151

−0.492**
(0.173)
0.880**
(0.350)
−1.180
(1.204)
−0.064
(0.124)
0.041*
(0.020)
0.014***
(0.004)
−0.175
(3.670)
Yes
Yes
No
735,903
0.152

(3)
−0.393**
(0.150)
0.944**
(0.368)
−0.785
(1.059)
−0.033
(0.122)
0.047**
(0.017)
0.014***
(0.004)
0.182
(3.258)
Yes
Yes
Yes
725,745
0.153

(4)
−0.379**
(0.145)
0.961**
(0.369)
−0.690
(1.058)
−0.022
(0.124)
0.043**
(0.017)
0.014***
(0.004)
0.252
(3.274)
Yes
Yes
Yes
725,748
0.153

(5)

(Continued)

−0.421**
(0.144)
0.867**
(0.356)
−0.963
(1.058)
−0.051
(0.120)
0.060***
(0.018)
0.014***
(0.004)
0.169
(3.308)
Yes
Yes
Yes
726,289
0.153

(6)

The Journal of Finance®

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Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

VOLAT

ROE

LOGPPE

HHI

INVEST/A

MOM

LEVERAGE

Dependent Variable: RET

Panel B: Growth in Emissions

Table VI—Continued

3712

Yes
Yes
Yes
No
735,121
0.151

0.016
(0.021)
0.429***
(0.086)

(1)

Yes
Yes
Yes
No
735,206
0.151

0.082**
(0.029)
0.221***
(0.068)

(2)

0.104***
(0.029)
1.138***
(0.279)
Yes
Yes
Yes
No
735,903
0.152

(3)

Yes
Yes
Yes
Yes
725,507
0.153

0.046***
(0.014)
0.430***
(0.087)

(4)

Yes
Yes
Yes
Yes
725,592
0.153

0.099***
(0.025)
0.213***
(0.069)

(5)

(Continued)

0.150***
(0.033)
1.135***
(0.285)
Yes
Yes
Yes
Yes
726,289
0.153

(6)

3713

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

S3CHG

LOGS3TOT

S2CHG

LOGS2TOT

S1CHG

LOGS1TOT

Dependent Variable: RET

Panel C: Joint Regressions

Table VI—Continued

Global Pricing of Carbon

Yes
Yes
Yes
Yes
703,278
0.155

Yes
Yes
Yes
Yes
703,267
0.155

0.214**
(0.070)

(2)
Lag 3

Yes
Yes
Yes
Yes
736,552
0.151

0.108***
(0.027)

(2)
Lag 3

Yes
Yes
Yes
Yes
736,023
0.151

0.042**
(0.015)

(4)

Yes
Yes
Yes
Yes
736,106
0.151

0.095***
(0.028)

(5)
Lag 6

1.009***
(0.273)
Yes
Yes
Yes
Yes
703,806
0.156

(3)

Yes
Yes
Yes
Yes
669,337
0.160

0.259***
(0.074)

(4)

Yes
Yes
Yes
Yes
669,305
0.160

0.165**
(0.074)

(5)
Lag 6

Panel E: Alternative Lags (Changes)

0.149***
(0.035)
Yes
Yes
Yes
Yes
737,057
0.151

(3)

0.684**
(0.310)
Yes
Yes
Yes
Yes
669,841
0.160

(6)

0.117***
(0.032)
Yes
Yes
Yes
Yes
736,623
0.151

(6)

Yes
Yes
Yes
Yes
600,010
0.172

−0.078
(0.075)

(7)

Yes
Yes
Yes
Yes
735,197
0.151

0.023
(0.015)

(7)

Yes
Yes
Yes
Yes
599,938
0.172

−0.054
(0.058)

(8)
Lag 12

Yes
Yes
Yes
Yes
735,208
0.151

0.074**
(0.025)

(8)
Lag 12

−0.079
(0.188)
Yes
Yes
Yes
Yes
600,466
0.172

(9)

0.080**
(0.027)
Yes
Yes
Yes
Yes
735,749
0.151

(9)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

S3CHG

S2CHG

0.377***
(0.078)

(1)

Dependent Variable: RET

S1CHG

Yes
Yes
Yes
Yes
736,433
0.151

0.056***
(0.016)

(1)

Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

LOGS3TOT

LOGS2TOT

LOGS1TOT

Dependent Variable: RET

Panel D: Alternative Lags (Levels)

Table VI—Continued

3714

3715

for any demand-side shocks affecting different countries and industries. The
estimated risk premia from these models are only slightly smaller than those
reported here, which suggests that our results are not affected by transitory,
business-cycle shocks but are more reflective of permanent shocks, such as
transition risk.
Note that the coefficient of LOGS3TOT is highly significant in the regressions without and with industry-fixed effects. It is also economically significant, as a one-standard-deviation increase in LOGS3TOT is associated with a
return premium of 1.81% for the specification without industry-fixed effects,
and 1.97% with the fixed effects.
The results with respect to the growth in carbon emissions are all highly
significant and are not affected at all by the inclusion of industry fixed effects,
as can be seen in Panel B. In the model with industry fixed effects, per onestandard-deviation change in scope 1 and scope 3, the corresponding return
premia amount to 2.17% and 3.38% per year, slightly smaller in magnitude
than the effects we observed for the levels of emissions. Of course, statistically
speaking, taking differences in emissions is close to including firm-fixed effects
in the model with levels of emissions.13
Our conceptual framework posits that the two different emission measures
proxy for two types of transition risk: a short-term and a long-term risk component. A natural question is to what extent these two measures capture independent variation in stock returns. Evidence in Table II shows that they are
largely independent of each other given the relatively small correlations. We
test this relative independence using a return regression model that jointly includes both measures. We report the results in Panel C. In columns (1) to (3),
we present the results with country- and time-fixed effects and in columns (4)
to (6) we add industry-fixed effects. We find that in the joint model both measures of emissions retain their positive coefficients and economic significance,
which further confirms our starting premise that they capture economically
different sources of risk.
In another test, we assess the predictions of our model with respect to carbon intensity, a measure of firms’ total emissions scaled by their revenues. This
measure has been the focus of other research on investment strategies based
on discriminating between green and brown firms, and on asset managers’ exclusionary screening policies (e.g., Garvey, Iyer, and Nash (2018), and CheemaFox et al. (2021)), but when it comes to carbon-transition risk, carbon intensity does not directly capture the transition effort of a firm to attain net zero.
As we have pointed out in the introduction, a reduction in emission intensity
does not necessarily correspond to a reduction in total emissions. The level of
13 We have also explored the robustness of our results to different cut-offs for our measure of
emission changes. Specifically, we have considered measures that are winsorized at the 1% level.
The results, reported in Table IA.II of the Internet Appendix, are broadly consistent with those we
obtain in the baseline specification. (The Internet Appendix is available in the online version of
the article on The Journal of Finance website). We note that the results for unwinsorized metrics,
even though statistically significant, would be less desired because of significant outliers in the
right tail of the empirical distribution.

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Global Pricing of Carbon

The Journal of Finance®

emissions is a more direct proxy for carbon-transition risk exposure than emission intensity. Dividing by sales revenue introduces noise: when emission intensity changes it could be because of a change in sales revenue or because of
a change in the level of emissions. One potential concern with linking emission levels to stock returns could be that, if variations in emissions are driven
entirely by variations in the firm’s operating activities, emission levels could
be a proxy for sales revenues, so that the effect of emissions on stock returns
could simply reflect the effect of sales revenue on stock returns. Note, however,
that we do control for firm size so that the effect of size on emission levels
is accounted for. With a noisier proxy for carbon-transition risk exposure, one
should expect a less significant result. When we link carbon intensity to stock
returns, we indeed find no statistically significant relation. These results are
presented in Table IA.III of the Internet Appendix.
As an additional robustness check, we also associate carbon emissions with
annual returns. The results are reported in Table IA.IV and corroborate our
main findings relating carbon emissions to monthly returns.
The overarching conclusion from this part of our analysis is that firmlevel global stock returns reflect firm-level variation in both total emissions
and growth in total emissions, which indicates that investors price carbontransition risk both from a short-term and long-term perspective.
A.4. Book-to-Market Ratios
It is well known that stock returns are noisy proxies for expected returns. It
is sometimes possible to get more precise measures of expected returns based
on analyst forecasts. However, a major challenge with this approach is that
(i) analyst forecasts are only available for a relatively small subset of global
stocks, (ii) analyst forecasts may be biased because of industry incentive structures, and (iii) the metric of implied cost of equity critically depends on the
postulated valuation model.
As an alternative, we look at the pricing of carbon emissions from a different perspective and relate our firm-level carbon emission measures to book-tomarket ratios, which tend to be more stable over time and are available for a
large set of firms. Looking at book-to-market ratios helps us to better distinguish the explanation of our results as one based on required expected returns
as opposed to one due to luck. Accordingly, we estimate the following regression
model:


LNBMi,t = a0 + a1 T OT Emissions i,t + a2Controlsi,t−1 +μt +i,t .

(3)

Our dependent variable is the natural logarithm of the firm book-tomarket ratio, LNBM. Our control variables include MSCI, MOM, VOLAT, and
SALESGR. In addition, we use 1- and 2-year-ahead measures of SALESGR
to proxy for future cash flow growth and LTG to proxy for long-term earnings growth forecasts. Finally, in all specifications, we include country- and

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3716

3717

year-month-fixed effects. Some variants of our tests also include industry-fixed
effects. As before, we double cluster standard errors at the firm and year level.
We present the results in Table VII.
In Panel A, the main independent variables of interest are LOGS1TOT,
LOGS2TOT, and LOGS3TOT. Consistent with our hypothesis of the presence
of carbon-transition risk, we find that companies with high emissions have
higher book-to-market ratios. The effects are statistically significant in the
model that does not account for industry-fixed effects, in columns (1) to (3).
As before, the magnitudes become even stronger when we add industry-fixed
effect. In terms of economic significance, a one-standard-deviation increase in
cross-sectional scope 1 emissions is associated with a 13.2% increase in bookto-market ratios. The results for scope 2 and scope 3 emissions are comparable
in magnitude.
A natural question is whether these magnitudes are comparable to those obtained from the return regressions. To answer this question, we take a simple
Gordon growth model with an expected growth rate of 4% and expected return
of 12% (these numbers roughly correspond to an average stock) and ask how
much of an increase in expected returns is required to get a 13% lower valuation for high carbon emission stocks. For these parameters, this would imply a
number that is slightly less than a 1.4% excess return. This value is slightly
higher in magnitude than that estimated using our return regressions, but
in general it falls within a one-standard-error bound of the return coefficient.
Hence, statistically speaking, the two numbers are not very different from each
other.
In Panel B, we consider the specification with the growth in emissions as the
main independent variable. We estimate the same empirical model as before
and find a strong positive effect of changes in emissions on the log-book-tomarket variable. The effect is statistically and economically highly significant
both in the model without and with industry-fixed effects.
We note that in the above tests our sample size is naturally restricted due
to data limitations imposed by the computation of LTG. To ensure that our
results are not spuriously driven by the smaller sample, we repeat our analysis
using the model without LTG, but with a sample size that is comparable to
that used in our return models. We report the results in Table IA.V of the
Internet Appendix. In these large data, we find the effects that are statistically
more significant but broadly consistent in terms of their magnitudes with our
baseline results.
Overall, we conclude that our baseline results on stock returns are unlikely
to be explained by unexpected returns (or noise therein). They are more consistent with a systematic repricing of assets with different levels of emissions
and changes thereof. Hence, in the remaining parts of the paper we continue
with the specifications with stock returns as a main dependent variable.

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Global Pricing of Carbon

Table VII

−0.208***
(0.034)
−0.634***
(0.070)
1.982**
(0.629)
−0.496***
(0.058)
−0.376***
(0.037)
−0.351***
(0.069)
−0.012***
(0.002)
Yes
Yes
No
88,390
0.263

0.021**
(0.007)

(1)

−0.173***
(0.036)
−0.623***
(0.069)
1.928**
(0.623)
−0.513***
(0.056)
−0.411***
(0.046)
−0.384***
(0.075)
−0.013***
(0.002)
Yes
Yes
No
88,349
0.259

−0.005
(0.010)

(2)

0.016
(0.014)
−0.203***
(0.035)
−0.631***
(0.069)
1.965***
(0.618)
−0.504***
(0.057)
−0.389***
(0.044)
−0.361***
(0.074)
−0.013***
(0.002)
Yes
Yes
No
88,426
0.260

(3)

−0.235***
(0.031)
−0.596***
(0.057)
2.151***
(0.426)
−0.487***
(0.058)
−0.307***
(0.038)
−0.282***
(0.046)
−0.008***
(0.002)
Yes
Yes
Yes
87,093
0.475

0.056***
(0.009)

(4)

−0.255***
(0.033)
−0.591***
(0.055)
2.028***
(0.410)
−0.498***
(0.058)
−0.311***
(0.038)
−0.282***
(0.049)
−0.008***
(0.002)
Yes
Yes
Yes
87,052
0.474

0.057***
(0.009)

(5)

(Continued)

0.079***
(0.012)
−0.274***
(0.033)
−0.597***
(0.056)
2.197***
(0.399)
−0.498***
(0.058)
−0.290***
(0.037)
−0.269***
(0.046)
−0.008***
(0.001)
Yes
Yes
Yes
87,129
0.477

(6)

The Journal of Finance®

15406261, 2023, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.13272 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

LTG

SALESGRt+24

SALESGRt+12

SALESGR

VOLAT

MOM

MSCI

LOGS3TOT

LOGS2TOT

LOGS1TOT

Dependent Variable: LNBM

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is LNBM. The main independent variables are carbon emission levels (Panel A) and
the growth in emissions (Panel B). All variables are defined in Tables I and II. We report the results of the pooled regression with standard errors (in
parentheses) double clustered at the firm and year level. All regressions include year-month-fixed effects and country-fixed effects. In columns (4) to
(6), we additionally include industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Book-to-Market Ratios: Full Sample

3718

−0.180***
(0.033)
−0.624***
(0.069)
1.909**
(0.623)
−0.566***
(0.063)
−0.411***
(0.044)
−0.379***
(0.071)
−0.013***
(0.002)
Yes
Yes
No
88,414
0.260

0.066***
(0.020)

(1)

−0.181***
(0.033)
−0.624***
(0.069)
1.917**
(0.623)
−0.552***
(0.052)
−0.412***
(0.044)
−0.379***
(0.071)
−0.013***
(0.002)
Yes
Yes
No
88,338
0.260

0.045***
(0.013)

(2)

0.030
(0.123)
−0.180***
(0.033)
−0.624***
(0.069)
1.916**
(0.628)
−0.541***
(0.134)
−0.406***
(0.044)
−0.379***
(0.071)
−0.013***
(0.002)
Yes
Yes
No
88,426
0.259

(3)

−0.165***
(0.029)
−0.587***
(0.056)
1.884***
(0.457)
−0.524***
(0.072)
−0.349***
(0.041)
−0.327***
(0.053)
−0.009***
(0.002)
Yes
Yes
Yes
87,117
0.466

0.029
(0.021)

(4)

−0.165***
(0.029)
−0.587***
(0.056)
1.882***
(0.457)
−0.521***
(0.060)
−0.350***
(0.040)
−0.325***
(0.054)
−0.009***
(0.002)
Yes
Yes
Yes
87,041
0.466

0.022*
(0.012)

(5)

−0.027
(0.037)
−0.165***
(0.029)
−0.587***
(0.056)
1.884***
(0.456)
−0.473***
(0.076)
−0.347***
(0.039)
−0.327***
(0.052)
−0.009***
(0.002)
Yes
Yes
Yes
87,129
0.466

(6)

3719

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Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

LTG

SALESGRt+24

SALESGRt+12

SALESGR

VOLAT

MOM

MSCI

S3CHG

S2CHG

S1CHG

Dependent Variable: LNBM

Panel B: Growth in Emissions

Table VII—Continued

Global Pricing of Carbon

The Journal of Finance®
A.5. Information Observability and Carbon Premium

An important aspect of any risk premium analysis concerns the measurability of information on which investors condition their investment choices. While
some elements of our analysis are typical of any standard approach in the literature, others are unique in the context of carbon-transition risk. As we have
noted, progress in the transition is reflected in the rate of change in emissions,
which is why we should expect a priori transition risk to be tied to both the
level and rate of change in emissions. Such horizon effects should be present
even over shorter time spans. Hence, one should not expect the risk premium
to be independent of when we observe emissions relative to stock prices. This
is an important difference with respect to classical asset pricing, which essentially presumes a stationary world and stochastic general equilibrium.
To ensure that all the conditioning information is in investors’ information
sets at the time of the realization of returns, we have performed several robustness checks with different lags of emission information, since investors’ information sets are not perfectly observable. We have considered lags of 3 months,
6 months, and 12 months between the end of the year for which emissions are
reported and the month when returns are realized. Using the different lags, we
estimate the models in equations (1) and (2). We report the results in Panels
D and E of Table VI for the levels and changes of emissions. In most specifications, the premium for the level of emissions remains large and significant for
the different lags. In turn, the premium based on emission changes is positive
and significant for up to 6 months but becomes insignificant after 12 months.
These results raise two questions. First, why does the premium persist for
such a long period? And second, why does it disappear after 12 months? Our
answer to the first question is that investors have limited attention and do
not immediately absorb all the new information about carbon emissions at the
firm level (Kacperczyk, van Nieuwerburgh, and Veldkamp (2016)). The information about carbon emissions for year t is gradually reflected in returns over
the year. A related way to micro-found the friction would be with a model of
slow-moving capital (Duffie (2010)). Our answer to the second question is that
carbon emission numbers become stale after a while, and after a year the information in these numbers is subsumed in the new numbers. Interestingly,
when we compare the effect of lagging emissions on returns for respectively
levels and changes, we find that the former retains information longer than
the latter. The rate of change in emissions is naturally less persistent and
conveys more transitory information. In other words, the news component is
larger for the rate of change in emissions numbers than for the emission levels
numbers.
In our benchmark specification, we measure carbon emissions 1 month before the returns are realized. The reason for this choice is largely dictated by
the horizon effects and information staleness discussed above. We also note
that investors can obtain more accurate forecasts of future cash flow risk related to carbon emissions from industry and firm characteristics. The more up
to date their information about firm characteristics is, the more accurate are

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3720

3721

their forecasts of emissions and returns, which is why basing returns predictions on too long lags for the firm characteristics would underestimate the true
return premium. As an example, if we lag emissions by 12 months, that would
be saying that investors do not condition their forecasts on any updates in firm
characteristics for an entire year. This does not seem plausible. Therefore, we
believe that shorter lags, of 1 or 3 months, are more natural than a 12-month
lag.
We have also explored the extent to which emissions are a persistent characteristic. We ask how different is the effect of emissions on stock returns when
we abstract from any news effect contained in the latest emission numbers?
To do this, we replace the actual emission numbers in years τ < t = 2018
in our sample with emission estimates based on a backward imputation of
the emissions in year 2018, the last year of the sample. We can then determine how different the carbon premium is when we relate it to emissions that
are imputed back in time versus the actual year-by-year emission numbers. If
the premia are similar, this would suggest that emissions in year t are a good
statistic for emissions in years t−τ for all τ < t in our sample. This is indeed
what we find and report in Table IA.VI, which suggests that carbon-transition
risk, as proxied by the level of emissions, is a persistent characteristic when
you take out any news effects.
Another important issue is with respect to the delayed availability of emissions numbers from Trucost. First, the fact that our analysis is based on data
from Trucost does not mean that Trucost is the only source of information on
carbon emissions for investors. Investors can acquire information about corporate carbon emissions from other sources. Indeed, large asset managers like
BlackRock or Amundi rely on multiple data sources for carbon emissions that
are not all available at the same time. For example, a lot of firms disclose their
emissions first to the Carbon Disclosure Project organization, data that then
are merged into and combined with other sources by Trucost. Different information that is likely to be highly correlated with Trucost information (given
that all providers use the same data collection protocols) becomes available
at different times. Furthermore, investors are likely to be heterogeneous with
respect to access to information about carbon emissions. Therefore, the information set of investors is likely to be updated earlier than the information
set of the econometrician. In fact, in an additional (untabulated) test, we explore whether there are announcement returns around the date when Trucost
enters the data on emissions into its database and we find no effect. Stated
differently, our analysis is not meant to identify a trading strategy based on
Trucost data; we use these data only as a proxy for carbon-transition risk.
A related concern is about how Trucost gathers and aggregates the data on
corporate carbon emissions: Could the methodology that Trucost uses directly
affect the size of the carbon premium? Trucost reports two types of data, one
that is directly taken from corporate reports and another that is estimated
using its own prediction model. Could it be that the estimated emission numbers are noisy or biased because of the methodology used by Trucost? We find
the possibility of a systematic bias that is correlated with future stock returns

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Global Pricing of Carbon

The Journal of Finance®

unlikely, given the weak evidence of autocorrelation in stock returns typically
found in empirical studies. To evaluate the differences in carbon-transition
risk, as they relate to whether the carbon emissions are based on corporate
disclosures or are estimated, we take advantage of information provided by
Trucost on how particular emissions data have been sourced. We define an
indicator variable Disclosure if emissions for firm i at time t are based on directly disclosed information, and zero if they come from an estimate based on
a model-based approach. We amend our return regression by adding this variable and its interactions with our measures of carbon emissions. We report the
results in Table IA.VII. The results show two effects. First, the level of the
carbon premium is lower for emissions based on directly disclosed data, a finding that is inconsistent with the uncertainty reduction hypothesis. Second, the
premium remains positive and significant for both types of data, especially in
the model with industry-fixed effects. Hence, we conclude that the source of
emission data does not alter the qualitative aspects of our results.14
While our analysis considers different information sets based on monthly
frequency, it is important to note that corporate emissions data from Trucost
are provided at an annual frequency. However, the annual measurement of
corporate emissions should not imply that our empirical tests should be cast
at an annual frequency for stock returns. Even if data for corporate carbon
emissions are released at an annual frequency, investors’ information sets get
updated at a greater than annual frequency. It is more plausible that investors’
learning process is continuous, and that more information gets processed over
time. This process can further rationalize the fact that the impact of emissions
gets progressively smaller with an increasing lag between when emissions are
available and when returns are measured.
Finally, a common concern could be that emissions and stock returns are endogenously related through the company’s production channel. For example,
better business opportunities could be associated with higher sales and could
generate both higher emissions and higher realized returns. We note that this
prediction is not borne out in our data. Market value does not increase with
higher emissions (consistent with business opportunities getting better). We
find the exact opposite result, that the book-to-market ratio is positively related to carbon emissions. Stock prices are lower rather than higher for firms
14 In a related paper, Aswani, Raghunandan, and Rajgopal (2023) find that the carbon premium
associated with the level of emissions goes to zero for companies that directly disclose their emissions and suggest that investors may not be pricing carbon risk at all. Our results differ in that
we find a positive premium for both types of emission sources in a sample that includes roughly
five times more firms than in their sample. More importantly, we note that the smaller magnitude of the carbon premium for directly disclosed emissions is consistent with a model in which
firms endogenously decide whether to disclose their emissions. In this model, a benefit for the firm
of disclosing emissions is a lower risk premium achieved by lowering the perceived uncertainty
investors face with respect to carbon-transition risk. Hence, our evidence is fully consistent with
the hypothesis that investors do price carbon-transition risk, but differently for different levels
of perceived uncertainty. We provide an extensive analysis of this economic mechanism in Bolton
and Kacperczyk (2021c).

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3722

3723

with higher levels and higher growth in emissions. Thus, to the extent that production endogeneity is a concern, the estimates we provide constitute a lower
bound on the true effect of carbon emissions on the risk premium.
A.6. Geographic Distribution
By looking at the geographic distribution of the carbon premium, we can
assess how our unconditional results are driven by a particular region. The
economics literature on climate change has emphasized the importance of the
spatial distribution of climate policies (Nordhaus and Yang (1996)) and physical impacts (Cruz and Rossi-Hansberg (2023)). Different regions have different exposures to climate change as well as different capacities to adapt. With
respect to transition risk, one might expect that a country’s economic development, social norms, or headline risk may be equally important. At the same
time, financial market integration may erase some of the country-level heterogeneity.
We evaluate the geographic distribution of carbon-transition risk pricing by
comparing four different regions: North America, Europe, Asia, and Southern
Hemisphere countries (defined as “Others”). We define the respective indicator
variables: (i) Namerica for firms that are located in North America, (ii) Europe
for firms located in Europe, and (iii) Asia for firms located in Asia. The omitted
category is firms located in the Southern Hemisphere. We test two hypotheses
simultaneously: whether risk premia are positive and statistically significant,
and whether they differ from each other.
We report the results in Table VIII, Panel A, for the level of emissions, and
in Panel B for the growth in emissions. For brevity, we focus on scope 1 and
scope 3 emissions. We find that the carbon premium is generally larger in
North America, Europe, and Asia than in the residual Southern Hemisphere
group of countries. However, the only statistically significant result, at the 10%
level, is for firms located in North America. Importantly, all premia, especially
those that absorb industry-fixed effects, are positive and statistically significant. When it comes to the growth in emissions, the magnitudes of the effects
for Europe are visibly smaller than those in North America and Asia. Still, they
are all positive and statistically significant. The regions of the world that stand
out are Africa, Australia, and South America, where the coefficient of S1CHG
is borderline significant in the baseline model and insignificant when we add
industry-fixed effects. This result is quite interesting, as these countries are
least aligned with the principle of carbon neutrality.
An important robustness question is what matters more? Where the company is headquartered (which is the determinant of classification in our data),
or where emissions are generated? This distinction may be particularly relevant for firms with global operations, which are subject to different social
pressures, policies, or headline risk. While the granularity of our data does not
allow us to attribute total firm emissions to individual plants, we can evaluate whether the impact of firm emissions differs in a sample of multinational
companies versus those operated in a single country. Empirically, we define an

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Global Pricing of Carbon

Table VIII

(1)

Yes
Yes
Yes
No
746,499
0.150

0.029
(0.022)

0.028
(0.019)

0.042*
(0.020)

−0.001
(0.031)

Yes
Yes
Yes
No
746,642
0.150

0.027
(0.036)

0.022
(0.029)

0.051
(0.039)

0.065
(0.038)

(2)

0.028
(0.039)
Yes
Yes
Yes
No
747,139
0.150

0.042
(0.031)

0.065
(0.042)

0.075
(0.043)

(3)

(4)

Yes
Yes
Yes
Yes
736,711
0.151

0.020
(0.021)

0.019
(0.020)

0.043*
(0.020)

0.041
(0.024)

Yes
Yes
Yes
Yes
736,854
0.151

0.020
(0.036)

0.014
(0.031)

0.044
(0.037)

0.092**
(0.036)

(5)

(Continued)

0.022
(0.041)
Yes
Yes
Yes
Yes
737,351
0.152

0.040
(0.033)

0.059
(0.043)

0.132***
(0.042)

(6)

The Journal of Finance®

15406261, 2023, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.13272 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Asia*LOGS3TOT

Asia*LOGS2TOT

Asia*LOGS1TOT

Europe*LOGS3TOT

Europe*LOGS2TOT

Europe*LOGS1TOT

Namerica*LOGS3TOT

Namerica*LOGS2TOT

Namerica*LOGS1TOT

LOGS3TOT

LOGS2TOT

LOGS1TOT

Dependent Variable: RET

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A) and
the growth in firm-level total emissions (Panel B). All variables are defined in Tables I and II. We report the results of the pooled regression with
standard errors (in parentheses) double clustered at the firm and year level. All regressions include year-month-fixed effects and country-fixed effects.
All regression models include the controls of Table VI (unreported for brevity). In columns (4) to (6), we additionally include Trucost industry-fixed
effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: Regional

3724

(1)

Yes
Yes
Yes
No
735,359
0.151

0.322**
(0.142)

−0.010
(0.091)

0.362**
(0.138)

0.230**
(0.098)

Yes
Yes
Yes
No
735,362
0.151

0.340***
(0.104)

0.039
(0.115)

0.211*
(0.114)

0.054
(0.090)

(2)

0.607
(0.420)
Yes
Yes
Yes
No
735,903
0.152

0.007
(0.457)

0.499
(0.337)

0.780**
(0.349)

(3)

(4)

Yes
Yes
Yes
Yes
725,745
0.153

0.287*
(0.142)

−0.050
(0.099)

0.341**
(0.136)

0.275**
(0.112)

Yes
Yes
Yes
Yes
725,748
0.153

0.314**
(0.105)

0.020
(0.120)

0.193
(0.112)

0.078
(0.098)

(5)

0.541
(0.430)
Yes
Yes
Yes
Yes
726,289
0.153

−0.028
(0.464)

0.464
(0.345)

0.843**
(0.383)

(6)

3725

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Asia*S3CHG

Asia*S2CHG

Asia*S1CHG

Europe*S3CHG

Europe*S2CHG

Europe*S1CHG

Namerica*S3CHG

Namerica*S2CHG

Namerica*S1CHG

S3CHG

S2CHG

S1CHG

Dependent Variable: RET

Panel B: Growth in Emissions

Table VIII—Continued

Global Pricing of Carbon

The Journal of Finance®

indicator variable, FORDUM, equal to 1 for firms that have at least some sales
generated abroad and 0 for firms whose sales are entirely from a single country. Next, we estimate the models in equations (1) and (2) with an additional
interaction term between measures of emissions and FORDUM.
We present the results in Table IA.VIII. Across all empirical specifications,
we find only weak evidence that firms with multinational operations exhibit
different sensitivities of their stock returns with respect to total firm emissions.
For the specifications with the level of emissions, the interaction terms are
small and statistically insignificant and for the specifications with the growth
in emissions, the interaction term is significant at the 10% level for scope 3
emissions. Overall, it does not seem that the geographic source of firm-level
emissions is a primary driver of the carbon premium in our data.
In sum, our continent-level results reveal that carbon-transition risk is economically relevant in most geographic regions and that there is some geographic variation in the carbon premium throughout the world, even though it
is mostly related to short-term measures of carbon-transition risk. In the final
part of this section, we turn to an investigation of whether carbon-transition
risk is tied to a country’s economic development, one of the main issues that
frames discussions of international climate mitigation agreements.
A.7. Economic Development
The level of a country’s economic development is an important consideration
when it comes to climate policy. Typically, richer countries are expected to, and
have for the most part, made stronger commitments to combat climate change.
Rich countries have a greater responsibility to combat climate change as they
are the source of the largest cumulative emissions over the past two centuries
by far. Another reason to expect a lower carbon premium in developing countries is simply that currently these countries have low levels of emissions. In
addition, these countries’ economies are not as deeply founded on fossil fuel
energy consumption and may therefore be able to transition more easily to
a renewable energy development path. On the other hand, if these countries
depend a lot on fossil fuels, they may be less willing to adjust in the short-run.
In this section, we explore the empirical relevance of these arguments. A
remarkable general finding, as we show in Table IA.IX, is that the carbon premium does not seem to be related to countries’ overall level of development. We
first broadly categorize developed countries as the G20 countries and the remaining group of countries as developing countries.15 When we add industryfixed effects, we observe from Table IA.IX (Panel A) that the G20 group of
countries have highly significant carbon premia related to the level of emissions for all three scope categories. But this is also the case for the most part
for the group of developing countries (scope 2 emissions are only significant at
the 10% level for this group). Moreover, the size of the coefficients is similar. As
15 The results are qualitatively very similar, reported in Panel B, if we define developed coun-

tries based on the Organisation for Economic Co-operation and Development (OECD) membership.

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3726

3727

for the short-run effects of carbon emissions on stock returns, we observe that
they are again highly significant for both the G20 countries (controlling for industry) and the group of developing countries. Also, the size of the coefficients
is again broadly similar.
Admittedly, the above classification of countries into two groups, developing and developed, is rather coarse, and there is substantial heterogeneity in
country characteristics within each group. Accordingly, we also investigate the
effect of interacting GDP per capita, and other development variables such
as the share of the manufacturing sector in GDP and health expenditure per
capita, with the level and changes in emissions. As we show in Panel A of
Table IX, the interaction of per capita GDP and the level of emissions is insignificant. The same is true for the interaction of the share of manufacturing
and the level of emissions, and for the interaction of per capita health expenditures and the level of emissions. Overall, these results indicate that differences
in development do not appear to explain much of the variation in long-run carbon premia across countries. On the other hand, when we interact the same
variables with the percentage change in emission, as a measure of short-term
risk, a slightly different picture emerges. Now, firms located in countries with
higher GDP per capita and a more developed health system have statistically
smaller stock returns. Further, firms located in countries with a higher dependence on the manufacturing sector in their output creation have higher stock
returns. These results are consistent with the view that firms in developed
countries face lower challenges in conforming to their country’s carbon neutrality objective. The growth in the emissions variable tells us the sustainability
of a country’s development path. If, for example, the growth in emissions in a
developing country is large because of high reliance on coal, then, in effect, the
companies in that developing country are exposed to greater future transition
risk when pressure grows to phase out coal.
Altogether, both regional and economic variation in carbon-transition risk
likely nest several specific factors that contribute to the observed results. Investigating the origins of these factors is the subject of our next section.
B. Carbon-Transition Risk Drivers
Even though the notion of carbon-transition risk has been commonly referred to in policy discussions, surprisingly little is known about the different
sources of this risk. Part of the reason is that most of the studies on carbontransition risk are either highly aggregated or focus on a single country or
industry (e.g., Bolton and Kacperczyk (2021a), Hsu, Li, and Tsou (2023)). Also,
many commentators often reduce carbon-transition risk purely to policy uncertainty, whereas other dimensions (for example, technological innovation or
the prevailing belief system) are clearly relevant.
We explore several channels through which carbon-transition risk could
manifest itself: technological, socioeconomic, regulatory policy, and reputation
risk, all of which affect future cash flows and changing investor attention to climate change as a source of variation for the discount-rate channel. The main

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Global Pricing of Carbon

Table IX

Yes
Yes
Yes
No
712,325
0.150

−0.113
(0.418)

Yes
Yes
Yes
No
712,965
0.150

−0.210
(0.655)

0.118***
(0.032)

−107.168**
(50.443)

−106.966**
(50.082)

0.030
(0.021)

(2)

(1)

Yes
Yes
Yes
Yes
702,742
0.152

−0.101
(0.402)

0.064***
(0.018)

−102.286**
(50.288)

(3)

Yes
Yes
Yes
Yes
703,382
0.152

−0.272
(0.612)

0.170***
(0.033)

Yes
Yes
Yes
No
679,747
0.152

−0.028
(0.112)

0.030
(0.023)

13.721
(8.422)

(5)

Panel A: Levels

−102.108**
(50.647)

(4)

Yes
Yes
Yes
No
680,362
0.152

−0.139
(0.173)

0.136***
(0.032)

15.378*
(8.635)

(6)

Yes
Yes
Yes
Yes
671,251
0.153

−0.068
(0.106)

0.072***
(0.019)

14.549*
(8.418)

(7)

Yes
Yes
Yes
Yes
671,866
0.153

−0.161
(0.164)

0.191***
(0.033)

16.083*
(8.586)

(8)

Yes
Yes
Yes
No
484,562
0.175

0.003
(0.003)

−0.048
(0.195)
0.009
(0.022)

(9)

0.008*
(0.005)
Yes
Yes
Yes
No
485,071
0.175

0.079**
(0.031)

−0.130
(0.202)

(10)

0.007
(0.005)
Yes
Yes
Yes
Yes
479,244
0.177

0.131***
(0.034)

−0.106
(0.196)

(12)

(Continued)

Yes
Yes
Yes
Yes
478,735
0.177

0.003
(0.003)

−0.040
(0.193)
0.047**
(0.018)

(11)

The Journal of Finance®

15406261, 2023, 6, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.13272 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

HLTHEXPPC*LOGS3TOT

HLTHEXPPC*LOGS1TOT

MANUFPERC*LOGS3TOT

MANUFPERC*LOGS1TOT

GDPPC*LOGS3TOT

GDPPC*LOGS1TOT

LOGS3TOT

LOGS1TOT

HLTHEXPPC

MANUFPERC

GDPPC

Dependent Variable: RET

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A) and
the growth in emissions (Panel B). GDPPC measures a country’s GDP per capita in current dollars in a given year, MANUFPERC is the percentage
of a country’s GDP that is produced in a given year in the manufacturing sector, and HLTHEXPPC is a country’s health expenditures per capita
in current dollars in a given year. All other variables are defined in Tables I and II. We report the results of the pooled regression with standard
errors (in parentheses) double clustered at the firm and year level. All regression models include the controls of Table VI (unreported for brevity),
year-month-fixed effects, and country-fixed effects. In selected columns, we additionally include Trucost industry-fixed effects. ***1% significance;
**5% significance; *10% significance.

Carbon Emissions and Stock Returns: Economic Development

3728

Yes
Yes
Yes
No
701,797
0.151

−4.601*
(2.466)

Yes
Yes
Yes
No
702,341
0.152

−11.536*
(6.250)

1.485***
(0.263)

−115.011**
(50.457)

−112.536**
(50.414)

0.587***
(0.112)

(2)

(1)

Yes
Yes
Yes
Yes
692,387
0.153

−4.510*
(2.461)

0.600***
(0.112)

−107.466**
(50.642)

(3)

Yes
Yes
Yes
Yes
692,931
0.153

−11.598*
(6.250)

1.505***
(0.266)

−109.815**
(50.689)

Yes
Yes
Yes
No
669,831
0.153

2.230***
(0.621)

0.088
(0.101)

11.674
(8.243)

(5)

Yes
Yes
Yes
No
670,340
0.153

3.863***
(1.453)

0.492*
(0.266)

10.472
(8.228)

(6)

Panel B: Growth in Emissions
(4)

Yes
Yes
Yes
Yes
661,480
0.154

2.163***
(0.625)

0.112
(0.102)

12.035
(8.256)

(7)

Yes
Yes
Yes
Yes
661,989
0.155

3.650**
(1.454)

0.543**
(0.264)

10.880
(8.244)

(8)

Yes
Yes
Yes
No
479,950
0.175

−0.045*
(0.024)

−0.044
(0.194)
0.654***
(0.131)

(9)

−0.093
(0.058)
Yes
Yes
Yes
No
480,373
0.176

1.439***
(0.287)

−0.072
(0.196)

(10)

Yes
Yes
Yes
Yes
474,176
0.177

−0.047**
(0.024)

−0.034
(0.193)
0.688***
(0.131)

(11)

−0.098*
(0.057)
Yes
Yes
Yes
Yes
474,599
0.177

1.501***
(0.291)

−0.064
(0.195)

(12)

3729

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

HLTHEXPPC*S3CHG

HLTHEXPPC*S1CHG

MANUFPERC*S3CHG

MANUFPERC*S1CHG

GDPPC*S3CHG

GDPPC*S1CHG

S3CHG

S1CHG

HLTHEXPPC

MANUFPERC

GDPPC

Dependent Variable: RET

Table IX—Continued

Global Pricing of Carbon

The Journal of Finance®

challenge in identifying each of the channels empirically is that to a large extent we can only measure transition risk drivers at the country level. As is well
known, regression specifications that relate stock returns to country-level characteristics, could yield biased estimates due to omitted country-level variables.
To mitigate this concern, we rely on firm-level variation in carbon emissions
and estimate the role of the different mechanisms by interacting the country
variables with firm-level emissions. This approach follows closely the identification strategy of Rajan and Zignales (1998), which also interacts country-level
financial development variables with industry-level financial constraints. In
our tests, we are also able to sharpen our empirical identification by absorbing
additional firm-level, industry-level, and country-level variation through a mix
of observable characteristics and fixed effects.
B.1. Technological Mix
An important source of carbon-transition risk is technological change in energy production and carbon capture. As they transition to carbon neutrality,
firms may find themselves at different points in their energy mix, carbon intensity, and outside demand for energy. The more distant the firms are from
their target technology profile in a new green equilibrium, the more they are
exposed to potential aggregate technology shocks. The resulting risk may come
from unexpectedly high costs of green energy production as well as uncertainty
about such costs.16
In this section, we explore the importance of these factors for the pricing
of carbon-transition risk. We classify technology factors into three categories;
the first two relate to the production side of carbon emissions and the third
relates to the consumption side. First, we investigate whether firms located in
countries with a higher share of renewable energy have lower carbon premia.
Second, we explore whether the size of the fossil fuel production sector affects
the carbon premium. We hypothesize that firms located in countries in which
the share of the energy sector is large would have a larger carbon premium.
Third, consumption of energy per capita may indicate how far the transition
to a low-emission economy has progressed. It may also indicate the expected
demand for fossil fuel energy going forward. We expect that firms in countries
with high energy consumption are exposed to higher transition risk.
The results of this analysis are reported in Table X. We uncover a few interesting patterns. First, we find that green and brown energy variables do not
matter much for how stock returns react to emission levels. Across all specifications, the coefficients of the interaction terms are small and statistically
insignificant. The exception is the interaction term between scope 3 emissions
and the reliance on renewable energy. This effect, however, is only marginally
significant. Second, the hypothesis that a more renewable energy–based
16 A separate issue that we do not explore formally in the paper is the uncertainty about the
depreciation of any stranded assets and their impact on firm value. Atanasova and Schwartz (2020)
analyze the empirical importance of this issue in the oil and gas industry.

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3730

Table X

Yes
Yes
Yes
No
438,446
0.185

0.028
(0.175)

0.006
(0.024)

7.809*
(4.150)

(1)

Yes
Yes
Yes
No
438,918
0.186

0.480*
(0.288)

0.077**
(0.030)

2.588
(5.042)

(2)

Yes
Yes
Yes
Yes
433,249
0.187

0.010
(0.176)

0.059***
(0.020)

8.161*
(4.164)

(3)

Yes
Yes
Yes
Yes
433,721
0.187

0.518*
(0.289)

0.132***
(0.034)

2.322
(5.059)

(4)

Yes
Yes
Yes
No
438,488
0.185

−0.443
(0.551)

0.030
(0.028)

Yes
Yes
Yes
No
438,960
0.185

−1.198
(0.844)

0.162***
(0.052)

2.400
(61.263)

(6)

Panel A: Levels

−7.864
(60.851)

(5)

Yes
Yes
Yes
Yes
433,291
0.187

−0.209
(0.525)

0.069**
(0.027)

−9.565
(60.818)

(7)

Yes
Yes
Yes
Yes
433,763
0.187

−1.299
(0.840)

0.222***
(0.053)

5.223
(61.358)

(8)

Yes
Yes
Yes
No
423,298
0.190

0.004
(0.005)

−1.386**
(0.545)
−0.005
(0.024)

(9)

0.006
(0.007)
Yes
Yes
Yes
No
423,770
0.190

0.085**
(0.039)

−1.427**
(0.550)

(10)

Yes
Yes
Yes
Yes
418,233
0.192

0.005
(0.005)
0.002
(0.007)
Yes
Yes
Yes
Yes
418,705
0.192

0.153***
(0.041)

−1.411**
(0.554)

(12)

(Continued)

−1.442***
(0.546)
0.038*
(0.021)

(11)

3731

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

ENUSEPC*LOGS3TOT

ENUSEPC*LOGS1TOT

ENINT*LOGS3TOT

ENINT*LOGS1TOT

ELRENEW*LOGS3TOT

ELRENEW*LOGS1TOT

LOGS3TOT

LOGS1TOT

ENUSEPC

ENINT

ELRENEW

Dependent Variable: RET

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A) and
the growth in emissions (Panel B). ELRENEW measures a country’s share of electricity generated by renewable power plants in total electricity
generated by all types of plants in a given year; ENINT is the ratio between energy supply and gross domestic product measured at purchasing
power parity in a given country. Energy intensity is an indication of how much energy is used to produce one unit of economic output in a given year;
ENUSEPC is a country’s energy consumption (in kg of oil equivalent per capita) in a given year. All other variables are defined in Tables I and II. We
report the results of the pooled regression with standard errors (in parentheses) double clustered at the firm and year level. All regression models
include the controls of Table VI (unreported for brevity), year-month-fixed effects, and country-fixed effects. In selected columns, we additionally
include industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: Energy Structure

Global Pricing of Carbon

Yes
Yes
Yes
No
433,851
0.186

−1.839*
(1.087)

0.597***
(0.113)

8.254**
(3.387)

(1)

Yes
Yes
Yes
No
434,226
0.186

0.005
(2.671)

1.201***
(0.289)

8.221**
(3.381)

(2)

Yes
Yes
Yes
Yes
428,710
0.188

−2.068*
(1.089)

0.644***
(0.114)

8.434**
(3.401)

(3)

Yes
Yes
Yes
Yes
429,085
0.188

−0.502
(2.675)

1.294***
(0.289)

8.389**
(3.395)

(4)

Yes
Yes
Yes
No
433,893
0.186

9.254**
(4.009)

0.021
(0.199)

−25.255
(60.766)

(5)

Yes
Yes
Yes
No
434,268
0.186

20.786***
(7.830)

0.113
(0.400)

−29.735
(60.556)

(6)

Panel B: Growth in Emissions

Yes
Yes
Yes
Yes
428,752
0.188

9.562**
(4.037)

0.039
(0.199)

−24.552
(60.724)

(7)

Yes
Yes
Yes
Yes
429,127
0.188

21.199***
(7.854)

0.158
(0.395)

−29.244
(60.459)

(8)

Yes
Yes
Yes
No
418,791
0.190

0.036
(0.033)

−1.397**
(0.553)
0.313**
(0.155)

(9)

0.097
(0.083)
Yes
Yes
Yes
No
419,166
0.191

0.728*
(0.373)

−1.385**
(0.552)

(10)

Yes
Yes
Yes
Yes
413,782
0.192

0.044
(0.033)

−1.446**
(0.553)
0.316**
(0.153)

(11)

0.107
(0.082)
Yes
Yes
Yes
Yes
414,157
0.193

0.760**
(0.372)

−1.431**
(0.553)

(12)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

ENUSEPC*S3CHG

ENUSEPC*S1CHG

ENINT*S3CHG

ENINT*S1CHG

ELRENEW*S3CHG

ELRENEW*S1CHG

S3CHG

S1CHG

ENUSEPC

ENINT

ELRENEW

Dependent Variable: RET

Table X—Continued

3732

3733

economy is associated with lower carbon premia is broadly borne out in the
data when it comes to firm-level growth in emissions. Firms located in countries with a larger fraction of renewable energy production have lower carbon
premia with respect to their year-to-year emissions growth, as indicated by
the negative highly significant coefficients for the interaction terms. Similarly,
we find that the coefficients of the interaction terms between the share of the
energy sector and the growth in emissions are highly significant and positive,
indicating that investors perceive the risk with respect to carbon emissions to
be greater in countries with large fossil fuel energy sectors. Interestingly, the
countries with higher reliance on renewables and lower reliance on fossil fuels are typically developed countries, which could partly explain why we found
that short-term transition risk is priced more for developing countries. At the
same time, we find that energy use is not significantly related to stock returns
irrespective of the risk measure on which we focus. One reason could be that
the energy source being consumed may be green. Also, the place of consumed
energy need not be the same as the country in which it is sourced. In sum, the
distinction between short-term and long-term reactions to technological mix
suggests that this variable is transitory in nature, at least when assessed from
the capital markets perspective. The energy mix cannot inform the long-term
costs of the transition, as any potential product or process innovation in this
market is likely to modify future expectations.
Overall, we find strong evidence that a country’s energy production mix is
an important predictor of how investors price risk with respect to short-term
changes in emissions, but not with respect to the level of emissions. The gist of
these results is broadly consistent with our hypothesis that uncertainty about
technological change increases transition risk. Our decomposition further reveals that production side factors are more relevant for investors than energy
consumption factors.
B.2. Sociopolitical Environment
Uncertainty about future carbon emission policies depends on the institutional and sociopolitical environment that shapes government action. We
should expect lower policy uncertainty in politically stable and socially harmonious societies, and in countries with more democratic institutions that
tend to reduce the risk of arbitrary policy swings. In contrast, less equal societies are more likely to waver in their policy commitments and make less
predictable progress toward carbon neutrality. This greater climate policy uncertainty, in turn, is likely to be reflected in a higher carbon premium. We
explore this channel by looking at whether a country’s “rule of law” and “voice”
affects the carbon premium of its companies. The rule of law captures perceptions of the extent to which agents have confidence in and abide by the rules of
society, and in particular the quality of contract enforcement, property rights,
the police, and the courts, as well as the likelihood of crime and violence. The
measure RULELAW, is standardized between −2.5 and 2.5. Voice reflects perceptions of the extent to which a country’s citizens are able to participate in

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Global Pricing of Carbon

The Journal of Finance®

selecting their government, as well as freedom of expression, freedom of association, and a free media. The standardized value, defined as VOICE, lies
between 2.5 and −2.5. The 2.5 indicates the situation in which there is no obstacle to expressing voice and −2.5 number reflects situations in which people
have no way of expressing their voices. Another indirect measure of social and
political stability we look at is the country’s income inequality, as measured
by the Gini coefficient. All three country measures are obtained at an annual
frequency from the World Bank. As before, we interact each of these variables
with the level and growth of emissions to distinguish between long-term and
short-term effects. We report the results in Table XI.
We do not find a significant effect of any of these variables on the premium
associated with the level of emissions and conclude from these results that
social factors do not appear to affect the long-run risk associated with carbon emissions. All coefficients of the interaction terms in Panel A are small
and statistically insignificant. In contrast, we find that sociopolitical factors
do matter for investors’ carbon-transition risk perceptions in the short-run. As
reported in Panel B, the coefficients of the interaction terms between “rule of
law” and changes in emissions, and between “voice” and changes in emissions,
are both highly significant and negative, indicating that the carbon premium
is lower in countries with better rule of law and more democratic political institutions. Similarly, the coefficient of the interaction term between the Gini
coefficient and changes in emissions is significant and positive, meaning that
in countries with higher inequality, the carbon premium is likely to be larger.
Overall, these results on the effect of sociopolitical factors are consistent with
the view that greater social harmony produces less climate policy uncertainty.
But these effects manifest themselves in the short-run, presumably because
the socioeconomic environment can evolve, so that current conditions are seen
as having a transitory impact on policy uncertainty by investors. For example, the political environment and social norms can change in the mediumand long-term; hence, any constraints imposed in the short-run may no longer
bind in the long-run. From a different angle, one can link our prior findings on
the heterogeneity in short-term risk premia between developed and developing
countries to the different states of socioeconomic capital across countries.
B.3. Climate Policy Tightness
Transition risk is often associated with expected regulatory changes dictating the adjustment to a green economy. Investor expectations of future climaterelated policies can be an important risk component. Firms located in countries
in which the government has made the most ambitious pledges to reduce carbon emissions may therefore be associated with a higher carbon premium. This
is particularly true when local regulations are reinforced by pan-governmental
policy actions, such as the United Nations-led COP initiative.
Climate change mitigation policies may originate from two sources: domestic regulators or international pan-governmental agreements. In this section,
we evaluate the importance of each of the channels separately using unique

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3734

Table XI

0.002
(0.009)

0.026
(0.017)

−0.677
(0.752)

(1)

0.004
(0.015)

0.108***
(0.025)

−0.721
(0.766)

(2)

0.002
(0.009)

0.061***
(0.015)

−0.660
(0.755)

(3)

0.003
(0.015)

0.162***
(0.028)

−0.705
(0.776)

(4)

−0.005
(0.011)

0.031*
(0.017)

−0.700
(0.805)

(5)

−0.009
(0.018)

0.120***
(0.024)

−0.676
(0.822)

(6)

−0.006
(0.011)

0.067***
(0.014)

−0.723
(0.803)

(7)

−0.010
(0.018)

0.173***
(0.027)

−0.697
(0.828)

(8)

−6.619
(12.017)
0.020
(0.081)

(9)

0.085
(0.115)

−7.181
(11.998)

(10)

0.081
(0.115)

−7.776
(11.998)

(12)

(Continued)

−6.753
(12.000)
0.023
(0.081)

(11)

3735

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VOICE*LOGS3TOT

VOICE*LOGS1TOT

RULELAW*LOGS3TOT

RULELAW*LOGS1TOT

LOGS3TOT

LOGS1TOT

GINI

VOICE

RULELAW

Dependent Variable: RET

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A) and
the growth in emissions (Panel B). RULELAW measures a country’s perceptions in a given year of the extent to which agents have confidence in and
abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood
of crime and violence. Estimate gives the country’s score on the aggregate indicator, in units of a standard normal distribution. VOICE captures
perceptions in a given year of the extent to which a country’s citizens are able to participate in selecting their government, as well as freedom of
expression, freedom of association, and a free media. Estimate gives the country’s score on the aggregate indicator, in units of a standard normal
distribution. GINI is a country’s GINI index in a given year. All other variables are defined in Tables I and II. We report the results of the pooled
regression with standard errors (in parentheses) double clustered at the firm and year level. All regression models include the controls of Table VI
(unreported for brevity), year-month-fixed effects, and country-fixed effects. In selected columns, we additionally include industry-fixed effects. ***1%
significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: Sociopolitical Environment

Global Pricing of Carbon

−0.145**
(0.060)
−0.331**
(0.151)

1.512***
(0.226)

−0.606
(0.744)

−0.627
(0.743)

0.599***
(0.097)

(3)

(4)

−0.144**
(0.060)

0.613***
(0.097)

Yes
Yes
Yes
No
746,289
0.150

(5)

Yes
Yes
Yes
No
746,929
0.150

(6)

−0.326**
(0.150)

1.524***
(0.228)

−0.587
(0.745)

(4)

−0.145***
(0.051)

0.535***
(0.075)

−0.778
(0.811)

(5)

−0.275**
(0.130)

(7)

(8)

−0.140***
(0.051)
−0.266**
(0.130)

1.339***
(0.180)

−0.804
(0.816)

(8)

Yes
Yes
Yes
Yes
737,141
0.152

0.547***
(0.075)

−0.806
(0.811)

(7)

Yes
Yes
Yes
Yes
736,501
0.151

1.327***
(0.179)

−0.782
(0.815)

(6)

Panel B: Growth in Emissions

Yes
Yes
Yes
Yes
737,141
0.152

−0.610
(0.743)

(3)

Yes
Yes
Yes
Yes
736,501
0.151

(2)

Yes
Yes
Yes
No
746,929
0.150

(2)

(1)

Yes
Yes
Yes
No
746,289
0.150

(1)

−7.074
(12.484)
−0.469
(0.396)

(9)

Yes
Yes
Yes
No
238,048
0.195

0.027
(0.219)

(9)

−1.072
(1.024)

−8.585
(12.489)

(10)

0.069
(0.296)
Yes
Yes
Yes
No
238,236
0.195

(10)

−0.887
(1.020)

−7.788
(12.419)

(12)

0.195
(0.302)
Yes
Yes
Yes
Yes
235,215
0.198

(12)

(Continued)

−6.232
(12.425)
−0.402
(0.399)

(11)

Yes
Yes
Yes
Yes
235,027
0.198

0.124
(0.219)

(11)

The Journal of Finance®

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VOICE*S3CHG

VOICE*S1CHG

RULELAW*S3CHG

RULELAW*S1CHG

S3CHG

S1CHG

GINI

VOICE

RULELAW

Dependent Variable: RET

Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

GINI*LOGS3TOT

GINI*LOGS1TOT

Dependent Variable: RET

Panel A: Levels

Table XI—Continued

3736

Yes
Yes
Yes
No
735,150
0.151

(1)

Yes
Yes
Yes
No
735,694
0.152

(2)

Yes
Yes
Yes
Yes
725,536
0.153

(3)

Yes
Yes
Yes
Yes
726,080
0.153

(4)

Yes
Yes
Yes
No
735,150
0.151

(5)

Yes
Yes
Yes
No
735,694
0.152

(6)

Yes
Yes
Yes
Yes
725,536
0.153

(7)

Yes
Yes
Yes
Yes
726,080
0.153

(8)

Yes
Yes
Yes
No
236,017
0.196

2.521**
(1.075)

(9)

6.030**
(2.677)
Yes
Yes
Yes
No
236,159
0.196

(10)

Yes
Yes
Yes
Yes
233,026
0.199

2.378**
(1.084)

(11)

5.687**
(2.675)
Yes
Yes
Yes
Yes
233,168
0.199

(12)

3737

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

GINI*S3CHG

GINI*S1CHG

Dependent Variable: RET

Panel B: Growth in Emissions

Table XI—Continued

Global Pricing of Carbon

The Journal of Finance®

data on country-specific regulatory tightness. Our policy data come from Germanwatch. To our knowledge, ours is the first large-sample study that evaluates the direct importance of both types of policies for global stock returns.
Each year, Germanwatch collects information on all climate-related policies
and converts this information into a numerical score, where a higher number
means a stricter regulatory regime. We define two variables that we interact
with firm-level carbon emissions. INTPOLICY is a normalized measure of international policy tightness; DOMPOLICY is a normalized measure of domestic policy tightness.17 We interact each of the two variables with the level and
growth in firm emissions.
We report the results in Table XII. Two interesting findings emerge. First,
in Panel A, we show that the effects of climate policy operate on the carbon
premium associated with carbon emission levels. The effect is positive and economically significant for both scope 1 and scope 3 emissions, and statistically
significant for scope 3 emissions. On the other hand, neither type of climate
policy tightness affects the carbon premium associated with the year-by-year
growth in emissions, as shown in Panel B. These results support the view that
carbon policies are seen by investors as permanent shocks to carbon-transition
risk. That is, investors’ perspective appears to be that climate policies that
are already in place are largely irreversible. Second, and perhaps more unexpectedly, we find that between the two types of climate policies, domestic
ones have a bigger effect on the carbon premium. This result sheds light on
many analysts’ concerns that the commitments made by countries in Paris or
Glasgow could be empty promises, that is, that commitments made through
international agreements lack credibility unless they are translated into domestic policy. It is only when these commitments are followed up by domestic
policy implementation that investors start paying attention.
B.4. Brown Reputation Risk
An important component of transition risk is reputation risk. A few fossil fuel-intensive industries that we define as “salient” are known to attract
negative media coverage, which could further amplify transition risk. Hence,
the question of whether the carbon premium is mostly concentrated in the oil
and gas, utilities, and motor sectors that are the focus of much negative press.
Could it be that the reason behind much cross-sector variation in the carbon
premium lies in the negative reputation earned by brown sectors? Given that
the media focus is largely on the salient brown industries, one would expect
that the investors in companies in these sectors price-in an additional risk
compensation for their exposure to the negative stigma of holding these stocks.
To explore this hypothesis, we estimate a modified regression specification
from that in Table VI, conditional on whether a company belongs to one of the
salient industries mentioned above, or not. We define an indicator variable,
17 Further details on the methodology behind the policy measures can be obtained from the

Germanwatch website, at https://www.germanwatch.org/en/21110.

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3738

Table XII

Yes
Yes
Yes
No
551,075
0.153

−0.015
(0.040)

0.044*
(0.023)

−0.684
(0.387)

(1)

Yes
Yes
Yes
No
551,642
0.153

0.027
(0.086)

0.123***
(0.038)

−1.171
(1.009)

(2)

Yes
Yes
Yes
Yes
544,127
0.155

−0.020
(0.041)

0.083***
(0.022)

−0.624
(0.384)

(3)

Yes
Yes
Yes
Yes
544,694
0.155

0.035
(0.084)

0.171***
(0.040)

−1.272
(0.983)

(4)

Yes
Yes
Yes
No
551,075
0.153

0.064
(0.050)

−1.087*
(0.566)
0.001
(0.024)

(5)

0.181**
(0.076)
Yes
Yes
Yes
No
551,642
0.153

0.041
(0.027)

−2.634**
(1.014)

(6)

Yes
Yes
Yes
Yes
544,127
0.154

0.065
(0.048)

−1.094*
(0.535)
0.037
(0.027)

(7)

(Continued)

0.188**
(0.072)
Yes
Yes
Yes
Yes
544,694
0.155

0.088**
(0.030)

−2.723**
(0.971)

(8)

3739

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

DOMPOLICY*LOGS3TOT

DOMPOLICY*LOGS1TOT

INTPOLICY*LOGS3TOT

INTPOLICY*LOGS1TOT

LOGS3TOT

LOGS1TOT

DOMPOLICY

INTPOLICY

Dependent Variable: RET

Panel A: Levels

The sample period is from 2005 to 2018. The dependent variable is RET. The main independent variables are carbon emission levels (Panel A) and
the growth in emissions (Panel B). INTPOLICY measures the strictness of a country’s international climate policy in a given year. DOMPOLICY
measures the strictness of a country’s domestic climate policy in a given year. All other variables are defined in Tables I and II. We report the
results of the pooled regression with standard errors (in parentheses) double clustered at the firm and year level. All regression models include the
controls of Table VI (unreported for brevity), year-month-fixed effects, and country-fixed effects. In selected columns, we additionally include Trucost
industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: Climate Policy Tightness

Global Pricing of Carbon

Yes
Yes
Yes
No
544,610
0.155

−0.175
(0.186)

Yes
Yes
Yes
No
545,073
0.155

−0.119
(0.574)

1.264**
(0.534)

−0.892**
(0.302)

−0.852**
(0.314)

0.570***
(0.125)

(2)

(1)

Yes
Yes
Yes
Yes
537,766
0.156

−0.176
(0.170)

0.593***
(0.109)

−0.842**
(0.316)

(3)

Yes
Yes
Yes
Yes
538,229
0.157

−0.038
(0.555)

1.252**
(0.513)

−0.891**
(0.306)

(4)

Yes
Yes
Yes
No
544,610
0.154

−0.001
(0.201)

−0.386
(0.272)
0.475***
(0.121)

(5)

0.364
(0.711)
Yes
Yes
Yes
No
545,073
0.155

0.984
(0.573)

−0.430
(0.280)

(6)

Yes
Yes
Yes
Yes
537,766
0.156

0.011
(0.194)

−0.383
(0.280)
0.492***
(0.105)

(7)

0.395
(0.679)
Yes
Yes
Yes
Yes
538,229
0.157

0.998*
(0.542)

−0.430
(0.289)

(8)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

DOMPOLICY*S3CHG

DOMPOLICY*S1CHG

INTPOLICY*S3CHG

INTPOLICY*S1CHG

S3CHG

S1CHG

DOMPOLICY

INTPOLICY

Dependent Variable: RET

Panel B: Growth in Emissions

Table XII—Continued

3740

3741

SALIENT, equal to 1 if the company belongs to one of the salient industries,
and 0 otherwise. Our coefficients of interest are those of the interaction effect
between SALIENT and respective emission measures. If these salient brown
industries are indeed more stigmatized, one would expect the carbon premium
to be smaller in the other sectors. In terms of our conditional regression specification, this would mean that the coefficient of the interaction term is positive
and statistically significant.
We report the results in Table XIII. By and large, we find that the premium
associated with the level of emissions is not statistically different for salient
and nonsalient industries, and, if anything, the direction of the effect goes
against the hypotheses of a premium being present mostly in salient industries. The results are slightly different for the premium associated with the
growth in emissions. Here, we find a slightly stronger effect for changes in
scope 3 emissions on returns for companies that operate in salient industries.
This finding could also mean that a stigma has mostly already been “baked
in” in these brown sectors but is yet to materialize in the other sectors that
have faced less analyst scrutiny. These findings are also consistent with the
results in Table VI that variations in stock returns associated with carbon
emissions across industries swamp within-industry variations. Another possibility is that the stigma could extend to an entire country when the country is
disproportionately dependent on brown sectors, as is the case for many countries in the “Others” category. By this interpretation, the weaker results we
found for this category could be due to this baked-in stigma associated with
an overdependence on brown sectors. Note, however, that our regressions include country-fixed effects, which to some extent absorb any such country-level
effects.
B.5. Physical Risk
Much of the economics literature on climate risk has sought to estimate the
expected physical damages due to climate change. A natural hypothesis is that
transition risk is positively correlated with physical risk. As countries are exposed to more severe weather events caused by climate change, one would expect that there will be greater support for policies combatting climate change
in these countries. In other words, the extent to which a country has been exposed to climate disasters may shape investors’ beliefs about the cost of longterm damage due to climate change. To test this hypothesis, we use a countrylevel, year-by-year index measuring physical risk (CRI) from Germanwatch.
This index is based on the frequency of climate-related damages. Countries
with higher values of the CRI index are considered to have higher physical
risk. We estimate the coefficients of the interaction terms between CRI and
firm-level emission measures, both their levels and growth rates. The results
are reported in Table IA.X. Columns (1) to (4) show the results based on total
emissions, and columns (5) to (8) show the results based on growth rates. Consistent with the hypothesis that physical risk amplifies the carbon premium
associated with transition risk, we find that positive values for the interaction

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Global Pricing of Carbon

Table XIII

Yes
Yes
Yes
No
744,864
0.150

0.047
(0.032)
0.417
(0.530)
−0.006
(0.040)

(1)

Yes
Yes
Yes
Yes
745,504
0.150

0.159***
(0.034)
−0.053
(0.045)

0.945
(0.651)

(2)

Yes
Yes
Yes
No
735,109
0.151

0.073**
(0.024)
0.331
(0.328)
−0.006
(0.028)

(3)

Yes
Yes
Yes
Yes
735,749
0.151

0.176***
(0.036)
−0.013
(0.033)

0.350
(0.403)

(4)

Yes
Yes
Yes
No
733,724
0.151

0.433**
(0.191)
0.010
(0.205)

0.247
(0.156)

(5)

0.555
(0.404)
0.710*
(0.369)
Yes
Yes
Yes
Yes
734,268
0.152

0.202
(0.155)

(6)

Yes
Yes
Yes
No
724,143
0.153

0.472**
(0.200)
−0.020
(0.209)

0.142
(0.119)

(7)

0.601
(0.412)
0.671*
(0.367)
Yes
Yes
Yes
Yes
724,687
0.153

0.095
(0.113)

(8)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

SALIENT*S3CHG

S3CHG

SALIENT*S1CHG

S1CHG

SALIENT*LOGS3TOT

LOGS3TOT

SALIENT*LOGS1TOT

SALIENT

LOGS1TOT

Dependent Variable: RET

The sample period is from 2005 to 2018. SALIENT is an indicator variable equal to 1 for all companies in the oil and gas (GICS = 2), utilities
(GICS = 65-69), and motor (GICS = 18, 19, 23) industries, and 0 for companies in all other industries. The dependent variable is RET. The main
independent variables are carbon emission levels (columns (1) to (4)) and the growth in emissions (columns (5) to (8)), all interacted with SALIENT.
All variables are defined in Tables I and II. We report the results of the pooled regression with standard errors (in parentheses) double clustered at the
firm and year level. All regressions include year-month-fixed effects and country-fixed effects. All regression models include the controls of Table VI
(unreported for brevity). In even-numbered columns, we additionally include Trucost industry-fixed effects. ***1% significance; **5% significance;
*10% significance.

Carbon Emissions and Stock Returns: Reputational Risk

3742

3743

terms with emission changes. However, all these coefficients are statistically
insignificant. Also, contrary to our prediction, the coefficients of the interaction
terms with emission levels are negative (again, however, these coefficients are
statistically and economically small). Hence, greater physical risk exposure for
a country because of climate change, and greater incidence of physical climate
shocks, does not result in greater carbon transition risk.
Overall, we conclude that transition risk does not appear to be significantly
linked to different exposures to physical risk, perhaps because physical risk is
a localized risk, and is unlikely to affect all regions with the same intensity,
whereas the carbon transition is a global issue, which is largely independent
of whether physical risks materialize in a specific country or not. It is simply
a reflection of the shift away from fossil fuels. Indeed, countries like Australia,
Brazil, and Russia, or U.S. states like Texas, Florida, or West Virginia, that
have experienced massive climate disasters, have not seen a political movement emerge to shut down coal mines and other fossil fuel-dependent economic
activity. Somehow the political process in these countries (and U.S. states) does
not seem to commingle physical and transition risk.
B.6. Changes in Investor Awareness
Our analysis so far has explored the carbon premium through the cash flow
uncertainty channel. Another force that could affect the carbon premium is the
discount rate channel related to changing investor perceptions about climate
change and carbon-transition risk. Bolton and Kacperczyk (2021a) find evidence of a discount rate channel, with investor perceptions of carbon-transition
risk changing over time, but their evidence is based purely on U.S. companies,
which naturally raises the question of external validity. More importantly, this
evidence has little to say about what aspects of transition risk are altered by
the changed beliefs. Although our analysis here includes 77 countries, we cannot clearly isolate the effects of this channel given that we are pooling all observations from 2005 to 2018 together. However, we can explore how the carbon premium reacts to salient events that could reshape public perceptions of
climate change. One such defining event is the landmark Paris climate agreement at the COP21 in December 2015. This event has enhanced the salience
of the climate debate worldwide and raised the importance of possible transition risk going forward. It is therefore to be expected that the event has likely
changed investors’ perception of risk along multiple dimensions, including future energy costs, social preferences, or policy changes. Our empirical analysis
around this event captures the aggregate effect, encompassing all the above
possibilities, of investors’ responses to this event.
Specifically, we define an indicator variable Paris that is equal to 0 for the
2 years (from 2014 to 2015) preceding the Paris agreement and equal to 1 for
the 2 years (from 2016 to 2017) following the agreement. Next, we regress
stock returns on carbon emissions interacted with Paris. We report the results
in Table XIV, which provides the estimates for the differences in levels and
changes in emissions for our aggregate sample of 77 countries. Notably, there

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Global Pricing of Carbon

Table XIV

Yes
Yes
Yes
No
301,993
0.061

0.132***
(0.048)

−0.045
(0.031)

(1)

Yes
Yes
Yes
No
302,309
0.061

0.098*
(0.053)

0.060
(0.047)

(2)

Yes
Yes
Yes
Yes
298,113
0.064

0.133***
(0.048)

−0.017
(0.031)

(3)

Yes
Yes
Yes
Yes
298,429
0.064

0.101*
(0.054)

0.119**
(0.050)

(4)

Yes
Yes
Yes
No
295,469
0.062

−0.207
(0.210)

0.658***
(0.158)

(5)

−0.716
(0.528)
Yes
Yes
Yes
No
295,780
0.062

1.864***
(0.344)

(6)

Yes
Yes
Yes
Yes
291,686
0.065

−0.198
(0.211)

0.662***
(0.157)

(7)

−0.757
(0.550)
Yes
Yes
Yes
Yes
291,997
0.065

1.856***
(0.350)

(8)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Paris*S3CHG

Paris*S1CHG

Paris*LOGS3TOT

Paris*LOGS1TOT

S3CHG

S1CHG

LOGS3TOT

LOGS1TOT

Dependent Variable: RET

The dependent variable is RET. The main independent variables are carbon emission levels (columns (1) to (4)) and the growth in emissions (columns
(5) to (8)). All variables are defined in Tables I and II. We report the results of the pooled regression with standard errors (in parentheses) double
clustered at the firm and year level. Paris is an indicator variable equal to 0 for the period January 2014–November 2015 (2 years before Paris COP21
conference) and equal to 1 for the period January 2016–December 2017 (2 years after Paris COP21 conference). All regression models include the
controls of Table VI (unreported for brevity), year-month-fixed effects, and country-fixed effects. In selected columns, we additionally include Trucost
industry-fixed effects. ***1% significance; **5% significance; *10% significance.

Carbon Emissions and Stock Returns: The Role of Investor Awareness

3744

3745

is no significant premium associated with the level of scope 1 emissions right
before Paris (even with industry-fixed effects), whereas there is a significantly
larger positive premium after Paris. We also find a significant increase in the
premium for the level of scope 3 emissions. In turn, the results for changes
in emissions are significant in the pre-Paris period and show no significant
difference with the post-Paris period. One way to interpret these contrasting
results is that, because of COP21, investors significantly updated their beliefs about long-term transition risk. Consistent with our previous findings,
these results also suggest that the Paris agreement has been particularly important in reshaping investor beliefs about forthcoming climate-related policies. Indeed, this has been a popular narrative among practitioners and policy
makers.
In which parts of the world did the Paris agreement have the biggest effect?
To explore this question, we estimate the same model as in Table XIV for each
continent. We report the results for the level of carbon emissions in Table XV.
Remarkably, there is no apparent change for North America. Both before and
after the Paris agreement, there is no significant carbon premium associated
with the level of emissions. In Europe, both before and after Paris, there is a
significant carbon premium (except that the premium for scope 1 emissions
becomes insignificant after Paris). As a result, there is no significant change
in the value of the premium around the Paris event for Europe. The biggest
and most statistically significant change is in Asia, where the carbon premium
was insignificant before Paris, but became highly significant after Paris. This is
true whether we exclude China or not. Finally, in the other continents (Africa,
Australia, and South America) there is also a significant positive change before
and after Paris, even though this change is based on a smaller sample size.
Another relevant breakdown is between the group of G20 countries and the
group of other countries. The results are reported in Table IA.XI. Again, the difference in the carbon premium before and after Paris is dramatic for the group
of G20 countries. Before the agreement there was no significant carbon premium, but after the agreement there is a highly significant positive premium,
whether we include industry-fixed effects or not. In contrast, the changes in
the other group of countries are much smaller. While there is a shift toward a
significant premium, it is mostly for scope 3 emissions.
We also undertake this analysis after excluding the salient industries associated with fossil fuels. Recall that our cross-sectional analysis when we pool
all years together established that the carbon premium is present even beyond
these industries. The results reported in Table IA.XII reveal similar robustness
in the carbon premium around the Paris shock. Indeed, there is a highly significant and positive premium associated with the level of emissions in other
industries as well after Paris.18
18 We have also tested whether the changing awareness results are driven by the sample of
new companies that Trucost has added to its database. The results, in Table IA.XIII, show similar
effects for the “legacy sample,” so it is unlikely that the addition of the new companies is driving
the results.

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Global Pricing of Carbon

Table XV

Yes
Yes
Yes
No
74,410
0.090

0.083
(0.081)

−0.035
(0.059)

−0.052
(0.109)
Yes
Yes
Yes
No
74,503
0.090

0.106
(0.093)

(1)
(2)
North America

Yes
Yes
Yes
Yes
73,442
0.098

0.079
(0.077)

−0.013
(0.060)

(3)

−0.044
(0.102)
Yes
Yes
Yes
Yes
73,535
0.098

0.071
(0.104)

(4)

Yes
Yes
Yes
No
12,978
0.105

0.072
(0.115)

−0.078
(0.078)

(5)

−0.211
(0.163)
Yes
Yes
Yes
No
13,025
0.106

0.209
(0.125)

Yes
Yes
Yes
Yes
12,876
0.119

0.090
(0.122)

0.009
(0.089)

(6)
(7)
North America (excl. USA)

(Continued)

−0.190
(0.170)
Yes
Yes
Yes
Yes
12,923
0.120

0.196
(0.159)

(8)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Paris*LOGS3TOT

Paris*LOGS1TOT

LOGS3TOT

LOGS1TOT

Dependent Variable: RET

Panel A: North America

The dependent variable is monthly RET. The main independent variable is carbon emission level. All variables are defined in Tables I and II. We
report the results of the pooled regression with standard errors (in parentheses) double clustered at the firm and year level. Paris is an indicator
variable equal to 0 for the period January 2014–November 2015 (2 years before the Paris COP21 conference) and equal to 1 for the period January
2016–December 2017 (2 years after the Paris COP21 conference). All regression models include the controls of Table VI (unreported for brevity),
year-month-fixed effects, and country-fixed effects. In selected columns, we additionally include Trucost industry-fixed effects. Panel A samples firms
from North America, Panel B from Europe, Panel C from Asia, and Panel D from all the remaining countries. ***1% significance; **5% significance;
*10% significance.

Carbon Total Firm Emissions and Stock Returns: Awareness (Regional)

3746

Europe

Yes
Yes
Yes
No
63,965
0.097

0.089
(0.061)

−0.022
(0.041)

(1)

0.065
(0.083)
Yes
Yes
Yes
No
64,034
0.097

0.099
(0.069)

(2)

Yes
Yes
Yes
Yes
62,911
0.105

0.091
(0.061)

−0.011
(0.043)

(3)

0.062
(0.082)
Yes
Yes
Yes
Yes
62,980
0.105

0.176**
(0.079)

(4)

Yes
Yes
Yes
No
63,965
0.097

0.089
(0.061)

−0.022
(0.041)

(5)

0.065
(0.083)
Yes
Yes
Yes
No
64,034
0.097

0.099
(0.069)

(6)
EU

Yes
Yes
Yes
Yes
62,911
0.105

0.091
(0.061)

−0.011
(0.043)

(7)

(Continued)

0.062
(0.082)
Yes
Yes
Yes
Yes
62,980
0.105

0.176**
(0.079)

(8)

3747

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Paris*LOGS3TOT

Paris*LOGS1TOT

LOGS3TOT

LOGS1TOT

Dependent Variable: RET

Panel B: Europe

Table XV—Continued

Global Pricing of Carbon

Yes
Yes
Yes
No
134,732
0.078

0.161***
(0.052)

−0.055
(0.033)

(1)
Asia

0.208***
(0.071)
Yes
Yes
Yes
No
134,814
0.078

0.007
(0.057)

(2)

Yes
Yes
Yes
Yes
133,201
0.082

0.166***
(0.051)

−0.034
(0.036)

(3)

0.216***
(0.074)
Yes
Yes
Yes
Yes
133,283
0.083

0.097
(0.067)

(4)

Yes
Yes
Yes
No
105,375
0.062

0.128***
(0.041)

−0.031
(0.029)

(5)

0.089
(0.081)
Yes
Yes
Yes
No
105,457
0.062

0.077
(0.073)

Yes
Yes
Yes
Yes
103,988
0.067

0.132***
(0.041)

−0.025
(0.030)

(6)
(7)
Asia (excl. China)

(Continued)

0.092
(0.083)
Yes
Yes
Yes
Yes
104,070
0.067

0.147*
(0.078)

(8)

The Journal of Finance®

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Paris*LOGS3TOT

Paris*LOGS1TOT

LOGS3TOT

LOGS1TOT

Dependent Variable: RET

Panel C: Asia

Table XV—Continued

3748

Yes
Yes
Yes
No
28,251
0.067

0.271***
(0.083)

−0.163***
(0.057)

(1)
Others

0.268**
(0.109)
Yes
Yes
Yes
No
28,323
0.067

−0.129
(0.081)

(2)

Yes
Yes
Yes
Yes
27,924
0.078

0.267***
(0.087)

−0.055
(0.084)

(3)

0.253**
(0.109)
Yes
Yes
Yes
Yes
27,996
0.077

−0.000
(0.112)

(4)

3749

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Controls
Year/month-fixed effects
Country-fixed effects
Industry-fixed effects
Observations
R-squared

Paris*LOGS3TOT

Paris*LOGS1TOT

LOGS3TOT

LOGS1TOT

Dependent Variable: RET

Panel D: Others

Table XV—Continued

Global Pricing of Carbon

The Journal of Finance®

All in all, these results paint a rather striking picture of the pricing of transition risk across countries. The expectation of a significant long-term change
in the carbon premium seems to be reflected in salient events, such as the
Paris agreement. The striking and surprising finding here is that awareness
about carbon risk, as reflected in the carbon premium, has changed the most
in Asia, where investor awareness has jumped after the Paris agreements,
whereas it has remained basically unchanged in Europe and North America,
either because these regions already had greater awareness of climate change
(Europe), or because they had less awareness and did not revise their beliefs
(North America). To further explore this conjecture, we look at the predictability of national reforms (measured by DOMPOLICY) from the previous year’s
international policy framework (measured by INTPOLICY), before and after
Paris, for the three different regions, Asia, Europe, and North America. In the
regression model, we also include country-fixed effects. Consistent with our
narrative, we find that there is predictive power of national policies in past
international commitments following the Paris agreement. It is the highest for
Asia, much lower for Europe, and the opposite for North America, the last result being consistent with the fact that the U.S. administration around Paris
has mostly moved in the opposite direction from the international framework.
We report these results in Table IA.XIV.
One potential concern with the risk premium interpretation is that we have
measured changes in the risk premium over relatively short periods, even if a
period of a decade and a half is not that short. Could it be that our findings are
just a random draw? Although it is not possible to test this luck hypothesis,
one should bear in mind that the Paris agreement is a particularly salient
event and its important consequences have been established in other contexts.
Also, the last decade has witnessed a significant increase in climate-related
events, and a sharp increase in media coverage of these events, so that our
interpretation based on changing risk (perceptions) has a solid grounding in
these trends.19
C. Transitioning to a Green Equilibrium
Our results are broadly consistent with the existence of a return premium
compensating investors for the carbon-transition risk they face. But at what
point did investors begin to demand compensation for this risk? Basic logic suggests that the period in which carbon-transition risk is compensated should be
preceded by a period during which assets are repriced to reflect the new risk.
This repricing can in principle be a protracted process that parallels the economic shift from a brown to a green equilibrium. Moreover, the repricing is
driven by changes in investor awareness about climate change risk. During
this transition phase, one would expect to see increased demand (and there19 In untabulated tests, we have also tested the change in the risk premium by using the long
period from 2005 to 2015 as the pre-period. The results for the interactions terms are qualitatively
similar.

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fore higher prices) for assets with low levels of emissions, and decreased demand (and lower prices) for assets with high levels of emissions. Although this
adjustment mechanism is straightforward, testing for such asset price adjustments is challenging, especially in the context of heterogenous global financial
markets, in which individual assets may transition at different times and at
different speeds.
In the absence of a clear large-scale empirical setting, we fall back on suggestive evidence from one individual sector, the tobacco industry, in which such
a repricing process accompanied the rebranding of tobacco companies as “sin
stocks.” As Hong and Kacperczyk (2009) show, the reclassification of the tobacco industry as a sin asset class meant that tobacco companies were added
to the divestment lists of many investors. This divestment movement resulted
in higher expected returns (Merton (1987)). Prior to the 1950s, the negative
health effects of tobacco consumption were not known; in fact, many considered tobacco a cure. This perception changed following the reports of the U.S.
Surgeon General, which resulted in a massive change in beliefs about the industry. Consequently, the 1950–1970 period saw a massive revaluation of the
industry, with tobacco companies being valued at much lower multiples. Following this repricing, however, tobacco companies over the subsequent four
decades delivered very large returns.
We believe that a similar process is underway in the energy industry, with
green energy companies being valued at much higher multiples and some
brown companies already being valued at lower multiples. We can infer some
of these repricing effects from some of our tests. As highlighted in Table XIII,
when we exclude salient industries from our sample the effect of scope 1 emission levels on stock returns increases relative to the unconditional value in
Table VI, which means that the salient industries, on an average, underperformed other sectors (with lower emissions) over our sample period. Interestingly, however, this difference only appears in regressions without industryfixed effects, which suggests that the repricing has been a broad categorical
repricing of the whole industry rather than individual firms in these industries. Of course, this repricing need not be a once-and-for-all revaluation as it
appears to have been for the tobacco industry. In fact, it seems to us that investors’ attitudes toward carbon emissions are much more dynamic, and thus
it is quite possible that one could witness multiple waves of repricing followed
by periods with high returns. This is in fact what we think our data capture.
Because the carbon transition process is ongoing, this can only be a speculative
inference, which we expect future out-of-sample tests of the carbon transition
will confirm.
V. Conclusion
If global warming is to be checked, the global economy will have to wean
itself off fossil fuels and reduce carbon emissions to zero by 2050 or 2060 at the
latest. This translates into a year-to-year rate in emissions reductions equal
to the drop we have witnessed in 2020 as a result of the COVID-19 pandemic.

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Global Pricing of Carbon

The Journal of Finance®

Whether the global economy will be able to stick to such a rate of reduction
in the use of fossil fuels, whether the reduction in emissions will be smooth
or highly nonlinear and abrupt, is impossible to say. But what is certain is
that in the coming years and decades investors will be exposed to substantial
transition risk. Given that stock markets are fundamentally forward looking,
it is natural to ask whether and to what extent this transition risk is reflected
in stock returns.
We have taken the broadest possible look at this question by analyzing the
pricing of carbon-transition risk at the firm level in a cross section of over
14,400 listed companies in 77 countries. To date, very little is known about
how carbon emissions affect stock returns around the world. Our wide-ranging
exploratory study provides a first glimpse into this question. We have found evidence of a widespread, significant, and rising carbon premium—higher stock
returns for companies with higher carbon emissions. This premium is not just
present in a few countries (the United States and the European Union) or in
a few sectors tied to fossil fuels. It is ubiquitous, affecting firms in all sectors
over three continents: Asia, Europe, and North America. Moreover, stock returns are related not just to firms’ direct emissions but also to their indirect
emissions through the supply chain and the carbon premium is associated both
with the year-to-year growth in emissions (a short-run carbon-transition risk
exposure) and the level of emissions (a long-run exposure).
Finally, we find that carbon-transition risk is not just a reflection of climate
policy uncertainty but is also tied to uncertainty with respect to technological
progress in renewable energy and the sociopolitical environment that could
support or undermine climate policies. In turn, time-series patterns point to a
time-varying carbon premium, with the premium rising significantly following
the COP21 meeting.
At a broad level, our study is relevant for the discussions centered on carbon taxation as a means to achieve reductions in emissions. While the idea of
a carbon tax is appealing based on economic first principles, it clearly faces
practical obstacles. A major impediment to the introduction of a global carbon
tax is coordination among political parties with diverse interests and financial
capacities. Our study suggests that financial markets could play an important
amplifying role. The increasing cost of equity for companies with higher emissions can be seen as a form of taxation through capital markets.
Our study is obviously not free of empirical challenges. One particular concern is that the shifting beliefs about climate change during our sample period are unusual and unlikely to be representative of the climate shocks that
will unfold in the foreseeable future. It could be that investors have overreacted to the Paris agreement and all the attention devoted to climate change
issues over our sample period. If that were the case, we would not really be
picking up a persistent expected return difference. Rather, we would be finding return premia driven by nonpersistent shocks to investor beliefs. This is a
possibility that we cannot rule out. But, given the climate science, this seems
highly unlikely. If anything, evidence of an overheating planet is building day
by day and alarm about climate change is rising. Given that carbon emissions

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3752

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continue to rise, the net zero commitments will be harder to achieve, which
means that carbon-transition risk is rising. It is therefore far more likely that
investor concerns about carbon-transition risk will grow. This, of course, means
that we are potentially underestimating the size of the carbon premium.
Initial submission: July 19, 2021; Accepted: July 7, 2022
Editors: Stefan Nagel, Philip Bond, Amit Seru, and Wei Xiong

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Supporting Information
Additional Supporting Information may be found in the online version of this
article at the publisher’s website:
Appendix S1: Internet Appendix.
Replication Code.

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==> JF2 - 2024 - ZHANG - Carbon Returns across the Globe.txt <==
THE JOURNAL OF FINANCE • VOL. LXXX, NO. 1 • FEBRUARY 2025

Carbon Returns across the Globe
SHAOJUN ZHANG*
ABSTRACT
The pricing of carbon transition risk is central to the debate on climate-aware investments. Emissions are tightly linked to sales and are available to investors only with
significant lags. The positive carbon return, or brown-minus-green return differential, documented in previous studies arises from forward-looking firm performance
information contained in emissions rather than a risk premium in ex ante expected
returns. After accounting for the data release lag, carbon returns turn negative in the
United States and insignificant globally. Developed markets experience lower carbon
returns due to intense climate concern shocks, while countries with stringent climate
policies exhibit higher carbon returns.

The pricing of carbon transition risk is a central question as investors consider
climate-aware investments. Theoretically, brown firms are more exposed to
policy risk during the transition to net zero and should earn higher expected
returns in equilibrium (Hsu, Li, and Tsou, 2023). Green firms, however,
can outperform when policy shocks kick in, consumer attention turns, and
investor tastes shift in transition to net-zero (Pastor, Stambaugh, and Taylor,
2021). Empirically, Bolton and Kacperczyk (2021) and Bolton and Kacperczyk (2023) (BK, 2021, 2023) find brown stocks exhibit outperformance (or,
* Shaojun Zhang is at Fisher College of Business, The Ohio State University. I am greatly indebted to Editor Jonathan Lewellen, an anonymous Associate Editor, and two anonymous referees for many constructive suggestions that have substantially improved the paper. I thank Anna
Cieslak, Isil Erel, Gino Cenedese, Jean Helwege, Harrison Hong, Po-Hsuan Hsu, Isil Erel, Harrison Hong, Kewei Hou, Wenxi Jiang, Kwok-Chuen Kwok, Lasse Pedersen, Michelle Lowry, Victor
Lyonnet, Lubos Pastor, Amin Shams, Matthew Serfling, Zacharias Sautner, Rene Stulz, Giorgio
Valente, Lu Zhang, Jean-Pierre Zigrand, and seminar participants at the American Finance Association annual meetings, European Finance Association annual meetings, AFFECT workshop,
City University of Hong Kong, Hong Kong Institute for Monetary and Financial Research, LSE
Systemic Risk Center, The Ohio State University, and University of Tennessee for insightful discussions and suggestions, and Rick Ogden and Yihan Zhang for outstanding research assistance.
I gratefully acknowledge financial support from Hong Kong Institute for Monetary and Financial Research (HKIMR). This paper subsumes an earlier working paper “Carbon Premium: Is It
There.” I have read The Journal of Finance disclosure policy and have no conflicts of interest to
disclose.
Correspondence: Shaojun Zhang, Fisher College of Business, The Ohio State University, 830
Fisher Hall, 2100 Neil Ave, Columbus, OH 43210, USA; e-mail: zhang.7805@osu.edu

This is an open access article under the terms of the Creative Commons Attribution License, which
permits use, distribution and reproduction in any medium, provided the original work is properly
cited.
DOI: 10.1111/jofi.13402
© 2024 The Author(s). The Journal of Finance published by Wiley Periodicals LLC on behalf of
American Finance Association.

615

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a carbon premium) both within the United States and globally, suggesting
that carbon transition risk is already priced in equity markets. However, In,
Park, and Monky (2017), Garvey, Iyer, and Nash (2018), Duan, Li, and Wen
(2023), Pastor, Stambaugh, and Taylor (2022), and Pedersen, Fitzgibbons, and
Pomorski (2021) find that green investments outperform in global equity, U.S.
equity, and U.S. corporate bonds, consistent with an ongoing transition to
the “carbon-aware” equilibrium. In addition, Görgen et al. (2020), Aswani,
Raghunandan, and Rajgopal (2024), and Lindsey, Pruitt, and Schiller (2021)
find mixed evidence. In light of the debates and challenges, while over 200
asset managers have committed to the Net Zero Asset Management initiative,
the two largest asset managers, Blackrock and Vanguard, have decided not to
divest brown firms.1
In this paper, I revisit the carbon return, which is the return spread between
brown and green firms, and find that the previously documented carbon premium arises from forward-looking sales information contained in emissions
instead of a risk premium in ex ante expected returns. After accounting for
the data release lag, the realized carbon return is significantly negative in the
United States in recent years and varies across countries as a function of cash
flow shocks, shifts in investor preferences, and local climate policies. Overall,
the evidence suggests that carbon transition risk is at least partially reflected
in global equity prices, but carbon returns in recent years are consistent with
an ongoing transition to a “carbon-aware” equilibrium.
A key empirical challenge in assessing carbon returns is real-time measurement of emissions known to investors due to the gradual release of carbon data.
I provide a first assessment of the lag of emission data release and find that
the lag is longer than that of typical accounting variables. The median lags are
10 and 12 months after the emission fiscal year-end for the U.S. and international samples, respectively. Because carbon emissions are often estimated as a
weighted sum of economic activity scaled by emission factors (Eggleston et al.,
2006), carbon emissions are tightly linked to firm sales in the data. Specifically,
firm sales contemporaneously account for 50% of the variation in U.S. scope 1
emissions and 71% of the variation in scope 2 emissions. Consequently, emissions contain substantial information about firm performance and should be
lagged sufficiently to avoid forward-looking bias (or look-ahead bias).
The main measure of carbon transition risk is carbon intensity or emissions
scaled by sales. Compared to total emissions, carbon intensity better captures
firm-level carbon transition risk for two reasons. First, because emissions grow
with firm operations, it is more informative to compare intensity across firms.
Second, while regulatory policies like cap-and-trade or carbon taxes focus on
total emissions, they affect the profitability of larger companies less than that
of smaller firms for a given level of carbon emissions.

1 See the statements by Blackrock at https://www.blackrock.com/corporate/about-us/our-2021sustainability-update/2030-net-zero-statement and by Vanguard at https://corporate.vanguard.
com/content/corporatesite/us/en/corp/climate-change.html.

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Using the point-in-time carbon emission data available to investors, I show
that brown firms as classified by carbon intensity earn significantly lower returns than green firms in the United States. Value-weighted carbon return
spreads per month are −0.39% and −0.27% for scope 1 and 2 carbon intensities. The negative carbon return is robust to factor adjustments and various robustness checks, including using firm-disclosed emissions only. Cross-industry
variation in emission intensity explains much of the variation in carbon excess
returns across firms. Globally, more carbon-intensive firms again tend to underperform, though the return spread is insignificant. In contrast, portfolios
based on year-over-year emissions growth or total emissions yield negative or
insignificant positive carbon returns in the United States or globally.
To highlight the role of forward-looking sales information, I replicate the
analysis in BK (2021, 2023), who relate emissions to returns before the actual release of emissions and accounting information for the emitting period.
Like BK, I find that stock returns are positively associated with contemporaneous and one-month-lagged emissions growth and total emissions in the
United States and globally. However, once firm performance during the same
emission period is taken into account, total emissions and emissions growth
are no longer positively associated with stock returns. The corrected carbon
coefficients tend to be negative, consistent with my baseline analysis. In sum,
the carbon premium documented in previous studies only sources from strong
performance of brown firms during the emitting period and does not reflect a
risk premium associated with carbon transition risk.
In additional analysis, I examine country-level evidence further to shed light
on the factors that drive carbon returns. Carbon returns exhibit large variation across countries and are lower in developed markets than in emerging
markets. International carbon returns can reflect disparities in expected risk
premia as well as unanticipated in-sample shocks, including cash flow shocks
and climate concern shifts. I find that developed countries have experienced
stronger growth in climate concerns, as measured by country-level sustainable
flows and climate concern surveys, leading to lower carbon returns in these
countries. In addition, cash flow shocks explain up to 7% of carbon return variation. After controlling for in-sample shocks, carbon returns tend to be higher
in countries with tighter climate policies, reflecting compensation for heightened policy risk as in equilibrium. Overall, the evidence suggests that investors
have started to price in carbon transition risk, but the risk premium associated
with brown stocks is muted in recent years.
This paper contributes to the literature on the pricing of carbon risks by
examining a critical methodological choice and reconciling conflicting findings
in previous studies. In addition, this paper contributes to international and
country-level evidence on climate finance. BK (2023) interpret cross-country
carbon return variation as expected return variation. In contrast, results in
this paper show that lower carbon returns in developed markets instead reflect
stronger climate concern shifts. Dyck et al. (2019) and Gibson Brandon et al.
(2022) study responsible institutional investing around the world but do not
address pricing implications. Görgen et al. (2020) and Aswani, Raghunandan,

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Carbon Returns across the Globe

The Journal of Finance®

and Rajgopal (2024) also study international or regional carbon returns but do
not examine cross-country differences, which is a focus of this paper.
This paper also adds to the literature that analyzes the role of institutional
investors and ESG investing. Pastor, Stambaugh, and Taylor (2022) characterize U.S. stock returns during the carbon transition, Berk and van Binsbergen
(2021), van der Beck (2021), Ardia et al. (2023), and Alekseev et al. (2022)
study price impacts of institutional investors in the United States and Hong,
Wang, and Yang (2021) study welfare implications. This paper extends this
work by turning to international markets and examines cross-country implications. Krueger, Sautner, and Starks (2020) document that the average respondent believes that climate risk is not fully priced in a survey-based study.
This paper provides complementary evidence based on asset prices. Finally,
Choi, Gao, and Jiang (2020) study short-term price implications when retail
investors revise their beliefs about climate change. This paper examines longer
term cross-country price impacts.
The remainder of the paper proceeds as follows. Section I discusses data
and characterizes the information set of investors. Section II studies U.S. and
global evidence. Section III benchmarks the analysis against previous studies. Section IV analyzes what drives cross-country variation in carbon returns.
Finally, Section V concludes.
I. Data and Methodology
A. Data
Data on firm-level climate performance come from S&P Trucost, which
provides annual information on firm-level carbon emissions in tons of carbon dioxide equivalent (tCO2e). Firm-level stock market and accounting
information source from CRSP and Compustat for the United States and
from Compustat Global for the international sample. I restrict the sample to
common stocks and focus only on the primary security listed on the primary
exchange. Trucost data are matched to the stock-level information by CUSIP,
ISIN, and SEDOL. Finally, I augment the data by natural gas price, Brent oil
price, and commodity index from FRED at the St. Louis Fed and by countrylevel information extracted from World Bank, World Risk Poll, and Climate
Change Performance Index.
I study scope 1 and 2 emissions. Scope 1 greenhouse gas (GHG) emissions
cover direct emissions from sources owned or controlled by the firm, such as
company vehicles or emissions from manufacturing facilities. Scope 2 GHG
emissions cover indirect emissions from the generation of purchased electricity,
steam, heating, and cooling consumed by the reporting company.
B. Sample and Summary Statistics
While most databases do not provide the date when emission data are made
available, Trucost updates various environmental variables simultaneously

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and provides the date when the final data are made available. In this paper,
I use the most recent carbon emission and accounting data based on their
respective data release dates. The final sample is the intersection between
monthly stock return data and annual carbon emissions data, ensuring that
carbon data are available before the stock return is known. The matched sample covers returns from June 2009 to December 2021.
The main measure of carbon transition risk is carbon intensity—emissions
scaled by sales—for a few reasons. First, because carbon emissions scale
with firms’ operations, it is more reasonable and informative to compare the
intensity across firms. Second, investors focus almost exclusively on carbon
intensity when discussing net-zero investment (see BK (2021), Hartzmark and
Shue (2023), and a statement by Blackrock.2 ) As such, one can expect carbon
intensity to be associated with stock returns if investors care about carbon
transition risk. Third, regulating policies, such as cap-and-trade or carbon taxes, focus on total emissions but have less impact on the profitability of
larger firms, conditional on the same amount of carbon emissions. To benchmark against the literature, I also construct measures of emissions growth, or
year-over-year (log) growth of emissions, and (log) total emissions. If the latest
carbon data for the fiscal year are not released yet, I fill in missing variables,
emissions, growth, or carbon intensity, with the latest available number.
Table I presents the distribution of countries and regions of firms as well
as summary statistics of average firm-level (log) carbon intensity, that is, log
emissions per million U.S. dollars of sales.3 Developed markets make up 67%
of the sample, with the United States and Japan presenting most observations
in the sample (22% and 14%). Among emerging markets, China represents the
largest fraction of the sample (6.1%), followed by Korea and Taiwan (5.9% and
5.1%).
Table II presents summary statistics for firm-level carbon measures in the
United States and in the global sample with all countries, respectively. For
the United States, both (log) scope 1 and 2 carbon intensity have a mean of
2.71 log tCO2e per million U.S. dollars while scope 1 intensity has a higher
standard deviation (2.19) than scope 2 (1.4). Carbon intensities are persistent,
with annual autocorrelations of 0.99 and 0.93 for scope 1 and 2 measures,
respectively. For the international sample, I screen international stock
returns following Hou, Karolyi, and Kho (2011) to minimize the impact of outliers. All nominal variables are denominated in U.S. dollars. Global summary
statistics are comparable to those of the United States, with slightly higher
mean intensity (3.04 and 2.92). Controls include market beta estimated over a
60-month rolling window, size calculated as log year-end market capitalization,
(log) book-to-market, momentum, idiosyncratic volatility from Fama-French
three-factor model, return on assets (ROA), asset growth, leverage, log PPE,
2 Available

at https://www.blackrock.com/corporate/about-us/our-2021-sustainability-update/
2030-net-zero-statement.
3 Average carbon intensity is calculated using all available data points in the sample and covers
different sample periods for different countries.

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Carbon Returns across the Globe

Table I

Summary Statistics by Country
This table presents the sample frequency and average scope 1 and 2 firm-level carbon intensities
by country.
Panel A: Developed Markets
Country
AUS
AUT
BEL
CAN
CHE
DEU
DNK
ESP
FIN
FRA
GBR
HKG
IRL
ISR
ITA
JPN
NLD
NOR
PRT
SGP
SWE
USA

Observations

Year

Scope 1 Intensity

Scope 2 Intensity

32,551
3,469
5,175
24,681
15,707
18,958
4,087
6,895
5,288
22,249
53,161
44,117
1,589
7,269
8,667
133,323
5,048
6,632
1,847
9,806
9,412
211,495

2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009

3.20
3.44
2.97
3.50
2.28
2.84
2.82
2.72
2.87
2.54
2.44
3.34
3.81
2.60
2.87
3.00
2.50
3.28
3.22
3.13
2.02
2.71

3.33
2.88
2.90
3.13
2.38
2.86
2.39
2.46
2.89
2.52
2.67
3.24
3.16
2.78
2.62
3.06
2.43
2.25
2.89
3.24
2.47
2.71

Panel B: Emerging Markets
ARE
ARG
BGD
BGR
BHR
BMU
BRA
BWA
CHL
CHN
CIV
COL
CYP
CZE
EGY
EST
GHA
GRC

1,928
1,110
441
270
295
29
8,012
18
4,090
57,325
172
1,047
33
868
3,562
132
136
2,645

2009
2009
2015
2015
2015
2019
2009
2020
2009
2009
2015
2009
2019
2009
2009
2015
2015
2009

2.37
3.62
3.48
3.33
0.18
−0.16
3.14
−0.55
3.46
3.68
2.35
3.94
0.04
2.75
3.53
4.12
3.47
3.41

2.72
2.85
3.06
3.16
1.42
0.10
2.30
−0.30
2.20
3.22
2.74
1.89
1.06
2.39
3.04
3.40
3.37
2.94
(Continued)

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The Journal of Finance®

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621

Table I—Continued
Panel B: Emerging Markets
Country

Observations

Year

Scope 1

Scope 2

HRV
HUN
IDN
IND
JAM
JOR
KAZ
KEN
KOR
KWT
LBN
LKA
LTU
LUX
MAR
MEX
MUS
MYS
NAM
NGA
NZL
OMN
PAK
PER
PHL
POL
QAT
ROU
RUS
SAU
SRB
SVN
THA
TUN
TUR
TWN
UKR
VNM
ZAF
ZWE

239
473
8,456
30,646
45
398
161
833
56,209
1,188
225
591
160
169
1,427
5,261
98
14,116
84
1,663
2,885
786
4,299
1,658
4,744
5,665
1,947
342
3,964
2,532
15
408
8,613
164
7,337
48,137
89
1,123
12,980
175

2009
2009
2009
2009
2018
2015
2014
2012
2009
2009
2015
2009
2015
2013
2009
2009
2015
2009
2015
2011
2009
2010
2009
2009
2009
2009
2014
2014
2009
2018
2015
2009
2009
2015
2009
2009
2015
2012
2009
2016

2.66
2.35
3.53
3.54
−0.14
1.83
1.09
2.44
3.28
1.63
0.72
2.53
2.07
−0.87
4.30
3.20
−0.06
3.59
2.64
2.68
3.04
2.11
4.36
4.16
3.86
3.08
2.90
3.13
4.94
3.63
−0.07
2.40
3.31
−0.27
3.78
3.31
4.56
3.22
2.96
4.13

3.39
2.43
2.98
2.82
1.24
2.36
0.85
1.41
3.12
2.31
2.22
2.88
3.21
1.42
3.74
3.27
1.11
2.96
3.79
2.36
2.38
1.85
2.84
3.73
3.11
2.79
2.48
1.38
2.92
3.30
−0.25
2.93
2.90
−0.19
3.12
3.29
3.49
2.64
3.88
3.91

sales growth, EPS growth, and exposures to natural gas, oil, and commodity
returns estimated over a 60-month rolling window. The carbon variables and
controls are winsorized at the 1% and 99% levels when used as explanatory
variables in regressions.

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Carbon Returns across the Globe

The Journal of Finance®
Table II

Summary Statistics
This table reports summary statistics of variables in the analysis. Carbon intensity is calculated as
the log ratio of total emissions to the year-end sales (tCO2e per million U.S. dollars); Emissions is
the log emissions growth. The autocorrelations (AR) are calculated at the annual frequency. Exposure to natural gas, oil, and commodity is the loading of stock returns on corresponding commodity
returns over a 60-month rolling window. Size is log year-end market equity; beta is estimated over
a 60-month rolling window; the (log) book-to-market ratio is the log ratio of book value of equity
to market value of equity; ROA is net income scaled by total assets; asset growth is the percentage change of total assets; momentum is past 12-month return skipping the most recent month;
leverage is book leverage defined as the book value of debt divided by the book value of assets;
ivol is idiosyncratic volatility from the Fama-French 3-factor model; and Sales and EPS are log
four-quarter sales and EPS growth.
U.S.

Scope 1 Intensity
Scope 2 Intensity
Scope 1 Emissions
Scope 2 Emissions
Scope 1 Log Emissions
Scope 2 Log Emissions
Log Sales
Beta
Size
Book-to-Market
ROA
Asset Growth
Momentum
Log PPE
Leverage
IVol (×100)
Sales
EPS
Natural Gas Exposure
Oil Exposure
Commodity Exposure

Global

AR

Mean

SD

AR

Mean

SD

0.99
0.94
−0.05
−0.10
0.98
0.97
0.98
0.87
1.01
0.85
0.72
0.10
0.00
0.06
0.74
0.68
−0.04
−0.28
0.75
0.78
0.75

2.71
2.71
0.04
0.06
10.08
10.08
7.47
1.23
7.97
−0.88
0.00
0.12
0.16
4.84
3.90
1.97
0.05
0.10
0.02
0.22
2.63

2.19
1.40
0.48
0.56
3.06
2.53
1.97
0.63
1.68
0.94
0.15
0.36
0.50
3.81
4.05
1.51
0.36
2.37
0.09
0.24
2.88

0.99
0.94
−0.06
−0.09
0.98
0.97
0.98
0.87
0.98
0.82
0.7
0.08
0.10
0.74
0.14
0.49
−0.08
−0.29
0.75
0.78
0.75

3.04
2.92
0.02
0.04
10.14
10.02
6.33
1.06
6.45
−0.52
0.02
0.14
0.15
3.47
1.67
2.08
0.08
0.03
0.16
0.01
1.67

2.27
1.49
0.53
0.54
2.93
2.29
2.01
0.48
1.78
0.9
0.13
0.4
0.53
4.01
4.98
1.36
0.42
1.58
0.29
0.11
2.48

C. Information Observability and Data Release Lag
A key empirical challenge in carbon and ESG investing is real-time measurement of emissions known to investors due to the gradual release of carbon data.
As such, the literature has made various timing choices. Görgen et al. (2020),
BK (2021), and Aswani, Raghunandan, and Rajgopal (2024) study the contemporaneous relation between returns and carbon footprint. BK (2023) links
monthly stock returns to emissions lagged by one month. Pedersen, Fitzgibbons, and Pomorski (2021), Duan, Li, and Wen (2023), and Lindsey, Pruitt,
and Schiller (2021) instead use a three-, six-, and six-month lag from the fiscal
year-end, respectively. For comparison, accounting variables are often lagged
by six months from the fiscal year-end in these papers following Fama and

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French (1992). As such, the lags adopted for carbon emissions are often less
than those for accounting variables, which can introduce forward-looking bias
for future accounting information. I now analyze the actual data release lags
and characterize investors’ information set.
C.1. Data Release Lag
S&P Trucost adds a new company-year observation to the database after
companies complete their fiscal year and the relevant data are publicly disclosed. For firm-disclosed carbon emissions, the Carbon Disclosure Project
(CDP) serves as the primary source. Participating companies submit underlying data for year t to the CDP disclosure system, which often opens in April
in year t + 1 and closes in September, allowing for the computation of overall
scores. Subsequently, CDP releases response data from individual companies
on an annual basis in October. Trucost updates its database as soon as CDP
releases these data on an ongoing basis as more information is made available
and provides its emission estimates.
Two observations arise from the inspection of the Trucost release dates.
First, Trucost reviewed and updated all pre-2008 data in May 2009. As such,
all data points before 2008 are backfilled. I therefore exclude all emissions
data prior to 2008. Second, emission data are updated with significant lags
compared to other types of data, such as accounting variables. Figure 1 plots
the histogram of lags between the fiscal year-end and data release date for
the 2008 fiscal year and onward. The 25th percentile of the U.S. distribution
is six months from the fiscal year-end, the typical lag adopted for accounting
variables, and the median is 10 months primarily influenced by the October
public releases by CDP. The distribution has a long right tail, with the 75th percentile equal to 24 months. For the international sample, 25th , 50th , and 75th
percentiles are seven, 12, and 22 months, respectively. The data lag compares
favorably with other data vendors. For example, for the July 2021 download of
MSCI ESG data, coverage for fiscal year 2020 is 5% that for the United States
and 16% that for the international sample in 2019.
C.2. Financial Information Contained in Emissions Data
The generalized methodological approach for constructing emissions data
is detailed in International Panel of Climate Change’s “2006 Guidelines for
National Greenhouse Gas Inventories” (Eggleston et al., 2006) and can be
described by
Emissions = Activity Data × Emission Factor.

(1)

The input economic activity data for different vendors and estimation procedures can range from readily available, aggregate company activity data from
companies’ annual reports, with default emission factors to more detailed and
granular activity data, including a wider range of process parameters and

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Carbon Returns across the Globe

The Journal of Finance®

Figure 1. Data release lags. This figure plots the frequency tabulation of reporting lags for
carbon emissions for the U.S. and international samples from the end of emission fiscal year. (Color
figure can be viewed at wileyonlinelibrary.com)

emission factors. In other words, emissions are often derived from accounting
information. The research process is consistent for emissions reported by
firms through CDP and emissions estimated by data vendors such as Trucost
and MSCI.
I now analyze the financial information contained in carbon data. First, I
regress log carbon emissions (growth) on log sales (growth) over the same year,
log Emissionit = α + β log Salesit + εit ,
Emissionit = α + βSalesit + εit ,

(2)

where  denotes the log change. The regression is conducted at the firmyear level, and standard errors are double-clustered at firm and year levels.
Table III presents results for the U.S. and global samples, respectively. Panel
A shows that emissions grow nearly linearly with firm sales. The coefficients
are statistically indistinguishable from unity at the 1% significance level for
both the U.S. and global sample, in line with the linear assumption that emissions are proportional to output as in Hong, Wang, and Yang (2021) among others. For example, scope 1 coefficients are 1.04 and 1.01 in the U.S. and global
samples, respectively. In terms of economic magnitude, sales explain as much

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624

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Table III

Scales of Carbon Emissions
This table studies the scale and determinants of carbon emissions. Panel A regresses scope 1
and 2 log emissions and emissions growth on log sales and sales growth for the U.S. and global
sample. Panel B regresses carbon intensity on various contemporaneous characteristics over the
same fiscal year. I report t-statistics in parentheses below the coefficients. ***, **, and * denote
significance at the 1%, 5%, and 10% levels, respectively. The sample period is 2007 to 2020.
Panel A: Emissions and Sales
U.S.
Log Emissions

Log Sales

Scope 1

2

1.04***
(44.51)

1.04***
(78.79)

Sales
Industry FE
Time FE
Country FE
R2
Observations

N
Y
N
0.50
21,783

N
Y
N
0.71
21,783

Global
Emissions

Log Emissions

Emissions

1

1

2

1

2

1.01***
(55.21)

0.97***
(74.03)
0.74***
(29.12)
N
Y
Y
0.18
84,247

0.72***
(27.59)
N
Y
Y
0.18
84,247

0.86***
(29.56)
N
Y
N
0.34
19,219

2

0.89***
(35.73)
N
Y
N
0.35
19,219

N
Y
Y
0.49
92,790

N
Y
Y
0.66
92,790

Panel B: Carbon Intensity and Firm Characteristics
U.S.
Scope 1

2

Global
1

2

1

2

1

2

−0.19
0.38*** −0.05** 0.04*** −0.12** 0.19***
0.01
0.05***
(−1.65)
(9.71)
(−2.48)
(3.07)
(−2.90)
(5.38)
(0.68)
(3.11)
Size
0.08*** 0.04*** −0.09*** 0.02***
0.02* −0.03*** −0.05*** 0.02***
(4.87)
(6.74) (−15.74) (3.21)
(2.16)
(−8.21) (−7.02)
(6.10)
Book-to-Market −0.03 −0.34*** 0.03*
0.01
0.21*** −0.05*** 0.10*** 0.04***
(−0.90) (−8.81)
(1.96)
(0.41)
(7.29)
(−3.21)
(8.18)
(5.24)
ROA
−0.13
0.51***
−0.07 −0.08** −0.22
0.11
0.05
−0.14***
(−0.54)
(4.01)
(−1.36) (−2.92) (−1.02)
(1.52)
(1.37)
(−3.34)
Asset Growth
−0.30*** −0.23*** −0.00 −0.06** −0.23*** −0.11*** −0.02
−0.04*
(−7.20) (−7.80) (−0.18) (−2.75) (−4.44) (−6.03) (−0.93) (−2.04)
Momentum
−0.10 −0.20***
0.03
−0.01
0.06
−0.03
0.08***
0.03
(−1.38) (−4.18)
(1.62)
(−0.56)
(0.84)
(−0.53)
(3.87)
(1.28)
Leverage
−0.15*** −0.10*** −0.01*** −0.00 −0.18*** −0.12*** −0.01*** −0.01***
(−36.12) (−28.45) (−3.83) (−1.75) (−39.18) (−32.28) (−3.13) (−4.51)
Log PPE
−0.01
0.00
0.00
0.01** −0.05*** −0.03*** −0.01*** −0.01**
(−1.03)
(0.62)
(0.51)
(2.19)
(−8.16) (−5.88) (−6.74) (−2.36)
IVol (×100)
0.19*** 0.17***
0.01
0.03*** 0.13*** 0.07***
0.01
0.03***
(5.68)
(10.70)
(1.42)
(6.86)
(5.45)
(7.28)
(1.68)
(3.45)
Sales
0.15
0.16**
0.35*** 0.28*** 0.22**
0.20*** 0.26*** 0.23***
(1.49)
(2.55)
(3.55)
(3.24)
(2.42)
(4.47)
(4.39)
(3.89)
EPS
−0.04** −0.02*
−0.01
−0.00
−0.02*
−0.01
−0.01**
−0.00
(−2.48) (−1.79) (−0.76) (−0.12) (−2.05) (−1.56) (−2.21) (−0.64)
Beta

(Continued)

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Carbon Returns across the Globe

Table III—Continued
Panel B: Carbon Intensity and Firm Characteristics
U.S.
Scope 1

2

Global
1

2

1

2

1

2

−0.16
−0.04
0.02
0.04
−0.02
0.08
0.02
0.07*
(−0.85) (−0.63) (0.23)
(0.60) (−0.11) (1.04) (0.28)
(2.02)
Natural Gas Exposure 2.18*** 0.43**
0.08
−0.10
0.57
0.05
0.18* 0.23***
(3.51)
(2.43)
(1.05) (−1.58) (1.49)
(0.31) (1.83)
(4.51)
Commodity Exposure 0.11*** 0.05*** 0.02*** 0.01* 0.08*** 0.02*
0.01
−0.01
(8.39)
(4.64)
(4.78)
(1.89)
(6.66)
(2.13) (1.30) (−1.32)
Industry FE
N
N
Y
Y
N
N
Y
Y
Time FE
Y
Y
Y
Y
Y
Y
Y
Y
Country FE
N
N
N
N
Y
Y
Y
Y
R2
0.14
0.19
0.78
0.63
0.14
0.14
0.69
0.53
Observations
18,573 18,573 18,572 18,572 80,987 80,987 80,987 80,987
Oil Exposure

as 71% of the variation in U.S. emissions and 66% of the variation in global
emissions.4 As such, sales are the most important determinant of emissions.
Emissions growth is significantly associated with sales growth, with coefficients of 0.86 and 0.89 in the U.S. sample and 0.74 and 0.72 in the global
sample. In terms of the R2 s, sales growth alone can explain up to 35% and
18% emissions growth variation in the U.S. and global sample, implying correlations with emissions growth of 0.59 and 0.42. For comparison, BK (2021,
table 7) and BK (2023, table 4) find that various lagged firm characteristics
together with additional industry fixed effects can explain less than 15% and
6% of the variation in the United States and globally. In short, contemporaneous firm performance, as measured by sales and sales growth, explains more
of the variation in emissions and emissions growth than do lagged characteristics combined. Moreover, sufficient lags in emissions and emissions growth
need to be included such that emission data are known at the time of the return analysis to avoid forward-looking bias. At the minimum, the lag of carbon
variables should be no less than that of accounting variables.
I further study the information contained in carbon intensity,
Intensityit = α + β · Characteristicsit + εit ,

(3)

where Intensityit denotes scope 1 and 2 log carbon intensities available to
investors at time t, and Characteristicsit denotes firm-level characteristics
available to investors at time t. The characteristics include beta, size, bookto-market, ROA, asset growth, momentum, leverage, log PPE, idiosyncratic
volatility, sales growth, EPS growth, and exposures to commodity factors.
4 For comparison, table 4 of BK (2023) can explain only up to 54% of the variation of the same
dependent variable using various lagged firm characteristics with the same fixed effects in the
global sample.

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Panel B shows that carbon intensity is associated with several firm-level characteristics. In particular, brown firms tend to have higher market beta, leverage, and more exposure to natural gas and commodity fluctuations but have
lower asset growth and idiosyncratic volatility. Together, these firm characteristics and temporal variation account for 14% and 19% of the variation in
intensity in the United States and globally.
Finally, the media and public recognize the industry aspect of carbon footprints and pay special attention to the transition risk of brown industries.
For instance, the Sustainability Accounting Standards Board has developed
industry-level sustainability accounting standards and materiality measures.
As such, columns 3 to 4 of Panel B further include GICS6 industry fixed effects.
The R2 s increase significantly to as high as 78% and 63% for scope 1 and 2 in
the United States and 69% and 53% globally. These results show that industry
variation drives most of the variation in carbon intensity.
II. U.S. and Global Carbon Returns
A. U.S. Baseline Analysis
The baseline empirical analysis conducts portfolio sorts using proxies for
firms’ carbon transition risk. For each month t, I use point-in-time carbon emission data available to investors to calculate carbon measures. I then sort stocks
into tercile portfolios.5 Thus, portfolio L contains firms with the lowest carbon
footprint and portfolio H contains firms with the highest carbon footprint. After forming the three portfolios, I calculate value-weighted monthly returns
on the portfolios at time t + 1. To examine the relationship between carbon
footprint and returns, I also form a high-minus-low portfolio that takes a long
position in brown portfolio H and a short position in green portfolio L.
I first examine the relationship between carbon intensity and stock returns
in the United States. Panel A of Table IV presents monthly average returns
from portfolio sorts using scope 1 and 2 carbon intensities, respectively. Carbon
intensity can predict stock returns in the cross-section. Portfolio L and M earn
similar average returns of 1.44% and 1.51%, while the most carbon-intensive
portfolio (H) earns a much lower return of 1.04% per month. The high-minuslow portfolio generates a significantly negative excess return of −0.39% per
month, which is consistent with investment managers divesting from brown
firms (BK, 2021). The pattern is similar for scope 2 carbon intensities, with the
tercile-sorted portfolios earning returns of 1.51%, 1.31%, and 1.24% per month,
respectively, and the high-minus-low portfolio generating a significant excess
return of −0.27% per month.
I next examine whether the negative carbon return can be explained by existing risk factors. Carbon intensity might be correlated with a firm’s profitability and investment decisions and, therefore, might be correlated with risk
5 Although emission data are inherently an annual series, portfolios are updated monthly as

new data become available.

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Carbon Returns across the Globe

Table IV

Carbon Sorted U.S. Portfolios
This table presents monthly value-weighted raw returns of carbon footprint-sorted portfolios. Sorting variables are carbon intensity, emissions growth, and total emissions, respectively. I report
t-statistics in parentheses below the coefficients. ***, **, and * denote significance at the 1%, 5%,
and 10% levels, respectively. The sample period is 2009:06 to 2021:12.
Panel A: Intensity
Scope 1
L

M

Scope 2
H

H-L

L

M

H

H-L

1.44***
1.51*** 1.04*** −0.39** 1.51***
1.31*** 1.24*** −0.27*
(4.03)
(4.51)
(3.00)
(−2.47)
(4.26)
(3.88)
(3.62)
(−1.87)
α
0.15**
0.11
−0.24** −0.40** 0.21***
0.01
−0.13 −0.34**
(2.16)
(1.39)
(−2.34) (−2.51)
(2.68)
(0.11)
(−1.57) (−2.40)
MKT
1.04***
0.99*** 0.96*** −0.09** 1.02***
1.00*** 0.98*** −0.04
(57.81)
(50.48)
(36.23) (−2.15)
(51.67)
(67.89)
(47.18) (−1.17)
SMB
−0.16***
0.07*
0.06
0.22*** −0.08** −0.08*** 0.08**
0.15**
(−5.20)
(1.95)
(1.35)
(3.22)
(−2.20)
(−3.15)
(2.12)
(2.46)
HML
0.12*** −0.19***
0.05
−0.07
0.09***
−0.05*
−0.03
−0.12*
(3.76)
(−5.38)
(1.04)
(−1.00)
(2.65)
(−1.73) (−0.81) (−1.94)
RMW
−0.20*** 0.14***
0.13** 0.33***
−0.08*
−0.07** 0.20*** 0.28***
(−5.07)
(3.33)
(2.31)
(3.79)
(−1.95)
(−2.06)
(4.36)
(3.62)
CMA
−0.13**
0.23*** 0.19*** 0.32*** −0.14***
0.03
0.29*** 0.43***
(−2.59)
(4.26)
(2.63)
(2.89)
(−2.63)
(0.83)
(4.99)
(4.37)
MOM
−0.02
0.03
−0.05
−0.03
−0.00
−0.04*
0.01
0.01
(−0.73)
(1.22)
(−1.54) (−0.69)
(−0.06)
(−1.95)
(0.29)
(0.20)
R2
0.97
0.96
0.93
0.19
0.96
0.98
0.95
0.21
Observations
151
151
151
151
151
151
151
151
Raw Return

Panel B: Emissions
Raw Return
α

1.29***
(3.95)
0.06
(0.91)

1.26***
(3.65)
−0.02
(−0.34)

1.49***
(4.04)
0.04
(0.44)

0.20
(1.37)
−0.02
(−0.17)

1.31***
(3.80)
0.07
(0.89)

1.31***
(3.89)
0.03
(0.46)

1.41***
(3.90)
−0.01
(−0.16)

0.10
(0.68)
−0.08
(−0.57)

1.50***
(4.14)
0.23**
(2.39)

1.30***
(3.86)
−0.05
(−1.30)

−0.09
(−0.42)
−0.33**
(−2.17)

Panel C: Emissions
Raw Return
α

1.62***
(4.03)
0.36***
(3.74)

1.41***
(3.70)
0.11
(1.34)

1.28***
(4.02)
−0.06
(−1.13)

−0.34*
(−1.77)
−0.42***
(−3.30)

1.39***
(3.61)
0.28**
(2.07)

factors commonly used in the literature. I use the FF6 factor model (Fama and
French, 2018), which includes profitability and asset growth factors together
with market, size, value, and momentum factors.
The intensity-sorted long-short portfolio loads strongly positively on
profitability and asset growth factors. After adjusting for factor exposure,
more carbon-intensive stocks earn significantly lower alphas than less

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Figure 2. U.S. carbon return. This figure plots U.S. carbon return spreads between high- and
low-carbon intensity portfolios. Panel A plots cumulative returns, and Panel B plots 12-month
rolling returns and FF6 factor-adjusted alphas. (Color figure can be viewed at wileyonlinelibrary.com)

carbon-intensive stocks. Portfolios sorted by scope 1 carbon intensities earn
abnormal returns of 0.15%, 0.11%, and −0.24% per month, and the long-short
alpha is −0.40% and significantly negative. The long-short portfolio alphas
sorted by scope 2 carbon intensity are −0.34% (t-statistics = −2.40).
Figure 2 plots the cumulative return, rolling return, and rolling alpha of
a strategy that longs the high carbon-intensity portfolio and shorts the low
carbon-intensity portfolio. Over the sample period, the high-minus-low portfolio loses as much as 50% of its initial value, suggesting a cumulative return of
100% for the green-minus-brown portfolio. Because the carbon return can move
together with various energy price movements, I further control for oil, natural gas, and commodity index price movements in the Internet Appendix and
again find significantly negative risk-adjusted returns.6 In sum, brown firms
have underperformed green firms in the United States. The return pattern
contrasts with the idea that brown firms earn a risk premium in equilibrium
and is more consistent with the pattern during transition.
6 The Internet Appendix is available in the online version of this article on The Journal of

Finance website.

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Carbon Returns across the Globe

Table IV, Panels B and C, repeats the analysis for portfolios sorted by
emissions growth and total emissions. The evidence suggests that investors
do not consider these variables as measures of carbon transition risk. The
FF6-adjusted high-minus-low carbon alphas are significantly negative for total
emissions but insignificant for emissions growth. In sum, carbon intensity is
negatively associated with future stock returns and alphas, while total emissions and emissions growth do not have consistent predictability.
B. Robustness Tests
In this section, I conduct several robustness analyses regarding carbon intensities. First, note that more than half of the data on emissions are estimated
by Trucost rather than reported by firms. While estimated carbon emissions
data can be subject to revisions by the data vendor, data reported by firms
are immune to vendor estimation and revisions. Indeed, Busch et al. (2022)
find that firm-reported scope 1 and 2 emissions are almost the same across
data providers. Accordingly, I study the subsample in which emissions are reported by firms only. Table V, Panel A, reports raw returns of sorted portfolios
and return spreads. Return spreads are −0.39% and −0.27% for scope 1 and
2 carbon intensities, respectively, and FF6-adjusted alphas are −0.40% and
−0.34%. These results point to a strong green return associated with reported
emission intensities, with results similar to the baseline. Related, the estimation process can differ across different vendors, leading to differences in the
timing of data releases to investors. I hence conduct robustness analysis, in
which I use year t emission data in October year t + 1. Results are again similar to the baseline and are reported in the Internet Appendix.
Table V, Panel B, considers two alternative measures of carbon transition
risk. I first use emissions divided by end-of-year market equity as in Ilhan,
Sautner, and Vilkov (2021). I find significantly negative carbon returns and alphas consistent with the baseline. I next use year-over-year changes in carbon
intensity (Intensity), measuring the extent to which carbon transition risk
has got better or worse. The high-minus-low return spreads in sorted portfolios are again negative, consistent with the baseline results. Panel C of Table V
analyzes carbon returns within different firm size groups. The results reveal
negative return spreads across all size groups, with the pattern most significant for larger stocks.
Finally, I conduct regression analysis using the model,
rit = α + βIntensityit−1 + γ Controlsit−1 + νt + εit .

(4)

The regression is run at the firm-month level and controls for time fixed effect.
Standard errors are double-clustered at firm and month levels. Here I use
weighted least squares regression to avoid excessive influence from small
stocks. I standardize carbon measures to have zero mean and unit variance
throughout these regressions, so the coefficients can be interpreted as the
change in monthly stock returns in response to a one-standard-deviation

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Table V

Robustness Analysis
This table conducts various robustness tests of U.S. carbon returns. Panel A focuses on the sample with emissions reported by firms only. Panel B presents return spreads of tercile portfolios
sorted by emissions scaled by year-end market equity and year-over-year change in carbon intensity, respectively. Panel C presents return spreads by size group of stocks. I report t-statistics in
parentheses below the coefficients. ***, **, and * denote significance at the 1%, 5%, and 10% levels,
respectively. The sample period is 2009:06 to 2021:12.
Panel A: Firm-Reported Emissions Only
Raw Return

Reported Only

Alpha

Scope 1

2

1

2

−0.37**
(−2.20)

−0.26*
(−1.79)

−0.39**
(−2.28)

−0.34**
(−2.41)

−0.39**
(−2.37)
−0.22**
(−1.98)

−0.35**
(−2.52)
−0.07
(−0.63)

−0.42***
(−2.62)
−0.34
(−1.36)
−1.18*
(−1.87)

−0.29**
(−1.98)
−0.60***
(−2.95)
−0.20
(−0.31)

Panel B: Alternative Measures
Emission/ME
Intensity

−0.42**
(−2.25)
−0.26**
(−2.47)

−0.24
(−1.41)
−0.14
(−1.28)
Panel C: By Size Group

Large
Mid
Small

−0.42**
(−2.55)
−0.13
(−0.53)
−0.68
(−1.14)

−0.25*
(−1.71)
−0.17
(−0.74)
0.23
(0.38)

increase in carbon footprint. Control variables include various firm characteristics that are shown to be related to stock returns, including beta, size,
book-to-market, ROA, asset growth, momentum, leverage, log PPE, sales
growth, EPS growth, and exposures to oil, natural gas, and commodity index.
Columns 1 to 2 of Table VI report the results. Similar to the sorting-based
evidence, more carbon-intensive stocks are associated with lower future excess
returns. In particular, a one-standard-deviation increase in scope 1 and 2 (log)
carbon intensity is associated with a 0.19% and 0.21% decrease in monthly
return, respectively. Turning to the controls, stocks more exposed to oil and
natural gas price fluctuations tend to be browner and earn a lower excess return in-sample, similar to carbon intensity.
Finally, the literature heatedly debates whether carbon returns are driven
more by cross-industry or within-industry variation. For example, Choi, Gao,
and Jiang (2020) and Ilhan, Sautner, and Vilkov (2021) highlight the role
of the industry-level carbon footprint. While BK emphasizes within-industry
firm-level measures, Sautner et al. (2023) find some pricing evidence for both.

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Carbon Returns across the Globe

The Journal of Finance®
Table VI

Regression Analysis
This table conducts weighted least square regressions of U.S. stock returns on lagged carbon intensities controlling for a number of firm characteristics. The regression includes time-fixed effects.
Standard errors are double-clustered at firm and monthly levels, accordingly. I report t-statistics
in parentheses below the coefficients. ***, **, and * denote significance at the 1%, 5%, and 10%
levels, respectively. The sample period is 2009:06 to 2021:12.
(1)
Scope 1
Scope 1

−0.19**
(−2.52)

Scope 2
Beta
Size
Book-to-Market
ROA
Asset Growth
Momentum
Leverage
Log PPE
IVol (×100)
Sales
EPS
Oil Exposure
Natural Gas Exposure
Commodity Exposure
Industry FE
Time FE
R2
Observations

(2)
2

0.31
(1.11)
−0.08
(−0.95)
−0.32**
(−2.05)
0.60
(0.44)
−0.08
(−0.37)
−0.03
(−0.06)
−0.03
(−1.39)
0.04*
(1.92)
−0.07
(−0.43)
−0.55
(−1.19)
−0.01
(−0.57)
−1.10*
(−1.92)
−2.02**
(−1.98)
0.10*
(1.68)
N
Y
0.27
206,025

(3)
1

(4)
2

−0.13
(−1.04)
−0.21**
(−2.46)
0.40
(1.43)
−0.06
(−0.69)
−0.35**
(−2.14)
0.78
(0.60)
−0.07
(−0.36)
−0.04
(−0.09)
−0.03
(−1.24)
0.04**
(1.99)
−0.08
(−0.46)
−0.52
(−1.12)
−0.01
(−0.49)
−1.08**
(−1.99)
−2.15**
(−2.04)
0.09
(1.57)
N
Y
0.27
206,025

0.09
(0.43)
−0.11
(−1.40)
−0.30*
(−1.66)
−0.87
(−0.75)
−0.02
(−0.12)
−0.37
(−0.86)
−0.02
(−1.12)
0.04*
(1.78)
−0.12
(−0.71)
−0.72
(−1.65)
−0.00
(−0.24)
−1.38**
(−2.49)
−1.75*
(−1.71)
0.16**
(2.23)
Y
Y
0.27
206,025

−0.06
(−0.80)
0.11
(0.51)
−0.10
(−1.25)
−0.30*
(−1.66)
−0.78
(−0.64)
−0.03
(−0.15)
−0.37
(−0.85)
−0.02
(−1.09)
0.04*
(1.81)
−0.12
(−0.70)
−0.72*
(−1.66)
−0.01
(−0.32)
−1.36**
(−2.48)
−1.82*
(−1.73)
0.16**
(2.19)
Y
Y
0.27
206,025

Columns 3 and 4 examine the evidence when including industry fixed effects.
Although carbon intensities are still negatively associated with stock returns,
the coefficients are −0.13% and −0.06%, smaller in magnitude than the specification without industry-fixed effects. The evidence suggests that industry

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Table VII

Carbon Sorted Global Portfolios
This table reports value-weighted returns of country-neutral carbon-sorted global portfolios. Alphas are obtained by regressing raw returns on DM FF6 factors. I report t-statistics in parentheses
below the coefficients. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.
The sample period is 2009:06 to 2021:12.
Panel A: Intensity
Scope 1

Raw Return
α

Scope 2

L

M

H

H-L

L

M

H

H-L

0.90***
(10.61)
0.06
(0.74)

0.84***
(9.70)
−0.07
(−0.88)

0.90***
(10.58)
−0.05
(−0.61)

−0.01
(−0.20)
−0.06
(−0.74)

0.90***
(10.66)
0.05
(0.62)

0.82***
(9.60)
−0.06
(−0.75)

0.93***
(10.74)
−0.03
(−0.41)

0.01
(0.08)
−0.03
(−0.43)

0.90***
(10.39)
0.00
(0.02)

0.88***
(10.29)
−0.06
(−0.74)

0.02
(0.25)
0.00
(0.00)

0.91***
(10.60)
0.00
(0.03)

0.78***
(9.61)
−0.11
(−1.51)

−0.20***
(−3.06)
−0.15**
(−2.07)

Panel B: Emissions
Raw Return
α

0.90***
(10.46)
0.01
(0.16)

0.88***
(10.35)
0.00
(0.03)

0.84***
(9.86)
−0.10
(−1.25)

−0.07
(−1.13)
−0.08
(−1.22)

0.85***
(10.11)
−0.02
(−0.25)

Panel C: Emissions
Raw Return
α

0.93***
(10.82)
0.07
(0.83)

0.88***
(10.42)
0.01
(0.11)

0.84***
(10.04)
−0.09
(−1.16)

−0.12*
(−1.77)
−0.11
(−1.44)

0.95***
(10.98)
0.06
(0.76)

variation explains most of the variation in carbon intensity and, correspondingly, accounts for the majority of negative carbon returns. Thus, investors are
attentive to both cross-industry and within-industry carbon transition risk,
with cross-industry variation carrying more significance.
C. Global Carbon Returns
In this section, I now study average carbon returns in global markets. Specifically, I sort stocks into terciles using firm-level carbon intensity in each country. The final portfolio consists of all stocks in the same tercile across countries,
including the United States. I adjust for raw returns with developed market
(DM) FF6 factors. Table VII presents the results. Average carbon excess return
and alpha are negative but statistically indistinguishable from zero. Valueweighted alphas are −0.06% and −0.03% for scope 1 and 2 intensity, respectively, compared to −0.40% and −0.34% in the United States. Return spreads
generated by emissions growth and total emissions again tend to be negative,
but mostly small and insignificant. In short, carbon returns are negative in

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Carbon Returns across the Globe

The Journal of Finance®

the United States but insignificant globally. I explore cross-country variation
in carbon returns in more detail in Section IV.
III. Information Observability and Carbon Returns
The results above show that, in recent years, carbon-intensive firms earn
lower returns than green firms in the United States and brown and green
firms yield similar returns globally. In contrast, total emissions and emissions
growth do not correlate with future stock returns. These results differ from
previous studies. In particular, BK (2021, 2023) document a carbon premium
associated with total emissions and emissions growth both in the United States
and globally. In this section, I first replicate their analysis. I then show that
forward-looking information contained in their emissions data overstates their
estimated ex ante carbon premium in returns.
A. The Role of Future Sales Information
As I document in Section I.C, emissions are tightly linked to firm sales.
Consequently, strong firm performance can simultaneously lead to higher
emissions and higher stock returns. BK (2021, 2023) relate stock returns
to contemporaneous emissions and emissions lagged by one month before
accounting and emission information for the emitting period is released. As
such, the analysis is effectively contemporaneous, and the documented carbon
premium could stem from future sales information contained in emissions.
It is reasonable to speculate, as BK argues, that investors can develop expectations regarding carbon emissions as the fiscal year progresses. However, it is
also reasonable to expect that investors can form equally accurate expectations
about firm sales during the same period. The accuracy of emission estimates
that investors can formulate depends on the accuracy of their sales estimates.
It, therefore, continues to be crucial to control for firm performance during the
emitting period to avoid forward-looking bias (or, look-ahead bias).
I start by studying the relation between U.S. stock returns and contemporaneous emission variables as in BK (2021) but using nonparametric portfolio
sorts as in the baseline analysis. Table VIII presents portfolio returns. First,
portfolio sorts with contemporaneous carbon intensity do not generate significant long-short excess returns, consistent with BK. Carbon intensity information is not available to investors contemporaneously and thus is not reflected
in stock returns.
Second, emissions growth-sorted portfolios exhibit significantly positive
high-minus-low carbon returns of 0.41% per month for scope 1 and as much
as 0.6% for scope 2, consistent with the positive carbon returns in BK (2021).
To gauge the impact of future sales information on estimated carbon returns,
I conduct double sorts with sales and emission information. The analysis first
sorts stocks into tercile portfolios by sales growth and then sequentially sorts
stocks by carbon variables into tercile portfolios within each sales-growth tercile. Sales and carbon variables are measured over the same period. After

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Table VIII

Contemporaneous Carbon-Sorted U.S. Portfolios
This table reports monthly value-weighted U.S. portfolio returns sorted by contemporaneous carbon variables. Panel A presents portfolio returns sorted by carbon variables, and Panel B presents
portfolio returns double-sorted first by sales growth and then by carbon variables sequentially. I
report t-statistics in parentheses below the coefficients. ***, **, and * denote significance at the
1%, 5%, and 10% levels, respectively. The sample period is 2009:06 to 2021:12.
Panel A: Contemporaneous Return
Scope 1

Intensity
Emissions
Emissions

Scope 2

L

M

H

H-L

L

M

H

H-L

1.03***
(3.15)
0.82***
(2.61)
1.13***
(3.10)

1.01***
(3.71)
0.93***
(3.37)
1.01***
(2.99)

0.98***
(3.20)
1.30***
(4.11)
0.99***
(3.69)

−0.05
(−0.29)
0.47***
(3.25)
−0.14
(−0.75)

1.08***
(3.43)
0.74**
(2.36)
1.10***
(3.37)

0.95***
(3.24)
0.97***
(3.53)
1.16***
(3.56)

1.03***
(3.40)
1.32***
(4.18)
0.95***
(3.31)

−0.04
(−0.28)
0.58***
(4.34)
−0.16
(−1.13)

Panel B: Controlling for Future Sales Growth
Scope 1

Sales L
2
H

Sales L
2
H

Sales L
2
H

Scope 2

L

M

H

−0.04
(−0.10)
0.95***
(3.20)
1.71***
(5.52)

0.13
(0.36)
0.91***
(3.15)
1.49***
(4.54)

−0.11
(−0.31)
0.74**
(2.57)
1.72***
(4.31)

0.04
(0.10)
0.75**
(2.15)
1.56***
(4.05)

−0.05
(−0.12)
0.75**
(2.36)
1.72***
(4.71)

0.01
(0.04)
0.99***
(3.70)
1.66***
(5.00)

0.09
(0.22)
0.92***
(3.06)
1.76***
(4.92)

0.13
(0.38)
1.02***
(3.74)
1.78***
(5.62)

0.12
(0.35)
1.02***
(3.77)
1.50***
(4.07)

H-L

L

B.1 Intensity
−0.07
−0.01
(−0.42)
(−0.01)
−0.21
0.80***
(−1.43)
(2.75)
0.01
1.63***
(0.04)
(5.26)
B.2 Emissions
−0.03
0.17
(−0.11)
(0.45)
0.24
0.80**
(1.25)
(2.58)
0.10
1.52***
(0.42)
(4.08)
B.3 Emissions
0.03
0.20
(0.11)
(0.52)
0.10
0.88***
(0.57)
(3.16)
−0.26
1.74***
(−0.91)
(5.16)

M

H

H-L

−0.07
(−0.17)
0.97***
(3.37)
1.47***
(4.04)

−0.13
(−0.37)
0.87***
(3.02)
1.80***
(4.64)

−0.12
(−0.71)
0.07
(0.50)
0.18
(0.81)

−0.00
(−0.01)
0.81***
(2.64)
1.84***
(4.95)

−0.08
(−0.24)
0.91***
(3.24)
1.62***
(4.91)

−0.25
(−1.31)
0.12
(0.81)
0.10
(0.46)

0.07
(0.21)
1.08***
(3.80)
1.67***
(4.73)

0.06
(0.17)
0.97***
(3.42)
1.73***
(5.13)

−0.14
(−0.73)
0.08
(0.49)
−0.02
(−0.06)

controlling for sales growth, emissions growth sorts no longer generate significant return spreads. For example, scope 1 carbon returns are small and
insignificant within each sales growth tercile (−0.03%, 0.24%, and 0.10%).
In other words, the carbon premium associated with contemporaneous emis-

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Carbon Returns across the Globe

sions growth does not represent compensation for higher carbon transition risk
but instead arises from forward-looking sales information. U.S. portfolio alphas and portfolio sorts, based on all global stocks, presented in the Internet
Appendix yield similar results. Finally, for portfolio sorts with total emissions,
in general, there is no evidence of a significant long-short return spread.
B. Regression Analysis
In this section, I conduct the regression analysis as in BK (2021, 2023) using
an updated sample and focus on emissions growth and total emissions, which
BK finds a significant carbon premium for. Specifically, I run the following
regression
rit = α + βCarboniτ + γ Controlsit−1 + δk + νt + εit .

(5)

The regression is conducted at the firm-month level, controlling for time and
industry fixed effects. The main independent variable, Carboniτ , represents
contemporaneous (log) emissions growth or (log) emissions. Controls are the
same as in the baseline regression (4). In addition, I include industry fixed
effects because BK finds that the estimated carbon premium strengthens using
this specification. Carbon measures are standardized to have zero mean and
unit variance.
Table IX presents results for U.S. stocks and finds that both emissions
and emissions growth are significantly associated with higher contemporaneous stock returns as in BK (2021). For example, a one-standard-deviation
increase in total emissions is associated with an increase in monthly stock returns, 0.19% and 0.23%, respectively. The coefficients are comparable to 0.23%
and 0.14% excess returns per unit of standard deviation in table 8 of BK
(2021).
Next, I control for sales information during the same period of carbon emissions,
rit = α + βCarboniτ + βSalesiτ + γ Controlsit−1 + νt + εit ,

(6)

where Salesiτ denotes log sales and sales growth during the same emission period. Table IX shows that forward-looking sales and sales growth information
is strongly associated with higher stock returns. However, carbon emissions
and emissions growth are no longer positively associated with returns once
sales information is controlled for. Instead, carbon return estimates tend to be
negative, more consistent with my baseline result.
Finally, I study the global evidence. BK (2023) studies the relationship
between stock returns and emissions lagged by one month and longer lags
using regression (5). I conduct the same analysis and present the carbon
coefficients in Figure 3. Emission variables are associated with higher stock
returns (“Baseline”) contemporaneously and when the lag is no more than
six months from the start of the fiscal year but not beyond, consistent with
table 6 in BK (2023). However, after controlling for sales information as in

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Table IX

U.S. Stock Returns and Contemporaneous Emissions
This table first regresses U.S. stock returns on contemporaneous emissions and emissions growth
and then controls for sales and sales growth over the same emitting period. The carbon variables
are standardized to have zero mean and unit variance. Standard errors are double clustered firm
and time levels. I report t-statistics in parentheses below the coefficients. ***, **, and * denote
significance at the 1%, 5%, and 10% levels, respectively. The sample period is 2009:06 to 2021:12.
Scope 1
Emissionsτ

2

0.28*** 0.24***
(5.98) (4.79)

1

2

0.01
(0.19)

−0.04
(−1.52)

1

2

1

2

−0.11 −0.11*
(−1.50) (−1.68)
Sales
1.43*** 1.50***
1.30*** 1.29***
(5.51)
(5.96)
(6.45)
(6.44)
Log Sales
0.16*
0.16*
0.22*** 0.23***
(1.93)
(1.93)
(2.61)
(2.66)
Oil Exposure
0.05
0.05
0.05
0.05
−0.17
−0.17
−0.13
−0.13
(0.15) (0.14)
(0.15)
(0.15) (−0.48) (−0.49) (−0.38) (−0.38)
Natural Gas Exposure −0.56 −0.56 −0.57
−0.57
−0.86
−0.84
−0.87
−0.88
(−0.69) (−0.69) (−0.70) (−0.70) (−1.22) (−1.19) (−1.25) (−1.25)
Commodity Exposure
0.00
0.00
0.00
0.00
0.03
0.03
0.03
0.03
(0.07) (0.08)
(0.03)
(0.03)
(0.78)
(0.75)
(0.65)
(0.66)
Beta
0.08
0.09
0.08
0.08
0.03
0.03
0.02
0.02
(0.61) (0.64)
(0.60)
(0.60)
(0.23)
(0.22)
(0.12)
(0.13)
Size
0.01
0.01
−0.15
−0.15
−0.14 −0.18* −0.26* −0.26*
(0.18) (0.15) (−1.13) (−1.13) (−1.47) (−1.70) (−1.93) (−1.90)
Book-to-Market
0.05
0.04
0.03
0.03
0.00
−0.01
0.04
0.04
(0.38) (0.35)
(0.22)
(0.22)
(0.02) (−0.10) (0.30)
(0.30)
ROA
0.09
0.07
0.15
0.15
0.02
−0.03
0.20
0.20
(0.13) (0.10)
(0.23)
(0.23)
(0.04) (−0.04) (0.34)
(0.33)
Asset Growth
0.04
0.05
−0.08
−0.08
0.04
0.05
−0.15
−0.15
(0.32) (0.36) (−0.65) (−0.64) (0.27)
(0.36) (−1.08) (−1.08)
Momentum
0.22
0.22
0.07
0.07
0.21
0.21
0.05
0.05
(0.87) (0.88)
(0.29)
(0.29)
(0.86)
(0.85)
(0.23)
(0.22)
Leverage
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
(1.12) (1.10)
(0.69)
(0.69)
(0.57)
(0.41)
(0.57)
(0.56)
Log PPE
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
(0.10) (0.13)
(0.01)
(0.01)
(0.98)
(0.98)
(0.86)
(0.85)
IVol
0.23
0.23
0.25*
0.25*
0.24*
0.24*
0.26*
0.26*
(1.64) (1.65)
(1.78)
(1.78)
(1.79)
(1.77)
(1.92)
(1.93)
Sales Growth
−0.51** −0.51** −0.63*** −0.63*** −0.42*** −0.42*** −0.55*** −0.55***
(−2.57) (−2.54) (−3.09) (−3.08) (−2.63) (−2.65) (−3.06) (−3.06)
EPS Growth
−0.05** −0.05** −0.05** −0.05** −0.05** −0.05* −0.05* −0.05*
(−2.18) (−2.16) (−2.05) (−2.05) (−1.99) (−1.95) (−1.92) (−1.93)
Industry FE
Y
Y
Y
Y
Y
Y
Y
Y
Time FE
Y
Y
Y
Y
Y
Y
Y
Y
R2
0.20
0.20
0.20
0.20
0.19
0.19
0.19
0.19
Observations
218,874 218,874 218,507 218,507 243,666 243,666 243,234 243,234
Log Emissionsτ

0.22**
(2.06)

0.24**
(2.36)

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Carbon Returns across the Globe

The Journal of Finance®

Figure 3. Global carbon returns and alternative lags. This figure (“Baseline”) first plots the
carbon coefficients by regressing global stock returns on x-month lagged emissions growth and log
emissions from the fiscal year start, controlling for firm characteristics, including beta, size, bookto-market, ROA, asset growth, momentum, leverage, log PPE, IVol, sales growth, EPS growth, and
oil, natural gas, and commodity exposures as well as country, industry, and time fixed effects. The
orange line in the figure (“Controlled”) further plots the corresponding coefficients after further
controlling for log sales and sales growth during the same period of emissions. The regressions
include industry and time-fixed effects. Standard errors are double clustered at firm and time
levels, and the shaded area denotes the 95% confidence intervals. The sample period is 2009:06 to
2021:12. (Color figure can be viewed at wileyonlinelibrary.com)

equation (6), the carbon coefficient (“Controlled”) decreases dramatically and
becomes consistently negative across different lags. The difference between
baseline and controlled coefficients is particularly large with the lag being
shorter, suggesting that the coefficient bias introduced by forward-looking bias
is particularly prominent in contemporaneous analysis or when shorter lags
are used. The Internet Appendix plots comparable U.S. coefficients and shows
that the results are unchanged.
In summary, the positive relation between stock returns and contemporaneous emissions in prior studies comes from strong forward-looking firm performance rather than a risk premium in ex ante expected returns. Lagging
emission data sufficiently can address forward-looking bias and avoid incorrect inference.

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639

IV. Cross-Country Variation in Carbon Returns
In this section, I now turn to country-level evidence beyond average global
carbon returns and study what drives differences in carbon returns. As global
warming is a global risk and carbon reduction requires global commitment
and collaboration, it is useful to examine international markets to gauge the
attitude of individual countries.
A. Geographic Dispersion
Here, I conduct portfolio sorts using carbon intensity as in baseline analysis for each country and then adjust for risk factors by running a time-series
regression for each country
rit = αi + βi f actorsit + εit ,

(7)

where rit is the value-weighted long-short carbon return in country i and
f actorsit denotes FF6 factors for each region or country, including the United
States, North America excluding the United States, Europe, Japan, the Asia
Pacific excluding Japan, and other countries as emerging markets. This approach allows for imperfectly integrated international markets in which factor
returns and factor loadings vary across countries (Fama and French, 2017).
I examine whether carbon returns display geographic dispersion. I start with
the G7 and Australia, which contain the United States and developed countries
most comparable to the United States. Panel A, Table X shows that carbon
alphas, value-weighted across countries, are −0.44% and −0.4% for scope 1
and 2, respectively, and are more comparable to the U.S. estimates (−0.4% and
−0.34%). I next split the international sample into developed and emerging
markets (DM and EM) and find more negative carbon returns in DM countries.
Value-weighted carbon alphas for DMs are −0.4% and −0.33% for scopes 1 and
2, respectively. In particular, the United States has negative carbon alphas
(−0.4% and −0.34%), and while China has positive alphas instead (0.53% and
0.23%). In contrast, carbon alphas for EMs are positive at 0.2% and 0.06%.
Panel B shows that carbon alphas, equally weighted across countries, reveal a
similar picture.
Alternatively, I conduct weighted least squares regression analysis for global
stocks as in equation (4) with the same set of firm-level control variables. Here
I control for country fixed effect in addition to time fixed effect. The results
in Panel C provide similar evidence. Coefficients for more developed countries
are significantly negative at −0.19% and −0.15% for G7+AUS and are more
comparable to U.S. estimates (−0.19% and −0.21%). For EM countries, the
coefficients are statistically indistinguishable from zero.
B. What Drives Carbon Return Variation?
The previous analysis shows that carbon returns vary significantly
across countries and are lower in more developed countries. A few possible

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Carbon Returns across the Globe

Table X

Country-Level Carbon Returns
Note: This table studies geographic variation in country-level carbon returns. Panel A presents
average raw carbon returns and corresponding FF6 factor-adjusted alphas, value weighted
by country-level market capitalization or equally. Panel B presents the carbon returns, equal
weighted across countries. Panel C conducts a weighted least square regression of stock returns
on lagged carbon intensities. The controls include various firm characteristics, including beta,
size, book-to-market, ROA, asset growth, momentum, leverage, log PPE, IVol, sales growth, EPS
growth, and oil, natural gas, and commodity exposures. The regression controls for time and country fixed effects. Standard errors are double-clustered at firm and monthly levels, accordingly. I
report t-statistics in parentheses below the coefficients. ***, **, and * denote significance at the
1%, 5%, and 10% levels, respectively. The sample period is 2009:06 to 2021:12.
Panel A: Value-Weighted Sorting
Scope 1

Raw Return
α

Scope 2

G7 + AUS

DM

EM

G7 + AUS

DM

EM

−0.38***
(−5.84)
−0.44***
(−7.24)

−0.32***
(−6.95)
−0.40***
(−9.52)

0.23***
(3.94)
0.20***
(3.55)

−0.25***
(−4.11)
−0.34***
(−6.10)

−0.22***
(−5.16)
−0.33***
(−8.36)

0.12**
(1.97)
0.06
(0.99)

−0.01
(−0.18)
−0.14**
(−2.00)

0.04
(0.40)
0.09
(0.97)

−0.14***
(−2.70)
Y
Y
Y
0.25
608,678

0.03
(0.36)
Y
Y
Y
0.21
297,577

Panel B: Equal-Weighted Sorting
Raw Return
α

−0.27***
(−2.81)
−0.37***
(−4.32)

−0.09
(−1.14)
−0.26***
(−3.54)

0.05
(0.54)
0.08
(0.86)

−0.17*
(−1.92)
−0.27***
(−3.41)

Panel C: Stock-Level Regression Analysis
Scope 1

−0.19***
(−3.28)

−0.15***
(−2.97)

−0.07
(−1.40)

Scope 2
Controls
Country FE
Time FE
R2
Observations

Y
Y
Y
0.26
486,821

Y
Y
Y
0.25
608,678

Y
Y
Y
0.21
297,577

−0.15**
(−2.42)
Y
Y
Y
0.26
486,821

interpretations follow. First, shifts in investor preferences have differed widely
across countries during the transition, generating cross-country differences
in carbon returns. Second, carbon return variation reflects differences in
the carbon risk premium in equilibrium. Third, carbon return variation is
driven by in-sample cash flow shocks unrelated to carbon transition risk or
climate concerns.
I construct two measures of changes in climate concern or climate tastes.
First, I measure investors’ demand for green assets as country-level

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sustainable investor flows each quarter scaled by end-of-quarter market
capitalization.7 Second, I proxy for the cumulative shift in consumer demand
using the level of climate concerns from the Lloyd’s Register Foundation
(2020) 2019 World Risk Poll. The survey asks whether interviewees perceive
climate change as a very serious threat, a somewhat serious threat, or not a
threat at all. The climate concern equals the total fraction who answer a “very
serious” and “somewhat serious” threat. Because climate change only started
concerning the public in recent years, the measure proxies for cumulative
increase in climate concern. Both sustainable flow and climate concern are
highly correlated with log GDP per capita, with coefficients of 0.47 and 0.43.
Next, I study additional country characteristics that can correlate with the
country’s required carbon premium. I measure current policy tightness using
the policy score in the Climate Change Performance Index. However, existing
climate policies are still in the preliminary stage, and investors expect most
policies to come into shape in future years.8 I thus consider additional socioeconomic conditions. The first measure is the fraction of renewable energy because countries with a higher proportion of renewable energy tend to enforce
more environmentally friendly policies while discouraging the use of fossil fuels. The second measure is a civil law dummy because civil law countries tend
to promote environmentally friendly corporate practices and civil law firms are
more responsive to CSR shocks (Liang and Renneboog, 2017). Empirically, the
fraction of renewable energy and civil law dummy exhibit correlations with climate policy tightness of 0.47 and 0.58, respectively, suggesting an inclination
toward implementing stricter climate policies.
Finally, I construct several cash flow shock measures. The first cash flow
measure is carbon returns on earnings days because most new earningsrelated information arrives on earnings days. Earnings day returns incorporate the impact of information arrival in the current period, and investors
accordingly update their beliefs and adjust stock prices. Second, I capture
investor belief updates directly by measuring long-short spread in consensus
analyst revisions of one-year-ahead EPS forecasts and long-term growth
forecasts. I also measure the long-short spread in sales growth next year to
be conservative. In addition, I explicitly account for the exposure of stocks
to energy price fluctuations by estimating exposures to oil, natural gas, and
commodity price fluctuations by using a rolling 60-month regression.
I examine the relation between abnormal carbon returns rsit and climate concern shocks using the specification,
rsit = a + b · Xit−1 + κ · Yit + νt + eit ,

(8)

7 Data are obtained from the report “Passive Sustainable Funds: The Global Landscape 2020”
published by Morningstar. The data on active sustainable flows are available for a subset of countries from 2016 onward. Active and passive sustainable flows are highly correlated, with a coefficient of 0.93.
8 Detailed climate policies are yet to be fleshed out in most countries, leaving much room for
policy uncertainty, and adding to the transition risk of brown firms. By 2021, a total of 131 countries have committed to reducing net carbon emissions to zero, but just six have enshrined that
commitment in law.

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Carbon Returns across the Globe

Table XI

Carbon Return Variation
This table reports variation in carbon returns. Panel A regresses country-level carbon returns on
cash flow shocks and climate taste shifts. Panel B studies additional country characteristics while
controlling for all measures in Panel A. These characteristics are standardized to have zero mean
and unit variance unless it is a dummy variable. The regressions include time-fixed effects and
standard errors are clustered at the monthly level. I report t-statistics in parentheses below the
coefficients. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. The
sample period is 2009:06 to 2021:12.
Panel A: In-Sample Shocks
Scope 1
(1)
GDP Per Capita

(2)

Et [LTG]
Salest+1
Oil Exposure
Natural Gas Exposure
Commodity Exposure
Time FE
R2
Observations

(4)

−0.10
(−1.37)

0.79***
(8.62)
3.87***
(3.10)
0.16
(0.71)
0.49
(1.41)
−0.01
(−1.29)
−0.02
(−1.12)
−0.00
(−0.45)
Y
0.07
7,325

(5)

(6)

−0.17**
(−2.35)

Climate Concern

Et [EPSt+1 ]

(3)

−0.18**
(−2.41)

Sustainable Flow

Earnings Day Ret

Scope 2

0.77***
(8.53)
3.65***
(2.88)
0.15
(0.66)
0.27
(0.80)
−0.01
(−1.24)
−0.02
(−1.61)
0.00
(0.79)
Y
0.07
6,571

−0.15**
(−2.11)
−0.11*
(−1.68)
0.78***
(8.46)
3.98***
(3.15)
0.17
(0.73)
0.53
(1.47)
−0.01
(−1.41)
−0.02
(−1.34)
−0.00
(−0.85)
Y
0.07
7,045

0.71***
(6.42)
4.68***
(3.56)
0.14
(0.51)
0.44
(1.23)
−0.01
(−1.47)
−0.02
(−1.11)
−0.00
(−0.57)
Y
0.06
7,325

0.69***
(6.41)
3.94***
(3.15)
0.12
(0.41)
0.24
(0.68)
−0.01
(−1.51)
−0.03
(−1.63)
−0.00
(−0.16)
Y
0.06
6,571

−0.15**
(−2.26)
0.71***
(6.39)
4.71***
(3.45)
0.22
(0.76)
0.47
(1.28)
−0.01
(−1.48)
−0.01
(−0.88)
−0.00
(−0.97)
Y
0.06
7,045

Panel B: Additional Country Characteristics
Policy

0.13**
(2.12)

%Renewable Energy

0.10
(1.33)
0.20**
(2.60)

1(Civil Law)
Controls
Time FE
R2
Observations

Y
Y
0.12
4,376

Y
Y
0.08
6,033

0.16**
(2.08)
0.55***
(3.38)
Y
Y
0.08
6,033

Y
Y
0.09
4,376

Y
Y
0.06
6,033

0.41**
(2.52)
Y
Y
0.07
6,033

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where abnormal carbon returns rsit = α + εit are calculated from equation (7)
and are unaffected by country-level market returns. Xit−1 denotes lagged country characteristics, such as log GDP per capita, sustainable investing flows, or
a snapshot of country characteristics. Yit denotes contemporaneous cash flow
shocks or earnings news. The X variables are standardized to have zero mean
and unit variance, allowing the coefficient b to be interpreted as the increase in
carbon return associated with a one-standard-deviation increase in X , unless
X is a dummy variable. Standard errors are clustered at the monthly level.
Table XI, Panel A, presents the results. Carbon returns are significantly negatively correlated with log GDP per capita, sustainable flows, and climate concerns. A one-standard-deviation increase in the sustainable flow is associated
with a decrease in scope 1 and 2 carbon returns of 0.1% and 0.15%, respectively. The magnitudes are economically large enough to explain the negative
carbon returns in DM countries and the zero or slightly positive returns in EM
countries. The evidence suggests that the transition to the equilibrium with
carbon-aware investment is underway. Cash flow shocks are positively associated with carbon returns across measures, with earnings-day returns and consensus EPS revisions being the most significant. Collectively, cash flow news
accounts for up to 7% of the variation in carbon returns.
Finally, I study the role of country characteristics in equation (8) after controlling for all in-sample climate concerns and cash flow shocks. Table XI, Panel
B, shows that countries with more stringent climate policies, more renewable
energy, and civil law yield higher carbon returns, consistent with tighter climate policies in these countries. A one-standard-deviation increase in climate
policy tightness is associated with an increase in scope 1 carbon returns of
0.13%. This finding reflects investors’ demand for a higher carbon premium in
these countries due to anticipation of higher policy risk and provides suggestive evidence that carbon transition risk is at least partially priced in global
equities.
V. Conclusion
Practitioners and academics heatedly debate whether investors materially care about carbon transition risk in their investments. Emissions are a
weighted sum of firm sales scaled by emission factors and grow almost linearly with firm sales. However, emissions data are released at significant lags
relative to accounting variables, including sales. After accounting for the data
release lag, more carbon-intensive firms underperform relative to less carbonintensive firms in the United States in recent years. International evidence on
carbon or green premium is largely absent. The carbon premium documented
in previous studies stems from forward-looking bias instead of a true risk premium in ex ante expected returns.
Further analysis shows that shifts in investor preferences, policy tightness,
and cash flow shocks are factors driving the cross-country carbon return variation. In summary, the global transition toward full carbon awareness seems to
be underway. Nonetheless, equilibrium carbon return may remain muted for

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Carbon Returns across the Globe

The Journal of Finance®

an extended period as the transition takes place. Additional research is necessary to enhance our understanding and refine the impact of these transitions
on asset prices. Exploring this relationship will provide valuable insights for
sustainable investing and aid asset managers in striking a balance between
positive ESG impact and fiduciary duty.
Initial submission: March 1, 2023; Accepted: November 22, 2023
Editors: Antoinette Schoar, Urban Jermann, Leonid Kogan, Jonathan Lewellen, and Thomas Philippon

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Supporting Information
Additional Supporting Information may be found in the online version of this
article at the publisher’s website:
Appendix S1: Internet Appendix.
Replication Code.

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Carbon Returns across the Globe

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==> JF3 - 2023 - SAUTNER - Firm‐Level Climate Change Exposure.txt <==
THE JOURNAL OF FINANCE • VOL. LXXVIII, NO. 3 • JUNE 2023

Firm-Level Climate Change Exposure
ZACHARIAS SAUTNER, LAURENCE VAN LENT, GRIGORY VILKOV,
and RUISHEN ZHANG*
ABSTRACT
We develop a method that identifies the attention paid by earnings call participants
to firms’ climate change exposures. The method adapts a machine learning keyword
discovery algorithm and captures exposures related to opportunity, physical, and regulatory shocks associated with climate change. The measures are available for more
than 10,000 firms from 34 countries between 2002 and 2020. We show that the measures are useful in predicting important real outcomes related to the net-zero transition, in particular, job creation in disruptive green technologies and green patenting,
and that they contain information that is priced in options and equity markets.

CLIMATE CHANGE WILL PROFOUNDLY AFFECT the way business is conducted.
Scientists have developed complex models that estimate the effect of greenhouse gas emissions on the global climate. At the same time, however, little
* Zacharias Sautner, Laurence van Lent, and Grigory Vilkov are at Frankfurt School of Finance
& Management. Ruishen Zhang is at Shanghai University of Finance and Economics. The climate
change exposure data are available at https://doi.org/10.17605/OSF.IO/FD6JQ. We thank Stefan
Nagel, an anonymous Associate Editor, two referees, Artur Hugon, Marcin Kacperczyk, Bryan
Kelly, Kelvin Law, Christian Leuz, Tim Loughran, Quentin Moreau, and Ane Tamayo for helpful
comments. We are grateful to Aakash Kalyani for preparing the green jobs data set and to Markus
Schwedeler for sharing his code. Participants at AFA 2022 Meetings, NBER, NYU Stern (PhD
Classes in Empirical Household Finance), University of Zurich, University of Dusseldorf, Stockholm Business School, SUFE, Bocconi University, Columbia University, CEIBS, LSE, Xiamen University, Duke Kunshan University, University of Miami, Tingshua University, Dongbei University
of Finance and Economics, Chinese University of Hong Kong, and University of Hong Kong provided helpful feedback. Funding for this project was provided by DFG Project ID 403041268 - TRR
266 (van Lent and Zhang), the Institute for New Economic Thinking (Van Lent), Shanghai Pujiang
Program (Zhang), the 111 Project (B18033)(Zhang), and National Natural Science Foundation of
China (Project ID 72202128, 72241405, Zhang). Parts of this project were conducted when Sautner was visiting NOVA School of Business and Economics and UCSD Rady School of Management
(funded in part by the Norwegian Finance Initiative). We have read The Journal of Finance disclosure policy. Sautner is a Regular Research Visitor at the ECB and a member of the Sustainability
Council of Lampe Asset Management (since November 2022). He has no other disclosure to make.
Van Lent, Vilkov, and Zhang have no conflicts of interest to disclose.
Correspondence: Zacharias Sautner, Frankfurt School of Finance & Management, Adickesallee
32-34, 60322 Frankfurt am Main, Germany; e-mail: z.sautner@fs.de.

This is an open access article under the terms of the Creative Commons Attribution License, which
permits use, distribution and reproduction in any medium, provided the original work is properly
cited.
DOI: 10.1111/jofi.13219
© 2023 The Authors. The Journal of Finance published by Wiley Periodicals LLC on behalf of
American Finance Association.

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evidence exists on the degree to which climate change impacts jobs, innovation, and risk sharing in capital markets. One key challenge in estimating
these impacts is that it is difficult to measure how individual firms are affected
by climate change (Giglio, Kelly, and Stroebel (2021)), as the effects are multifaceted, originating from multiple sources. For instance, while physical climate
changes and regulations implemented to combat global warming can impose
costs on some firms, climate change can provide opportunities for other firms,
such as those operating in renewable energy, electric cars, or energy storage.
It is therefore important to develop disaggregated measures that capture this
variation across firms. The measures should also reflect market participants’
assessments about how climate change affects individual firms. Such information is important to consider in a finance context given the critical role
that market participants play in the resource allocation and price discovery
process.
In this paper, we make progress on this front by using transcripts of earnings
conference calls to construct time-varying measures of how call participants
across the globe view firms’ exposures to different facets of climate change.
Earnings calls are key corporate events in which financial analysts listen to
management and ask questions about current and future developments material to the firm (Hollander, Pronk, and Roelofsen (2010)). We interpret these
measures as capturing the attention financial analysts and management devote to climate change topics at a given point in time. A benefit of these measures is that they reflect “soft” information originating from information exchanges between managers and analysts.1
To construct the climate change exposure measures, we build on recent work
using quarterly earnings calls as a source for identifying firms’ various risks
and opportunities (Hassan et al. (2019, 2021, 2023a, 2023b), Jamilov, Rey, and
Tahoun (2021)). These studies use the proportion of the conversation during
an earnings call that relates to a particular topic to capture the firm’s exposure to that topic. We follow these papers in defining “exposure” to an issue as the share of the conversation in a transcript devoted to that topic.2
We depart from these papers, however, along two dimensions. First, our measures capture the market’s perception of a firm’s exposure to various upside
or downside factors related to climate change, namely, physical threats, regulatory interventions, and technological opportunities. Second, to mitigate the
1 This feature allows us to provide economic insights beyond those derived from existing
firm-level exposure measures based on “hard” information (e.g., carbon emissions, extreme local
weather events). Note that the exchanges are not limited to soft information but might also discuss
specific quantitative data or restate “hard” information in conversational terms. Prior literature
provides important insights into the relations between “hard” information and real and financial outcomes at the firm level (e.g., Bolton and Kacperczyk (2021, 2022, 2023), Ilhan, Sautner,
and Vilkov (2021) or De Haas and Popov (2023) for carbon emissions, and Kruttli, Roth Tran, and
Watugala (2021), Hong, Li, and Xu (2019), Addoum, Ng, and Ortiz-Bobea (2020), or Pankratz and
Schiller (2021) for weather events).
2 This definition of “exposure” is different from how risk exposure is defined in the asset-pricing
literature. Our measure is not intended to capture the covariance with aggregate fluctuations.
Hassan et al. (2019) discuss the relationship between these two areas of literature.

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challenges of identifying “niche languages” that use specific wordings, particularly in the context of climate change, where language use varies among
policymakers, journalists, and financial market participants (Webersinke et al.
(2021)), we develop a new method that adapts the keyword discovery algorithm
proposed in King, Lam, and Roberts (2017) to construct four related sets of climate change bigrams in earnings calls. The first captures broadly defined aspects of climate change. The remaining three measures cover specific climate
change “topics:” opportunities, physical shocks (e.g., sea level rise), and regulatory shocks (e.g., carbon taxes, cap and trade markets). We then use these four
sets of bigrams to construct firm-level measures reflecting call participants’
topical attention. In particular, the measures count the frequency of specific
climate change bigrams in a transcript, scaled by the number of bigrams.3 The
algorithm only requires human input to specify a short list of initial keywords
associated with climate change. Our sample covers data from over 10,000 firms
in 34 countries between 2002 and 2020.
We conduct several validation exercises to verify our methodology. First,
we consider the face validity of the climate change bigrams. Second, we follow Baker, Bloom, and Davis (2016) and perform a structured human audit
in which 18 graduate students independently coded over 2,000 transcript text
fragments. Both of these exercises suggest that our algorithm reliably captures
bigrams identifying climate change discussions. Third, our exposure measures
are robust to excluding one keyword at a time from the initial keywords list.
Fourth, our keyword search-based measures substantially improve the identification of climate change discussions relative to an alternative approach using
the initial keywords only. And fifth, we find plausible industry patterns in the
exposure measures. When we aggregate exposure to the industry level, the
sector with the highest overall exposure is Electric, Gas, & Sanitary Services
(utilities), followed by Construction (top-ranked firms build power generation
systems or solar projects) and Transportation Equipment (top-ranked firms
build fuel-cell or zero-emission vehicles). Utilities top the exposure ranking
for opportunity and regulatory shocks, which indicates that this sector faces
both opportunities (e.g., renewable energy) and regulatory risks (e.g., carbon
taxes).4
Our results reveal sizeable within-industry variation for all measures, which
indicates that firms benefit or suffer from climate change to various degrees. A
case in point is the comparison between TotalEnergies and ExxonMobil. While
3 We also construct “sentiment” measures, which count the relative frequency of climate change
bigrams that occur in the vicinity of positive and negative tone words (Loughran and McDonald
(2011)), and “risk” measures, which count the relative frequency of climate change bigrams mentioned in the same sentence as the words “risk,” “uncertainty,” or their synonyms.
4 That firms with heightened regulatory risks also exhibit climate-related opportunities is consistent with Cohen, Gurun, and Nguyen (2021), who document that several major electricity, oil,
and gas firms are not only large CO2 emitters, but also innovators in green technologies. This finding is consistent with how analysts view sectors with high regulatory risks (e.g., “Morgan Stanley:
‘Second wave of renewables’ to drive 70 GW of coal retirements,” S&P Global Market Intelligence,
December 20, 2019).

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Firm-Level Climate Change Exposure

The Journal of Finance®

TotalEnergies and ExxonMobil have similar regulatory exposures, TotalEnergies scores more than seven times higher in terms of measured opportunities.
This divergence in perceived prospects is consistent with differences in the
perceived extent to which these firms embrace renewable energy and the
net-zero transition into their business models (Pickl (2019)).
In a final validity check, we find that climate exposure positively correlates
with carbon emissions and Engle et al.’s (2020, EGKLS) index of public climate change attention. The association with emissions stems from regulatory
and opportunity exposure (since physical exposure is unrelated to emissions).5
The effect of public attention also arises from positive associations between
EGKLS’s index and the opportunity and regulatory exposure measures.
We apply our measures to shed light on the nature of climate change exposure among our sample firms. Perhaps surprisingly, as climate change is often
seen as an aggregate risk factor associated with global changes in the physical climate, its within-sector impact is far from uniform. A variance analysis
that separates the relative contributions of aggregate, sectoral, and firm-level
exposure by including the corresponding sets of fixed effects shows that between 70% and 96% of the variation in the exposure measures plays out at the
firm level. Only half of this firm-level variation is persistent, suggesting that
firms within an industry are exposed to climate change to varying degrees over
time. Thus, the effects of climate change are heterogeneous across firms even
within an industry. This result is consistent with the idea that many factors
that affect a firm’s ability to adapt to a greener economy exhibit large firm-level
components (e.g., managerial skill, financing constraints).
We interpret the large share of firm-level variance as capturing economically
meaningful heterogeneity and argue that a firm’s idiosyncratic climate change
exposure is the key driver of this heterogeneity. That being said, a plausible
alternative is that part of the variation reflects idiosyncratic measurement error. Several tests dispel this alternative for several reasons. First, as discussed
below, we report robust associations between our measures and green job creation, green innovation, and risk-related outcomes. Second, following Hassan
et al. (2019), we directly quantify the amount of measurement error contained
in the firm-level variation. Approximately, 5% to 10% of the variation in measured exposure can be attributed to measurement error. The implied measurement error at the firm level is about 2 percentage points higher than that for
the overall variation. Although we interpret these results with due caution,
they suggest that measurement error in the firm-level dimension is higher
than that in the overall panel, but only modestly so.
Having bolstered confidence that the firm-level variation in measured climate change exposure is meaningful, we apply it to four real and financial
market outcomes. In the first two applications, we demonstrate that climate
5 This result may also reflect the fact that some firms’ emissions provides opportunities by supporting the transition to a greener economy (e.g., producers of building materials that make houses
more energy-efficient). Such “enabling activities” are also explicitly included in the EU Taxonomy,
which identifies activities that help reach the EU’s climate targets.

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change exposure predicts green-tech hiring and green patents, two key drivers
of the low-carbon transition. Using data compiled from Burning Glass (BG)
by Bloom et al. (2021), we establish that firms with higher measured climate
exposures create more jobs in disruptive green technologies over the subsequent year:6 a one-standard-deviation increase in climate change exposure
is associated with a 109% increase in green jobs in the following year. This
overall effect originates from more job creation at firms exhibiting higher
measured opportunities and regulatory exposures.
The results for green-tech job creation extend to green patenting. A onestandard-deviation increase in climate change exposure is associated with a
72% increase in the number of green patents in the following year. Once more,
this finding stems from firms with higher opportunities and regulatory exposures. High-exposure firms are not simply recruiting more across fields. They
are also not more innovative, in general. In fact, firms with higher exposure
hire less in nongreen-tech areas and generate fewer nongreen patents.
The remaining two applications relate climate change exposure to financial
market outcomes. We first show that measured exposure is related to risks and
risk premiums in the options market. Such relationships are plausible, as policy uncertainty surrounding regulation, including climate policy uncertainty, is
priced in options (Kelly, Pastor, and Veronesi (2016), Ilhan, Sautner, and Vilkov
(2021)). Likewise, there is plenty of uncertainty surrounding green technology
or renewable energy investment. Realizing these opportunities leads to significant gains if successful or large losses if unsuccessful. It is therefore plausible
that measured exposure relates to investors’ propensity to hedge extreme climate risks and/or gamble on climate outcomes. Indeed, for options written on
stocks with high overall exposure, the tail regions are relatively more expensive. Effects are similar at firms with high opportunity exposure, for which
investors are willing to pay a (variance risk) premium. In comparison, effects
are smaller but still statistically significant for firms with high regulatory exposure. This finding corroborates the view that some firms with high regulatory exposure face downside risks and upside potential (due to their innovation
activity).
We also document the conditional pricing of a factor that reflects innovations
to the aggregate level of climate change exposure. Firms with higher betas to
this factor face higher uncertainty related to future developments in climaterelated areas and, as a result, earn higher returns.7 Our estimation applies
the approach of Gagliardini, Ossola, and Scaillet (2016), which performs well
when—as in our case—the cross section is large relative to the time series. We

6 Our data do not cover all jobs potentially related to climate change, but they do identify job
postings with potential to have a lasting and meaningful real impact, as Bloom et al. (2021) only
consider job creation in “disruptive” technologies (e.g., solar or battery technology).
7 Our primary objective is to show that climate attention in earnings calls is linked to systematic
risk, with shocks to such attention being priced in the cross section. We do not want to propose a
new factor to be added to the factor zoo, and we do not try to use a conditional model framework
to explain asset pricing anomalies (Lewellen and Nagel (2006)).

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Firm-Level Climate Change Exposure

The Journal of Finance®

obtain a positive average conditional risk premium on the factor, and, more
importantly, find large time-series variability in the risk premium.8
Our keyword discovery approach of extracting climate-related information
from text offers an alternative approach to contemporaneous papers that try
to accomplish the same task by relying on other advances in natural language
processing (NLP). All of this work, including ours, is based on the understanding that standard NLP methods are not well suited for “niche languages,” that
is, specialized, highly technical vocabulary that varies substantially across textual sources (Varini et al. (2020), Webersinke et al. (2021)). These frictions
are exacerbated when the wordings associated with a topic are complex, ambiguous, and fast moving. A promising approach among these alternatives is
to use pretrained language models to learn word patterns in the language.
When implementing this pretraining approach in a specific domain of interest (e.g., climate change), rather than using large generic corpora, researcher
have found some promising results (Bingler, Kraus, and Leippold (2022),
Kölbel et al. (2022)). Work is ongoing on these problems. Which approach
works best in the context of climate finance is ultimately an empirical
matter.
A valid question is whether our approach delivers meaningful gains above
and beyond an alternative, off-the-shelves approach. Our main argument is
that keyword discovery is useful when the language of interest is not common.
We illustrate this claim by constructing, for comparison purposes, alternative
exposure measures using a list of pre-specified keywords from EGKLS. These
keywords appear more frequently in earnings calls than the bigrams we identify, probably because EGKLS’s set also contains unigrams and more general
terms. However, several of EGKLS’s unigrams are part of our top-100 list of
bigrams, and exposure measures based on the pre-specified keywords correlate positively with our measures. Beyond these correlations, a question is
why the approaches differ. As mentioned above, our measures have the benefit of capturing context-specific jargon used in specialized economic environments (earnings calls), while an approach using pre-specified keywords better captures broader discussions (e.g., in news media in the case of EGKLS’s
keywords). In addition, our approach adjusts the vocabulary over time, while
using pre-specified keywords fixes this vocabulary ex ante.9 Finally, especially
for the topic-based measures, it is easier to identify initial seed bigrams than
to develop keyword lists from authoritative texts.
Most closely related to our paper is the contemporaneous work by Li et al.
(2021, LSTY), who also use earnings calls to identify climate risks. We diverge
8 A caveat of all four applications is that any evidence of our measures’ ability to predict real
and financial outcomes is a success only if the true relationship exists in the data. We therefore
face the usual joint-hypothesis problem between the quality of our measures and the true economic
model generating the data.
9 Time-series variation in true (unobservable) climate change exposure, especially over long
horizons, is more likely to be picked up by such an “evolutionary” approach. Indeed, the selection
of pre-specified keywords may become obsolete over time with changing technologies or climate
change concerns.

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from their work in terms of our method, focus, and sample. More specifically,
LSTY use a pre-specified training library to identify climate risk words, which,
we argue, is unlikely to uncover the exact language used in earnings calls to
discuss climate change (see also Varini et al. (2020)). In addition, while LSTY
focus on physical and regulatory risks among U.S. firms, we provide a more
comprehensive analysis based on a global sample and include upside opportunity effects of climate change. Based on a textual analysis of 10K reports, Baz
et al. (2022) document that firms with more regulatory climate change exposure experience positive stock return effects after the 2016 Trump election.
Since making our data available, our measures have been related to a series
of real and financial outcomes. This “out-of-sample” evidence is reassuring, as
it indicates that the measures capture meaningful variation across firms and
do not reflect mostly noise. On the real side, as in our paper, von Schickfus
(2021) illustrates more green patenting when the overall measure and the
opportunity measure are higher, and Li, Lin, and Lin (2022) show that the
overall measure predicts depressed overall innovation. Furthermore, our
overall measure positively relates to cash holdings (Heo (2021)) and explains
how strongly U.S. firms’ emissions declined in response to the EPA’s 2010
Greenhouse Gas Reporting Program (Tomar (2023)). Our physical measure
is related to physical risk disclosure in 8K filings (Gostlow (2021)), and the
opportunity measure relates to firms’ carbon risk management (Duong et al.
(2021)). On the financial side, our physical measure is associated with lower
leverage after the Paris Agreement (Ginglinger and Moreau (2022)). Mueller
and Sfrappini (2022) show that after regulatory climate risks become salient,
bank lending is skewed toward firms with high regulatory exposure in the
United States, but away from such firms in the EU. We provide additional evidence in Sautner et al. (2022) that our measures are priced in equity markets,
and Kölbel et al. (2022) show that the overall measure is negatively associated
with credit default swap (CDS) spreads after the Paris Agreement. Di Giuli
et al. (2022) find that investors’ propensity to vote for climate proposals after
experiencing hot temperatures is higher at firms with more overall climate
change exposure. Heath et al. (2022) find that socially responsible investment
(SRI) funds invest less in firms with higher overall climate change exposure.
Our keyword dictionary is used by Hail, Kim, and Zhang (2021).
The rest of the paper proceeds as follows. Section I describes the data.
Section II presents our method to quantify firm-level climate change exposure. Section III validates the exposure measures. Section IV presents a
variance decomposition of the exposure measures and addresses measurement error. Section V presents four applications of the exposure measures.
Section VI concludes.
I. Data
A. Data on Earnings Conference Calls
We use transcripts of quarterly earnings calls held by publicly listed firms
to construct time-varying measures of the attention paid by call participants
to firm-level climate change exposure. The measures are constructed using

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Firm-Level Climate Change Exposure

The Journal of Finance®

the entire earnings call, including both the management presentation and the
Q&A session with analysts.10 The transcripts are collected from the Refinitiv
Eikon database. We use the complete set of English-language transcripts from
2002 to 2020. Unless indicated otherwise, as most of our other data vary at
the year level, we average quarterly transcript-based measures for each firm.
We exclude countries with 150 or fewer firm-year observations and drop SIC
codes 9900 to 9999 (“Nonclassifiable”) Our final sample includes 86,152 firmyear observations from 10,673 firms headquartered in 34 countries. Variable
definitions are presented in Table A.1.11
B. Data on Carbon Emissions
Some tests use data on carbon emissions (Total Emissions), calculated as
the sum of Scope 1 and Scope 2 emissions, from S&P Global Trucost. These
data include emissions reported by firms and emissions estimated by Trucost.
We use emission levels, rather than intensities, as emission levels are associated with a risk premium (Bolton and Kacperczyk (2021, 2023)), are the prime
target of policy and investor initiatives aiming to achieve net-zero emissions,
and are directly linked to carbon budgets (Bolton, Kacperczyk, and Samama
(2021)). Furthermore, many firms have witnessed strong investor opposition
on reporting emission intensities. To link the emissions data with our sample
firms, we apply a series of matching variables based on the following order: (i)
GVKEYs, (ii) ISINs, (iii) exact names, (iv) fuzzy names, and (v) tickers plus the
first two ISIN digits. We can match 33,789 firm-years with the emissions data
(4,999 unique firms from 34 countries between 2004 and 2020).12
C. Data on Public Attention to Climate Change
We borrow an index developed by EGKLS to capture how public climate
change attention varies in the time series. The WSJ CC News Index is constructed by measuring news about climate change in the Wall Street Journal
(WSJ). To quantify the intensity of climate news coverage, EGKLS compare
the WSJ’s news content to a corpus of authoritative texts on climate change.
The resulting measure reflects the fraction of the WSJ dedicated to the topic of
10 We also provide tests based on the measured exposure constructed from the Q&A session only.
The Q&A part is less scripted and may be less subject to strategic disclosure incentives than the
presentation part. In some calls, analysts ask no questions (we would calculate a climate change
exposure of zero in these cases). However, zero-question calls are a nonrandom event, and treating
these calls as if the firm is unexposed to climate change likely introduces bias (Chen, Hollander,
and Law (2014).)
11 Table IA.I in the Internet Appendix provides the distribution of firm-years across countries.
The Internet Appendix may be found in the online version of this article.
12 Table IA.II illustrates that Trucost data coverage is higher for firm-years with higher climate
change exposure, larger, more profitable, and less-R&D-intense firms, and non-U.S. firms. The
higher climate change exposure scores are expected given that Trucost caters to clients in need of
climate risk data (especially risks related to emissions).

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climate change each day (we use average annual values). For our sample, WSJ
CC News Index is available from 2002 to 2017.
D. Data on Green-Tech Jobs
Job data related to important green technologies come from Bloom et al.
(2021). These authors use textual analysis to identify 29 disruptive technologies over the past decades, of which four are broadly related to climate change
(“hybrid vehicle electric car,” “lithium battery,” “solar power,” and “fracking”).
Our data from Bloom et al. (2021) contain online job postings by firms related
to these four technologies. We refer to the jobs related to these technologies
as green-tech jobs.13 The data do not cover all jobs potentially related to climate change, but do identify those green jobs that, by Bloom et al.’s (2021)
construction, have a lasting and meaningful (“disruptive”) real impact. Bloom
et al. (2021) obtain these data from BG, which aggregates online job postings
using “spider bots” from job boards or employer websites.14 We match these
data by GVKEY and year. Jobs data are available for U.S. firms for 2007 and
2010 to 2020.
The measure #Green-Tech Jobs is the number of postings for disruptive
green-tech jobs in a firm-year. We assume that no green-tech job was posted
if a firm-year does not indicate disruptive green-tech job creation in the BG
database. (The results are robust to only considering firm-years within the BG
database; many firm-years in BG also show zero green-tech postings). Some
tests use #Nongreen-Tech Jobs, the number of job postings related to nongreen
disruptive technologies in a firm-year. We observe disruptive green job postings
in 5.4% of firm-years, and conditional on #Green-Tech Jobs being nonzero, the
average (median) number of green-tech jobs is 38 (3). The top-5 firms in the
cumulative count of new green-tech jobs include Tesla, Sunrun, First Solar,
Sunpower Corp, and Viviant Solar.
E. Data on Green Patents
To identify green patents, we collect patent data from the Google Patents
(GP) database. This database is also used by Kogan et al. (2017) and Kelly
et al. (2021). To identify “green” patents, we follow Cohen, Gurun, and Nguyen
(2021) and apply an OECD classification that identifies patents with the potential to address environmental problems. A description of how the OECD classifies patents into technology groups is provided by Haščič and Migotto (2015).
Green patents include patents on emission abatement technologies, renewable
13 It is unclear ex ante whether fracking has positive or adverse environmental effects. More
specifically, Acemoglu et al. (2019) argue that shale gas has the short-term benefit of lower emissions, when compared to conventional fossil fuels. However, the shale gas boom may lead to less
innovation in other emission-reducing technologies in the long run. Furthermore, fracking has
negative climate effects due to emission leakage. Our results are robust to excluding fracking jobs.
14 BG data are also used by Darendeli, Law, and Shen (2022) to measure green hiring. Campello,
Gao, and Xu (2021) additionally use BG data, though not in a climate context.

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Firm-Level Climate Change Exposure

The Journal of Finance®

energy, and energy storage. As in Kogan et al. (2017), we use name matching
to match patent assignee names to sample firms.15 Patent data are available
for U.S. firms from 2002 to 2019 (GP coverage for 2020 was still limited at the
time of writing).
The measure #Green Patents is the number of green patents filed in a firmyear. We assume that no green patenting occurred if we are unable to identify a
green patent in GP for a firm-year (results are robust to relaxing this assumption). Consistent with Acemoglu et al. (2019), new green patents are relatively
rare—we observe green patenting in only 1.4% of firm-years. However, the distribution is highly skewed. If we consider observations within GP, then green
patenting is observed in 15% of firm-years. Conditional on green patenting
being nonzero, the average (median) number of green patents equals 8.5 (2).
The top green patent producer is Caterpillar, with 1,364 green patents over
the sample period.16 We also use the total number of nongreen patents filed
(#Nongreen Patents).
F. Data on Risks and Risk Premiums in the Options Market
Data on option-implied variables are from the Volatility Surface File of Ivy
DB OptionMetrics. In these tests, we focus on S&P500 firms, for which data
on liquid options are available. We match options data through the historical
CUSIP link of OptionMetrics. We construct six measures: implied variance
(IVar), implied skewness (ISkew), implied kurtosis (IKurt), implied volatility
slopes (SlopeD and SlopeU ), and variance risk premium (V RP). The variable
construction process is detailed in Section II of the Internet Appendix. The high
frequency of the option-implied measures allows us to use quarterly values of
CCExposure.17
G. Data on Risk Premiums in the Equity Market
Our tests examining the climate change exposure factor use monthly data on
the standard factors from Ken French’s data library. Term and default spread
data are from the St. Louis Fed’s FRED library. The term spread is the difference between the 10-year and three-month Treasury constant maturity data
series (variable T10Y3MM). The default spread is the difference between the
15 We track the timing of an invention by matching patents using the priority year, that is, the
effective date of a patent filing (De Haas and Popov (2022)). While the “filing date” corresponds to
when a patent application is filed at the patent office, the “priority date” is when the novelty of an
invention is established.
16 Caterpillar traditionally manufactured diesel engines and mining equipment, but moved into
selling photovoltaic or energy storage technology. The firm also ranks in the top-10 in Cohen,
Gurun, and Nguyen’s (2021) sample; the slight ranking divergence is due to different sample periods.
17 To avoid look-ahead bias, we match quarterly exposure values covering earnings calls in quarter t (typically discusses events of quarter t − 1) with option-implied measures from the last day
of quarter t.

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Baa and Aaa corporate bond yield (BAA10YM and AAA10YM). Book-to-market
ratio data (defined in log terms as in Fama and French (2008)) come from Compustat North America. Term and default spreads and the book-to-market ratio
for each firm are centered and standardized in the time series, and then used
as instruments for conditional risk premium estimation. We restrict the risk
premium tests to S&P500 firms with more than 28 monthly returns (out of
228) during our sample period.
H. Financial Statement Data
Data on firm financial variables (e.g., total assets, debt, CAPEX, R&D, or
cash holdings) are from Compustat North America and Compustat Global.
II. Quantifying Firm-Level Exposure to Climate Change
A. Discovery of Climate Change Bigrams
To quantify exposure to climate change, we build on Hassan et al. (2019,
2021, 2023a). Extracting climate-related information from text sources is challenging (Webersinke et al. (2021)). Methods using training libraries or prespecified word lists do not cope well with the niche language used to describe climate change.18 In addition, discussion in earnings calls considers
climate change together with topics such as regulation, tax credits, technological breakthroughs, and performance. This results in substantial ambiguity
about when the discussion is genuinely about climate change. Finally, vocabulary used to discuss climate change is fast moving, changing to reflect shifting
opinions, regulations, and innovations related to climate change.
To address these challenges, we adapt the keyword discovery algorithm
proposed in King, Lam, and Roberts (2017).19 This algorithm does not require
a comprehensive “climate change” training library, but rather only a small
set of “initial” bigrams (see Table IA.III). These initial bigrams are chosen
because they relate unambiguously to climate change. The algorithm then
uses these initial bigrams to search for new bigrams that also likely indicate
climate change conversation and searches directly in the transcripts. Because
each initial bigram is connected to a specific group of new bigrams discovered
through the search algorithm, one can easily decompose the measure of
climate change exposure into its constituent parts based on the presence of
these bigrams. The initial bigrams allow the algorithm to identify sentences
that focus unambiguously on climate change. The algorithm then extracts
“features” by relying on supervised learning methods. Features are bigrams
beyond the initial set predicting climate change from the identified sentences.
18 That said, researchers have used the SEC Climate Disclosure Search tool, which looks for
pre-specified keywords in SEC filings, to develop a measure of climate risk (Berkman, Jona, and
Soderstrom (2019)).
19 Details, including how we define the set of initial bigrams, are presented in Section I of the
Internet Appendix.

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Firm-Level Climate Change Exposure

The Journal of Finance®

Finally, the algorithm constructs a model predicting whether a sentence is
related to climate change. We apply this prediction model to sentences that
do not include any initial bigrams and then assess whether the predicted sentences are related to climate change. To discover new climate change bigrams,
we reverse-engineer the machine-learning (ML) process and trace back the
bigrams that best discriminate climate-change-related sentences from other
sentences. The resulting set of climate change bigrams C includes the initial
bigrams and the newly identified bigrams.
That our approach generates meaningful climate change bigrams based on
the initial bigrams is helpful for several reasons. First, it extends the rather
broadly specified initial bigrams into more specialized word combinations.20
Second, C includes the names of several power stations and wind farms (e.g.,
“kibby wind” or “coughlin power”), which are of interest to call participants
who discuss the climate change exposure of these facilities’ operators. These
bigrams illustrate the challenge of using training libraries or pre-specified
word lists to identify climate change talk—few researchers have the detailed
field knowledge to recognize the relationship between these words and climate change.
Our approach allows us to adapt the bigram-search algorithm to discover
three unique sets of bigrams from C that capture opportunities as well as regulatory and physical climate shocks. Toward this end, we feed a set of initial
bigrams reflecting these three topics to the search algorithm. We then allow
the algorithm to discover bigrams related to the topic of interest. Table IA.IV
lists the initial bigrams used for the topic search. We construct new initial bigrams for these topics by hand-picking appropriate bigrams from the top-500
bigrams discovered after the first generic, nontopic-specific bigram search. We
then rerun the search algorithm to find a broader set of bigrams for each topic.
As the topic-based algorithm yields some general climate change bigrams, we
drop bigrams appearing in more than one topic to guarantee that we do not
have overlapping topic measures. In the final stage, we take the intersection
between C and each set of topic bigrams to obtain the sets of opportunity,
regulatory, and physical climate change bigrams (i.e., COpp , CReg, and CPhy ),
respectively.
B. Construction of Climate Change Exposure Measures
Using the bigram sets, we construct measures of climate change exposure
for each transcript. We interpret these measures as capturing the attention
devoted to climate change topics by call participants at a point in time, rather
than as measures of fundamental exposure. We use the broad set of climate
change bigrams C to illustrate how we construct these measures. The topic

20 For example, “rooftop solar” and “photovoltaic panel” come from the initial bigram “solar
energy,” while “nuclear power” and “event fukushima” come from “renewable energy,” and “tesla
battery” and “hybrid plug” come from “electric vehicle.”

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measures are constructed analogously; we simply replace C with the bigrams
that relate to the corresponding topic.
We construct an overall exposure measure, CCExposure, based on how frequently the specified bigrams appear in a transcript. This involves taking the
set of climate bigrams C to the transcript of firm i in quarter t and counting the
frequency of these bigrams. To account for the call length, we scale the count
by the number of bigrams in the transcript,
i,t

1 
1[b ∈ C] ,
Bi,t

B

CCExposurei,t =

(1)

b

where b = 0, 1, . . . , Bi,t are the bigrams in the earnings call transcripts of firm
i in quarter t and 1[·] is the indicator function. We create an annual measure for each firm by averaging the quarterly measures. We produce exposure
measures from COpp , CReg, and CPhy , respectively, by scoring each transcript
using the same method. We label the topic-based measures as CCExposureOpp ,
CCExposureReg, and CCExposurePhy .
Some of our tests employ two refinements. In the first refinement, we create
two sentiment measures by counting the number of climate change bigrams
after conditioning on the presence of the positive or negative tone words in
Loughran and McDonald (2011),


Bi,t
b∈S
 
1  
Pos/Neg
=
T Pos/Neg (b) ,
(2)
1[b ∈ C] ×
CCSentimenti,t
Bi,t
b

b

where S represents the sentence containing bigrams b = 0, 1, . . . , Bi,t and
T Pos/Neg (b) assigns sentiment to each bigram b:21

1 if b has a positive tone,
T Pos (b) =
0 if otherwise,

T

Neg

(b) =

1
0

if b has a negative tone,
if otherwise.

In the second refinement, we construct a measure of risk by counting the relative frequency of the climate change bigrams mentioned in the same sentence
21 Though not used in this paper, we also combine both sentiment measures into an overall
measure by counting the climate change bigrams after conditioning on the presence of positive
and negative tone words,
⎫
⎧
Bi,t
b∈S
⎬
 
1  ⎨
CCSentimenti,t =
T(b) ,
1[b ∈ C] ×
⎭
⎩
Bi,t
b

b

where T(b) = 1(−1) if b has positive (negative) tone, and zero otherwise.

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Firm-Level Climate Change Exposure

The Journal of Finance®

with the words “risk,” “uncertainty,” or their synonyms,
i,t

1 
CCRiski,t =
1[b ∈ C] × 1[b, r ∈ S] ,
Bi,t

B

(3)

b

where r contains the words “risk,” “uncertainty,” or a synonym.
The exposure measures do not adjust for the differences in the importance
or typical frequencies of individual bigrams. For robustness, we account for
such differences by constructing measures that weigh each bigram with a score
reflecting the bigram’s representativeness for climate discussions. We do this
so that common terms that appear in most transcripts receive low scores, as
these terms are less informative about a call’s content, as do rare terms in a
given transcript, as these terms have low text frequency. This approach follows
Hassan et al. (2019), Gentzkow, Kelly, and Taddy (2019), and EGKLS and is
commonly referred as “term frequency-inverse document frequency” (TFIDF).
Formally,
1 
1[b ∈ C] × log
Bi,t
Bi,t

=
CCExposureTFIDF
i,t

b

NT
fb,T


,

(4)

where NT refers to the number of transcripts and fb,T to the number of transcripts in which bigram b appears. A bigram appearing in many transcripts
therefore has low weight when calculating the TFIDF score, and—in the extreme case—if a given bigram appears in every transcript, it receives zero
T
) = 0).
weight (log( N
fb,T
Table I reports summary statistics for the exposure measures (for purposes
of exposition, the measures are multiplied by 103 ).22 Table IA.V reports the
correlations across the exposure measures. A few correlations deserve further comment. The correlation between CCExposureReg and CCExposureOpp
is positive at 33%, and CCExposurePhy is largely unrelated to CCExposureReg
and CCExposureOpp . In addition, the correlation between CCExposure and
CCExposureTFIDF is 99.7%.
Tables IA.VI to IA.VIII report the sample distribution at the earnings-call
(transcript) level across countries, years, and industries. We report the distributions for all sampled earnings calls and for those calls with nonzero climate change exposure. The tables show meaningful proportions of calls with
nonzero climate change exposure across all three sample cuts; transcripts with
CCExposure > 0 are not concentrated in certain countries, years, or industries.
Our analysis does not make use of a binary indicator for whether CCExposure
is nonzero, but instead uses a continuous measure.

22 The magnitudes of CCExposureTFIDF are larger than those of CCExposure as the inverse
document frequency of the climate change bigrams can be much larger than one (the document
frequencies of the climate change bigrams are much smaller than the total number of transcripts).

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Table I

Climate Change Exposure Variables: Summary Statistics
This table reports summary statistics for different measures of climate change exposure, carbon
emissions, and public attention to climate change at the firm-year level. For the climate change
exposure measures, we average values of the four earnings calls during the year. The sample
includes 10,673 unique firms from 34 countries over the period 2002 to 2020. Table A.1 provides
detailed variable definitions.
Mean

STD

25%

Median

75%

N

1.01
0.31

2.53
1.23

0.10
0.00

0.30
0.00

0.78
0.15

86,152
86,152

0.04

0.23

0.00

0.00

0.00

86,152

0.01

0.11

0.00

0.00

0.00

86,152

7.99
2.35

19.69
9.08

0.77
0.00

2.44
0.00

6.26
1.18

86,152
86,152

0.32

1.68

0.00

0.00

0.00

86,152

0.10
CC Q&A Measure (×103 )
0.67
CCExposureQ&A
i,t
CC Sentiment and Risk Measures (×103 )
Pos
CCSentimenti,t
0.38

0.81

0.00

0.00

0.00

86,152

1.95

0.00

0.12

0.54

86,152

1.10

0.00

0.07

0.32

86,152

CC Measures (×103 )
CCExposurei,t
CCExposureOpp
i,t
CCExposureReg
i,t

CCExposurePhy
i,t
CC Measures (TFIDF Version) (×103 )
CCExposurei,t
CCExposureOpp
i,t
CCExposureReg
i,t

CCExposurePhy
i,t

Neg
CCSentimenti,t
0.19
0.55
0.00
0.00
0.16
86,152
CCRiski,t
0.04
0.17
0.00
0.00
0.00
86,152
Carbon Emissions and Climate Change Attention
Total Emissionsi,t
2,961,549 13,608,989 27,472 133,847 751,772 33,789
W SJ CC News Indext
0.007
0.001
0.006
0.006
0.008 68,794

III. Validation
A. Validation at the Bigram Level
A.1. Face Validity of Climate Change Bigrams
We validate our exposure measures using a multipronged approach. First,
we consider the bigrams’ face validity. Table II lists the 100 highest-frequency
bigrams in C. The top bigrams associated with CCExposure capture aspects
of the opportunities and risks associated with climate change. The top bigrams include both opportunity-related word pairs (e.g., “battery power,”
“new energy”) and risk-related terms (e.g., “environmental concern,” “extreme
weather”).
Table IA.IX considers the three topic-based measures. When we construct
CCExposureOpp using initial bigrams such as “wind power” or “solar energy,”
we find several new bigrams that refer to new (green) technologies (e.g., “solar
farm,” “carbon free”) (Panel A). Several word combinations are linked to developments in “electric vehicles,” including “charge infrastructure” and “battery
electric.” With respect to CCExposureReg (Panel B), when we use initial bigrams

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Firm-Level Climate Change Exposure

Table II

Top-100 Bigrams Captured by Climate Change Exposure
(CCExposure)
This table reports the top-100 bigrams associated with CCExposure, which measures the relative
frequency with which bigrams related to climate change occur in earnings call transcripts. Table
A.1 defines all variables in detail.
Bigram

Frequency Bigram

Frequency Bigram

renewable energy
electric vehicle
clean energy
new energy
climate change

15,605
9,508
6,430
4,544
4,374

onshore wind
electric motor
provide energy
efficient solution
global warm

878
869
851
839
837

wind power
wind energy
energy efficient
greenhouse gas
solar energy
air quality
clean air

4,253
4,035
3,899
3,416
2,511
2,409
2,301

828
827
827
821
816
793
792

carbon emission

2,088

power generator
solar pv
scale solar
need clean
coastal area
energy star
environmental
footprint
design use

gas emission
extreme weather
carbon dioxide
water resource
autonomous vehicle

1,910
1,773
1,583
1,423
1,394

energy environment
wind resource
government india
battery power
air pollution
battery electric

1,279
1,245
1,201
1,147
1,127
1,121

integrate resource
clean power
carbon price

1,052
1,008
999

area energy
charge station
clean water
major design
vehicle manufacturer
future energy
motor control
combine heat
electric bus
distribute power
environmental
benefit
eco friendly
electrical vehicle
carbon neutral

world population
solar farm
energy regulatory
obama administration
heat power
carbon tax

977
971
967
957
941
928

unite nation

925

fast charge
cell power
energy team
cycle gas
coal gasification
environmental
concern

777

carbon intensity
energy application
produce electricity
help state
environmental
standard
power agreement
supply energy
electric hybrid
source power
sustainability goal
energy reform
plant power

Frequency
641
615
604
604
593
586
585
585
575
572
571
564

777
762
759
747
740

compare conventional
gas vehicle
effort energy
pass house
carbon free
driver assistance

560
560
559
558
545

737
726
718
709
703
695

electrical energy
solar installation
snow ice
renewable natural
promote use
farm project

543
541
538
536
536
531

695
695
690

laser diode
deliver energy
protect environment
sustainable energy
manage energy
invest energy
electric energy
forest land
capacity energy

528
526
525

675
657
650
646
643
643

560

523
522
521
519
512
512

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The Journal of Finance®

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“carbon tax,” “air pollution,” or “air quality”, that is, terms related to regulatory interventions, we discover bigrams that explicitly include the word “regulation” or its synonyms (e.g., “control regulation,” “environmental legislation”).
Turning to the top bigrams for CCExposurePhy (Panel C), we use initial bigrams
such as “natural hazard” or “sea level” to identify word pairs intuitively linked
to physical climate change (e.g., “area florida,” “ice control,” and “wind speed”).
For the 10 highest-scoring firms on CCExposure, Table IA.X provides “snippets.” These snippets are text fragments taken from the point in the transcript that the algorithm identifies as the moment when the participants discuss climate issues. Consider Ocean Power Technologies, a U.S. firm that turns
ocean wave power into electricity for offshore applications. In its 2008Q4 call,
bigrams such as “energy requirement,” “powerbuoy wave,” “wave condition,”
and “wave power” were heavily featured. In the top snippet, participants discuss the increased demand for the firm’s trademark technology (the PowerBuoy®) due to heightened attention to renewable energy. Not surprisingly,
high-scoring firms are involved in energy production or the broader energy
infrastructure. Indeed, when ECOtality call participants use climate change
bigrams, they discuss how charging infrastructures are central to advancing
zero-emissions transportation.
A.2. Audit Study Based on Human Reading
We developed a two-stage snippet-based audit to evaluate the scoring of our
algorithm (Baker, Bloom, and Davis (2016), Hassan et al. (2019)). While our
algorithm should be judged in the context of the entire transcript, a snippetbased audit improves our ability to sample across a large number of transcripts. In the first stage, we define a snippet as the 10 sentences around
the climate change bigram with the highest text frequency in a transcript.
For transcripts with CCExposure = 0, we randomly choose a snippet of 10 consecutive sentences for the audit. In our pilot study, each of the authors independently coded 250 identical and randomly selected snippets using a binary
coding scheme. The coding used the variable CCAudit, which equals one if
the rater classifies the text as providing evidence of climate change exposure,
and zero otherwise. In addition, for each snippet we record Coding Confidence,
which ranges from three (the rater is highly confident that their coding is correct) to one (“hard calls”). We identified some slight coding differences between
the authors and resolved discrepancies. Based on this iterative procedure, we
developed a detailed guide with definitions of what text should be coded as
climate change exposure and which snippets should not qualify as such. The
audit guide describes examples of snippets and offers interpretations and suggested coding to help the raters solve complex cases in the audit process. We
then instructed two graduate students based on the audit guide and asked
them to audit the same 250 snippets that the author team coded to assess any
remaining inconsistencies.
In the second stage, we recruited 19 graduate students to each independently code 250 new snippets from the audit universe. Together they

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Firm-Level Climate Change Exposure

The Journal of Finance®

Figure 1. Probability of correctly identified positives by decile. This figure plots on the
vertical axis the predicted probability of having a correctly identified positive (i.e., the audit study
of the snippet confirms climate change-related text) against deciles of the CCExposure distribution.
The median score of CCExposure in a given decile is shown on the axis. Predicted probabilities are
computed by estimating a logit model on the sample of 2,090 audited snippets. (Color figure can
be viewed at wileyonlinelibrary.com)

assessed 2,090 unique snippets.23 Auditors received training based on the audit guide. The snippets were partially overlapping to allow us to conduct some
inter-rater correspondence tests. Our goal is to verify the information content
of CCExposure at various points of its distribution. Following Hassan et al.
(2019), we create portfolios with the same number of transcripts based on their
percentile of the CCExposure distribution. We then count the number of transcripts at that percentile that the auditors rated as CCAudit = 1 (i.e., the snippet is classified as containing a clear discussion of a firm’s climate change exposure). We count 310 true positives out of 339 snippets (91% correct positives) in
the top-decile portfolio (transcripts with the highest value of CCExposure). The
rate of correct positives declines almost linearly as we move to the median and
bottom portfolios. This is displayed in Figure 1, which plots the relationship
between (the predicted probability of) true positives (as judged by the human
reading) at each decile and the median percentile score of CCExposure at that

23 We first sorted all transcripts with nonzero CCExposure into deciles. We then randomly selected 10 snippets from each decile and another 10 from CCExposure = 0 transcripts for each
sample year.

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percentile. The association is positive and nearly linear, as would be expected
if our algorithm reliably identifies climate change discussions.24
A.3. Comparison with Approach Using Pre-Specified Keywords
We construct alternative exposure measures from a list of pre-specified climate change keywords to compare these measures with those produced by our
algorithm. To obtain such a list, we use the set of unique stemmed unigrams
and bigrams CEGKLS used by EGKLS to build their time-varying, news-based
index of climate change attention. These keywords originate from 74 authoritative texts. To create CCExposureEGKLS , we replace C with CEGKLS and recompute the relative frequency with which the alternative terms appear in
the transcripts. We construct a frequency-unweighted and a TFIDF version,
denoted by CCExposureEGKLS−EW or CCExposureEGKLS−TFIDF , respectively.
Table IA.XI illustrates that the unigrams and bigrams in CEGKLS appear
more frequently in earnings calls than the bigrams in C. This finding is unsurprising as CEGKLS includes more unigrams and more general terms (the
top-3 bigrams are “market,” “increase,” and “time”). Using unigrams rather
than bigrams trades off the higher likelihood of a given term occurring in a
text against the higher probability of a false positive, that is, wrongly classifying a fragment as climate change text (van Zaanen and Kanters (2010)).
Several of the unigrams in CEGKLS are part of the top-100 bigrams in C
(e.g., “carbon,” “energy,” or “water”). As would be expected from Table IA.XI,
the mean values of both alternative exposure measures (Table IA.XII, Panel
A) are larger than those of CCExposure. Thus, larger parts of the earnings
calls are classified as discussing climate topics if we use CEGKLS instead of
C. At the same time, Table IA.XII, Panel B, indicates that the measures correlate positively with CCExposure. The correlation table illustrates that our
main measure and the alternative measures yield more similar assessments
when the public pays close attention to climate change (WSJ CC News Index is in the top quartile). One possible explanation is that at times when
the WSJ devotes a lot of space to climate topics, terms from a more general climate library (on which the index and pre-specified keyword measures build) become more commonly used in earnings calls. Intuitively, media attention might homogenize the language used to talk about climate
change. When the media pivots to other events, the vocabulary likely used
to discuss climate change in earnings calls becomes more idiosyncratic again.
Such instances are plausibly better reflected in our keyword-search-based
approach.
A question that remains is how our measure and a measure using predefined keywords differ economically. Our measure is well suited to capture
24 These findings suggest that our algorithm correctly identifies climate change text, even at
relatively low CCExposure scores. A benchmark is provided in Hassan et al. (2019), where the
number of correct positives reduces to below five out of 20 at the 90th percentile of their textbased political risk score. Weighting observations by Coding Confidence does not materially change
our findings.

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Firm-Level Climate Change Exposure

The Journal of Finance®

context-specific jargon used in specialized environments with experts and allows us to construct topic-based measures. The pre-specified keyword approach
better captures broader discussions by the public, as reflected in articles published in the WSJ, while identifying specific or emerging topics with a prespecified keyword approach is more challenging. A further difference is that
our approach is “evolutionary,” that is, it will reflect changes in the vocabulary
used in transcripts over time, while an approach using pre-specified keywords
fixes this vocabulary ex ante. Time-series variation in true (unobservable) climate change exposure, especially over long horizons, is more likely to be picked
up by such an “evolutionary” approach. Any selection of pre-specified keywords
is due to become obsolete the further out one moves in time.

A.4. Perturbation Tests for Individual Initial Bigrams
We evaluate the extent to which our overall exposure measure depends on
individual bigrams in the initial bigram list (Table IA.III) by performing a
perturbation test. We successively exclude one initial bigram at a time, recomputing the modified set of bigrams CPert as well as the modified CCExposurePert .
Given that our initial short list contains 50 bigrams, we construct 50 new
versions of CCExposurePert . After aggregating the measure to the firm-year
level, we calculate the correlation of each of these exposure measures with
CCExposure. These correlations are above 85%, which means that CCExposure
does not depend much on specific initial seed bigrams.

A.5. Comparison with Approach Using Initial Bigrams Only
Table II shows that the initial keywords dominate the top-100 bigrams used
in the construction of CCExposure. This raises the question of how big the
performance gain of the keyword discovery approach is relative to the alternative that only uses the initial seed bigrams. To address this question, we
construct the new exposure measure CCExposureInitial from the initial bigrams
only. Figure 2, Panel A, shows how frequently the new measure signals zero
exposure, while CCExposure instead reveals that climate topics are discussed.
Results are reported by CCExposure decile. In the top decile, CCExposureInitial
indicates no exposure in 27% of transcripts. Hence, even among the most exposed firms, there is a performance gain when applying our approach. This
gain increases when we consider other deciles—already in the second decile,
CCExposureInitial deviates from CCExposure, indicating the absence of exposure in more than 62% of transcripts. The effects increase monotonically as we
move to lower exposure deciles.
Panel B reports results of the topic-based exposure measures, with the alternative measures using only the topic-based initial bigrams (Table IA.IV).
For all three measures and deciles, significant fractions of the transcripts are
incorrectly classified as having zero exposure. Even in the three respective top
deciles, the alternative approach misses positive exposure in 10% to 40% of the

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transcripts. Across all deciles, the gain from the keyword discovery approach
is largest for CCExposureOpp (especially in the lower deciles).
Beyond these statistics, identifying exposure using bigrams beyond the initial seed words is economically important. Below we show that, among the
set of firms for which CCExposureInitial = 0, our exposure measures keep predicting green outcomes. These effects are identified purely from the bigrams
obtained through the keyword search algorithm.

B. Validation at the Climate Change Exposure Level
B.1. Climate Change Exposure: Industry Variation
We now move away from the bigram level to examine the properties of the
exposure measures. This involves several steps. In the first step, we compute
averages by industry sector (two-digit SIC code level) and present a ranking
of these means in Table III. In Panel A, using CCExposure, the sectors with
the highest overall exposure include Electric, Gas, & Sanitary (SIC49). Topranked firms within this sector include China Longyuan Power Group, China’s
largest producer of wind power, and the U.S. utility Allete. This sector is followed by Heavy Construction (SIC16) and Construction (SIC17). High-ranking
firms in these sectors include A-Power Energy Generation Systems, a Chinese
firm providing on-site power generation systems, ReneSola, a U.S. firm developing and operating solar projects, and Quanta Services, a U.S. infrastructure
solutions provider for firms in the energy and pipeline business. Top-ranked
firms in the Transportation Equipment sector (SIC37), ranked next, include
alternative fuel and zero-emission vehicle firms.
A few sectors are worth commenting on in Panels B to D, which report the
topic-based measures. Utilities top the list for CCExposureOpp (Panel B) and
CCExposureReg (Panel C). While the latter ranking position is expected, given
the sector’s exposure to carbon taxes or related regulations, the earlier position
is more surprising. Notwithstanding, it is consistent with Cohen, Gurun, and
Nguyen (2021), who find that this sector is a key innovator in the energy transition space. Coal Mining (SIC12) displays high exposure to regulatory and
physical shocks (Panels C and D). While high regulatory exposure is expected
given the large emissions associated with burning coal, high physical exposure
is less obvious. This may reflect mining firms’ exposure to heavy precipitation,
or heat, which pose physical challenges to their operations. Stone, Clay & Glass
Products (SIC32), in the top-5 for CCExposureReg, includes mostly cement producers among its top-ranked firms (they belong to the largest CO2 emitters).
A sector in the top-10 of CCExposurePhy (Panel D) is the insurance industry,
which, unsurprisingly, is highly exposed to the costs of storms or flooding.
The large variation in exposure between sectors masks important heterogeneity within each sector (apparent from the large within-sector standard
deviations). To illustrate this heterogeneity, we compare TotalEnergies and
ExxonMobil. Both firms operate in Petroleum Refining (SIC29), a sector ranking among the top 10 for CCExposureOpp and CCExposureReg. In terms of the

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Firm-Level Climate Change Exposure

The Journal of Finance®
Table III

Industry Distribution of Climate Change Exposure Measures
This table reports firms’ climate change exposure measures for the top-10 industries. Statistics
are reported at the firm-year level across different SIC2 industries. We rank sectors by the average values of the climate change exposure measures. CCExposure measures the relative frequency
with which climate change bigrams occur in earnings calls. CCExposureOpp measures the relative frequency with which bigrams that capture opportunities related to climate change occur in
earnings calls. CCExposureReg measures the relative frequency with which bigrams that capture
regulatory shocks related to climate change occur in earnings calls. CCExposurePhy measures the
relative frequency with which bigrams that capture physical shocks related to climate change occur in earnings calls. For all measures, we average values of the four earnings calls during the year.
We report results only those industries for which we have more than 20 firm-year observations.
Table A.1 defines all variables in detail.
Panel A: CCExposure (×103 )
Industry (SIC2)

Mean

Std.Dev.

Median

N

49 Electric, Gas, & Sanitary Services
16 Heavy Construction, Except Building
17 Construction
37 Transportation Equipment
36 Electronic & Other Electric Equipment
12 Coal Mining
29 Petroleum Refining
41 Local & Suburban Transit
55 Automative Dealers & Service Stations
33 Primary Metal

6.95
3.04
2.26
2.12
2.07
2.05
1.72
1.69
1.63
1.56

6.23
4.35
2.95
3.17
4.20
1.48
2.14
2.06
3.90
1.54

5.34
1.53
1.16
1.07
0.57
1.70
1.06
0.84
0.69
1.14

3,259
537
131
2,021
5,812
253
730
94
484
1,149

Industry (SIC2)

Mean

Std.Dev.

Median

N

49 Electric, Gas, & Sanitary Services
16 Heavy Construction, Except Building
17 Construction
36 Electronic & Other Electric Equipment
37 Transportation Equipment
55 Automative Dealers & Service Stations
29 Petroleum Refining
35 Industrial Machinery & Equipment
75 Auto Repair, Services, & Parking
87 Engineering & Accounting & Research

2.50
1.37
0.91
0.90
0.81
0.54
0.47
0.46
0.42
0.38

3.30
2.78
1.71
2.38
1.70
1.34
0.93
1.85
1.04
0.94

1.26
0.30
0.34
0.09
0.23
0.16
0.16
0.07
0.11
0.00

3,259
537
131
5,812
2,021
484
730
4,056
171
1,443

Industry (SIC2)

Mean

Std.Dev.

Median

N

49 Electric Gas & Sanitary Services
12 Coal Mining
29 Petroleum Refining
32 Stone Clay Glass Products
10 Metal Mining
33 Primary Metal
37 Transportation Equipment
35 Industrial Machinery & Equipment

0.34
0.14
0.14
0.12
0.08
0.08
0.08
0.08

0.61
0.24
0.32
0.35
0.32
0.22
0.27
0.47

0.10
0.00
0.00
0.00
0.00
0.00
0.00
0.00

3,259
253
730
622
1,465
1,149
2,021
4,056

Panel B: CCExposureOpp (×103 )

Panel C: CCExposureReg (×103 )

(Continued)

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Table III—Continued
Panel C: CCExposureReg (×103 )
24 Lumber & Wood
16 Heavy Construction

0.07
0.07

0.43
0.21

0.00
0.00

471
537

Industry (SIC2)

Mean

Std.Dev.

Median

N

41 Local and Suburban Transit
26 Paper & Allied Products
24 Lumber & Wood
49 Electric, Gas, & Sanitary Services
14 Mining & Quarrying
12 Coal Mining
64 Insurance Agents, Brokers, & Service
10 Metal Mining
15 Building Construction
35 Industrial Machinery & Equipment

0.17
0.08
0.07
0.06
0.05
0.04
0.03
0.03
0.03
0.03

0.47
0.35
0.26
0.24
0.14
0.19
0.15
0.12
0.09
0.25

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

94
852
471
3,259
208
253
297
1,465
600
4,056

Panel D: CCExposurePhy (×103 )

average regulatory exposure since 2010, TotalEnergies’ score is similar to that
= 0.21 vs. CCExposureReg
= 0.18),
of ExxonMobil (CCExposureReg
TotalEnergies
ExxonMobil
but the French oil major exhibits much higher average opportunity exposure (CCExposureOpp
= 1.13 vs. CCExposureOpp
= 0.15). This diTotalEnergies
ExxonMobil
vergence reflects a broader perception in the market about the extent to which
these firms embrace renewable energy and the net-zero transition in their
business models (see Pickl (2019)). More generally, the large within-industry
variation indicates that sectors have “winners” and “losers.” Investors may
therefore be able to address climate risks and opportunities by maintaining
a broad industry diversification (rather than banning some industries) and
then performing negative screening of climate change “losers.” This observation echoes arguments by both academics (Andersson, Bolton, and Samama
(2016)) and providers of low-carbon index solutions.
B.2. Climate Change Exposure: Time-Series Variation
In Figure 3, Panels A to D, we compute the cross-sectional means for
CCExposure and the topic-based measures and plot them over time (for each
measure, we focus on top-10 sectors). This figure also highlights key moments
in public awareness of climate change, covering climate policy events relevant
to regulatory and opportunity shocks (Panels B and C), select physical shocks
(Panel D), or both (Panel A). In Panel A, CCExposure generally increases over
the sample period, especially since the mid-2000s. The increase in the early
years indicates that earnings calls discussed climate issues earlier than we
might have expected. A plateau is reached around 2009 (the year of the unsuccessful Copenhagen Climate Summit). We then observe a slight decline in
the years leading up to the 2012 Doha Climate Summit. We note a renewed

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Firm-Level Climate Change Exposure

The Journal of Finance®

Figure 2. Climate change exposure calculated with initial bigrams. This figure shows
how frequently CCExposureInitial signals zero climate change exposure, while CCExposure instead
reveals that such exposure exists. Results are reported by CCExposure decile. CCExposureInitial
is a measure of climate change exposure based on the initial seed bigrams only. Panel A reports
results for the overall climate change exposure measure, and Panel B for the topic-based measures.
In the figure, the exposure measures are calculated at the quarterly (transcript) level. (Color figure
can be viewed at wileyonlinelibrary.com)

increase in CCExposure since around 2013. At the end of the sample,
CCExposure peaks with earnings calls exhibiting about four climate change
bigrams per 1,000 bigrams; this compares to about 0.1 political bigrams per
1,000 bigrams in Hassan et al. (2019).
In Panel B, the time series for CCExposureOpp is similar to that of the overall measure: CCExposureOpp trends upward, especially at the beginning of the
sample. In Panel C, CCExposureReg increases between 2002 and 2008, varies
around a markedly lower level between 2011 and 2013, spikes in 2015 (Paris
Agreement), and follows an increasing trend since 2017. This is consistent with
intensified policy discussions about how to achieve the Paris goals. In Panel
D, CCExposurePhy displays more swings than the other measures, albeit also
around an upward trend. It appears that CCExposurePhy does not strongly reflect highly salient climate events. For example, while there is a jump after
major U.S. hurricanes (i.e., Katrina, Sandy, and Harvey), the jumps occur with
a considerable lag. This pattern indicates that CCExposurePhy primarily reflects firm-specific exposures to physical climate events, (e.g., local heat waves
or droughts).
B.3. Climate Change Exposure and Carbon Emissions
We explore how well the exposure measures correlate with firms’ carbon
emissions. Carbon emissions constitute an essential variable to measure firmlevel exposure to climate change, especially for regulatory shocks (Bolton and
Kacperczyk (2021, 2023)). The analysis of carbon emissions is also the most frequently used climate risk management tool of institutional investors (Krueger,
Sautner, and Starks (2020)). A benefit of using carbon emissions is that they

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Figure 3. Climate change exposure over time. This figure shows firms’ average climate
change exposures over time. CCExposure measures the relative frequency with which climate
change bigrams occur in earnings calls. CCExposureOpp measures the relative frequency with
which bigrams that capture opportunities related to climate change occur in earnings calls.
CCExposureReg measures the relative frequency with which bigrams that capture regulatory
shocks related to climate change occur in earnings calls. CCExposurePhy measures the relative
frequency with which bigrams that capture physical shocks related to climate change occur in
earnings calls. For each exposure measure, we construct the time series for firms in the top-10
industries (see Table III). Table A.1 provides detailed variable definitions. (Color figure can be
viewed at wileyonlinelibrary.com)

are easy to understand and compute, readily available for subscribers of environmental, social, and governance (ESG) databases, and genuinely related to
changes in the global climate.
We expect that regulatory climate topics arise more frequently in earnings
calls of large carbon emitters, as they are more strongly affected by carbon
taxes or related regulations. At the same time, regulatory threats related to
emissions may also spur technological innovation that provides firms with
opportunities in the marketplace.25 Furthermore, some firms’ emissions may
be “good” in supporting the transition to a greener economy; these firms,
25 For example, utilities with a large carbon footprint may have strong incentives to develop low-

carbon alternatives (e.g., wind farms, solar farms), which provide future opportunities. Indeed, as

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Firm-Level Climate Change Exposure

The Journal of Finance®

called “climate enablers,” include, for example, manufacturers of building materials that help houses become more energy-efficient. Finally, carbon emissions should be unrelated to the exposure to physical shocks at the firm
level.
We test these predictions by regressing the exposure measures on lagged
emission values (we use lagged values because emissions covering year t −
1 are reported in year t). Table IV, Panel A, reports the results. In column (1), we observe a strong positive association between Total Emissions
and CCExposure. As predicted, this association originates from positive
correlations between emissions and both CCExposureOpp (column (2)) and
CCExposureReg (column (3)). A one-standard-deviation increase in the emissions variable is associated with an increase in CCExposureReg equal to 23% of
its standard deviation (using values for the regression sample). In column (4),
we find no association between emissions and physical exposure.
B.4. Climate Change Exposure and Public Attention to Climate Change
Time-series variation in public attention to climate change, as proxied by
WSJ CC News Index, has been shown to affect financial market participants
(e.g., Choi, Gao, and Jiang (2020) or Ilhan, Sautner, and Vilkov (2021)). Accordingly, we expect earnings call discussions to react to the salience of climate
topics in the public arena. Indeed, Table IV, Panel B, shows that measured climate change exposure is higher at times when public climate attention rises.
In column (1), a one-standard-deviation increase in WSJ CC News Index is
associated with an increase in CCExposure of 0.05 (5% of the mean within
the regression sample). This effect reflects a positive association between WSJ
CC News Index and both CCExposureOpp and CCExposureReg. Hence, when
public climate attention is high, earnings calls discuss regulatory shocks and
climate opportunities more extensively. Higher values of WSJ CC News Index do not translate into more discussions of physical shocks. This suggests
that CCExposurePhy mostly captures firm-specific physical shocks, rather than
economy-wide shocks that make it to the WSJ (this conclusion is consistent
with the time-series evidence in Figure 3).
IV. Variance Decomposition and Role of Measurement Error
A. Variance Decomposition
We conduct a variance analysis to examine the extent to which CCExposure
and its components quantify firm-level variation in climate change exposure.
Table V reports the incremental explanatory power from conditioning the
exposure measures on fixed effects that plausibly drive the variation. Time
fixed effects (i.e., economy-wide changes in aggregate exposure) explain little
mentioned above, Cohen, Gurun, and Nguyen (2021) demonstrate that some of the largest carbon
emitters produce more and better green innovation than other firms.

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Table IV

Climate Change Exposure Measures: Effects of Carbon Emissions
and Climate Change News
This table reports regressions that relate carbon emissions and climate change news to the climate change exposure measures. Regressions are estimated at the firm-year level. CCExposure
measures the relative frequency with which bigrams related to climate change occur in earnings
calls. CCExposureOpp measures the relative frequency with which bigrams that capture opportunities related to climate change occur in earnings call transcripts. CCExposureReg measures the
relative frequency with which bigrams that capture regulatory shocks related to climate change
occur in earnings calls. CCExposurePhy measures the relative frequency with which bigrams that
capture physical shocks related to climate change occur in earnings calls. For all measure, we
average values of the four earnings calls during the year. Total Emissions is the sum of a firm’s
Scope 1 and Scope 2 carbon emissions. W SJ CC News Index is a time-series index developed in
Engle et al. (2020) that captures climate change news in the Wall Street Journal. We divide the
coefficient on WSJ Climate Change News Index by 100. The regressions control for Log(Assets),
Debt/Assets, Cash/Assets, PP&E/Assets, EBIT/Assets, CAPEX/Assets, and R&D/Assets (all in
t − 1). In Panel B, we do not include time-varying industry fixed effects, as WSJ CC News Index
varies only in the time series. Standard errors, clustered at the industry-year level, are in parentheses. Table A.1 defines all variables in detail. *p < 0.1; **p < 0.05; ***p < 0.01.
Panel A: Carbon Emissions
CCExposurei,t CCExposureOpp
CCExposureReg
CCExposurePhy
i,t
i,t
i,t
(1)
(2)
(3)
(4)
Log(1 + Total Emissionsi,t−1 )
Model
Sample
Controls
Industry × Year Fixed Effects
Industry Fixed Effects
Country Fixed Effects
N
Adj. R2

0.169∗∗∗
(0.023)
OLS
All
Yes
Yes
No
Yes
30,905
0.390

0.036∗∗∗
(0.009)
OLS
All
Yes
Yes
No
Yes
30,905
0.267

0.023∗∗∗
(0.003)
OLS
All
Yes
Yes
No
Yes
30,905
0.145

−0.000
(0.001)
OLS
All
Yes
Yes
No
Yes
30,905
0.035

Panel B: Public Attention to Climate Change
CCExposurei,t CCExposureOpp
CCExposureReg
CCExposurePhy
i,t
i,t
i,t
(1)
(2)
(3)
(4)
W SJ CC News Indext
Model
Sample
Controls
Industry × Year Fixed Effects
Industry Fixed Effects
Country Fixed Effects
N
Adj. R2

0.427∗∗
(0.168)
OLS
All
Yes
No
Yes
Yes
54,824
0.298

0.154∗
(0.089)
OLS
All
Yes
No
Yes
Yes
54,824
0.185

0.034∗∗∗
(0.010)
OLS
All
Yes
No
Yes
Yes
54,824
0.090

0.002
(0.004)
OLS
All
Yes
No
Yes
Yes
54,824
0.024

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Firm-Level Climate Change Exposure

The Journal of Finance®
Table V

Variance Decomposition of Climate Change Exposure Measures
This table provides a variance decomposition of the climate change exposure measures. Regressions are estimated at the firm-year level. In Panel A, the table reports the incremental R2 from
adding a specific fixed effect. In Panel B, the table decomposes the variation into a firm fixed
effect and a residual component. CCExposure measures the relative frequency with which climate change bigrams occur in earnings calls. CCExposureOpp measures the relative frequency
with which bigrams that capture opportunities related to climate change occur in earnings calls.
CCExposureReg measures the relative frequency with which bigrams that capture regulatory
shocks related to climate change occur in earnings calls. CCExposurePhy measures the relative
frequency with which bigrams that capture physical shocks related to climate change occur in
earnings calls. For all measures, we average values of the four earnings calls during the year.
Table A.1 defines all variables in detail.
CCExposurei,t
(1)

CCExposureOpp
CCExposureReg
CCExposurePhy
i,t
i,t
i,t
(2)
(3)
(4)

Panel A: Incremental R2
Year Fixed Effect
Industry Fixed Effect
Industry × Year Fixed Effect
Country Fixed Effect
“Firm Level”
Sum

0.7%
27.1%
1.9%
0.6%
69.7%
100.0%

0.7%
16.9%
2.6%
0.7%
79.1%
100.0%

0.5%
7.8%
1.4%
0.4%
89.9%
100.0%

0.05%
2.0%
1.5%
0.3%
96.2%
100.0%

Panel B: Fraction of Variation
Firm Fixed Effect:
Permanent differences across firms
within sector and countries
Residual:
Variation over time in the identity
of firms within industries and countries
most affected by exposure variable
Sum

51.6%

56.4%

44.7%

45.1%

48.4%
100.0%

43.7%
100.0%

55.3%
100.0%

54.9%
100.0%

variation, yielding an incremental R2 below 1% for each measure. For industry
fixed effects, the same observation holds only for CCExposurePhy . In contrast,
exposures to opportunity or regulatory shocks have a sizeable industry component (17% and 8%, respectively), which might stem from regulation targeting
specific industries or technological developments affecting entire sectors. The
interaction between industry and time fixed effects accounts for, at most, an
additional 2.6% of the variation (in the case of CCExposureOpp ). Country fixed
effects provide little additional explanatory power, which mitigates concerns
that our measures are strongly affected by the native language in a country
or how distant this language is from English. Depending on the measure, between 70% and 96% of the variation is unexplained by these sets of fixed effects.
Thus, variation plays out at the firm level, rather than at the level of the country, industry, or over time. (The high unexplained variation for CCExposurePhy

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1477

is unsurprising given that exposure to physical shocks depends highly on the
location of a firm’s production sites or insurance policies.) Adding firm fixed
effects, permanent differences across firms in an industry and country account
for 52%, 56%, 45%, and 45% of the variation of CCExposure, CCExposureOpp ,
CCExposureReg, and CCExposurePhy , respectively. The remaining 48%, 44%,
55%, and 55%, respectively, come from variation over time in the identity
of firms in industries and countries most affected by the respective climate
change variables.
B. Assessing Measurement Error
We interpret the large share of variance within the firm-year as capturing
economically meaningful heterogeneity. Under this view, a firm’s idiosyncratic
exposure to climate change is the key determinant of the measured variation. A
plausible alternative explanation is that part of the firm-level variation reflects
idiosyncratic measurement error. We conduct several tests that dispel this alternative. First, we note that we find robust associations between CCExposure
and important real and financial outcomes (as do other papers). These findings suggest that the variation reflected in firm-level CCExposure is not simply noise.
Second, following Hassan et al. (2019), we quantify the amount of measurement error contained in the firm-level variation by assuming that a firm’s
“true” exposure follows a first-order autoregressive (AR) process. We then
assume that CCExposure measures this true exposure with classical (i.i.d.)
measurement error.26 Suppose a valid instrument for (lagged) CCExposurei,t−1
were available. In this case, one could back out the share of its variation consisting of measurement error by comparing the OLS and instrumental variable (IV) coefficients. Intuitively, the idea is that candidate IVs measure true
climate change exposure with error. Under the i.i.d. assumption, the measurement error in the IV is uncorrelated with that in CCExposurei,t and thus can
be used to “purge” the latter’s measurement error. For this procedure to work,
we do not assume that the IV has lower measurement error—indeed, it is
likely to have higher measurement error. We assume only that the measurement error in the IV and in measured climate change exposure are statistically
independent.
Table VI shows three implementations of this idea. One implementation uses
an alternative exposure measure constructed by applying our algorithm to the
“Management Discussion and Analysis” (MD&A) section in firms’ annual 10K
filings. The two other implementations use lags of this alternative measure
26 Under these assumptions, if the correlation between two different lags of the firm-year data
is known, the AR(1) parameter and the estimated measurement error can be backed out. For
example, if the first lag has a correlation of 0.45 (=0.5*0.9) and the second lag a correlation of 0.41
(=0.5*0.9*0.9), that would imply measurement error of 50% of the variation and an AR coefficient
of 0.9. If the first lag has a correlation of 0.9 and the second 0.8, this implies no measurement error
and an AR coefficient of 0.9.

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Firm-Level Climate Change Exposure

The Journal of Finance®
Table VI

Quantifying Measurement Error in Climate Change Exposure
Measures
This table shows AR(1) regressions of climate change exposure. Regressions are estimated at
the firm-year level. CCExposure measures the relative frequency with which climate change bigrams occur in earnings calls. We average values of the four earnings calls during the year.
CCExposure10K measures climate change exposure by applying our algorithm to the “Management Discussion and Analysis” (MD&A) section in firms’ annual 10K filings. Following Hassan
et al. (2019), CCExposure and CCExposure10K in this table are standardized by subtracting the
sample mean and dividing by the sample standard deviation. Implied Share Measurement Error is calculated as 1 − (β̂OLS /β̂IV ), where β̂OLS is the estimated coefficient in CCExposurei,t =
α + βCCExposurei,t−1 +  and β̂IV is the coefficient on the instrumented CCExposurei,t in the same
specification. To obtain bootstrapped standard errors for Implied Share Measurement Error, we
repeat the following procedure 500 times: draw a random sample of the same sample size (with
replacement and clustered by firm) from our regression sample, run the two regressions, and obtain the implied share of measurement error. These standard errors are clustered at the firm level.
Table A.1 defines all variables in detail. *p < 0.1; **p < 0.05; ***p < 0.01.
Panel A: Overall Variation

CCExposurei,t−1
Model
Instrument
Sample
Industry × Year Fixed Effects
N
Implied Share Measurement Error

(1)

(2)

0.922∗∗∗

1.008∗∗∗

(0.002)
OLS
U.S.
No
47,589

CCExposurei,t
(3)
0.991∗∗∗

(0.003)
(0.003)
IV
IV
10K
CCExposure10K
i,t−1 CCExposurei,t−2
U.S.
U.S.
No
No
47,589
41,794
0.085
0.069
(0.007)
(0.007)

(4)
0.958∗∗∗
(0.002)
IV
CCExposurei,t−2
U.S.
No
41,794
0.037
(0.005)

Panel B: Firm-Level Variation

CCExposurei,t−1
Model
Instrument
Sample
Industry × Year Fixed Effects
N
Implied Share Measurement Error

(1)

(2)

0.886∗∗∗

0.992∗∗∗

(0.002)
OLS
U.S.
Yes
47,502

CCExposurei,t
(3)
0.966∗∗∗

(4)

0.932∗∗∗
(0.004)
(0.002)
(0.003)
IV
IV
IV
10K
CCExposure10K
i,t−1 CCExposurei,t−2 CCExposurei,t−2
U.S.
U.S.
U.S.
Yes
Yes
Yes
47,502
41,712
41,712
0.107
0.083
0.050
(0.002)
(0.012)
(0.007)

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1478

1479

and CCExposure itself as instruments. While the estimates of the share of measurement error in CCExposure vary somewhat across the three approaches,
approximately 5% to 10% of the variation in measured CCExposure is due to
measurement error.27 The implied measurement error at the firm level (in
Panel B) is about 2 percentage points higher than in the overall variation
(Panel A). Although we interpret these results with due caution, they suggest
that measurement error in the firm-level dimension is higher than in the
overall panel, but only modestly. Thus, concerns that the variation displayed
at the firm level is subject to more measurement error than the overall climate
change exposure measure (before any fixed effects) are not substantiated.
V. Economic Applications
A. Real Outcomes: Green-Tech Jobs and Green Patents
Significant climate-related innovation is required to reach net-zero emissions by 2050 (Stern and Valero (2021)), implying huge investments by firms
in human capital and R&D. According to some estimates, incremental investments of $50 trillion are needed in solar technology, decarbonization, energy
efficiency, or carbon capture by 2050 (World Economic Forum (2021)). To illustrate that our exposure measures help predict real outcomes related to the
net-zero transition, we relate next year’s creation of disruptive green-tech jobs
and green patents to this year’s values of climate change exposure. Among the
sampled U.S. firms, for firm i and year t we estimate
Green Outcomei,t+1 = exp(αi + β log(1 + CCExposurei,t ) + γ Xi,t + δ j × δt + i,t+1 ),
(5)
where Green Outcomei,t+1 is #Green-Tech Jobsi,t+1 or #Green Patentsi,t+1 in
year t + 1 and CCExposurei,t is the climate change exposure measure in
year t (we include the overall and topic-based measures). The vector Xi,t
includes Log(Assets), Debt/Assets, Cash/Assets, PP&E/Assets, EBIT/Assets,
CAPEX/Assets, and R&D/Assets. The variables δ j × δt represent industryyear fixed effects. We account for industry shocks that vary over time, as firmlevel innovation-related activity contains a large time-varying industry component (Aghion et al. (2005)). As demonstrated in Table V, such variation is also
an important determinant of climate change exposure, making it important to
identify effects within industry-year pairs. We cluster standard errors at the
industry-year group level.
We estimate equation (5) using Poisson regressions, which have two advantages (Cohn, Liu, and Wardlaw (2022)). First, Poisson regressions account for
the distributional characteristics of our count-based outcomes (they provide
unbiased estimates for dependent variables with a large mass of values at
zero combined with severe skewness). Second, Poisson regressions allow use to
27 These estimates compare favorably to the amount of measurement error found using similar
assumptions in firm-level variables measured using accounting data (e.g., measures of total factor
productivity constructed by Bloom et al. (2018) and Collard-Wexler (2011)).

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Firm-Level Climate Change Exposure

The Journal of Finance®

include industry-year fixed effects without biasing the estimation. They thus
address the issue of separable group fixed effects (in our case at the industryyear level) by basing the estimation only on observations with at least one
nonzero value within a group. This is desirable, as it restricts the usable sample to those groups that are informative about the effects of CCExposure.28 For
robustness, we also estimate linear and log1plus-linear models (with and without industry-year fixed effects) on the unrestricted sample (we interpret these
models’ estimates with caution).
The estimation results for #Green-Tech Jobs are reported in Table VII. In
column (1), the estimates show that firms with higher overall exposure post
more vacancies for jobs in disruptive green technologies over the subsequent
year. A one-standard-deviation increase in CCExposure is associated with a
109% increase in the number of green-tech jobs over the next year.29 Columns
(2) to (4) consider the topic-based measures. As expected, the overall exposure
effect is due in large part to high-opportunity firms (column (2)). Firms with
higher regulatory exposure also plan to hire more green-tech workers than
firms with lower exposure (column (3)). We do not find that firms with larger
physical exposure post more green-tech jobs (column (4)). In column (5), we
continue to find that CCExposure positively predicts green-tech hiring if we
replace #Green-Tech Jobs with I(Green-Tech Jobs), an indicator for whether a
firm posts a green-tech job (we estimate a linear model with the same observations as in columns (1) to (4)). Similarly, in column (6) estimates are robust to
using the ratio of green-tech jobs to all tech jobs (Green-Tech Ratio). Column
(7) addresses the concern that high-exposure firms may simply recruit more
personnel in disruptive technologies across the board, without a specific focus
on green jobs per se (for example, because these firms happen to be more innovative). Specifically, we replace #Green-Tech Jobs with #Nongreen-Tech Jobs
and reestimate the regression in column (1). We do not find positive predictive effects of the exposure measure, which mitigates concerns of spurious
relationships. In fact, firms with higher climate change exposure hire less,
not more, nongreen-tech jobs. Overall, the data are more consistent with a recruiting shift from nongreen-tech jobs to green-tech jobs, rather than a general
expansion of tech-related hiring at high-exposure firms.
The results for green-tech jobs broadly extend to green patents in
Table VIII. In columns (1) to (3), firms with greater climate change exposure show more green patenting in the next year. A one-standard-deviation
28 Cohn, Liu, and Wardlaw (2022) show that log1plus-linear models may be biased in our context. The admission of separable group fixed effects in Poisson regressions differs from that in
other nonlinear count-data models. These alternative models are subject to the incidental parameter problem, which leads to biased and inconsistent estimates (Lancaster (2000)).
29 In a Poisson model, for a regression coefficient β, the magnitude of a one-standard-deviation
change in the independent variable is calculated as eβ×STD − 1. This effect size (when multiplied
by 100%) represents the percentage change in the dependent variable. We use the within-fixedeffects (rather than overall-panel) standard deviation to capture plausible variation. The large
magnitude of the effect also indicates that the average number of disruptive green-tech jobs is
relatively low.

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1480

Table VII

Poisson
U.S.
Yes
Yes
23,870
0.754
2.82
89.56
108.7

1.564∗∗∗
(0.199)

Poisson
U.S.
Yes
Yes
23,870
0.767
2.82
89.56
79.5

1.833∗∗∗
(0.229)

(2)

Poisson
U.S.
Yes
Yes
23,870
0.687
2.82
89.56
20.0

1.458∗∗∗
(0.445)

(3)

1.079
(1.217)
Poisson
U.S.
Yes
Yes
23,870
0.684
2.82
89.56
6.8

(4)

OLS
U.S.
Yes
Yes
23,870
0.116
0.07
0.26
14.0

0.077∗∗∗
(0.006)

I(#GreenTechJobs)i,t+1
(5)

OLS
U.S.
Yes
Yes
23,870
0.049
0.003
0.042
16.9

0.015∗∗∗
(0.003)

GreenTechRatioi,t+1
(6)

Poisson
U.S.
Yes
Yes
23,870
0.526
845.09
3613.42
−9.1

−0.204∗∗∗
(0.060)

#NongreenTechJobsi,t+1
(7)

1481

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Model
Sample
Controls
Industry x Year Fixed Effects
N
Adj./ps. R2
Dep. Variable: Mean
Dep. Variable: STD
Economic Effect, %

Log(1 + CCExposurePhy
i,t )

Log(1 + CCExposureReg
i,t )

Log(1 + CCExposureOpp
i,t )

Log(1 + CCExposurei,t )

(1)

#Green-Tech Jobsi,t+1

This table reports regressions that relate green-tech jobs to the climate change exposure measures. Regressions are estimated at the firm-year level.
#Green-Tech Jobs is the number of job postings for disruptive green-tech jobs. I(Green-Tech Jobs) is an indicator that equals one if #Green-Tech Jobs is
positive, and zero otherwise. #Nongreen-Tech Jobs is the number of job postings for nongreen disruptive tech jobs. Green-Tech Ratioi,t+1 is the number
of job postings for disruptive green jobs relative to the total number of all disruptive job postings. CCExposure, CCExposureOpp , CCExposureReg, and
CCExposurePhy are defined as in previous tables. The regressions control for Log(Assets), Debt/Assets, Cash/Assets, PP&E/Assets, EBIT/Assets,
CAPEX/Assets, and R&D/Assets (all in t). In columns (5) to (7), we use the same observations as in columns (1) to (4). In columns (1) to (4) and (7),
the economic effects are computed as the percentage change in the dependent variable for a one-standard-deviation change in the exposure variable
of interest. In columns (5) and (6), the economic effect is computed as the effect of a one-standard-deviation change in the exposure variable relative to
the standard deviation of the dependent variable. We use the within-fixed-effect standard deviations. Standard errors, clustered at the industry-year
level, are in parentheses. Table A.1 defines all variables in detail. *p < 0.1; **p < 0.05; ***p < 0.01.

Green-Tech Jobs and Climate Change Exposure Measures

Firm-Level Climate Change Exposure

Table VIII

Poisson
U.S.
Yes
Yes
21,914
0.617
0.28
4.07
71.7

1.102∗∗∗
(0.231)

Poisson
U.S.
Yes
Yes
21,914
0.603
0.28
4.07
32.0

0.854∗∗∗
(0.312)

(2)

Poisson
U.S.
Yes
Yes
21,914
0.614
0.28
4.07
47.3

3.061∗∗∗
(0.272)

(3)

−1.155
(2.865)
Poisson
U.S.
Yes
Yes
21,914
0.598
0.28
4.07
−6.9

(4)

OLS
U.S.
Yes
Yes
21,914
0.078
0.03
0.18
7.0

0.025∗∗∗
(0.003)

I(Green
Patents)i,t+1
(5)

OLS
U.S.
Yes
Yes
21,914
0.023
0.003
0.040
7.4

0.006∗∗∗
(0.001)

Green Patents
Ratioi,t+1
(6)

Poisson
U.S.
Yes
Yes
21,776
0.752
22.10
224.23
−19.3

−0.436∗∗∗
(0.118)

#Nongreen
Patentsi,t+1
(7)

The Journal of Finance®

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Model
Sample
Controls
Industry × Year Fixed Effects
N
Adj./ps. R2
Dep. Variable: Mean
Dep. Variable: STD
Economic Effect, %

Log(1 + CCExposurePhy
i,t )

Log(1 + CCExposureReg
i,t )

Log(1 + CCExposureOpp
i,t )

Log(1 + CCExposurei,t )

(1)

#Green Patentsi,t+1

This table reports regressions that relate green patents to the climate change exposure measures. Regressions are estimated at the firm-year level.
#Green Patents is the number of green patents. I(Green Patents) is an indicator that equals one if #Green Patents is positive, and zero otherwise.
Green Patents Ratioi,t+1 is the number of green patents relative to the total number of all patents. #Nongreen Patents is the number of nongreen
patents. CCExposure, CCExposureOpp , CCExposureReg, and CCExposurePhy are defined as in previous tables. The regressions control for Log(Assets),
Debt/Assets, Cash/Assets, PP&E/Assets, EBIT/Assets, CAPEX/Assets, and R&D/Assets (all in t). In columns (5) to (7), we use the same observations
as in columns (1) to (4) (the Poisson estimation in Column (7) drops some observations). In columns (1) to (4) and (7), the economic effects are computed
as the percentage change in the dependent variable for a one-standard-deviation change in the exposure variable of interest. In columns (5) and (6),
the economic effect is computed as the effect of a one-standard-deviation change in the exposure variable relative to the standard deviation of the
dependent variable. We use the within-fixed-effect standard deviations. Standard errors, clustered at the industry-year level, are in parentheses.
Table A.1 defines all variables in detail. *p < 0.1; **p < 0.05; ***p < 0.01.

Green Patents and Climate Change Exposure Measures

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1483

increase in CCExposure is associated with a 72% increase in the number of
green patents over the next year. The effect for CCExposureOpp is intuitive, as
green innovation provides business opportunities during the net-zero transition. To illustrate the intuition behind the effects for CCExposureReg, the case of
Caterpillar is insightful. This firm is not only the top green patent producer in
our sample (see Section I.E), but it also exhibits high measured regulatory exposure. This latter feature stems from its legacy business related to mining and
Reg
= 0.09, in the top decile of
diesel engines (sample mean of CCExposureCaterpillar
Reg
CCExposure ). We do not find that firms with larger physical exposure generate more green patents (column (4)). In columns (5) and (6), we continue to
find that CCExposure predicts green patenting if we replace #Green Patents
with an indicator for whether a firm created green patents (column (5)) or with
the green patents ratio as in Cohen, Gurun, and Nguyen (2021) (column (6)).
Column (7) shows that high-exposure firms are not simply more innovative
in general; the estimates indicate fewer, not more, nongreen patents by firms
with high values of CCExposure.
Table IA.XIII shows that the results in Tables VII and VIII are robust to
controlling for carbon emissions. This finding demonstrates that our measures
contain additional information beyond what is reflected in emissions (the sample size is reduced in the panel due to the lower number of observations on
carbon emissions).
In Table IA.XIV, a series of alternative specifications continue to show that
CCExposure predicts green-tech job creation. In column (1), we dispel concerns
related to strategic disclosure in earnings calls (Mayew (2008), Hassan et al.
(2019)). One specific potential concern is that managers may want to distract
attention from poor performance and strategically “cheap talk” about climate
change (Hail, Kim, and Zhang (2021)). Following Hassan et al. (2019), we test
for this possibility by adding a control for the firm’s overall sentiment (share
of positive and negative tone words across the earnings call transcript) and
two proxies for recent performance.30 The estimates show that our results are
robust to adding these controls. In column (2), we restrict the sample to firmyears within the BG database to ensure that the results are unaffected by
how we classify the firms missing in BG; recall that we assume no green-tech
job creation for these firms (BG may systematically miss scraping some firms’
postings). In column (3), exposure is based on a count of bigrams in the Q&A
session, that is, the part of the call that is less under management control and
in turn less subject to concerns of strategic (non)disclosure and greenwashing.
In column (4), CCSentiment Pos strongly predicts next-year green-tech job creation, while CCSentiment Neg is insignificant (albeit marginally). In column (5),
CCRisk is positively associated with green-tech job creation. In column (6) to
30 We measure performance as the precall stock return accumulated over the seven days prior
to the earnings call and the earnings surprise. Earnings surprise is defined as earnings per share
before extraordinary items minus earnings per share in the same quarter of the prior year, divided
by the price per share at the beginning of the quarter (Ball and Bartov (1996)). We average the
two variables across the earnings calls of a firm-year to obtain an annual measure.

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Firm-Level Climate Change Exposure

The Journal of Finance®

(9), results hold if we estimate OLS specifications to address potential concerns
with the Poisson specification. We estimate models with and without industryyear fixed effects, and with #Green-Tech Jobs or Log(1 + #Green-Tech Jobs). We
also provide estimates that replace the log1plus version of CCExposure with
an unlogged version. Table IA.XV applies the same alternative specifications
to green patenting. The estimates show that our results continue to hold.
Table IA.XVI reports regressions for the subsamples in which the exposure
measures that rely exclusively on the initial bigrams indicate zero exposure. In
these estimations, our exposure measures continue to predict green outcomes.
This finding corroborates the performance gain from using more subtle and
less visible climate change bigrams, as the estimation is identified from the
bigrams obtained through the keyword search algorithm.
Finally, Table IA.XVII documents the covariate balance of observations that
are either included or excluded from the estimations in Tables VII and VIII.
Excluded firm-years exhibit lower climate change exposure, implying that our
estimates are obtained within the set of firms for which climate change issues
are most pressing.
B. Financial Market Outcomes
B.1. Options Market Risks and Risk Premiums
Firms with higher regulatory exposure are more strongly affected by future
regulations to combat global warming, and uncertainty over such regulations
should be priced in the options market (Kelly, Pastor, and Veronesi (2016)).
Likewise, climate opportunities are risky, with plenty of uncertainty surrounding investments in green technologies or renewable energy. We therefore test
whether climate change exposure is related to option-implied risks and risk
premiums. We consider three sets of risk variables. First, to quantify general
risks, we use three implied central moments, namely, variance (IVar), skewness (ISkew), and kurtosis (IKurt). Second, we calculate two heuristic measures quantifying the relative expensiveness of protection against left (SlopeD)
and right (SlopeU ) tail risks.31 Third, we use the variance risk premium (V RP)
to measure the premiums that investors are willing to pay to hedge against
general climate-related variance risk (or uncertainty, as suggested in Bali and
Zhou (2016)). Using each of these variables, we run the regression:
OI Outcomei,t+1 = αi + β Log(1 + CCExposurei,t ) + γ Xi,t + δ j × δt + i,t+1 , (6)
where OI Outcomei,t+1 is an option-implied measure for firm i measured at the
end of quarter t (i.e., a conditional expectation of some quantity over the period

31 The variable SlopeD increases when the cost of left-tail protection goes up (relative to the cost
of at-the-money [ATM] options), and SlopeU decreases (becomes more negative) when the relative
cost of obtaining upside growth increases. Note that Sautner et al. (2022) define their measure of
SlopeU as minus one times SlopeU .

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1485

t + 1), and CCExposurei,t is firm i’s climate change exposure in quarter t.32 The
vector Xi,t includes the same controls as before (delayed to be available in the
third quarter after the annual close of the fiscal period). The variables δ j and
δt represent industry and year fixed effects, respectively. We cluster standard
errors at the industry-year level.
Table IX, Panel A, documents that CCExposure is strongly linked to forwardlooking risks and risk premiums. In columns (2) and (3), CCExposure predicts
a more negatively skewed return distribution (ISkew) and fatter tails (IKurt).
Furthermore, tail exposure is more costly for firms with higher climate change
exposure. More specifically, downside protection in column (4) (positive and significant coefficient on SlopeD) and upside potential in column (5) (negative and
significant coefficient on SlopeU ) become more expensive when CCExposure
is higher. In terms of magnitudes, the effects are strongest in column (3) for
IKurt. A one-standard-deviation change in CCExposure is associated with a
change in IKurt equivalent to 7% of its standard deviation. The effects for
SlopeD and SlopeU are 4.5% and 4.1%, respectively.
The three remaining panels consider the topic-based measures. Earnings
calls should contain more discussions of climate-related opportunities if a firm
is well positioned for the growth potential arising from climate change. The
realization of these opportunities could lead to large gains if successful and to
large losses if unsuccessful. Investors may in turn trade in the options market
to reflect the two-sided effects of climate opportunities. Panel B confirms this
intuition: the tail effects for CCExposureOpp in columns (4) and (5) are similar
compared to the corresponding estimates in Panel A. The magnitude of a onestandard-deviation increase in CCExposureOpp is 4.3% for SlopeD and 3.9%
for SlopeU , respectively. Thus, it is not only the case that options are more
expensive on both tails if climate opportunities are higher, but also that the
cost of upside potential grows faster than the cost of downside crash protection.
The link between CCExposureOpp and V RP in column (6) demonstrates that
the wedge between the implied and “historically fair” price of out-of-the-money
(OTM) calls increases with opportunity exposure. Thus, investors are ready to
pay an extra (volatility) premium when buying options on stocks with climaterelated upside potential. However, the effect is small in magnitude and only
marginally significant.
In Panel C, the pattern for CCExposureReg is similar to that for
CCExposureOpp , though the magnitudes are smaller. While the right-tail option expensiveness increases by 2.6% of its standard deviation (i.e., SlopeU
diminishes) for a one-standard-deviation change in CCExposureReg, the crash
protection grows by 2.3%. This confirms our earlier evidence that some firms
with high regulatory exposure face downside risks and upside potential due to
32 When computing quarterly versions of our measures, we encounter the issue that any specific
earnings call in a year might not discuss climate change, even though the conversation turns to
the issue in surrounding calls. These incidental gaps in the quarterly data (where the measured
CCExposure = 0) do not reflect business realities. Therefore, we preprocess the quarterly climate
change exposure following a method outlined in Sautner et al. (2022), which exponentially smooths
each metric for each firm with a half-life of three quarters.

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Firm-Level Climate Change Exposure

Table IX

Forward-Looking Risk Measures and Climate Change Exposure
Measures
This table reports regressions that relate forward-looking risk measures to the climate change
exposure measures. Regressions are estimated at the firm-quarter level. IVar is implied variance, ISkew is implied skewness, IKurt is implied kurtosis, SlopeD and SlopeU are implied
volatility slopes on the left and right of the distribution, and V RP is the variance risk premium. Construction of the option-implied measures is detailed in Section II of the Internet Appendix. CCExposure, CCExposureOpp , CCExposureReg, and CCExposurePhy are defined as in previous tables. The regressions control for Log(Assets), Debt/Assets, Cash/Assets, PP&E/Assets,
EBIT/Assets, CAPEX/Assets, and R&D/Assets (all in t). The economic effect is computed as the
effect of a one-standard-deviation change in the exposure variable of interest relative to the standard deviation of the dependent variable (in %). We use the within-fixed-effect standard deviation.
Standard errors, clustered at the industry-year level, are in parentheses. Table A.1 defines all
variables in detail. *p < 0.1; **p < 0.05; ***p < 0.01.
IVari,t+1
(1)

ISkewi,t+1
(2)

IKurti,t+1
(3)

SlopeDi,t+1
(4)

SlopeUi,t+1
(5)

V RPi,t+1
(6)

−0.002
(0.005)
42,093
0.424
−0.42

−0.049∗∗∗
(0.009)
42,093
0.140
−4.57

0.303∗∗∗
(0.049)
42,093
0.349
7.01

0.033∗∗∗
(0.007)
42,093
0.231
4.46

−0.026∗∗∗
(0.006)
42,093
0.236
−4.14

0.003
(0.002)
42,089
0.094
0.89

Panel A: CCExposure
Log(1 + CCExposurei,t )
N
Adj. R2
Economic Effect, %
Panel B: CCExposureOpp
Log(1 + CCExposureOpp
i,t )
N
Adj. R2
Economic Effect, %

0.004
(0.009)
42,093
0.424
0.56

−0.053∗∗∗
(0.012)
42,093
0.140
−3.27

0.403∗∗∗
(0.067)
42,093
0.348
6.18

0.048∗∗∗
(0.011)
42,093
0.231
4.30

−0.037∗∗∗
(0.010)
42,093
0.236
−3.91

0.006∗
(0.003)
42,089
0.094
1.19

−0.007
(0.014)
42,093
0.424
−0.46

−0.075∗∗∗
(0.024)
42,093
0.139
−2.19

0.453∗∗∗
(0.146)
42,093
0.346
3.28

0.054∗∗
(0.027)
42,093
0.230
2.28

−0.053∗∗∗
(0.019)
42,093
0.235
−2.64

0.005
(0.008)
42,089
0.094
0.47

−0.033
(0.020)
42,093
0.424
−1.02

−0.083
(0.059)
42,093
0.139
−1.13

0.145∗∗∗
(0.048)
42,093
0.230
2.85

−0.175*∗∗
(0.048)
42,093
0.236
−4.06

−0.012
(0.011)
42,089
0.094
−0.52

Panel C: CCExposureReg
Log(1 + CCExposureReg
i,t )
N
Adj. R2
Economic Effect, %
Panel D: CCExposurePhy
Log(1 + CCExposurePhy
i,t )
N
Adj. R2
Economic Effect, %

1.336∗∗∗
(0.319)
42,093
0.347
4.51

(Continued)

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The Journal of Finance®

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Table IX—Continued
Model
Sample
Controls
Industry × Year Fixed Effects
Dep. Variable: Mean
Dep. Variable: STD

OLS

OLS

OLS

OLS

OLS

OLS

S&P500
Yes
Yes
0.176
0.199

S&P500
Yes
Yes
−0.571
0.453

S&P500
Yes
Yes
4.678
1.823

S&P500
Yes
Yes
0.317
0.312

S&P500
Yes
Yes
−0.101
0.265

S&P500
Yes
Yes
0.042
0.142

their green innovation activity. In Panel D, the effects for CCExposurePhy are
similar to those of the other measures.33
Overall, climate change exposure is priced in the options market. Considering all the evidence, stocks with higher exposure have probability mass shifted
to the tails of the distribution, making crash protection and upside potential
relatively more expensive. Obtaining protection and upside growth potential
comes at a premium, which increases more strongly for firms facing higher opportunities. We acknowledge that the effect magnitudes are modest and hardly
tradeable after transaction costs.
B.2. Cross Section of Stock Returns
Climate change exposure is related to risks and risk premiums in the options
market. Consequently, systematic risk related to CCExposure may be associated with a risk premium in the cross section of returns. That said, testing
for the pricing effects of a climate change exposure factor, labeled CCEXPOSURE, is challenging for several reasons. A conceptual challenge arises because return effects are theoretically more ambiguous to predict compared to
the risk measures. On the one hand, firms with high betas for CCEXPOSURE
should be more risky and—in expectation—earn a risk premium.34 On the
other hand, the relations may actually be the opposite, with risks gradually
getting priced in during the sample period; as risks emerge, stock prices decline, implying lower realized returns. Pastor, Stambaugh, and Taylor (2021)
illustrate this difference between ex ante and ex post returns. An estimation
challenge arises because CCExposure reflects the attention devoted to climate
topics at a point in time. This implies that the pricing of CCEXPOSURE should
vary over time, requiring the estimation of conditional risk premiums. Another
33 Our inference for the pricing of physical exposure is different from the link between hurricane
uncertainty and variance pricing in Kruttli, Roth Tran, and Watugala (2021). For example, while
we concentrate on the unconditional pricing using the expected V RP, Kruttli, Roth Tran, and
Watugala (2021) study dynamics of the realized V RP. However, these authors also conclude that,
especially in the early sample years, investors underprice variance in options of firms strongly
exposed to extreme weather events.
34 For example, such firms face higher uncertainty related to future developments in climaterelated areas, that is, their valuation should include real option value depending on the path of
climate-related technologies, regulations, or physical climate shifts.

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Firm-Level Climate Change Exposure

The Journal of Finance®

challenge arises because the number of assets for such tests is large relative to
the time points available for the estimation—less than 20 years of data.
With these challenges in mind, we investigate the conditional pricing of CCEXPOSURE in the cross section of stocks. We follow Jamilov, Rey, and Tahoun
(2021) and construct the factor as an unexpected shock to the aggregate value
of CCExposure. This involves three primary steps. First, we convert quarterly transcript-level values of CCExposurei,t for U.S-traded firms to a monthly
frequency by propagating the last exposure values for up to three months forward (i.e., we match the month-year of each climate change exposure to the
month-year of the respective quarterly transcript). Second, we compute crosssectional monthly averages of CCExposurem . Third, we take the first differences in these monthly averages as a proxy for unexpected monthly shocks to
the aggregate exposure level, and use them as the CCEXPOSURE factor.35
To examine the conditional pricing of CCEXPOSURE among S&P500 firms,
we follow Gagliardini, Ossola, and Scaillet (2016, GOS), who provide a conditional extension of the two-pass regression approach (Fama and MacBeth
(1973)). We use this approach as it delivers good small-sample performance
when—as in our case—the cross section is large relative to the time series.
GOS assume a linear conditional factor model for excess returns with timevarying factor exposures and risk premiums. They model the parameters as
linear functions of lagged instruments. The factor loadings βi,m depend on
stock-specific instruments (Zi,m−1 ) as well as common instruments (Zm−1 ), and
the factor expectations only on common instruments. Under this framework,
the conditional expected return on stock i in month m is

E[Ri,m |Zi,m−1 , Zm−1 ] = βi,m
λm ,

(7)

where the risk premium λm is the sum of the conditional factor expectation
E[Fm |Zm−1 ] and the process νm , estimated from the cross section of stocks. The
process νm allows the estimated risk premium to deviate from the conditional
expectation of a factor due to market imperfections for tradeable factors (Cremers, Petajisto, and Zitzewitz (2013), GOS) and it also reveals an “implicit
cost” of projecting a nontradeable factor (like ours) on returns. A similar framework is used, for example, in Barras and Malkhozov (2016). As in GOS, we use
as common instruments the term spread and the default spread and as the
stock-specific instrument the log of the book-to-market ratio (see Section I.G
for definitions). We estimate the time-varying components of the risk premiums with the four-factor model by Carhart (1997) that is augmented with the
CCEXPOSURE factor.36
When performing the estimation, we obtain average conditional risk premiums in line with expectations (risk premiums for the market, size, value, and
35 The factor is standardized to have zero mean and annual volatility of 10%. Results are robust

to using the residuals from an AR(1) process fitted to the monthly exposure series, as implemented
in Jamilov, Rey, and Tahoun (2021) (the resulting factors are almost perfectly correlated). However,
fitting an AR(1) process may introduce look-ahead bias.
36 The factor is essentially orthogonal to the other factors, with all unconditional correlations
being smaller than 0.05. The results are robust to using three- and five-factor models.

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Table X

Climate Change Exposure Factor: Components of F and ν
This table reports the estimated annualized components of F and ν for the four-factor Carhart
(1997) model augmented by a CCEXPOSURE factor. The estimation is based on the conditional
framework by Gagliardini, Ossola, and Scaillet (2016). The factor is constructed as the monthly
change in the cross-sectional average of CCExposure across U.S.-traded sample firms. The factor
is standardized to have zero mean and an annual volatility of 10%. All instruments are centered
and standardized in the time series. The common instruments are the default spread and the
term spread, and the firm-specific instrument is the log of the book-to-market ratio. *p < 0.1;
**p < 0.05; ***p < 0.01.

Factors

Instruments

F
(1)

SE(F )
(2)

ν
(3)

SE(ν)
(4)

Market

Constant
Default Spread
Term Spread
Constant
Default Spread
Term Spread
Constant
Default Spread
Term Spread
Constant
Default Spread
Term Spread
Constant
Default Spread
Term Spread

8.9838∗∗∗
−1.0201
−1.9715
2.3669
2.5406
2.1356
−2.1553
−3.6834
4.8748∗∗
1.3199
−14.359*
2.4766
−0.0032
0.0805
−0.2941

3.4981
5.4550
3.3962
1.9164
2.0404
1.8985
2.0893
3.9437
2.2504
3.5668
8.2567
2.9728
2.3008
2.7644
2.6282

2.3908∗∗∗
2.4676∗∗∗
1.4489∗∗
2.6523∗
−1.3983
−4.6391***
−3.5959***
3.7360∗∗∗
−0.0444
7.2011∗∗∗
7.8356∗∗∗
−0.6825
3.7273∗∗∗
3.1262∗∗∗
−0.1834

0.7110
0.8715
0.6705
1.3459
1.0227
0.9302
1.0965
0.8545
0.8434
1.6444
1.7552
1.2843
1.1654
1.0855
0.9978

SMB

HML

MOM

CCEXPOSURE

momentum factors are 11.4%, 5.0%, −5.8%, and 8.5% per annum (p.a.), respectively). The CCEXPOSURE premium is positive, on average (3.7% p.a.), and
we obtain positive point estimates for most months. More importantly, the risk
premium is not constant over time, and we reject the hypotheses that its two
components are constant (p-values of 0.0137 and 0.0001, respectively).
In Table X, we report the estimated annualized components of the risk premium λm , that is, the estimates of F and ν. Similar to the results in GOS, most
of the action for the risk premiums comes through the cross-sectional component ν. For CCEXPOSURE, ν has a positive unconditional mean (constant of
3.73%) and a positive link to the default spread (3.13%)—both are highly significant. This indicates that stocks with high exposure to the CCEXPOSURE
factor are expected to earn higher returns, especially when market-wide default risk increases.
The time series of the estimated risk premium on CCEXPOSURE is depicted
in Figure 4. The series illustrates significant variability over time, with a large
spike around the financial crisis. Further tentative interpretations indicate a
temporary spike around the time of Hurricane Sandy (October 2012) and the
Doha Climate Summit (November 2012). Another temporary spike occurs just
after the Paris Agreement (December 2015). Considering the most recent five
years, the risk premium was lowest around the time President Trump took

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Firm-Level Climate Change Exposure

The Journal of Finance®

Figure 4. Risk premium on the climate change exposure factor. This figure shows the time
series of the risk premium on the CCEXPOSURE factor, estimated together with the four-factor
Carhart (1997) model using the conditional framework of Gagliardini, Ossola, and Scaillet (2016).
The factor is constructed as the monthly change in the cross-sectional average of CCExposure
across U.S.-traded sample firms. The factor is standardized to have zero mean and an annual
volatility of 10%. (Color figure can be viewed at wileyonlinelibrary.com)

office (January 2017); it gradually increased thereafter with a drop around the
onset of the COVID pandemic.37
We emphasize that our objective is not to create an ultimate climate factor
to be added to the factor zoo (Feng, Giglio, and Xiu (2020)), but instead to show
that attention to climate topics in earnings calls is linked to systematic risk,
with shocks to such attention potentially being priced in the cross section (following a narrative as in Shiller (2017)).
VI. Conclusion
In this paper, we introduce a new method that identifies firm-level climate
change exposure from word combinations signaling climate change conversation in earnings conference calls. As these calls reflect the demand side
(analysts) and the supply side (management) of a “market for information,”
37 As in the previous applications, we estimate the risk premiums separately by topic. The topicbased premiums are on average positive, but demonstrate distinct time-series patterns. For example, when the physical risk premium goes up, the opportunity risk premium tends to go down. We
do not want to overemphasize the topic-based differences here, as our framework uses the same
set of instruments for all topic-based factors.

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our measures reflect the combined views of key stakeholders about a firm’s
climate change exposure. Furthermore, earnings calls are largely forwardlooking; while analysts review past results, they also spend much of their time
probing management about future plans (Huang et al. (2018)).
Our measures build on recent work that identifies earnings calls as a source
for identifying the various risks and opportunities that firms face over time. We
adjust the approach of this prior work along several critical dimensions, allowing us to capture aspects of both the opportunities and the (physical and regulatory) risks associated with climate change. For this purpose, we adapt the
machine-learning keyword discovery algorithm proposed by King, Lam, and
Roberts (2017) to produce several sets of climate change bigrams. Rather than
choosing a training library, we start with a short list of initial bigrams that
most experts would agree are related to climate change. Our exposure measures capture the proportion of the earnings call related to climate change topics. These measures are available for a global sample of more than 10,000 firms
covering the period 2002 to 2020. We demonstrate that our measures are helpful in predicting important real outcomes related to the net-zero transition,
notably, green-tech growth and green patenting. We also document that the
measures contain information that is priced in the options and equity markets.
ACKNOWLEDGMENTS
Open access funding enabled and organized by Projekt DEAL.
Initial submission: May 10, 2021; Accepted: June 23, 2022
Editors: Stefan Nagel, Philip Bond, Amit Seru, and Wei Xiong

Appendix A
.
Table A.1

Variable Definitions
Variable

Years

Definition

CCExposure

2002 to 2020

CCExposureOpp

2002 to 2020

Relative frequency with which bigrams related to
climate change occur in the transcripts of earnings
conference calls. We count the number of such
bigrams and divide by the total number of bigrams
in the transcripts. Source: Self-constructed.
Relative frequency with which bigrams that capture
opportunities related to climate change occur in the
transcripts of earnings conference calls. We count
the number of such bigrams and divide by the total
number of bigrams in the transcripts. Source:
Self-constructed.
(Continued)

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Firm-Level Climate Change Exposure

The Journal of Finance®
Table A.1—Continued

Variable

Years

Definition

CCExposureReg

2002 to 2020

CCExposurePhy

2002 to 2020

CCExposureQ&A

2002 to 2020

CCSentiment Pos

2002 to 2020

CCSentiment Neg

2002 to 2020

CCRisk

2002 to 2020

CCExposure10K

2002 to 2020

Total Emissions

2004 to 2020

Relative frequency with which bigrams that capture
regulatory shocks related to climate change occur in
the transcripts of earnings conference calls. We
count the number of such bigrams and divide by the
total number of bigrams in the transcripts. Source:
Self-constructed.
Relative frequency with which bigrams that capture
physical shocks related to climate change occur in
the transcripts of earnings conference calls. We
count the number of such bigrams and divide by the
total number of bigrams in the transcripts. Source:
Self-constructed.
Relative frequency with which bigrams related to
climate change occur in the Q&A session part of
transcripts of earnings conference calls. We count
the number of such bigrams and divide by the total
number of bigrams in the Q&A session. Source:
Self-constructed.
Relative frequency with which bigrams related to
climate change are mentioned together with
positive tone words that are summarized by
Loughran and McDonald (2011) in one sentence in
the transcripts of earnings conference calls. We
count the number of such bigrams and divide by the
total number of bigrams in the transcripts. Source:
Self-constructed.
Relative frequency with which bigrams related to
climate change are mentioned together with the
negative tone words that are summarized by
Loughran and McDonald (2011) in one sentence in
the transcripts of earnings conference calls. Source:
Self-constructed.
Relative frequency with which bigrams related to
climate change are mentioned together with the
words “risk” or “uncertainty” (or synonyms thereof)
in one sentence in the transcripts of earnings
conference calls. We count the number of such
bigrams and divide by the total number of bigrams
in the transcripts. Source: Self-constructed.
Climate change exposure constructed by applying our
algorithm to the “Management Discussion and
Analysis” (MD&A) section in firms’ annual 10K
filings. Source: Self-constructed.
Sum of annual Scope 1 and Scope 2 carbon emissions
(metric tons of CO2) at the end of the year. Scope 1
emissions are caused by the combustion of fossil
fuels or releases during manufacturing. Scope 2
emissions originate from the purchase of electricity,
heating, or cooling. Source: Trucost.
(Continued)

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Table A.1—Continued
Variable

Years

Definition

W SJ CC News Index

2002 to 2017

#Green-Tech Jobs

2007, 2010 to
2020

I(Green-Tech Jobs)

2007, 2010 to
2020

Green-Tech Ratio

2007, 2010 to
2020

#Nongreen-Tech Jobs

2007, 2010 to
2020

#Green Patents

2002 to 2019

I(Green Patents)

2002 to 2019

Green Patents Ratio

2002 to 2019

#Nongreen Patents

2002 to 2019

Assets

2002 to 2020

Time-series index of the fraction of the Wall Street
Journal dedicated to the topic of climate change.
Source: Engle et al. (2020).
Number of job postings for disruptive green-tech jobs
in a year according to the Burning Glass (BG)
database. Disruptive green-tech job postings relate
to jobs in one of four climate-related technology
areas identified by Bloom et al. (2021) as having
been disruptive (“hybrid vehicle electric car,”
“lithium battery,” “solar power,” and “fracking”). We
assume that no disruptive green-tech job has been
posted if a firm-year is not included in the BG
database. Source: Bloom et al. (2021) and BG.
Indicator equal to one if #Green − Tech Jobs is
positive, and zero otherwise. Source: Bloom et al.
(2021) and BG.
Number of job postings for disruptive green-tech jobs
relative to the total number of all disruptive job
postings. Set to zero if the number of disruptive job
postings is zero. Source: Bloom et al. (2021) and BG.
Number of job postings for nongreen disruptive tech
jobs in a year according to the BG database.
Nongreen disruptive tech job postings relate to jobs
in one of 25 climate-related technology areas
identified by Bloom et al. (2021) as having been
disruptive and are unrelated to climate change. We
assume that no nongreen disruptive tech job has
been posted if a firm-year is not included in the BG
database. Source: Bloom et al. (2021) and BG.
Number of green patents obtained in a year according
to the Google Patents (GP) database. To identify
“green” patents, we follow Cohen, Gurun, and
Nguyen (2021) and apply the OECD classification
to identify what constitutes a patent with the
potential to address environmental problems. We
assume that no green patenting has occurred if we
are unable to identify a green patent in the GP
database for a firm-year. Source: GP.
Indicator equal to one if #Green Patents is positive,
and zero otherwise. Source: GP.
Number of green patents (#Green Patents) relative to
the total number of patents. Set to zero if the
number of total patents is zero. Source: GP.
Number of nongreen patents obtained in a year
according to the GP database. We assume that no
patenting has occurred if we are unable to identify
a nongreen patent in the GP database for a
firm-year. Source: GP.
Total assets (in $ millions) at the end of the year
(Compustat item AT). Winsorized at the 1% level.
Source: Compustat NA/Global
(Continued)

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Firm-Level Climate Change Exposure

The Journal of Finance®
Table A.1—Continued

Variable

Years

Definition

Debt/Assets

2002 to 2020

Cash/Assets

2002 to 2020

PPE/Assets

2002 to 2020

EBIT/Assets

2002 to 2020

R&D/Assets

2002 to 2019

CAPEX/Assets

2002 to 2020

IVar

2002 to 2020

ISkew

2002 to 2020

IKurt

2002 to 2020

SlopeD

2002 to 2020

Sum of the book value of long-term debt (Compustat
data item DLTT) and the book value of current
liabilities (DLC) divided by total assets (Compustat
data item AT). Winsorized at the 1% level. Source:
Compustat NA/Global.
Cash and short-term investments (Compustat data
item CHE) divided by total assets (Compustat data
item AT). Winsorized at the 1% level. Source:
Compustat NA/Global.
Property, plant, and equipment (Compustat data item
PPENT) divided by total assets (Compustat data
item AT). Winsorized at the 1% level. Source:
Compustat NA/Global.
Earnings before interest and taxes (Compustat data
item EBIT) divided by total assets (Compustat data
item AT). Winsorized at the 1% level. Source:
Compustat NA/Global
R&D expenditures (Compustat data item XRD)
divided by total assets (Compustat data item AT).
Missing values set to zero. Winsorized at the 1%
level. Source: Compustat NA/Global.
Capital expenditures (Compustat data item CAPX)
divided by total assets (Compustat data item AT).
Winsorized at the 1% level. Source: Compustat
NA/Global.
Implied variance of log returns computed from 30-day
out-of-the-money options following Bakshi,
Kapadia, and Madan (2003). Winsorized at the 1%
level. Source: Ivy DB OptionMetrics Volatility
Surface File.
Implied skewness of log returns computed from
30-day out-of-the-money options following Bakshi,
Kapadia, and Madan (2003). Winsorized at the 1%
level. Source: Ivy DB OptionMetrics Volatility
Surface File.
Implied kurtosis of log returns computed from 30-day
out-of-the-money options following Bakshi,
Kapadia, and Madan (2003). Winsorized at the 1%
level. Source: Ivy DB OptionMetrics Volatility
Surface File.
Slope of the implied volatility smile on the left side
from the at-the-money level (i.e., for negative
returns relative to ATM), computed as the slope
coefficient from regressing implied volatilities of
out-of-the-money puts on the respective option
deltas (and a constant). The variable is computed
from 30-day options. Winsorized at the 1% level.
Source: Ivy DB OptionMetrics Volatility Surface
File.
(Continued)

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Table A.1—Continued
Variable

Years

Definition

SlopeU

2002 to 2020

V RP

2002 to 2020

Slope of the implied volatility smile on the right side
from the at-the-money level (i.e., for positive
returns relative to ATM), computed as the slope
coefficient from regressing implied volatilities of
out-of-the-money calls on the respective option
deltas (and a constant). The variable is computed
from 30-day options. Winsorized at the 1% level.
Source: Ivy DB OptionMetrics Volatility Surface
File.
Variance risk premium computed as the difference
between the implied variance of log returns (IVar)
and the realized variance of daily log returns over a
historical monthly window. Winsorized at the 1%
level. Source: Ivy DB OptionMetrics Volatility
Surface File for options data and CRSP for daily
returns.

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Supporting Information
Additional Supporting Information may be found in the online version of this
article at the publisher’s website:
Appendix S1: Internet Appendix.
Replication Code.

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==> JF4 - 2025 - BANERJEE - Feedback Effects and Systematic Risk Exposures.txt <==
THE JOURNAL OF FINANCE • VOL. LXXX, NO. 2 • APRIL 2025

Feedback Effects and Systematic Risk Exposures
SNEHAL BANERJEE, BRADYN BREON-DRISH, and KEVIN SMITH*
ABSTRACT
We model the “feedback effect” of a firm’s stock price on investment in projects exposed to a systematic risk factor, like climate risk. The stock price reflects information about both the project’s cash flows and its discount rate. A cash-flow-maximizing
manager treats discount rate fluctuations as “noise,” but a price-maximizing manager
interprets such variation as information about the project’s net present value. This
difference qualitatively changes how investment behavior varies with the project’s
risk exposure. Moreover, traditional objectives (e.g., cash flow or price maximization)
need not maximize welfare because they do not correctly account for hedging and
risk-sharing benefits of investment.

SINCE HAYEK (1945), IT HAS BEEN recognized that prices aggregate
information that is dispersed across the economy and convey it to real
decision makers. The “feedback effects” literature studies this mechanism
in the context of corporate investment, emphasizing how asset prices reflect
information about future investment opportunities, and how this information
affects firms’ production and investment decisions (see Bond, Edmans, and
Goldstein (2012) and Goldstein (2023) for insightful surveys). Existing analyses focus on the extent to which prices reflect information about future cash
flows and interpret noncash-flow variation in prices as noise that needs to be
filtered out by decision makers.
* Snehal Banerjee is at the University of Michigan, Ann Arbor. Bradyn Breon-Drish is at the
University of California San Diego. Kevin Smith is at Stanford University. We thank Philip Bond
(Editor), the Associate Editor, and two anonymous referees for their feedback. We also thank Cyrus
Aghamolla, Jesse Davis, Peter DeMarzo, Simon Gervais, Itay Goldstein, Naveen Gondhi, Ilja Kantorovitch (discussant), Pete Kyle (discussant), Alan Moreira, Christian Opp (discussant), Tarun
Ramadorai, Avanidhar Subrahmanyam, Dimitri Vayanos, Liyan Yang, and Bart Yueshen (discussant), participants at the Accounting and Economic Society Webinar, the 2021 JEDC Conference
on Markets and Economies with Information Frictions, the 2022 Future of Financial Information
Conference, the 2022 FIRS Conference, and the 2022 WFA Meeting, and seminar participants at
McGill University, University of Michigan (brown bag), Michigan State University, Baruch College, Northeastern University, Cornell University, Penn State University, University of Toronto
(brown bag), University of Western Ontario, and University of Amsterdam for helpful feedback.
All errors are our own. An earlier version of this paper was entitled “Risk Sharing, Investment
Efficiency, and Welfare with Feedback Effects.” We have read The Journal of Finance disclosure
policy and have no conflicts of interest to disclose.
Correspondence: Kevin Smith, Graduate School of Business, Stanford University, 655 Knight
Way, Stanford, CA 94305, USA; e-mail: kevinsm@stanford.edu.

DOI: 10.1111/jofi.13427
© 2025 the American Finance Association.

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Yet, a fundamental tenet of capital budgeting is that firms’ optimal investment decisions should depend on not only projects’ expected cash flows, but also
their discount rates. Moreover, a project’s discount rate is driven by its loadings on systematic sources of risk and investors’ aggregate preferences over,
and exposures to, these risks. While a firm’s manager is unlikely to directly
observe these preferences and exposures, they impact investors’ demands
and equilibrium asset prices. This suggests that prices are crucial sources of
information about discount rates for managers making investment decisions.
To study feedback effects when managers learn about discount rates from
prices, we develop a model in which a firm’s stock price conveys information about both future cash flows and investors’ risk exposures. When the
manager chooses investment to maximize expected cash flows, she interprets
noncash-flow variation in prices as noise. In contrast, when the manager
chooses investment to maximize the future share price, noncash-flow variation in prices conveys useful information about the project’s discount rate.1
Consequently, she no longer explicitly seeks to filter out such information and
instead incorporates the information in prices on both cash flows and discount
rates when making her investment decisions.
This difference has important implications for how investment in a project
depends on its risk exposure. For a cash-flow-maximizing manager, an increase in a project’s risk exposure makes the stock price a noisier signal
about the project’s expected cash flows. This makes the manager’s investment
decision less sensitive to the information in the price. In contrast, for a pricemaximizing manager, an increase in the project’s risk exposure makes the
price more volatile, which, as we show, causes her conditional expectation of
the project’s net present value (NPV) to vary more. All else equal, this makes
the investment decision more sensitive to the price, as we clarify below.
Finally, we show that traditional managerial objectives, like cash-flow
or price maximization, do not generally lead to investment decisions that
maximize investor welfare. Clearly, since cash-flow maximization ignores the
impact of the project’s risk exposure on investors’ ability to “hedge” the systematic risk factor, it can lead to underinvestment or overinvestment relative
to welfare maximization.2 Price maximization leads to inefficient investment
decisions for two reasons. First, while the share price does reflect information
about risk exposures through the discount rate, the risk premium in price
reflects the disutility that the risk of a marginal share of the stock imposes on
an investor. Welfare, however, depends on an investor’s disutility from bearing
the risk of her entire share holdings. Second, the price does not account for
the fact that investing in a risk-exposed project makes the stock a better
instrument for risk-sharing across investors, which increases welfare.
1 As we discuss below, the project’s risk exposure is known to both the manager and investors,

but the stock price conveys information about the associated factor risk premium to the manager.
2 In what follows, our terminology explicitly distinguishes between hedging and risk-sharing.
The former refers to investors’ desire to buy more (less) of assets that pay out more (less) during
adverse systematic factor outcomes. The latter refers to investors’ ability to share and reallocate
differential exposures to systematic risk by trading a risk-exposed security.

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Model and Intuition. Our analysis applies quite broadly to investment in
risky projects when market feedback plays an important role. A particularly
salient application is to climate-sensitive investment, and so, we use this
setting to describe our model’s economic forces and predictions. A firm’s
manager decides whether to invest in a project that is exposed to a systematic
climate risk factor. The firm’s stock is traded by risk-averse investors who
are informed about the project’s expected cash flows and have heterogeneous
exposures to climate risk. The price aggregates not only investors’ information
about cash flows, but also their dispersed exposures toward the project’s
climate risk exposure, or “greenness.” A “green” (“brown”) project is defined
as one that pays higher (lower) cash flows when climate outcomes are worse,
while a “neutral” project’s cash flows are uncorrelated with climate outcomes.
As such, green projects are negatively exposed to the climate risk factor, while
brown projects are positively exposed to this factor.3
For example, consider a consumer electronics firm deciding whether to
invest in electric vehicle (EV) technology, such as batteries or semiconductors.
Such green investment is negatively exposed to climate risk. For instance,
shifts in regulatory policy in response to climate change may lead to more
favorable treatment of EVs relative to traditional vehicles.4 Thus, the firm’s
price and the information it conveys to the manager depend in part on the fact
that such investments are likely to perform better when aggregate climate
outcomes are worse.5
We compare two managerial objectives. First, in line with the existing feedback literature, we consider the case in which the manager chooses investment
to maximize expected cash flows. In this case, we show that a higher (absolute)
exposure to climate risk shocks makes the price a noisier signal about cash
flows, which, in turn, makes the manager’s investment decision less sensitive
to the price. As a result, for ex-ante unattractive projects (i.e., projects with
negative ex-ante net expected cash flows), the manager is less likely to invest
in green (or brown) projects than in climate-neutral projects.
Second, we consider the case in which the manager’s objective is to maximize the firm’s expected stock price. In this case, she invests only when the
stock price is sufficiently high, because this implies that the project’s NPV,
3 Our definitions of “green” versus “brown” projects are consistent with the empirical literature
(e.g., Engle et al. (2020), Bolton and Kacperczyk (2021)), as we discuss in Section I.A. Moreover,
there is substantial evidence that investors have time-varying exposures to climate risk that affect
their demands for green and brown stocks and, in turn, these stocks’ discount rates (e.g., Choi, Gao,
and Jiang (2020), Pástor, Stambaugh, and Taylor (2022), Bolton and Kacperczyk (2023)).
4 For example, Panasonic, historically associated with consumer electronics, is now also a leading manufacturer of rechargeable batteries for EV companies. Such investments are likely to benefit from regulatory changes that provide tax subsidies to encourage the purchase of EVs, which is
an example of climate transition risk (e.g., Giglio, Kelly, and Stroebel (2021)).
5 Consistent with managers responding to the information that prices contain about cash flows
and discount rates, empirical evidence shows that firms’ investment in climate-exposed projects
often responds to changes in their stock prices, even when driven by shocks to investor demand
for green exposure rather than cash flow news (e.g., Li et al. (2020), Bai et al. (2021), Briere and
Ramelli (2021)).

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Feedback Effects and Systematic Risk Exposures

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conditional on the price information, is positive. In effect, when conditioning
on the price, she learns about both investors’ cash flow information and their
aggregate risk exposure, which drives the project’s discount rate. In fact, we
show that price aggregates these two types of information in an efficient manner from the manager’s perspective, in that she makes the same investment
decision that she would if she observed them separately.6
Once again, when the project has a greater absolute exposure to climate
risk, the firm’s price is a noisier signal of cash flows. Yet, in stark contrast to
cash-flow maximization, this causes her investment decision to become more
sensitive to the price. This is because the price signal, and consequently, the
manager’s conditional expectation of the project’s NPV, is more volatile. For an
ex-ante unattractive project, this increased volatility increases the likelihood
that the project will have a positive conditional NPV and as a result increases
the likelihood of investment.7
An increase in the project’s climate exposure also affects its expected NPV:
greener projects provide a hedge against bad climate outcomes and thus,
all else equal, carry lower discount rates. The overall effect of a project’s
climate exposure on the likelihood of investment trades off the impact of these
channels. In fact, when the ex-ante uncertainty over the aggregate demand
for a climate hedge is sufficiently high, the effect of climate exposure on the
volatility of a project’s NPV dominates its effect on its expected NPV. This
implies, for example, that the manager may be more likely to invest in brown
projects that are ex-ante unattractive than in comparable neutral projects.
Welfare. Differences in managerial objectives also have important implications for investor welfare. We first consider a benchmark in which all investors
have identical exposures to the climate risk factor. In this case, maximizing
cash flows clearly does not align with maximizing shareholder welfare because
it ignores the impact of investment on investors’ aggregate climate exposure—
for example, it leads to underinvestment in green projects. More surprisingly,
we show that the price-maximizing investment rule also does not align with
the welfare-maximizing price-contingent investment rule as long as the firm is
not arbitrarily small (i.e., as long as the investment decision has an effect on
aggregate exposures). Analogous to the intuition of Spence (1975) in the context of a monopolist’s choice of product quality, this is because the price reflects
the marginal disutility from bearing the risk of the last outstanding share,
while welfare depends on the average disutility from bearing the risk of all
outstanding shares. Because the marginal disutility of the last share is higher
than the average disutility of all shares, the price-maximizing rule tends to
6 This establishes an equivalence between our setting, where the manager infers their project’s
discount rate and cash-flow information from prices, and traditional production-based asset pricing models, where the manager is assumed to exogenously know these two types of information
(e.g., Cochrane (1991)).
7 Intuitively, the manager’s investment decision is a real options problem, and higher volatility
in the project’s NPV increases the likelihood of exercise for an “out-of-the-money” option (ex-ante
unattractive project) but decreases the likelihood of exercise for an “in-the-money” option (ex-ante
attractive project).

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underinvest. Finally, we show that for brown projects, price and cash-flow incentives can be balanced through appropriate weighting to induce the manager
to maximize investor welfare, while for green projects this may not be possible.
We next consider the general setting in which investors have heterogeneous
exposures to climate risk. This is a realistic feature: investors’ climate exposures differ with age, geography, and adaptability (Giglio, Kelly, and Stroebel
(2021)), and, as evidenced by the swath of actively traded climate-based
exchange-traded funds (ETFs), investors appear to use financial markets as
a means to hedge and share such risk exposures.8 For example, an investor
who lives in coastal California is more exposed to climate risk due to rising
sea levels, and therefore, has a different demand for green stocks than an
investor who lives in central Kansas.9 In such settings, a firm’s investment
in a climate-sensitive project has an additional impact on welfare because
it allows investors to use the firm’s stock to help share risk: all else equal,
both investors are better off when the Kansas investor sells some shares of a
firm that invests in green EV projects to the California investor. However, the
welfare improvement as a result of this “risk-sharing” channel is not captured
by the stock price, which reflects investors’ disutility of risk of a marginal
share of the stock and not the heterogeneity in their exposures.
This implies that, even when the per-capita endowment of shares is negligible (so that the investment decision does not affect aggregate risk), both price
maximization and cash-flow maximization lead to underinvestment relative
to welfare maximization. Moreover, while feedback necessarily increases
the firm’s expected cash flows or share price (depending on the manager’s
objective), we show that it can decrease investor welfare.10 Intuitively, without
feedback, the manager would always invest in an ex-ante attractive project,
whereas with feedback, she would not invest in such a project if the equilibrium price were sufficiently low. This lower investment increases welfare due
to higher valuations, but decreases welfare due to the risk-sharing channel.
When investors’ exposures to climate risk are sufficiently diverse or per-capita
ownership of the firm is sufficiently small, the latter effect dominates and
welfare is higher without feedback than with. In such settings, our analysis
suggests that providing additional incentives for managers to invest in green
projects (e.g., by linking their compensation to climate scores) can increase
8 There is ample evidence that investors use financial assets to attempt to hedge and share
climate risks—see, for example, Ilhan (2020), Krueger, Sautner, and Starks (2020), Ilhan et al.
(2023), Giglio, Kelly, and Stroebel (2021), and our discussion in Section I.A. Moreover, total assets
under management in sustainability-focused funds roughly doubled from Q4 2019 to Q3 2022, concurrent with over 200 sustainability fund launches per year (see Morningstar’s “Global sustainable
fund flows: Q3 2022 in review”).
9 Consistent with this, Ilhan (2020) documents that households with differential exposures to
sea-level rise have different participation in equity markets and consequently different portfolios.
10 For simplicity, we assume that investors do not have access to other securities that let them
share climate risks. However, we expect that similar results would arise if the market for trading
climate risk shocks is imperfect. As we discuss in Section I.A, this is consistent with the empirical
evidence that suggests that investors have different exposures to climate risk and find this risk
difficult to hedge.

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Feedback Effects and Systematic Risk Exposures

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investor welfare even though it may lead to lower valuations and lower
future profitability.
Overview. The rest of the paper is organized as follows. Section I introduces
the model and discusses key assumptions. Section II characterizes the equilibrium under cash-flow maximization and price maximization. Section III
presents our results on investor welfare. Section IV discusses the related
literature. Section V concludes. Proofs of our results are in the Appendix and
additional analysis is presented in the Internet Appendix.11
I. Model
We consider a model of feedback effects where the investment is exposed to
a systematic risk. We present the model in the context of climate risk as it is
a significant and direct application, but as we discuss in the conclusion, our
analysis has other applications.
Payoffs. There are four dates t ∈ {1, 2, 3, 4} and two securities. The risk-free
security is normalized to the numeraire. A share of the risky security is a claim
to terminal per-share cash flows V generated by the firm at date four, and
trades on dates one and three at prices P1 and P3 , respectively.
Investors. There is a continuum of investors, indexed by i ∈ [0, 1], with
constant absolute risk aversion (CARA) utility over terminal wealth with
risk-aversion γ . Investor i has initial endowment of n shares of the risky asset
source of income that has
and zi = Z + ζi units of exposure to a nontradeable






−1
−1
payoff of −ηC , where Z ∼ N μZ , τZ , ζi ∼ N 0, τζ , and ηC ∼ N 0, τη−1 are
independent of each other and all other random variables.12 Investor i chooses
trades Xit , t ∈ {1, 3} to maximize her expected utility over terminal wealth,
which is given by
Wi = (n + Xi1 + Xi3 )V − Xi3 P3 − Xi1 P1 − zi ηC .

(1)

We interpret ηC as climate risk shocks, which reduce investor wealth and
in turn utility.13 Furthermore, Z captures investors’ aggregate exposure to
climate risk shocks, and μZ is the average exposure to climate risk. The
natural restriction for this interpretation is μZ > 0, which implies that shocks
to the climate (i.e., positive innovations to ηC ) have, in expectation, a negative
impact on the average investor. In our analysis, we focus on this restriction
to clearly distinguish between projects that are positively versus negatively
exposed to the climate.
11 The Internet Appendix is available in the online version of the article on The Journal of
Finance website.
12 We let τ
2
(·) denote the unconditional precision and σ(·) the unconditional variance of all random variables.
13 While, for concreteness, we refer to η as a nontradeable payoff, we could equivalently interC
pret it as a nonmonetary climate shock to which investors are differentially exposed and thus that
affects their utility directly.

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

We further require the parameter restriction 1 > γ 2 τ1η τ1Z + τ1ζ to ensure
that the unconditional expected utility is finite. Intuitively, if this condition is
violated, the climate payoffs zi ηC are sufficiently uncertain ex-ante that the
expected utility diverges to −∞. This is a natural condition that arises when
characterizing ex-ante expected utility in any CARA-Normal model in which
traders have random endowments, and therefore, the unconditional distribution of wealth involves a product of normally distributed random variables.14
We summarize these restrictions in the following assumption, which we maintain throughout our analysis.
ASSUMPTION 1: (i) The average exposure to climate risk μZ is positive, that is,
μZ > 0.
(ii) Uncertainty

 about overall climate payoffs is sufficiently small, that is,
1
1
2 1
1 > γ τη τZ + τζ .


The firm. The firm generates cash flows per share, A ∼ N μA , τA−1 , from assets in place. In addition, the firm’s manager decides whether to invest in a
new project. The investment decision is binary and denoted by k ∈ {0, 1}. The
firm’s cash flow per share, given an investment choice k, equals



 
(2)
V k = A + k θ + αηC + 1 − α 2 ηI − c ,




where θ ∼ N μθ , τθ−1 and ηC , ηI ∼ N 0, τη−1 are independent of each other and
other random variables, α ∈ [−1, 1], and c ≥ 0. The component θ reflects the
learnable component of cash flows for the investment opportunity, ηC reflects
shocks to the “climate” component of cash flows, and ηI reflects shocks to the
“idiosyncratic” component of cash flows. The cost of investment is c, which is
assumed to be nonnegative.
The parameter α captures the extent to which the project’s cash flows are
correlated with climate risk shocks. When α = 0, the new project’s cash flows
are uncorrelated with climate risk and therefore are not useful for hedging—
we refer to such projects as “neutral” projects. When α > 0, the project’s cash
flows are higher when climate outcomes are worse (ηC is higher)—we refer to
these projects as “green” projects. This increase in cash flows may be due to
higher demand for the product (e.g., EVs) or regulatory changes (e.g., higher
taxes on greenhouse gas emissions) driven by adverse changes in the climate.
Analogously, when α < 0, the project’s cash flows are lower when climate outcomes are worse—we refer to these projects as “brown” projects.15
14 See, for instance, Assumption 1.1 in Rahi (1996), Assumption 1 in Marín and Rahi (1999),
equation (1.2) in Vayanos and Wang (2012), and equation (8) in Bond and Garcia (2022),
among others.
15 Note that since positive realizations of η shocks increase marginal utility, green projects
C
are negatively exposed to climate risk, while brown projects are positively exposed. While there
is some disagreement in the literature regarding how different types of stocks’ returns correlate with climate outcomes (e.g., Giglio, Kelly, and Stroebel (2021)), our definitions of “green” and
“brown” projects correspond to how they are classified by the empirical literature (e.g., Bolton and

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

Figure 1. Timeline of events.

Information and timing of events. Figure 1 summarizes the timing of events.
At date 1, all investors
observe θ perfectly. Let Fi1 = σ (θ , zi , P1 ) and Fi3 =

σ θ , zi , P1 , P3 , k denote investor i’s information set at the trading stages, with
expectation, covariance, and variance operators Eit [·], Cit [·], and Vit [·], respectively. Then, investor i chooses trade Xi to maximize her expected utility,


Wi ≡ sup Ei1 −e−γ Wi .
(3)
x∈R

The date 1 price is determined by the market-clearing condition
Xi1 di = 0.

(4)

i

At date 2, the manager chooses investment k given her information. Importantly, the manager does not observe θ directly, but can condition on the information in the stock price P1 . Hence, her information set is Fm = σ (P1 ). We
consider two natural objectives for the manager. A cash-flow-maximizing manager chooses investment to maximize her conditional expectation of the terminal cash flow,
k(P1 ) = arg max E[V |Fm ],

(5)

k

while a price-maximizing manager chooses investment to maximize her conditional expectation of the date 3 price,
k(P1 ) = arg max E[P3 |Fm ].

(6)

k

As we discuss below, these objectives lead to different investment rules and
differ in their effect on investor welfare.
The date 3 price is again determined by the market-clearing condition (4),
evaluated at the t = 3 trades Xi3 that maximize investor expected utilities at
that date. Note, however, that since the manager’s investment decision is perfectly anticipated by investors at date 1, and there are no additional shocks or
information, we show that in equilibrium the date 3 price is equal to the date
Kacperczyk (2021) and Hsu, Li, and Tsou (2023)). Specifically, as we shall see, green stocks carry
a price premium, while brown stocks carry a discount, as a result of their exposure to climate risk.
For tractability, we abstract from other sources of systematic risk and focus only on exposure to
climate risk.

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1 price. At date 4, the firm’s terminal cash flows per share V are realized and
paid to the investors.
Equilibrium. An equilibrium consists of trades {Xi1 , Xi3 }, prices {P1 , P3 }, and
an investment rule k(P1 ) such that (i) the trades Xit maximize investor i’s expected utility, given her information Fit and the investment rule k (P1 ), (ii) the
investment rule k(P1 ) satisfies (5) or (6), and (iii) the equilibrium prices {P1 , P3 }
are determined by market clearing at dates 1 and 3, respectively.
A. Discussion of Assumptions
The manager’s objective. We consider two possible objectives for the manager: cash-flow maximization and price maximization. The former corresponds
to the benchmark in the existing feedback effects literature and speaks to the
incentives created by compensation linked to earnings and other accountingbased performance metrics that are widely used in practice (e.g., Guay, Kepler, and Tsui (2019), Li and Wang (2016), and Bettis et al. (2018)). The latter
corresponds to maximizing the project’s risk-adjusted NPV in our setting and
speaks to the incentives created by equity compensation. This benchmark is
consistent with prior work that builds on the investment capital asset pricing
model (CAPM) and q-theory of investment, which typically assumes that the
firm invests to maximize its market capitalization (e.g., Cochrane (1991), Liu,
Whited, and Zhang (2009)).
Considering the benchmarks separately allows us to provide a sharp comparison of the impact of feedback on investment decisions under these different
objectives. Moreover, as we discuss further in Section III, we show that neither
objective alone necessarily maximizes welfare, even though in some settings, a
combination of the two can be used to do so.
Two trading dates. The assumption of two trading dates is for the sake of
exposition. The second trading date does not play a role when the manager
maximizes cash flows. When she maximizes price, we expect the results to be
the same in a setting without date 3, but in which the manager commits to
an investment schedule k(P) to maximize the date 1 price. In this case, the
manager commits to exactly the same investment schedule as we characterize because, as we show in Section II.B, this investment schedule solves the
relaxed problem of maximizing the expected price by choosing an investment
rule that is an arbitrary function of θ and Z.16
Homogeneous investor information. Since our primary focus is on managerial
learning from prices, we shut down investor learning from prices by assuming
that all investors share a common signal about fundamentals. The assumption simplifies the analysis and ensures that the financial market equilibrium
does not exhibit multiplicity of the type studied by Ganguli and Yang (2009).
Moreover, this assumption ensures that the traditional Hirshleifer (1971) effect does not arise in our setting, in contrast to results from existing literature
(e.g., Marín and Rahi (2000), Dow and Rahi (2003)). Finally, we have confirmed
16 We thank the editor and a referee for highlighting this equivalence.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

that our main results are qualitatively similar when investors have private
signals and learn from the price.
Assets in place and divestment decisions. The presence of assets in place
is not qualitatively important for our results but aids tractability by ensuring that the firm’s cash flows remain uncertain in the absence of investment.
Moreover, the assumption that assets in place are uncorrelated with climate
risk is made for expositional clarity and can be relaxed.17 Since the investment
decision is binary, one can equivalently apply our analysis to study divestment
decisions. For instance, a firm with k = 1 and α < 0 has an existing negative
climate exposure (e.g., a traditional car manufacturer). In this case, a decision
of k = 0 corresponds to divesting brown technology, or equivalently, investing
in green technology to mitigate the firm’s existing exposure (e.g., by transitioning to EV technology).
Aggregate demand for hedging. The assumption that Z is stochastic reflects
the feature that investors’ concern about, and desire to hedge, climate vary
over time. For instance, one can interpret news that suggests climate change
is accelerating as an increase in Z. This assumption is further consistent with
the empirical evidence that aggregate demand for climate hedges varies over
time and with economic conditions. For instance, Bolton and Kacperczyk (2021)
show that the pricing of carbon transition risk varies across countries and has
risen over time. Moreover, Choi, Gao, and Jiang (2020) show that the price
premium applied to green versus brown stocks varies with weather patterns,
and Alekseev et al. (2021) show that weather patterns influence mutual fund
demand for climate-exposed stocks. As we discuss below, this variation generates changes in the discount rate that the manager applies to the project when
making her investment decision.
Discrete investment, market incompleteness, and hedging ability. Our model
is one of incomplete markets. The firm’s investment decision endogenously
changes the completeness of the market by allowing investors to trade the climate risk factor (we refer to this as the risk-sharing channel; see Section III).
The starkness of this result is a consequence of discrete investment choice, but
the economic mechanism arises more generally. Under a continuous investment choice, as the firm invests more, its cash flows are more sensitive to the
risk that investors seek to hedge versus the assets in place. All else equal, this
makes it less costly for investors to hedge their exposures using the stock, in
the sense that they are exposed to less extraneous risk.18
A potential concern is that this channel would disappear if markets were
complete and investors could trade ηC directly. In practice, markets appear
to be far from complete: investors have different exposures to climate risk
due to differences in their demographic characteristics and risk preferences
17 For instance, if A is positively correlated with η , one can decompose A as A = λη + ε for
C
C
A

λ > 0 and C (εA , ηC ) = 0. In this case, the investment decision still changes the overall exposure of
the firm to climate risk (i.e., λ with no investment versus λ + α with investment) and the economic
forces underlying our analysis continue to operate.
18 An earlier version of the paper considered more general investment decisions and found that
the key economic forces that drive our results obtain in this more general setting.

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(e.g., Ilhan et al. (2023)), and they find this risk difficult to hedge (e.g.,
Krueger, Sautner, and Starks (2020), Pástor, Stambaugh, and Taylor (2021),
Giglio, Kelly, and Stroebel (2021)). Indeed, Engle et al. (2020) find that a
dynamic equity portfolio optimized to hedge climate risk is at most 30%
correlated with news about such risk.19
Another potential concern is that the investment decision of a single firm will
not have a meaningful effect on market completeness. A multifirm model with
discount rate variation and feedback effects is not analytically tractable. However, we expect the impact of climate investment on market completeness to
aggregate across firms and thus continue to be relevant in such a setting. That
is, one can interpret our model as that of a representative firm in an industry or sector with correlated shocks to profitability and climate exposures. In
practice, we expect that correlated investment choices (e.g., several automakers investing in EV technology) should affect investors’ ability to hedge climate
risk. Moreover, since stock prices do not fully reflect the risk-sharing benefit of
climate-sensitive investment, our observation that managers fail to internalize
this welfare externality would continue to hold in a multifirm economy.
II. Equilibrium
In general, solving for an equilibrium with feedback effects is complicated by
the fact that the asset price must simultaneously clear the market, be consistent with manager and investor beliefs, and be consistent with the anticipated
real investment decision. We focus on equilibria of the following form.
DEFINITION 1: A threshold equilibrium is one in which:
(i) the price at both dates depends on the underlying random variables
through a linear statistic, s p = θ + β1 Z, where β is an endogenous constant,
(ii) the price takes an identical piecewise linear form at both dates,
P3 = P1 =

A1 + B1 s p
A0

when s p > s
,
when s p ≤ s

(7)

where the price coefficients A0 , A1 , and B1 and the threshold s̄ are endogenous, and
(iii) the manager invests in the project if and only if P1 (s p ) = P1 (s̄), that is,
the share price is not equal to the constant no-investment price.
This type of equilibrium has an intuitive structure and several desirable
properties. First, the equilibrium price is a generalized linear function of
19 The multidimensional nature of climate risk may also contribute to market incompleteness.
Different types of investments may be necessary to hedge the various dimensions of climate risk.
For instance, green energy may serve as a hedge of carbon-transition risk, while green real estate
may better hedge the potential for sea-level rise.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

fundamentals—it depends on θ and Z only through a linear statistic, s p =
θ + β1 Z. Second, there is a price level P1 (s̄) that reveals to the manager that
the market anticipates she will not invest, and, consistent with this, she finds
it optimal not to invest. Thus, the price naturally is piecewise linear in s p ,
increasing in s p when the manager invests, and constant when she does not.
These properties ensure that the analysis is tractable and facilitate comparison with existing work.
As is common in feedback effects models, in general there can exist multiple equilibria with each characterized by a different investment policy. For
instance, if the project is ex-ante sufficiently unprofitable, there is an equilibrium in which investors do not trade on their information and the manager
relies on her ex-ante optimal choice, which is not to invest. These equilibria
are sustained only because the price does not reveal any information when the
market expects the manager not to invest. We focus on the equilibrium with
the lowest threshold s̄, that is, with the most investment. This equilibrium
is the natural one as it would be the unique equilibrium if the price always
revealed s p , which would arise, for instance, if the firm’s assets in place were
correlated with the payoff on the project. This is a common feature of feedback
effects models—Dow, Goldstein, and Guembel (2017) follow a similar approach
in choosing among equilibria, selecting the most informative equilibrium (see,
e.g., the discussion immediately following their Lemma 1). See also Dow and
Gorton (1997), who consider another feedback setting that generally features
multiple equilibria.20
In the Appendix, we formally solve the model by working backwards. We
sketch the approach here. Given an investment decision k ∈ {0, 1} at date 2,
investor i’s beliefs about the asset payoff at t = 3 are conditionally normal,
with
  
  
 kα
  
1
k2
, and Vi3 V k =
+ , (8)
Ei3 V k = μA + k(θ − c ), Ci3 V k , ηC =
τη
τA
τη
and hence her optimal trade is
  
  

Ei3 V k + γ Ci3 V k , ηC zi − P3
  
Xi3 =
− (n + Xi1 ).
γ Vi3 V k

(9)

In turn, market clearing implies
P3 = μA −

γ
γ
n + k θ − c − (n − αZ ) .
τA
τη

(10)

20 Note that if investors in our model also learned noisy information from the equilibrium price
(e.g., if they received heterogeneous private signals), then there would be a further potential source
of nonuniqueness, even holding fixed the manager’s investment policy. As Pálvölgyi and Venter
(2015) show, in standard static, noisy rational expectations models, investor learning from prices
generally leads to a continuum of discontinuous equilibria in the financial market. Characterizing
such equilibria in a version of our model with heterogeneous information would be an interesting
problem for future work but is beyond the scope of the current paper.

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This immediately implies that, in any equilibrium, regardless of the manager’s
τ
objective function, we must have s p = θ + τγη αZ, or equivalently, β = γ ηα .
At date 2, the manager chooses whether to invest to maximize her objective,
given her information set Fm = σ (P1 ). Below we characterize the equilibrium
under cash-flow maximization and price maximization separately. As we will
see, these equilibria differ only in the threshold price P1 (s̄) above which the
manager chooses to invest.
A. Cash-Flow Maximization
The manager’s conditional expectation of cash flows, given s p , is
   


 
E V k |s p = μA + k E θ |s p − c , where


γ
τ
s
μ
+
τ
−
αμ
θ θ
p
p
Z


τη
τη
, and τ p = τZ
E θ |s p =
τθ + τ p
γα

(11)
2

.

(12)

This implies that if the manager were directly able to observe the signal s p in
all states of the world, her optimal investment rule would be
k=

1
0

when
when

E[θ |s p ] > c
E[θ |s p ] ≤ c.

(13)

The manager cannot always observe s p because the price does not vary with
s p when the market expects her not to invest. However, in the threshold equilibrium with the most investment, this creates no additional difficulty for the
manager, because the price is a sufficient statistic for s p in making her investment decision. In this equilibrium, the investment threshold, which we refer
to as s̄C , satisfies E[θ |s p = s̄C ] = c, so that the manager is indifferent between
investing and not investing when s p = s̄C . Applying (11), we obtain
s̄C = c −

τθ (μθ − c )
γ
+ αμZ .
τp
τη

(14)

Given the conjectured price function, if the manager observes P1 = A0 , she infers that with probability one s p ≤ s̄C , and hence chooses not to invest. If she
observes any P1 = A0 , she infers the realized value of s p , necessarily strictly
greater than s̄C , and so she chooses to invest. Thus, in equilibrium, she is able
to implement the same investment rule almost everywhere that she would if
she directly observed s p .
Finally, stepping back to t = 1, note that the manager’s investment decision
is a deterministic function of P1 . Thus, investors can anticipate the manager’s
investment decision by observing the date 1 price. In turn, in equilibrium
investors can perfectly anticipate P3 and therefore the equilibrium price at
t = 1 must satisfy P1 = P3 for the market to clear. Following this reasoning,

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Feedback Effects and Systematic Risk Exposures

the next proposition characterizes the threshold equilibrium with maximum
investment.
PROPOSITION 1: Suppose that the manager maximizes expected cash flows. In
the investment-maximizing threshold equilibrium, equilibrium prices are
P1 = P3 = μA −

γn
γ
+ k sp − c − n ,
τA
τη

(15)

and the manager’s investment decision is

k = 1 P1 = μA − τγA n ,
where s p ≡ θ + τγη αZ, τ p ≡



τη
γα

2

(16)

τZ , and s̄C ≡ c − τθ (μτθp−c) + τγη αμZ .

It is worth noting that investors’ beliefs about the asset payoff remain normal given their information set in all states of the world, since the manager’s
investment decision is determined by the date 1 price P1 . This ensures that the
equilibrium is tractable.
For a cash-flow-maximizing manager, discount rate variation (i.e., shocks to
Z) adds noise to the information about θ that is relevant for her investment decision. Proposition 1 clarifies how the project’s greenness affects the manager’s
inference about cash flows from the price. First, an increase in the project’s
sensitivity to climate risk (i.e., higher |α|) makes the price less informative
about cash flows (i.e., decreases forecasting price efficiency [FPE])—this is
apparent from the expression for τ p . Second, since μZ > 0, an increase in
greenness α leads to a higher threshold s̄C . Intuitively, since a green project
provides a hedge to investors, the price P1 is higher on average, and this leads
to a positive bias in the price signal s p . Since the manager wants to learn
about cash flows (θ ), she corrects for this bias in her threshold.
Together, these effects reflect that for a cash-flow-maximizing manager, an
increase in climate sensitivity makes the price a noisier and more biased signal. As we show in the next subsection, this is no longer the case when the
manager chooses investment to maximize the expected price.
B. Price Maximization
We can follow similar steps to derive the equilibrium when the manager
maximizes the firm’s stock price. Recall that the date 3 market-clearing price
can be expressed as
P3 =

μA − τγA n



s p − c − τγη n

μA − τγA n + k

when k = 0
when k = 1

.

(17)

This implies that if the manager observed s p in all states, she would invest when s p > c + τγη n. Similar to the cash-flow-maximization case, in the

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The Journal of Finance®

994

995

equilibrium with maximum investment, the price reveals s p whenever knowing the value of s p would lead the manager to invest. As a result, she is able
to implement the same investment rule that she would if she could directly
observe s p , and so, the investment threshold satisfies
s̄ = s̄P = c +

γ
n.
τη

(18)

Finally, the manager’s investment decision is again known given the price at
date 1, so that no new information arrives between dates 1 and 3, and P1 and
P3 must be equal. The following proposition formally establishes these results.
PROPOSITION 2: Suppose that the manager maximizes the expected date 3
price. In the investment-maximizing threshold equilibrium, equilibrium prices
are
P1 = P3 = μA −

γ
γ
n + k sp − c − n ,
τA
τη

(19)

and the manager’s investment decision is



k = 1 P1 = μA − τγA n = 1 s p > s̄P ,

(20)

where s p = θ + τγη αZ and s̄P ≡ c + τγη n.
The manager’s optimal investment takes the form of a NPV rule, whereby
she invests if and only the statistic
− c − τγη (n − αZ )
NPV ≡ s p − s̄ = θ 
  
cash flows

(21)

discount rate

is greater than zero. The first term, θ − c, reflects the expected cash flows from
the project net of investment costs—this captures the “cash-flow news” contained in the price. The second term, − τγη (n − αZ ), reflects a discount due to
the risk premium investors demand for holding shares of the stock. We refer to
this as “discount rate news” because it reflects variation in the project’s impact
on price that is driven by factors other than its expected cash flows. Consistent
with intuition, the discount is higher (the NPV is lower) when the firm is larger
(i.e., n is higher) because investors have to bear more aggregate risk. Moreover,
the discount is lower (higher) for green (brown) projects when Z > 0.21 This is
because green projects reduce investors’ exposure to (negative) climate shocks,
while brown projects exacerbate it.
While the cash-flow and discount rate news in prices are not separately observable to the manager, they both factor into her decision of whether to invest
21 It is possible that Z < 0 in our model, so that brown projects are priced at a premium.
However, the probability of this outcome can be made arbitrarily small by setting μZ and τZ
appropriately.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

because they both influence how the project will impact the date 3 price. In
principle, this implies that the manager must learn about both from the date
1 price, that is, she must separately compute E[θ |P1 ] and E[Z|P1 ]. However,
her inference problem takes a transparent form in our setting because the
price signal that she conditions on and the objective she intends to maximize
put the same (relative) weights on θ and Z. In particular, the equilibrium date
1 and date 3 prices put the same weights on θ and Z. This implies that the
manager does not need to separately update on θ and Z to determine whether
investment will lead to a higher price. Instead, she can directly infer the
relevant combination θ + τγη αZ from the date 1 price.22
Note that this simplification of the manager’s learning problem in the case
of price maximization is a derived result, not an assumption. In Section III
of the Internet Appendix, we show that this result extends to the case in
which investors are endowed with dispersed, private noisy signals about θ and
learn about θ from prices, similar to Hellwig (1980). The reason is that, in this
setting, the date 1 and 3 prices continue to place the same weights on cash flow
and discount rate news. However, this result needs not arise when the date 1
price puts different relative weights on θ and Z than the manager’s objective
does. For instance, the simplification does not obtain if the manager maximizes
a combination of expected cash flows (or earnings) and expected price.
Similarly, if a public signal about ηC becomes available before trade at date 3
but after the date 2 investment decision, then the relative weights on θ and Z
will differ across the two dates. We focus on the simpler specification without
a public signal in our model because it is a natural benchmark that transparently illustrates the main economic mechanisms that result from the manager
learning about discount rates from the price. We expect similar forces to apply
in richer settings, although the analysis would be less transparent.
The above also clarifies that while feedback plays an important role in the
equilibrium, the equilibrium of our specific setting turns out to be identical
to one in which the manager directly observes θ and Z. As such, our analysis highlights an important equivalence between a class of feedback effects
models in which the manager maximizes the expected price of the firm and
traditional, production-based asset pricing models in which the manager is assumed to exogenously know the profitability and discount rate of the project
she is considering. To the extent that, in practice, managers rely on prices to
learn about discount rate information, our analysis of the price-maximization
benchmark provides a microfoundation for the latter class of models. In particular, if investors’ exposures to climate risk, which affect the project’s discount
rate, are heterogeneous across investors and privately known, then prices provide a natural source of such information to managers.

22 One may be able to capture similar forces with a single trading date if the manager could
simultaneously commit to a real investment schedule k(P) to maximize the equilibrium price P at
the same time that investors trade.

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C. Probability of Investment
In this section, we compare how feedback from prices affects investment
decisions under the two managerial objectives. The results below generate
testable predictions that relate managerial incentives, the “greenness” of a
project, and the probability of investment. We begin by characterizing the likelihood of investment with cash-flow maximization.
PROPOSITION 3: Suppose that the manager maximizes E [V |Fm ]. In equilibrium, the unconditional probability of investment is given by
⎛  
⎞


E s p − s̄C
(22)
Pr s p > s̄C = ⎝    ⎠,
V sp
 2
 
 
τ
where E s p = μθ + τγη αμZ , V s p = τ1θ + τ1p , τ p = γ ηα τZ , and (· ) denotes the
cumulative distribution function (CDF) of a standard normal random variable.
The probability of investment:
(i) increases with ex-ante profitability μθ − c,
(ii) does not depend on firm size n or the average climate risk exposure μZ ,
(iii) increases with τθ and |α| and decreases with τZ if the project is ex-ante
profitable (i.e., μθ − c > 0), and
(iv) decreases with τθ and |α| and increases with τZ if the project is ex-ante
unprofitable (i.e., μθ − c < 0).
Consistent with intuition, the probability of investment increases with the
ex-ante profitability μθ − c of the project. Moreover, since the manager’s objective is to maximize expected cash flows, the firm’s systematic risk (e.g., n)
and investors’ aggregate exposure to climate risk (i.e., μZ ) do not affect the
likelihood of investment.
The above also clarifies that, for a cash-flow-maximizing manager, variation
in the project’s risk premium, as captured by τγη αZ, generates noise in her price
signal. To see this more explicitly, note that if such a manager were to directly
observe θ as opposed to the price signal s p , she would invest if and only if θ > c.
In this case, the probability of investment can be expressed as
Pr(θ > c) =

μθ − c
.
√
V[θ ]

This depends on the project’s ex-ante profitability μθ − c and prior precision τθ
in the same manner as when the manager observes only s p , but is independent
of the variation in the project’s risk premium (as driven by α and τZ ).
In contrast, when the manager relies on (noisy) price information about cash
flows, the likelihood of investment depends on this premium. In fact, a higher
exposure to climate risk (i.e., higher |α|) serves to make the price a noisier
signal about cash flows, and so, the manager is more likely to invest in line
with her prior beliefs. This implies that for ex-ante profitable projects (i.e., if

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

μθ − c > 0), the manager is more likely to invest in climate-exposed projects
than in climate-neutral ones. On the other hand, for unprofitable projects, an
increase in climate exposure leads to a decrease in the likelihood of investment.
The results above are largely consistent with traditional feedback effects
models in which the manager maximizes expected cash flows and so treats
noncash-flow variation in prices as noise. As we show next, this is no longer
the case when the manager maximizes the share price.
PROPOSITION 4: Suppose the manager maximizes E [P3 |Fm ]. In equilibrium,
the unconditional probability of investment is given by


Pr s p > s̄P =

⎛  
⎞
E s p − s̄P
⎝ 
⎠.
 
V sp

(23)

The probability of investment:
(i) increases with ex-ante profitability μθ − c,
(ii) decreases with firm size n,
(iii) increases with μZ for green firms (i.e., α > 0) but decreases with μZ for
brown firms (i.e., α < 0),
(iv) increases with τθ and τZ if and only if E[s p ] − s̄P = μθ − c − γτηn + αγτημZ >
0, and


τ τ
(v) decreases with greenness α if and only if μθ − c − γτηn − γη αZ τ1θ μZ sgn(α) >
0.
Consistent with intuition, Proposition 4 establishes that the probability of
investment increases in the expected NPV of the project E[s p ] − s̄P and decreases (increases) with the variance of the price signal V[s p ] when E[s p ] − s̄P >
0 (E[s p ] − s̄P < 0). This directly implies parts (i) to (iv) of the proposition. From
equation (21), we know that the expected NPV increases with expected profitability μθ − c, decreases with firm size n, and increases with μZ if and only
if α > 0, which implies parts (i) to (iii). Similarly, part (iv) follows because an
increase in τθ or τZ leads to a reduction in the variance of the price signal
V[s p ], which leads to more investment when the expected NPV is positive (i.e.,
E[s p ] − s̄P > 0) but less investment when it is negative.
Part (v) of Proposition 4 shows that the project’s sensitivity to the risk
factor, α, has a nuanced impact on the likelihood that the manager invests.
An increase in α has two, potentially offsetting, effects. First, an increase in
α increases the expected NPV E[s p ] − s̄P because it reduces the on-average
discount due to climate risk. Since the manager’s objective is to maximize
the share price, this implies that all else equal, investment is likelier in
green projects than brown projects. We refer to this as the “expected NPV”
channel.
Second, an increase in the magnitude of the project’s climate exposure |α|
increases the variance of the price signal V[s p ], which, in turn, makes the conditional NPV of the project more variable. All else equal, this makes it more

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998

999

Figure 2. Probability of investment. This figure compares the probability that the firm invests
as a function of α and μZ under the cash-flow and price-maximization benchmarks. Unless otherwise mentioned, the parameters employed are: τθ = τη = τA = γ = 1, τZ = μZ = 0.5, and n = 0.1.
Panel A depicts results for projects that have positive ex-ante NPV (i.e., μθ > c), while Panel B
considers projects that have negative ex-ante NPV (i.e., μθ < c). In the solid (dashed) lines, we consider price maximization (cash-flow maximization). In Panel A (B), we set μθ − c = 1 (μθ − c = −1),
which implies that the project is ex-ante desirable
(undesirable)
 
 cash-flow and price  in both
 the
maximization cases, that is, ∀α ∈ [−1, 1], E s p > s̄P and E s p > s̄C (E s p < s̄P and E s p < s̄C ).
(Color figure can be viewed at wileyonlinelibrary.com)

likely that a project with negative expected NPV will be desirable ex-post (i.e.,
increases the likelihood that the investment option will be “in the money”), and
hence increases the likelihood of investment of such a project. Similarly, it reduces the likelihood that a project with positive expected NPV will be ex-post
desirable, and thus decreases the likelihood of investment in such a project. We
refer to this as the “variance of NPV” channel. The overall effect of α depends
on the relative magnitude of these two channels.
As Figure 2 illustrates, this is in sharp contrast to the case in which the
manager maximizes cash flows. The figure compares the probability of investment as a function of climate exposure α for the two managerial objectives.
Consistent with the above results, for ex-ante profitable projects (i.e., μθ > c),
an increase in |α| leads to more investment under cash-flow maximization but
can lead to less investment under price maximization—see Panel A. In contrast, for ex-ante unprofitable projects (i.e., μθ < c), Panel B illustrates that
the opposite results hold.
The characterization of the equilibrium thresholds under the two managerial objectives immediately gives us the following result.
COROLLARY 1: Cash-flow maximization leads to more investment than price
maximization (i.e., s̄P > s̄C ) if and only if
γ
τθ
(n − αμZ ) > − (μθ − c ).
τη
τp

(24)

In particular, cash-flow maximization leads to “overinvestment” relative
to price maximization when the project is expected to be highly profitable

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

ex-ante (i.e., μθ − c is sufficiently high), investors’ expected climate exposures
are small (i.e., μZ is low), or the project is sufficiently brown (i.e., α is small or
negative).23
More generally, the price- and cash-flow-maximization benchmarks can be
thought of as lying on the opposite end of a spectrum. While we focus on these
two extremes to simplify the exposition and clarify the intuition for our results, we expect that in practice a manager’s decision reflects a weighted average of both considerations. Importantly, our analysis implies that when the
manager focuses more on prices and less on cash flows, she will treat prices
as less noisy signals and place more weight on them when making investment
decisions.
Our results also imply that how shareholders or regulators can incentivize
managers to pursue green investment depends on the ex-ante desirability of
the projects. For ex-ante unprofitable projects (i.e., μθ < c), tilting the manager’s incentives toward price maximization (e.g., by proving more short-term,
price-sensitive compensation) increases the likelihood of investing in green
projects. This is likely to apply to speculative investments in green technology,
which may be ex-ante unprofitable on a purely cash-flow basis. In contrast, for
ex-ante profitable projects (i.e., μθ > c), making compensation more sensitive
to accounting-based measures of expected cash flows (e.g., earnings) tilts the
manager towards cash-flow maximization and consequently increases investment in green projects.
III. Welfare
In this section, we explore the relationship between feedback, investment,
and investor welfare. We begin in Section III.A by characterizing the channels
through which investment affects investor welfare. In Section III.B, we consider the special case in which investors have homogeneous climate exposures
(i.e., τζ → ∞). This allows us to explicitly characterize the welfare-maximizing
price-contingent investment rule and compare it to price-maximizing and cashflow-maximizing rules. In Section III.C, we reintroduce heterogeneity in risk
exposures and show how the manager’s use of the information in price may
harm investor welfare.
A. The Impact of Investment on Welfare
Existing models of feedback effects focus on the impact that feedback has on
a firm’s expected cash flows. In many such models, investors are risk-neutral
so that maximizing expected cash flows aligns with welfare maximization.24
However, in our model, investor risk aversion implies that investment has

23 Note that when investors are risk-neutral (i.e., γ = 0), s̄ = s̄ = c and so the investment
P
C
rules coincide.
24 Section IV discusses notable exceptions, like Dow and Rahi (2003).

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1001

multiple, potentially offsetting, effects on investor welfare, due to the riskiness
of the project and the stock’s usefulness as a hedge.
Because investors are ex-ante symmetric, the ex-ante expected utility of an
arbitrary investor is an unambiguous measure of welfare,


W ≡ E −e−γ Wi (k(s p ))

 


 

= Pr k = 1 E −e−γ Wi (1) |k = 1 + Pr k = 0 E −e−γ Wi (0) |k = 0 ,

(25)
(26)

where

 
Xi (V (1 ) − P ) + nV (1 ) − zi ηC
Wi k =
nV (0 ) − zi ηC

k=1
.
k=0

(27)

Proposition I.A10 in Section I of the Internet Appendix characterizes this expression in closed form. However, to understand the relevant economic forces,
it is helpful to study the simpler special case in which investment is fixed at arbitrary level k, in which case the model reduces to a standard unconditionally
linear-normal form. In this case, we have


E −e−γ Wi (k) = −e−γ CE(k) ,

(28)

where the certainty equivalent CE(k) can be expressed, after grouping terms,
as
 
CE k =

−

E[V (k)]n
  
Cash flow channel

1
γ 1
1 − α2
+ k2
+
2 τA
τθ
τη



n2


Nonclimate risk channel

−

2
γ 1
1
μZ − kαn (1 + ) − log(D(k)),
2 τη
γ




(29)

Climate risk channel

where


  
D k =



1
+ k2 τ1η
τA
1
+ k2
τA



1
+ β 2 τ 1+τ
τη
( Z ζ)



Value of information







γ 2 τ1η



1
+ τ1ζ
τZ



(30)

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Feedback Effects and Systematic Risk Exposures

and

⎛

(k) ≡
1 − γ 2 τ1η



γ 2 τ1η



1
+ τ1ζ
τZ



⎜
1
⎜
k2 α 2
τη
1
1 ⎜
+ τζ ⎜1 − 1
×
τZ
1
1
⎜
+
+k2
τA
β 2 (τZ +τζ ) τη
⎝



⎞.

(31)

!2 ⎟
⎟
⎟
⎟
1
1
⎟
+
τZ τζ
⎠

1
τζ

Risk-sharing channel

We label all five terms in these expressions that depend on the investment
choice k and we discuss them in turn.

r The cash flow channel reflects that investment k affects the investor’s expected wealth via their ownership of n shares. Investment increases (decreases) welfare through this channel when the project’s expected cash
flows are positive (negative).
r The nonclimate risk channel reflects that the investment k increases investors’ exposure to nonclimate risks via the θ and ηI shocks.
r The climate risk channel captures the fact that the investment k affects investors’ aggregate exposure to climate shocks. The average investor’s total
climate exposure is given by μZ − kαn, which reflects both the direct exposure and the exposure through ownership of the stock. When the direct
exposure is sufficiently large (i.e., μZ > n), investment in green projects
(α > 0) decreases aggregate climate exposure and hence increases welfare,
while investment in brown projects (α < 0) increases aggregate climate exposure and decreases welfare. This channel is further scaled by the term
1 + , which reflects uncertainty about the exposure to climate risk. When
investors’ total exposure to climate risk Z + ζi is constant (i.e., τZ , τζ → ∞),
we have = 0. However, when investors face uncertainty about their exposure from either source, we have > 0, which amplifies the disutility of
climate exposure.
r The risk-sharing channel reflects that the project enables investors to
share their idiosyncratic exposures to climate risk, ζi , by trading the stock.
All else equal, investment improves welfare through this channel. By
sharing risk, investors reduce the dispersion in their climate exposures,
reducing the effect of uncertainty about exposures, .
The overall amount of risk-sharing reflects both the effectiveness of the
stock as a hedging instrument (i.e., the correlation of the stock return with
climate risk), and the proportion of climate exposures that are shared (i.e.,

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1003

the proportion of climate exposures that are idiosyncratic, ζi ),
1
τη
1
1
+
β 2 (τZ +τζ ) τη
k2 α 2

Risk-sharing channel =

1
+k2
τA





1
τζ

×


Hedging effectiveness of stock
=Corr2 (V −P,ηC |zi )



1
1
+
τZ τζ



!2
.


% shareable climate exposure

(32)

r The value of information channel captures the fact that investors’ information about cash flows renders the stock more useful in hedging. Observing θ increases the conditional correlation between the stock’s payoff
and ηC . Moreover, this effect is relevant only when the project is undertaken, and so disappears when k = 0. This takes the familiar form of the
ratio of investors’ conditional variance of the asset return with and without conditioning on θ .25
Importantly, when the manager chooses investment to maximize the expected price, she fails to appropriately account for the impact of her decision
on the other components of welfare, as we discuss next.
B. Homogeneous Risk Exposures
We begin with the special case of our model in which all investors have homogeneous exposures to climate risk. In this case, we can explicitly characterize
the welfare-maximizing price-contingent investment rule, as we show in the
following proposition.
PROPOSITION 5: Suppose that investors have identical exposures to climate
risk (i.e., τζ → ∞). Then, the welfare-maximizing investment policy is






arg max W k; θ , Z = arg max W k; s p = 1 s p > s̄W ,
k∈{0,1}

(33)

k∈{0,1}

where s̄W ≡ c + 12 τγη n. Moreover,

25 In our model, investors are endowed with information. However, this term still captures the
improvement in utility as a result of observing θ relative to being uninformed. Specifically, given
V(V |θ,zi ,P)
fixed k, this ratio can be represented as V(V −P|z
, which reflects the proportional improvement
i)
in expected utility from conditioning on θ , zi , and P versus zi alone. The welfare expressions in
Bond and Garcia (2022) include a similar term, which they further decompose into a product of
V(V |θ,zi ,P)
, and the value of providing versus demanding
the classic value of cash-flow information, V(V |z ,P)
i

V(V |z ,P)

i
liquidity (i.e., using a price-contingent schedule versus not), V(V −P|z
. Because these effects are
i)
not a primary focus of our analysis, we choose to concisely represent them in a single term.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

(i) cash-flow maximization leads to underinvestment relative to welfare
maximization if and only if
s̄C − s̄W =

γ
τθ (μθ − c ) 1 γ
αμZ −
−
n > 0,
τη
τp
2 τη

(34)

but overinvestment otherwise, and
(ii) price maximization always leads to underinvestment relative to welfare
maximization, since s̄P − s̄W = 12 τγη n.
As we show in the Appendix, the expressions for welfare simplify considerably when investors have homogeneous exposures to climate risk because there
is no trade in equilibrium. Consequently, neither the risk-sharing channel nor
the value of information channel are operational. In this case, we show that
the welfare-maximizing investment rule, conditional on full information (i.e.,
knowledge of θ and Z), depends on θ and Z only through the linear combination
s p and thus coincides with the welfare-maximizing s p -contingent (i.e., pricecontingent) investment rule.26 Importantly, a fully-informed manager would
optimally put the same weights on θ and Z as the equilibrium price does if her
objective were to maximize welfare.
However, as Proposition 5 clarifies, the cash-flow-maximizing investment
rule does not maximize welfare. In particular, cash-flow maximization tends
to lead to underinvestment in green projects but overinvestment in brown
projects that are ex-ante profitable, relative to welfare maximization. Using
the investment thresholds, we can characterize the values of θ for which the
manager invests in each case. Specifically, for a given Z, the above implies that
under welfare maximization, the manager invests if and only if
θ >c+

γ
1γ
∗
n − αZ ≡ θW
,
2 τη
τη

(35)

while under cash-flow maximization the manager invests if and only if
θ >c+

γ
τθ (μθ − c )
α (μZ − Z ) −
≡ θc .
τη
τp

(36)

As a result, cash-flow maximization with noisy (price) information leads to
∗
> 0.
underinvestment relative to welfare maximization if and only if θc − θW
To gain intuition into what drives this difference, recall that if the manager
perfectly observes θ and maximizes cash flows, she invests if and only if θ > c.
26 To streamline the presentation and derivation, we formulate the investment rule as s p
contingent. However, as in the baseline model, it can be implemented as a price-contingent rule.
Intuitively, with probability 1, the equilibrium price reveals s p when investors anticipate that the
investment is undertaken and does not reveal s p otherwise. This allows one to directly map the
s p -contingent investment rule to an equivalent price-contingent rule under which the manager
does not invest if she observes a price realization that anticipates no investment, P1 = μA − τγ n,
A
and invests otherwise.

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1004

1005

Thus, the distortion in investment decisions stems from two factors: (i) the
misalignment between the manager’s preferences and those of investors, even
when the manager is fully informed, and (ii) the noise in the information that
price conveys about cash flows to the manager. Specifically, note that
∗
=
θc − θW

∗
c − θW
  

+

impact of different
preferences

θc − c
  

,

(37)

impact of noisy
price information

where
∗
=
c − θW

1
γ
αZ − n
τη
2

and

θc − c =

γ
τθ (μθ − c )
α (μZ − Z ) −
.
τη
τp

(38)

∗
When c − θW
> 0, which holds when αZ is large relative to n, the difference in
the manager’s preference pushes her to underinvest relative to the welfaremaximizing level. Intuitively, the manager disregards both the welfare impact of the investment’s climate exposure (determined by its greenness α and
the aggregate climate exposure Z), and its nonclimate risk (determined by n).
Taken together, this pushes her to underinvest when the project is sufficiently
green and investors’ climate exposures are large, and to overinvest otherwise.
Next, when θc − c > 0, noisy learning from prices pushes toward underinvestment. Specifically, relative to the full-information cash-flow-maximizing
benchmark, noisy learning drives the manager to overinvest in ex-ante attractive projects (i.e., μθ − c > 0) but underinvest in ex-ante unattractive projects
(i.e., μθ − c < 0). This is because the manager continues to weight her prior
beliefs when deciding whether to invest. Moreover, when the climate risk premium is higher than expected (i.e., Z > μZ ), noisy learning leads to overinvestment in green projects and underinvestment in brown projects, relative to the
full-information cash-flow-maximizing benchmark.
Interestingly, these two sources of distortion partly offset each other via their
dependence on Z. The noisy price information wedge θc − c reflects the fact
that a cash-flow-maximizing manager would like to ignore Z when choosing
investment but cannot do so because she can only condition on the noisy price
signal s p , which is driven in part by αZ. However, this is beneficial from a
welfare perspective because it implies that the manager is more likely to invest
when αZ is higher, which is when the investment is more valuable as a climate
∗
).
hedge (as captured in the difference in preference wedge c − θW
Somewhat surprisingly, we find that the price-maximizing rule also leads
to underinvestment relative to the welfare-maximizing rule whenever n > 0.
Note that in this case, there is no distortion from noisy information—as previously discussed, the date 1 price puts the same weights on θ and Z, as does
her objective. The difference between the two thresholds stems from the fact
that, while welfare depends on the average risk borne by investors, the price
reflects the marginal disutility from the risk of holding the last outstanding
share of the firm. Since the marginal disutility from holding the last share
is higher than the average disutility from bearing the risk of all shares that

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Feedback Effects and Systematic Risk Exposures

investors hold, the price-maximizing rule leads to underinvestment relative to
the welfare-maximizing rule. However, it is worth noting that this difference
disappears when the per-capita endowment of shares per firm becomes arbitrarily small (i.e., n → 0).
The point that decisions based on prices may be socially suboptimal because
prices reflect marginal and not average valuations was first raised by Spence
(1975) in the context of a monopolist’s choice of product quality. He shows that
the chosen quality may be too high or too low from the perspective of social
welfare. The intuition for this result is analogous to ours: quality is chosen
based on information contained in a good’s price, which reflects the valuation
of the marginal consumer, while welfare depends on information about the
average consumer.27
Proposition 5 also implies that, in this benchmark, one can implement the
welfare-maximizing investment rule by inducing the manager to maximize a
weighted average of cash flows and the date 3 price, as summarized by the
following result.
PROPOSITION 6: Suppose that the manager maximizes a weighted average of
expected price and expected cash flows,
k(P1 ) = arg max δ E[P3 |P1 ] + (1 − δ)E[V |P1 ],

(39)

k

where
δ=


τp γ 
τθ
αμZ − 12 n
μ − c ) − τθ +τ
τθ +τ p ( θ
p τη
 1 1 .
τp γ 
τθ
1
αμ
−
n
+ 2 γ τη n
μ − c ) − τθ +τ
Z
τθ +τ p ( θ
τ
2
p η

(40)

Then, in the maximum-investment threshold equilibrium, the manager invests if and only if s p > s̄W . When the project is unexposed to the climate
θ
(α = 0), we have that δ = 12 . Moreover, δ ∈ (0, 1) if and only if τθ τ+τ
(μθ − c ) >
p

τp γ 
1
αμZ − 2 n .
τθ +τ p τη
Recall that price maximization leads to underinvestment relative to welfare maximization, but cash-flow maximization can lead to overinvestment for
brown (α < 0), ex-ante profitable (μθ > c), projects. In such cases, the above
result implies that there exists a δ ∈ (0, 1) such that a weighted-average objective of the form in (39) leads the manager to follow a welfare-maximizing
investment rule. In particular, by incentivizing the manager to maximize a
weighted average of expected price and expected cash flows, where δ is set as
in (40), investors can ensure that the manager’s investment rule maximizes
ex-ante welfare.
27 An analogous difference is also highlighted by Levit, Malenko, and Maug (2022), who show
that while prices are determined by the valuation of the marginal investor, valuation is determined by the valuation of the average (posttrade) shareholder in their setting. Bernhardt, Liu,
and Marquez (2018) highlight a similar difference in the context of takeovers.

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The Journal of Finance®

1006

1007

However, the above result also implies that such compensation schemes may
not be appropriate when the manager is considering whether to invest in green
projects. For instance, consider a green project with μθ = c. If 2αμZ > n > αμZ ,
Proposition 6 shows that welfare maximization requires the manager to place
2αμ τ 2 τz

η
a negative weight on the price (i.e., δ < 0). However, if n < α2 γ 2 τθZ+2τ
2 τ , welfare
z
η

maximization requires the manager to place a negative weight on cash flows
(i.e., δ > 1). Intuitively, both price maximization and cash-flow maximization
lead to underinvestment, so the welfare-maximizing combination puts negative weight on the objective that leads to greater underinvestment. However,
such negative sensitivity to prices or earnings is difficult to implement in practice. Moreover, traditional compensation schemes that put positive weights on
prices and earnings-based incentives may actually lead to lower investor welfare relative to exclusively focusing on one type of objective or the other.
C. Heterogeneous Risk Exposures
The previous discussion illustrates that even when investors have identical
climate exposures, neither cash-flow maximization nor price maximization are
generally equivalent to welfare maximization. These differences are further
amplified when investors have heterogeneous climate exposures.
When the manager maximizes expected cash flows, she does not account for
either the nonclimate risk channel or the climate risk channel. Heterogeneity in investors’ climate exposures amplifies the effect that her neglect of the
climate risk channel has on welfare. Intuitively, as can be seen from the expression for the certainty equivalent in (29), this heterogeneity amplifies the
disutility that climate risk creates. Specifically, one can show that the amplification factor increases in τζ−1 , and so, the project’s impact on welfare via
aggregate climate risk rises with τζ−1 .
To gain intuition for the price-maximization case, note that the share price
P(k) can be expressed as
P(k) = Ei [V ] + γ ZCi [V, ηC ] − γ nVi [V ].

(41)

This expression reveals that the price reflects the aggregate climate exposure,
Z, but does not reflect the diversity in climate exposures (i.e., τζ−1 ), which
determines the gains from sharing climate risk (i.e., the risk-sharing channel).
Similarly, the price does not reflect the value of information channel because
it does not capture the additional hedging benefit that investors gain from
having observed θ in the event that the manager invests (i.e., when k = 1).
Because each of these channels improves welfare, this implies that a pricemaximizing manager tends to underinvest in climate-sensitive projects relative to a welfare-maximizing rule. Finally, to reiterate, heterogeneity in exposures, as captured by τζ−1 , amplifies the welfare effect of the climate risk channel. Thus, the price also does not fully account for the climate risk channel,

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

leading to underinvestment in green projects, which reduce aggregate climate
risk, and overinvestment in brown projects, which increase it.
While we are not able to analytically characterize the welfare-maximizing
s p -dependent investment rule in the general heterogeneous exposures case,
we can establish that if the firm is arbitrarily small (i.e., n → 0), then the
welfare-maximizing rule is to always invest. We record this in the following
proposition.
PROPOSITION 7: Suppose that the share endowment is zero (n = 0) and exposures are heterogeneous τ1ζ > 0. Then, the welfare-maximizing s p -dependent
investment policy is to always invest, that is,


arg max W k; s p = 1.

(42)

k∈{0,1}

Hence, both cash-flow maximization and price maximization lead to underinvestment relative to welfare maximization in any states in which they lead the
manager to not invest.
The intuition for this result is straightforward. When the firm is in zero
supply, investment affects welfare only through the risk-sharing and value of
information channels. Moreover, this implies that, irrespective of the information revealed by s p , investors strictly prefer that the firm takes the project, so
that the firm’s shares are useful for sharing risk. This result further clarifies
that traditional managerial incentives can be misaligned relative to welfare
maximization, even if the investment decision has no effect on aggregate expected cash flows or aggregate risk, when investors have heterogeneous risk
exposures. The effect of investment on risk-sharing can be sufficient to lead
investment to be socially suboptimal.
The misalignment between the manager’s objective and investor welfare
implies that feedback from prices need not always improve welfare. To formalize this intuition, we compare investor welfare to a benchmark in which the
manager ignores the information in price and instead chooses to maximize the
ex-ante expectation of cash flows or the share price. In this case, the manager
invests if and only if the unconditional expectation of the price signal s p
exceeds the corresponding threshold s̄ ∈ {s̄C , s̄P }.
The next proposition characterizes sufficient conditions under which feedback reduces welfare.
PROPOSITION 8: Suppose that the no-feedback investment policy is k = 1 (i.e.,
E[s p ] > s̄ for the relevant threshold s̄ ∈ {s̄C , s̄P }) and the project is exposed to
climate risk (i.e., α = 0). Then feedback reduces welfare if
(i) n is sufficiently small, or
(ii) gains from risk-sharing are sufficiently large (i.e., τζ is sufficiently
small).

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1008

1009

Figure 3. Ex-ante welfare: Feedback versus no feedback. This figure plots ex-ante welfare
(i.e., ex-ante expected utility) as a function of τζ and n for a project with positive expected NPV.
Unless otherwise mentioned, the parameters employed are: τθ = 0.5, τζ = 3, τZ = 2, μA = 0, τA =
5, and μθ = c = τη = γ = μZ = n = α = 1. These parameters ensure that the expected NPV of the
project is positive. (Color figure can be viewed at wileyonlinelibrary.com)

Figure 3 illustrates these results for the case in which the manager maximizes the price. The intuition is as follows.28 When the ex-ante NPV of the
project is positive, in the no-feedback benchmark, the manager always invests.
In contrast, given feedback, the firm does not invest for s p ≤ s̄P . On the one
hand, feedback improves the expected price of the stock, which tends to improve welfare through the cash-flow channel. On the other hand, because it
leads to no investment in some states, feedback reduces the ability of investors
to use the stock as a hedge, and so reduces welfare via the risk-sharing channel. It also affects the aggregate exposure to nonclimate and climate risk (with
the direction depending on the sign of α).
When the per-capita endowment of shares n is small, the cash flow and nonclimate risk channels are relatively small. Moreover, the firm’s investment decision has a small effect on the aggregate climate exposure, and so, the climate
risk channel is muted. However, the risk-sharing channel remains important
since it is unaffected by n: regardless of the firm’s size, its stock remains a useful hedge in the event of investment. Consequently, the risk-sharing channel
dominates, and investors are better off with a rule that always invests, yielding
hedging benefits in all states of the world. Analogously, when τζ is small, investors’ exposures to the climate are highly diverse, so that the ability to share
risk provides them with large welfare gains. Hence, the risk-sharing channel
dominates in the limit, once again leading investors to prefer an investment
rule that ensures that the asset is always useful for hedging.
It is worth noting that the manager’s use of price information always
increases the firm’s expected cash flows (share price) under cash-flow maximization (price maximization): any additional information that she infers from
the price can only improve investment efficiency as measured by her objective
28 The economic intuition for cash-flow maximization is analogous.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

function. As a result, Proposition 8 implies that an increase in investment
efficiency need not align with an improvement in investor welfare.
D. Implications for Managerial Compensation
Our welfare results speak to the recent debate on the effectiveness of the use
of climate-risk metrics in executive compensation. On the one hand, there has
been a rapid increase in the use of such measures. Edmans (June 27, 2021)
cites that “51% of large U.S. companies and 45% of leading U.K. firms use ESG
metrics in their incentive plans,” and Hill (November 14, 2021) cites a survey
conducted by Deloitte in September 2021 that suggests “24 per cent of companies polled expected to link their long-term incentive plans for executives to
net zero or climate measures over the next two years.” 29
On the other hand, there is ample skepticism about the effectiveness of such
incentives. In addition to issues around the measurement and monitoring of
such objectives and the possibility of unintended consequences, Edmans (June
27, 2021) argues that incentivizing environmental, social, and governance
(ESG) performance may not necessarily lead to better financial performance.
Instead, he advocates for the use of long-term stock-based compensation,
arguing that “[s]ince material ESG factors ultimately improve the long-term
stock price, this holds CEOs accountable for material ESG issues – even if
they aren’t directly measurable.”
Our analysis suggests that this may not be true because the stock price (even
in the long term) does not fully account for the benefit of investing in climateexposed projects. As such, providing additional incentives based on climate
metrics (e.g., bonuses linked to climate targets) can improve overall investor
welfare. This is despite the fact that such incentives may decrease stock prices
and future profitability on average by leading to inefficient overinvestment
(from the perspective of a price-maximization or cash-flow maximization objective) in green projects. Yet, when investors have diverse climate risk exposures
and find it difficult to hedge these exposures, such incentives improve their
ability to hedge risks and consequently can improve overall welfare.
IV. Related Literature
Our paper adds to the literature on feedback effects (see Bond, Edmans,
and Goldstein (2012) and Goldstein (2023) for recent surveys and early work
by Khanna, Slezak, and Bradley (1994), Subrahmanyam and Titman (2001),
and others). In contrast to our setting, much of this literature focuses on
economies in which (i) investors are risk-neutral or the stock price is set by a
risk-neutral market maker, (ii) the noise in prices arises due to noise traders
with unmodeled utility functions, and (iii) the manager’s investment choice
29 More broadly, Edmans, Gosling, and Jenter (2023) find that over 50% of surveyed directors
and investors report that offering variable pay to the CEO is useful to help “motivate the CEO to
improve outcomes other than long-term shareholder value.”

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maximizes the firm’s expected terminal cash flow. As a result, such models
are not well suited to study how discount rate variation affects investment
decisions or how feedback affects investor welfare.30 To our knowledge, our
paper is the first to develop a model of feedback effects in which managers
learn about not only cash flows but also discount rates from prices, even
though prior work alludes to this channel (Diamond (1967)).
Bond, Edmans, and Goldstein (2012) highlight the important distinction
between FPE, which measures how well prices predict future cash flows, and
revelatory price efficiency (RPE), which captures how useful prices are for real
investment decisions. While in many settings, more informative prices lead
to better investment decisions, a key takeaway of their analysis is that, in
some cases, RPE may be low even when FPE is high. Our analysis provides an
instance in which the opposite is true: with price maximization, we show that
feedback raises investment efficiency and so RPE is high even through FPE
may be low since prices are noisy signals of cash flows.
The most closely related papers in this literature are Dow and Rahi (2003),
Hapnes (2020), and Gervais and Strobl (2021). Dow and Rahi (2003) explore
how increases in informed trading affect investment efficiency and risksharing in a setting in which investors are risk-averse but prices are set by
a risk-neutral market maker. They argue that investment efficiency always
improves with more informed trading, but risk-sharing may either worsen
due to the Hirshleifer (1971) effect or improve when information decreases
uncertainty over the component of the asset’s payoffs that is unrelated to the
component that investors wish to hedge. Hapnes (2020) characterizes managerial investment behavior and investor information acquisition in a Grossman
and Stiglitz (1980)-type model with feedback; however, the analysis does not
study the effect of feedback on welfare. Gervais and Strobl (2021) consider the
impact of informed, active money management on investment decisions in a
setting with feedback. They study how the gross and net performance of the
actively managed fund compares with the market portfolio and study how the
presence of an informed money manager affects welfare.
We view our analysis as complementary. We focus on how investment in a
project affects the risk exposure of a firm’s cash flows, which, in turn, affects
how useful the stock is for hedging. This highlights a novel channel through
which feedback affects welfare: intuitively, firms’ investment decisions endogenously affect the degree of market completeness in the economy.31 Also, since
investors are identically informed in our analysis, the traditional Hirshleifer

30 See Diamond and Verrecchia (1981), Wang (1994), Schneider (2009), Ganguli and Yang
(2009), Manzano and Vives (2011), and Bond and Garcia (2022) for models in which noise is driven
by hedging needs as in our model. Existing feedback models with risk-neutral pricing include Dow,
Goldstein, and Guembel (2017), Davis and Gondhi (2019), and Goldstein, Schneemeier, and Yang
(2020).
31 This also distinguishes our analysis from Marín and Rahi (1999, 2000) and Eckwert and
Zilcha (2003), who consider how exogenous differences in market completeness influence investor welfare.

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Feedback Effects and Systematic Risk Exposures

The Journal of Finance®

(1971) effect is turned off, which allows us to clearly distinguish our novel
channel from earlier work.32
Our focus on welfare is also complementary to recent work by Bond and
Garcia (2022), who show that while indexing may reduce price efficiency, it
improves retail investor welfare due to improvements in risk-sharing. Bond
and Garcia (2022) also make substantial progress on characterizing welfare in
CARA-Normal settings, which we leverage in our derivations. Tension between
notions of firm profitability and welfare also appears in Goldstein and Yang
(2022), who show that improvements in price informativeness increase producer profits due to better-informed real investment, but may harm welfare by
destroying risk-sharing opportunities, similar to the Hirshleifer (1971) effect.
Similar to our findings, other papers studying discrete investment choice also
emphasize the importance of the firm’s “default” investment decision in the
absence of feedback.33 Our analysis complements this earlier work by identifying a novel tension between managerial investment choices and welfare that
is driven by how investment affects the ability of investors to use the stock to
hedge risk.
Our paper is also related to the growing theoretical literature on ESG
investing and climate risk.34 Our work is most closely related to Pástor,
Stambaugh, and Taylor (2021) and Goldstein et al. (2021). Pástor, Stambaugh,
and Taylor (2021) show that green assets have lower costs of capital because
investors enjoy holding them and they hedge climate risk. Goldstein et al.
(2021) consider a model in which traditional and green investors are informed
about a firm’s financial and ESG output, and demonstrate that this can lead
to multiple equilibria. Our setting generates distinct predictions for green
investment decisions and welfare by incorporating the feedback effect and
considering green investment’s impact on risk-sharing efficiency.
The production-based asset pricing literature beginning with Cochrane
(1991) also considers how variation in firms’ discount rates affects the relationship between investment, expected cash flows, and expected returns. This
work assumes that a manager knows not only her project’s risk factor loadings,
32 While the Hirshleifer (1971) effect and our risk-sharing channel both affect the ability of investors to share risk, the two mechanisms are distinct. The Hirshleifer (1971) effect refers to the
phenomenon whereby the introduction of public information destroys risk-sharing opportunities.
In contrast, our risk-sharing channel captures the fact that endogenous investment decisions can
affect the effective completeness of the market by directly changing the risk exposures of traded securities.
33 For instance, Dow, Goldstein, and Guembel (2017) show that investors’ equilibrium information acquisition hinges on whether the firm defaults to a risky or a riskless project. Davis and
Gondhi (2019) show that complementarity in learning depends on both the default investment
decision and the correlation between the investment and assets in place. Goldstein, Schneemeier,
and Yang (2020) study information acquisition in a feedback model with multiple sources of uncertainty. They show that investors seek to acquire the same information as management for positive
NPV projects, but different information for negative NPV projects.
34 Additional studies include Heinkel, Kraus, and Zechner (2001), Friedman and Heinle (2016),
Chowdhry, Davies, and Waters (2019), Oehmke and Opp (2020), Pedersen, Fitzgibbons, and
Pomorski (2021), and Jagannathan et al. (2023).

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but also the conditional risk premia associated with these factors. However, in
practice, factor risk premia depend on dispersed information (e.g., investors’
risk exposures and preferences) and thus are difficult for managers to observe directly. Instead, prices are a crucial source of information about discount
rates. Our analysis explores the implications of such managerial learning on
investment decisions and investor welfare.

V. Conclusions
In this paper, we develop a model of informational feedback effects in which
a firm’s investment alters its exposure to an aggregate risk, and we discuss
its application to climate-exposed investment. When a firm invests in a project
that is exposed to climate risk, it affects how useful the asset is as a hedge
for climate risk. As a result, the firm’s stock price reflects information about
investors’ climate exposures and the project’s expected cash flows, which are
both relevant to the manager’s investment choice. We show that this has novel
implications for how a project’s greenness affects the likelihood of investment,
conditional expected returns and future profitability. Moreover, we show that
because the price does not fully reflect the welfare externality generated by
investment in climate-sensitive projects, price-maximization tends to lead to
underinvestment in green projects.
In addition to climate-exposed investments, our model’s predictions on
investment and managerial incentives apply broadly to investments that
are exposed to systematic risks with variable risk premia. For instance,
investments that are exposed to commodity prices may serve as inflation
hedges and thus may have discount rates that vary with investors’ aggregate
inflation concerns. Moreover, investments in emerging markets are exposed to
aggregate demand in those markets and so are likely to have discount rates
that vary with uncertainty over this demand. Our model’s implications for
feedback’s impact on welfare also apply more generally, whenever the market
is incomplete with respect to the investment’s risk exposure.
A notable contribution of our analysis is to provide a tractable feedback
effects framework with investor risk-aversion and priced risk factors. Immediate extensions include generalizations to the structure of cash flows and
information. For instance, allowing for both public and private information
signals would enable future research to assess the merits of disclosure regarding firms’ climate risk exposures. Similarly, introducing multiple dimensions
of fundamentals as in Goldstein and Yang (2019) and Goldstein, Schneemeier,
and Yang (2020) could enable future work to assess how climate-exposed
investments interact with the other risks that firms face. Finally, it may be
interesting to consider how dynamics and multiple traded assets influence
managers’ ability to infer discount rate information from prices.
Initial submission: June 17, 2021; Accepted: November 3, 2023
Editors: Stefan Nagel, Philip Bond, Amit Seru, and Wei Xiong

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Feedback Effects and Systematic Risk Exposures

Appendix: Proofs
A. Proof of Proposition 1
We first establish the existence of the stated equilibrium. We then argue
that, among all threshold equilibria, the stated equilibrium involves the most
investment. Begin by conjecturing an equilibrium of the form posited in the
text. That is, suppose that there is a random variable of the form s p = θ + β1 Z
and a threshold s ∈ R such that the asset prices at the two trading dates are
identical and take the form
P1 = P3 =

A1 + B1 s p
A0

s p > s̄
.
s p ≤ s̄

(A.1)

We can now derive the equilibrium, and confirm the above conjecture, by working backwards. At date t = 3, investors can observe the actual investment decision made at t = 2. Hence, they perceive the asset payoff as conditionally
normally distributed with conditional moments

(A.2)
Ei3 [V (k)] = Ei3 [A + k(θ + αηC + 1 − α 2 ηI − c)] = μA + k(θ − c),
Ci3 (V (k), ηC ) = kα τ1η ,

(A.3)

Vi3 (V (k)) = τ1A + k2 τ1η .

(A.4)

An arbitrary investor i solves the following static optimization problem at this
date:
max Ei3 [−e−γ Wi4 ].
x∈R

(A.5)

Given her demand x, the investor’s terminal wealth Wi4 is
Wi4 = (n + Xi1 + x )V − xP3 − Xi1 P1 − zi ηC ,

(A.6)

where Xi1 , the trade from the t = 1 trading round, is taken as given.
Applying well-known results for CARA utility, this problem leads to a standard mean-variance demand function:
Xi3 =

Ei3 [V (k)] + γ Ci3 (V (k), ηC )zi − P3
− (n + Xi1 ).
γ Vi3 (V (k))

(A.7)

Plugging in for the conditional moments from above and enforcing market
clearing yields the equilibrium price


P3 = μA + k(θ − c ) + γ kα τ1η Z − γ τ1A + k2 τ1η n
(A.8)

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1014

1015



= μA − γ τ1A n + k θ + γ α τ1η Z − c − γ τ1η n ,

(A.9)

where the second line collects terms and uses the fact that k ∈ {0, 1} implies
k = k2 to simplify. Hence, to be consistent with our initial conjecture, the endogenous signal s p must have coefficient β1 = γτηα on Z. To be consistent with our
conjecture, the price coefficients must satisfy
A0 = μA − γ τ1A n,

(A.10)

A1 = μA − γ τ1A n − c − γ τ1η n,

(A.11)

B1 = 1.

(A.12)

Stepping back to t = 2, the manager’s problem is to solve
max E[V (k)|P1 ],

k∈{0,1}

(A.13)

where she can condition on the first-period price, P1 . The optimal investment
is therefore
k=

1 E[θ |P1 ] > c
.
0 E[θ |P1 ] ≤ c

(A.14)

Now, let s̄C denote the level of s p such that the manager would be indifferent
to investing and not investing if she observed s p , that is,
E[θ |s p = s̄C ] − c = 0.


τp
1
Because E[θ |s p ] = μθ + τθ +τ
s
, with τ p ≡ β 2 τZ , we have
−
μ
−
μ
p
θ
Z
β
p
τθ + τ p
γα
μZ −
(μθ − c )
τη
τp
γ
τθ (μθ − c )
+ αμZ .
=c−
τp
τη

E[θ |s p = s̄C ] − c = 0 ⇔ s̄C = μθ +

We claim that the threshold s̄ = s̄C is consistent with our conjectured equilibrium, that is, the manager invests if and only if s p > s̄C . Under such a threshold, when the manager observes A0 , she knows s p lies below s̄C with probability
1, and so infers that it is suboptimal to invest. In contrast, when she observes
P1 = A0 , she infers s p and knows that s p lies above s̄C , and so chooses to invest.
Thus, the investment threshold s̄C is indeed consistent with conjectured form
of equilibrium.

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Feedback Effects and Systematic Risk Exposures

Stepping back to t = 1, the problem of an arbitrary investor is
max Ei1 [−e−γ Wi4 ],
x∈R

where her terminal wealth is
Wi4 = (n + x + Xi3 )V − Xi3 P3 − xP1 − zi ηC
and where the optimal t = 3 demand Xi3 was derived above. Given the functional form for P3 , the realization of P3 is perfectly anticipated under the investor’s information set Fi1 = σ (θ , zi , P1 ). Hence, to rule out arbitrage, the price
must satisfy P1 = P3 , and consequently, all investors are indifferent to trading
at t = 1 at this equilibrium price. Thus, we have now shown that the equilibrium stated in the proposition exists.
Finally, we argue that this equilibrium maximizes investment over all possible threshold equilibria. Suppose by contradiction that there were an equilibrium with a lower investment threshold s̄ < s̄C . Then, the date 1 price would
reveal s p to the manager for s p ∈ (s̄, s̄C ) and the manager would invest for such
s p . However, by the definition of s̄C , investment reduces expected cash flows
in this region, and so, the manager could improve the expected cash flows by
deviating to not investing when she observes s p in this region. This contradicts
the purported existence of an equilibrium with s̄ < s̄C and hence establishes
the claim.

B. Proof of Proposition 2
The proof proceeds similarly to the proof of Proposition 1 above. Again, we
begin by conjecturing asset prices in the two trading dates that take the form
in (A.1). At date t = 3, investors can observe the actual investment decision
made at t = 2. Hence, the date 3 equilibrium, given the manager’s investment
choice, follows exactly as in the previous proof: they perceive the asset payoff
as conditionally normally distributed with conditional moments as in equations (A.2) to (A.4), their optimal demands take the form in (A.7), the date 3
price takes the form in (A.9), and the endogenous signal s p again must have
coefficient β1 = γτηα on Z.
Stepping back to t = 2, the manager’s problem is now to solve
max E[P3 |P1 ],

k∈{0,1}

(A.15)

where she can condition on the first-period asset price, P1 . Using the expression
for P3 derived in the first step of the proof, the manager’s problem reduces to
$ %
#
$
max kE s p − c − γ τ1η n$$P1 .

k∈{0,1}

(A.16)

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1017

The optimal investment is therefore

k=

1 E[s p |P1 ] > c + γ τ1η n
0 E[s p |P1 ] ≤ c + γ τ1η n

.

(A.17)

Note that the threshold s̄P , defined by s̄P ≡ c + γ τ1η n, is the value such that
if the manager always observed s p , she would invest if and only if s p > s̄P . We
claim that this threshold is consistent with our conjectured equilibrium. To see
this, note that if the manager observes P1 = A0 , she infers s p ≤ s̄P , and so, she
chooses not to invest. In contrast, if she observes any P1 = A0 , she infers the
realized value of s p , necessarily strictly greater than s̄P , and therefore finds it
optimal to invest. Hence, the investment threshold s̄P is indeed consistent with
our initial conjecture.
Stepping back to t = 1, as in the prior proof, since the manager’s investment decision is a function of P1 , investors can anticipate k given the price.
Thus, they can perfectly anticipate the date 3 price, and, to rule out arbitrage,
the price must satisfy P1 = P3 . Consequently, all investors are indifferent to
trading at t = 1 at this equilibrium price. This completes the construction of
the equilibrium.
This equilibrium maximizes investment over all possible threshold equilibria. Suppose by contradiction that there were an equilibrium with a lower
investment threshold s̄ < s̄P . Then, the price would reveal s p to the manager
for s p ∈ (s̄, s̄P ). Moreover, by the definition of s̄P , investment lowers price on
this region, and so, the manager prefers to deviate to not investing when

observing s p in this region.
C. Proof of Proposition 3
The probability of investment is given by
⎛  
⎞
E s p − s̄C
= ⎝    ⎠
V sp

⎛ 
⎞
τθ τ1θ + τ1p (μθ − c )
⎝
⎠

1
1
+
τθ
τp
&
!
1
1
+ (μθ − c ) .
τθ
τθ
τp



Pr s p > s̄C = 1 −

=

=

Recalling that τ p = β 2 τZ =
claimed results.



τη
γα

s̄C − E[s p ]
V[s p ]

2

(A.18)

(A.19)

(A.20)

τZ , direct inspection immediately yields the


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Feedback Effects and Systematic Risk Exposures

D. Proof of Proposition 4
The probability of investment is given by




Pr s p > s̄ = 1 −

sP − E[s p ]
V[s p ]

=

⎛
=

⎛  
⎞
E s p − s̄P
⎝ 
⎠
 
V sp
⎞

γn
αγ μ
⎜ μθ − c − τη + τη Z ⎟
⎟.
⎜ '
⎠
⎝
 2
αγ
1
1
+
τθ
τη
τZ

(A.21)

(A.22)

This immediately implies that the probability of investment is increasing in
μθ − c, decreasing in n, and increasing in μZ . Moreover, for any arbitrary parameter b, after applying the monotonic transformation −1 (· ) and using the
definition NPV = θ − c − γ τ1η (n − αZ ) from the text to condense notation, we
have


∂
∂
Pr s p > s̄ ∝
∂b
∂b

γ n αγ μZ
+
μθ − c −
τη
τη
&
1
αγ 2 1
+
τZ
τθ
τη

∂ E[NPV ]
√
∂b V(NPV )
√
√
∂
∂
V(NPV ) ∂b
E[NPV ] − E[NPV ] ∂b
V(NPV )
=
V(NPV )
∂
∂ √
|E[NPV ]| ∂b E[NPV ]
V(NPV )
∂b
=√
−
sgn
E
NPV
( [
]) √
V(NPV )
V(NPV ) |E[NPV ]|
∂
∂
|E[NPV ]| ∂b
E[NPV ]
V(NPV )
1
∂b
.
=√
sgn
E
NPV
−
(
[
])
2
V(NPV )
E[NPV ]|
|
V(NPV )
=

(A.23)

(A.24)
(A.25)
(A.26)
(A.27)

For α, we have


∂
Pr s p > s̄ ∝
∂α

∂
V(NPV )
∂
1
∂α
E
NPV
−
E
NPV
[
]
[
]
∂α
2
V(NPV )

(A.28)

=

γ μZ
γ n αγ μZ
− μθ − c −
+
τη
τη
τη

⎛

⎞2

1
+
τθ

αγ
τη

1 ⎝ αγ ⎠ 1
α
τη τZ
2

(A.29)
1
τZ

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1018

1019

⎛

⎞
αγ 2 1
1
+
⎜γ μ
τZ
γ n αγ μZ ⎟
τη
⎜ Z τθ
⎟
(A.30)
=
− μθ − c −
+
⎛
⎞2
⎜
⎟
⎝ τη
⎠
τη
τη
1
αγ
1 ⎝ αγ ⎠ 1
1
+
α
τZ
τη τZ
τθ
τη
⎛
⎞
⎛
⎞2
1
αγ 2 1
1 ⎝ αγ ⎠ 1
+
α
τZ
γ n αγ μZ ⎟
τη τZ ⎜
τη
⎜ αγ μZ τθ
⎟
=
−
μ
−
c
−
+
⎛
⎞
⎜
⎟ (A.31)
θ
2
2
⎝
⎠
τη
τη
τη
αγ 1
1
αγ
1
⎝
⎠
+
τZ
τZ
τη
τθ
τη
⎛
⎛
⎞
⎞
⎛
⎞2
1
1 ⎝ αγ ⎠ 1
⎜
⎟
α
γ n αγ μZ ⎟
τη τZ ⎜
⎜ αγ μZ ⎜
⎟
⎟
τ
=
+
⎜
⎜1 + ⎛ θ⎞2 ⎟ − μθ − c −
⎟ (A.32)
2
⎝
⎝
⎠
⎠
τ
τ
τ
αγ
1
αγ
η
η
η
1
⎝
⎠ 1
+
τZ
τZ
τη
τθ
τη
⎛
⎞2
⎞
⎛
⎛
⎞
1
1 ⎝ αγ ⎠ 1
α
⎟
⎜
⎟
τη τZ ⎜
⎜⎜ ⎛ τθ⎞ ⎟μZ − μθ − c − γ n ⎟
=
(A.33)
2
⎝⎝ αγ 1 ⎠
τη ⎠
1
αγ
1
⎝
⎠
+
τZ
τη τZ
τθ
τη
⎛
⎞2
1 ⎝ αγ ⎠ 1
α
τη τZ
2

=−

⎛
⎞2
1 ⎝ αγ ⎠ 1
α
τη τZ
2

1
+
τθ

αγ
τη

μθ − c −
1
τZ

γ n τη τZ 1
− αγ τθ μZ ,
τη

(A.34)

which implies


∂
γ n τη τZ 1
Pr s p > s̄ < 0 ⇔ sgn(α) μθ − c −
− αγ τθ μZ
∂α
τη

> 0.

(A.35)

Moreover, note that because the parameters τ ∈ {τZ , τθ } do not enter the expected NPV and increases in these τ strictly decrease the variance of the NPV,
we have
∂

 ∂


∂
V(NPV )
Pr s p > s̄ ,
Pr s p ≥ s̄ ∝ − 12 sgn (E[NPV ]) ∂τV(NPV )
∂τZ
∂τθ
∝ sgn (E[NPV ]),

(A.36)
(A.37)

so that the dependence is pinned down by the sign of the expected NPV, which
immediately establishes the claimed result.

E. Proof of Proposition 5
To establish the claim on the welfare-maximizing policy, we compute the
conditional expected utility of an arbitrary trader given (θ , Z), show that the
investment rule that maximizes this utility is the one stated in the proposition,

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Feedback Effects and Systematic Risk Exposures

and note that this rule depends on (θ , Z) only through the linear combination
s p = θ + γτηα Z. Hence, it can be implemented as an s p -contingent (i.e., pricecontingent) rule.
The conditional expected utility given (θ , Z) follows from the expression for
investors’ expected utility in equation (I.A16), after recognizing that in the case
of homogeneous exposures, we have that the nontradeable endowment is zi = Z
for all i, and consequently, the (θ , Z) information set is precisely the investor
information set. However, we can derive the expression more directly by noting
that in the case of homogeneous exposures, there is no trade in equilibrium
and so investors simply hold their initial endowment of n shares. Hence, the
realized utility of an arbitrary trader is
√

−e−γ (nV −ZηC ) = −e−γ n(A+k(θ+αηC + 1−α ηI )−c)+γ ZηC .
2

The conditional expectation of this expression given (θ , Z) is
$
%
#
√
$
−γ n(A+k(θ+αηC + 1−α 2 ηI )−c)+γ ZηC $
W(k; θ , Z) ≡ E −e
$θ , Z
−γ (μA +k(θ−c))n+ 12 γ 2

= −e




1
α
1 2 1 2
2 1
2
2
τ +k τη n −γ kn τη Z+ 2 γ τη Z
A





−γ μA +k θ+ γτηα Z−c n+ 12 γ 2 τ1 +k2 τ1η n2 + 12 γ 2 τ1η Z2

(A.38)

(A.39)
(A.40)



= −e

A

−γ (μA +k (s p −c ))n+ 12 γ 2

= −e




1
2 1
2 1 2 1 2
τ +k τη n + 2 γ τη Z
A

,

(A.41)
(A.42)

where the second line uses standard expressions for computing the expectation
of exponential-quadratic forms of normally distributed random variables, the
third line groups terms, and the final line recognizes that s p = θ + γτηα Z.

Now, since we have k2 = k for
 k ∈ {0, 1}, it follows that the investment k ∈
{0, 1} that maximizes W k; θ , Z is



1
1
1
1 1
n2 − γ 2 Z2
k(·) = arg max γ μA + k s p − c n − γ 2
+k
2
τ
τ
2
τη
η
A
k∈{0,1}
)
(
1 1
= 1 sp − c − γ n > 0 .
2 τη

Defining sW ≡ c + 12 τγη n delivers the investment rule in the proposition. Because this rule depends on (θ , Z) only through s p , it can be implemented as
an s p -contingent rule.
Furthermore, using the expressions for the price-maximizing threshold, s =
c + τγη n, from Proposition 2, and the cash-flow-maximizing threshold, s̄C = c −
τθ (μθ −c)
+ τγη αμZ , from equation (14), yields the expressions for s − sW and s̄C −
τp

sW . The claims about over- and underinvestment are immediate given the signs
of these expressions.


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F. Proof of Proposition 6
Given our expressions for P1 and P3 in a threshold equilibrium, we can write
δE[P3 |P1 ] + (1 − δ)E[V |P1 ]

δ μA − γ τ1A n + k(s p − c − γ τ1η n) +



=
2
(1 − δ) μA + k μθ − c + τθ β+βτ2ZτZ (s p − E[s p ]) .


(A.43)
(A.44)

The k ∈ {0, 1} that maximizes this expression is
(
)
τp
1
k(s p ) = 1 δ s p − c − γ n + (1 − δ) μθ − c +
(s p − E[s p ]) > 0
τη
τθ + τ p
(A.45)
*
τp
1
1
δ c + γ n + (1 − δ) c − μθ +
E[s p ]
= 1 sp >
.
τp
τη
τθ + τ p
δ + (1 − δ) τθ +τ
p
(A.46)
Setting the threshold in this expression equal to s̄W = c + 12 γ τ1η n and solving
for δ yields
τ

δ=

τ

p
p
μθ − c − τθ +τ
E[s p ] + τθ +τ
s̄W
p
p

τ

p
θ
μθ + γ τ1η n − τθ +τ
E[s p ] − τθ τ+τ
s̄W
p
p




τp
τp
μθ + β1 μZ + τθ +τ
c + 12 γ τ1η n
μθ − c − τθ +τ
p
p




=
τp
τθ
1
1 1
μ
−
c
+
μθ + γ τ1η n − τθ +τ
+
μ
γ
n
θ
Z
β
τθ +τ p
2 τη
p


τp
τθ
1
μ − 12 γ τ1η n
μ − c ) − τθ +τ
τθ +τ p ( θ
β Z
p


.
=
τp
τθ
1
1 1
1 1
−
c
−
μ
−
γ
n
+
γ
n
μ
)
(
θ
τθ +τ p
τθ +τ p β Z
2 τη
2 τη

After substituting in β1 = γτηα and τ p = β 2 τZ , this matches the expression in the

proposition. If α = 0, then β1 → 0 and τ p → ∞, and thus, this expression reduces to
1 1
γ n
1
2 τη
= ,
1
1 1
2
γ n + 2 γ τη n
2 τη

δ= 1

(A.47)

ω
as claimed. More generally, note that one can express δ = ω+υ
, where ω =


τp
τθ
1
1 1
1 1
μ − c ) − τθ +τ p β μZ − 2 γ τη n and υ = 2 γ τη n > 0. This implies δ ∈ (0, 1)
τθ +τ p ( θ
if and only if ω > 0.


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Feedback Effects and Systematic Risk Exposures

G. Proof of Proposition 7
Consider the conditional welfare expression from Proposition I.A9 for an arbitrary investment k and price signal realization s p . We will show that this
expression is strictly increasing in k for k ∈ [0, 1], from which it follows that
the welfare-maximizing investment is k = 1.
For n = 0, the conditional welfare is
W(k; s p ) = −D(k; s p ) exp{Q(k; s p )},

(A.48)

where

 1 1



Q k; s p = γ 2 E2p [Z] 1 + k; s p ,
2 τη
and where the determinant term D and the function
are as given in Proposition I.A9:



D(k; s p ) = 


1
+ k2 τ1η
τA
1
+ k2
τA


V p (θ |zi ) + τ1η








1
1
V p (Z ) +
k; s p = γ 2
τη
τζ
⎛

do not depend on n and



k; s p



γ 2 τ1η V p (Z ) + τ1ζ

⎛

⎜
1
1
⎜
V p (Z ) +
× ⎜1 − γ 2
⎝
τη
τζ

2

1
τζ

k2 α 2 τ1η

⎞⎞−1

⎟⎟
⎜
V p (Z)+ τ1
⎟⎟
⎜
ζ

 ⎟⎟ .
⎜1 −
1
1 ⎠⎠
⎝
2
+ k V (θ |z ) +
p

τA

i

τη

Because of the negative sign in front of the expression in equation (A.48), to
show that conditional expected utility increases in k, it suffices to show that the
functions Q and D are decreasing functions of k for k ∈ [0, 1]. Moreover, because
k enters these expressions only in terms of k2 , it suffices to characterize their
behavior as functions of k2 for k2 ∈ [0, 1].
Consider first the function , which appears in both Q and D. We have
2

1
τ

ζ
k2 α 2 τ1η V (Z)+
1
p
∂
τζ


∂k2 1 + k2 V (θ |z ) + 1
p
i
τA
τη

=

1 2 1
α τη
τA
1
+ k2
τA

1
τζ

V p (Z)+ τ1
ζ

(A.49)

2


2 ,
V p (θ |zi ) + τ1η

(A.50)

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1023

which is strictly positive when τ1ζ > 0, from which it follows that

is decreasing

in k2 , and consequently, Q is decreasing in k2 .

Considering D, it remains only to show that the term
creasing since we have already shown that

τA

i

τη

V p (θ|zi )+ τ1η

 is de-

is decreasing. We have

1
+ k2 τ1η
∂
τA

=
∂k2 1 + k2 V (θ |z ) + 1
1
p

1
2 1
τA +k τη


1
2
τA +k

− τ1A V p (θ |zi )

2 ,
1
2
+ k V p (θ |zi ) + τη
τA

(A.51)

which is strictly negative when τ1ζ > 0. Hence, we have verified that investors
are strictly better off when k = 1 than k = 0 for a given price signal realization s p . Because this holds for all realizations of s p , it follows that the ex-ante
welfare-maximizing policy is to always invest.

H. Proof of Proposition 8
Consider either threshold s ∈ {sC , sP }. If the unconditional policy is to invest
(i.e., E[s p ] − s > 0), then a manager who does not condition on price optimally
invests in all states of the world, leading to “no feedback” investment kNF ≡
1. Hence, to establish that feedback reduces welfare, it suffices to show that
welfare is higher with kNF = 1 than with the threshold policy k(s p ) = 1{s p >s} .
The small n limit in the proposition follows immediately from Proposition 7
and continuity of the expected utility in n since Proposition 7 establishes that
the welfare-maximizing investment policy for n = 0 is for the manager to always invest. Hence, because feedback causes the manager to not invest with
strictly positive probability, feedback strictly reduces ex-ante welfare.
The τζ limit is easier to establish using the unconditional welfare expression in Proposition I.A10 directly. Establishing the limit as τζ ↓, is equivalent
to establishing the limit as 1/τζ ↑. For unconditional expected utility to exist,
τ
we must have 1 1 1 − γ 2 τ1η > 0 ⇔ 0 ≤ τ1ζ < γ η2 − τ1Z . Hence, the relevant limit
1
τζ

+
τZ τζ
τη
1
↑ γ 2 − τZ . Using the unconditional welfare from Proposition I.A10, wel-

⇔




D(0) exp Q(0)





s−E[s p ]+m(1)
√
− 1−
D(1) exp Q(1)
v(1)








s−E[s p ]+m(0)
s−E[s p ]+m(1)
√
√
D(0)
exp
Q(0)
>
D(1) exp Q(1) .
v(0)
v(1)

is
fare under the no-feedback investment level kNF = 1 is higher than under the
feedback policy k(s p ) = 1{s p >s} if and only if


−D(1) exp Q(1) > −



s−E[s p ]+m(0)
√
v(0)

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Feedback Effects and Systematic Risk Exposures

Hence, to establish the claimed result, it suffices to show

lim

1
1 τη
↑ −
τζ γ 2 τZ

s−E[s p ]+m(0)
√
v(0)




D(0) exp Q(0) >


lim

1
1 τη
↑ −
τζ γ 2 τZ

s−E[s p ]+m(1)
√
v(1)




D(1) exp Q(1) .



s−E[s p ]+m(0)
√
We will show this by establishing that lim 1 τη 1
D(0)
v(0)
↑ −
τζ γ 2 τZ






s−E[s p ]+m(1)
√
exp Q(0) = ∞, while lim 1 τη 1
D(1) exp Q(1) < ∞.
v(1)
↑ −
τζ γ 2 τZ
τη
1
Letting a = γ 2 − τZ to reduce clutter, note first that

lim (k) = lim γ 2
1
↑a
τζ

1
↑a
τζ

1 1
1
+
τη τZ
τζ

⎛

⎛
k2 α 2 τ1η

⎜
1 1
1
⎜
× ⎜1 − γ 2
+
⎝
τη τZ
τζ

=

⎞⎞−1

2

1
τζ

1
1
⎜
⎟⎟
τZ + τζ
⎜
⎟⎟

 ⎟⎟
⎜1 −
1
1
1
⎝
2
+ k τη + β 2 τ +τ ⎠⎠
τA
( Z ζ)

∞
k=0
,
Finite k = 1

where the finite limit in the k = 1 case relies on the assumption α = 0.
It follows that we have



lim D(k) = lim 

1
↑a
τζ

1
↑a
τζ

=

1
+ k2 τ1η
τA
1
+ k2
τA



1
+ β 2 τ 1+τ
τη
( Z ζ)






γ 2 τ1η



 
k
1
+ τ1ζ
τZ



∞
k=0
.
Finite k = 1

Similarly,
(
1
1
1 − α2
lim Q(k) = lim −γ E p [V ]n + γ 2
+ k2 V p (θ ) +
1
1
2
τA
τη
↑a
↑a
τζ

τζ

=

n2

)


2 
1 1
+ γ2
E p [Z] − kαn − γ kC p (Z, θ )n 1 + k; s p
2 τη
∞
k=0
.
Finite k = 1

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1025

Because the function

is bounded, together these results imply that




s−E[s p ]+m(1)
√
D(1) exp Q(1) < ∞
lim
v(1)
1
↑a
τζ

as claimed.
It remains to show that lim 1



s−E[s p ]+m(0)
√
v(0)

↑a





D(0) exp Q(0) = ∞. Consid-

τζ
s−E[s p ]+m(0)
s−E[s p ]+m(0)
√
√
ering
, if 1/β = 0, then
is constant in τζ and we are done.
v(0)
v(0)

Considering 1/β = 0, we have
lim

1
↑a
τζ

s−E[s p ]+m(0)
√
= lim √m(0)
v(0)
v(0)
1
↑a
τζ

= lim

1
↑a
τζ

γ C (s p ,V (0) )n−γ 2 C (s p ,Z ) τ1η μZ (1+ (0))

V (s p )+γ 2 C2 (s p ,Z ) τ1η (1+ (0))

= lim 
1
↑a
τζ

=

−γ 2 β1 V(Z) τ1η μZ (1+ (0))

V (s p )+γ 2 C2 (s p ,Z ) τ1η (1+ (0))

⎧
⎨−∞

1
>0
β

⎩∞

1
<0
β

where we use the fact that lim 1

τζ

↑a

,

(0) = ∞.

If 1/β <0, the proofis complete, since Q(0) →∞, D(0) → ∞ and in this case,


s−E[s p ]+m(1)
s−E[s p ]+m(0)
√
√
> 0, so that lim 1
D(0) exp Q(0) =
lim 1
v(1)
v(0)
↑a
↑a
τζ
τ
ζ

s−E[s p ]+m(1)
√
∞. If 1/β > 0, then lim 1
= 0, so the limit is still indetermiv(1)
↑a
τζ 



s−E[s p ]+m(0)
√
nate. Write
D(0) exp Q(0) as
v(0)


s−E[s p ]+m(0)
√
v(0)






D(0) exp Q(0) =

s−E[s p ]+m(0)
√
v(0)

1
exp
D(0)





−Q(0)



and note that the relevant limit ultimately depends on the relative rate at

−1

approaches ∞, so
which the various terms grow as x ≡ 1 − γ 2 τ1η τ1Z + τ1ζ
that we can write


s−E[s p ]+m(0)
 √ 
√
− x
v(0)
,
lim 1

 = lim 1
x→∞ √ exp {−x}
1
↑a D(0) exp −Q(0)
x
τζ

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Feedback Effects and Systematic Risk Exposures

s−E[s ]+m(0)

√p
where we have used the fact that
and D(0) grow at order
v(0)
and Q grows at order x with x. Using L’Hospital’s rule yields

lim

 √ 
− x

x→∞ √1 exp {−x}
x

= lim

√
x with x

 √ 
− 12 x−1/2 φ − x

x→∞ − √1 exp {−x} − 1 x−3/2 exp {−x}
2
x

 √ 
φ − x
= lim
x→∞ 2 exp {−x} + x−1 exp {−x}


√1 exp − 1 x
2
2π
= lim
x→∞ 2 exp {−x} + x−1 exp {−x}
= ∞,

which establishes lim 1

τζ

↑a

s−E[s p ]+m(0)
√
v(0)
1
exp{−Q(0)}
D(0)

= ∞ and completes the proof.



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Supporting Information
Additional Supporting Information may be found in the online version of this
article at the publisher’s website:
Appendix S1: Internet Appendix.
Replication Code.

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==> JF5 - 2023 - HSU - The Pollution Premium.txt <==
THE JOURNAL OF FINANCE • VOL. LXXVIII, NO. 3 • JUNE 2023

The Pollution Premium
PO-HSUAN HSU, KAI LI, and CHI-YANG TSOU*
ABSTRACT
This paper studies the asset pricing implications of industrial pollution. A long-short
portfolio constructed from firms with high versus low toxic emission intensity within
an industry generates an average annual return of 4.42%, which remains significant
after controlling for risk factors. This pollution premium cannot be explained by existing systematic risks, investor preferences, market sentiment, political connections,
or corporate governance. We propose and model a new systematic risk related to environmental policy uncertainty. We use the growth in environmental litigation penalties to measure regime change risk and find that it helps price the cross section of
emission portfolios’ returns.

PRIOR FINANCE RESEARCH SHOWS THAT consumption and production
influence expected stock returns. Little is known, however, about the role
of their by-product—industrial pollution—in asset pricing. On the one hand,
polluting firms may save costs by not investing in emission abatement and
environmental recovery in the short run. On the other hand, the negative
* Po-Hsuan Hsu is with the College of Technology Management, National Tsing Hua University.
Kai Li is with Peking University HSBC Business School and PHBS Sargent Institute of Quantitative Economics and Finance. Chi-Yang Tsou is with the Alliance Manchester Business School,
University of Manchester. We are indebted to Wei Xiong (the Editor), an anonymous Associate
Editor, two anonymous referees for highly valuable comments and suggestions that helped significantly improve the paper. We are grateful for helpful comments from Hengjie Ai; Ivan Alfaro;
Ronald Balvers; Frederico Belo; Patrick Bolton; David Chapman; Steven Davis; Stefano Giglio;
Gautam Gowrisankaran; John Griffin; Thomas Hellmann; Weiwei Hu; Mingyi Hung; Chuan Yang
Hwang; Chanik Jo; Kuan-Cheng Ko; Hao Liang; Roger Loh; Evgeny Lyandres; Christopher Malloy;
Kalina Manova; Gustav Martinsson; Roni Michaely; Jun Pan; Ivan Png; Vesa Pursiainen; Tatsuro
Senga; Clemens Sialm; Ngoc-Khanh Tran; Kevin Tseng; Rossen Valkanov; K.C. John Wei; Tingyu
Yu; Bohui Zhang; Chendi Zhang; Hong Zhang; Lei Zhang; Lu Zhang; Yao Zhou; and seminar and
conference participants at the NCTU International Finance Conference, the Taiwan Economics Research Conference, the TFA Asset Pricing Symposium, the 2nd World Symposium on Investment
Research, and the ABFER conference. We thank Yaojun Ke and Lianghao Shen for their excellent
research assistance. Kai Li gratefully acknowledges the General Research Fund of the Research
Grants Council of Hong Kong (Project Number: 16506020) for financial support. Po-Hsuan Hsu
gratefully acknowledges the E.SUN Academic Award. We are responsible for any remaining errors or omissions. We have read The Journal of Finance disclosure policy and have no conflicts of
interest to disclose.
Correspondence: Kai Li, Peking University HSBC Business School and PHBS Sargent Institute of Quantitative Economics and Finance, Xili University Town, Nanshan District, Shenzhen,
Guangdong Province, China, 518055; e-mail: kaili825@gmail.com.

DOI: 10.1111/jofi.13217
© 2023 the American Finance Association.

1343

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externalities created by such firms are monitored by the general public, media, and governments in the long run, and polluting firms could be subject
to activist protests, litigation and reputational risk, and penalties imposed by
regulatory authorities.1 Motivated by this gap in the literature, in this paper
we empirically examine the pricing impact of industrial pollution.
Our investigation proceeds in two stages. In the first stage, we construct empirical proxies for firm-level pollutants and examine the cross-sectional variation in the relation between stock returns and industrial pollution. In the
second stage, we propose an extensive list of possible explanations for such
return predictability and perform various tests to shed light on the true underlying mechanism.
To study the empirical relation between industrial pollution and expected
stock returns at the firm level, we construct a measure of “emission intensity”
using pollution data from the Toxic Release Inventory (TRI) database. Specifically, for each year over period 1991 to 2016, we first capture a firm’s toxic
emissions by summing the amount of emissions of all types of chemicals across
all plants listed in the TRI database, a comprehensive database of mandatory
pollution reports maintained by the United States Environmental Protection
Agency (EPA). Institutional background on the TRI database is provided in
Section I.A in the Internet Appendix.2 We then calculate a firm’s emission intensity as its ratio of toxic emissions to total assets: which we obtain from Compustat. Firms with higher emission intensity are associated with a higher frequency or probability of being involved in environment-related lawsuits. These
firms are also associated with significantly higher contemporaneous profits.
We next assign firms to quintile portfolios based on their emission intensity
relative to industry peers, given that chemical emissions tend to vary across
industries. Such portfolio sorts show that firms producing more emissions are
associated with higher subsequent stock returns: a high-minus-low (H-L) portfolio strategy that takes a long (short) position in the quintile portfolio with the
highest (lowest) emission intensity yields a statistically significant average return of 4.42% per annum. We also find that the significant alphas of the H-L
portfolio are unaffected by known return factors for other systematic risks. In
a cross-validation test, we perform Fama and MacBeth (1973) regressions by
introducing a wider set of controls and find that the emission-return relation
remains economically and statistically significant irrespective of the control
variables that we consider.

1 Anecdotal evidence abounds of environmental contamination cases associated with wellknown, publicly listed firms that trigger governmental interventions. For example, in 2002 Dow
Chemical agreed to settle a lawsuit in California by spending $3 million on wetlands restoration, in 2008 the federal government intervened and claimed damages for nearby residents negatively impacted by airborne contamination from Dow Chemical’s nuclear weapon plant in Colorado, and in 2011 Dow Chemical negotiated with the regulators regarding violations of the Clean
Air Act that caused the dioxin contamination in Michigan. See the Corporate Research Project:
http://www.corp-research.org/dowchemical.
2 The Internet Appendix may be found in the online version of this article.

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To further examine whether such return predictability is related to
environmental policies, we calculate quintile portfolio cumulative abnormal
returns (CARs) in response to Donald Trump 2016 U.S. presidential election
win.3 Following Trump’s win, high-emission firms had significantly positive
CARs that were higher than those of lower-emission counterparts. Specifically, we find a monotonic pattern in CARs across quintile portfolios and a
prominent contrast between the top portfolio (6.31%) and the bottom portfolio (3.64%) within a 10-day window around the 2016 U.S. presidential election.
This finding supports the view that the general public—and equity investors in
particular—pay attention to environmental policies and firm-level emissions.
We consider several possible explanations proposed in the literature for the
cross-sectional variation in emission portfolios’ returns, including existing systematic risks, investors’ preferences and underreaction, corporate governance,
and political connections.4 Fama and MacBeth (1973) regressions and twoway-sorted portfolios suggest that the emission-return relation is not eliminated when we control for firm characteristics related to these explanations.
We also consider policy uncertainty exposures as in Bali, Brown, and Tang
(2017) and show that the emission-driven return spread cannot be attributed
to general policy uncertainty.
Given the results above, we propose a new systematic risk based on environmental policy uncertainty following Pástor and Veronesi (2012, 2013) and
develop a general equilibrium model in which firms’ cash flows are subject to
policy changes with respect to environmental regulation.5 In our model, the
3 We consider this event as it is exogenous to environmental policies, as argued by Wagner, Zeckhauser, and Ziegler (2018), Ramelli et al. (2021), and Child et al. (2021). Di Giuli and Kostovetsky
(2014) also show that firms with low social responsibility scores observe significantly positive 3-day
CARs after Republican election victories.
4 First, existing systematic risks that may explain the documented pollution premium include
capital age (Lin, Palazzo, and Yang (2020)), financial constraints (Li (2011), Lins, Servaes, and
Tamayo (2017)), economic and political uncertainty (Brogaard and Detzel (2015), Bali, Brown, and
Tang (2017)), and adjustment costs (Kim and Kung (2016), Gu, Hackbarth, and Johnson (2017)).
Second, both retail and institutional investors have preferences against firms with a poor social image, such as those that perform poorly with respect to corporate social responsibility (CSR) issues
(Hong and Kacperczyk (2009), Fabozzi, Ma, and Oliphant (2008), Renneboog, Ter Horst, and Zhang
(2008), Starks, Venkat, and Zhu (2017), Riedl and Smeets (2017), Gibson and Krueger (2018), Dyck
et al. (2019), Pástor, Stambaugh, and Taylor (2021), Hartzmark and Sussman (2019), and Ramelli
et al. (2021)). Third, retail investors are more subject to behavioral bias and may panic in response to some firms’ emission news (Krüger (2015) and Ottaviani and Sørensen (2015)), selling
all of their stocks at deep discounts. Fourth, high-emission firms could operate under weaker governance or monitoring (Masulis and Reza (2015), Cheng, Hong, and Shue (2013), Glossner (2018),
Hoepner et al. (2019)), and their stock prices may be discounted by investors who are concerned
about governance or the associated risk and uncertainty (e.g., Gompers, Ishii, and Metrick (2003)).
Fifth, since political connections are positively related to future stock returns (e.g., Liu, Shu, and
Wei (2017)) or may result a risk premium (Santa-Clara and Valkanov (2003)), high-emission firms
may be more politically connected, with their profits and stock prices subject to greater uncertainty
with respect to governmental oversight.
5 Our model differs from that of Pástor and Veronesi (2012, 2013) in several ways. First, we consider an endogenous decision problem whereby firms to choose emission intensity. In addition, we
introduce into agents’ utility with the environmental costs that trigger governmental policy shifts.

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The Pollution Premium

The Journal of Finance®

government acts as a social planner and considers the negative externality
of toxic emissions. It optimally replaces the weak-regulation regime with
the strong-regulation regime if environmental costs are sufficiently high
(i.e., above a given endogenous threshold). Before the government makes
its decision, agents learn about the welfare costs of toxic emissions under
the weak-regulation regime in a Bayesian fashion by observing signals,
which determines their perceived probability that the government will adopt
strong-regulation regime. Adopting a strong-regulation regime will lower
emissions but reduce firms’ profitability. In particular, the profitability of
high-emission firms drops more than that of low-emission firms, leading to a
stronger negative impact on valuations of firms with high emission intensity.
On the one hand, a shift to the strong regime is assumed to negatively affect
economy-wide average profitability, which leads to an upward spike in the
stochastic discount factor (SDF); on the other hand, since high-emission firms’
profitability is more sensitive to such the regime shift than the profitability
of low-emission firms, high-emission firms observe a larger stock price decline
when a regime shift occurs and are more negatively exposed to the risk of a
regulation regime shift, which results in higher average excess returns ex ante.
Our model assumptions and predictions are supported by additional empirical tests. We first measure regime shift risk (i.e., the perceived likelihood
of tighter environmental regulations) using the growth rate in the aggregate
amount of all civil penalties level against pollution by the EPA.6 We find that
when regime shift risk increases, firms with higher emissions experience a
more pronounced decline in their long-term profits. When we use the generalized method of moments (GMM) estimation of Cochrane (2005) to test the price
of regime change risk (i.e., λc ) and the exposure to such risk of emission portfolios, we find that regime change risk is significantly negatively priced and that
emission portfolios’ betas on regime change risk decrease with emission intensity, both of which are consistent with the model. As a result, the H-L emission
portfolio delivers higher expected returns because it has negative exposure to
regime change risk that is negatively priced.
In sum, our emission intensity measure captures risk characteristics that
are distinct from others documented in the literature, and our model identifies a new source of systematic risk for investors: the risk of a regime shift
in environmental regulation that impacts high-emission firms more than
low-emission firms. While we acknowledge that environmental regulation uncertainty is only one (particular) type of policy uncertainty, such uncertainty is
a substantial yet under explored part of policy uncertainty. More importantly,
JT difference test results show that our measure of environmental policy
However, while agents know about the policy impact and know that the price of risk is negative
in our model, they must learn about the policy impact as in Pástor and Veronesi (2012, 2013). In
terms of differences in empirical tests, we focus on the cross-sectional variation in expected stock
returns, while Pástor and Veronesi (2012, 2013) focus on time-series fluctuations in the aggregate
equity market value. In the Internet Appendix, we further introduce the role of debt financing,
which amplifies the emission-return relation.
6 We thank an anonymous reviewer for suggesting this measure to us.

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change risk is distinct from general policy uncertainty, as adding our measure
of environmental policy change risk to the SDF of the general economic policy
uncertainty factor of Bloom (2009) significantly reduces pricing errors.
This paper builds on a growing literature that investigates the policy implications of environmental pollution. Most of the papers in this literature
focus on the economic consequences of global warming and climate change.7
Here, we focus instead on the asset pricing implications of environmental policy changes.
Our work also adds to the literature that explores investment strategies
related to climate change, CSR, and environmental, social, and governance
(ESG) scores. Prior studies in this literature can be classified into several
classes: long-run risk, downside risk, attention, preferences, and cost of capital. Climate change and environmental issues constitute long-run risks, and
polluting firms therefore carry higher risk exposure (Bansal and Ochoa (2011),
Bansal, Kiku, and Ochoa (2016), Bolton and Kacperczyk (2019, 2020)).8 Some
studies suggest that high-CSR firms are less risky because their CSR reputation helps them survive financial downturns (Lins, Servaes, and Tamayo
(2017), Hoepner et al. (2019), and Albuquerque, Koskinen, and Zhang (2019)).9
In addition, investor under- or overreaction to news about pollution or climate
change can result in return predictability (Krüger (2015), Chen, Kumar, and
Zhang (2019), Hong, Li, and Xu (2019)),10 and it is well known that investors
are more willing to hold socially responsible firms and funds due to social reputation, or liquidity concerns, which also impact stock prices.11 Such preferences
7 Acemoglu (2002) shows that two major forces bias technological change: price effects and market size effects. Acemoglu et al. (2012) suggest policy interventions to direct innovation from dirty
technologies to clean ones, if two types of technologies are substitutable. If the dirty technology
is more advanced, Acemoglu et al. (2016a) show that interventions, such as taxes and subsidies,
can promote transitions to clean technology. In their study of the automobile industry, Aghion
et al. (2016) find that cost-saving motivations encourage firms to develop clean technologies, and
Brown, Martinsson, and Thomann (2022) show that country-level taxes on noxious emissions lead
to substantial increases in polluting firms’ R&D spending. In contrast to studies that consider carbon emissions, Currie et al. (2015) investigate the impact of toxic emissions on housing value and
infant health.
8 Bansal and Ochoa (2011) and Bansal, Kiku, and Ochoa (2016) use climate change risks to
proxy for long-run risks in dividends and consumption dynamics, and Andersson, Bolton, and
Samama (2016) propose a hedging strategy against climate risks. Bolton and Kacperczyk (2019,
2020) find that high-CO2 emitters deliver significantly higher stock returns and suggest that these
firms carry higher systematic risk, such as renewable technology risk.
9 Dunn, Fitzgibbons, and Pomorski (2018) provide empirical evidence showing that higher-ESG
firms have lower future risk, including total risk and beta.
10 Krüger (2015) finds that investors show strongly negative CSR responses to adverse CSR
news. Hong, Li, and Xu (2019) find that food companies in drought-stricken countries underperform those in countries that do not experience droughts, and they attribute this pattern to investor
inattention. Chen, Kumar, and Zhang (2019) find that stocks that are more sensitive to CSR have
significantly higher returns due to investors’ social sentiment.
11 Hong and Kacperczyk (2009) and Fabozzi, Ma, and Oliphant (2008) find that firms in “sin”
industries (i.e., alcohol, tobacco, and gaming) outperform those in non-sin industries in stock
returns because the former group is subject to funding constraints due to social norms. Cao
et al. (2019) find that institutional investors are reluctant to sell high-CSR stocks but are more

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The Pollution Premium

The Journal of Finance®

may also influence systematic risk exposure (Bansal, Wu, and Yaron (2019),
Pástor, Stambaugh, and Taylor (2021)).12 Heinkel, Kraus, and Zechner (2001),
Chava (2014), and Hong, Wang, and Yang (2021) further show that firms associated with environmental concerns face high equity and debt financing costs.
Distinct from most prior empirical studies in this direction, we derive regulation regime change risk in a general equilibrium setting, and we use actual
toxic emissions, which are less subject to errors than estimations or surveys.
Our paper also adds a new perspective to asset pricing implications of
macroeconomic uncertainty, a topic for which Pástor and Veronesi (2012, 2013)
provide a comprehensive literature review. Prior empirical studies examine
the role of uncertainty in economic policy, politics and elections, and tax and
fiscal conditions.13 Distinct from these papers, we explore the financial effect
of uncertainty in environmental policies and regulations. Finally, our paper
contributes to the literature that relates consumption or productivity risk to
stocks’ risk premium from the perspective of pollution, which is an unavoidable by-product of production and consumption.14
willing to sell low-CSR stocks, which leads to return predictability. Renneboog, Ter Horst, and
Zhang (2008), Starks, Venkat, and Zhu (2017), Riedl and Smeets (2017), Gibson and Krueger
(2018), Dyck et al. (2019), and Hartzmark and Sussman (2019) document that both retail and institutional investors are more willing to hold socially responsible firms and funds. One possible
explanation for this preference could be liquidity and funding risk. Stocks with bad reputations
may be subject to greater financing constraints due to insufficient investor demand (e.g., Hong
and Stein (2007)). However, Bessembinder (2016) points out that such preferences may incur substantial costs due to liquidity. Pedersen, Fitzgibbons, and Pomorski (2021) suggest that firms’ ESG
activities may predict stock returns because these activities are correlated with firm fundamentals
and investor preferences.
12 Pástor, Stambaugh, and Taylor (2021) propose that investors’ ESG preferences for the stocks
and products of green firms give rise to ESG systematic risk in equilibrium. Bansal, Wu, and
Yaron (2019) argue that socially responsible investment carries higher systematic risk exposure
because households have stronger preferences for socially responsible investment during good economic times.
13 With respect to economic uncertainty, Brogaard and Detzel (2015) examine how stock returns
relate to the economic policy uncertainty (EPU) index constructed by Baker, Bloom, and Davis
(2016). In similar work, Bali, Brown, and Tang (2017) suggest that uncertainty is priced in the
cross section using the alternative economic uncertainty index proposed by Jurado, Ludvigson, and
Ng (2015). With respect to political uncertainty, Santa-Clara and Valkanov (2003) relate the equity
risk premium to political cycles, and Liu, Shu, and Wei (2017) provide direct evidence that stock
prices of politically sensitive firms respond more to political uncertainty. Other studies examine
tax and fiscal uncertainty (Sialm (2006, 2009), Croce et al. (2012a), Croce, Nguyen, and Schmid
(2012b), and Belo, Gala, and Li (2013)).
14 A large number of theoretical and empirical papers relates consumption or productivity risk
to the equity risk premium. Ait-Sahalia, Parker, and Yogo (2004) and Lochstoer (2009) show
that luxury consumption can explain the equity premium. Yogo (2006) separates durable consumption from nondurable consumption to study time-series asset pricing implications, while
Gomes, Kogan, and Yogo (2009) further show that durable good producers are riskier than nondurable good producers since the demand for durable goods is more procyclical. Savov (2011)
uses garbage release data to capture volatile consumption, and Da, Yang, and Yun (2015) use
electricity data to proxy for missing homemade goods. Kroencke (2017) suggests that unfiltered consumption explains why garbage data outperform National Income and Product Accounts (NIPA) consumption data in matching the equity premium. The literature also explores

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The rest of the paper is organized as follows. In Section I, we discuss data
construction and present summary statistics as well as our baseline results.
In Section II, we discuss and empirically test several possible explanations
for the positive emission-return relation that we document. In Section III,
we examine how litigation risk and profits relate to emission intensity using
an event study analysis. We describe an equilibrium model and analyze its
quantitative asset pricing implications in Section IV. We further test our
model and its testable implications in Section V. We conclude in Section VI.
Details on data construction are provided in the Internet Appendix. The
Internet Appendix also contains additional empirical evidence, details on our
model solution, calibration and sensitivity analyses, and an extended model
that introduces debt financing.
I. Firm-Level Emissions and Pollution Premium
In this section, we first discuss our measurement of firm-level toxic emissions. We then examine the relation between toxic emissions and the cross section of stock returns. We show that emissions positively predict stock returns in
one-way portfolio sorts and that such an emission-return relation is unaffected
by known return factors for other systematic risks. In the third subsection,
we implement Fama and MacBeth (1973) regressions to examine whether the
positive relation between emissions and stock returns is mitigated by other
firm characteristics, and in the fourth subsection we double sort on size and
emissions and confirm that the pollution premium is not driven by the size
effect.
A. Data Sources
To obtain firm-level emissions of U.S. public companies, we collect plantlevel chemical pollutants data from the TRI database constructed and maintained by the EPA.15 The TRI database contains detailed information on all
the asset pricing implications of production risk referred to as production-based asset pricing,
which links investment to stock returns. Zhang (2005) provides an investment-based explanation for the value premium. Eisfeldt and Papanikolaou (2013) develop a model of organizational capital and expected returns. Kogan and Papanikolaou (2013, 2014) study the relation
between investment-specific technology shocks and stock returns. van Binsbergen (2016) documents the cross-sectional return spread by sorting on producer prices. Finally, Loualiche (2022)
studies the cross-sectional difference in exposure to the globalization risk premium, and argues
that such risk is an extension of the displacement risk proposed by Gârleanu, Kogan, and Panageas
(2012).
15 The U.S. Congress passed the Community Right to Know Act (EPCRA) in 1986 in response
to public concerns over the release of toxic chemicals from several environmental accidents, both
domestic and overseas. The EPCRA entitles residents in their respective neighborhoods to know
the source of detrimental chemicals, especially in terms of their potential impacts on human health
from routes of exposure. The EPCRA also requires that firms disclose chemical releases to the
environment that exceed allowed limits for all listed toxic substances. Following the EPCRA, the
EPA set up the TRI database to track and supervise certain classifications of toxic substances from
chemical pollutants that can endanger human health and the environment.

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The Pollution Premium

The Journal of Finance®

U.S. chemical emissions at the plant level each year since 1986. Specifically, the
TRI data contain report year, level of chemical pollutants in pounds, name of
chemical categories, location Federal Information Processing Standards (FIPS)
code, and company names.16 While the TRI database has been a publicly available since 1986, its coverage was fairly limited and contains data errors until
1990. As a result, we use the emission data from 1991 to 2016 to construct our
emission-related variables.
Our sample consists of firms that lie in the intersection of Compustat, Center
for Research in Security Prices (CRSP), and the TRI database (Xiong and Png
(2019)). We obtain accounting data from Compustat and stock price data from
CRSP. Our sample firms include those with nonmissing TRI data and nonmissing standard industrial classification (SIC) codes, as well as those with
domestic common shares (SHRCD = 10 and 11) trading on NYSE, AMEX, or
NASDAQ. We identify firms in our sample that were involved in litigation from
Key Developments in Capital IQ. Following the literature, we exclude financial firms that have four-digit SIC codes between 6000 and 6999 (e.g., finance,
insurance, trusts, and real estate sectors). To mitigate backfilling bias, we require that firms to be listed on Compustat for two years before we include them
in our sample.
We collect civil cases about firms involved in environmental litigation from
the Enforcement and Compliance History Online (ECHO) system provided by
the EPA. Section I.B in the Internet Appendix details our procedure for quantifying environmental litigation. ECHO contains information on federal- and
state-level administrative and judicial cases and tracks all formal administrative and judicial enforcement actions taken by the U.S. EPA. This database
provides information on the dollar amount of penalties for pollution in each
civil case in the EPA record. We search these civil cases in the database from
1990 to 2017. We then identify firms involved in litigation that is related to
violations of environmental regulations and count the frequency of these cases
for each firm and year.
Finally, we collect firm-level environmental scores from Thomson Reuters’
ASSET4 Environmental, Social, and Corporate Governance database.17 We
use the environmental score (ENVSCORE) and its components, which are assigned to a firm annually.
16 We acknowledge that the TRI database is subject to some data limitations, such as a failure
to report and reporting errors, as Currie et al. (2015) pointed out. The EPA checks report quality
to correct errors and conducts regular quality analysis that is further examined by the Office of
Enforcement and Compliance Assurance (OECA). In a quality check report, EPA (1998) shows
that reporting errors in the TRI are within a 3% range for most industries. Akey and Appel (2021)
and Kim and Kim (2020) affirm that TRI data must be high quality and argue that misreporting
in the TRI can lead to criminal or civil penalties.
17 The database has been used in previous studies of ESG issues (e.g., Ferrell, Liang, and Renneboog (2016), Liang and Renneboog (2017), Dyck et al. (2019), and Hsu, Liang, and Matos (2021)).
The ASSET4 sample covers more than 4,500 global public firms included in major equity indices,
such as the S&P 500, Russell 1000, and NASDAQ 100, among others. Data are collected from multiple sources, including company reports, company filings, company websites, nongovernmental
organization (NGO) websites, CSR reports, and reputable media outlets.

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1350

1351

B. Summary Statistics
Table I, Panel A reports pooled summary statistics. Specifically, Panel A reports the pooled mean, median, standard deviation (Std), 5th percentile (P5),
25th percentile (P25), 75th percentile (P75), and 95th percentile (P95) of the
variables of interest, as well as the valid number of observations for each variable. Our main variable, Emissions, is the sum of all emissions (in pounds)
produced in all plants owned by firm i in year t − 1 scaled by total assets (in
million dollars). Because a firm’s emissions in year t − 1 are recorded in the
TRI database and become public information by the end of September of year
t, we scale its emissions by its total assets disclosed by the end of March of year
t. The emission data are discussed in more detail in Sections I.A and I.C of the
Internet Appendix. The other variables include market capitalization (ME),
book-to-market ratio (B/M), investment rate (I/K), return on assets (ROA), return on equity (ROE), tangibility (TANT), a Whited and Wu (WW) index to capture financial constraints, operating leverage (OL), and book leverage (Lev).18
We have a total of 9,989 firm-year observations with nonmissing emissions.
The average Emissions is 6,568, suggesting that one million dollars in book
assets is associated with 6,568 pounds of chemical emissions. Industry-level
summary statistics for Emissions are presented in Section I.D in the Internet
Appendix.
Table I, Panel B presents a correlation matrix for all of variables considered
in Panel A. We find that Emissions is generally not highly correlated with the
other variables, with the exception of its correlation coefficients with size (ME),
asset tangibility (TANT), financial constraints (WW), and operating leverage
(OL), which are −0.03, 0.05, 0.07, and 0.07, respectively.
To shed light on whether some of the firm characteristics above predict firm
Emissions, we run pooled regressions in which we regress the logarithm of
firm-level emission intensity (Emissions) in year t + 1 on the logarithm of current emission intensity in year t, all firm characteristics in year t, and industryyear joint fixed effects. As shown in Table IA.1 in the Internet Appendix, we
find that only firm size and asset tangibility have consistent predictive ability for future emissions.19 Emission intensity significantly decreases with firm
size and significantly increases with asset tangibility. These findings are intuitive because firms with higher market value can rely more on intangible assets and thus are less dependent on manufacturing, while firms with more tangible assets are naturally more manufacturing-oriented.20 Below we conduct
factor regressions, Fama-MacBeth regressions, and two-way portfolio sorts to
18 Detailed information on variable construction can be found in Table I.
19 Standard errors are clustered at the firm level to accommodate firm-level autocorrelation
(Panel A) or at the industry-year level to accommodate variation within an industry (Panel B).
The B/M is the only firm characteristic in the specification (column (2)); the marginal predictive
power of B/M disappears when we pool the other characteristics together in column (9). In contrast, the financial constraint measure (WW index) is significant only when we include the other
firm characteristics.
20 We also examine whether some macroeconomic variables predict aggregate emission intensity in a time-series regression in which we regress the logarithm of aggregate emission intensity

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The Pollution Premium

Table I

1

6,567.88
44,586.41
1.80
75.67
465.04
2,372.91
23,254.81
9,989

0.67
0.61
0.16
0.35
0.55
0.83
1.50
9,736

−0.01
−0.11
1

−0.03
1

B/M

6,272.44
21,765.23
47.44
362.96
1,302.75
4,448.09
26,056.43
9,691

ME

ROA

ROE

0.01
0.03
−0.19
1

0.19
2.71
−0.10
0.12
0.20
0.30
0.58
9,989

0.02
0.05
−0.37
0.22
1

0.00
0.02
−0.11
0.00
0.16
1

Panel B: Correlation

0.09
0.08
−0.02
0.05
0.09
0.13
0.22
9,989

Panel A: Summary Statistics
0.18
0.11
0.06
0.11
0.16
0.22
0.37
9,934

I/K

0.05
0.00
0.16
−0.27
−0.10
−0.02
1

0.33
0.18
0.09
0.19
0.30
0.44
0.71
9,989

TANT

0.07
−0.41
0.1
0.16
−0.05
−0.02
−0.21
1

−0.35
0.10
−0.51
−0.42
−0.35
−0.29
−0.19
9,698

WW

0.07
−0.17
−0.02
0.16
0.13
0.04
−0.23
0.41
1

0.99
0.56
0.24
0.62
0.90
1.25
1.97
9,989

OL

0.00
0.07
0.09
−0.24
−0.20
0.12
0.21
−0.22
−0.18
1

0.23
0.17
0.00
0.15
0.26
0.37
0.56
9,973

Lev

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Emissions
ME
B/M
I/K
ROA
ROE
TANT
WW
OL
Lev

Mean
Std
P5
P25
Median
P75
P95
Observations

Emissions

This table presents summary statistics in Panel A and a correlation matrix in Panel B for the firm-year sample. Emissions are measured as the sum
of all emissions in pounds produced in all plants owned by a firm, scaled by total assets (item AT) in million dollars. ME is market capitalization
deflated by CPI (measured in 2009 millions USD) at the end of September. B/M is the ratio of book equity to market capitalization. I/K is capital
expenditures (item CAPX) divided by property, plant, and equipment (PPENT). Return on assets (ROA) is operating income after depreciation (item
OIADP) scaled by total assets. Return on equity (ROE) is operating income after depreciation scaled by total assets. Tangibility (TANT) is property,
plant, and equipment divided by total assets. WW index (WW) is the Whited and Wu index used to measure financial constraint, following Whited
and Wu (2006). Operating leverage (OL) is the summation of cost of goods sold (item COGS) and selling, general, and administrative expenses (item
XSGA) scaled by total assets. Book leverage (Lev) is the summation of current liabilities (item DLC) and long-term debt (item DLTT) scaled by
total assets. We report the pooled mean, standard deviation (Std), 5th percentile (P5), 25th percentile (P25), median, 75th percentile (P75), and 95th
percentile (P95). Observations denote the valid number of observations for each variable. The sample period is 1991 to 2016 at an annual frequency.

Statistics and Correlations

1352

1353

separate the pollution effect from the size effect. We consistently find that other
firm characteristics cannot predict emissions.
C. Univariate Portfolio Sorting: Returns, Firm Characteristics, and Factor
Regressions
To investigate the link between emissions and the cross section of stock returns, we construct quintile portfolios sorted on firms’ emissions scaled by total assets (AT) in Panel A, property, plant, and equipment (PPENT) in Panel
B, sales (SALE) in Panel C, and market equity (ME) in Panel D, and report
each portfolio’s postformation average stock return. As mentioned above, because the EPA updates each emission data by the end of September each year,
we form portfolios at the end of each September in year t (from 1992 to 2017)
(see Section I.A and Figure IA.1 in the Internet Appendix). Specifically, each
year we first sort all sample firms with positive scaled emissions in year t − 1
into five groups from low to high within the 49 Fama and French (1997) industries. As a result, we have industry-specific break points for quintile portfolios
for each September. We then assign all firms with positive scaled emissions
in September of year t into quintile portfolios. The low (high) quintile portfolio
contains firms with the lowest (highest) emissions in each industry. After forming the five portfolios sorts (from low to high), we calculate the value-weighted
monthly returns on these portfolios over the next 12 months (i.e., October of
year t to September of year t + 1). To examine the emission-return relation,
we also form an H-L portfolio that takes a long position in the high-emission
portfolio and a short position in the low-emission portfolio and calculate the
return on this portfolio.
In Panels A to D of Table II, the top row presents the annualized average
excess stock return in percentage (E[R]-Rf , in excess of the risk-free rate), tstatistic, standard deviation, and Sharpe ratio for the six portfolios we consider. The table shows that a firm’s emissions forecast stock returns. Taking
Panel A, which uses emissions scaled by total assets (our primary proxy of
emission intensity), as an example, the quintile portfolio sorts from low to high
have annualized excess returns of 6.90%, 9.68%, 9.08%, 9.11%, and 11.32%, respectively. More importantly, the H-L portfolio has an annualized excess return
of 4.42% with a t-statistic of 3.66. In addition, the Sharpe ratios of the quintile portfolios are 0.45, 0.57, 0.58, 0.55, and 0.69, respectively, and that of the
H-L portfolio is 0.46, which is comparable to the Sharpe ratio of the aggregate
equity premium. Similar patterns obtain in other panels. The finding that the
(across all sample firms) in year t + 1 on lagged emission intensity as well as on a battery of
macroeconomic variables in year t including unemployment rate (Unep), GDP growth (dy), EPU
index, price-dividend ratio (P/D), cyclically adjusted price-to-earnings (CAPE), TED spread (TED),
and default premium (DEF). We calculate the aggregate emission intensity as the market valueweighted average of public firms’ emissions scaled by their total assets. As Table IA.2 shows, we
find that none of these variables is able to predict aggregate emissions. As a result, the industrial
emissions that we focus on likely comprise a unique variable that is distinct from other macroeconomic variables and hence, merits further investigation.

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The Pollution Premium

Table II

Univariate Portfolio Sorting
This table shows average excess returns for five portfolios sorted on emissions scaled by total
assets (AT) in Panel A, by property, plant, and equipment (PPENT) in Panel B, by sales (SALE)
in Panel C, and by market equity (ME) in Panel D relative to their industry peers, for which we
use the Fama and French (1997) 49 industry classifications, and rebalance portfolios at the end
of each September. The sample runs from October 1992 to September 2018 and excludes financial
industries. We report average excess returns over the risk-free rate (E[R]-Rf ), t-statistics, standard
deviations (Std), and Sharpe ratios (SR) across five portfolios in each panel. Portfolio returns are
value-weighted by firms’ market capitalization, and are multiplied by 12 to make the magnitude
comparable to annualized returns. t-Statistics are based on standard errors using the Newey-West
correction for 12 lags.
L

2

3

4

H

H-L

9.11
2.73
16.46
0.55

11.32
3.30
16.30
0.69

4.42
3.46
9.53
0.46

10.64
3.14
16.25
0.66

2.78
2.00
9.00
0.31

9.62
2.85
15.58
0.62

2.17
1.73
8.51
0.25

12.44
3.73
16.65
0.75

5.21
2.63
10.11
0.52

Panel A: AT
E[R]-Rf (%)
[t]
Std (%)
SR

6.90
2.02
15.33
0.45

9.68
2.91
16.94
0.57

9.08
2.84
15.64
0.58

Panel B: PPENT
E[R]-Rf (%)
[t]
Std (%)
SR

7.87
2.71
14.77
0.53

8.60
2.24
17.39
0.49

8.66
2.74
15.34
0.56

9.37
2.67
16.71
0.56

Panel C: SALE
E[R]-Rf (%)
[t]
Std (%)
SR

7.45
2.41
14.71
0.51

10.43
3.33
16.03
0.65

7.51
1.90
17.33
0.43

9.49
2.83
17.36
0.55

Panel D: ME
E[R]-Rf (%)
[t]
Std (%)
SR

7.23
2.39
14.76
0.49

9.10
2.60
16.86
0.54

8.95
2.70
16.02
0.56

7.94
1.99
17.73
0.45

return on the H-L portfolio is economically large and statistically significant
across all panels suggests significant predictive ability of firm-level emissions
for stock returns.
Overall, Table II provides empirical evidence that firm-level emissions help
explain subsequent stock returns. In the rest of our analyses, we focus on emission intensity defined as annual emissions scaled by total assets and the associated portfolios.
Table III reports the average firm characteristics across quintile portfolios.
We find that, on average, firms in the high-emission group generate emissions
of 3,106,629 pounds per year, while firms in the low-emission group generate

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1354

1355

Table III

Firm Characteristics
This table reports the time-series average of the cross-sectional medians of firm characteristics
for five emission-sorted portfolios. Raw emissions are measured as the sum of all emissions in
pounds produced in all plants owned by a firm. Emissions are measured as raw emissions in
pounds scaled by total assets in million dollars. Portfolio characteristics are described in Table I.
The sample period is 1991 to 2016.

Raw Emissions
Emissions
Log ME
B/M
I/K
ROA
TANT
WW
OL
Lev
Num

L

2

3

4

H

18,808.25
15.52
7.51
0.56
0.16
0.08
0.26
−0.36
0.81
0.27
79

243,610.89
134.09
7.45
0.57
0.16
0.08
0.24
−0.36
0.88
0.27
76

796,053.89
487.54
7.45
0.56
0.16
0.09
0.28
−0.36
0.86
0.26
76

1,488,382.07
1,501.08
7.42
0.57
0.15
0.09
0.31
−0.37
0.87
0.26
76

3,106,629.16
8,146.43
7.09
0.57
0.15
0.10
0.34
−0.34
0.97
0.27
72

emissions of 18,808 pounds per year. In addition, the emission intensity of
the high (low) group is 8,146.43 (15.52). We further find that high-emission
firms are smaller and have higher asset tangibility as well as higher operating
leverage, while there is little variation in B/M, I/K, ROA, financial constraints,
and financial leverage across emission-sorted portfolios. These results confirm
our earlier regression results.
In Table IV, we follow standard procedure and investigate the extent to
which the variation in the average returns of the emission-sorted portfolios
can be explained by existing risk factors. The table reports the alphas from the
leading risk factor models, including the capital asset pricing model (CAPM),
the Fama-French five-factor model (Fama and French (2015)), and the HXZ
q-factor model (Hou, Xue, and Zhang (2015)). We find that the cross-sectional
return spread across portfolios sorted on emission intensity cannot be captured by these risk factors, and the alphas in the long-short portfolio remain
statistically significant. Therefore, the positive emission-return relation that
we document cannot be attributed to common risk exposure.
D. Fama-MacBeth Regressions and Double Sorting on Size
In Table V, we examine the emission-return relation by running FamaMacBeth regressions to control for a variety of firm characteristics as described
in Section II.B of the Internet Appendix. The results of these regressions are
consistent with the results that obtain we sort portfolios on emission intensity, which show that emission intensity significantly positively predicts future stock returns. In addition, the predictability of emission intensity is not

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The Pollution Premium

Table IV

−1.82
−1.54
0.96
28.85
0.00
0.01
0.30
4.10

L

0.67
0.42
1.05
24.70
−0.11
−2.18
0.28
4.27

2

−0.88
−0.61
0.93
13.94
4

1.01
0.72
0.92
16.91
0.01
0.10
0.15
1.73

0.37
0.24
0.97
21.30
−0.05
−0.49
0.35
2.45

Panel B: FF3

3

H

2.90
2.17
0.99
37.41
−0.02
−0.31
0.11
1.50

1.22
0.61
1.01
16.11

2

4.72
3.73
0.02
0.71
−0.02
−0.34
−0.19
−2.57

H-L

−1.16
−0.89
0.93
25.23
0.02
0.25
0.27
4.75
−0.07
−1.96

L

Panel A: CAPM

αFF4
[t]
MKT
[t]
SMB
[t]
HML
[t]
UMD
[t]

1.49
0.94
0.91
12.02

3

0.60
0.39
1.06
24.50
−0.12
−2.11
0.29
4.17
0.01
0.21

2

1.33
0.66
0.93
11.19

4

4

1.29
0.93
0.91
13.79
0.01
0.22
0.14
1.63
−0.03
−0.56

0.75
0.53
0.96
18.73
−0.04
−0.43
0.33
2.40
−0.04
−0.76

Panel C: FF4

3

3.19
2.13
0.97
31.07

H

4.15
3.33
0.05
1.33
−0.03
−0.65
−0.17
−2.64
0.06
1.75

H-L

(Continued)

2.99
2.10
0.98
28.91
−0.02
−0.26
0.10
1.60
−0.01
−0.22

H

4.07
3.41
0.04
0.86

H-L

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αFF3
[t]
MKT
[t]
SMB
[t]
HML
[tt

αCAPM
[t]
MKT
[t]

L

This table shows asset pricing factor tests for five portfolios sorted on emissions scaled by total assets relative to their industry peers, for which
we use the Fama and French (1997) 49-industry classifications and rebalance portfolios at the end of each September. The results reflect monthly
data. The sample runs from October 1992 to September 2018 and excludes financial industries. To adjust for risk exposure, we perform time-series
regressions of emission-sorted portfolios’ excess returns on the market factor (MKT) as the CAPM model in Panel A, on the Fama and French (1996)
three factors (MKT, the size factor-SMB, and the value factor-HML) in Panel B, on the Fama and French (1996) three factors plus Carhart (1997)
factor (MKT, SMB, HML, and the momentum factor-UMD) in Panel C, on the Fama and French (2015) five factors (MKT, SMB, HML, the profitability
factor-RMW, and the investment factor-CMA) in Panel D, and on the Hou, Xue, and Zhang (2015) q-factors (MKT, SMB, the investment factor-I/A,
and the profitability factor-ROE) in Panel E, respectively. Data on the Fama-French five factors and Carhart factor come from Kenneth French’s
website. Data on the I/A and ROE factors are provided by Kewei Hou, Chen Xue, and Lu Zhang. These betas, together with alphas, are annualized
by multiplying by 12. t-Statistics are based on standard errors estimated using the Newey-West correction for 12 lags.

Asset Pricing Factor Tests

1356

Table IV

−3.26
−2.49
1.02
25.78
0.05
0.70
0.19
2.81
0.18
3.04
0.14
2.12

−0.89
−0.52
1.12
19.77
−0.09
−1.62
0.13
1.83
0.14
2.12
0.26
2.26

2

4

−1.24
−0.79
1.02
15.55
0.05
0.92
−0.07
−0.92
0.21
2.96
0.36
3.05

−3.08
−1.82
1.12
23.72
0.06
1.10
0.09
0.78
0.42
6.67
0.33
3.23

Panel D: FF5

3

0.52
0.32
1.09
26.83
0.05
0.81
−0.09
−1.11
0.27
4.34
0.28
2.63

H

3.78
2.98
0.06
1.62
0.00
0.03
−0.28
−2.76
0.09
1.27
0.14
1.19

H-L

αHXZ
[t]
MKT
[t]
SMB
[t]
I/A
[t]
ROE
[t]

−2.54
−1.90
1.01
25.48
−0.02
−0.31
0.38
3.50
0.08
1.56

L

−0.38
−0.24
1.14
27.61
−0.10
−2.65
0.41
3.66
0.15
2.00

2

4

−0.04
−0.03
1.00
16.74
0.02
0.35
0.27
2.74
0.12
1.90

−2.12
−1.21
1.11
25.46
−0.05
−0.59
0.56
4.06
0.24
2.84

Panel E: HXZ

3

2.12
1.72
1.05
32.23
−0.02
−0.44
0.23
2.33
0.11
1.77

H

4.66
3.70
0.04
0.80
−0.00
−0.00
−0.15
−1.23
0.03
0.59

H-L

1357

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αFF5
[t]
MKT
[t]
SMB
[t]
HML
[t]
RMW
[t]
CMA
[t]

L

This table shows asset pricing factor tests for five portfolios sorted on emissions scaled by total assets relative to their industry peers, for which
we use the Fama and French (1997) 49-industry classifications and rebalance portfolios at the end of each September. The results reflect monthly
data. The sample runs from October 1992 to September 2018 and excludes financial industries. To adjust for risk exposure, we perform time-series
regressions of emission-sorted portfolios’ excess returns on the market factor (MKT) as the CAPM model in Panel A, on the Fama and French (1996)
three factors (MKT, the size factor-SMB, and the value factor-HML) in Panel B, on the Fama and French (1996) three factors plus Carhart (1997)
factor (MKT, SMB, HML, and the momentum factor-UMD) in Panel C, on the Fama and French (2015) five factors (MKT, SMB, HML, the profitability
factor-RMW, and the investment factor-CMA) in Panel D, and on the Hou, Xue, and Zhang (2015) q-factors (MKT, SMB, the investment factor-I/A,
and the profitability factor-ROE) in Panel E, respectively. Data on the Fama-French five factors and Carhart factor come from Kenneth French’s
website. Data on the I/A and ROE factors are provided by Kewei Hou, Chen Xue, and Lu Zhang. These betas, together with alphas, are annualized
by multiplying by 12. t-Statistics are based on standard errors estimated using the Newey-West correction for 12 lags.

(Continued)

The Pollution Premium

Table V

Fama-MacBeth Regressions
This table reports Fama-MacBeth regressions of individual stock excess returns on their emission
intensity in logarithm and other firm characteristics. We conduct cross-sectional regressions for
each month from October of year t to September of year t + 1. In each month, monthly returns
of individual stock returns (annualized by multiplying by 12) are regressed on emission intensity
in logarithm of year t − 1 (that is reported by the end of September of year t), different sets of
control variables known by the end of September of year t, and industry fixed effects. Control
variables include the natural logarithm of market capitalization (Size), the natural logarithm of
book-to-market ratio (B/M), investment rate (I/K), return on equity (ROE), tangibility (TANT),
WW index, book leverage, and industry dummies based on Fama and French (1997) 49-industry
classifications. All independent variables are normalized to zero mean and unit standard deviation
after winsorization at the 1st and percentiles to reduce the impact of outliers. t-Statistics based
on standard errors estimated using the Newey-West correction are reported. The sample period is
October 1992 to September 2018.

Log Emissions
[t]
Log ME
[t]
Log B/M
[t]
I/K
[t]
ROE
[t]
TANT
[t]
WW
[t]
Lev
[t]
Observations
R2
Industry FE

(1)

(2)

1.39
2.74
6.11
6.08
6.19
6.15
0.55
0.77
1.64
1.50

0.91
2.40
33.72
12.24
13.48
11.86
−1.05
−1.48
3.68
3.44
−0.63
−0.89
30.70
12.96
3.23
4.75
109,679
0.16
Yes

112,848
0.13
Yes

subsumed by known predictors of stock returns in the literature, even when
we include all control variables jointly to run a horse race.
We also implement independent double sorts for emission intensity and
size to alleviate the concern that the return predictability we document is
driven by firm size. We find that high-emission firms continue to outperform
low-emission firms in stock returns for both large-firm and small-firm groups.
We provide further discussion of these results in Section II.C of the Internet
Appendix.
II. Possible Explanations for the Pollution Premium
In this section, we examine whether the positive emission-return relation can be attributed to any of several possible explanations, including

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The Journal of Finance®

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behavioral explanations, corporate policies and governance, and relevant risks
documented in the literature. Due to space limitations, all tables are provided
in the Internet Appendix.
A. Behavioral Explanations
A.1. Emissions Preferences
The literature documents that both retail and institutional investors disfavor firms with a poor social image, such as those that perform poorly with respect to CSR concerns.21 Prices of these firms therefore tend to be discounted
by the market, resulting in higher dividend yields. In a context, when polluting firms reduce their emissions in response to CSR concerns, their prices will
be discounted less, resulting in a positive emission-return relationship. There
may also exist investors who prefer high dividend yields to a stock’s reputation.
When these investors earn more dividends, they may buy more high-emission
stocks, pushing up the prices of these stocks. In sum, the emission-return relation could be driven by investors’ preferences on emissions.
To test this explanation, we measure institutional investors’ “emission preferences” and examine whether the emission-return relation varies across different types of institutional investors.22 If the emission preference explanation
holds, we expect emission-driven return predictability to be absorbed by institutional investors’ emission preferences. We control for emission preferences
in our Fama-MacBeth regressions in column (1) Table IA.3 in the Internet Appendix. The results show that emission intensity continues to significantly positively predict future stock returns after controlling for emission preferences.
We also form double-sorted portfolios based on firm emissions and institutional investors’ emission preferences.23 We present the average returns of
our double-sorted (5 by 2) portfolios as well as t-statistics in Panel A of Table
IA.5; we annualize portfolio returns by multiplying them by 12. In the high21 See Hong and Kacperczyk (2009), Fabozzi, Ma, and Oliphant (2008), Renneboog, Ter Horst,
and Zhang (2008), Starks, Venkat, and Zhu (2017), Riedl and Smeets (2017), Gibson and Krueger
(2018), Dyck et al. (2019), Pástor, Stambaugh, and Taylor (2021), Hartzmark and Sussman (2019),
Ramelli et al. (2021), and Goldstein et al. (2022), among others.
22 We capture institutional investors’ emission preferences following a two-step procedure. In
the first step, we collect institutional holdings data at the end of September of year t from the
Thomson Reuters Institutional Holdings (13F) database and calculate an institutional investor’s
exposure to emissions in year t as the value-weighted emission intensity in year t − 1 of the firms
that it holds. This method is motivated by the sustainability footprint of Gibson and Krueger
(2018), and the weighting factor is based on the market values of all firms held by an institutional
investor. In the second step, we calculate the pressure on a firm from institutional investors’ emission preferences in year t as the value-weighted average of institutional investors’ exposure to the
firm’s emissions. The weighing factor is based on the shares owned by all institutional investors
who hold the focal firm.
23 In particular, we independently sort firms into two portfolios based on their institutional
investors’ emission preferences and into five portfolios based on their emission intensity at the
end of September of year t, all relative to industry peers. We then calculate the value-weighted
return on each portfolio from October of year t to September of year t + 1.

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The Pollution Premium

The Journal of Finance®

emission-preference group, the H-L return spread based on emission-sorted
portfolios is 4.98%, significant at the 1% level; in the low-emission-preference
group, the H-L return spread based on emission-sorted portfolios is 4.72%, significant at the 5% level with a t-statistic of 2.03. These results suggest that
the emission-related return predictability holds in the sample without emission preferences, consistent with the main Fama-Macbeth regression results.
Therefore, the pollution premium cannot be attributed to differences in investor preferences with respect to pollution.
A.2. Investor Underreaction to Emission Abatement
High-emission firms may be subject to greater pressure from the community
and government and may be thus more likely to cut back emissions. However,
the literature documents that investors may underreact to market news due
to limited attention or a lag in information diffusion.24 If investors who prefer
firms with a higher social image underreact to high-emission firms’ reduction
in emissions in the future, the stock prices of these firms may increase, resulting in the emission-return relation that we find. This explanation is not
supported by Table IA.1, which shows a persistent pattern in firm-level emissions. That said, this table does not rule out the possibility that the pollution
premium may be driven by a subset of high-pollution firms that significantly
reduce their emissions in the future, leading subsequent stock prices to rise.
To provide further evidence on this possibility, we focus on firms in the highest emission quintile portfolios that we further sort into two portfolios based
on their emission intensity in year t (i.e., future emissions). The HL portfolio includes firms with future emission intensity below the median of the
high group and the HH portfolio includes firms with future emission intensity above the median of the high group.25 If the underreaction explanation
holds, the emission-return relation should be evident in the HL group but not
in the HH group. Panel B of Table IA.5 presents the average portfolio return
in the lowest quintile portfolio (L) as well as the return difference between the
HL and L groups and the return difference between the HH and L groups.
The empirical results show that although the HL-L difference is significantly
positive on average (3.96% with a t-statistic of 3.31), the HH-L difference is
also significantly positive on average (5.39% with a t-statistic of 2.34). In other
words, even high-pollution firms that do not reduce their emissions in the future provide significantly higher returns than low-pollution firms. Hence, the
24 Prior studies suggest that investors tend to underreact to new information (e.g., Bernard
and Thomas (1990)), especially complex information (e.g., You and Zhang (2009)). For example, in
the innovation literature, the evidence suggests that investors tend to overdiscount the cash flow
prospects of R&D-intensive or patenting firms due to high uncertainty and complexity associated
with innovations or fail to account for the benefits of innovation due to limited attention, which
results in the underpricing of innovation (see, e.g., Hall (1993), Lev and Sougiannis (1996), Aboody
and Lev (1998, 2000), Chan, Lakonishok, and Sougiannis (2001), and Hirshleifer, Hsu, and Li
(2013, 2017)).
25 We present the transition matrix in Section I.E of the Internet Appendix.

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underreaction explanation is unlikely to explain the cross-sectional variation
in stock returns due to emissions.
A.3. Retail Investors’ Behavioral Bias
In contrast to institutional investors who are more rational and have more
complete information, retail investors may be subject to greater behavioral
bias (See Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998), and Hong and Stein (1999), among others). For example, retail investors may panic in response to negative emission news (Krüger
(2015) and Ottaviani and Sørensen (2015)) and sell all their stock holdings at
deep discounts. If such overreaction explains the pollution premium, we would
expect the emission-return relation to exist only among stocks that experience
a significant drop in the share of retail investors.
To test this explanation, we first conduct the percentage share of retail investors as one minus the percentage share owned by institutional investors
at the end of each quarter. We control for changes in retail investors’ share
(Share) in our Fama-MacBeth regressions in column (2) of Table IA.3. We
find that emission intensity significantly positively predicts future stock returns, while the coefficient on changes in retail investors’ share is statistically insignificant. We next form double-sorted portfolios based on firm emissions and changes in retail investors’ share. At the end of September of year
t, we sort all stocks with emission intensity into three portfolios (30-40-30)
based on the change in retail investors between June and September of year
t within each industry. The high (low) group includes stocks that experience
the strongest increase (decrease) in retail investors’ share. Then, within each
group, we further sort stocks into quintile portfolios based on firm emissions
within an industry. Panel C of Table IA.5 shows that, for the middle tercile
(Group 2), the return spread (4.08% with a t-statistic of 2.96) is significant
and comparable to that in the univariate portfolio sorting, and the change
in retail investors’ share is close to zero (the mean and median are 0.05
and 0.04, respectively). In contrast, for other groups (Group 1 or 3, respectively) the lowest and highest changes in retail investors’ share, the return
spread (i.e., the return on the H-L portfolio) is insignificant. These results
suggest that the emission-return relation is orthogonal to the ownership of
retail investors, who are more subject to overreaction bias. As a result, the
positive emission-return relation does not reflect retail investors’ behavioral
bias.
B. Corporate Governance and Political Connections
B.1. Corporate Governance
Another possible explanation for the emission-return relation is that
high-emission firms are subject to weaker governance or monitoring
(Cheng, Hong, and Shue (2013), Masulis and Reza (2015), Glossner (2018),

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The Pollution Premium

The Journal of Finance®

Hoepner et al. (2019)) and hence their stock prices are discounted by investors
concerned about weak governance and the associated risk and uncertainty
(e.g., Gompers, Ishii, and Metrick (2003)). Such low prices may attract bidders or active investors who seek to these firms’ governance and monitoring, in
which case, stock prices show increase and lead to return predictability. If such
channels are responsible for the emission effect, we would expect there to be
no emission-return relation among firms with strong corporate governance. To
test this explanation, we control for firms’ G index and E index, respectively,
in our Fama-MacBeth regressions in columns (3) and (4) of Table IA.3. We
find that emission intensity continues to significantly positively predict future
stock returns, while G index or E index loads insignificantly.
We also double sort firms’ G index or E index into two portfolios (low and
high) and firms’ emission intensity into quintile portfolios (low, 2, 3, 4, and
high), all relative to their industry peers.26 Panel A of Table IA.6 shows that
returns on the H-L portfolio sorted on emission intensity remain statistically
significant among firms in the strongest governance (i.e., low G index or E
index) group. In particular, within the low G index group (upper panel), the
H-L portfolio return is equal to 5.52%, significantly at 1% level. Therefore,
our emission-return relation cannot be attributed to differences in governance
and monitoring.
B.2. Political Connections
It is also possible that high-emission firms may be more politically connected. Since political connections are positively related to future stock returns
(e.g., Liu, Shu, and Wei (2017)), and results in a risk premium (Santa-Clara
and Valkanov (2003)), the emission-return relation may, therefore, reflect the
asset pricing implications of political connections. Under this explanation, we
would expect there to be no emission-return relation among firms with low
political connections.
To test this explanation, we collect annual firm-level political donation data
from OpenSecrets.org maintained by the Center for Responsive Politics.27 We
define a firm’s political connections as the total amount of its political donation
(regardless of party) in a year scaled by total assets.28 We control for political
donations in our Fama-MacBeth regressions in columns (5) and (6) of Table
IA.3. We find that emission intensity significantly positively predicts future
stock returns, while political donations do not. We also double sort firms by
political connections into portfolios (low and high) and by emission intensity
into five portfolios (low to high). Panel B of Table IA.6 shows that returns on
the H-L portfolio sorted on emission intensity are statistically significant in
26 Detailed information on the G index and E index comes from Gompers, Ishii, and Metrick

(2003) and Bebchuk, Cohen, and Ferrell (2008), respectively.
27 This database is used by Bertrand, Bombardini, and Trebbi (2014) to measure firms’ lobbying activities.
28 If a firm with positive emission intensity does not make any political contributions, we set its
political connections to zero.

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both political donation groups. The return spread is as high as 6.20% (with a
t-statistic of 2.29) in low political donation group, which is even larger than the
return spread of 4.26% (with a t-statistic of 4.85) in the high political donation
group and the return spread of 4.42% in the univariate portfolio. These results
indicate that political connections cannot explain the pollution premium.

C. Existing Systematic Risks
We also explore possible explanations based on systematic risks posited
in prior studies. In particular, we consider four alternative channels that
may drive variations in our emission-sorted portfolios: technology obsolescence
(Lin, Palazzo, and Yang (2020)), financial constraints (Li (2011), Lins, Servaes,
and Tamayo (2017)), economic and political uncertainty (Brogaard and Detzel
(2015), Bali, Brown, and Tang (2017)), and adjustment costs (Kim and Kung
(2016), Gu, Hackbarth, and Johnson (2017)). The rationale for these explanations in a context is as follows. High-emission firms employ more obsolete
technology as they invest less in advanced production capital. The arrival of
new technology forces these firms to upgrade their production capital, and
hence their cash flows are likely sensitive to frontier technology shocks. In
addition, high-emission firms may be subject to financial constraints due to
litigation and penalties related to environmental issues. High-emission firms
may also be more subject to risk associated with macroeconomic uncertainty,
such as economic downturns or trade conflicts, and political uncertainty, such
as changes of the ruling party. Finally, high-emission firms may deliver higher
expected returns because it is costly for them to adjust their capital stock, especially during economic downturns.

C.1. Technology Obsolescence
To capture firm-level technology obsolescence, we follow Lin, Palazzo, and
Yang (2020) and employ both capital age and the I/K. A firm with older capital or a lower investment rate faces higher exposure to technology frontier
shocks and hence is more exposed to risk. We control for capital age and I/K
in our Fama-MacBeth regressions in columns (7) and (8), respectively, of Table
IA.3. We find that emission intensity significantly positively predicts future
stock returns. We also implement two-way sorting. In Panel A of Table IA.7,
we show that the H-L emissions return spread is comparable to that in the
univariate portfolio sort in both of the capital age and both of the I/K groups.
Specifically, the return spread is 4.07% (with a t-statistic of 2.44) in the young
capital age group and 4.24% (with a t-statistic of 2.50) in the old capital age
group, and it is 4.16% (with a t-statistic of 4.28) in the low I/K group and 5.31%
(with a t-statistic of 3.22) in the high investment rate group. If technology obsolescence is the main force driving the pollution premium, we should observe
significant return spreads only in the old capital age and low investment rate
groups. In contrast, the return spreads are significant in the young capital age

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The Pollution Premium

The Journal of Finance®

and high I/K groups. Therefore, the pollution premium cannot be explained by
technology obsolescence.
C.2. Financial Constraints
To test the role of financial constraints, we employ the financial constraints
measures of the WW index (Whited and Wu (2006)) and Size-Age (SA) index
(Hadlock and Pierce (2010).)29 A higher value of the SA or WW index suggests that the firm is likely subject to greater financial constraints. We control for the SA index and the WW index in columns (9) and (10), respectively,
in our Fama-MacBeth regressions in Table IA.3. We find that emission intensity continues to significantly positively predict future stock returns. In
Panel B of Table IA.7, we further show that the return spread from emissions is significantly positive in both less and more financially constrained
groups. The fact that financially unconstrained firms’ emissions still predict
stock returns suggests that financial constraints cannot explain the pollution
premium.
C.3. Economic and Political Uncertainty
To measure the exposure to political and macroeconomic uncertainty, we
estimate the firm-level exposure using rolling window regressions, following
Bali, Brown, and Tang (2017) to estimate firm-level exposure to the macroeconomic uncertainty index based on Jurado, Ludvigson, and Ng (2015) and
the political uncertainty index based on Bloom (2009).30 We control for firmlevel exposure to macroeconomic uncertainty (UNC Beta) and political uncertainty (EPU Beta) in columns (11) and (12), respectively, in our Fama-Macbeth
regressions of Table IA.3. We find that emission intensity continues to significantly positively predict future stock returns. We also implement two-way
sorts. The left and right sides of Table IA.7, Panel C present the returns of
the 12 portfolios sorted on macroeconomic uncertainty and political uncertainty, respectively. Within both high and low macroeconomic or political uncertainty exposure groups, the return spreads sorted on emission intensity are
significantly positive. These findings suggest that the emission-return relation is not driven by different levels of exposure to macroeconomic or political
uncertainty.

29 Detailed information on the construction of the SA and WW indexes can be obtained from
Farre-Mensa and Ljungqvist (2016).
30 For each stock with positive emissions in each month in our sample, we estimate the uncertainty exposure from monthly regressions of excess returns on the macroeconomic uncertainty
index over a 60-month rolling window controlling for empirical risk factors, including the market (MKT), size (SMB), value (HML), momentum (UMD), liquidity (LIQ), investment (I/A), and
profitability (ROE).

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C.4. Adjustment Costs
We follow Kim and Kung (2016) and Gu, Hackbarth, and Johnson (2017)
to measure a firm’s asset redeployability and inflexibility, respectively.31 If
the adjustment costs of asset redeployability (inflexibility) drive the pollution
premium, we would expect such a premium not to exist in firms with the
high asset redeployability (low inflexibility), which is associated with lower
adjustment costs. We control for asset redeployability and inflexibility in our
Fama-MacBeth regressions in columns (13) and (14), respectively, of Table IA.3
and find that emission intensity again significantly positively predicts future
stock returns. When we implement two-way sorts in Panel D of Table IA.7,
the emission-return relation appears significantly positive in both high-assetredeployability and low-inflexibility groups, which suggests that the return
predictability we document is unrelated to systematic risk associated with adjustment costs.
Overall, we find that high-emission firms earn higher stock returns than
low-emission firms in all groups with less exposure to systematic risks, as documented in the literature. These results thus point to the unique role that
emissions play with respect to return predictability.
III. Additional Empirical Evidence
In this section, we examine the association between firm-level emissions and
environmental litigation and profits. We also examine whether the emissionreturn relation is related to Trump’s U.S. presidential election win on November 8, 2016, which is an exogenous event with respect to environmental policies.
A. Environmental Litigation
To check that our emission intensity measure is a valid proxy for firms’ pollution, we examine whether firms with higher emission intensity have a significantly higher probability of facing litigation for pollution.
To do so, We begin by collecting all federal- and state-level cases against
pollution to obtain a more accurate estimate of the probability of litigation
associated with environmental issues.32 Using these data, we estimate the regression
Ni,t+5 = a + b1 × Emissionsi,t + c × Controlsi,t + εi,t ,

(1)

where the left-hand-side variable denotes firm i’s future litigation status.
Specifically, Ni,t+5 is defined as a binary variable that indicates whether a firm
is involved in litigation or as a count variable that reflects the total number of
31 Detailed information on the construction of the asset redeployability index is provided in
Table IA.7.
32 More details about these data sources are provided in Section I.B of the Internet Appendix.

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The Pollution Premium

The Journal of Finance®

lawsuits from year t + 1 to year t + 5. When we use binary measure, we estimate equation (1) using a Probit regression; when we use count variable, we
estimate equation (1) using a Poisson count and negative binomial regression,
respectively. We control for a firm’s fundamentals, including size, B/M, I/K,
current profitability, TANT, financial constraints, book leverage, and operating
leverage in year t. We also include industry-year fixed effects.33
In Table VI, we find that emissions in all predictive regressions significantly
positively predict environmental-related lawsuits in all specifications. In our
sample, 26% of firms will be sued for environmental issues in the following
five years, and an average firm will be involved in 1.56 lawsuits in the following five years. The coefficients suggest that a one-standard-deviation increase
in emission intensity is associated with a 16.20% higher probability or 2.46
times higher frequency of litigation. Such an increase in litigation probability or frequency is value-relevant because the mean and standard deviation of
penalties are as high as 1.57 and 8.93 million dollars (real), respectively. These
results indicate that our emission intensity well captures firm-level pollution
as it predicts firms’ likelihood of experiencing environmental litigation.
B. Current Cash Flows (Profitability)
We next examine the relation between firm-level emissions and profits by
estimating the OLS regression
ROAi,t = a + b1 × Emissionsi,t + c × Controlsi,t + εi,t ,

(2)

where ROAi,t is firm i’s profitability as measured by ROA, Emissionsi,t denotes
firm i’s emission intensity in year t, and control variables include lagged ROA
in year t − 1, size, B/M, I/K, lagged profitability, TANT, financial constraints,
Lev, and OL in year t, as well as industry-year fixed effects.34 Specifications
(1) and (2) of Table VII show that the estimated coefficient on Emissions (b1 )
is significantly positive, suggesting that high-emission firms enjoy higher current profitability by saving on pollution abatement and environmental recovery costs.
33 Standard errors are clustered at the industry-year level to accommodate within-industry
variation (Specifications (1) and (3)) or at the firm level to accommodate firm-level autocorrelation (Specifications (4) to (6)). We standardize all explanatory variables in equation (1) to facilitate
interpretation of economic magnitudes, and report the estimated coefficients in Table VI.
34 All independent variables are normalized to have zero mean and unit standard deviation
after winsorization at the 1st and 99th percentiles to reduce the impact of outliers. We standardize all explanatory variables to facilitate interpretation of economic magnitudes. Standard errors
are clustered at the firm level to accommodate firm-level autocorrelation (Specification (1)) or at
the industry-year level to accommodate within-industry variation (Specification (2)). We include
industry-year fixed effects in Table VII for current and future profitability for the following reasons. First, it is well known that industry-specific, time-varying competition, business cycles, or
technological development influence the profits of all firms in an industry (Giroud and Mueller
(2010)). Second, in an unreported test, we add industry-average ROA (excluding the focal firm)
as a control variable in all regressions of Table VII and find that it carries significantly positive
coefficients, which supports industry-specific, time-varying trends in firm-level ROA.

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Table VI

Predictive Regressions for Litigation
This table reports the impact of firms’ emission intensity on their frequencies of being litigated
for pollution. We collect a firm’s lawsuits relevant to environmental issues from the Integrated
Compliance Information System. We estimate a Probit (negative binomial and Poisson regression)
by regressing firm i’s future litigation status over the next five years (i.e., t + 1 to t + 5), which
is defined as a binary variable reflecting whether a firm is involved in litigation or as a count
variable reflecting the total number of cases from year t + 1 to year t + 5, on firm i’s emission
intensity in logarithm in year t and other controls for firm i’s fundamentals, including size, bookto-market ratio (B/M), investment rate (I/K), current profitability, tangibility (TANT), WW index,
book leverage, and operating leverage in year t, as well as industry-year fixed effects. All independent variables are normalized to zero mean and unit standard deviation after winsorization at
the 1st and 99th percentiles to reduce the impact of outliers. t-Statistics based on standard errors
that are clustered at the firm level or at the industry-year level are reported. The sample period is
from 1991 to 2016 based on coverage of the Enforcement and Compliance History Online (ECHO)
system.

Log Emissions
[t]
Log ME
[t]
Log B/M
[t]
I/K
[t]
ROA
[t]
TANT
[t]
WW
[t]
Lev
[t]
OL
[t]
Observations
Industry × Year FE
Cluster SE by Firm
Cluster SE by Industry × Year

(1)
Probit

(2)
NB

(3)
Poisson

(4)
Probit

(5)
NB

(6)
Poisson

0.66
24.99
0.50
11.04
0.09
3.71
−0.05
−2.41
0.01
0.46
0.07
2.88
−0.20
−4.85
0.09
3.57
0.13
4.64
8,707
Yes
No
Yes

1.24
26.74
0.70
7.83
0.05
1.10
−0.03
−0.66
−0.05
−1.09
0.19
4.07
−0.64
−8.06
0.18
5.28
0.24
4.90
8,707
Yes
No
Yes

1.24
17.38
0.34
2.45
−0.07
−1.35
−0.00
−0.06
0.02
0.38
0.16
4.24
−1.03
−6.46
0.16
2.68
0.19
4.82
8,707
Yes
No
Yes

0.66
12.41
0.50
6.29
0.09
2.25
−0.05
−1.41
0.01
0.28
0.07
1.49
−0.20
−2.68
0.09
1.90
0.13
2.82
8,707
Yes
Yes
No

1.24
15.12
0.70
5.96
0.05
0.87
−0.03
−0.51
−0.05
−0.76
0.19
2.45
−0.64
−5.41
0.18
2.82
0.24
3.34
8,707
Yes
Yes
No

1.24
8.88
0.34
1.63
−0.07
−0.73
−0.00
−0.04
0.02
0.21
0.16
1.30
−1.03
−4.71
0.16
1.53
0.19
2.04
8,707
Yes
Yes
No

To shed light on the negative relation between pollution abatement costs
and contemporaneous profitability, we provide direct evidence by including
the firm-level abatement costs into control among the control variables in
the regressions.35 In Panel A of Table VIII, we find a significantly negative
35 The abatement cost measure refers to the ENER and ENRR variables from the ASSET4

database. ENER measures a company’s commitment and effectiveness in reducing air emissions,
waste, water discharge, and spills or its impact on biodiversity. ENRR measures a company’s
ability to reduce the use of materials, energy, or water and to pursue more eco-efficient solutions
by improving supply chain management.

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The Pollution Premium

The Journal of Finance®
Table VII

Cash Flow Sensitivity
This table shows firms’ cash flow sensitivity to litigation shocks. In Panel A, we report panel
regressions of future and current profitability on their emission intensity, litigation shocks, and
their interactions, together with other firm characteristics in year t, where future profitability
refers to moving-average profitability from year t + 1 to t + 10. The sample excludes financial
industries. We control for industry-year fixed effects based on Fama and French (1997) 49-industry
classifications. We measure litigation shocks (n) using the log difference (i.e., growth rate) of
civil penalties provided by the EPA. All independent variables are normalized to zero mean and
unit standard deviation after winsorization at the 1st and 99th percentiles to reduce the impact
of outliers. t-Statistics based on standard errors that are clustered at the firm level or at the
industry-year level are reported. In Panel B, we show the cash flow sensitivity of emission-sorted
portfolios to the litigation shock. Portfolio-level cash flow refers to future profitability as used in
Panel A. We regress portfolio-level future profitability on litigation shocks together with other
firm characteristics, and then report estimated coefficients on cash flow. Coefficients on litigation
shocks are multiplied by 100. Standard errors are estimated using Newey-West correction. All
regressions are conducted at the annual frequency. The sample period is from 1991 to 2016.
Panel A: Profitability Regressions
Current ROA

Log Emissions
[t]
Log Emissions × n
[t]
Log ME
[t]
Log B/M
[t]
I/K
[t]
ROA
[t]
ROA
[t]
TANT
[t]
WW
[t]
Lagged ROA
[t]
Lev
[t]
OL
[t]
Observations
R2
Industry × Year FE
Cluster SE by Firm
Cluster SE by Industry × Year

Future ROA

(1)

(2)

(3)

(4)

0.017
2.154

0.017
2.433

0.146
7.110
−0.260
−15.750
0.007
0.680

0.146
7.257
−0.260
−19.710
0.007
0.738

−0.001
−0.071
0.081
3.940
0.549
33.023
−0.701
−10.636
0.070
5.415
13,857
0.639
Yes
Yes
No

−0.009
−0.076
0.081
4.283
0.549
33.007
−0.701
−12.486
0.0700
6.387
13,857
0.639
Yes
No
Yes

0.005
5.991
−0.128
−2.596
0.023
12.357
−0.003
−3.227
−0.005
−5.514
0.023
18.178
−0.095
−9.151
−0.001
−1.111
0.013
7.247

0.005
12.525
−0.128
−2.516
0.023
20.154
−0.003
−5.565
−0.005
−8.105
0.023
32.676
−0.095
−9.181
−0.001
−2.236
0.013
12.171

−0.010
−1.861
0.004
3.444
13,849
0.549
Yes
Yes
No

−0.010
−3.701
0.004
6.531
13,849
0.549
Yes
Yes
Yes
(Continued)

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Table VII—Continued
Panel B: Portfolio-Level Future Profitability

n
[t]

L

2

3

4

5

H-L

−0.31
−1.01

−0.44
−1.26

−0.23
−0.49

−0.44
−2.97

−0.54
−1.98

−0.35
−2.18

Table VIII

Profitability, Emission, and Abatement Costs
This table shows the joint link between profitability, emissions, and abatement costs. In Panel A,
we present the correlation matrix to document the correlation between emissions and measures
of abatement costs (ENER and ENRR). In Panel B, we report panel regressions of current profitability on abatement costs and their interactions, together with other firm characteristics. The
sample excludes financial industries. We control for industry and year fixed effects based on Fama
and French (1997) 49-industry classifications. All independent variables are normalized to zero
mean and unit standard deviation after winsorization at the 1st and 99th percentiles to reduce the
impact of outliers. t-Statistics based on standard errors clustered at the firm level are reported.
All regressions are conducted at the annual frequency. *** , ** , and * indicate significance at the
1%, 5%, and 10% level.
Panel A: Correlation

Emission
ENER
ENRR

Emission

ENER

ENRR

1

−0.09***

−0.11***
0.80***
1

1

Panel B: Regressions
(1)
ENER
[t]
ENRR
[t]
Log ME
[t]
Log B/M
[t]
I/K
[t]
TANT
[t]
WW
[t]
Lev
[t]
Observations
R2
Industry FE
Year FE
Cluster SE

−0.009
−2.495

0.010
1.317
−0.031
−5.859
0.008
1.406
−0.006
−0.9556
−0.005
−0.512
−0.016
−4.660
1,513
0.468
Yes
Yes
Yes

(2)

−0.012
−3.483
0.012
1.542
−0.031
−6.076
0.008
1.405
−0.006
−1.062
−0.005
−0.479
−0.016
−4.783
1,513
0.473
Yes
Yes
Yes

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The Pollution Premium

Table IX

Event Studies
This table presents cumulative abnormal returns around the 2016 U.S. presidential election of
stocks sorted into emissions-sorted portfolios. The table reports daily and annualized cumulative
returns over a 10-day window from 1 day after the presidential election date to 10 days after the
election, which we refer to as a (0,10) window. These cumulative abnormal returns are equally
weighted across emissions-sorted portfolios.
Event Studies: Presidential Election
CAR (%)
Daily Ret.
Annualized Ret.
[t]

L

2

3

4

H

H-L

3.64
90.89
4.55

5.35
133.87
5.62

5.03
125.82
5.14

3.75
93.85
3.84

6.31
157.86
5.11

2.68
66.97
1.98

correlation between firms’ emission intensity and their efforts to reduce
environmental pollution (as measured by ENER and ENRR in Thomson
Reuters’ ASSET4 database). In Panel B of Table VIII, Specifications (1)
and (2) present consistent results when we control for various proxies for
firm fundamentals.
C. Event Study
To provide additional evidence on whether the emission-return relation is
related to environmental policies, we analyze stock price reactions on the date
of Trump’s U.S. presidential election win on November 8, 2016 as a prominent
environmental policy shock, following Ramelli et al. (2021), Brown and Huang
(2020), and Child et al. (2021).36 To isolate the impact of new information on
stock prices, we consider CARs calculated with respect to the CAPM.37 We
then compute the average CAR of all stocks in each quintile portfolio (based
on firms’ emission intensity at the end of September 2016) in response to the
presidential election and include them in Table IX.
The CARs of emission-sorted portfolios display a largely monotonic increasing pattern from the lowest to the highest portfolios in relation to the U.S.
presidential election event. In addition, the difference in CARs for stocks in
36 Di Giuli and Kostovetsky (2014) also show that firms with low social responsibility scores
provide significantly positive 3-day CARs after Republican election victories. The authors in Acemoglu et al. (2016b) document positive CARs for financial firms connected with Timothy Geithner
following his nomination for U.S. Treasury Secretary in 2008. Wagner, Zeckhauser, and Ziegler
(2018) present evidence of positive spikes in stock prices among firms with high tax burdens following the 2016 U.S. presidential win. Brown and Huang (2020) find that firms with connections to
the Obama administration experienced lower stock returns following Trump’s victory. Child et al.
(2021) show that firms with presidential ties enjoyed greater CARs around the 2016 election.
37 Following standard practice in the literature, we adopt a 250-trading day estimation window
ending 25 days prior to the event day. To do so, we first calculate the market-adjusted CAR of each
stock over one date after the U.S. presidential election to 10 days after the event date, which we
refer to as the (0,10) window.

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The Journal of Finance®

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the lowest and highest portfolios is sizable at 66.97% in annualized terms,
significant at the 5% level. This result suggests that the stock market perceived the 2016 U.S. presidential outcome as good news for high-emission
firms, anticipating that environmental regulations were likely to be relaxed.
High-emission firms therefore retain their profitability advantage when weak
regulation regimes are confirmed, with their stock prices reacting positively.
More importantly, this finding indicates that the documented emission-return
relation is indeed related to governments’ environmental regulation policies.
This result calls for more theoretical work.
IV. A General Equilibrium Model
Given the pollution premium and several interesting empirical patterns that
we document above, we next build a general equilibrium asset pricing model
that features risk related to environmental policy regime shifts to explain the
role that industrial pollution plays with respect to expected stock returns. Our
specification of policy regime shifts is similar to that of Pástor and Veronesi
(2012, 2013). The basic intuition is that high-emission firms are more exposed
to risks of environmental policy regime change and therefore require higher
expected returns as compensation.
A. The Model Economy
Production. We consider an economy with a finite horizon [0, T] and a continuum of firms i ∈ [0, 1]. Let Bti denote firm i’s capital at time t. Debt financing
is not taken into account—firms in our economy rely entirely on equity financing.38 Therefore, firm i’s total capital equals Bti . At time 0, all firms are endowed
with the same amount of capital, which we normalize to Bi0 = 1. Firm i invests
its capital in a linear production technology with a stochastic rate of return
denoted by dti . All profits are reinvested, so that firm i’s capital dynamics
are given by dBti = Bti dti . Since dti equals profits over capital, we refer to it
as the profitability or ROA of firm i. For all t ∈ [0, T], profitability follows the
process
dti = (μ + ξ i g)dt + σ dZt + σI dZti ,

(3)

where (μ, g, σ, σI ) are observable and constant parameters, Zt is a Brownian
motion, and Zti is an independent Brownian motion that is specific to firm i.
The parameter g denotes the impact of different environmental policy regimes
(i.e., weak- or strong-regulation regimes) on mean profitability process across
firms. When g = 0, the environmental policy regime is “neutral” with zero impact on firm i’s profitability.
38 In Section IV of the Internet Appendix, we further extend our model to explicitly allow for
regime-switching debt financing. We show that this additional channel amplifies the emissionreturn relation.

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The Pollution Premium

The Journal of Finance®

The impact of an environmental policy regime shift, g, is constant when the
regime is not changed. At time τ (i.e., 0 < τ < T), the government makes an
irreversible decision as to whether to change its environmental policy from the
weak regulatory regime to the strong regulatory regime. As a result, g is a
simple step function over time,
⎧
W
⎪
for t ≤ τ
⎨g
W
(4)
g= g
for t > τ if no policy regime shift occurs
⎪
⎩ S
for t > τ if a policy regime shift occurs,
g
where gW denotes the impact of environmental policy under the weakregulation regime at the onset. An environmental policy change replaces the
weak regulation, denoted by W, by the strong regulation, denoted by S. Such
a policy decision replaces gW by gS , inducing a permanent change in firms’ average profitability. We further assume that firms with different levels of emission intensity have heterogeneous exposure to the environmental policy regime
shift, as captured by the parameter ξ i . We assume that ξ i is positively proportional to firms’ emission intensity and is drawn from a uniform distribution on
the interval [ξ min , ξ max ] at time 0 after which it remains unchanged. For now,
we take ξ i to be exogenously given. In Section IV.E, we discuss how emission
intensity is endogenously chosen ex ante by firm i. Without loss of generality,
we normalize the distribution of ξ i , which has a mean equal to one. As we detail in Section V of the Internet Appendix, we calibrate the parameters such
that gS < 0 < gW and establish the interval of ξ as [0,2].39
This setup together with its calibrated parameters has two implications.
First, as gS < gW and ξ i has unit mean, the environmental policy change from
the weak- to the strong-regulation regime has an adverse effect on average
profitability in the economy.
Second, the parameter ξ i governs the heterogeneous exposure of firms’ profitability with respect to regime change risks across firms with different levels
of emission intensity. Suppose that there are two firms: a high-emission firm
(ξ H ) and a low-emission firm (ξ L , such that ξ L < ξ H ). Owing to lower abatement costs under the weak regime, a high-emission firm’s average profitability is higher than that of a low-emission firm by the magnitude gW (ξ H − ξ L ).
This assumption is consistent with the empirical evidence in Section III.B:
that high-emission firms enjoy higher current ROA than their low-emission
counterparts, as take on fewer costs of pollution abatement and environmental recovery. In stark contrast, because gS < 0, high-emission firms’ average
profitability drops more than low-emission firms under the strong-regulation
regime.40 As another piece of suggestive evidence, in Section V.B we show
that, upon the arrival of policy change shocks that increase the perceived
39 In Section V of the Internet Appendix, we show that such calibration allows our model to reproduce a monotonically increasing pattern of firms’ current profitability (ROA) and a flat pattern
of firms’ future ROA, consistent with our data.
40 For this assumption, we present supportive evidence in Section V of the Internet Appendix for
the quantitative implication. In particular, we show that although high-emission firms’ current

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likelihood of a regime shift, high-emission firms’ future ROA drops more than
that of low-emission firms. As we discuss below, the cross-sectional dispersion
in firms’ emission intensity, ξ i s, by the assumption above is an important factor
in generating heterogeneous firms’ exposure to aggregate regime changes and
therefore in determining different risk premia across emission-sorted portfolios in equilibrium.
The firms are owned by a continuum of identical households that maximize
expected utility derived from terminal wealth.41 For all j ∈ [0, 1], investor j’s
utility function is given by
U (WTj ) =

(WTj )1−γ
,
1−γ

(5)

where WTj is investor j’s wealth at time T and γ > 1 is the coefficient of relative risk aversion. At time 0, all investors are equally endowed with the same
shares of firm stocks. Stocks pay dividends at time T.42 Households observe
whether regime shifts occur at time τ .
When making its policy decision at time τ , the government maximizes the
same objective function as households, except that it internalizes the negative
externalities of pollution as the environmental cost (c) if the economy is under the weak environmental regulation regime. The government commits to a
change in environmental policy only if the government’s expected utility under the strong regulation is higher than that when under the weak regulation.
Specifically, the government solves the optimization problem
 1−γ 

 
(c)WT1−γ 
WT 
W , Eτ
S ,
(6)
max Eτ

τ >t
1−γ
1−γ
1

where WT = BT = 0 BiT di is the final value of aggregate book equity and
(c) = 1 + ec is the environmental cost if the government retains the weakregulation regime. We refer to (c) > 1 as the cost to the society because, given
γ > 1 , a higher value of (c) translates into lower utility since WT1−γ /(1 − γ ) <
0. The value of c is randomly drawn at time τ from a normal distribution as
below, which implies that E[ec ] = 1, and
1
c ∼ Normal − σc2 , σc2 ,
2

(7)

where c is independent of the Brownian motion in equation (3). We assume that
the environmental cost c is unknown to all agents until time τ and follows a
prior distribution as in equation (7). We refer to σc as regime shift uncertainty.
ROA is higher, their average future ROA is similar to that of their low-emission counterparts.
This implies that high-emission firms’ ROA tends to be more negatively affected than that of lowemission firms when strong regulation is enacted with some positive probability.
41 This setting is consistent with our empirical design of scaling emissions by total assets.
42 No dividends are paid before time T because households’ preferences do not involve intermediate consumption. Firms in our model reinvest all of their earnings, as mentioned above.

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The Pollution Premium

The Journal of Finance®

Due to the uncertainty about environmental costs before time τ , stock prices
respond to environmental cost signals, as we show* in Section III.C.
B. Learning about Environmental Costs
The environmental cost c is unknown to all agents until time τ . At time
t < τ , agents start to learn about c by observing unbiased signals. We model
these signals as the true value of signals plus noise, which takes the following
form in continuous time:
dst = cdt + dZtc .

(8)

The signal dst is assumed to be independent of other shocks in the economy.
We refer to these shocks as environmental cost signals, and note that they
capture the steady flow of news related to environmental issues that are of
concern to both the media and regulatory authorities. Combining the signals in
equation (8) with the prior distribution in equation (7), we obtain the posterior
distribution of c at any time t < τ ,
2
),
c ∼ Normal(ĉt , σ̂c,t

(9)

where the posterior mean and variance evolve according to
2
dẐtc , and
dĉt = σ̂c,t

2
σ̂c,t
=

1
1
+t
σc2

.

(10)

(11)

Equation (10) shows that agents’ beliefs about c are driven by the Brownian
motion shocks dẐtc , which reflect the differences between the cost signals dst
and their expectations (dẐtc = dst − Et [dst ]). Since the cost signals are independent of all fundamental shocks in the economy (i.e., dZt and dZti ), the innovations dẐtc represent signal shocks to the true value of environmental costs.
These shocks shape agents’ beliefs about which environmental policy is likely
to be adopted in the future, above and beyond the effect of fundamental economic shocks. Accordingly, we refer to such signal shocks as regime change
risks. Later, we emphasize that these shocks command a risk premium in equilibrium. Moreover, since firms with different levels of emission intensity have
heterogeneous exposure to regime shifts, they exhibit different levels of risk
compensation with respect to regime change risks.
C. Optimal Regulation Regime Changes
After a period of learning about c, the government decides whether to change
policy regime at time τ . If the government changes the policy regime, then the

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value of g changes from gW to gS . According to equation (6), the government
changes policy regime if and only if
 1−γ 


WT 
(C)WT1−γ 
W > Eτ
S .
(12)
Eτ
1−γ
1−γ 
Since a regime change permanently affects future profitability, the two expectations in equation (12) are determined by different stochastic processes for
1
aggregate capital BT = 0 BiT di.43
According to Lemma A.1 in Section III.A of the Internet Appendix, the inequality can be further simplified into a rule that explains the policy regime
change, as we show in the following proposition.
PROPOSITION 1: A regulation regime change occurs at time τ if and only if

where

c(τ ) < c,

(13)



W
S
c(τ ) = log e(γ −1)(g −g )(T−τ ) − 1 > 0.

(14)

The probability of the policy regime change at τ − is denoted by pτ − ,
2
pτ − = 1 − Normal(c(τ ); ĉτ − , σ̂c,τ
− ),

(15)

2
where Normal(x; ĉτ − , σ̂c,τ
− ) denotes the cumulative density function (c.d.f.) of a
2
normal distribution with mean ĉτ − and variance σ̂c,τ
−.

Proof: See the Proof in Section III.B of the Internet Appendix.
COROLLARY 1: Agents’ time-t perceived probability of policy regime change at
time τ conditional on information at time t (t < τ ) is given by pτ |t ,
2
),
pτ −|t = 1 − Normal(c(τ ); ĉt , σ̂c,t

(16)

2
where Normal(x; ĉt , σ̂c,t
) denotes the c.d.f. of a normal distribution with mean ĉt
2
and variance σ̂c,t .

Proof: See the Proof in Section III.C of the Internet Appendix.
The intuition behind Corollary 1 provides us two testable implications for
our empirical analysis in Section V. First, using the growth in civil penalties
as a proxy for regime change shocks, we show that such shocks that increase
the perceived probability of a regime change lead to negative changes in asset
prices. Second, Corollary 1 is consistent with our finding in Section III.C: upon
Trump’s U.S. presidential victory as a negative regime change shock, the perceived probability of switching to a strong policy regime is revised downward.
43 The aggregation of capital at time T

Appendix.

is further derived in Section III.A of the Internet

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The Pollution Premium

The Journal of Finance®

Thus, high-emission firms’ stock prices react more positively to these events
than to those of low-emission firms.
D. Asset Pricing Implications
In this section, we derive the asset pricing implications of regime change
risks as follows. First, we show the impact of regime change risks on the state
price density. Second, we show how stock prices vary with fundamental shocks
and regime change shocks. Finally, we decompose firms’ risk premia into risk
compensation to fundamental shocks and risk compensation to regime change
shocks. We find that the heterogeneity in firms’ emission intensity translates
into cross-sectional differences in expected stock returns with respect to regime
change risks.
D.1. State Price Density
Our main focus is on the response of stock prices before regime shift uncertainty is resolved at time τ . Before time τ , agents learn about the environmental cost under weak regulation. This learning generates stochastic variation in
the posterior mean of c according to equation (8), which represents a stochastic
state variable that affects asset prices before time τ . In contrast, the posterior
variance of c varies deterministically over time as in equation (9).
The dynamics of the state price density πt are essential for understanding
the source of risks in this economy.44 An application of Ito’s Lemma to πt determines the SDF as shown in Proposition 2.
PROPOSITION 2: The SDF follows the process


dπt
dπt
− λdZt − λc,t dẐtc ,
= Et
πt
πt

(17)

where the price of risk for fundamental shocks is given by
λ = γ σ,

(18)

and the price of risk for uncertainty shocks is given by
λc,t =

1 ∂ t 2 −1
σ̂c,t η < 0.
t ∂ ĉt

(19)

Proof: See the Proof of Proposition 2 in the Internet Appendix.
Equation (17) shows that the prices of risk λ and λc,t measure the sensitivity
of the SDF with respect to fundamental shocks and regime change shocks. Fundamental shocks are represented by the Brownian motion dZt , which drives
44 We determine the level of the state price density in Section III.D of the Internet Appendix.

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1377

the aggregate fundamentals (profitability) of the economy. The first term of
the SDF shows that fundamental shocks affect the SDF in the same way when
all parameters are known. The second type of shocks consists of regime change
shocks. Although unrelated to fundamental shocks (i.e., dZt · dẐc,t = 0), regime
change shocks affect expected utility by affecting the perceived probability of a
regime change and hence are priced. Equation (19) shows that regime change
shocks impact the SDF more when the sensitivity of marginal utility to variation in ĉt is larger (i.e., ∂ t /∂ ĉt is larger) and when the posterior variance σ̂c,t
is larger. As we prove in the Internet Appendix, the sign of λc,t is negative.
Thus, upon a positive regime change shock, both the marginal value of wealth
and the state price of density increase and hence regime change shocks carry
a negative price of risk.
D.2. Stock Prices and Risk Premia
In this subsection, we present analytical expressions for the dynamics of firm
i’s stock price, which are summarized in the following proposition.45
PROPOSITION 3: Firm i’s realized stock returns at t < τ follow the process


dMti
dMti
i
+ σ dZt + σI dZti + βM,t
=
E
dẐtc ,
t
Mti
Mti

(20)

where firm i’s risk exposures to fundamental and firm-specific shocks are denoted by σ and σI , respectively, and risk exposure to policy regime change shocks
is denoted by
i
≡
βM,t

1 ∂ti 2
σ̂ < 0,
ti ∂ ĉt c,t

(21)

i
where the functional form of βM,t
is given by equation (IA.60) in the Internet
Appendix. Firm i’s exposure to policy regime shift shocks depends on ξ i , which
is the sensitivity of profitability to policy regime changes,
i
∂βM,t

∂ξ i

< 0.

(22)

Proof: See the Proof of Proposition 3 in the Internet Appendix.
Since firms’ exposure to fundamental shocks is homogeneous, the emissionsorted portfolios’ return spread in the cross section is determined solely by
i
heterogeneous levels of exposure to regime change shocks, βM,t
, the properties
of which are summarized in Proposition 3. In equation (22), we show that a
45 Detailed derivations for the level of firm i’s stock price are provided in Section III.F of the

Internet Appendix.

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The Pollution Premium

firm with a higher ξ i experiences a larger collapse than does a firm with a
lower ξ i in realized stock returns.
In equilibrium, risk premia are determined by the Euler equation that characterizes the covariance of a firm’s returns with the SDF. To characterize
the risk compensation for fundamental shocks and regime change shocks, we
derive the expression for the conditional risk premium. In particular, firm i’s
expected stock return equals its risk premia,

Et

dMti
Mti


= −covt

dMti dπt
,
Mti πt

i
= σ λdt + βM,t
λc,t dt.

(23)

In equation (23), we show that firm i’s risk premia are determined by its exposure to fundamental shocks and regime change shocks. The first term captures
the risk premium of fundamental shocks and is homogeneous across firms. The
risk premium of regime change shocks is given by the second term of equation (23). As we show in Propositions 2 and 3, upon a positive regime change
shock, stock prices decrease precisely when the marginal utility—and thus the
SDF—is high. Thus, agents demand positive compensation for their exposure
to such regime change shock.
More importantly, the heterogeneous risk compensation for regime change
risks is responsible for the cross-sectional difference in expected returns across
firms with different levels of emission intensity. As shown in equation (22),
i
) depends negatively
firm i’s risk exposure to a regime change shock (i.e., βM,t
on its emission intensity ξi . When the regulatory regime changes, stock values
of high-emission firms with high ξ decrease more than do those of low-emission
firms. Heterogeneous levels of exposure to regime change risks translate into
cross-sectional differences in expected stock returns. Our model predicts that
high-emission firms require a higher expected return than do low-emission
firms. This prediction is strongly supported by a statistically significant H-L
return spread among emission-sorted portfolios. We refer to this return spread
as the pollution premium.
E. Endogenous Decision to Choose Emission Intensity
In this section, we endogenize firm i’s decision to choose emission intensity
ξ i . Our key idea is to introduce a trade-off between firm value and costly
emission abatement. Based on our previous benchmark model, due to a higher
discount rate (i.e., the pollution premium), choosing a higher emission intensity leads to a lower valuation (i.e., market-to-book ratio). As a trade-off for a
lower valuation, a higher emission intensity leads to lower abatement costs.
For model tractability, we consider a static decision whereby firm i chooses ξ i
at time 0 and maintains the same emission intensity until terminal time T.
Firm value immediately after the choice of ξ i is given by M0i ≡ M0i /Bi0 , where
i
B0 = 1 for all firms at time 0. Based on the choice of parameter values given in

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The Journal of Finance®

1378

1379

Section V of the Internet Appendix, a firm’s valuation decreases in its emission
intensity at a decreasing rate. By using the log-linear approximation around
the average ξ i , denoted by ξ0 , firm i’s marginal value with respect to ξ i can be
express as
∂M0i
≈ −ω0 + ω1 ξ i ,
∂ξ i

(24)

where ω0 > 0 and ω1 > 0 are the Taylor expansion parameters evaluated at
ξ0 , which are provided in Section III.G of the Internet Appendix. We focus on
∂M i
ξ i < ξ max ≡ ωω01 so that the marginal value is negative (i.e., ∂ξ i0 < 0). This implies that a higher ξ i reduces a firm’s value, mainly due to a higher discount
rate to reflect the pollution premium. In addition, ω1 > 0 implies that firm i’s
valuation decreases at a slower rate as ξ i increases.
We denote firm i’s abatement cost by 0i ≡ 0 (ξ i ; ηi ), paid at time 0. We directly specify the marginal abatement cost with respect to emission intensity
ξ i as
∂0 (ξ i , ηi )
= ω1 ηi (ξ i − ξ¯ ),
∂ξ i

(25)

where ξ¯ is the emission intensity when it incurs zero marginal abatement cost.
We assume that a firm’s marginal cost depends on firm characteristic ηi . This
assumption has two important implications. First, over the range ξ i ∈ [0, ξ¯],
the marginal abatement cost is negative, which implies a benefit of abatement
cost savings when allowing a higher level of emissions. Second, it is increasingly costly to further reduce emissions when emission intensity is low. The
marginal abatement cost increases to ω1 ηi ξ¯ as firm i’s emission intensity approaches zero.
Firm i determines its level of emission intensity by maximizing its stock
price subject to abatement cost 0i :
max M0i − 0i .
ξi

(26)

The optimal ξ i∗ is defined by the first-order condition in the following
proposition.
PROPOSITION 4: In the equilibrium with ξ¯ < ξ max , the optimal emission intensity ξ i∗ satisfies
∂M0i
∂0i
=
,
∂ξ i
∂ξ i

(27)

and
ξ i∗ = ξ¯ +

−ω0 + ω1 ξ¯
.
ω1 (ηi − 1)

(28)

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The Pollution Premium

The Journal of Finance®

We show that the optimal ξ i∗ exhibits the following properties:
(i) When ξ¯ < ξ max , ξ i∗ must exist and is smaller than ξ¯.
(ii) ξ i∗ is increasing in ηi , and limηi →∞ ξ i∗ = ξ¯.
(iii) 0H < 0L for two firms with ηH > ηL > 1.
Proof: See the Proof of Proposition 4 in the Internet Appendix.
At the optimal emission intensity level, the marginal value improvement of
lower emission intensity is equal to the marginal abatement cost. The intuition
behind the above proposition is as follows. First, when we assume ξ¯ < ξ max ,
the optimal emission intensity ξ i∗ in equation (28) must exist over the range
[0, ξ¯]. Second, since the marginal cost of reducing emission intensity increases
in ηi , a firm with a higher ηi chooses a higher optimal emission intensity at
the optimum. Second, when we assume ξ¯ < ξ max , the optimal level of emission
intensity ξ i∗ in equation (28) must exist over the range [0, ξ¯]. In the extreme
case, the optimal level of emission intensity ξ i∗ converges to the ξ¯ with zero
abatement cost as ηi goes to infinity. The intuition is that an infinitely high
marginal abatement cost motivates firm i to choose the maximum emission
intensity level. Finally, the marginal abatement cost is heterogeneous across
firms. Because firms with higher ηi optimally choose higher levels of emission intensity, we can prove that they pay a lower overall abatement cost than
firms with lower ηi . In this study, we do not intend to endogenize the crosssectional heterogeneity in ηi . That said, we provide a plausible interpretation
by relating ηi to financial constraints and leave the microfoundation of ηi to
future research. We conjecture that firms with higher ηi are more financially
constrained. It is more costly for these firms to further reduce lower levels of
emission intensity since they are financially constrained and since the shadow
value of internal funds is high. Such an interpretation is consistent with the
empirical finding documented by Xu and Kim (2022) that more financially constrained firms tend to spend less on abatement costs.
COROLLARY 2: Suppose that ηi is drawn from an inverse uniform distribution on the interval [ηmin , ηmax ] at time 0 and then remains unchanged. The
optimal emission intensity ξ i∗ follows a uniform distribution on the interval
[ξ min∗ , ξ max∗ ].
Proof: See the Proof of Corollary 2 in the Internet Appendix.
Corollary 2 shows that the distribution ξ i is consistent with the exogenously
specified distribution of ξ i in our model presented in Section IV.A.
In summary, in this extension we characterize the endogenous choice of
emission intensity across firms and provide a microfoundation for higher
current profitability among firms with higher emission intensity since highemission firms save costs associated with pollution abatement and environmental recovery. In particular, our model suggests a negative correlation
between emission intensity and firms’ abatement costs, consistent with the
negative link between emission intensity and measures of abatement costs

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1380

1381

(i.e., ENER and ENRR) in Table VIII. Moreover, our model further provides a
testable implication for our empirical analysis in Section III.B.
V. Empirical Tests for Regime Change Risk
In this section, we explore the predictions of our model in the data by
examining several key testable implications that would support a regime
change risk explanation. First, we use the growth in aggregate civil penalties
initiated against polluting firms to proxy for the perceived likelihood of an
environmental regulation policy change (i.e, regime change risk). Second, we
find that regime change risk affects the profitability of high-emission versus
low-emission firms in a manner that is consistent with our model assumption.
We then implement a GMM test to show that our regime change risk proxy is
negatively priced in the cross section of test assets’ returns. Together with a
decreasing pattern of emission portfolios’ exposure to regime change risk, we
are able to clearly identify the mechanism underlying the pollution premium.
A. Our Proxy for Regime Change Risk
To empirically test the regime change risk explanation, we proxy for regime
change risk using the annual log growth of aggregate civil penalties initiated
against polluting firms in the EPA’s statistics since 1991, nt .46 This measure is intuitive, observable, and quantifiable: a larger number of aggregate
civil penalties initiated by federal and state governments against polluting
firms would suggest an increase in the perceived probability of an environmental policy regime change.47 Figure 1 plots the time series of the growth rate
(orange line) and the total emissions (blue line).
B. Future Profitability and Regime Change Risk
One key premise of our model is that high-emission firms’ future profitability
drops following a strengthening of environmental regulations, which impose
higher costs on polluting firms. We acknowledge that it is difficult to directly
test this premise because our model allows for only one regime change. For feasibility’s sake, we test whether high-emission firms’ future profitability drops
more when the growth of aggregate civil penalties against pollution increases.
To validate this premise, in Table VII we estimate
ROAi,t+1→t+10 = a + b1 Emissionsi,t + b2 nt + b3 Emissionsi,t × nt
46 These data source are available on the EPA website at: https://echo.epa.gov/facilities/
enforcement-case-search. More details about these data are provided in Section I.B in the Internet Appendix. The mean and standard deviation of settlements across all cases are 1.57 and
8.93 million dollars (real), respectively.
47 A higher level of aggregate civil penalties can be regarded as a positive signal shock d Ẑc as
t
in equation (10), which would lead directly to an increase in the perceived probability of a policy
regime change.

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The Pollution Premium

The Journal of Finance®

Figure 1. Time-series patterns of the number of civil cases. This figure plots the time series
of total emissions in the EPA’s TRI database (blue line on the left vertical axis) and the log growth
in civil penalties (nt ) (orange line on the right vertical axis). The data are downloaded from the
Enforcement and Compliance History Online (ECHO) system that contains information on civil
penalties provided by the EPA. Shaded bands are labeled as recession periods according to NBER
recession dates. The sample period is 1992 to 2017. (Color figure can be viewed at wileyonlinelibrary.com)

+c Controlsi,t + εi,t ,

(29)

where ROAi,t+1→t+10 is firm i’s moving-average ROA from year t + 1 to t + 10
and Emissionsi,t denotes firm i’s emission intensity in year t. We interact
Emissionsi,t and nt to examine the prediction that high-emission firms are
more likely to be adversely influenced by regime changes. The vector Controls
includes control variables ROA, change in ROA, size, B/M, I/K, TANT, financial constraints, book leverage, and operating leverage in year t, as well as
industry-year fixed effects.
Specifications (3) and (4) of Table VII, Panel A report the estimation results
for equation (29). The estimated coefficient on the interaction term b̂3 is significantly negative, which suggests that firms producing more toxic emissions observe larger profitability decline in the future when regulation is more likely to
be tightened. This is consistent with our model setting, and also highlights that
the relation between emissions and future profitability is conditional on governments’ environmental policies and regulations. In contrast, the estimated
coefficient b̂1 on emissions remains significantly positive when we control for
the interaction term; nevertheless, its economic magnitude is fairly small when
compared to the interaction term, which is consistent with our model premise
that high-emission firms observe lower profits under stronger regulation.

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1382

1383

Our model also suggests that the pollution premium comes from the variation in cash flow sensitivity to changes in environmental regulations.
To test this prediction, we measure cash flows using the value-weighted
future profitability (i.e., moving-average ROA from year t + 1 to t + 10) at
the portfolio level and examine whether the cash flows of portfolios with
higher emission levels exhibit more negative loadings on regime change risk.
Panel B of Table VII shows that the cash flow sensitivity of emission-sorted
portfolios displays a downward-sloping pattern, ranging from −0.31 to −0.54
with respect to regime change risk. Such a finding again highlights the main
economic mechanism in our paper, namely, that high-emission firms carry
more negative exposure to regime change risk.
C. Market Price and Regime Change Risk Exposure
In this section, we first test the price of regime change risk, which is negative as suggested in equation (20). We then examine emission-sorted portfolios’
exposure to regime change risk. Our model implies a two-factor model in which
the market excess return is the first factor and the regime change risk is the
second factor. To test the prices of these two factors using the procedure detailed in Cochrane (2005) (revised edition, pp. 236–239), we first specify the
SDF as
SDFt = 1 − λ × MKTt − λc × nt .

(30)

In equation (30), investors’ marginal utility is driven by two aggregate shocks:
MKTt , the market factor in the CAPM, and nt , the growth of the logarithmic
amount of all civil cases’ penalties as our proxy for regime change risk. We seek
to estimate λc , which is the sensitivity to nt and is proportional to the price
of regime change risk λc,t in equation (19).
To estimate λc , we consider the following test assets: our six emission-sorted
portfolios (as presented in Table II), six size-momentum portfolios, and five
industry portfolios.48 We then conduct GMM estimation for the following empirical approximation to equation (23) (e.g., Kogan and Papanikolaou (2014))
E[Rei ] = −cov(SDF, Rei ),

(31)

but with the conditional moments replaced by their unconditional counterparts. In effect, we assess the ability of nt to price test assets on the basis
of residuals of the Euler equation.
In addition, we follow the literature (e.g., Papanikolaou (2011), Eisfeldt and
Papanikolaou (2013), and Kogan and Papanikolaou (2014)) to estimate two
statistics for the cross-sectional fit—the sum of squared errors (SSQE) and
48 This choice of test assets follows Lewellen, Nagel, and Shanken (2010), Belo et al. (2017),
Lin, Palazzo, and Yang (2020), and a suggestion from an anonymous reviewer. The return data on
the six size-momentum portfolios and the five industry portfolios are collected from the website of
Professor Kenneth French.

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The Pollution Premium

The Journal of Finance®

mean absolute percent errors (MAPE)—as well as the J-statistic of overidentifying model restrictions.49 An insignificant J-statistic would suggest that the
null hypothesis of an SDF model’s pricing errors being equal to zero is not
rejected.
In Panel A of Table X, we present the results of a CAPM and our two-factor
SDF model. In Specifications (1) and (2), we separately report the price of
regime change risk and market risk. We find that the price of regime change
risk λc is significantly negative in Specification (1), while the price of market risk λ is significantly positive in Specification (2). When we combine the
market factor with the regime change risk in Specification (3) as our benchmark, the price of regime change risk remains significantly negative (−0.99).
In terms of asset pricing errors, the SSQE and MAPE of CAPM (Specification
(2)) are 2.16% and 8.47%, respectively. After we introduce regime change risk
to our model (Specification (3)), the SSQE and MAPE decrease to 1.54% and
6.63%. Although the J-test is statistically insignificant in Specifications (2) and
(3), we show that regime change risk still improves the model fit by reducing
pricing errors. The JT difference test between the CAPM model and our twofactor model is 2.725 with marginal significance. Overall, regime change risk
improves upon the performance of the CAPM model in pricing stock returns.
To differentiate our regime change risk from general political uncertainty, we
first compare an alternative two-factor model that includes the market factor
and the EPU index of Bloom (2009), which reflects general EPU risk according
to Bali, Brown, and Tang (2017). As shown in Specification (4), the estimated
price of risk with respect to economic uncertainty is negatively significant, and
the JT difference test supports a substantial improvement in pricing when
we include the economic uncertainty index in the SDF. In Specification (5),
when our regime change risk measure is further considered in the SDF, we find
that both the economic uncertainty index and regime shift risk are negatively
priced. Finally, in comparison with Specification (4), the inclusion of regime
change risk rejects the JT difference test by significantly reducing pricing errors. These results thus support the view that our environmental policy risk is
distinct from general policy risk.
To further differentiate our regime change risk from aggregate economic
growth, we consider an alternative two-factor model that includes the market
factor and GDP shocks.50 As shown in Specification (6), the estimated price of
risk with respect to GDP shocks is significantly positive, and the JT difference
test supports a substantial pricing improvement when we include GDP shocks
in the SDF. In Specification (7), when regime change risk is further added to
the SDF, we find that it is significantly negatively priced and reduces pricing
49 Given the Euler equation E[SDF × Re ] = 0, our SSQE and MAPE are based on each test
i
T 
asset i’s moment error ui as follows: ui = T1 t=1
[SDF × Rei,t ]. SSQE and MAPE are defined as
N
1 N
i=1 ui × ui and N
i=1 |ui |, respectively, where N denotes the number of testing assets.
50 Following Covas and Den Haan (2011), our measure of GDP shocks is real GDP of the corpo-

rate sector filtered using the Hodrick-Prescott filter (Hodrick and Prescott (1997)) to extract the
cyclical component of GDP.

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1384

Table X

t=1

i,t

i=1

N

i=1

21.78
30.12
6.600
0.97

−1.66
−6.23

2.16
8.47
6.776
0.99

0.69
10.57

(2)

1.54
6.63
6.667
0.95
2.725
0.099

0.67
8.6
−0.99
−4.37

(3)

1.89
9.10
6.405
0.96
9.266
0.002

−0.99
−8.43

0.47
3.16

(4)

1.43
6.66
6.260
0.93
3.65
0.056

0.51
5.10
−0.81
−5.42
−0.64
−6.42

(5)

0.48
5.22
1.88
7.51
6.489
0.95
7.173
0.007

0.55
7.50

(6)

(Continued)

0.18
1.47
1.55
6.56
6.379
0.93
2.748
0.097

0.63
7.85
−0.95
−3.81

(7)

1385

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MKT
[t]
n
[t]
Uncertainty
[t]
GDP
[t]
SSQE (%)
MAPE (%)
J-Test
p
JT-Diff
p

(1)

Panel A: Price of Risk

i
i ) to the market factor and litigation shocks, together with estimated
and βn
In Panel B, we present GMM-implied test portfolios’ risk exposure (βMKT
i
i
pricing errors (α = R̄ − β × λ) in percentage.

T

In Panel A, we present GMM estimates of the parameters of the stochastic discount factor, SDF = 1 − λ × MKT − λc × n, using the quintile portfolios
sorted on emission intensity. n denotes the log difference (growth rate) in the number of civil cases to proxy for litigation shocks (n). We do the
normalization such that E[m] = 1 (see, for example, Cochrane (2005)). We report t-statistics based on standard errors estimation using the NeweyWest procedure adjusted for three lags. As a measure of fit, we report the sum of squared errors (SSQE), mean absolute pricing errors (MAPE), and
the J-statistic of overidentifying model restrictions. Given the Euler equation E[SDF × Rei ] = 0, SSQE and MAPE are based on each testing asset i’s

 × Re ]. SSQE and MAPE are defined as N ui × ui and 1 N |ui |, where N denotes the number of test assets.
moment error ui : ui = 1 T [SDF

Estimating the Market Price of Risk

The Pollution Premium

15.39
10.12
−1.47
−1.49
−4.36
−1.60

4

H

17.14
16.9
−0.60
−0.26

17.49
10.05
−1.35
−0.58

17.83
8.18
−1.28
−0.55

16.59
14.28
0.82
0.35

16.94
11.42
−0.81
−0.95
−0.74
−0.27

17.74
8.56
1.01
1.08
−0.42
−0.16

17.86
7.18
0.14
0.11
−0.88
−0.32

16.09
10.58
−2.10
−3.81
−0.06
−0.02

Panel D: SDF (MKT+EPU) in Panel A (4)

15.74
11.94
−3.89
−1.66

3

Panel B: SDF (MKT) in Panel A (2)

2

0.69
0.71
−0.64
−0.53
−3.26
−1.16

0.18
0.26
−3.53
−1.47

H-L

i
βMKT
[t]
i
βn
[t]
i
βEPU
[t]
α i = R̄-β i × λ
[t]

i
βMKT
[t]
i
βn
[t]
α i = R̄-β i × λ
[t]

3

4

H

17.2
11.95
2.69
3.05
0.65
0.26

17.49
8.61
−0.41
−0.33
−1.57
−0.60

17.81
7.07
−0.85
−0.65
−1.74
−0.67

16.55
11.13
−1.46
−1.24
0.19
0.07

Panel C: SDF (MKT + n) in Panel A (3)

2

0.78
0.90
−2.91
−3.45
−3.48
−1.37

H-L

15.41
9.76
1.55
1.55
−1.56
−1.51
−3.74
−1.41

16.96
11.01
2.75
2.99
−0.99
−1.15
0.13
0.05

17.73
8.43
−0.47
−0.36
1.04
1.05
−0.73
−0.28

17.85
7.12
−0.86
−0.63
0.20
0.14
−1.26
−0.47

16.08
10.8
−1.34
−1.19
−2.02
−3.6
−0.35
−0.13

0.67
0.81
−2.89
−3.32
−0.46
−0.35
−3.23
−1.21

Panel E: SDF (MKT+EPU+n) in Panel A (5)

15.77
9.63
1.45
1.39
−3.09
−1.19

L

The Journal of Finance®

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i
βMKT
[t]
i
βEPU
[t]
α i = R̄-β i × λ
[t]

i
βMKT
[t]
α i = R̄ − β i × λ
[t]

L

Table X—Continued

1386

1387

errors according to the JT difference test. Our environmental policy risk is
thus different from economic growth in asset pricing.
In Panels B to E of Table X, we present emission-sorted portfolios’ risk exposure (GMM-implied betas) with respect to various factors in the SDF, together with their alphas estimated from E[Rei ] − β i λ in Specifications (2) to
(5) in Panel A, respectively.51 We find that the betas with respect to the mari
ket factor (βMKT
) are flat across emission-sorted portfolios in all panels. More
i
from the low-emission
importantly, we observe a decreasing pattern in βn
portfolio to the high-emission portfolio. These portfolios present a downwardsloping pattern of covariances with our proxy for regime change risk. Taken
together, these results support our environmental risk argument that highemission firms provide higher expected stock returns because they carry more
negative betas on regime change risk that is negatively priced. We also find
that the addition of regime change risk reduces the economic magnitude and
statistical significance of emission portfolios’ alphas when we compare Panels
C to B and when we compare Panels E to D. These findings further support our
environmental risk argument for the pricing errors associated with emissions.
VI. Conclusion
Environmental protection awareness has surged over the past several
decades. This paper investigates the implications of industrial pollution on
asset pricing. We use firm’s mandatory emission reports filed with EPA to
capture firms’ annual toxic releases. A long-short portfolio constructed from
firms with high versus low toxic emission intensity relative to their industry
peers generates an average excess return of around 4.42% per year. This positive emission-return relation cannot be explained by common risk factors and
holds in Fama and MacBeth (1973) regressions that control for other firm characteristics. When we empirically examine if this positive emission-return relation can be attributed to several explanations proposed in the literature, such
as investors’ emission preferences, underreaction to emission abatement, retail investors’ behavioral bias, corporate governance, political connections and
risk, and other potentially related systematic risks (including technology obsolescence, financial constraints, economic and political uncertainty, and adjustment costs). We find that the return predictability related to toxic emissions
cannot be satisfactorily explained by these aforementioned factors.
In additional tests, we find some interesting patterns. First, firms with more
toxic emissions are associated with higher current profitability and more environmental litigation. Second, high-emission firms’ future profitability is lower
after governments impose stricter environmental regulations. Third, highemission firms observe a favorable shock as response to Donald Trump’s 2016
U.S. presidential election win, which suggests a connection between emissionrelated return predictability and changes in environmental policies and
51 In this revision, we modify the code of Kan, Robotti, and Shanken (2013) to calculate test

assets’ alphas and t-statistics based on Chapter 12 of Cochrane (2005).

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The Pollution Premium

The Journal of Finance®

regulations. Motivated by these findings, we develop a general equilibrium
asset pricing model in which firms’ cash flows face regime change uncertainty
with respect to emission regulation policies. We argue that the government
optimally replaces a weak regulation regime by a strong one if pollution costs
are perceived to be sufficiently high. Since high-emission firms’ profitability is
more negatively affected than that of low-emission firms upon a shift from a
weak to a strong regulation regime, high-emission firms are more exposed to
regulation regime change risk and thus earn higher average excess returns as
risk premia. This model is supported by our asset pricing tests: regime change
risk is negatively priced, and high-emission firms carry more negative exposure to this risk, thereby earning higher risk premia.
Initial submission: December 1, 2018; Accepted: January 31, 2022
Editors: Stefan Nagel, Philip Bond, Amit Seru, and Wei Xiong

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Supporting Information
Additional Supporting Information may be found in the online version of this
article at the publisher’s website:
Appendix S1: Internet Appendix.
Replication Code.

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==> JF6 - 2007 - STREBULAEV - Do Tests of Capital Structure Theory Mean What They Say.txt <==
THE JOURNAL OF FINANCE • VOL. LXII, NO. 4 • AUGUST 2007

Do Tests of Capital Structure Theory
Mean What They Say?
ILYA A. STREBULAEV∗
ABSTRACT
In the presence of frictions, firms adjust their capital structure infrequently. As a
consequence, in a dynamic economy the leverage of most firms is likely to differ from
the “optimum” leverage at the time of readjustment. This paper explores the empirical
implications of this observation. I use a calibrated dynamic trade-off model to simulate
firms’ capital structure paths. The results of standard cross-sectional tests on these
data are consistent with those reported in the empirical literature. In particular, the
standard interpretation of some test results leads to the rejection of the underlying
model. Taken together, the results suggest a rethinking of the way capital structure
tests are conducted.

RECENT EMPIRICAL RESEARCH IN CAPITAL STRUCTURE focuses on regularities in the
cross section of leverage to discriminate between various theories of financing
policy. In this research, book and market leverage are related to profitability, book-to-market, and firm size. Changes in market leverage are largely explained by changes in equity value. Past book-to-market ratios predict current
capital structure. Firms seem to use debt financing too conservatively, and the
leverage of stable, profitable firms appears particularly low. Even if firms have
a target level of leverage, they move toward it slowly. Firms with low leverage
react differently to external economic shocks from firms with high leverage.1
∗ Strebulaev is at the Graduate School of Business, Stanford University. Most of the work on this
paper was carried out at the London Business School. I wish to acknowledge with deep gratitude
the counsel and never-failing kindness of Steve Schaefer. I am much obliged for many illuminating conversations and constructive suggestions to an associate editor, an anonymous referee, Viral
Acharya, Anat Admati, Nick Barberis, Dick Brealey, Ian Cooper, Sergei Davydenko, Paul G. Ellis,
David Goldreich, Denis Gromb, Rajiv Guha, Tim Johnson, Jan Mahrt-Smith, Pierre Mella-Barral,
Felix Meschke, Kjell Nyborg, Sergey Sanzhar, Robert Stambaugh (the editor), Alexander Triantis,
Raman Uppal, Rang Wang, Ivo Welch, and Toni Whited, and to the seminar participants at the
Anderson School of Business at UCLA, Cambridge, Carnegie-Mellon, Columbia Business School,
Cornell, Harvard Business School, Goizueta Business School, Kellogg, London Business School,
Michigan Business School, McCombs School of Business, Oxford, Simon School of Business, Stanford GSB, and Stern School of Business. I am also thankful to the participants of the Western
Finance Association 2004 meeting in Vancouver and the European Finance Association 2004 meeting in Maastricht. I am solely responsible for all remaining errors.
1
See Graham (2000) on conservatism in financing decisions; Titman and Wessels (1988), Rajan
and Zingales (1995), Fama and French (2002), among others, on cross-sectional determinants;
Fama and French (2002), Hovakimian, Opler, and Titman (2001), and Graham and Harvey (2001)
on slow mean-reversion of debt ratios; Baker and Wurgler (2002) on the influence of past book-tomarket ratios; Welch (2004) on the inf luence of changes in the market value of equity; Opler and

1747

The Journal of Finance

These findings are typically evaluated in terms of the comparative statics of
various capital structure models. Each of these models is supported by some
evidence and challenged by other evidence. This paper attempts to understand
whether our interpretation of cross-sectional tests would change if firms optimally adjusted their leverage only infrequently.
The starting point for this study is a simple but fundamental observation. In
a dynamic economy with frictions the leverage of most firms, most of the time, is
likely to deviate from the “optimal leverage,” as prescribed by models of optimal
financial policy, since firms adjust leverage by issuing or retiring securities infrequently, at “refinancing points.” Consequently, even if firms follow a certain
model of financing, a static model may fail to explain differences between firms
in the cross section since actual and optimal leverage differ. It has been long
recognized that deviations from optimal leverage may create problems in interpreting the results of empirical research. For example, Myers (1984, p. 578)
emphasizes that “any cross-sectional test of financing behavior should specify
whether firms’ debt ratios differ because they have different optimal ratios or
because their actual ratios diverge from optimal ones.”
This paper contributes to the literature by addressing exactly how the above
problem has manifested itself in empirical studies. It also offers the intuition
behind the ways in which this problem operates. I start by constructing a model
of time-consistent optimal dynamic financing in the presence of frictions and
then use the model to generate dynamic paths of leverage. The resulting crosssectional data resemble data used in empirical studies along a number of dimensions. This allows me to replicate tests commonly used in such studies and
ask to what extent the results are similar. My findings can be summarized as
follows: (1) Cross-sectional tests performed on data generated by dynamic models can produce results that are profoundly different from their predictions for
corporate financing behavior at refinancing points; (2) moreover, some results
may lead to the rejection of precisely the model on which these tests are based,
if the null hypothesis is formed on the basis of the relationships at the refinancing point; and (3) even a stylized trade-off model of dynamic capital structure
with adjustment costs can produce results that are numerically consistent with
some of those observed empirically.
The basic economic intuition behind these results lies in the observation that
in any cross section firms are at different stages of their refinancing cycles,
with almost no firms being at “date zero”, that is at a refinancing point. At any
point in time, any two firms are likely to exhibit different reactions to the same
shock even if these firms are identical from the date zero perspective. What
causes their responses to differ are the histories of idiosyncratic shocks and
the accumulations of past financial decisions. To relate any dynamic model to
empirical studies, it is necessary to produce within the model a cross section of
leverage ratios that is structurally similar to those that could have been studied
Titman (1994) on the reaction of highly leveraged companies to industry shocks; Korajczyk and
Levy (2003) on their reaction to macro shocks; and Leary and Roberts (2005) and Kisgen (2006) on
the frequency of refinancing.

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by an empiricist. This also suggests that we may need to rethink empirical tests
in this area and also highlights the importance of developing dynamic models
of financing that are capable of delivering quantitative predictions.
While in principle the approach developed here is applicable to any theory
of financial policy, a prerequisite for my analysis is a model that captures the
dynamics of firms’ financing behavior. Among the many existing explanations
of capital structure, only the trade-off argument has a fully worked out dynamic
theory that produces quantitative predictions about leverage ratios in dynamics. This theory suggests that firms arrive at their optimal capital structure by
balancing the corporate tax advantage of debt against bankruptcy and agency
costs. Using a trade-off model might seem questionable because the empirical
evidence for this model is, at best, mixed. However, as I show in this paper, the
data are more consistent with the dynamic trade-off theory than is traditionally
thought, and so, ex post, using a trade-off model is more justified. I employ a
standard state-contingent model of dynamic capital structure rooted in a tradeoff argument. While several features differentiate the model from others in the
field, the basic setup is widely used in the literature. In the model, firms are
always on their optimal capital structure path, but, due to adjustment costs,
they refinance only occasionally. Small adjustment costs can lead to long waiting times and large changes in leverage, a result consistent with the findings
of Fischer, Heinkel, and Zechner (1989). Firms that perform consistently well
re-leverage to exploit the tax shield of debt. Firms that perform poorly face a
liquidity crisis and sell their assets to pay down debt. If their financial condition
deteriorates still further, they resort to costly equity issuance to finance their
debt payments and, when all other possibilities are exhausted, they default and
ownership is transferred to debt holders. The benefit of having a more realistic
model is that it allows for the assessment of the magnitude of economic effects.
I use the model in two ways. First, I determine the path of a firm’s optimal
financing decisions. This enables me to study the cross section of optimal leverage at times when firms change their leverage, that is, at refinancing points.
Naturally, when firms are at their refinancing points, all the comparative statics predictions are in line with the predictions of the standard dynamic trade-off
theory.
In the second stage of the analysis, I perform a number of cross-sectional
tests on simulated dynamic data generated by the model. Several results stand
out. First, the analysis highlights difficulties in interpreting the leverage–
profitability relationship. According to the pecking order argument, more profitable firms reduce their dependence on costly external financing and thus
decrease their leverage. According to the trade-off theory, higher profitability decreases the expected costs of distress and allows firms to increase their
tax benefits by increasing leverage. Thus, an inverse relation between leverage
and profitability, frequently found in the data and identified by Myers (1993) as
perhaps the most pervasive empirical capital structure regularity, represents
a significant failure of the trade-off model and is considered by some writers
to be decisive in its rejection. In my model, expected profitability is positively
related to leverage at the refinancing points. However, I show that in a dynamic

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Tests of Capital Structure Theory

The Journal of Finance

economy cross-sectional tests reveal a negative relation. The intuition is simple: With infrequent adjustment, an increase in profitability lowers leverage
by increasing future profitability and thus the value of the firm. Similarly, a
decrease in profitability increases leverage. For those firms that do not refinance, this results in a negative relation between leverage and profitability. Of
course, in any period some firms refinance. In the simulations the subset of
firms that do not refinance dominates and the cross-sectional relation between
profitability and leverage is always negative. This effect is strengthened by the
presence of systematic shocks in the firms’ cash f low. In a number of cases, the
magnitude of the coefficient is also consistent with empirical estimates.
Second, again using the model to simulate dynamic data, I replicate almost
exactly the test recently conducted by Welch (2004). His main finding is that
debt ratios are largely explained by past stock returns, implying that corporations do not readjust their debt levels to counteract the mechanistic effect
of stock returns on leverage. This observation is important, not least because
other determinants used in the literature are found to affect leverage, largely
through stock returns. The results of the same regression tests conducted on
the simulated data are numerically very similar to those obtained by Welch,
suggesting that a stylized dynamic model with small adjustment costs may be
consistent with these findings.
In addition, the framework can provide an explanation for the “debt issuance
mystery” (Welch (2004)), that is, the apparent inconsistency between the passive behavior of managers in response to mechanistic changes in equity value
and the overall active capital structure policies of corporations. Managers are
passive, since, over a short horizon, there is almost a one-to-one relation between leverage and variables whose change is entirely determined by stock
returns. These results obtain in the model since managers decide to change the
firm’s leverage based on changes in value over a long period, a variable that
is largely orthogonal to recent equity returns. Thus, both in the cross section
and consistent with empirical observation, changes in outstanding debt value
are contemporaneously almost independent of the changes in market value of
equity.
Third, since the behavior of the cross section in a dynamic economy is radically different from the comparative statics properties at the refinancing points,
comparing empirical findings with the theoretical properties of leverage at refinancing points can be misleading. An example is provided by the debate on
possible explanations for the so-called “low leverage puzzle.” This refers to the
observation that the median corporate debt-to-capital ratio in the United States
over 1965 to 2000 averaged only 31.4%, with two out of five firms having an average debt-to-capital ratio of less than 20%,2 while traditional trade-off models
produce substantially higher numbers. That dynamic trade-off models imply
2
Estimates are based on COMPUSTAT data on the book value of debt and market value of
equity. The debt-to-capital ratio is defined as: COMPUSTAT data items d9 + d34 divided by d9 +
d34 + d25×d199. These are unadjusted figures. Adjusted figures (see Rajan and Zingales (1995))
would be lower.

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excessively high leverage is not surprising in light of Merton Miller’s (1977
p. 264) famous remark about “horse and rabbit stew:” Bankruptcy costs are
simply negligible compared to the tax benefits of debt. To explain the observed
low levels of leverage, we need to better understand the factors that might offset the tax benefits. One proposed solution is to consider a dynamic framework.
Studies by Goldstein, Ju, and Leland (2001) and Ju et al. (2003) show that if
firms are allowed to increase debt in the future, they will opt for lower leverage
initially. My results suggest that average leverage measured over time, that is,
in “true dynamics,” tends to be larger than the leverage measured at refinancing points. Empirical estimates of leverage should therefore be compared with
the model estimates of leverage ratios obtained in a dynamic economy.
My paper builds on several strands of previous research. First, it shares with
recent papers such as Leland (1998), Goldstein, Ju, and Leland (2001), and Ju
et al. (2003) a theoretical framework in which the standard structural models
of risky debt pricing are extended to incorporate dynamic financing behavior.
These models follow, on the one hand, static capital structure models developed
by, among others, Leland (1994) and, on the other, dynamic capital structure
models developed by Fischer, Heinkel, and Zechner (1989), whose research is, in
turn, based on insights by Kane, Marcus, and McDonald (1984, 1985). Fischer
et al. (1989) are also the first to suggest that empirical studies of capital structure in the cross section might be more fruitful if the dependent variable were
to ref lect the behavior of leverage over time, for example, its range, rather than
its value at a point in time.
My model most closely resembles that of Goldstein et al. (2001). A distinct
feature of my model is that the firms whose value falls substantially face a
prolonged period of turbulence instead of simply running up a large debt burden
and then defaulting. The model is thus consistent with the empirical findings
of Asquith, Gertner, and Scharfstein (1994), according to whom firms unable to
service their debt obligations sell a fraction of their assets in order to pay down
their debt.
The simulation approach followed here resembles, for example, Berk, Green,
and Naik (1999), who focus on the cross-sectional relation between a firm’s
investment policy, systematic risk, and expected returns. To investigate crosssectional patterns and regularities in their nonlinear dynamic economy they
perform simulations, an approach I endeavor to replicate since my model also
has strong nonlinearities. I calibrate firms’ technology parameters to resemble,
in a sense discussed later, the properties of samples of firms typically used
in empirical studies. I then simulate data on firm values, leverage, etc. for
dynamic economies and conduct a number of cross-sectional tests similar to
those performed in the empirical literature. The evolution of firms’ asset values,
and therefore their financing decisions, are cross-sectionally dependent due to
the presence of systematic shocks.
Several recent papers address issues similar to those considered here. Gomes
(2001) examines the investment behavior of financially constrained firms. Using a related approach, he finds that standard investment regressions that use
cash f low as an explanatory variable produce misleading results. Hennessy and

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Tests of Capital Structure Theory

The Journal of Finance

Whited (2005) show that a trade-off model can explain a number of empirically
observed stylized facts by expanding the set of financial choices available to a
firm. In their model, firms take into account internally generated funds when
they choose the method of financing. Compared with my model, their model
features endogenous investment, a richer tax environment, and more financial choices. On the other hand, it does not model adjustment costs for debt
and also it does not allow for default. While their model and methods are substantially different from mine, the idea that it is essential to consider firms’
behavior beyond date zero is central to both approaches. Using an empirical
duration model, Leary and Roberts (2005) find that firms do rebalance their
capital structure infrequently in the presence of adjustment costs. Theirs is a
pure empirical paper, which derives its tests from the literature. However, it
is closely related to my paper in that its hazard model estimation is justified
by a model of infrequent adjustment. Their result lends empirical support to
the main assumption of my analysis that imperfections make firms willing to
refinance discontinuously. In addition, they find that the financing gap is an
important determinant of the adjustment hazard, a phenomenon that a model
with exogenous investment policy cannot explain.
The paper proceeds as follows. Section I presents and solves the model. Section II presents the simulation procedure and replicates a number of empirical
tests on data generated from the model. Section III describes the robustness
tests. Section IV concludes. The Appendix contains details of the simulation
method.
I. The Model
A. The Case of an All-Equity Firm
My model employs a standard contingent claims framework to analyze an
individual firm and is closely based on Goldstein et al. (2001). Specifically, I
consider an economy populated by N firms, each of which is endowed with
monopoly access to some infinitely lived project operating in continuous time.
The value of each firm stems from a perpetual entitlement to the current and
future income from the project (EBIT-generating machine). Income is divided
between the net payout to claimholders and retained earnings. In line with
many other models of capital structure, I retain the Modigliani and Miller assumption that the project’s cash f lows are invariant to financial policy.3 Investment is financed by retained earnings where the latter are net of depreciation
and result in book assets growing at a rate g. The growth of book assets is modeled similarly to Brennan and Schwartz (1984). The initial value of book assets,
A0 , is equal to the initial value of the firm. The state variable in the model is
the total time t net payout to claimholders, δt , where claimholders include both
insiders (equity and debt) and outsiders (government and various costs). The
3
Several papers analyze interactions between financing and investment policy, including joint
decisions on production and capital structure (Brennan and Schwartz (1984), Mello and Parsons
(1992), Mauer and Triantis (1994)) and the effects of asset substitution (Leland (1998)).

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evolution of δt is governed by the following process under the pricing measure
Q:4
d δt
= µ dt + σ dZt ,
δt

∀t ≥ 0, δ0 > 0,

(1)

where µ and σ are constant parameters
and Z

 t is a Brownian motion defined on
a filtered probability space , F, Q, (Ft )t≥0 . Here, µ is the risk-neutral drift
and σ is the instantaneous volatility of the project’s net cash f low.
I assume that management always acts in the best interest of shareholders
and, throughout the paper, I use the terms manager and equity holder interchangeably. To avoid further complication, the default-free term structure is
assumed to be f lat with an instantaneous after-tax riskless rate r at which investors may lend and borrow freely. The marginal corporate tax rate is given
by τc . The marginal personal tax rates, τd on dividends and τi on interest income, are assumed to be identical for all investors. Finally, all parameters in
the model are assumed to be common knowledge.
Under these assumptions, consider a debtless firm with current cash f low δ 0 .
The firm’s current value is divided between equity and government, with the
shareholders’ value being equal to
 ∞

δ
−rs
e (1 − τ )δs ds = (1 − τ )
,
(2)
E(δ0 ) = Eδ0
r −µ
0
where τ = 1 − (1 − τc )(1 − τd ) and expectations, here and throughout the paper,
are taken under the pricing measure Q.
B. The Case of a Levered Firm
Now, consider an otherwise identical firm whose management decides to
choose the dynamic capital structure that will maximize the wealth of current
equity. The fundamental driving force of the model is the inherent conf lict of
interest between the different claimholders since ex ante (prior to the issuance
of debt) and ex post (after debt has been issued) incentives of equity holders
are not aligned. Debt holders foresee the future actions of equity holders and
value debt accordingly.
All corporate debt is in the form of a perpetuity entitling debt holders to a
stream of continuous coupon payments at the rate of c per annum and allowing
equity holders to call the debt at the face value at any time. To illustrate the
model’s structure in the presence of debt, Figure 1 shows a number of possible
paths for the firm’s value. At every date t, equity holders decide on their actions.
As in Fischer et al. (1989), Leland (1998), and Goldstein et al. (2001), firms
whose net payout reaches an upper threshold will optimally choose to retire
4
Since I consider an infinite time horizon, some additional technical conditions on the Girsanov
measure transformation (e.g., uniform integrability) are assumed here. In addition, the existence
of traded securities that span the existing set of claims is assumed. Thus, the pricing measure is
unique.

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Tests of Capital Structure Theory

The Journal of Finance

Firm Value

Ref.Point
Ref.Point

path1

path2
Initial

Liq.Crisis

path3

Default
time

Figure 1. Possible paths of firm value. The figure shows possible model scenarios. Path 1
depicts a successful firm that refinances when firm value increases substantially. Paths 2 and 3
show firms that face a liquidity crisis. After selling assets and issuing equity the firm in Path 2
recovers and refinances when it reaches the upper restructuring threshold. The firm in Path 3 does
not recover and equity holders decide to default when firm value is sufficiently low.

their outstanding debt at par and sell a new, larger issue to take advantage of
the tax benefits associated with debt (path 1). Refinancing thus takes the form
of a debt-for-equity swap. I refer to these thresholds as “refinancing points.”
For firms whose condition deteriorates sufficiently (paths 2 and 3), managers
must take corrective action. Empirical research shows that firms often become
insolvent on a f low basis but not on a stock basis. For such firms, the present
value of future income exceeds their debt obligations but they experience a
temporary liquidity crisis since fixed assets are a poor substitute for cash. In the
model, this occurs whenever a firm’s cash f low is insufficient to cover its interest
expense and thus the liquidity boundary is triggered for the first time at TL
whenever δTL < c and δt ≥ c for all t < TL . This boundary closely resembles the
definition of a financially distressed firm in Asquith et al. (1994) and a similar
boundary is considered in Kim, Ramaswamy, and Sundaresan (1993). To resolve
financial distress, firms are assumed to resort first to selling a fraction of assets
to decrease their debt burden. In the Asquith et al. (1994) sample, the majority
of firms do sell assets, with 18 out of 102 companies selling over 20% of their

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assets. Additional assumptions capture several features of asset sales that are
observed in practice. First, asset sales occur in discrete amounts: When firms
divest assets, the transaction typically involves a significant fraction of their
assets.5 Second, asset sales are costly: Firms in financial distress realize less
from asset sales than the present value of the cash f lows from these assets since
potential buyers are likely to be financially constrained, less well informed, and
less experienced; sellers are time constrained and detach their human capital
from sold assets. In other words, a discount can be viewed in terms of the
traditional measure of liquidity (Shleifer and Vishny (1992)).
The corrective action is modeled as follows.6 The firm sells a fraction 1 − k
of its assets immediately upon entering financial distress, which results in a
reduction by a fraction w of the firm’s outstanding debt:
(1 − q A )(1 − k)VL (1 − τ ) =

(1 − w)D0
.
1 − q RC

(3)

In (3) D0 is the par value of debt at the time of issuance and VL is the present
value of the project’s future cash f lows at time TL . The parameter qA represents
the proportional costs incurred in selling assets, and τ is the effective corporate
tax rate on the asset sale.7 Thus, the left-hand side is the after-tax income
received by the firm as a result of the asset sale. Equality in (3) implies that
all the proceeds are used to pay down debt. The proportional adjustment costs,
qRC are incurred by issuing/retiring debt.
An asset sale may lead to the firm’s fortunes improving substantially, in which
case it subsequently refinances (path 2), or it may provide the firm with only
temporary breathing space (path 3). In the latter case, equity holders resort to
equity issuance (effectively, negative dividends), as in earlier models. A number
of empirical studies have shown that issuing equity is costly (Altinkilic and
Hansen (2000), Hansen (2001), Corwin (2003)). In the model, the direct costs of
external equity financing, qE , are proportional to the amount issued.8 Finally,
equity holders optimally default if the firm’s condition continues to worsen
and the firm enters costly restructuring, which is modeled in reduced form.
The absolute priority rule is enforced and all residual rights on the project are
transferred to debt holders. Default costs are assumed to be a fraction α of the
value of assets upon default.
5
Models of debt pricing also use “asset sales” or “asset liquidation” terminology (see, e.g., Black
and Cox (1976)), but refer to the case of proportional asset liquidation that is equivalent to the
net payout ratio being positive, since in those models cash flows originate exclusively via asset
liquidation.
6
Morellec (2001) also considers the effect of asset liquidity in a model of static optimal capital
structure. Asset sales here differ from his case since they are conducted exclusively in financial
distress, at prices that ref lect a discount proportional to the firm’s value at the time of sale, and
are conducted in discrete amounts.
7
The maximum price any buyer is willing to pay for these assets in the absence of frictions is
(1 − k)VL (1 − τ ). I assume for simplicity that the buyer is unlevered. Note that since all firms face
the same marginal tax rate, τ is also the effective tax rate of an unlevered carbon copy of the firm.
8
Acharya et al. (2002) introduce costly equity issuance in a structural model of credit spreads,
but do not consider optimal leverage decisions.

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Tests of Capital Structure Theory

The Journal of Finance

The above discussion illustrates the model structure that gives rise to an optimal single-sided adjustment policy. To proceed with the valuation of financial
claims, note that the model satisfies the so-called scaling feature since all costs
are proportional to the value of the firm or its claims. In other words, at any
refinancing point the firm is just a larger replica of itself. Therefore, I start
by considering the values of equity and debt over one refinancing cycle (i.e.,
before the upper barrier is hit). These values, once debt is issued and before the
liquidity barrier is hit, can be written as the sum of the present values of cash
f lows accruing to claimholders in four regimes: (i) while the firm is financially
healthy, (ii) at the time the liquidity barrier is hit for the first time, (iii) in continuation after the barrier is hit, and (iv) in default. Thus, the values of equity
and debt in one refinancing cycle at time t = 0 are

E (δ0 ) = Eδ0



T

R

e

(1 − τ )(δs − c) ds

0


+ Eδ0

−rs



T

e

−rs

TL



q (1 − τ )(kδs − wc) − τl wc1[δs <δτ ] ds





 +∞
B
+ Eδ0 e−rTB max (1 − α)
e−rs k(1 − τ )δs ds − wD0 , 0 φ LU
=0 ,
TB

(4)
and

D R (δ0 ) = Eδ0



T

e

−rs

(1 − τi ) c ds

0

+ Eδ0 e

−rTL


+ Eδ0 e

−rTB


φUL = 0

(1 − w)D0 + Eδ0


min (1 − α)

 +∞
e
TB

−rs



T

e

−rs

(1 − τi ) wc ds

TL


k(1 − τ )δs ds, wD0


B
φ LU
=0

,
(5)

where R stands for one refinancing cycle, T = min (TL , TU ), and T = min (TB ,
j
TLU ). The functions φi take the value zero if event j occurs before event i, and
one otherwise.
The first term in expression (4) is the present value of cash f lows to equity
holders when neither the liquidity barrier, δL , nor the first refinancing barrier,
δU , have been reached. The second term is the present value of cash f lows in
continuation after the liquidity barrier has been hit and until either default
occurs at time TB or the second refinancing barrier, δLU , is reached at TLU . The
function q(x) accounts for costly equity issuance and can be written as

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1756

q(x) =

x,

if kδs > wc

(1 + qE )x,

qE > 0,

otherwise.

1757
(6)

As in Goldstein et al. (2001), if corporate income, δt , is sufficiently small, the firm
loses part of its tax shelter and this results in a lower effective tax benefit, τ − τl .
This reality is an important determinant of the leverage ratio at a refinancing
point. The first and third terms in expression (5) are the net present values
of payouts to debt holders before and after a liquidity crisis, respectively. The
second term ref lects the amount of debt purchased when assets are sold. In
default equity holders receive either nothing or the residual after the remaining
debt is repaid at its face value (the third term in (4) and the fourth in (5)).
The total value of a debt claim issued at date zero is thus
−rTLU
D(δ0 ) = D R (δ0 ) + Eδ0 e−rTU D0 φ U
wD0 φ BLU = 0 .
L = 0 + Eδ0 e

(7)

Equity holders make decisions taking into consideration what happens after
refinancing occurs. The total value of all payouts to equity (except at refinancing
points) is given by
E D (δ0 ) = E R (δ0 ) + Eδ0 e−rTU γU E D (δ0 ) φ U
L =0
+ Eδ0 e−rTLU γ LU k E D (δ0 ) φ BLU = 0

(8)

and the value of all debt issues is
D D (δ0 ) = D(δ0 ) + Eδ0 e−rTU γU D D (δ0 ) φ U
L =0
+ Eδ0 e−rTLU γ LU k D D (δ0 ) φ BLU = 0 ,

(9)

where γU and γLU are the proportions by which the net payout increases between two refinancing points if the liquidity barrier has or has not been hit,
respectively.
Combining these values yields the total value of the firm that equity holders
maximize at time t = 0, and after scaling, at each subsequent refinancing point:
F (δ0 ) =

E R (δ0 ) + (1 − q RC )D(δ0 )
.
1 − γU Eδ0 [e−rTU | φ L (U ) = 0] − kγ LU Eδ0 [e−rTLU | φ B (LU ) = 0]

(10)

Thus, (10) states that managers maximize the sum of (1) the present value
of the after-tax cash f lows accruing to equity and (2) the present value of the
after-tax income payments to all debt claims yet to be issued. Note that the
total value takes into account the present value of future adjustment costs that
will be incurred at subsequent refinancing points.
Equity holders choose the coupon and barriers to maximize the ex ante value
of their claim, that is,
c∗ = arg

max

{c,γU ,γ LU }∈R3+

[F (δ0 )].

(11)

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Tests of Capital Structure Theory

The Journal of Finance

An additional feature of realism, in which I follow Goldstein et al. (2001), is
that the firm’s financial decisions affect its net payout ratio. Empirically, higher
reliance on debt leads to a larger net payout (see, e.g., Goldstein et al. (2001)).
Here, for simplicity, I assume that the net payout ratio depends linearly on the
after-tax coupon rate,
δ
c
= a + (1 − τc ) ,
Vt
V0

(12)

where Vt is the present value of all future net payouts at time t.
To characterize the default threshold, note that equity holders balance the
present value of future equity cash f lows if they remain in control, with the cost
of equity issuance that is incurred in this case. The relevant value of equity is
E(δt ) = F(δt ) − D(δt ), where the fact that the liquidity barrier has been hit is
taken into account in calculating the value of claims. It is well known that this
threshold satisfies the smooth-pasting condition:
∂ E(δt )
= 0.
∂δt δt =δ B

(13)

The full problem facing equity holders thus consists of solving (11) subject to
(12) and (13). A closed-form solution to this problem does not exist, and thus
standard numerical procedures are used.
C. Comparative Statics
The purpose of this subsection is to compare the properties of firms’ financial
decisions at refinancing points in my model with the earlier literature. Table I
summarizes the comparative statics of the main financial variables. The market
leverage ratio, ML, is defined as the ratio of market value of debt (D(δ0 )) to total
capital (F(δ0 )),
M L0 =

D(δ0 )
.
F (δ0 )

(14)

Not surprisingly, many results are similar to the comparative statics results
obtained by Leland (1994) for the static case (his table II for unprotected debt)
and by Goldstein et al. (2001) for the dynamic case (their table 2). In particular,
as expected, higher business risk, bankruptcy costs and a lower tax advantage
all reduce optimal leverage. Contrary to the result given in Leland (1994), a
higher risk-free interest rate unambiguously reduces leverage since the higher
costs of borrowing more than offset the larger tax advantage to debt. Finally, an
increase in the costs of asset sales and equity issuance also lowers borrowing.
The relation between the leverage ratio and adjustment costs exhibits an
inverted U-pattern. Firms with either high- or low-cost access to external markets optimally prefer lower leverage than those with intermediate costs. This
is because firms face a trade-off between the frequency of refinancing and the
amount of borrowing. Firms with low costs prefer to rebalance frequently: As
costs increase, the level of the refinancing boundaries rises (note that δU and

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1759

Table I

Comparative Statics of Financial Variables at the Refinancing Point
The table gives the comparative statics at the refinancing point of the following variables: the
optimal market leverage ratio (ML), bankruptcy boundary (δB ), restructuring boundaries (δU and
δUL ), total firm value (F(δ0 )), coupon rate (c), and liquidity barrier (δL ). The corporate tax rate is
τc , τd is the dividend tax rate, τi is the interest income tax rate, r is the pre-tax risk-free interest
rate, σ is the volatility of the firm’s cash f low, α is the fraction of asset value lost in bankruptcy, qRC
is the adjustment cost, qA is the cost of selling assets in a liquidity crisis, qE is the cost of equity
issuance, and k is the fraction of asset value that remains after an asset sale.
Sign of Change in Variable for an Increase in:
Variable

Shape

τc , τd

τi

r

σ

α

qRC

qA

qE

k

ML

Invariant to δ

>0

<0

<0

<0

<0

<0

<0

>0

δB

Linear in δ

>0

<0

<0

<0

<0

<0

<0

>0

δU , δUL
F(δ0 )
c, δL

Linear in δ
Linear in δ
Linear in δ

<0
<0
>0

>0
<0
<0

<0
>0
>0

>0
<0
<0

<0
<0
<0

>0, qRC small
<0, qRC large
>0, qRC small
<0, qRC large
>0
<0
>0, qRC small
<0, qRC large

>0
<0
<0

>0
<0
<0

<0
>0
>0

δUL are increasing functions of qRC ) and firms therefore borrow more, initially.
As costs rise further, however, debt becomes less advantageous and is replaced
by equity.
Rows 2 and 3 of Table I illustrate the behavior of the default and upper
refinancing boundaries. The behavior of the default boundary, including its response to changes in the risk-free rate, is very similar to that of the leverage
ratio. Higher costs of bankruptcy lead to a reduction in the level of the refinancing boundaries to offset the lower amount of borrowing. Higher volatility might
also be expected to lower the level of the refinancing boundaries for the same
reason, but it does not: Unlike bankruptcy costs, higher business risk increases
both the expected costs of bankruptcy and the expected costs of refinancing
in the future. The latter effect dominates and leads to the higher refinancing
boundary.
The value of equity that managers maximize is negatively related to the
tax rates on both corporate income and interest. This intuitive result is different from, for example, Fischer et al.(1989) and Leland (1994) since the state
variable in their framework is the value of an unlevered firm and therefore
tax benefits are accounted for as inf lows of funds. The coupon level (and thus
the liquidity boundary) is negatively related to firm volatility; the difference
between “investment-grade” and “junk” firms observed by Leland (1994) disappears in a dynamic model. In Leland’s world, firms with very high levels
of business risk optimally commit to pay sizable coupons since they expect a
dramatic improvement in their fortunes with a nonnegligible probability. That
would lead to a reduction in debt payments relative to firm value. In a dynamic
world, they instead commit to refinancing at the same terms when their fortune
improves.

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Tests of Capital Structure Theory

The Journal of Finance

Before turning to the investigation of the dynamic economy, it is worth pointing out brief ly certain features that this class of models is not able to explain.
First, these models have no endogenous investment and thus are unable to
explain a number of observed phenomena, for example, the financing gap. Consequently, equity is never issued in good states of nature and the model cannot explain the negative relationship between current leverage and the past
market-to-book ratio (Baker and Wurgler (2002)). Second, refinancing costs as
modeled here are proportional to all debt outstanding and are not truly fixed
costs. Therefore, the model cannot say anything about the relationship between
firm size and capital structure.9 Third, the model does not include an optimal
cash policy, which in practice arises endogenously with the debt policy. Finally,
the changes in firm value and contemporaneous cash f lows are perfectly correlated, leading to an unrealistic correlation between some variables of interest.
For example, the model produces too high a correlation between profitability
and the market-to-book ratio.
II. Capital Structure in a Dynamic Economy
The objective of this section is to investigate the cross-sectional properties
of leverage ratios in a dynamic economy. Ultimately, I am interested in building a bridge between empirical research and the empirical hypotheses that the
model delivers. The first step is to relate the leverage ratio and other variables of interest used in empirical studies to the variables used in the model.
If firms adjust their leverage only periodically, most firms most of the time will
be optimally off their optimal leverage at a refinancing point. Quite clearly, if
an empiricist studies an economy generated by the model, the data would typically contain few “refinancing point” leverage ratios. Thus, to relate the model
to empirical studies, it is necessary that the model produces a cross section of
leverage ratios that is structurally similar to those that would have been studied
by an empiricist.
The fact that using the implications of comparative statics may cloud inferences has been recognized for some time in studies of leverage mean-reversion
and debt issuance (see, e.g., Hovakimian, Opler, and Titman (2001), Fama and
French (2002)). If leverage deviates from its target substantially, an assertion
that is supported empirically, then the response of firms to changes in economic
conditions will not be in line with the predictions of comparative statics at refinancing points. Thus, I first study whether the cross-sectional relations in a
dynamic economy are different from those at a refinancing point. Next, I use
the data generated by the model to replicate a number of conventional crosssectional studies of capital structure. This takes me to the crux of the existing
empirical evidence. The two questions in which I am especially interested are
whether my model can produce results that are qualitatively similar to those
found in empirical research, and, if so, whether the empirical estimates could
9
Kurshev and Strebulaev (2005) develop a dynamic trade-off model of capital structure with
truly fixed costs of debt and investigate the ability of the model to explain the size–leverage relationship.

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1760

1761

have been generated by the model with reasonable probability under a feasible
set of parameters.
As in, for example, Berk et al. (1999), my model is highly nonlinear in a number of important parameters. As a result, individual dynamic leverage ratios,
the main variable of interest, are difficult to obtain analytically. The complexity
of dynamic effects in cross-sectional patterns of leverage means that it is impossible to identify the dynamic interaction between leverage and its determinants
by performing a simple comparative statics exercise in dynamics. For example,
a positive shock of a given magnitude can have different effects on firms in
the same leverage group, leading to a complex interaction in the cross section,
since some firms will refinance while others will not. Similarly, high leverage
can be the result of either optimally high borrowing due to lower business risk
or substantial refinancing costs and unsuccessful past returns.
Therefore, I use simulation to generate artificial data from the model. Simulation takes the solution to a dynamic problem faced by equity as given and
does not involve any additional optimization. Since individual leverage ratios
and some commonly used regressors are observable in the simulation, I am
able to replicate a number of empirical research methods. In particular, I compare the cross-sectional properties of leverage in the simulated economy with
those predicted from the comparative statics of leverage at refinancing points,
the focus of most current theory, and then investigate the empirical hypotheses
on the issues that have been the focus of many empirical studies. These issues
include the average level of leverage in the economy, the cross-sectional relation
between profitability and leverage, the mean-reversion of leverage ratios, and
the impact of past stock returns on capital structure.
A. Running Simulations
This section describes the simulation procedure. Simulations take the solution to the optimal capital structure at a refinancing point as given and do
not involve any optimization mechanism. Technical details are given in the
Appendix.
To begin, observe that while only the total risk of the firm matters for pricing and capital structure decisions, economy-wide shocks lead to dependencies
in the evolution of the cash f low of different firms. To model such dependencies, shocks to their earnings are drawn from a distribution that has a common systematic component. Thus, cross-sectional characteristics of leverage
are attributable both to firm-specific characteristics and to dependencies in the
evolution of their assets. In particular, equation (1) may be rewritten as
d δt
= µ dt + σ I dZ I + βσ S dZ S ,
δt

∀t ≥ 0,

δ0 > 0.

(15)

Here, σI and σS are constant parameters and ZIt and ZSt are Brownian motions defined on a filtered probability space (, F, Q, (Ft )t≥0 ). The shock to
each project’s cash f low is decomposed into two components, namely, an idiosyncratic shock that is independent of other projects (σI dZI ) and a systematic

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Tests of Capital Structure Theory

The Journal of Finance

(market-wide or industry) shock that affects all firms in the economy (σS dZS ).
The parameter β is the systematic risk of the firm’s assets, which I refer to
as the firm’s “beta,” and systematic shocks are assumed independent from idiosyncratic shocks. The Brownian motion dZ in equation (1) is thus represented
as an affine function of two independent Brownian motions, dZ = dZI + β dZS ,
and

1
σ ≡ σ I2 + β 2 σ S2 2 .

(16)

At date zero all firms in the economy are “born” and choose their optimal capital
structure. The comparative statics of the system at date zero (where all firms
are at their refinancing points) is thus analogous to that described in Section
C. For the benchmark estimation, I simulate 300 quarters of data for 3,000
firms. To minimize the impact of the initial conditions, I drop the first 148
observations, leaving a sample period of 152 quarters (38 years). I refer to
the resulting data set as one “simulated economy.” Using this resulting panel
data set, I perform cross-sectional tests similar to those in the literature. The
presence of a systematic shock makes cross-sectional relations dependent on
the particular realization of the market-wide systematic component. Therefore,
I repeat the simulation and the accompanying analysis a large number (1,000)
of times. This allows me to study the sampling distribution for statistics of
interest produced by the model in a dynamic economy.
In any period, each firm observes its asset value dynamics over the last quarter. If the value does not cross any boundary, the firm takes no action. It is
important to stress that it is optimal, under these conditions, for the firm to
remain passive. If its value crosses an upper refinancing boundary, it conducts
a debt-for-equity swap, resetting the leverage ratio to the optimal level at a refinancing point, and so starting a new refinancing cycle. If the liquidity boundary
is hit for the first time in the current refinancing cycle, asset sales are conducted
in the same period. If the firm defaults, bondholders take over the firm and it
emerges in the same period as a new firm with a new optimal leverage ratio.
Observe that thus the procedure implies a constant population of firms in the
economy. This is not an important restriction since the parameters for new
firms would be drawn from the same sampling distribution as existing firms.
B. Choice of Parameters
This section describes how firms’ technology parameters and the economywide variables are calibrated to satisfy certain criteria and match a number
of sample characteristics of the COMPUSTAT and CRSP data.10 An important
10
As becomes clear below, to compare the cross-sectional results of a date zero economy and
a dynamic economy, I choose to present the scenario in which firm parameters are different. An
alternative is to consider the case in which all firms are identical at refinancing points and thus
any difference between them is accounted for only by random shocks. Similar qualitative results
are obtained for this case, as shown in Section III.

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1762

1763

caveat is that for most parameters of interest, there is little empirical evidence permitting precise estimation of sampling distributions or even their
ranges. In addition, the model requires that all parameters be estimated as
time-invariant. Overall then, the parameters used in the simulations must
be regarded as ad hoc and approximate. There are two ways I deal with this
problem. First, whenever possible (e.g., for tax rates), I use established empirical estimates. Second, and more importantly, I perform numerous robustness checks (see Section III). These robustness tests show that my results are
not qualitatively affected by changing the parameters within a feasible range.
Table II summarizes the descriptive information for the parameters described
below.
B.1. Firm Technology Parameters
The present values of the net payout and book assets at date zero are identical for each firm and scaled to 100. In the model, the rate of return on firm
value is perfectly correlated with changes in earnings. In calibrating the standard deviation of net payout, I therefore use data on securities’ returns. Firms
differ in their systematic risk, represented by β. I obtain a distribution of β
by running a simple one-factor market model regression for monthly equity
returns for firms in the CRSP database having at least 3 years of data between
1965 and 2000 with the value-weighted CRSP index as the proxy for the market
portfolio.
The distribution of firms’ volatility is calibrated to match the parameters of
the distribution of the standard deviation of rates of return on firm assets reported by Schaefer and Strebulaev (2005).11 The mean and standard deviation
of this distribution are 0.255 and 0.10, respectively. The standard deviation of
the systematic shock, σS , is estimated as
σS =

2 σ 2 + 2L (1 − L )σ
(1 − Lav )2 σ E2 + Lav
av
av ED .
D

(17)

Here, σE is the volatility of monthly returns on the CRSP value-weighted equity
return index, σD is the volatility of monthly returns on the CRSP 10-year T-note
index over the period 1965 to 2000, and σED is the covariance between equity
and debt returns. Estimates of these parameters, 0.155, 0.081, and 0.023, respectively, are close to those reported by Campbell and Ammer (1993). Leverage,
Lav , is computed from annual COMPUSTAT data for 1965 to 2000, averaging
first for each year over firms and then over time. Leverage is defined as the ratio
of book debt to the sum of book debt and market equity. The volatility of idiosyncratic shocks, σI , must be chosen to be consistent with the distribution of total
risk. After considering a number of alternatives, individual shocks are assumed
11
Note that the sample used in that paper is confined to firms that issue public debt. Faulkender
and Petersen (2006) show that for firms without access to public debt markets, implied volatility is
much higher. In robustness checks, I show that changing assumptions on the volatility distribution
has an economically significant quantitative impact on average leverage ratios, though without
affecting any qualitative cross-sectional results.

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Tests of Capital Structure Theory

The Journal of Finance
Table II

Parameter Values for Benchmark Simulations
Listed are the values and sampling distributions chosen for all parameters required to simulate
the benchmark case of the model. V0 is the present value of all future net payouts at time 0, A0 is
the initial book value of firm assets, β is the systematic risk of the firm’s assets, σE is the volatility
of monthly returns on the CRSP value-weighted equity return index, σD is the volatility of monthly
returns on the CRSP 10-year T-note index over the period 1965 to 2000, σED is the covariance
between equity and debt returns, Lav is average leverage computed from annual COMPUSTAT
data for 1965 to 2000, averaging first for each year over firms and then over time, and defined as
the ratio of book debt to the sum of book debt and market equity. σI is the volatility of idiosyncratic
shocks, σ is the instantaneous volatility of the project’s net cash f low, qA is the proportional costs
incurred in selling assets, qRC is the proportional adjustment costs of issuing/retiring debt, qE is
the proportional direct costs of external equity financing, α is the proportional restructuring costs,
k is the fraction of assets that remains after an asset sale, κ defines the partial loss-offset boundary,
g is the growth rate of book assets, a is the shift parameter in the net payout ratio estimation, RPA
is the asset risk premium, τκ is the loss per dollar of full offset in the case of distress, τc is the
marginal corporate tax rate, τd is the marginal personal tax rate on dividends, τi is the marginal
personal tax rate on interest income, and r is an instantaneous after-tax riskless rate. U indicates
uniform distribution.
Parameter
V0
A0
β
σE
σD
σED
Lav
σI
σ
qRC
qE
α
qA
k
κ
g
a
RPA
τκ
τc
τi
τd
r

Distribution

Mean

Constant
Constant
Empirical
Constant
Constant
Constant
Constant
a0 + a1 χ 2 (n)
1
, 5}
{a0 , a1 , n} = {0.05, 30
Empirical
U[0.0005, 0.0025] + 0.001s
U[0.02, 0.06] + 0.02s
U[0.03, 0.077] + 0.023s
U[0.05, 0.183] + 0.067s
U[0.6, 1]
U[0.7, 0.9]
Constant
U[0.03, 0.04]
Constant
Constant
Constant
Constant
Constant
Constant

100
100
0.993
0.155
0.081
0.023
0.314
0.22
0.255
0.002
0.05
0.065
0.15
0.8
0.8
µ + RPA
0.035
0.065
0.5
0.35
0.351
0.122
0.05

Std. Dev.

0.47

0.107
0.10
0.0006
0.013
0.015
0.043
0.116
0.058
0.003

to have a distribution with probability density function f (σ I ) ∼ a0 + a1 χ 2 (n).
This distribution implies that projects with both low risk and very high risk
are relatively common. A positive value of a0 also ensures that there will be no
cash f lows with negligible total risk.

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Since the proportional costs of restructuring in default, adjusting leverage,
selling assets, and issuing equity are all likely to be related to either the
liquidity of firm assets and/or ease of access to external markets, all these
costs are postulated to have a common covariance matrix. In particular, each
cost, qx , is drawn from the following distribution: qx ∼ U[ax , ax + 23 (bx − ax )] +
1
(b − ax )s, where ax and bx are bounds for the value of costs and s ∼ U[0, 1] is
3 x
the common component. This formulation implies that 20% of each cost’s value
is due to the common component. This distribution is symmetric and its trapezoid probability density function implies that the values close to the boundaries
are less likely to occur, while the values in a range around the mean are equally
likely to occur.
For the proportional cost of restructuring in default, α, the bounds ax and
bx are assumed to be 0.03 and 0.10, respectively. Most of the empirical values
reported in, for example, Weiss (1990) and Altman (1984) lie in this range. Recent evidence by Andrade and Kaplan (1998) suggests somewhat higher values.
Leland (1994) uses a similarly defined cost of 0.5, Leland (1998) uses 0.25, and
Goldstein et al. (2001) use 0.05.
Fischer, Heinkel, and Zechner (1989) and Goldstein et al. (2001) define adjustment costs, qRC , in the same way and use a value of 1%. Datta, Iskandar-Datta,
and Patel (1997) report total expenses of new debt issuance over 1976 to 1992
of 2.96%. Mikkelson and Partch (1986) find underwriting costs of 1.3% for seasoned offers, and Kim, Palia, and Saunders (2003), in a study of underwriting
spread over a 30-year period, find them to be 1.15%. This author’s unreported
calculation using the Fixed Income Securities Database (see Davydenko and
Strebulaev (2007) for a description) over the period 1980 to 2000 suggests that
the average underwriting and management spread is about 0.05% in yield,
which is consistent, for example, with a proportional cost of 1% for a riskfree perpetuity when the risk-free rate is 5%. Note, however, that costs in this
framework are proportional to the total amount of debt issued rather than to
the incremental amount. I therefore choose substantially smaller adjustment
costs, with a range of 0.05% to 0.35%, to be consistent with costs per unit of new
debt issued of the order of 1%.
Proportional equity issuance costs are assumed to be distributed in the range
(0.02, 0.08). Recent empirical research emphasizes that in initial public offerings, a simple 7% solution is used to settle underwriter costs (Hansen (2001)).
The costs of seasoned equity offerings are likely to be smaller, however. Corwin
(2003) reports a gross spread of 5.4% and direct expenses of 1.5%. In addition,
there is evidence (Altinkilic and Hansen (2000)) that equity costs derive mainly
from the variable component.
The costs of asset sales in a liquidity crisis are assumed to be distributed
in the range (0.05, 0.25). These costs are, admittedly, enormously difficult to
estimate. In one of the most elaborate empirical attempts to date, Pulvino (1998)
estimates that on average these costs are around 14% for companies with an
above median debt ratio. The fraction of assets that remains after an asset
sale, k, is assumed to have a uniform distribution with support (0.6,1). Asquith
et al. (1994) report that, on average, companies sell 12% of their book assets.

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Tests of Capital Structure Theory

The Journal of Finance

The median level of asset sales among the firms that take visible steps in this
direction is 48%.
The rate of net investment growth, g, is assumed equal to the expected growth
rate of the firm’s net cash f low. This is consistent with a finite nonzero expected
market-to-book ratio at an infinite time horizon. It is also consistent with the
fact that investment equal in magnitude to depreciation is needed to maintain the firm as a going concern. The net payout ratio increases with interest
payments according to (12) and the parameter a depends, ultimately, on firms’
price–earnings ratios and dividend policies. The range of the net payout ratio’s
value is between 0.03 and 0.04; the value of 0.035 is also used in Goldstein
et al. (2001).
When the net payout f low is very small, the firm starts to partially lose its tax
shelter. I model the partial loss offset boundary as δκ = κδL + (1 − κ)δB , where κ
is uniformly distributed on (0.7, 0.9). It is assumed that, when the net payout is
below δκ , the loss per dollar of full offset is τκ , where τκ is set equal to 0.5. Note
that this formulation assumes that full tax benefits are once again in effect
when the firm comes out of distress.
B.2. Economy-Wide Parameters
The corporate tax rate is assumed to be equal to the highest existing marginal
tax rate, τc = 0.35. To decide on marginal personal tax rates on interest income and dividend payments, I follow Graham (1999, 2000). In particular,
Graham (1999) estimates τi as 0.351 and τd as 0.122 over the period 1980
to 1994. Thus, the maximum tax benefit to debt, net of personal taxes, is
(1 − τi ) − (1 − τc )(1 − τd ) = 7.8 cents per one dollar of debt. In estimating tax
rates, I ignore at least two important real-world features; the variability of tax
rates both across firms and across time. Introducing time-varying taxes would
destroy the scaling feature of the model. Since we do not know whether marginal
firm-specific tax rates are correlated with firm characteristics, I choose to deal
with firm-invariant tax rates.
The after-tax risk-free interest rate is 0.05. It is estimated as the mean
3-month Treasury bill rate over the period 1965 to 2000, multiplied by (1 − τi ).
Ibbotson Associates (1995) report an average annual equity risk premium of
about 0.08 and expected default premium of about 0.01 for the postwar period.
Using Lav (see the definition after equation (17)), the risk premium on the rate
of return on firm assets is estimated in the region of 0.065.
C. Preliminary Empirical Analysis
I now bring together the calibrated model with the results of comparative
statics at the refinancing point and some empirical results from the literature.
I use two definitions of leverage, both based on the market value of equity.
The first, the market leverage ratio, has already been defined for date zero in
(14); for any other period, it is defined analogously. Typically, however, market
values of debt are not available and book values are used. I therefore introduce
a second definition, the quasi-market leverage ratio, defined as the ratio of the

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par value of outstanding debt to the sum of this par value and the market value
of equity, that is,12
QMLt =

D0 (δt )
.
D0 (δt ) + F (δt ) − D(δt )

(18)

Typically, the difference between ML and QML is very small. For financially
distressed firms it can be more substantial, however. Intuitively, these ratios
ref lect how the firm has financed itself in the past since both the par and
market values of debt ref lect decisions taken early in a refinancing cycle. To
determine how close the firm is to financial distress, a f low measure that shows
whether the firm can meet its debt payments is more relevant as firms may
encounter distress at different levels of leverage. Therefore, I also consider the
interest coverage ratio, which is defined as the ratio of the net payout to the
coupon.
Table III summarizes the cross-sectional distribution of these various measures in both a dynamic economy and at the refinancing point. The average
leverage ratio at the refinancing point is 0.26, compared with 0.37 in a similar
model by Goldstein et al. (2001). The two main reasons for the difference are (1)
the presence in my model of additional financial constraints such as liquidity
crisis costs and (2) a lower tax advantage to debt since the tax rate on dividends
that I use is smaller.
Of more importance, however, are the descriptive statistics for the dynamic
economy. Means for dynamic statistics are estimated in a two-step procedure.
First, for each simulated economy statistics are calculated for each year in
the last 35 years of data. Second, statistics are averaged across years for each
simulated economy and then over economies. To get a f lavor of the impact of
systematic shocks, for market and quasi-market leverage I also present minimum and maximum estimates over all economies. I begin by comparing the
leverage statistics in the dynamic economy with those at refinancing points,
where the impact of the dynamic evolution of firms’ assets is ignored. What
Table III shows is that leverage ratios in the dynamic cross section are larger
than at refinancing points. An intuition for this observation is quite general:
Unsuccessful firms tend to linger longer than successful firms who restructure
fairly soon, especially so because firms who opt for higher leverage at refinancing points also choose a lower refinancing boundary.
Next I turn to a comparison with empirical data on leverage. Bernanke,
Campbell, and Whited (1990) give the distribution of leverage for the 3 years
1986 to 1988. Their mean leverage ratio (0.33) is close to one given here (0.36).
More interestingly, the right tail of my distribution mirrors theirs closely,
suggesting that a cross section of leverage ratios in a dynamic economy can
replicate an empirically observed distribution, while the cross section at a refinancing point cannot. Rajan and Zingales (1995) report, among other statistics,
12

Where, in line with (7), D0 (δt ) is the par value of debt outstanding in the current refinancing
cycle.

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Tests of Capital Structure Theory

The Journal of Finance
Table III

Descriptive Statistics
The table reports descriptive statistics for the following variables: market leverage (ML), quasimarket leverage (QML), interest coverage ratio (the ratio of net payout, δ, to coupon, c), tax advantage to debt (i.e., the increase in firm value if the firm moves from no-leverage to its optimal
− τ )V (δt )
, where F is firm value, τ is the effective tax
leverage ratio, given by the formula F (δt(1) −−(1τ )V
(δt )
rate, V is the value of firm assets, and δt is the level of cash f low at time t). Ref. point refers to the
case in which all firms are at their refinancing points. All other statistics are given for dynamics.
One thousand data sets are generated, each containing 75 years of quarterly data for 3,000 firms.
For each data set the statistics are first calculated for each year in the last 35 years of data and
then are averaged across years. Finally, they are averaged over data sets. Min and Max give the
minimum and maximum of the annual averages over the 1,000 data sets.
Percentiles
Mean

1%

50%

90%

95%

99%

Std. Dev.

N

Market leverage, ML
Ref. point
0.26
Average
0.36
Min
0.30
Max
0.43

0.04
0.06
0.06
0.07

0.27
0.34
0.29
0.41

0.40
0.56
0.46
0.71

0.43
0.66
0.53
0.80

0.50
0.87
0.76
0.94

0.10
0.16
0.13
0.20

3,000
3,000
3,000
3,000

Quasi-market leverage, QML
Average
0.37
0.06
Min
0.31
0.06
Max
0.44
0.07

0.35
0.29
0.42

0.59
0.47
0.74

0.70
0.56
0.84

0.91
0.82
0.96

0.17
0.14
0.21

3,000
3,000
3,000

Interest coverage ratio
Ref. point
3.98
Average
3.08

2.01
0.69

3.22
2.64

5.74
4.78

7.80
6.08

17.83
11.26

3.24
2.35

3,000
3,000

Tax advantage to debt
Ref. point
0.05
Average
0.04

0.02
0

0.05
0.04

0.07
0.07

0.07
0.08

0.08
0.09

0.01
0.02

3,000
3,000

quasi-market leverage ratios. For 1991, the U.S. mean and median values are,
respectively, 0.32 and 0.28, as compared with 0.37 and 0.35 in my model.13
Rajan and Zingales report a median interest coverage ratio of 2.41 (4.05)
when deducting (not deducting) depreciation. For the former case, Bernanke,
Campbell, and Whited (1990) report a mean value slightly above 5. Both results
are similar in magnitude to the model values. The tax advantage to debt is
calculated as the ratio of the difference between the current value of the firm
and the after-tax value of unlevered assets to the after-tax value of unlevered
assets. This ratio ranges between 0% and 10% with a mean of 5%. The gain in
moving from no-leverage to optimal dynamic leverage, accounting for personal
taxation, is comparable to the results on the net tax advantage of debt estimated
by Graham (2000).
13
To complement the comparison, I construct an empirical distribution of the quasi-market debtto-capital ratio on COMPUSTAT data each year over 1965 to 2000. The 90th and 95th percentiles
of the distribution are between 57% and 89%, and 62% and 92%, respectively. Footnote 2 defines
the debt-to-capital ratio.

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In summary, because firms at different stages in their refinancing cycle react
differently to economic shocks of the same magnitude, the cross-sectional distribution of leverage is drastically different in dynamics and at the refinancing
point, as is also the case for the other variables. Thus, care needs to be taken
in using leverage properties at refinancing points in making any empirical
claims.
D. Cross-Sectional Regression Analysis
This section examines several further applications of the approach developed
in this paper. The main purpose of this exercise is to compare the results of regressions on simulated data to the results of empirical cross-sectional research.
An example of the leverage–profitability relationship demonstrates that conventional methods can lead to the rejection of the model on which the data
are based. An investigation of the impact of stock returns on leverage shows
that this approach can be instrumental in providing an economic rationale for
puzzling empirical observations.
D.1. Leverage–Profitability Relationship
This section shows that the dynamic relation between leverage and profitability is a particularly striking example for testing the credibility of empirical cross-sectional research. Profitability, πt , is defined as the ratio of earnings
before interest and taxes (the sum of the net payout (δt ) and retained earnings
(change in the value of book assets)) to the book value of assets in place, At−1 :
πt =

δt + At
.
At−1

(19)

The trade-off theory predicts that a persistent increase in earnings leads firms
to more extensive use of debt financing by increasing the tax advantage to debt
and reducing the expected costs of distress and bankruptcy. This is ref lected,
for example, in a positive correlation (0.76) between leverage and profitability
at the refinancing point.14
Why is the leverage–profitability relation singled out? First, as Myers (1993)
points out, perhaps the most pervasive empirical capital structure regularity
is the inverse relation between debt usage and profitability. Indeed, the relationship is one of several widely established results in the empirical capital
structure literature.15 More importantly, it is also one of a few, if not the only,
cross-sectional relations that disentangles the (static and dynamic) trade-off
14
Note that all changes in earnings in the model are persistent and thus firms with higher
profitability at date zero expect to be more profitable in the future and opt optimally for higher
borrowing.
15
See, for example, Titman and Wessels (1988), Fama and French (2002), and Baker and Wurgler
(2002). Rajan and Zingales (1995) establish that the inverse relationship holds for six out of seven
developed countries and Booth et al. (2001) report that it also holds for most developing countries.

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Tests of Capital Structure Theory

The Journal of Finance

model and the various concepts associated with the pecking order idea, according to which, holding investment fixed, persistently higher profitability enables
firms to use less leverage. For other determinants of leverage, either the predictions of both the pecking order argument and the trade-off theory are the
same or the predictions of the various versions of the pecking order argument
themselves differ.16 The ambiguity attached to the impact of other determinants means that a consistently negative relation found between leverage and
expected profitability is interpreted as major failure of the trade-off model.
I turn now to whether the cross-sectional leverage–profitability relation that
my framework delivers is consistent with those reported in the empirical capital structure research. Recall that each simulated data set (economy) consists
of 3,000 firms for 300 quarters and that economies differ because of a systematic shock. As described in Section A, I simulate 1,000 economies, dropping the
first half of the observations in each economy. For each economy, I then conduct the regression tests outlined below. For each set of regressions, I report
mean coefficients and t-statistics over all simulated economies and for several
coefficients I also give the distribution.17
Table IV reports the results of the first set of experiments. Column 1 reports
the regression for market leverage at the refinancing point and columns 2 to
4 report on simulated economies. Specifically, column 2 reports on attempts
to replicate early empirical tests of capital structure (e.g., Bradley, Jarrell, and
Kim (1984)) by performing an ordinary least squares (OLS) regression of quasimarket leverage, QML, at the end of the last year in each simulated economy
against profitability and the constant “firm technology” parameters. Thus, the
regressand and profitability are measured contemporaneously. Column 3 reports the results of the procedure that replicates the method implemented by
Rajan and Zingales (1995) in which OLS regression of quasi-market leverage
in year t is run against 4-year averages of the regressors over years (t − 4) to
(t − 1), where year t is the last year in each economy.
Fama and French (2002) estimate “target leverage” using a two-step procedure. They first estimate year-by-year cross-sectional regressions and then use
the Fama–MacBeth (1973) methodology to estimate time-series standard errors
that are not clouded by the problems encountered in both single cross section
and panel studies. The main problem with these methods stems from correlation in the regression residuals across firms and the presence of autocorrelation
in the regression coefficients. In the simulated economy, correlation in the regression residuals exists because firm values are correlated via the systematic
16
For example, both the pecking order and trade-off models predict that higher volatility of the
firm’s cash f low is likely to lower the optimal amount of borrowing (see, e.g., Fama and French
(2002)). Also, the static pecking order theory suggests that higher investment leads to higher
borrowing when retained earnings are fixed, while the dynamic version predicts higher expected
investment to decrease current debt so that the debt capacity is preserved for the future (see, e.g.,
Myers (1984)).
17
Empirical studies include a number of variables (such as R&D) to control for firm heterogeneity
that are clearly unnecessary in simulation. Conversely, the regressions on simulated data include
firm-specific time-invariant parameters to control for firm heterogeneity.

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Table IV

Cross-Sectional Regressions
The table reports the results of cross-sectional regressions on the level of the quasi-market leverage
ratio, QML. One thousand data sets are generated, each containing 75 years of quarterly data for
3,000 firms. Coefficients and t-statistics are means over 1,000 simulations. Independent variables
are profitability (π), volatility of cash f lows (σ ), bankruptcy costs (α), asset sale costs (qA ), and
restructuring costs (qRC ). The Ref. Point column gives the results obtained by running the regression
at the refinancing point. The BJK, RZ, and FF columns report the results of regressions that
replicate the empirical procedures used, respectively, by Bradley, Jarrel, and Kim (1984), Rajan
and Zingales (1995), and Fama and French (2002). Each of the regressions is of the form:
QML P = d 0 + d 1 π P + d x +  P ,
where x are firm technology parameters and P, P ∈ {BJK, RZ, FF}, refers to the method. For
BJK and FF, Q M L P = Q M Lend and π P = πend−1 ; for RZ, Q M L R Z = Q M Lend and π R Z =
1 end−4
π , where “end” is the last year in each data set. FF uses the Fama–MacBeth (1973)
4
m=end−1 m
method, with the regressions run over the last 35 years of each data set and then averaged. The
last three columns report additional information on the FF regression: the standard deviation of
coefficients and t-statistics, and the 10th and 90th percentile values of these coefficients across
simulations. BJK and RZ regression standard errors are standard. FF standard errors are Fama–
MacBeth (1973) with the Newey–West correction.
FF

Constant
π
σ
α
qRC
qA
R2
N

Ref. Point
(1)

BJK
(2)

RZ
(3)

Coeff.
(4)

Std. Dev
(5)

10%
(6)

90%
(7)

0.24
(22.29)
5.88
(30.95)
−0.78
(−91.22)
−0.32
(−7.30)
3.67
(3.54)
−0.17
(−10.94)

0.61
(29.36)
−0.76
(−6.81)
−0.39
(−13.05)
−0.47
(−2.28)
−3.16
(−0.64)
−0.28
(−3.93)

0.58
(28.06)
−0.47
(−4.18)
−0.38
(−12.55)
−0.47
(−2.28)
−3.14
(−0.63)
−0.29
(−3.93)

0.62
(34.02)
−0.78
(−7.47)
−0.40
(−26.79)
−0.47
(−10.25)
−3.28
(−3.09)
−0.29
(−16.53)

0.06
(21.03)
0.58
(4.20)
0.04
(13.35)
0.11
(5.66)
2.53
(2.90)
0.04
(8.67)

0.55
(14.60)
−1.53
(−12.46)
−0.45
(−43.01)
−0.60
(−17.50)
−6.56
(−6.48)
−0.34
(−26.59)

0.71
(62.22)
−0.22
(−3.54)
−0.36
(−13.64)
−0.33
(−4.84)
−0.11
(−0.08)
−0.24
(−8.48)

0.89
(1)
3,000

0.07
(1)
3,000

0.07
(1)
3,000

0.08
(35)
3,000

0.01
(35)
−

0.06
(35)
3,000

0.10
(35)
3,000

shock and the slopes are also autocorrelated because leverage is a cumulative
outcome of past idiosyncratic shocks. I choose to report Fama–MacBeth (1973)
standard errors with the Newey–West correction.18 The results are in column
4 of Table IV.
18
Following the results of Petersen (2005), I used a number of methods to estimate standard
errors. Petersen (2005) finds that Fama–MacBeth standard errors underestimate true errors even
after the correction for autocorrelation. I also estimate Rogers (1993) standard errors clustered
by firm and by time. Unreported, Rogers standard errors clustered by firm are smaller than the

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Tests of Capital Structure Theory

The Journal of Finance

To summarize, each of the regressions above can be written as
QML P = d 0 + d 1 π P + d x +  P ,

(20)

where x are firm technology parameters and P, P ∈ {BJK, RZ, FF}, refers to

the method. For example, QMLRZ = QMLt , π RZ = 14 t−4
m=t−1 πm , and so forth.
For refinancing points, column 1 in Table IV reports that a 1% increase in
expected profitability increases target leverage by 5.88% and a 1% increase in
the firm’s business risk produces a 0.78% reduction in leverage. The effect of
bankruptcy and distress costs is smaller in absolute magnitude, demonstrating
again that by themselves, these costs are not sufficient to offset the tax advantage to debt in the dynamic trade-off model. Insignificance of adjustment costs
is due to their nonmonotonic relation to leverage.
Columns 2 to 4 show that consistent with empirical findings the relationship between profitability and leverage can be negative in a dynamic economy
even for the trade-off model. The results of columns 2 to 4 are roughly similar,
consistent with Fama–French’s observation that their results are mainly supportive of previous findings, demonstrating that subtle variation in definition
of leverage and profitability or in particular empirical method does not matter
much. The Fama–MacBeth estimates with the Newey–West correction produce
statistically negative average slopes.
Note that this result is of particular importance: An empiricist would be
likely to interpret this finding as evidence in favor of the pecking order argument and contrary to the predictions of the dynamic trade-off model. Yet, we
know that firms in the simulated economies do indeed follow the prescription
of the dynamic trade-off theory. Why, in this case, is the profitability coefficient
significantly negative in the dynamic economy? An increase in profitability affects future profitability and thus the value of the firm. But while an increase
in the value of the firm always lowers leverage, it does not necessarily lead to
refinancing in a world with infrequent adjustment. Note that under the model,
the target leverage for any firm is constant, and so the observed positive relation between leverage and profitability at the refinancing point is purely a
cross-sectional effect. The negative relation is at the individual firm level since
higher profitability lowers the current leverage of an individual firm, unless
it refinances in that period. The negative coefficients in Table IV imply that
the effect at the individual firm level dominates in the simulated data. The
presence of a systematic shock magnifies this effect.
That the presence of frictions may complicate inferences has been recognized
in a number of previous studies. For example, Fama and French (2002) note
Fama–MacBeth ones with adjustment for time-varying regressors and larger for time-invariant
regressors. Under all methods, the results are statistically significant. Fama and French assume for
simplicity that the standard errors of the average slopes should be multiplied by a certain factor
to account for autocorrelation before judging the significance of a variable. Unreported results
demonstrate that the average coefficient on profitability is autocorrelated and behaves like an
AR(1) process with observed maximum of about 0.75 and thus (see Fama and French (2002, p. 12))
the corresponding multiplication factor is 2.5.

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that their result may overstate the long-term relation between leverage and
profitability by picking up transitory variation in leverage rather than variation
in target leverage. This would make it difficult to disentangle the dynamic
trade-off and pecking order models since a negative coefficient may be the result
of the transitory component, pecking order behavior, or both. It is therefore
instructive to look at the size of the coefficient in the simulated data to judge
whether a dynamic trade-off model can give rise to values that are similar to
those found empirically.
The population mean of the profitability regression coefficient is above those
found by previous researchers. Profitability coefficients reported by previous
studies include −0.90 (Fama and French (2002)),19 −0.6 (Rajan and Zingales
(1995)), and −0.61 (Baker and Wurgler (2002)). However, my estimate of −0.78
for the Fama and French type of regression is simply the population mean across
all economies. To gauge the likelihood of obtaining estimates in the range of
−0.6 to −0.9 under the model, I examine the distribution of the profitability
coefficient. Columns 6 and 7 of Table IV report its 10th and 90th percentiles. All
the coefficients are negative and most of them are significant. Thus, under the
chosen set of parameters, the reported empirical estimates can be consistent
with the value of the coefficient.
There are several possible ways in which this result may be qualified. First,
the parameter set may be unrepresentative because, for example, I do not allow
for correlation between volatility and distress/bankruptcy costs. Indeed, in a
number of robustness checks the resulting coefficient, while still negative, is
substantially smaller in magnitude. In particular, smaller restructuring costs
and more widely dispersed “betas” result in a smaller coefficient. For many
other parametrization changes, the result is unchanged or stronger.
Second, I use the leverage ratio based on the market value of equity. Fama and
French (2002) argue that the profitability–leverage relation holds theoretically
only for book leverage. In empirical regressions, however, the values of the slope
are very similar. Therefore, while for book leverage the result is likely to hold
under a broader set of conditions than for market leverage, it is unlikely that
this drives the observed difference.
Third, in my model as well as most dynamic models of optimal structure, the
investment process is independent of the process that determines the leverage
ratio. In deriving the book value of assets, I make an assumption that book
assets grow at a rate equal to the growth rate of the net payout under the actual
distribution—the only rate under which the market-to-book ratio has a finite
nonzero expected value at an infinite time horizon. I choose a conservative value
of one for an initial market-to-book ratio since my firms may be characterized
as value firms. A decrease in the book value of assets, however, would lead to an
19
Fama and French report several profitability coefficients, ranging from −0.42 to −0.96, since
they study both book and market leverage, divide the sample of firms into two groups (dividend
payers and nonpayers), and include in some regressions a simultaneously estimated target payout
ratio. The coefficient of −0.9 is for the regression on market leverage for dividend payers, not
allowing for the target payout ratio.

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Tests of Capital Structure Theory

The Journal of Finance

increase in profitability without changing quasi-market leverage and in turn
to a decrease in the magnitude of the profitability–leverage coefficient.
In a nutshell, notwithstanding all these caveats, the analysis here and the
robustness tests in Section III suggest that, at the very least, the model is able
to explain a substantial part, if not most, of the negative relation between profitability and leverage. All other coefficients in Table IV have the same sign in
dynamics as at the refinancing points, although the magnitude of the volatility
coefficient is smaller in the dynamic context. Adjustment costs become significant in a dynamic economy since their increase leads to higher refinancing
boundaries, and thus the longer average waiting times between successive adjustments, and correspondingly the change in leverage, is larger.
D.2. Leverage and Stock Returns
In a recent paper, Welch (2004) obtains empirical results that to some extent
parallel those presented here. Welch’s main finding is that U.S. corporations do
not change their capital structure to offset the mechanistic effect on leverage
of changes in their stock price. The ongoing debate surrounding these results
is motivated by at least two observations: the conventional firm characteristics
lose their significance in the presence of lagged equity returns and several
empirical stylized facts that remain largely unexplained.
As I emphasize above, the absence of a response by the firm to these mechanistic changes in leverage may, indeed, be optimal in the presence of adjustment
costs. It is therefore instructive to investigate the extent to which the mechanistic effect observed by Welch is ref lected in my dynamic economies. To this end,
I replicate, again using simulated data, the regression test that he performs
on the COMPUSTAT data set (Welch (2004), table 3). For each year t, I run a
cross-sectional regression of the level of the market leverage ratio against (1)
the implied market debt ratio, IDRt−k,t in Welch’s notation, that is, what the
market leverage ratio would have been if the firm had not issued any securities
between years t − k and t, and (2) the actual observed quasi-market leverage
ratio in year t − k, QMLt−k in my notation:
QMLt = f 0 + f 1 IDRt−k,t + f 2 QMLt−k + .

(21)

The implied debt ratio shows the response of leverage only to changes in equity.
Thus, if the coefficient f 1 is equal to 1, firms do not readjust at all. Alternatively,
a value of f 2 equal to 1 would imply that firms perfectly offset any change in
equity.
The estimated regression (21) is identical to that studied by Welch. The only
point of departure between my simulations and the empirical procedure followed by Welch is that the number of firms in the empirical study varies across
years while in the simulations the number of firms is fixed.
To be precise, I compute the average of the time series of cross-sectional
regression coefficients à la Fama–MacBeth. Then, as usual, the results are
averaged over many simulated economies. Table V shows that for all four choices

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Table V

Leverage and Stock Returns
The table reports the results of the following cross-sectional regressions on the level of the quasimarket leverage ratio, QML.
QMLt = f 0 + f 1 IDRt−k,t + f 2 QMLt−k + .
Independent variables are the implied debt ratio (IDRt−k,t ) and lagged quasi-market leverage ratio
(QMLt−k ). Coefficients and t-statistics in Panel A are means over 1,000 simulations. Row 1 of Panel
B reports Welch’s (2004) estimates of the IDR coefficients. Other rows report the mean and the 5th
and 95th percentiles of my estimates. One thousand data sets are generated, each containing 75
years of quarterly data for 3,000 firms. For each data set the above regressions are run over the
last 35 years of data and then averaged. Standard errors are Fama–MacBeth (1973) with the
Newey–West correction.
k Years
1

3

5

10

Panel A
Constant
IDRt−k,t
QMLt−k
R2
N

0.034
(34.241)
1.022
(92.327)
−0.105
(−7.971)
0.926
(37)

0.088
(41.942)
0.886
(75.677)
−0.095
(−5.868)
0.802
(35)

0.130
(45.289)
0.781
(71.356)
−0.089
(−5.445)
0.698
(33)

0.199
(46.679)
0.592
(53.735)
−0.063
(−5.028)
0.502
(28)

3,000

3,000

3,000

3,000

0.869
0.780
0.735
0.825

0.708
0.591
0.552
0.628

Panel B: IDR Coefficients
Welch
This paper
5%
95%

1.014
1.022
0.980
1.072

0.944
0.885
0.839
0.935

of k, between 1 and 10 years, the results appear to conform closely to those
obtained by Welch. In particular, the slope of nearly one for the implied debt
ratio for the 1-year regression (average slope of 1.014 in Welch and 1.022 in the
model) indicates that financing behavior in the short term is almost passive;
in other words, corporations do not react to changes in the value of equity by
adjusting their leverage. Figure 2 demonstrates that the coefficient over the
1-year horizon, obtained by Welch for the implied debt ratio, is well within the
observed frequency of average coefficients in the model, and Table V shows
that my model produces slightly lower estimates for longer horizons. Overall, I
find that my model does not reject Welch’s coefficient on the implied debt ratio
over a short horizon and that the term structure patterns of the coefficients are
also similar. The simulations clearly show that a model with small adjustment
costs can produce results on the persistence of leverage that are consistent with
those observed in reality.

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Tests of Capital Structure Theory

0.9

The Journal of Finance

0.95

1

1.05

1.1

1.15

coefficient

Figure 2. IDRt−1,t coefficient. The figure shows the distribution of the implied debt ratio coefficient in regressions of the quasi-market leverage level against the implied debt ratio and last
year’s leverage (Welch (2004)).

There is one particular feature that deserves special attention. Welch (2004)
points out that while corporations do change their capital structure, their motives “remain largely a mystery” given that the mechanistic effect of the change
in equity value is not offset. The same apparent puzzle is observed in my framework. A coefficient close to 1 might be interpreted as extreme passivity on the
part of shareholders in their debt decisions. At the same time, about 12% of
firms refinance every year in the model, consistent with the observation of
changing capital structure. In fact, my model provides a simple explanation
of this “puzzle” since firm “passivity” in the Welch (2004) sense also obtains
if firms issue debt quite frequently, but the contemporaneous cross-sectional
covariance between new debt issues and equity returns over the chosen period
is zero. This is exactly what happens in the model since managers issue debt
in response to a factor that is largely orthogonal to short-term equity returns,
namely, long-term past stock returns. The model provides an additional insight:
If the covariance between changes in outstanding debt and equity returns over
t − k to t is weakly positive, then the coefficient on IDRt−k,t increases slightly.
For k = 1 year, the empirically observed covariance is indeed weakly positive,

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1777

explaining why the coefficient slightly exceeds 1. Observe that in the model,
while the equity return over the last year does not trigger debt issuance by
itself, debt will be issued only if equity returns are positive (otherwise the refinancing barrier would not be reached). In addition, debt reduction due to a
liquidity crisis occurs only if the last-period equity return is negative, leading
again to weakly positive covariance and a 1-year coefficient slightly exceeding
1, on average. It also provides an explanation for why, over a long horizon, my
coefficients are smaller than Welch’s: Firms may issue debt for reasons related
to investment opportunities that can be positively related to changes in equity
value.
Thus, managers react to long-term as opposed to short-term shocks. In the
present model, each firm takes into account what has happened since the start
of the last refinancing cycle. The thrust of the economic intuition is that in a
dynamic economy refinancing cycles of firms overlap. By forcing explanatory
variables to be taken at one point in time for the whole cross section, the analysis
always tends to suggest passivity. It is thus tempting to suggest that adjustment costs are entirely responsible for these stylized facts. However, as Welch
himself points out, there are some drawbacks to this explanation: (1) Direct
transaction costs are small; (2) readjustment patterns are similar across firms
while transaction costs are very different; and (3) firms do not seem to lack
the inclination to actively adjust capital structure, but they seem to lack the
proper inclination to readjust when equity value changes. My analysis sheds
light on some of these concerns. First, even small transaction costs can lead
to stickiness in the firm’s debt policy. Robustness checks in Section III show
that even taking a highly conservative estimate of transaction costs leaves the
results essentially unchanged. Second, in the model, debt issuance costs are
smaller than equity issuance costs, thus the firms that reduce debt when they
are in distress experience relatively higher transaction costs. In other words,
after substantially negative equity returns firms face higher transaction costs.
However, these firms are no more eager to readjust. Third, as I explained above,
the framework accounts for both the capital structure activity and the unwillingness to readjust in response to past equity returns. At the same time, at
least two issues raised by Welch (2004) cannot be addressed satisfactorily in
the present framework. First, there is no difference between small and large
firms, and second, no richer set of debt instruments is allowed that would enable
corporations to lower transaction costs.
D.3. Changes in Leverage and Mean-Reversion
I turn next to the question of the extent to which leverage is mean reverting
in my model. Table VI summarizes estimates of a number of partial adjustment
models, where the dependent variable in all cases is the annual change in the
quasi-market leverage ratio. Columns 1 and 2 of the table report the results
of a two-stage cross-sectional regression estimation. In the first stage, target
leverage, TL, is estimated using equation (20); the resulting value is then used
in the regression for changes in leverage:

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Tests of Capital Structure Theory

The Journal of Finance
Table VI

Cross-Sectional Regressions for Leverage Changes
The table reports the results of the following Fama–MacBeth (1973) cross-sectional regressions on
changes in the quasi-market leverage ratio, QMLt − QMLt−1 :
QMLt − QMLt−1 = h0 + h1 TQMLt−1 + h2 QMLt−1 + h3 X t−1 + .
Independent variables are the target quasi-market leverage ratio (TQMLt−1 ), past leverage
(QMLt−1 ), implied debt ratio adjustment (IDRt−1,t − QMLt−1 ), profitability (πt ), change in profitability (πt−1 = πt−1 − πt−2 ), and the cross-term ((πt−1 × (IDRt−1,t − QMLt−1 )). One thousand
data sets are generated, each containing 75 years of quarterly data for 3,000 firms. For each data
set the above regressions are run over the last 35 years of data and then averaged. Coefficients
and t-statistics are means over 1,000 simulations.

Constant
TQMLt−1
QMLt−1

(1)

(2)

(3)

(4)

0.00
(0.54)
0.16
(5.49)
−0.17
(−12.56)

0.01
(0.58)
0.16
(−4.98)
−0.17
(−12.47)

0.03
(12.90)

0.12
(28.40)

1.02
(85.33)
0.02
(1.38)

0.76
(69.77)
0.06
(2.23)

0.08
(10.78)

0.33
(24.25)

0.79
(36)
3,000

0.72
(31)
3,000

IDRt−1,t − QMLt−1
πt−1
πt−1

−1.20
(−7.68)

πt−1 × (IDRt−1,t − QMLt−1 )
R2
N

0.10
(36)
3,000

0.13
(36)
3,000

QMLt − QMLt−1 = h0 + h1 TLt−1 + h2 QMLt−1 + h3 X t−1 + ,

(22)

where Xt−1 represents other possible lagged regressors. A partial adjustment
model predicts that h1 is positive and h2 is negative and, furthermore, that they
are equal in absolute value. Coefficient h2 measures the speed of adjustment
of leverage to its target level.
Not surprisingly, I find that leverage is mean reverting. A coefficient of −0.17
indicates that the mean reversion of leverage is 17% per year. Fama and French
(2002) report a similar mean reversion speed of 7 to 10% for dividend payers
and 15 to 18% for nondividend payers, which they refer to as a “snail’s pace.”
My firms may be better characterized as “crouching tigers:” most of the time
firms do nothing to the level of their book debt, but when they do make changes
it is by a large amount. Also, in line with the results reported by Fama and
French (2002), the average slopes on lagged leverage are similar in absolute
value to those on target leverage and are therefore consistent with the partial
adjustment model.

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Column 2 adds change in profits as an additional regressor. While the results
are very similar to those of Fama and French (2002), the interpretation in
the context of the present model is slightly different. In particular, while they
suggest that this result shows that short-term variation in earnings is largely
absorbed by debt, in the model developed here a change in profitability that
affects the leverage ratio is due exclusively to persistence of its effect on firm
value.
Columns 3 and 4 of Table VI report estimations of regressions of the change
in the leverage ratio of the type studied by Welch (2004). The regression can be
written as
QMLt − QMLt−k = l0 + l 1 (IDRt−k,t − QMLt−k ) + l 2 πt−k
+ l 3 πt−k (IDRt−k,t − QMLt−k ) + .

(23)

The idea is that a significant coefficient on profitability, πt−k , shows that profitability incrementally explains leverage after controlling for equity returns. If
the cross term is significant, then profitability also helps to explain leverage
adjustment.
The estimates in Table VI indicate that, once stock returns are controlled for,
profitability loses most of its power in explaining leverage but is still able to
account for the adjustment behavior of firms in the cross section. The latter
result is similar to the finding of Welch (2004). Empirically, profitability is
found to retain some explanatory power that could be due to its temporary
component.
D.4. Discussion and Extensions
The main results of this paper emerging from the previous discussion are
as follows. First, empirical hypotheses should be based on model properties in
true cross-sectional dynamics. Second, the inability of standard cross-sectional
tests to distinguish between the competing explanations of capital structure
behavior suggests the importance of looking for other empirical tests. The crosssectional test fails because (1) it considers all firms simultaneously irrespective
of their position in the refinancing cycle and (2) it utilizes the same historical
information for all firms despite the fact that firms differ in the starting points
of their refinancing cycles. All future successful empirical tests have to satisfy
these two conditions.
An empirical procedure that would resolve the first problem above is running
cross-sectional regressions conditional on the decision to refinance. An example of such a procedure is a discrete choice model (Hovakimian et al. (2001)).
Table VII reports the results of conducting an identical test to that run by Fama
and French (2002), on two subsamples, namely, firms that refinanced by issuing
more debt in the last year (active firms), and firms that did not change their
book debt over the last year (passive firms). Firms that defaulted or sold assets
over the same period are excluded. A number of important results emerge. First,

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Tests of Capital Structure Theory

The Journal of Finance
Table VII

Cross-Sectional Regressions on Subsamples
The table reports the results of cross-sectional regressions on the level of the quasi-market leverage ratio, QML. Independent variables are profitability (π), volatility of cash f lows (σ ), bankruptcy
costs (α), asset sale costs (qA ), and restructuring costs (qRC ). The Ref. Point column gives the results
obtained by running the regression at the refinancing point. The FF column reports the results
of benchmark Fama and French (2002) regression using the Fama–MacBeth (1973) empirical procedure on the whole sample. Column “Active” reports the results of the same regression run on
the subsample of firms that restructured over the last year. Column “Passive” reports the results
of the same regression run on the subsample of firms that did not restructure over the last year.
For each data set the above regressions are run over the last 35 years of data and then averaged.
Coefficients and t-statistics are means over 1,000 simulations.

Constant
π
σ
α
qRC
qA
R2
N

Ref. Point

FF

Active

Passive

0.24
(22.29)
5.88
(30.95)
−0.78
(−91.22)
−0.32
(−7.30)
3.67
(3.54)
−0.17
(−10.94)

0.62
(34.02)
−0.78
(−7.47)
−0.40
(−26.79)
−0.47
(−10.25)
−3.28
(−3.09)
−0.29
(−16.53)

0.60
(143.56)
−0.03
(−2.48)
−1.09
(−106.80)
−0.50
(−15.97)
5.52
(7.47)
−0.22
(−18.90)

0.63
(32.77)
−0.84
(−7.89)
−0.37
(−24.77)
−0.46
(−9.39)
−5.55
(−4.90)
−0.30
(−16.54)

0.89
(1)
3,000

0.08
(35)
3,000

0.77
(35)
346

0.07
(35)
2,606

for the subsample of active firms, the cross-sectional regression has almost the
same degree of explanatory power as the refinancing-point regression (in which
all firms are active by construction). Second, asset volatility and restructuring
costs have a larger magnitude relative to the refinancing-point regression. This
is because a set of active firms in the dynamic economy is not a random selection
from the set of all firms. Firms with lower volatility and restructuring costs are
represented in the subsample disproportionately. Third, and for this study most
importantly, profitability, while still slightly negative, almost loses its explanatory power. Changing the firm-specific characteristics can change the direction
of the profitability effect (see Section III). The cross-sectional regression on the
active subsample resolves the problem of sample contamination with passive
firms but it still uses only the information over the very short period, not resolving the problem that firms restructure at different times. This result is very
close to the empirical result on profitability by Hovakimian et al. (2001).
Another empirical procedure is to use the duration model (Leary and Roberts
(2005)) with the estimation of the hazard function of refinancing depending on
all information in the current refinancing cycle. Applying the same method to

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the simulated data of my model (unreported), two interesting results emerge.
First, the model replicates the hump-shaped hazard function for fixed costs.
The economic intuition behind the model can explain the rationale behind the
hump-shaped form of the hazard rate. In the presence of fixed costs, firms optimally wait before restructuring again (this explains an initial increase in the
hazard rate). However, the firms that wait too long are likely to be the firms
whose fortunes deteriorated substantially and thus, conditional on waiting long
enough, the probability of restructuring in the next period is reduced. The second interesting finding is that an increase in profitability shifts the hazard
curve up and thus increases the probability of refinancing. In the pecking order
world, for example, we would expect a different sign from that found by Leary
and Roberts (2005). Thus, the duration model has the potential to distinguish
various theoretical models.
III. Robustness Tests
In this section, I describe the results of a number of robustness tests designed
to investigate the extent to which the results above are sensitive to changes in
parameter values and estimation procedure. The tests fall into two categories.
First, using the benchmark data set, I investigate whether the results are inf luenced by the way in which the sample is constructed. In particular, outliers
in the simulation of the evolution of firm asset values may have an undue inf luence. Second, I study whether perturbing the parameters or the model features
has a significant impact on the results. For each robustness test I redo the whole
analysis but, to keep the computations within practical bounds, the results are
averaged over 50 simulated economies.
The key question is whether the main results of the paper survive the robustness tests. These include: (1) The relation between the average level of leverage
at refinancing points and in a dynamic economy; (2) the average slope of the
leverage–profitability relationship; (3) the results relating to Welch’s (2004)
finding on capital structure and stock returns, and (4) the degree of mean reversion. To save space, Table VIII reports only a summary of some of the main
results.
The evolution of a dynamic economy leads to some outliers. While there is no
measurement error in my benchmark data set, an empiricist using the data generated by any simulated economy might be concerned that some observations
dominate the results and therefore should be excluded. Following the approach
used in the literature, I examine how the results are changed when: (i) The true
volatility of firm cash f lows is trimmed at the 5th and 95th percentile thresholds;
(ii) in a dynamic economy, the time-series volatility in each year is estimated
for each firm over the previous 5 years and estimates outside the 5th and 95th
percentiles are excluded; (iii) in a dynamic economy, for each year firms whose
profitability lies outside the 5th and 95th percentiles are excluded; (iv) firms
that experience default over the previous 5 years are excluded. I find that none
of these changes in procedure inf luence the main results in any significant
way.

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Tests of Capital Structure Theory

The Journal of Finance
Table VIII

Robustness Tests
The table summarizes the robustness tests. Column (i) reports the difference between average
leverage in dynamics and at Ref. Point (See Table III). Column (ii) reports the average value of the
profitability coefficient in Fama–French regressions (Table IV). Column (iii) reports the average
value of IDRt−1,t (Table V). Column (iv) reports the average value of the mean-reversion coefficient
f 2 (Table VI). The tests are as follows: (1) Adjustment cost qRC = 0.05% for all firms; (2) qRC =
0.35% for all firms; (3) qRC = 0.20% for all firms; (4) qRC ’s distribution is shifted to the right
by 0.15%; (5) Personal tax on interest income τi = 25%; (6) τi = 40%; (7) Interest rate r = 0.07;
(8) r = 0.03; (9) Asset risk premia are 0.09%; (10) Asset risk premia are 0.04%; (11) Volatility of
systematic component σS = 0.18% (mean of total volatility, σ , is 0.299 with std. dev. of 0.106); (12)
σS = 0.18 (σI is multiplied by 0.9 × (σI − 0.05) so that σ has mean and std. dev. similar to the
benchmark case); (13) σS = 0.05 (mean of σ is 0.23 with std. dev. of 0.106); (14) σS = 0.05 (σI is
multiplied by 0.93 × (σI + 0.043) so that σ has mean and std. dev. similar to the benchmark case);
(15) σS = 0.0 (σI is multiplied by 0.91 × (σI + 0.055) so that σ has mean and std. dev. similar to the
benchmark case); (16) σ has a mean of 0.35 and std. dev. of 0.14 by multiplying original volatility by
1.37; (17) σ has a mean of 0.15 and std. dev. of 0.06 by multiplying original volatility by 0.59; (18) σ
is 0.247 for all firms (by taking the mean of σI and β); (19) β distribution is wider by 50% (so that σ
has a mean of 0.288 and std. dev. of 0.104); (20) β distribution is wider by 50% (σI shifts to the right
by 0.05 so that σ has mean and std. dev. similar to the benchmark case; (21) All firms have the
same firm-specific parameters, which are equal to the mean of the corresponding parameters; (22)
τl = 0 for all firms; and (23) net payout ratio is 0.035 for all firms. Each test is run for 3,000 firms
and 50 economies. In each test, other parameter values and empirical procedures are unchanged.
Test

Description

(i)

(ii)

(iii)

(iv)

1
2
3
4
5
6
7
8
9
10
11
12

qRC = 0.05% for all firms
qRC = 0.35% for all firms
qRC = 0.20% for all firms
qRC : distribution is shifted to the right
τi = 25%
τi = 40%
r = 0.07
r = 0.03
Asset risk premia are 0.09%
Asset risk premia are 0.04%
σS = 0.18 (and thus σ is larger)
σS = 0.18 (and σI is smaller so that σ
does not change)
σS = 0.05 (and thus σ is smaller)
σS = 0.05 (and σI is larger so that σ
does not change)
σS = 0 (and σI is larger so that σ does
not change)
σ has a mean of 0.35
σ has a mean of 0.15
σ = 0.247 for all firms
β has a wider distribution (so that σ
increases)
β has a wider distribution (σI is
changed so that σ is the same)
All firm-specific parameters equal to
their cross-sectional means
No loss of tax shelter, τl = 0
Net payout ratio is 0.035 for all firms

0.13
0.10
0.11
0.09
0.14
0.06
0.08
0.14
0.08
0.14
0.13
0.11

−0.62
−0.61
−0.69
−0.53
−0.60
−0.72
−0.43
−0.81
−0.45
−0.70
−1.07
−0.64

1.02
1.04
1.03
1.04
1.02
1.05
0.99
1.06
0.99
1.07
1.06
1.07

−0.16
−0.17
−0.17
−0.17
−0.22
−0.12
−0.18
−0.16
−0.17
−0.17
−0.17
−0.15

0.09
0.11

−0.29
−0.39

1.00
1.01

−0.17
−0.17

0.11

−0.33

1.01

−0.17

0.09
0.12
0.09
0.12

−0.94
−0.12
−1.32
−0.79

1.03
1.00
1.02
1.04

−0.12
−0.31
−0.20
−0.17

0.10

−0.48

1.05

−0.16

0.10

−0.80

1.00

−0.16

0.19
0.12

−0.89
−0.66

1.02
1.01

−0.20
−0.17

13
14
15
16
17
18
19
20
21
22
23

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The next tests examine the dependence of the results on changes in the parameters. First, for each exogenous parameter that varies across firms, I consider five cases. For the first two, the distribution of the parameter is identical
to the benchmark case except that its mean is changed; in one case increased
and in the other decreased. In the remaining three cases, the parameter value
is set equal across firms at (i) the upper boundary of the benchmark distribution, (ii) the lower boundary, and (iii) a value equal to the mean in the
base case. Again I find that, qualitatively, the main results are unchanged.
However, changing the volatility parameters does result in noticeable changes
in the cross-sectional distribution of leverage. For a hypothetical sample of
firms without access to public debt markets volatility is higher (Faulkender
and Petersen (2006)) and test 16 shows that the cross-sectional result on profitability is stronger. Under some parameter values, empirical estimates of profitability are less likely to be obtained by the model. The coefficients on the
implied debt ratio and mean reversion are more stable. An important observation is presented by test 15 in Table VIII, where the distribution of total
volatility is similar to the benchmark case but there is no systematic component. As discussed above, the absence of a systematic component leads to a decrease in the magnitude of the profitability–leverage relation. Test 15 provides
a quantitative assessment, with a coefficient of −0.33 as opposed to −0.78 in the
benchmark case. In addition, I consider the case with identical firm-specific parameters, where the only dynamic effect comes from random changes in value.
Test 21 demonstrates that this does not change any results. To study the importance of some model features, I consider two cases of the benchmark model:
(i) without the loss of the tax shelter (τl = 0), and (ii) with constant net payout ratio equal to 0.035. Tests 22 and 23 show that the qualitative results are
unchanged.
Third, I investigate the effect of changes in macroeconomic and tax parameters. Unsurprisingly, decreasing the tax advantage to corporate debt results
in lower leverage in the economy. One result not shown in Table VIII is that a
decrease in τi from 0.35 to 0.25 lowers the average market leverage ratio from
0.36 to 0.28. A decrease in τi also leads to a substantial increase in the difference
between the average leverage ratio in dynamics and at the refinancing point.
Finally, I consider the effect of measurement errors. Erickson and Whited
(2000) find that the market-to-book ratio contains a great deal of measurement
error. Since, in the simulated model, the market-to-book ratio and profitability are highly correlated, I introduce a classical error-in-variables problem by
adding a stochastic component to the evolution of profitability, similar to Gomes
(2001, eq. (35) on p. 1281). Note that these measurement errors are assumed
not to affect the optimal decisions by firms. Similar to Gomes (2001), I find (unreported in the table) that the coefficient on profitability changes substantially,
from −0.78 to −0.33. A similar perturbation of the book value of assets only
changes the coefficient from −0.78 to −0.71.
Overall, the results appear to be quite robust with respect to changes in firmspecific and environmental parameters, and to changes in empirical procedure.

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Tests of Capital Structure Theory

The Journal of Finance

This applies particularly to the cross-sectional results, which are also the most
important.
IV. Concluding Remarks
This paper is the first to describe a methodology for deriving the quantitative
and qualitative predictions of capital structure theories in a dynamic economy
with infrequent adjustment. Using a model of dynamic optimal capital structure, I generate data that structurally resemble data used in empirical studies.
In this way, the method allows us to compare the predictions of a capital structure model in “true dynamics” both to the findings of the empirical literature
and to the comparative statics predictions of the same model. In particular, it
enables us to provide greater insight into the qualitative aspects of the cross
sectional properties of leverage. The main findings of the paper are that (1) the
properties of leverage in the cross section in true dynamics and in comparative statics at refinancing points differ dramatically, and (2) the model gives
rise to data that are consistent with a number of empirical results and that,
using methodologies commonly employed in the literature, may lead to rejection of the model. These findings highlight the need for further research in this
area.
There are two principal directions in which the framework developed here
could most usefully be extended. First, because the dynamics of financing decisions have such a profound inf luence on the empirical properties of the cross
section, competing theories of capital structure—beyond the dynamic tradeoff theory—ought to be developed in fully dynamic form. Some first attempts
have been made. Dasgupta and Sengupta (2002), for example, develop a model
with moral hazard in which, interestingly, dynamic interaction leads to another
explanation for a positive relation between leverage and profitability. Nevertheless, development of alternative dynamic models that lead to quantitative
predictions is still a subject for future research.
Second, a proper study of the evolution of capital structure requires a model
that combines both dynamic capital structure decisions and real investment.
Examples of capital structure models with endogenous investment are Brennan
and Schwartz (1984), Hennessy and Whited (2005), and Titman and Tsyplakov
(2003). Berk et al. (1999) provide another excellent basis for studying real investment, enabling researchers to analyze book values in addition to market
values, while the model developed here contributes to dynamic capital structure. The modeling approach of firm behavior in Berk et al. (1999) is both richer
than mine in some areas and less rich in others. In particular, they are able to
analyze a wider spectrum of questions by considering separately existing assets in place and future growth opportunities. However, their firms are myopic
since the fact that investment projects are assumed independent, combined
with a complete lack of any financial policy, means that in taking investment
decisions, a firm does not take into account the evolution of its assets over time.
Research that combines these two strands is likely to be a fruitful avenue for
future research in capital structure, and more generally, corporate finance.

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1784

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Appendix: Details of Simulation Analysis
The process for δ is discretized using the following approximation:
σ2

√

δt = δt−t e(µ A − 2 )t+σ tz t ,

(A1)

where t is one quarter, zt is a standard normal variable, and µA is the growth
rate of the net payout ratio under the physical measure. The benchmark simulation is for 300 quarters and 3,000 firms. Note that while I discretize the model
for the purpose of simulation, firms still operate in a continuous environment.
In particular, firms sometimes “overshoot” boundaries and make their financial decisions at times different from the prescribed optimal times. Unreported
robustness checks show that increasing the frequency of observations does not
change the results.
To minimize the impact of initial conditions, I implement the following ad hoc
procedure to choose the number of observations that will be dropped. I simulate
the panel data set for 3,000 firms with the benchmark set of parameters, in the
absence of a systematic shock, 250 times. For each economy the average leverage
ratio is calculated. I then estimate the rolling sum of the first differences in
average leverage ratios (quarter by quarter) over the last 10 quarters. The
stopping rule for this variable is to be less than 0.5% in absolute magnitude
(for comparison, the average value of this variable in the first 10 quarters is
5%), at which point the economy is defined as converged to its steady state. The
resulting distribution of steady-state stopping times across all economies has
a mean of 30 quarters, a 95th percentile value of 50 quarters, and a maximum
of 76 quarters. For a conservative estimate I double the maximum. Since this
procedure is largely ad hoc, I check the result by simulating 20 economies for
1,000 quarters and confirm that there is no difference in the average leverage
ratio behavior for the last 900 quarters by investigating rolling sums over the
entire period.
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Tests of Capital Structure Theory


==> JF7 - 2016 - LIANG - On the Foundations of Corporate Social Responsibility.txt <==
THE JOURNAL OF FINANCE • VOL. LXXII, NO. 2 • APRIL 2017

On the Foundations of Corporate Social
Responsibility
HAO LIANG and LUC RENNEBOOG∗
ABSTRACT
Using corporate social responsibility (CSR) ratings for 23,000 companies from 114
countries, we find that a firm’s CSR rating and its country’s legal origin are strongly
correlated. Legal origin is a stronger explanation than “doing good by doing well”
factors or firm and country characteristics (ownership concentration, political institutions, and globalization): firms from common law countries have lower CSR than
companies from civil law countries, with Scandinavian civil law firms having the
highest CSR ratings. Evidence from quasi-natural experiments such as scandals and
natural disasters suggests that civil law firms are more responsive to CSR shocks
than common law firms.

THE CLASSICAL VIEW IN FINANCE on modern corporations takes a shareholder
value maximization perspective, which holds that corporations are accountable only to profit-maximizing shareholders, and apart from their contractually determined obligations, have no responsibility to serve other stakeholders’ interests or to enhance society’s welfare (Friedman (1970), Bénabou and
Tirole (2010)). In reality, however, corporations often focus on objectives beyond profit maximization and participate in activities that improve other
∗ Hao Liang is from Singapore Management University. Luc Renneboog is from Tilburg University. We acknowledge that we are aware of the Journal of Finance’s submission guidelines and
policies and conflict of interest disclosure policy and that there are no conflicts of interest that
exist for this paper. We are very grateful to Andrei Shleifer and Holger Spamann for comments
and suggestions on early versions of the paper. We also wish to thank Ian Appel, Lucian Bebchuk,
Gennaro Bernile, Daniel Beunza, Archie Carroll, Martijn Cremers, Hans Degryse, Frank De Jong,
Elroy Dimson, Joost Driessen, Tore Ellingsen, Fabrizio Ferraro, Allen Ferrell, Caroline Flammer,
Edward Freeman, Richard Friberg, Jesse Fried, Marc Goergen, Jarrad Harford, Oguzhan Karakas,
Philipp Krueger, Amir Licht, Paul Malatesta, Alberto Manconi, Chris Marquis, Mark Roe, Amir
Rubin, Paola Sapienza, Enrique Schroth, Roy Shapira, Oliver Spalt, Matt Spiegel, Gaspar van
Weerbeke, Jörgen Weibull, Bernard Yeung; seminar participants at Harvard Law School, Harvard
Business School, Tilburg University, London Business School, University of Cambridge (Judge),
Stockholm School of Economics, University of Zurich, University of Antwerp, Institut Bachelier
and Ecole Polytechnique Paris, Humboldt-Berlin University, Ghent University, University Paris
Dauphine, Norwegian School of Economics, Cardiff Business School, and Singapore Management
University; as well as conference participants at the 10th and 11th Corporate Finance Day (Ghent
and Liège), EFMA 2014 Conference, 2014 China International Conference in Finance, Harvard
Business School Conference on Sustainability and the Corporation: the Big Ideas, Vigeo’s Corporate Social Responsibility Conference ‘Assessing Corporate and Sovereign Intangible Capital’
(Paris), and the 2nd Geneva Summit of Sustainable Finance for helpful comments and suggestions.
All errors are our own.

DOI: 10.1111/jofi.12487

853

The Journal of FinanceR

stakeholders’ welfare, such as providing employee benefits, investing in
environment-friendly production processes, selecting suppliers that avoid the
use of child labor, and organizing projects to help the poor in less-developed
countries. Indeed, corporate social responsibility (CSR), a term frequently used
to describe such stakeholder-oriented behaviors, has increasingly become a
mainstream business activity (Kitzmueller and Shimshack (2012)). This raises
the question of why do some firms want to be socially responsible rather than
pure profit maximizers, and more importantly, why firms in some countries
engage in CSR to a greater extent than firms in other countries.
The common explanation for why companies invest in CSR is that doing so
enhances profitability and firm value,1 a relationship often referred to as “doing
well by doing good” (e.g., Dowell, Hart, and Yeung (2000), Orlitzky, Schmidt,
and Rynes (2003), Renneboog, Ter Horst, and Zhang (2008, 2011), Guenster
et al. (2011), Deng, Kang, and Low (2013), Flammer (2015), Krueger (2015),
Dimson, Karakaş, and Li (2015)). Other studies consider the inverse, that is,
“doing good by doing well,” by examining whether it is only well-performing
firms that can afford to invest in CSR (e.g., Hong, Kubik, and Scheinkman
(2012)). However, neither of these “doing good—doing well” arguments can
explain the cross-firm or cross-country variation in CSR. For instance, if on
average CSR enhances firm value, why do some companies adopt a CSRoriented strategy whereas others do so to a lesser extent, and why do companies in some countries systematically invest more in CSR than companies in
other countries? In addition, these “doing good—doing well” arguments mostly
take CSR to be a voluntary initiative. Extant studies also usually take only
one perspective on CSR, such as employee satisfaction (Edmans (2011, 2012),
Edmans, Li, and Zhang (2014)), environmental protection (e.g., Dowell, Hart,
and Yeung (2000), Konar and Cohen (2001)), corporate philanthropy (e.g.,
Seifert, Morris, and Bartkus (2004), Masulis and Reza (2015), Liang and Renneboog (2016)), or consumer satisfaction (e.g., Luo and Bhattacharya (2006),
Servaes and Tamayo (2013)), and test CSR relations for only one country (typically the United States). However, CSR spans multiple dimensions of firm
behavior and captures a firm’s effort to address various externalities that it
generates in the process of pursuing profit maximization (Tirole (2001)) that
are not internalized by shareholders (Magill, Quinzii, and Rochet (2015)). This
multidimensional and externality-driven nature of CSR suggests that it should
be fundamentally related to not only a firm’s own choice but also regulations,
institutional arrangements, and societal preferences. Moreover, beyond looking
at CSR as a mechanism to address externalities, we consider CSR as a more
fundamental tradeoff between a shareholder focus and an other-stakeholder
focus (at the firm level) (Ferrell, Liang, and Renneboog (2016)), as well as between rules and discretion by institutions governing economic life. Such tradeoffs, as we argue, hinge crucially on a firm’s explicit and implicit contractual
1 Bénabou and Tirole (2010, p. 2) define CSR as “sacrificing profits in the social interest.” Following many other studies, here we adopt a broader definition of CSR that focuses on firm activities
that improve social welfare but not necessarily at the expense of profits (or shareholder value).

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environment, which is likely to be shaped by legal rules and enforcement mechanisms that differ across countries.
In this paper, we examine whether differences in CSR practices across countries can be explained by relating CSR to a country’s legal origin, which has
been shown to systematically shape various country-level institutions and
the firm-level contracting environment (Doidge, Karolyi, and Stulz (2007), La
Porta, López-de-Silanes, and Shleifer (2008)). In the context of CSR, a country’s legal regime determines how “public goods” should be provided by the
private sector (corporations): through regulations and rules, firm discretion,
or government involvement in business (Kitzmueller and Shimshack (2012)).
A country’s legal regime also shapes the explicit and (more often) implicit
contracts between shareholders and other stakeholders through its effect on
governance structures and the decision-making process.2 A common law origin
is a more discretion-oriented system that supports private market outcomes,
places fewer ex ante restrictions on managerial behavior (but discourages inappropriate or unacceptable behavior by relying on ex post sanctions such as
litigation or other judicial mechanisms), and favors shareholder protection. A
civil law origin, in contrast, is associated with state intervention in economic
life through rules and regulations (e.g., an ex ante delineation of acceptable
behavior) and a “stakeholder view” (La Porta, López-de-Silanes, and Shleifer
(2008), Allen, Carletti, and Marquez (2015), Magill, Quinzii, and Rochet (2015)).
The level of CSR in a country is therefore a result of both a governance tradeoff
concerning the rights and preferences of shareholders and other stakeholders,
and the form in which this tradeoff is made (i.e., by rules or discretion).
To empirically test the legal origin view of CSR, we employ several newly
assembled international databases on firm-level CSR that together cover more
than 25,000 large public companies around the globe. Our CSR data measure
corporations’ engagement in and compliance with environmental, social, and
traditional corporate governance (“ESG”) issues, where engagement refers to a
firm’s voluntary investment in CSR projects while compliance refers to behavior that a firm is required or encouraged to follow.3 Engagement and compliance activities across the different ESG dimensions capture various aspects of
2 For example, in Germany, corporations are legally required to take into account the interests of
employees through the system of codetermination, which requires that employees and shareholders
have an equal number of seats on the supervisory board (Allen, Carletti, and Marquez (2015)).
Moreover, the harmonization laws of the European Community include provisions permitting
corporations to take into account the interests of creditors, customers, potential investors, and
employees and the corporate laws in Japan presume that Japanese corporations exist within a
tightly connected and interrelated set of stakeholders, including suppliers, customers, lending
institutions, and friendly corporations (Donaldson and Preston (1995)).
3 For example, engagement in ESG may include a company’s voluntary R&D investment in an
environmentally friendly project (the “E” dimension), an employee training program designed to
increase employee welfare or productivity (the “S” dimension), or a voluntary increase in gender
and racial diversity of the board of directors (the “G” dimension). Compliance with ESG may
include following environmental regulations on CO2 emissions (the “E” dimension), guaranteeing
working conditions above the minimum requirements in factories located in developing countries
(the “S” dimension), or consulting investors on management compensation (say on pay) (the “G”
dimension).

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

stakeholder issues.4 As our main focus is on nonfinancial stakeholders (stakeholders other than shareholders, which are protected by corporate governance
mechanisms), our CSR samples mostly rely on the “E” and “S” dimensions,
giving little weight to the “G” dimension.
Using these comprehensive global CSR data, we find that legal origin appears
to be the strongest predictor of CSR adoption and performance at the firm level,
stronger than alternative factors such as political institutions, regulations, social preferences, and a firm’s financial and operational performance. Firms
with a common law origin score significantly lower on various CSR ratings
than civil law firms, while firms from the Scandinavian legal regime obtain the
highest scores on most of the CSR ratings. These results survive the inclusion
of a large set of country- and firm-level control variables and the use of different estimation methods such as Ordinary Least Squares (OLS), generalized
least squares (GLS), and random-effects ordered probit models. The results
are further supported by several quasi-natural experiments of global disasters
and scandals that shift societal demand for CSR that allows us to control for
country fixed effects to rule out alternative explanations based on country-level
channels. In these experiments, we find that firms in civil law countries are
more responsive to large natural disasters and industry scandals such as food
safety and oil spill pollution. Such responsiveness does not appear to be explained by changes in firms’ market shares. When we investigate a number of
economic mechanisms for the association between legal origin and CSR, we find
that firms in civil law countries face less shareholder litigation risk but more
regulations concerning stakeholder welfare, rely more on supermajority rules
among shareholders, and have stronger state involvement in their businesses,
all of which are strongly related to higher CSR scores. Overall, the results suggest that there is a strong link between firm-level CSR and country-level legal
origin, which may help explain cross-country variation in CSR.
The paper proceeds as follows. Section I lays out the theoretical foundations
on the relation between legal origin and CSR. Section II describes the data and
empirical strategies. Section III presents empirical results from our baseline
models. Section IV presents additional evidence from disasters and scandals.
In Section V, we present evidence on the economic mechanisms behind our
main results. Section VI concludes.
I. The Legal Origins and CSR
Social arrangements between private citizens, corporations, and the government vary significantly across countries of different legal origin. La Porta,
López-de-Silanes, and Shleifer (2008) consider a country’s legal origin as the
style of social control behind its economic life. Common law countries rely more
4 Similarly, the European Federation of Financial Analysts Societies (EFFAS) interprets ESG
as the need to focus on: (1) energy efficiency, (2) greenhouse gas emissions, (3) staff turnover, (4)
training and qualification, (5) maturity of workforce, (6) absenteeism rate, (7) litigation risks, (8)
corruption, and (9) revenues from new products.

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856

857

heavily on private market outcomes. The idea is that, under perfect markets,
maximizing profit in the interest of shareholders leads a firm to act in the
best interest of all stakeholders such as consumers, workers, and shareholders
(Magill, Quinzii, and Rochet (2015)). In contrast, in civil law countries, the
state plays a stronger coordinating role in factor markets. These countries typically have stronger unions, which has led to, for example, stricter regulations
regarding dismissal or a wider scope of collective bargaining agreements (at
the industry level), as well as stricter consumer protection laws, which place
more restrictions on prices and regulate product markets to address various
stakeholders’ interests (Botero et al. (2004), Djankov et al. (2008), La Porta,
López-de-Silanes, and Shleifer (2008)).
In addition, countries under different legal regimes manage conflicts between firms, their suppliers, and their customers differently. Countries with a
common law origin rely to a greater degree on ex post settling up through judicial mechanisms, whereas civil law countries rely more heavily on rules-based
mechanisms that restrict behavior ex ante (Enriques (2004), Cheffins and Black
(2006), La Porta, López-de-Silanes, and Shleifer (2008), Issacharoff and Miller
(2009), Cox and Thomas (2009), Gelter (2012)). The different balance between
rules and discretion in corporate decision making in civil versus common law
countries is likely driven by supply- and demand-side considerations, which
lead to predictions about differences in CSR activity across legal regimes. On
the supply side, CSR may arise as an alternative response to market failures
due to inefficient regulations (e.g., de Bettignies and Robinson (2015)). The fact
that a wide variety of stakeholders can more easily make claims, and benefit
from stronger protection, in civil law than in common law countries implies that
there may be less need for firms in civil law countries to behave in a socially
responsible way over and above meeting regulatory requirements, in which
case CSR strategies would be largely redundant in light of the constraints
and requirements already in place under the civil law regime. On the demand
side, the level of CSR in a country may reflect consumers’ and other citizens’
preferences for corporations to be altruistic and prosocial (Bénabou and Tirole
(2006, 2010)). Based on this demand-side view, the fact that civil law countries
have stricter regulatory protection of stakeholders may reflect stronger social
preferences, in which case we would expect stronger CSR behavior in civil
law countries because more is expected of firms in this environment. In sum,
CSR is likely to be an equilibrium outcome reflecting the demand for voluntary
“good behavior” and the availability, as well as efficacy, of substitutes for this
behavior. In this context, the relation between CSR and legal origin depends
on which set of forces (supply- vs. demand-side considerations) dominates.
The above tradeoff leads to empirical predictions on the underlying mechanisms that connect legal origin and CSR. In common law countries, CSR
adoption is determined largely by corporate discretion, whereas in civil law
countries, CSR adoption is determined by rules, which can be either explicit
(such as laws and regulations) or implicit (such as societal preferences). For
example, in civil law countries where the risk of shareholder litigation against
management or directors is lower, firms have more freedom to engage in CSR

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

activities (which are often beyond regulation) (Enriques (2004), Cheffins and
Black (2006), La Porta, López-de-Silanes, and Shleifer (2008), Issacharoff and
Miller (2009), Cox and Thomas (2009), Gelter (2012)). Similarly, when a firm’s
decision-making process is ex ante insulated from the short-term pressures of
shareholders (for example, through the presence of a supermajority vote requirement in the corporate charter or bylaws), the firm will be more willing to
engage in CSR activities, which are often more long-term oriented in nature
(Cremers and Sepe (2016)). Furthermore, CSR is expected to be more prevalent
under stronger regulations and government interventions on stakeholder issues, as CSR could potentially “safeguard” a firm’s fiduciary duty as mandated
by law, with this function under different legal regimes again depending on the
relative supply- versus demand-side forces.
II. Data and Empirical Strategy
Detailed definitions and data sources for all of our variables are summarized
in Table I (for various CSR variables and sustainable country ratings) and
Appendix A (for explanatory variables).
A. CSR Data and Descriptive Statistics
In recent years, a variety of ESG indices measuring firm-level CSR performance have been constructed using different rating methodologies (e.g., some
are based on a box-ticking approach—“compliance,” while others are based on
interpretative analysis—“engagement”). We have extensively discussed the reliability of these different ratings with practitioners, policy makers, and data
providers. Because of the concern that the “G” component of ESG measures
overlaps with traditional corporate governance issues, which are materially
different from the other stakeholder issues (Krueger (2015)), in this paper we
deliberately employ databases that minimize the weight on corporate governance issues while putting more emphasis on environmental and social issues.
Our main data on CSR performance come from Morgan Stanley Capital International’s (MSCI) Intangible Value Assessment (IVA) database.5 The IVA
indices measure a corporation’s environmental and social risks and opportunities, that is, large environmental and social externalities, the costs of which
the firm may be forced to internalize in the future. The ratings also take into
account the extent to which a company has developed CSR strategies designed
to manage its specific risks and opportunities. Such rating methods capture
both the legally mandated aspects (unanticipated costs associated with regulatory penalties and lawsuits) and voluntary aspects (risk management strategies and strategies to capture potential opportunities) of CSR. Importantly,
companies are rated in comparison to their industry peers across international
5 In contrast to credit rating agencies, which are paid by the firms (whose products) they rate,
CSR rating agencies are financially independent from the rated firms and thus conflicts of interest
are largely avoided.

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858

(Continued)

The IVA rating identifies key environmental, social, and governance issues that hold the greatest potential risk or opportunity
for each industry sector. Environmental themes include climate change, natural resources, pollution and waste, and
environmental opportunities. Social themes include human capital, product liability, stakeholder opposition, and social
opportunities. More detailed decompositions of key issues under each theme are listed below in Environmental score and
Social score. IVA analyzes each company’s risk exposure, measuring the extent to which a company’s core business is at risk
of incurring unanticipated losses. When comparing companies, the data are normalized by the most relevant, available
factor, such as sales or production levels. The data are then converted to a relative rating by giving the company with the
best performance in its industry sector in a given category an AAA rating, the top rating, while giving the company with the
worst performance a CCC rating, the lowest rating, and then converting these ratings to scores between 6 and 0. The IVA
ratings are in two waves (as in our sample): 1999 to 2011 and 2011 to 2014. Source: MSCI Intangible Value Assessment.
The environmental score is the environmental pillar of IVA and applies the same rating metrics based on potential risk or
opportunity in each industry. The score rates the following issues: carbon emissions, product carbon footprint, energy
efficiency, insurance against climate change risk, water stress, biodiversity and land use, raw material sourcing, financing
environmental impact, toxic emissions and waste, packaging material and waste, electronic waste, opportunities in clean
tech, opportunities in green building, opportunities in renewable energy, etc. The data are converted to a relative score by
giving the company with the best performance in its industry sector in a given category a 10, the top score, and giving the
company with the worst performance a 0, the lowest score. Source: MSCI Intangible Value Assessment (2011 to 2014 wave).
The social score is the social pillar of IVA and applies the same rating metrics based on potential risk or opportunity in each
industry. The score rates the following issues: labor management, human capital development, health and safety,
supply-chain labor standards, controversial sourcing, product safety and quality, chemical safety, privacy and data security,
responsible investing, insuring health and demographic risk, opportunities in health and nutrition, access to
communications, access to healthcare, etc. Similar to the environmental score, the social score is industry-adjusted
(compared within the same industry sector on a global scale) and ranges from 0 to 10. Source: MSCI Intangible Value
Assessment (2011 to 2014 wave).

Panel A: Descriptions of CSR Ratings Used as Dependent Variables and the Sustainable Country Rating

859

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Social score

Environmental
score

Overall IVA
rating

Table I

Description of the CSR Indices
On the Foundations of Corporate Social Responsibility

(Continued)

The EcoValue ratings measure a company’s environmental performance in three major areas: (1) environmental strategy and
management, (2) environmental risks, and (3) environmental strategic profit opportunities. The rating methods are similar
to those of the overall IVA ratings, and also range from AAA to CCC (which are then converted to 6 to 0). Source: RiskMetrics
(provided by the MSCI Intangible Value Assessment: the 1999 to 2011 wave).
The Social ratings measure a company’s social performance on aspects similar to those in the Social score. The rating methods
are similar to that of the overall IVA ratings, and also range from AAA to CCC (which are then converted to 6 to 0). Source:
RiskMetrics (provided by the MSCI Intangible Value Assessment: 1999 to 2011 wave).
The customer/product responsibility category measures a company’s management commitment and effectiveness in creating
value-added products and services upholding customers’ security. It reflects a company’s capacity to maintain its license to
operate by producing quality goods and services preserving the customer’s health, safety, integrity, and privacy also through
accurate product information and labeling. Source: ASSET4 ESG data.
A score measuring a company’s product quality, health and safety initiatives, and controversies related to the quality or safety
of the company’s products, including legal cases, recalls, and criticism. The score is normalized on a scale of 0 to 10, with a
higher score indicating greater product safety. Source: MSCI Intangible Value Assessment.
The amount of cash donations to charitable (i.e., tax-exempt) organizations scaled by total cash. Cash donations include direct
cash giving and cash giving via a corporate foundation. The variable is calculated as: Ln (1 + cash donations/cash) × 103 ,
then winsorized at the 1% level. Source: ASSET4 ESG data.
A score measuring the extent to which the company is directly or indirectly (through a supplier) under the spotlight of the
media because of a controversy linked to the spill of chemicals, oils and fuels, gases (flaring), or the overall impact of the
company on the environment. The score is normalized on a scale of 0 to 100. Source: ASSET4 ESG data.
A score measuring the extent to which the company invests in R&D on new environmentally friendly products or services that
limit the amount of emissions and resources needed during product use. The score is normalized on a scale of 0 to 100.
Source: ASSET4 ESG data.
A score measuring the extent to which the company develops products or technologies for use in clean, renewable energy (such
as wind, solar, hydro, geothermal, and biomass power). The score is normalized on a scale of 0 to 100. Source: ASSET4 ESG
data.
Country-level sovereign ESG scores and benchmarks based on 120 ESG risk and performance indicators in three areas: (1)
environmental protection, (2) social protection and solidarity, (3) rule of law and governance. Countries are graded on a scale
of 0 to 100 on their commitment and performance in the measured areas (e.g., ratification of the Kyoto convention, the
Vienna convention, the Stockholm convention, CO2 emissions per head, Gini index, etc.). Source: Vigeo.

The Journal of FinanceR

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Sustainable
country
rating

Clean energy
products

Spill and
pollution
control
Environmental
R&D

Cash donations
to cash

Product safety

Product
responsibility

Social rating

EcoValue rating

Panel A: Descriptions of CSR Ratings Used as Dependent Variables and the Sustainable Country Rating

Table I—Continued

860

<2%
20%
<2%

HC2) Labor relations

HC3) Health and safety

<2%

SC3) Supply chain

<2%
<2%

EM1) EM strategy

EM2) Human rights/child
and forced labor
EM3) Oppressive regimes

Emerging
markets

(Continued)

861

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<2%

<2%

PS1) Intellectual
capital/product
development
PS2) Product safety

<2%

<2%

SC1) Stakeholder
partnerships
SC2) Local communities

Policies, support for values in Universal Declaration of Human Rights, initiatives
to promote human rights, human rights controversies.
Controversies, substantive involvement in countries with poor HR records.

Board independence, management of CSR issues, board diversity, compensation
practices, controversies involving executive compensation and governance.
Workforce diversity, policies and programs to promote diversity, work/life
benefits, discrimination-related controversies.
KEY ISSUE: Labor Relations
Benefits, strikes, union relations, controversies, risk of work stoppages, etc.
H&S policies and systems, implementation and monitoring of those systems,
performance (injury rate, etc.), safety-related incidents and controversies.
Customer initiatives, customer-related controversies, firm’s support for public
policies with noteworthy benefits for stakeholders.
Policies, systems, and initiatives involving local communities (especially
indigenous peoples), controversies related to firm’s interactions with
communities.
Policies and systems to protect supply-chain workers’ and contractors’ rights,
initiatives for improving labor conditions, supply chain–related controversies.
Beneficial products and services, including efforts that benefit the
disadvantaged, reduce consumption of energy and resources, and production of
hazardous chemicals; average of two scores.
Product quality, health and safety initiatives, controversies related to the quality
or safety of a firm’s products, including legal cases, recalls, criticism.
Default = 5, unless there is company-specific exposure that is highly significant.

<2%

<2%

Management of CSR issues, partnership in multistakeholder initiatives.

<2%

SG2) Strategic
capability/adaptability
SG3) Traditional
governance concerns
HC1) Workplace practices

Products and
services

Stakeholder
capital

Human capital

Overall governance; rating composed of total scores of nonkey issues.

<2%

SG1) Strategy

Strategic
governance

Key Metrics

Weight

IVA Subscore

IVA Factor

Panel B: Decomposition of the Intangible Value Assessment (IVA) Rating (Based on the 1999 to 2011 Wave)

Table I—Continued

On the Foundations of Corporate Social Responsibility

Presence of environmental training and communications programs for employees.
Certifications by ISO or other industry- and country-specific third-party auditors.
Positive and negative impact of products and services, end-of-life product
management, controversies related to environmental impact of P&S.
Policies to integrate environmental considerations into all operations and reduce
environmental impact of operations, products and services, environmental
management systems, regulatory compliance.
KEY ISSUE: Opportunities in clean technology

25%

<2%
<2%
<2%

<2%
<2%
<2%
<2%

35%

<2%

ER4) Industry-specific carbon
risk

EMC1) Environmental strategy

EMC2) Corporate governance

EMC3) Environmental
management systems
EMC4) Audit
EMC5) Environmental
accounting/reporting
EMC6) Environmental training
and development
EMC7) Certification
EMC8) Products/materials

EO1) Strategic competence

EO2) Environmental
opportunity

EO3) Performance

<2%
<2%

Board independence, management of CSR issues, board diversity, compensation
practices, controversies involving executive compensation and governance.
Establishment and monitoring of environmental performance targets, presence
of environmental training, stakeholder engagement.
External independent audits of environmental performance.
Reporting frequency, reporting quality.

<2%

ER3) Leading/sustainability
risk indicators

Product development in clean technology, R&D relative to sales and trend,
innovation capacity.
Percent of revenue represented by identified beneficial products and services.

Targets, emissions intensity relative to peers, estimated cost of compliance.
Policies to integrate environmental considerations into all operations,
environmental management systems, regulatory compliance, controversies.

<2%

ER2) Operating risk

The Journal of FinanceR

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Environmental
opportunity
factors

Environmental
management
capacity

Controversies including natural resource–related cases, widespread or egregious
environmental impacts.
Emissions to air, discharges to water, emission of toxic chemicals, nuclear energy,
controversies involving non-GHG emissions.
Water management and use, use of recycled materials, sourcing, sustainable
resource management, climate change policy and transparency, climate change
initiatives, absolute and normalized emissions output, controversies.
KEY ISSUE: Carbon

<2%

ER1) Historic liabilities

Environmental
risk factors

Key Metrics

Weight

IVA Subscore

IVA Factor

Panel B: Decomposition of the Intangible Value Assessment (IVA) Rating (Based on the 1999 to 2011 Wave)

Table I—Continued

862

863

markets, and therefore a firm’s rating does not depend on the local environment
and rules. Companies with the best CSR “performance” (CSR score) within
its industry on a global scale are rated AAA (the top rating), while companies with the worst CSR performance are rated CCC (the lowest rating); the
remaining firms are rated AA, A, BBB, BB, and B. We convert these alpha
ratings to numeric scores from 6 to 0. Information needed to complete the IVA
ratings comes from several sources, including corporate documents (environmental and social reports, annual reports, securities filings such as 10Ks and
10Qs, Web sites, etc.), environmental groups and other NGOs, trade groups
and other industry associations, government databases,6 periodical searches
(e.g., Factiva and Nexis), and financial analysts’ reports. Following a review
of various corporate documents, the MSCI analysts usually interview senior
executives at the companies, most often in the environmental area. When comparing companies, the data are normalized by the most relevant, available
factor, such as domestic sales or production. The ratings are available from
1999 to 2014,7 and cover over 23,000 large public companies (past and current)
in major equity indices worldwide, including all companies of the MSCI World
Index, the MSCI Emerging Markets Index, the MSCI US, Canada, United
Kingdom, Australia, and South Africa indices, the FTSE 100 and FTSE 250
(excluding investment trusts) indices, the ASX 200 Index, and the Barclays
Global Aggregate—Corporate Index. For this large sample with global coverage, MSCI constructs 29 ESG categories,8 among which a few categories
such as Labor Relations, Industry-Specific Carbon Risk, and Environmental
Opportunity receive the highest weights in the global rating, while the weight
on traditional corporate governance is below 2%. The detailed composition of
the IVA ratings is shown in Table I. We triangulate our analysis based on
the IVA rating (the overall CSR rating) using the RiskMetrics EcoValue21
Rating and the RiskMetrics Social Rating (hereafter EcoValue Rating and
Social Rating), which capture the environmental and social aspects of CSR,
respectively.
6 Government databases include, for example, central bank data, U.S. Toxic Release Inventory,
Comprehensive Environmental Response and Liability Information System (CERCLIS), and RCRA
Hazardous Waste Data Management System. For European companies, many other information
sources are available.
7 There are two waves of IVA data: the first wave is from 1999 to 2011, and the second wave is
from 2011 to 2015. To match our financial data, we truncate the IVA ratings to 2014. The method
for calculating the overall IVA ratings is the same across the two waves. The first-wave data have
more detailed information on the ratings of the 29 sub-ESG categories.
8 A key ESG issue is defined as an environmental and/or social externality that has the potential
to become internalized by the industry or the company through one or more of the following triggers:
(1) pending or proposed regulation, (2) a potential supply constraint, (3) a notable shift in demand,
(4) a major strategic response by an established competitor, or (5) growing public awareness or
concern. Once up to five key issues have been selected, analysts work with sector team leaders to
make any necessary adjustments to the weights in the model. Each key issue typically comprises
10% to 30% of the total IVA rating. The weights take into account the impact of companies, their
supply chains, their products, and the financial implications of these impacts. For each key issue,
a wide range of data is collected to address the question: “To what extent is risk management
commensurate with risk exposure?”

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

Our main sample comprises 403,633 firm-time observations from 114 countries that span 123 industries (based on MSCI’s industry classification). We
employ other CSR indices provided by various ESG rating agencies with a
global scope to cross-validate our results. These indices include Vigeo’s corporate ESG ratings and Thomson Reuters’s ASSET4 ratings. The country coverage and number of observations are shown in Appendices B to D. In contrast to
the MSCI IVA data, which focus on engagement (developing strategies to manage risks and opportunities), the Vigeo ESG data are more CSR complianceoriented as they apply a check-the-box approach to rate firm- and country-level
compliance with the conventions, guidelines, and declarations of international
organizations such as the United Nations, International Labor Organization,
and Organization for Economic Co-operation and Development (OECD).
B. Methodology
As the IVA ratings measuring a company’s ESG performance are integers
ranging from 0 to 6 and are not normally distributed, we first use the nonparametric Wilcoxon rank-sum (Mann-Whitney) test in a univariate analysis
that compares median ESG values across different legal origins and between
capitalist and socialist countries. We then apply reduced-form regressions to
analyze the association between a company’s CSR and its country’s legal origin,
political institutions, social preferences, and corporate characteristics (including financial performance). Given that some of our key explanatory variables
(e.g., legal origin) are time invariant and we would like to draw inferences
on the population, we use random-effects models in this panel setting. We
conduct our estimations using OLS, random-effects GLS, and random-effects
ordered probit models. The latter are estimated by means of maximum likelihood and consider the discrete, ordinal nature of the ratings and rating changes
in a panel data setting (the same method has been used in, e.g., Alsakka and
Gwilym (2010)). The general specification can be expressed as:
yit∗ = αt + β  Legalc + δ  Xit + γ  Zct + εit ,

(1)

where Legal is a vector of different types of civil law origin, Xit is a vector of
firm-level financial and governance variables, and Zct is a vector of country-level
control variables. Except for legal origin, all of the variables are time-variant
in nature. Note that i, t, and c denote firm, time, and country, respectively.
The dependent variable, yit∗ , is the firm-level CSR rating. In the case of ordered
probit models, yit∗ is an unobserved latent variable linked to the observed ordinal
response categories yit :
⎡
⎤
0 if yit∗ ≤ μ1
⎢ 1 if μ1 < y∗ ≤ μ2 ⎥
it
⎢
⎥
⎢ 2 if μ2 < y∗ ≤ μ3 ⎥
it
⎢
⎥
∗
⎥
(2)
yit = ⎢
⎢ 3 if μ3 < yit∗ ≤ μ4 ⎥ .
⎢ 4 if μ4 < y ≤ μ5 ⎥
it
⎢
⎥
⎣ 5 if μ5 < yit∗ ≤ μ6 ⎦
6 if μ6 < yit∗

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864

865

The μ’s represent thresholds to be estimated (along with the coefficients
β and γ ) using maximum likelihood estimation, subject to the constraint that
μ1 < μ2 < μ3 < μ4 < μ5 < μ6 .
We also run a few quasi-natural experiments on some (largely) exogenous
shocks to CSR demand and examine the differences in response by legal regime
using OLS estimation while controlling for country, industry, and year fixed effects. Controlling for country fixed effects in the quasi-natural experiments
enables us to rule out alternative explanations based on other country-level
factors such as ideologies, cultures, and social norms. In these quasi-natural
experimental settings, we also investigate changes in market share to disentangle them from possible consequences induced by legal origin. Furthermore,
we explicitly include several institutional and governance variables to explore
potential mechanisms linking a firm’s CSR and its country’s legal origin in a
two-stage setup.
C. Variables
In our main analysis, the dependent variable in equation (1) is the overall IVA rating, which aggregates all environmental and social dimensions of
CSR after converting them to ordered integer scores ranging from 0 to 6. In
robustness tests, we use individual dimensions of the IVA rating as alternative dependent variables, as well as the CSR ratings from two alternative CSR
samples—Vigeo and ASSET4—which are normalized ratings ranging from 0
to 100. Explanatory variables in the main analysis are as follows.
C.1. Legal Origin
Our main explanatory variable is legal origin, which captures the legal tradition of the country in which the firm is headquartered. Following La Porta
et al. (1998), La Porta, López-de-Silanes, and Shleifer (2008), Djankov et al.
(2008), and Spamann (2010), we classify legal traditions into five categories, as
denoted by the following dummy variables: English Common Origin, French
Civil Origin, German Civil Origin, Scandinavian Civil Origin, and Socialist
Origin (both current and former socialist countries). In robustness tests, we reclassify current and former socialist law countries into their presocialist legal
origin (either French civil law or German civil law).
C.2. Political Institutions
We use several country-level variables to capture the effects of political institutions, which may both shape and reflect social preferences for CSR. First,
we include Political Executive Constraints, developed by Polity IV, to proxy for
the constraints on expropriation by the political elites. As Glaeser et al. (2004)
explain, “[Political executive constraints] is the only measure that is clearly not
a consequence of dictatorial choices, and [ . . . ] can at least loosely be thought
of as relating to constraints to government” (p. 282).

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

Second, we include Corruption Control, which measures the extent to which
politicians are constrained from pursuing their self-interest (through corruption). While other political variables capture democracy and aggregate social (stakeholder) preferences, we focus on limits to corruption because they
are most closely connected to North’s (1981) conception of institutions as
“constraints.”
Third, we include a country’s Regulatory Quality from the World Bank to
proxy for the government’s effectiveness in addressing social responsibility and
market externalities in implementing policies and regulations that promote
private sector development. CSR investment may be supported or limited by a
country’s regulatory environment.
In robustness tests, we also control for a country’s capitalist model using
the Heritage Index of Economic Freedom (Economic Freedom Index), which
consists of a broad series of subindices measuring different aspects of government interference in business activities, such as government spending, fiscal
freedom, business freedom, labor freedom, and monetary freedom. Not surprisingly, these subindices are highly correlated with one another, and thus we only
include the overall score as a control, rather than the individual subindices. In
unreported regressions, we also include the subindices in the regression one at
a time; the results for our key explanatory variables do not change.
C.3. Blockholder Ownership
Including different types of blockholder ownership in our model is important
as different ownership types reflect different investor preferences. In particular,
different types of blockholders may favor different CSR policies and can use
their voting power to implement those policies. Blockholders are defined as
investors who hold more than 5% of the company’s total shares. We classify
their ownership stakes into Government Held Shares, Corporation Held Shares,
Pension Fund Held Shares, Investment Company Held Shares, Employee Held
Shares, Other Holdings, and Foreign Held Shares. The sum of all blockholder
ownership stakes equals a company’s Total Strategic Holdings. The remaining
holdings comprise Free Float Shares.
C.4. Firm-Level Financial Variables
A standard control variable is Firm Size, measured by the (logarithm of)
total assets of the company. To capture the “doing good by doing well” effect,
we also control for firm performance as proxied by the return on assets (ROA).
In robustness tests, we add the market valuation of the firm, which we capture
using Tobin’s Q (market-to-book ratio of assets, MTB Assets).
C.5. Other Country-Level Controls
In equation (1), we further control for a country’s level of economic development using the (logarithm of) GDP per capita (Ln (GDP Per Capita)) and

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866

867

Figure 1. Corporate social responsibility and legal origin by country.

a Globalization Index. GDP per capita captures income and wealth effects, as
people in richer countries are more likely to care about sustainability, whereas
those in poor countries are more worried about daily economic survival. The
globalization index captures the spillover of CSR standards across countries, as
corporations in more globalized countries are under greater pressure to comply with international conventions and principles that prescribe acceptable
corporate social conduct.
From Vigeo, we also obtain country-level sustainability ratings that comprise
the ESG scores of more than 170 sovereign countries. These ratings are based
on the analysis of more than 130 CSR risk and performance indicators in three

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

domains: (1) environmental protection, (2) social protection and solidarity, and
(3) rule of law and governance. By supplementing our firm-level CSR ratings,
these country-level ESG ratings give a more comprehensive picture of social
responsibility and stakeholder orientation around the world.
III. Results
A. Descriptive Results
We first plot in Figure 1 (Panel A) the distribution of country-level sustainability ratings on a world map using the adjusted Vigeo sustainability ratings.
Ratings are rescaled to eight categories representing the degree of a country’s
sustainable development in terms of environmental responsibility, social responsibility, and institutional responsibility (rule of law and governance), with
darker shading indicating a higher rating. In Figure 1 (Panel B), we plot the
distribution of legal origins around the world. As can be seen comparing the
two panels, countries with a higher social responsibility (sustainability) rating are more likely to be civil law countries than common law countries, with
Scandinavian countries having the highest scores.
We turn the above color maps into numbers in Table II, but here we use
firm-level CSR data and compare the mean CSR ratings for countries belonging to different legal origins. In addition to the overall CSR rating (IVA Rating)
and two general ratings on environmental and social policies (EcoValue Rating and Social Rating), we also report results for the various components of
the CSR subcategories, which represent benefits for different types of stakeholders.9 The variance of the ratings is shown in parentheses. Comparisons
of the means of the CSR indices across legal origins show that firms under
the English common law system have lower CSR scores along most ESG dimensions than those under civil law systems. Firms from the Scandinavian
and German legal origins have higher CSR scores than those from the English common law system, especially in terms of environmental issues, as indicated by EcoValue Rating and the subcategories Environment, Environmental
Management Capacity, Environmental Opportunity, Industry-Specific Carbon
Risk, Environmental Strategy, Environmental Management Systems, Environmental Accounting Reporting, Certification (e.g., ISO14000), etc. Among socialand labor-related issues, firms with a French legal origin assume more CSR
than those with an English or German legal origin, as can be seen from
the scores on Social Rating and the subcategories Human Capital, Stakeholder Capital, Employee Motivation and Development, Labor Relations, Health
Safety, Customer Stakeholder Partnerships, Human Rights Child and Forced
9 For example, the CSR benefits for shareholders and creditors can be inferred from Strategic
Governance, Strategic Capability and Adaptability, Traditional Governance Concerns, etc. CSR
benefits for employees—the recognition of human capital—are captured by Employee Motivation
Development, Labor Relations, Health and Safety, etc. The benefits for customers are summarized
by the categories Customer Stakeholder Partnerships, Intellectual Capital and Product Development, Product Safety, etc. Environmental issues are crucial to all types of stakeholders.

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868

Table II

2.65 (1.58)
2.72 (1.74)
2.65 (1.77)
2.75 (1.73)
2.64 (1.50)
4.68 (2.25)
4.55 (1.83)
5.42 (1.85)
5.47 (2.23)
5.28 (2.30)
5.57 (1.97)
5.56 (1.69)
5.93 (2.00)
5.26 (1.85)
5.45 (2.14)
5.33 (1.87)
5.21 (2.14)
5.86 (2.21)
5.12 (2.31)
5.42 (2.34)

3.15 (1.59)
3.10 (1.73)
2.92 (1.78)
2.99 (1.75)
3.16 (1.57)
5.48 (2.27)
5.22 (1.75)
5.58 (1.85)
5.91 (2.23)
5.63 (2.15)
5.31 (2.00)
5.88 (1.74)
6.30 (2.01)
5.62 (2.03)
5.51 (2.01)
5.44 (1.86)
5.46 (2.14)
5.63 (2.10)
5.09 (2.20)
5.78 (2.25)

French Origin
1.77 (1.53)
1.26 (1.21)
1.20 (1.21)
1.40 (1.36)
1.81 (1.53)
4.07 (2.28)
3.67 (2.10)
3.89 (1.57)
4.01 (2.09)
3.83 (2.17)
4.56 (2.21)
4.06 (1.67)
4.85 (2.12)
4.25 (2.25)
3.75 (1.97)
3.97 (1.25)
4.01 (2.03)
4.84 (1.88)
3.65 (2.32)
3.98 (1.96)

Socialist
Origin
2.98 (1.61)
2.83 (1.72)
3.59 (1.85)
2.84 (1.63)
3.02 (1.58)
5.17 (2.17)
4.83 (1.71)
5.49 (1.82)
6.01 (2.05)
5.76 (2.16)
4.93 (2.07)
5.44 (1.73)
5.71 (1.92)
5.51 (1.76)
5.27 (2.09)
5.23 (1.78)
5.42 (2.00)
5.51 (2.01)
5.21 (2.15)
6.18 (2.29)

German
Origin

(Continued)

3.83 (1.50)
3.93 (1.74)
3.88 (1.70)
3.85 (1.66)
3.79 (1.41)
5.63 (1.82)
5.45 (1.72)
6.66 (1.73)
6.76 (2.02)
6.38 (2.17)
6.60 (1.84)
6.39 (1.72)
6.61 (2.10)
6.13 (2.01)
6.07 (2.11)
5.78 (1.91)
6.09 (2.10)
5.28 (1.96)
5.75 (2.38)
6.34 (1.95)

Scandinavian
Origin

869

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Overall IVA Rating (full sample)
Overall IVA Rating (1999 to 2011 wave)
EcoValue Rating (1999 to 2011 wave)
Social Rating (1999 to 2011 wave)
Overall IVA Rating (2011 to 2014 wave)
Environmental Score (2011 to 2014 wave)
Social Score (2011 to 2014 wave)
Strategic Governance
Strategic Governance Strategy
Strategic Capability Adaptability
Traditional Governance Concerns
Human Capital
Employee Motivation Development
Labor Relations
Health Safety
Stakeholder Capital
Customer Stakeholder Partnerships
Local Communities
Supply Chain
Intellectual Capital Product Development

English
Origin

Overall IVA Rating is the weighted average score for different subcategories. EcoValue Rating and Social Rating are from RiskMetrics. A higher score
indicates that the company put more effort in the area. Standard deviations are in brackets.

Average CSR Score across Different Legal Origins
On the Foundations of Corporate Social Responsibility

5.17 (2.02)
5.37 (1.90)
5.10 (2.12)
5.11 (2.13)
4.66 (1.64)
5.13 (1.92)
5.22 (2.59)
4.96 (2.40)
4.80 (2.02)
4.35 (2.59)
4.07 (2.19)
4.93 (2.41)
4.00 (2.45)
3.93 (2.57)
4.03 (2.77)
3.54 (2.54)
4.18 (2.77)
2.75 (2.54)
3.51 (2.53)
5.14 (1.89)
4.38 (2.54)
4.47 (2.25)
4.20 (2.71)

5.37 (2.25)
5.61 (1.87)
5.16 (2.05)
5.00 (1.98)
4.87 (1.76)
5.09 (1.75)
4.92 (2.35)
4.52 (2.46)
5.01 (1.99)
4.39 (2.75)
4.55 (2.13)
5.34 (2.38)
4.06 (2.30)
4.68 (2.66)
4.26 (2.79)
4.26 (2.47)
4.71 (2.64)
3.07 (2.52)
4.11 (2.43)
5.17 (2.09)
4.92 (2.48)
4.93 (2.21)
4.63 (2.64)

French Origin
3.84 (2.34)
4.54 (1.85)
4.60 (2.08)
4.78 (2.08)
3.06 (1.29)
3.57 (1.38)
3.21 (1.64)
3.01 (2.08)
3.41 (1.65)
3.66 (2.35)
3.21 (1.76)
4.06 (2.13)
3.38 (2.18)
2.98 (2.20)
3.36 (2.66)
2.72 (2.18)
3.52 (2.62)
2.13 (2.11)
2.28 (1.81)
4.17 (1.62)
3.52 (1.93)
3.49 (1.83)
3.30 (2.15)

Socialist
Origin
5.39 (2.11)
5.27 (1.80)
5.11 (1.94)
4.97 (1.97)
5.49 (1.70)
5.47 (1.57)
5.25 (2.14)
5.14 (2.22)
5.63 (1.94)
4.84 (2.54)
5.46 (2.13)
6.15 (2.28)
5.09 (2.31)
5.83 (2.64)
5.35 (2.84)
5.57 (2.90)
5.67 (2.60)
3.46 (2.55)
4.94 (2.68)
5.59 (1.90)
6.06 (2.43)
5.75 (2.21)
5.57 (2.68)

German
Origin

5.88 (2.07)
5.85 (1.97)
5.98 (2.13)
5.34 (2.05)
5.70 (1.56)
6.03 (1.40)
6.02 (2.03)
5.59 (2.48)
5.83 (1.90)
5.33 (2.38)
5.59 (2.17)
6.54 (2.24)
4.90 (2.31)
5.77 (2.62)
5.20 (2.94)
5.39 (2.71)
5.69 (2.84)
3.57 (2.85)
5.36 (2.61)
6.09 (1.83)
5.98 (2.51)
5.87 (2.08)
5.65 (2.45)

Scandinavian
Origin

The Journal of FinanceR

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Product Safety
Emerging Market Strategy
Human Rights Child and Forced Labor
Oppressive Regimes
Environment (overall)
Environmental Risk Factors
Historic Liabilities
Operating Risk
Leading Sustainability Risk Indicator
Industry-Specific Carbon Risk
Environmental Management Capacity
Environmental Strategy
Corporate Governance
Environmental Management Systems
Audit
Environmental Accounting/Reporting
Environmental Training Development
Certification
Products Materials
Environmental Opportunity Factors
Strategic Competence
Environmental Opportunity
Performance

English
Origin

Table II—Continued

870

871

Labor, etc. The English common law system has higher scores than civil law
systems in the domain of the firm’s interactions with local communities and
traditional corporate governance concerns. Companies with a socialist legal
origin have the lowest levels of CSR across the board.
We further compare differences across legal origins for various aspects of
CSR using a nonparametric test (Wilcoxon rank-sum (Mann-Whitney) test).
Table III shows that the differences in ESG performance (overall and by component) are highly statistically significant across legal families, and that civil
law countries consistently score higher than common law countries along all
ESG subfields. Among the civil law countries, we find that firms in countries with a German legal origin have higher CSR scores than their counterparts with a French legal origin in terms of environmental policy (EcoValue Rating, Industry-Specific Carbon Risk, and Environmental Opportunity), but the French legal origin firms have higher CSR scores in terms of
social issues and labor relations than German legal origin companies. Finally, firms from capitalist economies attach more attention to ESG issues
than those from current and former socialist countries (Russia, China, and
some Eastern European countries). Overall, the descriptive results suggest that
there are systematic differences in various ESG ratings across different legal
origins.
B. Main Results
We now turn to regression analysis to formally test the relation between
CSR and legal origin as well as other country- and firm-level characteristics.
In Table IV, we present results using different estimation methods. Column (1)
reports OLS results using the baseline set of control variables. Column (2)
uses the same variables as in column (1) but the model is estimated by GLS.
Columns (3) to (5) extend the GLS model by including additional control variables. Columns (6) and (7) report results obtained using random-effects ordered
probit models (with some control variables missing due to convergence in maximum likelihood estimations). The dependent variable in all regressions is the
overall IVA rating at the firm level, which is a proxy for a company’s engagement
in and compliance with various environmental and social issues. Following La
Porta et al. (1998), La Porta, López-de-Silanes, and Shleifer (2008), Djankov
et al. (2008), and Spamann (2010), we take the English common law origin as
our benchmark and therefore omit it from the models, and we exclude former
and current socialist countries, which, as Aghion et al. (2010) argue, are in
transition and not in equilibrium.10 Only in a robustness test do we include
the socialist countries and recategorize them according to their presocialist legal origin (either German civil law or French civil law) (see, e.g., column (7)).
10 This is confirmed by consistent CSR underperformance of firms in (current or former) socialist
countries, which are still under an autocratic or dictatorial regime. We exclude these countries from
the sample used in our main specification, focusing on differences between common law systems
and civil law systems (and their subsystems).

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On the Foundations of Corporate Social Responsibility

Table III

85.010***
66.356***
44.281***
68.193***
16.692***
–36.843***
–45.155***
61.978***

82.855***
64.520***
45.354***
59.590***
13.235***
–30.505***
–36.963***
58.472***

IVA Rating
(2011 to 2014)
80.125***
69.198***
44.484***
37.251***
20.393***
–3.232***
–15.533***
33.561***

76.784***
74.000***
32.746***
40.801***
34.411***
–9.323***
–27.377***
46.198***

20.492***
16.631***
5.932***
30.167***
10.060***
–19.514***
–26.137***
16.994***

57.952***
15.241***
58.977***
40.474***
–30.546***
–28.764***
–8.600***
27.184***

18.915***
12.046***
5.906***
32.592***
6.623***
–23.121***
–29.329***
22.259***

EcoValue
Environmental
Rating
Social Rating
Score
Social Score
IVA Rating
(2011 to 2014) (2011 to 2014) (1999 to 2011) (1999 to 2011) (1999 to 2011)

The Journal of FinanceR

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Civil versus common legal origin
French versus English origin
German versus English origin
Scandinavian versus English origin
French versus German origin
French versus Scandinavian origin
German versus Scandinavian origin
Capitalist versus Socialist origin

Overall IVA
Rating

The Wilcoxon rank-sum (Mann-Whitney) test compares legal origins to assess whether their population firm-year mean ranks differ. *, **, and ***
indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

Nonparametric Tests on the Means of CSR Indices by Legal Origin

872

Table IV

0.468**
(0.213)
0.355***
(0.131)
0.502***
(0.177)
–0.454**
(0.175)
0.0757***
(0.025)
–0.0357
(0.024)
0.0351***
(0.0124)
–0.121
(0.354)
0.608***
(0.195)

French Civil Origin

0.521**
(0.212)
0.524***
(0.179)
0.757***
(0.188)
–0.0808
(0.101)
0.0341***
(0.010)
0.0282*
(0.0156)
0.0275**
(0.0111)
0.104
(0.155)
0.083
(0.126)

GLS

(2)

0.555***
(0.215)
0.541***
(0.176)
0.801***
(0.171)
–0.0912
(0.0941)
0.0337***
(0.0098)
0.0279*
(0.0161)
0.0271**
(0.0113)
0.0787
(0.162)
0.0748
(0.125)

GLS

(3)

0.581***
(0.216)
0.556***
(0.171)
0.800***
(0.177)
–0.0688
(0.0973)
0.0323***
(0.0100)
0.027
(0.0178)
0.0274**
(0.0111)
0.0753
(0.162)
0.0698
(0.124)

GLS

(4)

0.905***
(0.249)
0.845***
(0.188)
1.027***
(0.198)
–0.062
(0.101)
0.0328***
(0.010)
0.0263*
(0.018)
0.0337***
(0.0123)
0.0868
(0.161)
0.0338
(0.126)

GLS

(5)

0.141***
(0.032)
–0.052***
(0.019)

0.0157*
(0.008)

0.234***
(0.0168)
0.124***
(0.0125)
1.881***
(0.025)
0.0112
(0.0148)

RE Ordered
Probit

(6)

(Continued)

0.221***
(0.028)
–0.0675***
(0.022)

0.0224***
(0.00343)

1.801***
(0.0176)
0.0848***
(0.0138)
1.862***
(0.0238)
–0.00774
(0.0101)

(7)
RE Ordered
Probit (Socialist
Relabeled)

873

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Corruption Control

Regulatory Quality

Globalization Index

ROA (winsorized .05)

Ln(Total Assets)

Ln(GDP per Capita)

Scandinavian Civil Origin

German Civil Origin

Pooled OLS

DV = IVA Rating

(1)

The dependent variable (DV) is the ordinal (ranging from 0 to 6) CSR rating from MSCI IVA. Model (1) is estimated using a pooled OLS regression,
models (2) to (5) are estimated using random-effects GLS, and models (6) and (7) are estimated using random effects ordered probit. All models control
for year and industry fixed effects. Definitions of the dependent variables are in Table I and of the independent variable in Appendix A. *, **, and
*** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country level and reported in
parentheses.

Main Results on CSR and Legal Origin
On the Foundations of Corporate Social Responsibility

201,420
Yes
Yes

0.0222
(0.0227)

Pooled OLS

201,420
Yes
Yes

–0.0029
(0.0020)

GLS

(2)

201,324
Yes
Yes

–0.00284
(0.0021)
0.00554
(0.0095)

GLS

(3)

195,378
Yes
Yes

–0.00486
(0.0035)
0.00556
(0.0096)
0.0188
(0.0298)

GLS

(4)

–0.005
(0.003)
0.004
(0.010)
0.020
(0.030)
0.138**
(0.066)
193,982
Yes
Yes

GLS

(5)

195,474
Yes
Yes

0.00696
(0.00472)

–0.012***
(0.004)

RE Ordered
Probit

(6)

201,836
Yes
Yes

0.015***
(0.004)

0.00954***
(0.003)

(7)
RE Ordered
Probit (Socialist
Relabeled)

The Journal of FinanceR

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Observations
Year FE
Industry FE

Anti-Director Rights Index

MTB Assets (winsorized .05)

Economic Freedom Index

Political Executive Constraints

DV = IVA Rating

(1)

Table IV—Continued

874

875

We include industry and year fixed effects, and cluster standard errors at the
country level in all estimations.
Several important observations can be made. First, the coefficients on the
French, German, and Scandinavian civil law origins are positive and statistically significant across all specifications, regardless of the estimation method
used. The results further imply that on average firms under a civil law system
have a higher CSR score than those under the English common law system.
The economic effects are substantial: on average firms in civil law countries
have a 7% higher CSR score (or a half-grade on a 0 to 6 scale) than firms in
common law countries (columns (1) and (2)). The difference is even larger—at
more than 14%, or 0.85 to 1 of a grade—when we add more control variables
such as a firm’s investment opportunities (market-to-book ratio), the firm’s degree of shareholder orientation (Anti-Director Rights Index), and the economic
freedom index capturing the degree to which the country follows a capitalist
model (column (5)). Taken together, the results support that civil law firms
score significantly higher than common law firms on the overall IVA index. The
legal origin theory in the law and finance literature argues that common law
(French civil law) countries generally have the strongest (weakest) investor protection, financial development, and economic efficiency (La Porta et al. (1998),
La Porta, López-de-Silanes, and Shleifer (2008)). Our findings echo this theory
and are consistent with the prediction under the demand-side story that higher
CSR reflects stronger social preferences for stakeholder claims in civil law
countries.
The second main observation from Table IV is that political institutions—
Corruption Control, Political Executive Constraints, Regulatory Quality, and
Economic Freedom Index (the type of capitalist model)—are not strongly associated with firm-level CSR. GDP per capita is not a predictor of CSR, whereas
a country’s degree of globalization (whose correlation with the legal origins
dummies is low (below 20%)) is a strong predictor of firm-level CSR: companies
in more open and globalized economies have higher CSR scores.11
Looking at the firm-level variables, Table IV shows that firm size is strongly
related to CSR performance: on average larger firms invest more in CSR. The
coefficients on ROA are positive and significant in most specifications, in line
with the “doing good by doing well” hypothesis. Market valuation (Tobin’s Q)
is not strongly related with CSR, except in specification (7). We also find that
on average a firm that has stronger investor protection (a high score on the
Anti-Director Rights Index) invests more in CSR.

11 Before we conducted the regression analysis, we checked the correlations between different
explanatory variables to determine whether multicollinearity is a concern, but this is not the
case. For example, the correlations between Ln(GDP per capita) and the legal origin dummies
French Civil Origin, German Civil Origin, and Scandinavian Civil Origin are 30.2%, 8.7%, and
9.2%, respectively, and the correlations between Political Executive Constraints and the regulatory
constraint and corruption control measures are 35.6% and 32.1%, respectively.

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

C. Robustness Tests
C.1. Alternative Theories
As La Porta et al. (1998, 1999) state that legal origin may shape the ownership structure of a company, we examine whether the relation between CSR
and legal origin captures the effect of a firm’s ownership structure. To do so,
we add to the benchmark GLS model (model (2) of Table IV) total ownership
concentration and the ownership share held by different types of shareholders. The results are reported in Panel A of Table V. We find that both the
statistical and economic effects of legal origin hold after including the various
ownership variables. Furthermore, the coefficients on the ownership variables
themselves are mostly insignificant. Therefore, the percentage stakes in the
hands of different blockholders are not likely to be proxies for legal origin.
One criticism of the legal origin theory is that legal origin dummies are proxies for national culture and values, which have been shown to be strongly related to economic outcomes (Stulz and Williamson (2003), Guiso, Sapienza, and
Zingales (2006), Tabellini (2010)). To address this concern, we follow La Porta,
López-de-Silanes, and Shleifer (2008) and control for religion as well as the Hofstede cultural dimensions, which are widely used cultural indices that capture
social attitudes and norms (Hofstede and Hofstede (2005)). The six cultural
indices comprise Power Distance, Individualism, Masculinity, Uncertainty
Avoidance, Pragmatism, and Indulgence (for definitions, see Appendix A).
In addition, in line with the Weber thesis that differences between Protestantism and Catholicism in terms of work and social ethics have affected capitalist development and corporate growth (see Iannaccone (1998) for an overview
of the economics of religion), we include the binary variable Protestant, which
captures whether a country has a Protestant majority. The results are reported
in Panel B of Table V. Again, the cultural and religion variables do not make
much of a dent in the explanatory power of legal origin, and the explanatory
power of the cultural variables themselves is statistically insignificant, weak,
or not persistent. We therefore conclude that the cultural explanation does not
hold.
C.2. Alternative Dependent Variables
As mentioned above, we obtained the IVA data in two waves: the first wave
spans the period 1999 to 2011, and the second wave spans 2011 to 2014. The
overall IVA rating that we use in the above tests combines the IVA ratings from
the two waves, but we also have ratings for different dimensions of CSR for
the first wave. Thus, in additional robustness checks, we repeat the baseline
tests but replace the dependent variable in Tables IV and V—the overall IVA
rating—with (i) the general IVA scores for each of the two waves (models (1)
and (4) of Table VI) to shed light on whether possible changes in CSR measurement methodology affect the results, (ii) environmental scores capturing
a CSR focus on various ecological targets and efficiency (Environmental Score
for the 2011 to 2014 wave in model (2), RiskMetrics EcoValue Rating for the

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876

Table V

(2)
GLS

(3)
GLS

(4)
GLS

(5)
GLS

(6)
GLS

(7)
GLS

(8)
GLS

(9)
GLS

(10)
GLS

(Continued)

0.572*** 0.591*** 0.575*** 0.596*** 0.592*** 0.596*** 0.582*** 0.579*** 0.584*** 0.584***
(0.216)
(0.216)
(0.221)
(0.218)
(0.220)
(0.212)
(0.217)
(0.216)
(0.212)
(0.212)
German Civil Origin
0.540*** 0.550*** 0.538*** 0.556*** 0.551*** 0.552*** 0.549*** 0.542*** 0.549*** 0.549***
(0.165)
(0.169)
(0.169)
(0.165)
(0.171)
(0.168)
(0.170)
(0.171)
(0.170)
(0.170)
Scandinavian Civil Origin
0.811*** 0.802*** 0.792*** 0.826*** 0.804*** 0.804*** 0.800*** 0.800*** 0.799*** 0.798***
(0.169)
(0.175)
(0.180)
(0.170)
(0.179)
(0.177)
(0.180)
(0.176)
(0.178)
(0.178)
Government Held Shares %
0.0296
0.0301
(0.263)
(0.244)
Corporation Held Shares %
0.0451
0.104
(0.133)
(0.0973)
Pension Fund Held Shares %
–1.205*
–1.321*
(0.687)
(0.777)
Investment Companies Held Shares % –0.0227
0.00840
(0.138)
(0.143)
Employees Held Shares %
–0.146
–0.181
(0.389)
(0.379)
Other Holdings %
0.207
0.269
(0.210)
(0.264)
Foreign Held Shares %
0.227
0.262
(0.219)
(0.216)
Total Strategic Holdings %
0.0420
(0.111)
Total Free-float Shares %
–0.0435
(0.114)
Observations
196,232 196,232 196,232 196,232 196,232 196,232 196,232 196,232 196,232 196,232
Control variables
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Industry FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

(1)
GLS

877

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French Civil Origin

DV = IVA Rating

Panel A: Blockholder Ownership

This table repeats the GLS estimations of model (2) of Table IV but adds control variables on ownership concentration and ownership by type of
shareholder (Panel A) and cultural dimensions (Panel B). Variable definitions are given in Table I and Appendix A. *, **, and *** indicate statistical
significance at the 10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country level and reported in parentheses.

Robustness Tests: Alternative Theories

On the Foundations of Corporate Social Responsibility

185,705
Yes
Yes
Yes

0.774***
(0.282)
0.873***
(0.185)
0.660***
(0.179)
0.201
(0.155)

(1)
GLS

199,938
Yes
Yes
Yes

–0.00498
(0.00767)

0.667***
(0.226)
0.600***
(0.179)
0.749***
(0.175)

(2)
GLS

199,938
Yes
Yes
Yes

0.00178
(0.00497)

0.633***
(0.243)
0.635***
(0.233)
0.822***
(0.206)

(3)
GLS

199,938
Yes
Yes
Yes

0.00739*
(0.00407)

0.667***
(0.229)
0.445**
(0.179)
1.116***
(0.236)

(4)
GLS

199,938
Yes
Yes
Yes

0.00405
(0.00626)

0.465*
(0.268)
0.421*
(0.241)
0.796***
(0.183)

(5)
GLS

197,295
Yes
Yes
Yes

0.00926
(0.00670)

0.507**
(0.213)
0.101
(0.428)
0.762***
(0.173)

(6)
GLS

–0.00679
(0.00522)
196,628
Yes
Yes
Yes

0.579***
(0.201)
0.471**
(0.202)
0.803***
(0.175)

(7)
GLS

The Journal of FinanceR

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Observations
Control variables
Year FE
Industry FE

Hofstede Indulgence

Hofstede Long-term Orientation

Hofstede Uncertainty Avoidance

Hofstede Masculinity

Hofstede Individualism

Hofstede Power Distance

Protestant

Scandinavian Civil Origin

German Civil Origin

French Civil Origin

DV = IVA Rating

Panel B: Cultures

Table V—Continued

878

Table VI

0.695*
(0.382)
0.774***
(0.295)
1.258***
(0.192)
75,632
Yes
Yes
Yes

(11)
Environmental
Opportunity
Factors

0.699***
(0.219)
0.490***
(0.189)
0.748***
(0.275)
167,076
Yes
Yes
Yes

IVA Score
(2011 to 2014)
0.566***
(0.198)
0.445*
(0.261)
0.931***
(0.258)
167,075
Yes
Yes
Yes

0.514*
(0.311)
0.536**
(0.232)
0.727***
(0.273)
39,769
Yes
Yes
Yes

IVA Rating
(1999 to 2011)

(4)

0.389
(0.332)
0.678**
(0.273)
0.854**
(0.332)
75,054
Yes
Yes
Yes

0.0975
(0.241)
0.451*
(0.273)
0.634*
(0.370)
64,862
Yes
Yes
Yes

0.621
(0.490)
0.975***
(0.330)
1.292***
(0.407)
75,638
Yes
Yes
Yes

(12)
(13)
(14)
Leading
Sustainability Industry-Specific Environmental
Risk Indicator
Carbon Risk
Strategy

1.108***
(0.244)
0.743***
(0.213)
0.591*
(0.315)
156,621
Yes
Yes
Yes

(2)
(3)
Environmental
Score (2011 to
Social Score
2014)
(2011 to 2014)

(6)

(7)

0.720
(0.518)
1.266***
(0.417)
1.691***
(0.513)
75,689
Yes
Yes
Yes

(15)
Environmental
Management
Systems

1.087**
(0.442)
0.780***
(0.301)
1.117***
(0.349)
75,303
Yes
Yes
Yes

1.042*
(0.611)
1.385***
(0.416)
1.745***
(0.475)
75,436
Yes
Yes
Yes

(16)
Environmental
Accounting
Reporting

0.566***
(0.198)
0.445*
(0.261)
0.931***
(0.258)
51,193
Yes
Yes
Yes

0.822*
(0.433)
0.908***
(0.351)
1.300***
(0.340)
75,252
Yes
Yes
Yes

(17)
Environmental
Training
Development

0.611**
(0.306)
0.648***
(0.163)
0.815***
(0.173)
51,224
Yes
Yes
Yes

EcoValue Rating Social Rating
Product
(1999 to 2011) (1999 to 2011) Development

(5)

0.942**
(0.453)
1.048***
(0.312)
1.788***
(0.417)
75,373
Yes
Yes
Yes

Products
Materials

(18)

0.709*
(0.379)
0.743**
(0.305)
1.260***
(0.194)
75,047
Yes
Yes
Yes

Opportunity
in Cleantech

(8)

0.661
(0.490)
1.179***
(0.385)
1.380***
(0.305)
75,518
Yes
Yes
Yes

(19)
Environmental
Strategic
Competence

0.592**
(0.279)
0.305
(0.250)
0.374*
(0.201)
51,462
Yes
Yes
Yes

Labor Relations

(9)

0.542
(0.355)
0.789***
(0.286)
1.247***
(0.206)
75,236
Yes
Yes
Yes

Environmental
Performance

(20)

0.597***
(0.225)
0.607**
(0.283)
0.929***
(0.143)
50,521
Yes
Yes
Yes

Product Safety

(10)

879

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Observations
Control variables
Year FE
Industry FE

Scandinavian Civil Origin

German Civil Origin

French Civil Origin

Dependent Variable =

Observations
Control variables
Year FE
Industry FE

Scandinavian Civil Origin

German Civil Origin

French Civil Origin

Dependent Variable =

(1)

This table shows 20 different models estimated using the same methodology and the same control variables as model (2) of Table IV, but with different
CSR indices from the MSCI IVA ratings as dependent variables. The definitions are given in Table I. All regressions control for year and industry
fixed effects. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country
level and reported in parentheses.

Robustness Tests: Alternative Dependent Variables
On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

1999 to 2011 wave in model (5), Opportunity in Cleantech in model (8), Environmental Opportunity Factors in model (11), Sustainability Risk in model
(12), Industry-Specific Carbon Risk in model (13), Environmental Strategy in
model (14), Environmental Management Systems in model (15), Environmental
Accounting Reporting in model (16), Environmental Training and Development
in model (17), Environmental Strategic Competence in model (19), and Environmental Performance in model (20)), and (iii) social scores capturing a CSR
focus on employees, customers, suppliers, and the community at large (Social
score for the 2011 to 2014 wave in model (3), RiskMetrics Social Rating for
the 1999 to 2011 wave in model (6), Labor Relations in model (9), and Product
Development, Safety, and Materials in models (7), (10), and (18)). The results in
Table VI reveal that the wave-specific IVA scores and the various environmental and social indices are strongly and consistently correlated to legal origin.
Moreover, we confirm that, relative to firms with English legal origin, firms
from civil law countries have higher CSR scores. In 18 of the 20 models (the
exceptions being models (2) and (9)), firms with a Scandinavian legal origin
have the highest CSR scores.
C.3. Alternative CSR Samples
Another concern with our main analysis could be that our finding that civil
law firms have higher CSR ratings than their common law counterparts is
driven by our CSR data. Although we have shown that the results hold across
specifications with different dependent variables, such similarity could be due
to the fact that the different dependent variables are based on similar rating
methodologies (developed by MSCI). To address this concern, we repeat our
main tests using two alternative CSR samples with global coverage: (i) Vigeo’s corporate ESG (panel) data, which cover the environment, human rights,
human resources, business behavior (customers and suppliers), community
involvement, and corporate governance, and (ii) Thomson Reuters’ ASSET4
(panel) data, which comprise a company’s engagement in and compliance with
environmental and social aspects.12 Table VII shows that that our previous results largely survive: firms with a civil law origin continue to have higher CSR
scores than those with a common law origin. The only exception is in model (6),
where Corporate Governance is the dependent variable: the three civil law dummies have a negative sign, indicating that firms with an English legal origin
have higher corporate governance scores than firms with a French or German
legal origin. This finding is not unexpected in light of extant empirical evidence, as this Vigeo subindex measures traditional governance concerns that
focus on shareholder protection (rather than stakeholder protection). The fact
12 ESG information is available for more than 4,300 global companies based on more than 250
key performance indicators and more than 750 individual data points covering every aspect of
sustainability reporting. The sample includes MSCI World, MSCI Europe, STOXX 600, NASDAQ
100, Russell 1000, S&P 500, FTSE 100, ASX 300, and MSCI Emerging Market. On average,
10 years (from 2002) of history is available for most companies.

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880

Table VII

16.74***
(5.056)
12.69***
(4.680)
18.90***
(3.507)
7,765
Yes
Yes
Yes

18.58***
(6.882)
9.227**
(4.027)
12.92**
(6.202)
8,341
Yes
Yes
Yes

Environment

(2)

7.663***
(2.614)
5.787***
(1.937)
7.379***
(2.544)
4,163
Yes
Yes
Yes

3.205**
(1.379)
1.374
(0.889)
3.191**
(1.308)
5,786
Yes
Yes
Yes

(3)
(4)
Customer
Community
and Supplier Involvement
6.516***
(2.163)
3.410**
(1.326)
10.37***
(1.520)
7,707
Yes
Yes
Yes

(5)
Human
Rights

–16.12***
(3.750)
–17.86***
(3.454)
–2.223
(4.218)
8,341
Yes
Yes
Yes

(6)
Corporate
Governance

8.330*
(4.646)
12.80***
(3.414)
16.34***
(3.975)
20,692
Yes
Yes
Yes

(7)
Environment
Score

12.83***
(4.815)
3.598
(3.170)
14.27***
(5.244)
20,692
Yes
Yes
Yes

Social Score

(8)

ASSET4 ESG Sample

881

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Observations
Control variables
Year FE
Industry FE

Scandinavian Civil Origin

German Civil Origin

French Civil Origin

Dependent Variable =

(1)
Human
Resources

Vigeo Corporate ESG Sample

This table repeats the GLS estimations of model (2) of Table IV but uses alternative samples (Vigeo Corporate ESG sample and ASSET4 ESG sample)
with different ESG subindices as dependent variables (human resources, environment, customer and supplier, community involvement, human rights,
corporate governance from Vigeo Corporate ESG, and the environment and social scores from ASSET4 ESG) as defined in Appendix A. All regressions
control for year and industry fixed effects. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors
are clustered at the country level and reported in parentheses.

Robustness Tests: Alternative CSR Samples

On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

that firms with a common law origin have a stronger shareholder orientation
(i.e., stronger corporate governance) is indeed consistent with the traditional
law and finance view. In sum, the results across our various robustness tests
support the demand-side prediction that firms in civil law countries invest
more in CSR.
IV. Evidence from Scandals and Disasters
The results so far show that there is a strong and consistent correlation
between a firm’s level of CSR investment and its country’s legal origin, with
civil law firms investing more in CSR than common law firms. This is an
average effect. Based on the demand-side arguments, a potential reason why,
on average, firms in civil law countries have higher levels of CSR investment
than firms in common law countries may be that they are more responsive
to the change in the demand for CSR. This argument describes a marginal
effect. To examine the role of a “responsiveness” channel, we conduct several
quasi-natural experiments of “shocks” to CSR demand. Doing so also allows us
to control for country fixed effects (to take into account the influence of timeinvariant country-level factors) while still examining the effects of legal origin
by means of interaction terms. We estimate these tests using a differences-indifference (DiD) approach. In general, a DiD estimation can be specified as:
C SRict = Ac + Bt + Cs + β Xict + γ Ilt + ict ,

(3)

where Ac , Bt , and Cs are country, year, and sector (industry) fixed effects,
respectively, Xict are the relevant firm- and country-level controls, Ilt is the
interaction between legal origin (civil law) and the year dummy such that the
estimated impact of legal origin (civil law in year t) is captured by the OLS
estimate γ̂ , and ict is an error term. Standard errors are clustered across firms
and over time to account for serial and cross-sectional correlations.
We conduct three quasi-experiments related to unexpected corporate scandals or natural disasters, which, as we argue, move firms in the relevant industries “out of equilibrium” and magnify the costs and benefits of different
legal regimes. We deliberately choose shocks that had a huge global impact
so that we can make comparisons across legal regimes. These shocks include
the Chinese milk scandal in November 2008, the Deepwater Horizon oil spill
in March/April 2010, and the Asian earthquake and tsunami in December
2004. We distinguish two responsiveness channels of CSR. One is a consumer
channel, whereby the unexpected shocks trigger shifts in consumer demand
and changes in firms’ market share that force companies to adjust their CSR.
The other is a legal channel, whereby firms in a more CSR-friendly legal environment (stronger stakeholder orientation in the spirit of the law) tend to be
more responsive to shocks and supply more social goods. In our analyses below, we try to disentangle these two channels. We use the ASSET4 sample for
these analyses because it has detailed sub-CSR scores for items such as cash

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882

883

donations and spill and pollution controls, which directly correspond to each of
the shocks considered.
A. The Chinese Milk Scandal and Product Responsibility
The 2008 Chinese milk scandal was a food safety incident in China involving
milk and infant formulas as well as other food materials and components that
had been adulterated with melamine. Twenty-two Chinese diary companies,
including market leaders such as Mengniu, were reported to have contaminated
products. By November 2008, China reported an estimated 300,000 victims,
with six infants dying from kidney stones and other kidney damage, and an
estimated 54,000 babies hospitalized. The World Health Organization referred
to the incident as one of the largest food safety events it had faced in recent
years. The incident raised severe concerns about food safety, not only in China
but all over the world, as many food manufacturing and processing companies
import food materials and components from China or have foreign operations
in China. The European Union, European Commission, and the U.S. Food and
Drug Administration all tightened food safety checks and regulations in the
wake of this incident.
The Chinese milk scandal also raised food-related companies’ awareness
about their responsibility to ensure their product safety. We therefore use the
Product Responsibility rating of ASSET4 to compare companies’ reactions—
across legal regimes—in terms of improving their own product safety as measured by their product responsibility scores. We exclude Chinese firms from
the sample to avoid the (expectedly strong) local impact on our international
results. Column (1) of Table VIII presents the results. The DiD estimator is
the coefficient on Civil Law × Post-2009. The coefficient is positive and statistically significant with a nontrivial economic magnitude, indicating that on
average food-related companies in civil law countries improved their product responsibility performance by more than 5% (a coefficient of 5.344 on a
scale of 100) in relation to firms in common law countries. As a robustness
check, we run the same regression on the product safety rating from the IVA
sample. As can be seen in column (2) of Table VIII, the coefficient on Civil
Law × Post-2009 is still positive and significant. Given that the IVA rating is on a scale of 0 to 10, the economic magnitudes are similar across the
two regressions (5% to 7%). Taken together, the results point to a higher responsiveness of firms in civil law countries following this food product safety
scandal.
B. The Indian Ocean Earthquake and Corporate Donations
The 2004 Indian Ocean earthquake and tsunami was one of the deadliest
natural disasters in recorded history. On December 26, 2004, an undersea
megathrust earthquake triggered a series of devastating tsunamis along the
coasts of most landmasses bordering the Indian Ocean, killing over 230,000
people in 14 countries and inundating many coastal communities. The plight
of the people affected prompted a worldwide humanitarian response. In all,

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On the Foundations of Corporate Social Responsibility

Table VIII

Panel B:
Indian Ocean
Tsunami

1,212
Yes
Yes
Yes
Yes

5.344**
(2.693)

2,380
Yes
Yes
Yes
Yes

0.667***
(0.196)

10,353
Yes
Yes
Yes
Yes

16.87*
(9.563)

1,522
Yes
Yes
Yes
Yes

6.393**
(2.801)

(4)
Spill and
Pollution
Control

1,509
Yes
Yes
Yes
Yes

7.578**
(2.944)

1,522
Yes
Yes
Yes
Yes

6.587**
(2.691)

(6)
Clean
Environmental Energy
R&D
Products

(5)

7.679***
(2.533)
1,522
Yes
Yes
Yes
Yes

(7)
Spill and
Pollution
Control

(8)

7.393*
(4.081)
1,509
Yes
Yes
Yes
Yes

6.208*
(3.387)
1,522
Yes
Yes
Yes
Yes

(9)
Clean
Environmental Energy
R&D
Products

Panel C:
Deepwater Horizon Oil Spill

The Journal of FinanceR

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Observations
Control variables
Country FE
Year FE
Industry FE

Civil Law × Post-2010

Civil Law × Year-2010

Civil Law × Year-2005

Civil Law × Post-2009

(1)
(2)
(3)
Product Responsibility
Product
Cash
Dependent Variable = (ASSET4) Safety (IVA) Donation/Cash

Panel A:
Chinese Milk Scandal

The dependent variables are product responsibility (from ASSET4) and product safety (from MSCI IVA) ratings in Panel A; the amount of corporate
donations (from Datastream) in Panel B; and the spill and pollution control index, the environmental R&D investment score, and the clean energy
product score (from ASSET4) in Panel C. The differences-in-differences (DiD) estimator is the coefficient on Civil Law × Post-2009 in Panel A, the
coefficient on Civil Law × Year 2005 in Panel B, and the coefficients on Civil Law × Year 2010 and Civil Law × Post-2010 in Panel C. The control
variables are the same as in Table VII. All regressions control for country, year, and industry fixed effects. *, **, and *** indicate statistical significance
at the 10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country level and reported in parentheses.

Evidence from Scandals and Disasters: Direct Effects on CSR

884

885

the worldwide community donated more than $14 billion in humanitarian aid;
while some funds came from national governments, most were corporate cash
donations.
While corporations regularly donate money in normal times, the earthquake
and tsunami led to a surge in corporate donations as part of the relief effort. Godfrey (2005) and Patten (2008) argue that philanthropic giving (as
a response to disasters) is perceived as a genuine manifestation of a firm’s
underlying social responsiveness. We therefore compare cash donations (including both direct cash giving and cash giving via a corporate foundation)
made in 2005, right after the disaster, by corporations in our sample. We calculate corporate cash donations following the standard approach as in Masulis
and Reza (2015), and focus on cash donations as a proportion of total cash:
Ln(1 + cash donations/total cash) × 103 . Column (3) of Table VIII reports the
results from this experiment with the same control variables as before. Here,
the coefficient on Civil Law × Year 2005 is the DiD estimator. The reason
for interacting the civil law dummy with a year dummy rather than with a
postdisaster dummy (e.g., Post-2005) is that, unlike the food scandal, which
likely shifted CSR demand and had lasting effects on corporate CSR policies,
donations are disaster-specific and are made only in the year of or following
a disaster, rather than in all subsequent years. (Below, in a placebo test, we
examine the role of donation timing). Again, the interaction coefficient is positive and statistically significant, indicating that firms in civil law countries
donated on average more money than those in common law countries right
after the Asian earthquake disaster. This finding suggests that a firm’s underlying social responsiveness (as manifested by philanthropic giving after natural
disasters) is stronger in civil law countries than in common law countries.
C. The Deepwater Horizon Oil Spill and Corporate Environmental Concerns
The Deepwater Horizon oil spill, also known as the BP oil disaster, began
on April 20, 2010 in the Gulf of Mexico on the BP-operated Macondo Prospect,
as a result of the Deepwater Horizon oil rig exploding and sinking. This incident is considered the largest accidental marine oil spill in the history of
the petroleum industry. The spill had a severe environmental impact. The
U.S. government estimated the total discharge at 4.9 million barrels (210 million U.S. gallons, or 780,000 m3 ), which directly polluted 68,000 square miles
(180,000 km2 ) of ocean and had a devastating effect on marine life in the
Gulf.
The Deepwater Horizon oil spill was an environmental shock to all energyrelated industries in terms of the environmental consequences of their production and operations. We therefore compare, across legal regimes, corporations’
environmental CSR activities after the oil spill. Using the detailed CSR indices of ASSET4, we measure a company’s environmental CSR investment
with three variables most closely related to oil spills and pollution controls
under the ASSET4 environment classification, all of which are on a scale of
100: (1) Spill and Pollution Control, which captures a company’s direct risk

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

management policies related to oil spills and pollution, (2) Environmental R&D
Spending, which captures a company’s efforts in developing new technologies
that are more environmentally friendly, and (3) Clean Energy Products, which
captures whether a company substitutes its energy-intensive products with
products using new technologies and clean energies. Columns (4) to (6) of Table
VIII report the results using similar tests as in columns (1) and (2), except that
the DiD estimator is now the coefficient on Civil Law × Post-2010. The coefficients on the three environmental performance variables are all positive and
statistically significant, indicating that on average energy-related firms in civil
law countries upgraded various aspects of their environmental performance—
by strengthening their spill and pollution controls, investing more in environmental R&D, and developing more clean-energy products—by 7% (7-grade
increase on a 100-point scale) relative to energy-related firms in common law
countries. In a robustness check we interact the civil law dummy with the
year 2010 dummy (columns (7) to (10)), and find similar results, both statistically and economically. Taken together, these results suggest that companies
from different legal regimes respond differently to the oil spill shock, with such
differences in responses both immediate and persistent over time.
D. Placebo Tests
We conduct several placebo tests on alternative industries and event years
for the scandals and disasters analyzed above to rule out potential industryand year-specific confounding effects. For the food scandal, we estimate identical models for several nonfood industries (including the oil and gas industry).
Similarly, for the oil spill disaster, we estimate identical models for several
nonoil-and-gas industries (including the food industry). The alternative industries other than the food and the oil and gas industries include software and
IT services, professional and commercial services, and financials. For the Indian Ocean earthquake and tsunami disaster, which triggered corporate donations from firms across all industries, we rerun the model for alternative years
during our sample period. The results for these placebo tests are reported in
Table IX, with Panels A and B presenting results for product responsibility
and environmental performance ratings in alternative industries after the food
scandal and the oil spill disaster, respectively, and Panel C presenting results
on corporate donations for alternative years. We find that the milk scandal had
no impact on nonfood industries for firms in civil law countries, as the coefficients on interaction Civil law × Post-2009 are not statistically significant.
This finding supports the results presented in Table VIII and suggests that
firms’ CSR reactions in the area of food safety are specific to the food industry.
Likewise, we note that the oil spill disaster did not affect other industries in
terms of corporate environmental actions after the disaster. The placebo tests
on alternative years for the Indian Ocean earthquake and tsunami also support
our previous results: the interactions between the civil law dummy and years
not affected by a global disaster are not statistically significant, in contrast to
the interaction between the civil law dummy and the postdisaster year (Year

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886

Table IX

4.159
(3.846)
1,517
Yes
Yes
Yes
Yes

Oil and Gas
(1)
0.291
(4.723)
665
Yes
Yes
Yes
Yes

Software and IT Services
(2)

–4.583
(4.669)
780
Yes
Yes
Yes
Yes

Professional and Commercial Services
(3)

(Continued)

15.87
(13.53)
1,754
Yes
Yes
Yes
Yes

Financials
(4)

887

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Observations
Control variables
Country FE
Year FE
Industry FE

Civil Law × Post-2009

DV = Product Responsibility

Panel A: Chinese Milk Scandal: Alternative Industries

This table reports placebo tests related to the results of Table VIII. In Panel A, the dependent variable is the product responsibility score (from
ASSET4) for which differences-in-differences (DiD) estimation is conducted for industries not expected to be affected by the Chinese milk scandal.
In Panel B, a DiD estimation is performed for the spill and pollution control index, the environmental R&D investment score, and the clean energy
product score (from ASSET4) on industries not expected to be affected by the oil spill disaster. In Panel C, a DiD estimation is performed for cash
donations on years not expected to be affected by the tsunami disaster. The control variables are the same as in Table VIII. All regressions control for
country, year, and industry fixed effects. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors
are clustered at the country level and reported in parentheses.

Evidence from Scandals and Disasters: Placebo Tests

On the Foundations of Corporate Social Responsibility

0.746
(0.950)
2,381
Yes
Yes
Yes
Yes

4.667
(3.747)
1,296
Yes
Yes
Yes
Yes

2.508
(1.981)
2,382
Yes
Yes
Yes
Yes

(3)
Clean
Environmental Energy
R&D
Products

(2)

1.114
(0.807)
663
Yes
Yes
Yes
Yes

(4)
Spill and
Pollution
Control
4.001
(4.970)
652
Yes
Yes
Yes
Yes

5.968
(4.140)
667
Yes
Yes
Yes
Yes

(6)
Clean
Environmental Energy
R&D
Products

(5)

2.535
(1.580)
773
Yes
Yes
Yes
Yes

(7)
Spill and
Pollution
Control
9.553
(9.962)
264
Yes
Yes
Yes
Yes

–5.261
(4.543)
780
Yes
Yes
Yes
Yes

(9)
Clean
Environmental Energy
R&D
Products

(8)

Professional and Commercial Services

Panel B: Deepwater Horizon Oil Spill: Alternative Industries
Software and IT Services

0.812
(0.942)
216
Yes
Yes
Yes
Yes

(10)
Spill and
Pollution
Control

–2.383
(6.074)
101
Yes
Yes
Yes
Yes

(Continued)

–8.779***
(2.367)
1,759
Yes
Yes
Yes
Yes

(12)
Clean
Environmental Energy
R&D
Products

(11)

Financials

The Journal of FinanceR

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Observations
Control variables
Country FE
Year FE
Industry FE

Civil Law × Post-2010

Dependent Variable =

(1)
Spill and
Pollution
Control

Consumer Goods

Table IX—Continued

888

10,353
Yes
Yes
Yes
Yes

11.82
(18.03)

(1)

10,353
Yes
Yes
Yes
Yes

16.87*
(9.563)

(2)

10,353
Yes
Yes
Yes
Yes

–15.90
(9.813)

(3)

10,353
Yes
Yes
Yes
Yes

2.971
(6.119)

(4)

10,353
Yes
Yes
Yes
Yes

10.79
(9.493)

(5)

10,353
Yes
Yes
Yes
Yes

5.840
(7.049)

(6)

10,353
Yes
Yes
Yes
Yes

–24.80
(19.77)

(7)

10,353
Yes
Yes
Yes
Yes

–0.233
(6.389)

(8)

10,353
Yes
Yes
Yes
Yes

4.664
(11.88)

(9)

–0.888
(7.778)
10,353
Yes
Yes
Yes
Yes

(10)

889

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Observations
Control variables
Country FE
Year FE
Industry FE

Civil Law × Year-2013

Civil Law × Year-2012

Civil Law × Year-2011

Civil Law × Year-2010

Civil Law × Year-2009

Civil Law × Year-2008

Civil Law × Year-2007

Civil Law × Year-2006

Civil Law × Year-2005

Civil Law × Year-2004

DV = Cash Donation/Cash

Panel C: Indian Ocean Tsunami: Alternative Years

Table IX—Continued

On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

2005), which is positive and significant. This implies that the difference in cash
donations between common law firms and civil law firms is likely to be driven
by year-specific disaster events.
E. Changing Market Shares Following Scandals
As mentioned above, differences in CSR responsiveness across legal regimes
may be driven by changes in firms’ market share, that is, consumers in some
countries may react more to these shocks, with their demand for CSR shifting
more, which would force companies to react more strongly in terms of improving
their CSR performance (de Bettignies and Robinson (2015)). Differences in such
consumer demand shifts may coincide with differences across legal regimes. An
alternative explanation is that firms in more CSR-friendly legal regimes (i.e.,
civil law countries) respond more per unit of shock, which is a direct legal
channel.
To disentangle these two channels, we investigate whether the above shocks
are associated with changes in firms’ market share, whether market share
changes, if any, are further related to changes in CSR practices, and whether
these relations differ across legal regimes. The Chinese milk scandal and the
Deepwater Horizon oil spill disaster provide distinct settings in terms of industry composition, and thus are ideal for investigating the impact of the consumer
channel. In particular, the oil and gas industry is dominated by large international firms originating from different legal regimes (such as Total S.A. in
France, BP in the United Kingdom, ExxonMobil in the United States, Royal
Dutch Shell in the Netherlands, and Statoil in Norway), whereas the food
industry comprises many smaller local firms. The food scandal may shift consumer demand away from the larger food companies (which are tracked by CSR
data providers) toward small, local producers (which are largely untracked),
whereas domestic consumer demand for oil and gas is relatively inelastic due
to the oligopolistic nature of the local industry (though consumers may shift
their demand across large international firms following an energy scandal). If
our findings above regarding differences in CSR responsiveness across legal
regimes are driven mainly by changes in market share (i.e., companies change
their CSR practices in response to a decline in market share as consumers shift
to other companies), we would expect variation in the effect of the shock on market shares for food/energy, as well as in the effect of market share changes on
firms’ CSR practices across legal regimes.
We test this consumer channel by using the change in a company’s market share of sales revenue in its industry following the shock as a proxy for
consumer demand shifts. For the food scandal, we define an “industry” as the
domestic industry of all companies in a certain year, while for the oil spill disaster, we define an “industry” as the global industry of companies within our
sample13 in a certain year. Panel A of Table X reports results on changes in the
13 Market shares for oil and gas companies are calculated on an “in-sample” basis: all firms in
the ASSET4 database with a CSR score are considered. When we calculate the market shares on

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890

Table X

3,216
No
Yes
Yes

–20.18***
(2.318)

3,216
Yes
Yes
Yes

–6.387***
(2.379)

(2)

3,216
No
Yes
Yes

–1.433
(1.022)

(3)

3,216
Yes
Yes
Yes

1.265
(1.194)

(4)

0.127
(0.236)
–0.139
(0.126)
1,184
Yes
Yes
Yes

Civil Law
Countries
(5)

(Continued)

–0.0350
(0.0304)
–0.0282
(0.0224)
1,193
Yes
Yes
Yes

Common Law
Countries
(6)

DV = Product Responsibility
(ASSET4)

891

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Observations
Year FE
Country FE
Industry FE

Post-2009 × Market Shares

Market Shares

Year 2009 × Civil Law

Year 2009

Post-2009 × Civil Law

Post-2009

(1)

DV = Domestic Market Shares

Panel A: Chinese Milk Scandal and Domestic Market Shares

This table reports results on changes in market shares in the food industry and the oil and gas industry following the Chinese milk scandal (Panel A)
and the oil spill disaster (Panel B), respectively. Each panel also reports results of the relation between changes in firm CSR indices such as product
responsibility and spill and pollution control scores and changes in consumer demand (proxied by changes in market share) across different legal
regimes following these two shocks. Each model includes country, industry, and year fixed effects. *, **, and *** indicate statistical significance at the
10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country level and reported in parentheses.

Evidence from Scandals and Disasters: The Role of Consumer Demand

On the Foundations of Corporate Social Responsibility

2,186
No
Yes
Yes

–0.0012***
(0.0004)

2,186
Yes
Yes
Yes

–0.0028
(0.0019)

(2)

2,186
No
Yes
Yes

–0.0017***
(0.0004)

(3)

2,186
Yes
Yes
Yes

–0.003
(0.002)

(4)

28.10
(23.01)
–20.99
(14.42)
359
Yes
Yes
Yes

Civil Law
(5)

–5.790
(32.82)
23.09
(25.81)
1,154
Yes
Yes
Yes

Common Law
(6)

DV = Spill and Pollution Control

The Journal of FinanceR

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Observations
Year FE
Country FE
Industry FE

Post-2010 × Market Shares

Market Shares

Year-2010 × Civil Law

Year-2010

Post-2010 × Civil Law

Post-2010

(1)

DV = International Market Shares

Panel B: Deepwater Horizon Oil Spill Scandal and International Market Shares

Table X—Continued

892

893

domestic market shares of our sample companies, which are mostly large firms,
in response to the Chinese milk scandal and the correlation between these market share changes and the product responsibility score (ASSET4) of companies
in food-related industries after the scandal. We find that the domestic market
share of our sample firms (mostly large firms with CSR ratings) declines following the scandal, likely toward smaller, local food producers (which do not
have CSR ratings), and that this effect arises not in the year of the scandal but
over the five-year period subsequent to the scandal. We next test whether the
shifts in our sample firms’ market share following the food scandal are related
to the product responsibility scores of food sector firms in civil and common law
countries in the postscandal period. We find that the changing market shares
after the scandal are not significantly correlated with changes in CSR in either
civil law or common law countries, which works against the argument that differences in CSR responsiveness between common law and civil law countries
are driven by a decline in market shares. Panel B of Table X reports results on
changes in international market shares in response to the oil spill and their
correlation with oil and gas companies’ spill and pollution control scores after
the shock. Subsequent to the oil spill shock, we observe a small though significant change in market share in firms operating in the traditional energy sector
(which could result from a consumer demand shift away from the legacy energy
firms toward firms active in alternative energy). A large shift in market share
is unexpected given that alternative energy production, while growing, is still
a small part of the market relative to traditional carbon-based energy production. Panel B also shows that the market share shift does not differ between
firms with civil or common law origin: we do not find a significant correlation
between changes in oil and gas companies’ market shares after the spill and
changes in the spill and pollution control index. Taken together, these results
support the legal channel for the differences in CSR responsiveness across legal
regimes that we document.
V. Economic Mechanisms
The results above show that systematic differences in CSR across legal
regimes are not likely to be driven by changing market shares. In addition, in
our benchmark models in Table IV, we find that institutional variables such as
Regulatory Quality, Political Executive Constraints, and Anti-Director Rights
Index are not statistically significant and that their inclusion does not affect
the significance of the legal origin dummies, which suggests that they are not
likely to be the channels through which legal origin operates. In this section,
we directly test additional possible mechanisms at both the country level and
the firm level as outlined in Section I. These tests are based on the idea that
CSR in civil law countries is more rule-driven whereas CSR in common law
countries relies more on ex ante discretion and ex post settlement.
all listed firms (on a global scale), irrespective of the availability of a CSR score, the results do not
change.

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR

We first use the shareholder litigation risk index developed by La Porta et al.
(1998) and Djankov et al. (2008) to test for the ex post settling up mechanism
in common law countries (as opposed to the rule-based mechanism in civil law
regimes). When the risk of shareholder litigation is low, firms are more willing
to engage in CSR activities that often go beyond what is required by law, and
common law countries tend to utilize ex post shareholder litigation mechanisms
to a greater extent to empower shareholders to sue corporate directors (La
Porta et al. (1998), Issacharoff and Miller (2009), Cox and Thomas (2009),
Gelter (2012)). Similarly, we investigate whether the level of CSR is higher
when a firm’s decision-making process is ex ante insulated from the pressures
of its (different types of) shareholders through the presence of a supermajority
vote requirement in its corporate charter or bylaws, which is more prevalent
under civil law systems (Hopt (1997), Cheffins and Black (2006)).
Another mechanism of interest relates to regulations and the direct involvement of the government in business. As argued by La Porta et al. (1999) and
Botero et al. (2004), legal origin proxies for the state’s tendency to intervene
in economic life: civil law countries tend to rely more on regulation and state
intervention, whereas common law countries tend to rely more on markets and
contracts. To test for this mechanism, we use several country-level indices including an employment laws index, a collective bargaining laws index, and the
prevalence of state involvement in the economy.
We conduct our tests on these economic mechanisms in two stages: in the
first stage we regress each of the channel variables on the civil law dummy, and
in the second stage we regress the overall CSR rating on the channel variable
“predicted” from the first stage, that is, on the variation in the channel variables
that is explained by legal origin. Control variables are included in both stages.
This approach is akin to an IV approach except that the civil law dummy is not
treated as the IV for the channel variable, as it is possible that civil law can
operate on CSR through channels other than those that we consider here.
Table XI presents the results. We find that, in the first stage, civil law origin
is negatively correlated with shareholder litigation risk (model (1)), and positively correlated with the presence of supermajority rules (model (3)), labor
and union laws (models (5) and (7)), and the degree of state involvement in
the economy (model (9)). In the second stage, we find that shareholder litigation risk is negatively correlated with the level of CSR (model (2)), whereas
the other channel variables are all positively correlated with CSR (models (4),
(6), (8), and (10)). These results are consistent with the notion that civil law
countries rely more heavily on rules-based mechanisms that restrict behavior
ex ante and reflect a stronger focus on (or demand for) stakeholder orientation
in these societies, which implies that rule-based mechanisms are related to
higher levels of CSR. We again point out that this analysis is not conclusive
as other channels could potentially explain the link between legal origin and
CSR, and civil law may function through other mechanisms that are positively
related to firms’ CSR. Nevertheless, the significance in both stages is indicative
of greater reliance on ex ante constraints and less ex post settling up in civil
law countries driving the link between civil law regimes and CSR.

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894

Table XI

(3)

(4)

(5)

(6)

199,769
Yes
Yes
Yes

–0.490***
(0.0013)

199,769
Yes
Yes
Yes

–1.174***
(0.059)

69,799
Yes
Yes
Yes

0.2895***
(0.0068)

69,799
Yes
Yes
Yes

1.702***
(0.0983)

200,492
Yes
Yes
Yes

0.2405***
(0.0006)

200,492
Yes
Yes
Yes

2.362***
(0.119)

200,492
Yes
Yes
Yes

0.2745***
(0.0004)

(7)
DV =
Collective
Relations
Laws

(9)

(10)

200,492
Yes
Yes
Yes

2.069***
(0.104)

134,424
Yes
Yes
Yes

0.0336***
(0.0003)

15.55***
(1.353)
134,424
Yes
Yes
Yes

DV = IVA DV = State DV = IVA
Rating
Involvement
Rating

(8)

895

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Observations
Control variables
Year FE
Industry FE

State Involvement

Collective Bargaining Laws

Employment Laws

Supermajority

Shareholder Litigation

Civil Law Origin

(2)

DV =
DV =
Shareholder DV = IVA DV = Super- DV = IVA Employment DV = IVA
Laws
Rating
Litigation
Rating
majority
Rating

(1)

This table reports results on potential mechanisms (“channels”) behind the link between legal origin and CSR. The channel variables include the
shareholder litigation index, supermajority rule, the employment laws index, the collective bargaining laws index, and state involvement in the
economy. Variable definitions are provided in Appendix A. Each set of tests contains two stages of regressions (but not an IV regression). In the first
stage, a channel variable is regressed on the civil law origin dummy; and in the second stage, the overall IVA rating is regressed on the channel
variable “predicted” from the first-stage regression. The same control variables as in model (2) of Table IV are included in both stages. *, **, and
*** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are clustered at the country level and reported in
parentheses.

Economic Mechanisms
On the Foundations of Corporate Social Responsibility

The Journal of FinanceR
VI. Conclusions

La Porta, López-de-Silanes, and Shleifer (2008, p. 326) claim that “Legal
origins—broadly interpreted as highly persistent systems of social control
of economic life—have significant consequences for the legal and regulatory
framework of the society, as well as for economic outcomes.” Motivated by this
insight, in this paper we examine whether legal origin helps explain crosscountry variation in an increasingly important business activity, namely, CSR.
We assess a firm’s CSR by using proxies for corporate stakeholder concerns,
such as environmental and social policies, and by analyzing large-scale public
and proprietary databases covering over 25,000 securities of large corporations
around the world. We find strong support for the legal origin explanation of
CSR scores, much more so than for alternative explanations, such as CSR’s
relation with social preferences, regulatory quality, political institutions, and
culture at the country level and ownership structure, corporate governance,
and financial performance at the firm level. CSR scores are higher in civil law
countries than in common law countries, and on average companies with a
Scandinavian legal origin have the highest CSR scores. This is consistent with
demand-side arguments that CSR reflects social preferences for good corporate
behavior and a stakeholder orientation, and that such social preferences are
more embedded in rule-based mechanisms that restrict firm behavior ex ante,
mechanisms that are more prevalent in civil law countries. Such rule-based
managerial constraints are less common in common law countries where ex
post settling up mechanisms (i.e., judicial resolutions) are more important. In
additional evidence we find that the positive link between civil law origin and
CSR can be explained by, among other potential channels: lower shareholder
litigation risk, the presence of supermajority rule in a firm, stronger labor regulations, and a high degree of state involvement in business. Evidence from
exogenous scandals and disasters further suggests that companies in civil law
countries are more responsive than those in common law countries in terms of
improving their CSR practices when these shocks occur, and that this responsiveness is not likely to be driven by shifts in market share.
The relevance of our findings is twofold. At the macro level, our results shed
light on the role of legal origin in driving financial and other economic outcomes,
a question subject to debate since La Porta et al. (1998) first introduced this
thesis (e.g., Rajan and Zingales (2003), Roe (2006), La Porta, López-de-Silanes,
and Shleifer (2008), Spamann (2010)). Still, while the debate in the law and
finance literature focuses mostly on the protection of investor rights as well
as economic freedom and efficiency based on contracting and institutional arrangements as governed by legal rules (areas in which the common law origin
appears to be “superior”), little is known about how similar mechanisms relate
to the welfare of other stakeholders. We show that the common law system
supports CSR to a lesser extent than civil law regimes. This is consistent with
La Porta et al.’s premise: the common law tradition emphasizes shareholder
primacy and a private market-oriented strategy of social control, and perhaps
because of this emphasis, it is also less stakeholder-oriented. Stakeholder rights

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896

897

are usually protected by rules and a state-desired approach to social control.
Of course, CSR may be a result of both rules and discretion, as we find that
the level of CSR is highest under the Scandinavian legal regime, which lies
somewhere between heavily rule-based and discretion-oriented systems.
At the micro level, our findings contribute to our understanding of what
drives CSR, which has recently attracted much interest in finance. While existing studies focus mostly on the financial and strategic motives for CSR in
specific countries and in specific economic settings, we extend the scope of CSR
research to a global scale by using several large CSR samples with international coverage to analyze the determinants of CSR at the country level, a
question that has received little attention to date. In addition, we show that
our results hold for both CSR engagement and CSR compliance, which suggests that CSR does not merely focus on corporate strategic actions to boost
financial performance (engagement), or compliance with the rules. Rather, both
engagement and compliance are systematically related to differences in legal
regimes across countries. This focus on the legal contexts underlying CSR also
contributes to the broader theme of corporate governance, especially to the
shareholder-stakeholder tradeoff in modern corporations.
We caution that none of our arguments or findings are meant to suggest that
the equilibrium level of “total” social responsibility is higher in civil countries.
Rather, the results simply show that on average common law societies invest
less in CSR. Indeed, some recent studies consider the extent to which CSR
crowds out the provision of public goods provided by other actors (Graff Zivin
and Small (2005), Baron (2008)). In this sense, the higher levels of CSR in
civil law countries may reflect constraints to a larger degree than managerial
objectives. Therefore, firms in different countries may have different valuemaximizing levels of CSR, and it is possible that the legal regimes in some
countries can constrain their firms from achieving such value-maximizing levels, either due to regulations or by shaping a firm’s attitude toward stakeholders via governance devices. Overall, the level of CSR in a country reflects
the intersection of the supply of socially responsible behavior by firms and the
demand for CSR practices by society, and our findings suggest that a country’s legal origin may be a primary force behind the equilibrium result. This
result underscores the profound role that the legal regime plays in economic
life and suggests that CSR—an increasingly important business activity—is
fundamentally related to the legal origin of a country.
Initial submission: December 8, 2014; Accepted: July 28, 2016
Editors: Bruno Biais, Michael Roberts, and Kenneth J. Singleton

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On the Foundations of Corporate Social Responsibility

Appendix A: Definitions of Independent Variables
Variable

Definition
Laws and Regulation

Legal Origins

Anti-Director
Rights Index
(ADRI)

Shareholder
Litigation

Employment
Laws Index

Collective
Bargaining
Laws Index

The legal origin of the company law or commercial code of each country in
which the focal firm is headquartered. We distinguish five major legal
origins: English common law, French commercial code (civil law),
German commercial code (civil law), Scandinavian civil law, and
socialist (former or current) law. In alternative specifications, socialist
law is classified as either French civil law (e.g., Russian Federation) or
German civil law (e.g., China). Source: La Porta et al. (1998), Djankov
et al. (2008), La Porta, López-de-Silanes and Shleifer (2008), and
Spamann (2010).
The Anti-Director Rights Index (ADRI) was first developed by La Porta
et al. (1998) as a measure of investor protection against corporate
management, and later revised by La Porta et al. (2008) and Spamann
(2010). All three ADRIs consist of the same six key components: (1)
proxy by mail allowed, (2) shares not blocked before shareholder
meeting, (3) cumulative voting/proportional representation, (4)
oppressed minority protection, (5) preemptive rights to new share
issues, and (6) percentage of share capital to call an extraordinary
shareholder meeting. Each component is a dummy variable and the
ADRI is formed by aggregating the value of all six components. The
index ranges from 0 to 6, whereby a higher value of the index indicates
stronger shareholder protection. Source: La Porta et al. (1998), La Porta,
López-de-Silanes and Shleifer (2008), and Spamann (2010).
The shareholder litigation index is from the “judicial remedies” component
of the ADRI and measures whether shareholders can challenge
resolutions of the board and/or management if they are “unfair,
prejudicial, oppressive, or abusive.” It equals one if the company law or
commercial code grants shareholders either a judicial venue to challenge
the decisions of management or of the assembly or the right to step out
of the company by requiring the company to purchase their shares when
they object to certain fundamental changes, such as mergers, asset
dispositions, and changes in the articles of incorporation, and zero
otherwise. Minority shareholders are defined as those shareholders who
own 10% of share capital or less. Source: La Porta et al. (1998), La Porta,
López-de-Silanes and Shleifer (2008), and Spamann (2010).
This index measures the protection of labor and employment laws,
calculated as the average of alternative employment contracts, the cost
of increasing hours worked, the cost of firing workers, and dismissal
procedures. Source: Botero et al. (2004).
This index measures the protection of collective bargaining laws as the
average of labor union power and collective disputes. Source: Botero
et al. (2004).
(Continued)

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The Journal of FinanceR

898

899

Appendix A—Continued
Variable
Political
Executive
Constraints

Corruption
Control

Regulatory
Quality

Economic
Freedom
Index

GDP per Capita

Globalization
Index

Definition
Political Institutions
The Political Executive Constraints (Decision Rules) Index consists of the
following dimensions: (1) Unlimited Authority: There are no regular
limitations on the political executive’s actions (as distinct from irregular
limitations such as the threat or actuality of coups and assassinations);
(2) Intermediate Category; (3) Slight to Moderate Limitation on Political
Executive Authority: There are some real but limited restraints on the
executive; (4) Intermediate Category;
(5) Substantial Limitations on Political Executive Authority: The
executive has more effective authority than any group to which is it is
accountable but the executive is subject to substantial constraints that
group imposes on it; (6) Intermediate Category; (7) Executive Parity or
Subordination: Accountability groups have effective authority equal to
or greater than the executive in most areas of activity. Source: Polity IV.
The extent to which public power is exercised for private gain, including
petty and grand forms of corruption, as well as the “capture” of the state
by elites and private interests. Coded from –2.5 to 2.5, with higher
values corresponding to better governance outcomes. Source: World
Governance Indicator—World Bank.
The ability of the government to implement sound policies and regulations
that promote private sector development. Coded from –2.5 to 2.5, with
higher values corresponding to higher levels of regulatory quality.
Source: World Governance Indicator—World Bank.
The Heritage Index of Economic Freedom focuses on four key aspects of
the economic environment over which governments typically exercise
policy control: rule of law (including property rights and freedom from
corruption), government size (including fiscal freedom and government
spending), regulatory efficiency (including business freedom—the
efficiency of government regulation of business, labor freedom, and
monetary freedom), and market openness (including trade freedom,
investment freedom, and financial freedom). The index ranges from 0 to
100, with a higher score indicating the country has a higher degree of
freedom (e.g., 0 indicating “repressive” and 100 indicating “negligible
government interference”). More detailed definitions of each individual
category of freedom can be found at: www.heritage.org. Source: Heritage
Index of Economic Freedom.
Economic Development
GDP per capita is gross domestic product divided by midyear population.
GDP is the sum of the gross value added by all resident producers in the
economy plus any product taxes and minus any subsidies not included in
the value of the products. It is calculated without making deductions for
the depreciation of fabricated assets or for the depletion and degradation
of natural resources. Data are in current U.S. dollars. Source: World
Bank.
The KOF Index of Globalization measures three main dimensions of
globalization: (1) economic, (2) social, and (3) political. In addition to the
three indices measuring these dimensions, an overall index of
globalization and subindices are also calculated, which capture (1)
actual economic flows, (2) economic restrictions, (3) data on information
(Continued)

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On the Foundations of Corporate Social Responsibility

The Journal of FinanceR
Appendix A—Continued

Variable

State Involvement

Power Distance

Individualism

Masculinity/
Femininity

Uncertainty
Avoidance

Pragmatism

Indulgence/
Restraint

Protestant

Government Held
Shares %
Corporation Held
Shares %

Definition
flows, (4) data on personal contact, and (5) data on cultural proximity.
Data are available on a yearly basis over the period 1970 to 2010. A
higher score indicates a higher degree of globalization. Source: Swiss
Federal Institute of Technology Zurich (ETH).
Fraction of nonagricultural GDP due to state-owned enterprises (SOEs).
Source: World Bank.
Culture
“Power distance” is defined as the extent to which the less powerful
members of institutions and organizations within a country expect and
accept that power is distributed unequally. A higher score indicates a
large power distance between individuals. Source: Hofstede and
Hofstede (2005).
“Individualism” refers to the degree of interdependence among members of
a group and defines people’s self-image in terms of “I” or “We.” In
individualist societies, people focus on themselves and their immediate
family whereas in collectivist societies people belong to “in-groups” that
take care of them in exchange for loyalty. A higher score indicates more
individualism. Source: Ibid.
A high score on the “masculinity/femininity” dimension indicates that a
masculine society is driven by competition, achievement, and success,
with success being defined by the “winner” or “best-in-field.” A low score
means that the dominant values in the feminine society consist of caring
for others and quality of life. A feminine society is one where quality of
life is the sign of success and standing out from the crowd is not
admirable. Source: Ibid.
“Uncertainty avoidance” captures how a society deals with the fact that
the future is uncertain and the extent to which the members of a culture
feel threatened by ambiguous or unknown situations and have created
beliefs and institutions that try to avoid uncertainty. A higher score
implies a higher level of uncertainty avoidance. Source: Ibid.
“Pragmatism” describes how society reconciles some links with its past
while responding to the challenges of the present and future. Normative
societies that score low, prefer to maintain time-honored traditions while
viewing societal change with suspicion. Societies with a high score
encourage thrift and efforts in modern education as a way to prepare for
the future. Source: Ibid.
This dimension captures the extent to which people try to control their
desires and impulses, based on the way they were raised. Relatively
weak control scores high on “Indulgence” and relatively strong control
scores high on “Restraint.” Source: Ibid.
A binary variable that indicates if the country has a Protestant majority or
not. Source: Chen (2013).
Ownership and Board Structure
The percentage of total shares held by a government or government
institution if these holdings amount to 5% or more of the company’s total
shares. Source: Datastream.
The percentage of total shares held by one company in another if these
holdings amount to 5% or more of the company’s total shares. Source:
Datastream.
(Continued)

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900

901

Appendix A—Continued
Variable

Definition

Pension Fund Held The percentage of total shares held by pension funds or endowment funds if
Shares %
these holdings amount to 5% or more of the company’s total shares.
Source: Datastream.
The percentage of total shares held as long-term strategic holdings by
Investment
investment banks or institutions seeking a long-term return if these
Company Held
holdings amount to 5% or more of the company’s total shares. Holdings by
Shares %
hedge funds are not included. Source: Datastream.
Employees Held
The percentage of total shares held by employees, or by those with a
Shares %
substantial position in a company that provides significant voting power
at an annual general meeting (typically family members) if these holdings
amount to 5% or more of the company’s total shares. Source: Datastream.
Other Holdings %
The percentage of total shares held strategically, and outside one of the
above categories (government, corporations, pension funds, investment
companies, employees), if these holdings amount to 5% or more of the
company’s total shares. Source: Datastream.
Foreign Held
The percentage of total shares held by a shareholder domiciled in a country
Shares %
other than that of the issuer if these holdings amount to 5% or more of the
company’s total shares. Source: Datastream.
Total Strategic
The percentage of total shares held strategically and not available to
Holdings %
ordinary investors if these holdings amount to 5% or more of the
company’s total shares. Holdings of 5% or more held by the hedge fund
owner type or the investment advisor/hedge fund owner type are regarded
as active, and not counted as strategic. Total strategic holdings represent
the sum of all the above categories (government, corporations, pension
fund, investment company, employees, other holdings, foreign held, etc.).
Source: Datastream.
Total Free Float
The percentage of total shares available to ordinary investors or the total
Shares %
number of shares less the strategic holdings as defined above. Source:
Datastream.
Supermajority
Dummy variable equal to one if the company has a supermajority vote
Rule
requirement (75%) or qualified majority for amendments of charters and
bylaws or lock-in provisions. Source: ASSET4 (Thomson Reuters),
BoardEx, and Orbis.
Financial Variables
ROA
Return on assets: net income divided by total assets. Source: Compustat
Global and Compustat North America, cross-validated and supplemented
with Datastream.
Tobin’s Q
The sum of the market value of equity and the book value of debt, divided by
the sum of the book value of equity and the book value of debt (MTB
assets). Source: Datastream.
Firm Size
The logarithm of total assets. Total assets reported in local currencies are
converted to U.S. dollars using the corresponding year-end exchange
rates. Source: Compustat Global and Compustat North America,
cross-validated and supplemented by means of Datastream.
Market Shares
The market share, calculated as the company’s sales revenue as a
proportion of the total sales revenues of its industry.

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On the Foundations of Corporate Social Responsibility

IVA

2.390
2.437
3.606
3.231
3.117
2.407
2.000
1.691
3.380
3.159
3.111
3.000
2.102
2.757
2.088
4.467
2.000
2.906
3.396
3.115
2.769
1.126
2.848
3.861
1.971
2.205
3.142
3.559
3.689
2.000
2.433

United Arab Emirates
Netherlands Antilles
Argentina
Austria
Australia
Aruba
Azerbaijan
Barbados
Bangladesh
Belgium
Burkina Faso
Bulgaria
Bermuda
Brazil
Bahamas
Botswana
Belarus
Canada
Switzerland
Côte d’Ivoire
Chile
China
Colombia
Costa Rica
Curaçao
Cyprus
Czech Republic
Germany
Denmark
Dominican Republic
Egypt

English
French
French
German
English
French
French
English
English
French
French
Socialist
English
French
English
English
French
English
German
French
French
Socialist
French
French
French
English
Socialist
German
Scandinavian
French
French

Legal Origin
372
135
648
1,431
18,237
108
4
81
50
1,720
27
44
1,866
5,233
147
107
24
17,851
6,326
139
1,317
5,165
961
101
314
44
607
7,557
2,013
17
356

Observations
Republic of Korea
Kuwait
Cayman Islands
Kazakhstan
Lebanon
Sri Lanka
Lithuania
Luxembourg
Latvia
Morocco
Monaco
Macao
Malta
Mauritius
Malawi
Mexico
Malaysia
Namibia
Nigeria
Netherlands
Norway
New Zealand
Oman
Panama
Peru
Papua New Guinea
Philippines
Pakistan
Poland
Puerto Rico
State of Palestine

Country
2.652
3.056
2.689
0.870
5.000
3.362
4.577
3.031
3.941
3.272
4.000
1.543
2.494
2.400
5.815
2.376
2.039
5.173
4.809
3.520
3.685
3.669
2.089
3.225
3.285
2.588
2.001
3.311
2.752
2.339
3.056

IVA
German
French
English
French
French
English
French
French
German
French
French
French
French
French
English
French
English
English
English
French
Scandinavian
English
French
French
French
English
French
English
Socialist
French
English

Legal Origin

(Continued)

6,948
18
4,668
92
27
94
26
2,657
17
305
11
140
87
35
27
2,644
3,615
81
89
6,758
1,736
1,515
45
111
855
80
867
209
1,168
401
18

Observations

The Journal of FinanceR

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Country

Appendix B: MSCI IVA Sample Country (Region) Distribution
902

IVA

3.673
3.817
2.000
3.882
3.000
3.450
5.000
2.209
4.278
4.105
2.438
1.786
2.974
3.130
2.607
2.748
2.459
1.057
1.990
1.600
3.142
2.264
3.982
4.000
3.040
4.642

Spain
Finland
Faroe Islands
France
Gabon
United Kingdom
Georgia
Guernsey
Ghana
Gibraltar
Greece
Hong Kong
Croatia
Hungary
Indonesia
Ireland
Israel
Isle of Man
India
Iceland
Italy
Jersey
Jamaica
Jordan
Japan
Kenya

French
Scandinavian
French
French
French
English
German
English
English
English
French
English
German
Socialist
French
English
English
English
English
Scandinavian
French
English
English
French
German
English

Legal Origin
4,528
2,166
5
9,954
27
35,437
8
521
54
76
995
7,304
78
442
2,104
2,897
1,008
106
5,475
40
5,992
1,452
56
26
30,779
159

Observations
Portugal
Paraguay
Qatar
Romania
Serbia
Russian Federation
Saudi Arabia
Sweden
Singapore
Slovakia
El Salvador
Togo
Thailand
Tunisia
Turkey
Trinidad and Tobago
Taiwan
Ukraine
Uganda
United States
Uruguay
Venezuela
Virgin Islands, British
Virgin Islands, United States
South Africa
Zambia

Country
3.339
4.519
2.794
3.236
0.000
1.908
3.690
3.969
2.894
3.411
3.118
5.000
2.647
4.000
2.205
4.368
1.792
2.822
5.725
2.460
6.000
3.119
1.534
1.364
3.131
4.380

IVA
French
French
French
Socialist
Socialist
Socialist
English
Scandinavian
English
Socialist
French
French
English
French
French
English
German
French
English
English
French
French
English
English
English
English

Legal Origin

1,077
54
136
187
24
2,296
29
4,500
3,665
248
17
1
1,302
9
1,473
19
4,233
309
51
157,085
10
84
1,831
22
4,776
158

Observations

903

15406261, 2017, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.12487 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Country

Appendix B—Continued
On the Foundations of Corporate Social Responsibility

40.44
52.58
50.99
27.66
10.12
44.5
7.5
30.22
18
15.55
44.32
18.59

50.67
30.25

39.85
18.48
42.54
14
39.64
19.66
4
9.33
20.87

Human
Resources

43.64
50.95
43.79
34.33
30.97

32.23
33.33
27.5
39.99
41.19

23.56
15
8.15
49.8
33.41

42.35

40.04
36.18
42.77
22.5
28.25
34.15
44.5
23.11
25.81
49.4

Customer
and Supplier

55.93
62.27
47.24
27
12.29
42

46
41.05
30
49.83
15.59
19.33
51.33
39.14

22.11
27.81
50.55

Environment
40.87
68.1
40.29
24
37.25
60.17
19
26.86
37.39
35.15
49.67
48.01
28
66.37
40.25
34.7
30.33
37.75
27.14
47.5
35.94
33.96
42.14
41.87
21.47

Corporate
Governance

36.31
41.24
36.18
41.97
35.6

30.16
35.08
37.92
19
39.07
28.5
39.68
46.65
41.89
41.25
35.99
27.33

38.81
38.3
40.33
35
40.76
42.38

Community
Involvement
33.63
29.54
39.28
35.5
31.53
29.83
26
27.64
25.94
34.92
22
38.09
24
39.69
46.75
43.13
34.38
25.45
56.43
25
29.81
28.76
24.31
40.45
29.5

Human
Rights
German
English
French
English
French
English
English
French
Socialist
French
Socialist
Scandinavian
French
Scandinavian
French
German
French
English
Socialist
Scandinavian
English
French
English
French
German

Legal
Origin

(Continued)

103
259
179
4
72
272
3
22
54
13
3
119
2
168
1,423
898
47
208
7
4
52
25
90
395
1,114

Observations

The Journal of FinanceR

15406261, 2017, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.12487 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Austria
Australia
Belgium
Bermuda
Brazil
Canada
Cayman Islands
Chile
China
Colombia
Czech Republic
Denmark
Egypt
Finland
France
Germany
Greece
Hong Kong
Hungary
Iceland
India
Indonesia
Ireland
Italy
Japan

Country

Appendix C: Vigeo Corporate ESG Sample Country (Region) Distribution

904

26.49
0
47.51

23
39.08
27.83
11.71
32.79
41.61
42.63
28.78
14.25
18

12.4
9
25.06

38.79
14
33.44
14.56
24.47
27.16
40.87

Environment

43.33
30
38.67
33
45.8
42
18.75
14.67
43.1
45.39
47.41
15.47
19.5

20.41
28.83
7
34.42
25.14
25.42
38.7
7.42
39.93
50

Human
Resources

28
27.75
48.2
27.33
33
27.79
40.32
48.58
39.09
26.08
32.57
27.5
32.22
27
41.37

29.84
36.33
26
34.45
38.67
41.06
46.74
36.11
35.19

Customer
and Supplier
26.46
32.57
48.29
28.49
6.56
48.4
61.98
71.54
61.38
32
32.67
39.08
36.83
39.55
49.84
54.63
33.49
58.88
53.38
19.99
36.64
25.19
48.85
27.25
69.33

Corporate
Governance
36.62
30.95
37.23
40.45
46
42.2
40.75
29.56
47.77
39
39.27
32.67
42.91
28.88
39.14
41.37
40.81
41.79
35.47
34.79
31.37
34.5
37.78
31.5
37.19

Community
Involvement
26.44
25.46
25.69
30.86
31.72
30.87
40.26
25
44.52
28
23.92
24.67
39.88
28.78
27.24
31.67
41.77
45.2
36.02
25.46
25.5
24.81
27.91
24.75
34.97

Human
Rights
German
French
English
French
French
English
French
English
Scandinavian
French
French
Socialist
French
Socialist
English
English
French
Scandinavian
German
German
English
French
English
English
English

Legal
Origin

96
32
35
35
98
262
403
13
94
1
12
12
84
20
92
48
427
237
427
74
22
16
2,201
4
1,482

Observations

905

15406261, 2017, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/jofi.12487 by Department Of Geological Sciences, Wiley Online Library on [19/03/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Republic of Korea
Luxembourg
Malaysia
Mexico
Morocco
Namibia
Netherlands
New Zealand
Norway
Peru
Philippines
Poland
Portugal
Russian Federation
Singapore
South Africa
Spain
Sweden
Switzerland
Taiwan
Thailand
Turkey
United States
United Arab Emirates
United Kingdom

Country

Appendix C—Continued
On the Foundations of Corporate Social Responsibility

19.65
43.29
44.46
53.16
55.02
47.59
52.05
33.41
25.59
34.40
39.18
48.56
48.45
37.39
14.55
72.26

71.45
58.25
35.42
30.27
73.29
29.02
47.16
45.46
43.04
38.44
52.92
38.18
52.16
34.92

France
Germany
Greece
Hong Kong
Hungary
Iceland
India
Indonesia
Ireland
Israel
Italy
Japan
Jordan
Kazakhstan

Overall CSR
Rating

75.70
67.07
47.10
33.72
76.18
20.45
51.60
41.95
42.65
42.65
53.05
61.62
60.71
15.74

38.32
38.13
51.84
54.88
55.19
37.64
49,82
43.66
33.38
34.52
30.20
48.72
56.43
44.24
19.29
73.25

Environmental
Rating

76.36
67.16
49.62
35.51
80.80
36.06
57.93
60.83
39.33
39.33
62.93
45.47
62.99
27.17

25.68
38.77
50.40
49.63
67.72
38.65
53.02
45.61
32.78
40.94
36.71
60.01
52.69
33.76
27.22
66.86

Social Rating

French
German
French
English
Socialist
Scandinavian
English
French
English
English
French
German
French
French

French
German
English
French
French
English
French
French
Socialist
French
English
Socialist
Scandinavian
French
French
Scandinavian

Legal Origin

1,212
1,068
300
1,800
48
36
960
300
216
168
708
5,196
12
12

12
4,020
252
336
1,008
3,864
24
252
984
108
12
48
324
12
132
324

Firm-Year
Observations
Kuwait
Luxembourg
Malaysia
Mexico
Morocco
Netherlands
New Zealand
Nigeria
Norway
Oman
Peru
Philippines
Poland
Portugal
Qatar
Russian
Federation
Saudi Arabia
Singapore
South Africa
South Korea
Spain
Sri Lanka
Sweden
Switzerland
Taiwan
Thailand
Turkey
United Kingdom
United States
Zimbabwe

Country

19.22
34.66
66.17
47.12
66.26
51.25
62.79
57.88
29.02
55.76
44.33
64.32
51.91
11.75

18.92
55.00
42.32
38.96
21.57
75.30
49.47
7.18
56.90
27.00
41.33
39.59
33.22
67.52
10.77
37.52

Overall CSR
Rating

32.12
33.58
56.74
62.00
68.54
51.09
66.58
58.71
44.74
47.93
48.36
59.63
40.22
38.42

24.30
58.48
41.12
46.03
20.13
68.86
45.42
10.89
55.26
27.42
31.05
36.07
33.62
66.20
12.87
39.92

Environmental
Rating

25.65
35.60
73.06
56.77
73.82
66.59
63.91
56.98
36.30
56.73
52.90
63.16
44.17
35.57

36.60
52.83
50.21
49.47
53.42
75.36
42.40
19.71
58.87
33.00
34.41
40.79
42.06
73.95
24.64
50.64

Social Rating

English
English
English
German
French
English
Scandinavian
German
German
English
French
English
English
English

French
French
English
French
French
French
English
English
Scandinavia
French
French
French
Socialist
French
French
Socialist

Legal Origin

72
648
1,092
1,212
696
12
660
852
1,536
264
288
4,776
14,436
12

48
60
540
324
36
540
144
12
300
12
12
252
312
144
24
408

Firm-Year
Observations

The Journal of FinanceR

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Abu Dhabi (UAE)
Austria
Australia
Belgium
Brazil
Canada
Channel Islands
Chile
China
Colombia
Cyprus
Czech Republic
Denmark
Dubai (UAE)
Egypt
Finland

Country

Appendix D: ASSET4 ESG Country (Region) Coverage

906

907

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On the Foundations of Corporate Social Responsibility

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The Journal of FinanceR
910


==> JFE01 - Pricing of sustainability-linked bonds.txt <==
Journal of Financial Economics 162 (2024) 103944

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/finec

Pricing of sustainability-linked bonds✩
Peter Feldhütter a ,∗, Kristoffer Halskov b , Arthur Krebbers c
a

Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A4.02, 2000 Frederiksberg, Denmark
Department of Finance, Copenhagen Business School, Solbjerg Plads 3, D4.17, 2000 Frederiksberg, Denmark
c
Department of Accounting and Finance, Strathclyde Business School, 199 Cathedral Street, Glasgow G4 0QU, United Kingdom
b

ARTICLE

INFO

Dataset link: Pricing of Sustainability-Linked Bo
nds Dataset (Reference data)
JEL classification:
G12
Keywords:
ESG
Sustainability-linked bond
Corporate bonds
Step-up coupon
Sustainium

ABSTRACT
We examine the pricing of sustainability-linked bonds (SLBs), where the cash flows depend on the bond issuer
achieving one or more Environmental, Social and Governance (ESG) goals. Investors are willing to accept a
1–2bps lower yield due to the bond’s ESG label, providing evidence of investors caring about environmental
impact. Furthermore, we find the average probability of missing the target is 14%–39% so firms set ESG targets
that are easy to reach. We find that the SLB market is efficient: the prices of SLBs depend strongly on the size
of the potential penalty and there is no evidence of mispricing. Finally, our results suggest that SLBs serve as
financial hedges against ESG risk.

1. Introduction
Sustainability has become a central concern for governments, corporations, regulators and investors. A number of financial securities,
particularly debt instruments, designed to align financial incentives
with ESG objectives have come to existence in the past decade. For
example, sustainable bonds where revenues from the bond issue are
limited to funding ESG investments, have grown tremendously in recent
years. Critics argue that companies have no direct financial incentive
to act ESG-friendly once such bonds are issued. As a potential solution to this incentive problem, firms have recently begun to issue
sustainability-linked bonds (SLBs). In contrast to sustainable bonds
there are no limitations on how the proceeds are used, but bond cash
flows are tied to the company achieving future ESG goals. In a typical
SLB structure, the firm commits to a future carbon reduction target,
and if the target is not met, the bond’s coupon increases. Compared
to standard sustainable bonds, SLBs may be more effective at directing
companies to contribute to a sustainable economy. However, if firms
choose easy targets or SLBs are mispriced as Kölbel and Lambillon
(2023) find, SLBs will not work as intended.

In this paper, we extensively examine the pricing of SLB. We calculate the SLB price premium as the price difference between an SLB
and a synthetic identical ordinary bond with no ESG label and find (1)
investors are willing to pay a premium for the ESG label itself, (2) there
is a strong relation between the SLB price premium and the penalty size
for missing the target, (3) the average SLB price premium is less than
the sum of penalties, i.e. ‘‘no arbitrage’’, (4) the average probability
of meeting the target is high at 61%–86%, and (5) evidence that SLBs
serve as hedges against ESG risk.
We calculate the SLB price premium as the price difference between
the SLB and an ordinary bond. To take into account differences in
coupon rates between the SLB and ordinary bonds, we start by calculating an SLB yield premium and then convert it to an SLB price premium.
The SLB yield premium is calculated in the secondary market as the
difference in yield spread between an ordinary non-labelled bond and
an SLB, both issued by the same firm. Specifically, on a daily basis, we
match each SLB with two non-labelled bonds that have a longer and
shorter maturity and interpolate the non-labelled bonds’ yield spreads
to generate a non-SLB synthetic yield spread with the same maturity
as the SLB. The difference between the synthetic yield spread and the

✩ We thank Dimitris Papanikolaou who was the editor for this article and an anonymous referee for very useful comments. We are also grateful for valuable
comments and suggestions received from Jens Dick-Nielsen, Thomas Geelen, Lena Jaroszek, David Lando, Lasse Heje Pedersen and seminar participants at
Copenhagen Business School. Peter Feldhütter gratefully acknowledges support from the Danish Finance Institute (DFI) and the Center for Big Data in Finance
(Grant no. DNRF167).
∗ Corresponding author.
E-mail addresses: pf.fi@cbs.dk (P. Feldhütter), kh.fi@cbs.dk (K. Halskov), arthur.j.krebbers@strath.ac.uk (A. Krebbers).

https://doi.org/10.1016/j.jfineco.2024.103944
Received 13 September 2023; Received in revised form 6 September 2024; Accepted 6 September 2024
Available online 12 September 2024
0304-405X/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

SLB yield spread is the SLB yield premium. We convert the SLB yield
premium to an SLB price premium,

assumption about the firm’s commitment, that the future commitment
is the same as the historical commitment, the probability of missing
the target is only 39%. This suggests that targets are indeed too soft
and business-as-usual, interpreting business-as-usual as continuing a
historical trajectory in the future.
Finally, we estimate the risk premium associated with ESG risk
for the SLBs with ESG-linked cash flows. To do so, we first regress
the yield sustainium on firm characteristics for the subset of SLBs
with no ESG-linked cash flows, and use the regression coefficients to
estimate the yield sustainium for the larger sample. Then, we use the
estimated yield sustainium to calculate the price of a synthetic SLB
bond – sustainium-only price – with the same maturity and coupon, but
without ESG-linked cash flows. We compute the price of the optional
ESG cash flows as

SLB price premium = SLB bond price - ordinary bond price,
using our pricing model.
We first investigate if investors are willing to pay a markup for the
ESG label itself. Evidence from the literature on green bonds has established that investors are willing to pay a markup for a green bond label
(Zerbib, 2019; Caramichael and Rapp, 2024; Feldhütter and Pedersen,
2024 and others), implying that ESG investors accrue non-pecuniary
benefits through indirect ownership of green assets (Bonnefon et al.,
2022). Since SLBs are not tied to specific assets, a green bond markup
does not imply an SLB markup. If the impact of investment decisions
is important for investors (Moisson, 2022), however, they would pay
a premium for SLBs because the bonds incentivize firms to take ESGfriendly actions. Testing if investors are willing to pay a markup for
the ESG label of SLBs on its own is difficult since one would need to
separate the value of potential additional cash flows to bondholders
from the value of the ESG label itself. To circumvent this difficulty, we
use a subset of SLBs that have a penalty defined in terms of donations
or carbon offset. These bonds are ideal for studying the value of the
ESG label, because there are no potential additional payments to bond
holders and therefore the SLB premium must be due to the ESG label
itself. We find a positive but modest SLB yield premium of 1.9 bps
– which we call the sustainium – for this subset of SLBs providing
empirical support for the importance of impact investing.
Turning next to our main sample of SLBs where investors do receive
additional cash flows if the firm fails to reach the ESG target(s), we
investigate the size and determinants of the SLB price premium. We
find that the SLB price premium is strongly positively related to the
penalty size — the sum of penalty cash flows in case the firm fails to
reach the ESG target(s). This result indicates that, as basic financial
theory predicts, the market accounts for the size of optional cash flows.
Surprisingly, Kölbel and Lambillon (2023) report that the SLB premium
is larger than the sum of penalties. This may be the case if investors
misprice cash flows or are willing to pay a sufficiently large sustainium.
If so, firms can engage in greenwashing by issuing overpriced SLBs with
no intention of reaching the ESG target(s). We find that the average
SLB premium is significantly less than the sum of penalties and, thus,
our results suggest no evidence of such greenwashing potential in the
market.
Investors and regulators voice concerns that targets ‘‘lack ambition
and are too easy to meet’’,1 which is why the International Capital Market Association recommends that targets are ambitious and
‘‘beyond a Business as Usual trajectory’’ (ICMA, 2020). In a survey
of professional investors in 2021, investors’ main concern regarding
SLBs is the ‘‘risk of greenwashing’’.2 If correct, firms can engage in
greenwashing behaviour by issuing SLBs with targets that are easy
to reach and then earn the sustainium. We investigate whether these
concerns are warranted by estimating the probability of firms missing their ESG target(s). To do so, we exploit that many SLB issuers
follow the International Capital Market Association’s guidance and
publish historical values of Key Performance Indicators (KPIs) on which
the targets are based. We assume that the KPI follows a generalized
Wiener process, calibrate the parameters to historical values and use
the parameters to calculate the probability that the future target will
be missed. We calculate the probability under different scenarios and
we find that the average probability of missing the target is only
14%–39%, depending on assumptions. Even under the most relaxed

ESG cash flow price = SLB bond price - sustainium-only bond price,
and use the estimates of probabilities of missing the target in conjunction with our pricing model to[ compute the expected present value of
the optional ESG cash flows, E ESG cash flows]. The ESG risk premium
is then
[
ESG risk premium = E ESG cash f lows]−ESG cash f low price.
There is no consensus on the sign of the ESG risk premium, and for the
most common targets related to greenhouse gas (GHG) emissions, there
are arguments for both a positive and negative risk premium.3 The risk
premium would be positive if, when the economy experiences a positive
growth shock, output and GHG emissions increase (Nordhaus, 1977).
In these states of high consumption, firms are more likely to miss their
ESG targets and SLBs pay out additional cash flows. The risk premium
would be negative if global warming, caused by GHG emissions, results
in higher risk of climate disasters leading to a negative macro-economic
shock (Bansel et al., 2019). In such a scenario, SLBs act as a hedge
against climate risk, since firms have not reduced GHGs and SLBs pay
out extra cash flows.
We find that the average risk premium is negative and statistically
significant in most specifications, providing evidence that SLBs serve as
financial hedges against ESG risk. However, the evidence for a negative
risk premium is weak for SLBs where targets are tied to GHC emissions,
suggesting that the negative risk premium is not driven by a negative
climate change risk premium.
The theoretical model uses the intensity-based method proposed
by Lando (1998) and Duffie and Singleton (1999). There is a stochastic
riskfree interest rate, the firm defaults with a stochastic default intensity and, in case of default, bondholders receive a stochastic recovery
rate. Investors may have a stochastic convenience of holding an SLB,
which we denote the sustainium. The firm sets one or more future
ESG targets and for each target there is an incremental set of future
cash flows bondholders receive if the target is not met. We derive the
bond price and provide closed-form solutions in the case of a constant
interest rate, default intensity, sustainium and recovery rate.
Our work is most closely related to Kölbel and Lambillon (2023)
who compare the SLB yield at issuance with the issuance yield of a
non-SLBs from the same issuer issued no more than five years apart.
We refine their approach as we match the secondary market SLB yield
spread with an interpolated yield spread from non-SLB bonds from the
same issuer on the same day. Thus, while we compare SLB and nonSLB yield spreads from the same issuer on the same day, Kölbel and
Lambillon (2023) compare SLB issuance yields with yields of ordinary
bonds that are on average issued 1 1/2 years earlier and changes in
riskfree rates, macro variables, and issuer-specific credit risk introduce
noise in their results. Furthermore, in contrast to their paper, we
estimate a model, estimate the sustainium, the probability of hitting
the target and investigate ESG risk premiums. We focus on pricing

1
See for example Reuters, November 9, 2022, ‘‘Explainer: Decoding COP27:
the many shades of green bonds’’ (https://www.reuters.com/business/cop/
decoding-cop27-many-shades-green-bonds-2022-11-09/.
2
https://gsh.cib.natixis.com/api-website-feature/files/download/11818/
SLB-Survey-Short-Results_2021-03-FinalVersion_LAST.pdf.

3

2

See Giglio et al. (2021) for an extensive review.

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Fig. 1. SLB issued by General Mills in 2021. This figure illustrates the possible cash flows of the SLB issued by General Mills on October 14, 2021. The bond has a fixed semi-annual
coupon of 1.125% and if General Mills fails to achieve a target reduction of 21% in scope 1 and scope 2 greenhouse gas emissions by 2025, the semi-annual coupon increases by
0.125%.
Table 1
General Mill’s greenhouse gas emissions. Historical data for scope 1 and scope 2
greenhouse gas emissions by General Mills, provided in the second party opinion by
Institutional Shareholder Services Inc ahead of General Mill’s issue of a 10-year SLB
on October 2021.

SLBs in this paper and do not study the optimal design of SLBs. Our
anecdotal evidence indicates that the size of penalties relative to overall
interest expenses is low, making it unlikely that the value of the ESGrelated penalties in itself have a material impact on firms’ transition
to a greener economy, and Berrada et al. (2022) provide a theoretical
framework for understanding the relation between firm effort and size
of penalties. Erlandsson and Mielnik (2022) provide a pricing model
for SLBs and calibrate it to two bonds at issuance while we have an
extensive sample of SLB bonds over a longer period.4
The structure of the paper is the following. In Section 2 we provide
an overview of the market for SLBs. Section 3 describes the model
and estimation approach, while Section 4 details the data. Section 5
describes the empirical results and Section 6 concludes.

GHG scope 1 and 2 emissions
(million metric tons of CO2e)
YoY reduction (%)

2018

2019

2020

2025 (Target)

0.88

0.71

0.75

0.59

−19.32

5.63

$2.25 mio if General Mills miss both targets. For comparison, the firm’s
interest expenses in 2021 was $430.9 mio according to their annual
report, so missing sustainable-linked targets would only increase their
interest rate expenses by 0.52%. The firm may issue more SLBs with
higher penalties in the future as the market matures, but the current
penalties are too small to affect the firm in a material way.
A recent example of triggered SLB penalties is Enel. The Italian
energy company triggered a penalty of 25 bps on ten SLBs on April
23, 2024 by missing its greenhouse-gas emissions targets (Fitch, 2024).
The penalties imply an additional interest expense of 𝐸𝑈 𝑅 25 mio
($26.8 mio) amounting to 0.44% of Enel’s overall interest expenses
(according to their 2023 annual report), suggesting that the SLB market
has not yet matured to an extent that penalties have a sizeable impact
on total interest expenses.
It is advised by the International Capital Market Association that
firms publish at least three years of historical values of their target
KPIs and the historical greenhouse gas emissions of General Mills are
shown in Table 1. General Mills must reduce emissions by 32.9% in
2025 compared to 2018. A reduction of 19.3% was made in 2019 alone,
but this was followed by an increase of 5.6% in 2020.
The development of the SLB market is depicted in Fig. 2. Both the
number and notional amount issued have dramatically increased, as
shown in Panel A. Between 2018 and March, 2024, 722 SLBs have been
issued. The total notional amount issued for the 722 SLBs is 273 USD
billions. Panel B shows that half of the bonds were issued in Europe,
followed by 33 percent in Asia and 12 percent in North America.
Different KPIs, KPI targets, penalty types, and penalty sizes are used
to structure SLBs as Table 2 shows. The most common KPI measures
greenhouse gas emissions (GHG), intended to lower scope 1, 2, or
3 greenhouse gas emissions for the entire company or a particular
segment of the firm’s operations. The second-most popular group of
KPIs is related to renewable energy, such as an increase in the portfolio
of renewable energy assets for energy companies or a greater reliance
on renewable energy for non-energy firms. A significant number of KPIs
are concerned with maintaining or raising a company’s ESG rating.
Finally, some KPIs are related to diversity, typically the proportion
of minority groups to the majority. For instance, on September 13,
2021 Suzano Austria GmbH issued an SLB with one of the KPI targets
being to reach a level of at least 30% women in leadership roles by

2. Sustainability-linked bonds
A variety of new debt securities have been introduced in recent
years to aid firms make the transition to a greener and more socially
responsible economy. For instance, the proceeds from green bonds are
restricted to green projects, the proceeds from blue bonds are used for
investments in healthy oceans, while funds raised from social bonds are
used for projects that have a positive impact on society. Such debt securities do not impose any limitations on the company’s future behaviour
once the underlying projects have been funded. Sustainability-linked
bonds (SLBs), a more recent innovation that was introduced in 2018,
are fundamentally different from other ESG-related securities. SLBs
directly link the cash flows of the bond to one or several ESG-related
Key Performance Indicators (KPIs) rather than placing restrictions on
how bond proceeds are used. This implies that the firm have financial
incentives to act in an ESG-friendly manner after the bonds are issued.
For the purpose of illustration, consider a typical SLB: a 10-year
bond issued by General Mills on October 14, 2021, with a fixed coupon
rate of 2.25% and semi-annual payments. General Mills’ annual coupon
rate will increase by 25 basis points starting on April 14, 2026, if it is
unable to reduce scope 1 and scope 2 greenhouse gas emissions by 21
percent by the target date May 25, 2025, in comparison to a benchmark
for 2020. The cash flows of the bond is illustrated in Fig. 1.
To assess how large the penalty is relative to the size of General
Mills, we note that the offering amount of the SLB is $500 mio, so
the annual penalty amounts to $1.25 mio. Additionally, General Mills
had a sustainability-linked loan with a notional amount of $1000 mio
and a maximum penalty of 10 bps. Overall, this implies a penalty of

4
More broadly, there is a growing literature on green bonds including Zerbib (2019), Baker et al. (2022), Caramichael and Rapp (2024), Flammer
(2021), and Larcker and Watts (2020). Pedersen et al. (2021), Pastor et al.
(2021) and Feldhütter and Pedersen (2024) investigate pricing in presence of
ESG investors and Engle et al. (2020), Ilhan et al. (2021), Huynh and Xia
(2021), Seltzer et al. (2022), Bolton and Kacperczyk (2021, 2023), Oehmke
and Opp (2024) and Avramov et al. (2022) look at the pricing of ESG risk.

3

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Fig. 2. This figure shows the growth of the SLB market since its inception in 2018. The left (blue) bars show the number of SLBs issued each year while the right (green) bars
show the notional amount of SLBs issued (in USD billions). The data is from Bloomberg and includes all bonds that have a sustainability-linked indicator equal to 1. The data for
2024 ends March 4. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2025. ‘‘Other’’ KPIs includes metrics that are company-specific, such as
decreased food and water waste for food and beverage companies or
the building of affordable housing for construction companies.
Table 2 Panel B lists type of penalties and we see that most SLBs
are accompanied by a coupon step up, i.e. an increase in the bond’s
coupon. Some bonds have a coupon step-down reducing the coupon
if the company achieves the target. Pure step-downs are uncommon,
whereas coupon step up/down, where the coupon rate can change
based on the KPI’s performance at the target observation date, are more
frequent (a common structure is to let the coupon depend on the firm’s
ESG rating). A cash/redemption penalty implies that the company pays
a one-time cash premium or increases the bond’s redemption price.
There are 62 bonds where the penalty is to donate money to a charity or

buy carbon offset certificates. The distribution of the size of the penalty
for targets with a step-up feature is displayed in Panel C. Out of 427
SLBs with a coupon step up, 220 (52%) have a 25 bps coupon increase,
120 (28%) have less than a 25 bps increase, and 76 (18%) have more
than a 25 bps increase.
3. A model for sustainability-linked bonds
In Section 3.1 we derive a model for pricing SLBs using the defaultintensity method proposed by Lando (1998) and Duffie and Singleton
(1999). We derive the model with multiple ESG targets, a stochastic interest rate, default intensity, recovery rate, and a premium for
4

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.
Table 2
Structure of SLBs. Panel A shows types of KPIs, Panel B types of penalties and Panel C
the distribution of penalty size for SLBs that have a coupon step up penalty. In Panel
A 268 SLBs have multiple KPIs and can thus enter into multiple rows of the panel.
The KPI information is manually collected using a combination of Bloomberg notes,
bond prospectuses, company websites, and second party opinions. The data period is
December, 2018 to March, 2024.

+

+𝐸0𝑄
=

Issuance amount (USD Billions)

GHG (Greenhouse Gas)
Other
Renewables
ESG rating
Diversity
Missing Info

410
233
125
65
38
36

195.4
72.0
37.6
16.8
16.5
8.2

Multiple KPIs

268

108.2

# of SLBs issued

Issuance amount (USD Billions)

427
86
68
62
36
33
8

198.3
29.1
16.9
11.3
7.9
7.7
0.5

𝑀
∑

[

𝑡𝐶
𝑀

∫0

𝑗

(1)

𝑖=1

]
𝑢
𝛿𝑢 𝜆𝑢 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 −𝜔𝑠 )𝑑𝑠 𝑑𝑢

𝐶𝑖 𝐷(𝑟0 , 𝜆0 , 𝜔0 , 𝑡𝐶
𝑖 )+

𝑁𝑗
𝐾 ∑
∑

(2)

𝑆𝑖𝑗 𝐹 (𝑟0 , 𝜆0 , 𝐺0𝑗 , 𝐾𝑗 , 𝑡𝑗𝑖 , 𝑇𝑗 )

(3)

𝑗=1 𝑖=1

+ 𝑅(𝑟0 , 𝜆0 , 𝜔0 , 𝛿0 , 𝑡𝐶
𝑀 ),

(4)

where

[
]
𝑡
𝐷(𝑟0 , 𝜆0 , 𝜔0 , 𝑡) = 𝐸0𝑄 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 −𝜔𝑠 )𝑑𝑠 ,
[
]
𝑡
𝐹 (𝑟0 , 𝜆0 , 𝐺0 , 𝐾, 𝑡, 𝑇 ) = 𝐸0𝑄 1{𝐺𝑇 >𝐾} 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 )𝑑𝑠 ,
]
[ 𝑡
𝑢
𝛿𝑢 𝜆𝑢 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 −𝜔𝑠 )𝑑𝑠 𝑑𝑢 .
𝑅(𝑟0 , 𝜆0 , 𝜔0 , 𝛿0 , 𝑡) = 𝐸0𝑄
∫0

(5)
(6)
(7)

Note that the model takes into account that ESG-investors value penalty
cash flows less than the other bond cash flows since the sustainium
is not included when discounting potential penalties in the last term
in Eq. (1). We decompose the price of the SLB into a standard bond
component and an option:
𝑃0𝑆𝐿𝐵 = 𝑃0𝑆𝑈 𝑆 + 𝑂0 ,

Panel C: Coupon step up penalty

=25 BPS
<25 BPS
>25 BPS
Missing info

𝑇𝑗

𝑖=1

Panel B: Penalty type

Coupon step up
Cash/Redemption
Coupon step up/Down
Carbon offset/Donation
Missing info
Complex
Coupon step down

𝑁
𝑗
[
∑𝑗 𝑗 − ∫ 𝑡𝑖 (𝑟 +𝜆 )𝑑𝑠 ]
𝐸0𝑄 1{𝐺𝑗 >𝐾 }
𝑆𝑖 𝑒 0 𝑠 𝑠

𝑗=1

Panel A: KPI type
# of SLBs issued

𝐾
∑

# of SLBs issued

Issuance amount (USD Billions)

220
120
76
11

131.8
26.0
39.5
1

𝑃0𝑆𝑈 𝑆 =

𝑀
∑

(8)

𝐶
𝐶𝑖 𝐷(𝑟0 , 𝜆0 , 𝜔0 , 𝑡𝐶
𝑖 ) + 𝑅(𝑟0 , 𝜆0 , 𝜔0 , 𝛿0 , 𝑡𝑀 ),

(9)

𝑖=1
𝑁

𝑂0 =

𝐾 ∑
𝑗
∑

𝑆𝑖𝑗 𝐹 (𝑟0 , 𝜆0 , 𝐺0 , 𝐾𝑗 , 𝑡𝑗𝑖 , 𝑇𝑗 ),

(10)

𝑗=1 𝑖=1

where 𝑃0𝑆𝑈 𝑆 is the price of a ‘‘sustainium bond’’ without any optionlinked cash flows and 𝑂0 is the value of the option-linked cash flows.
The price of an ordinary (non-ESG) bond with no option features is

sustainability. In Section 3.2 we simplify the model by assuming constant values for the interest rate, default frequency, recovery, and
sustainability premium, and detail how we estimate the model.

𝑃0𝑜 =

3.1. A general model

𝑗

(11)

where

[
]
𝑡
𝐷′ (𝑟0 , 𝜆0 , 𝑡) = 𝐸0𝑄 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 )𝑑𝑠 ,
]
[ 𝑡
𝑢
𝑅′ (𝑟0 , 𝜆0 , 𝛿0 , 𝑡) = 𝐸0𝑄
𝛿 𝜆 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 )𝑑𝑠 𝑑𝑢 .
∫0 𝑢 𝑢

𝑗

𝑡𝐶
𝑖

𝐶𝑖 𝑒− ∫0 (𝑟𝑠 +𝜆𝑠 −𝜔𝑠 )𝑑𝑠

(12)
(13)

The lower bound of the option price is zero, 𝑂0𝐿𝐵 = 0, while the upper
bound is given by

𝑡𝐶
, 𝑖 = 1, … , 𝑁𝐽 .
𝑀
We consider a low ESG factor to be favourable in an ESG sense.
For instance, if the ESG factor is carbon emissions, a firm that has not
sufficiently reduced its carbon emissions will be penalized by having
to pay additional coupons if the factor is above the target. A high ESG
factor is positive in some cases, for instance when the goal is to reach
a certain percentage of female employees. In this case we look at −𝐺𝑡
and the condition is then −𝐺𝑡 > −𝐾. Some bonds (although none in
our empirical sample) have a step-down coupon structure, such that
the coupons are reduced if the firm reaches the ESG target. In this case
we think of the cash flows 𝐶1 , … , 𝐶𝑀 as the cash flows in case the
𝑗
firm reaches the ESG target and additional cash flows 𝑆1𝑗 , … , 𝑆𝑁
as
𝑗
the negative value of the step-down coupons.
Independent of the cash flows, investors may have a convenience of
holding the bond, the sustainability premium or ‘‘sustainium’’, which
we denote 𝜔𝑡 .
Let 𝜆𝑡 be the default intensity for the bond-issuing firm and 𝑟𝑡 the
riskfree rate. If the firm defaults at time 𝜏 bondholders receive 𝛿𝜏 . We
can think of the investor as selling the bond at default in which case
𝛿𝜏 is the trading price of the bond. The value of bond cash flows is
(see Lando (1998) and Duffie and Singleton (1999)):
𝑀
[∑

′
𝐶
𝐶𝑖 𝐷′ (𝑟0 , 𝜆0 , 𝑡𝐶
𝑖 ) + 𝑅 (𝑟0 , 𝜆0 , 𝛿0 , 𝑡𝑀 )

𝑖=1

The bond has promised cash flows 𝐶1 , … , 𝐶𝑀 at times 𝑡𝐶
, … , 𝑡𝐶
and
𝑀
1
without loss of generality we assume that we are pricing the bond at
time 0. The firm has 𝐾 ESG factors 𝐺𝑡𝑗 , 𝑗 = 1, … , 𝐾 and if factor 𝑗 is
above some target at time 𝑇𝑗 , 𝐾𝑗 , bond investors receive additional
𝑗
positive cash flows 𝑆1𝑗 , … , 𝑆𝑁
at times 𝑡𝑗1 , … , 𝑡𝑗𝑁 , where 𝑇𝑗 ≤ 𝑡𝑗𝑖 ≤

𝑃0𝑆𝐿𝐵 = 𝐸0𝑄

𝑀
∑

𝑁

𝑂0𝑈 𝐵 =

𝐾 ∑
𝑗
∑

𝑆𝑖𝑗 .

(14)

𝑗=1 𝑖=1

If the ESG factor(s) 𝐺 are independent of the risk free rate 𝑟 and the
default intensity 𝜆, Eq. (6) reduces to
[
]
(15)
𝐹 (𝑟0 , 𝜆0 , 𝐺0 , 𝐾, 𝑡, 𝑇 ) = 𝐸0𝑄 1{𝐺𝑇 >𝐾} 𝐷′ (𝑟0 , 𝜆0 , 𝑡),
and the required dollar compensation for ESG-related cash flow risk –
the ESG premium – is
𝑁

𝐸𝑆𝐺𝑃0 =

𝐾 ∑
𝑗
∑

[
]
𝑆𝑖𝑗 𝐸0𝑃 1{𝐺𝑇 >𝐾} 𝐷′ (𝑟0 , 𝜆0 , 𝑡𝑗𝑖 ) − 𝑂0

(16)

[
]
𝑆𝑖𝑗 𝐸0𝑃 1{𝐺𝑇 >𝐾} 𝐷′ (𝑟0 , 𝜆0 , 𝑡𝑗𝑖 )

(17)

𝑗

𝑗=1 𝑖=1
𝑁

=

𝐾 ∑
𝑗
∑

𝑗

𝑗=1 𝑖=1
𝑁

−

𝐾 ∑
𝑗
∑

[
]
𝑆𝑖𝑗 𝐸0𝑄 1{𝐺𝑇 >𝐾} 𝐷′ (𝑟0 , 𝜆0 , 𝑡𝑗𝑖 )
𝑗

𝑗=1 𝑖=1
𝑁

]

=

𝐾 ∑
𝑗
∑
𝑗=1 𝑖=1

𝑖=1

5

(18)

( [
]
[
])
𝑆𝑖𝑗 𝐸0𝑃 1{𝐺𝑇 >𝐾} − 𝐸0𝑄 1{𝐺𝑇 >𝐾} 𝐷′ (𝑟0 , 𝜆0 , 𝑡𝑗𝑖 ). (19)
𝑗

𝑗

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

between ordinary bonds and these SLBs is solely due to a convenience
of holding the SLB bond. We call these bonds for sustainium-only
bonds.
Specifically, for sustainium-only bond 𝑗 at time 𝑡 with a yield spread
𝑆
of 𝑠𝑆𝑈
𝑗,𝑡 , and a corresponding synthetic yield spread of an ordinary bond

3.2. A tractable model: Formulas and estimation
We now assume that the recovery rate, default intensity, sustainability premium, and riskfree rate are constant and estimate the model
using a three-step procedure. For a given bond-day, as Section 3.2.1
details, we first estimate the price of a synthetic ordinary non-ESG
bond with the same fixed cash flows as the SLB bond but with no
option features and no sustainium. Then, we estimate the price of a
bond with a sustainability premium but no option-linked cash flows as
outlined in Section 3.2.2 and finally we estimate the ESG risk premium
as Section 3.2.3 explains.

𝑆 as:
of 𝑠𝑜𝑗,𝑡 , we estimate the sustainium 𝜔𝑆𝑈
𝑗,𝑡
𝑆
𝑆
𝜔𝑆𝑈
= 𝑠𝑜𝑗,𝑡 − 𝑠𝑆𝑈
𝑗,𝑡
𝑗,𝑡 .

Using all sustainium-only bond-day observations we estimate the regression
𝑆
𝜔𝑆𝑈
= 𝛽𝑋𝑗,𝑡 + 𝜖𝑗,𝑡
𝑗,𝑡

3.2.1. Ordinary bond and estimation of 𝜆
The price of an ordinary (non-ESG) bond with no option features,
given in Eqs. (11)–(13) simplifies to
𝑃0𝑜 =

𝑀
∑

′
𝐶
𝐶𝑖 𝐷′ (𝑟, 𝜆, 𝑡𝐶
𝑖 ) + 𝑅 (𝑟, 𝜆, 𝛿, 𝑡𝑀 )

(27)

(28)

where 𝑋𝑗,𝑡 is a vector containing a constant and firm-level characteristics, and compute a firm-time level sustainium for the full sample as

(20)

̂ 𝑗,𝑡
𝜔̂ 𝑗,𝑡 = 𝛽𝑋

𝑖=1

(29)

𝐷′ (𝑟, 𝜆, 𝑡) = 𝑒−(𝑟+𝜆)𝑡 ,
(21)
(
)
𝛿𝜆
−(𝑟+𝜆)𝑡
1−𝑒
𝑅 (𝑟, 𝜆, 𝛿, 𝑡) =
.
(22)
𝑟+𝜆
To estimate the price of an ordinary bond, we first compute the yield
spread 𝑠𝑜𝑗,𝑡 of an ordinary synthetic bond at time 𝑡 with the same time-

where 𝛽̂ is the vector with regression coefficients. The price of a
sustainium bond is calculated as

to-maturity as that of SLB 𝑗, 𝑇𝑗,𝑡 , by interpolating the yield spread of
two ordinary bonds, one with a shorter maturity 𝑇𝑆,𝑡 and one with a
longer maturity 𝑇𝐿,𝑡 ,

where

′

𝑠𝑜𝑗,𝑡 =

𝑇𝐿,𝑡 − 𝑇𝑗,𝑡
𝑇𝐿,𝑡 − 𝑇𝑆,𝑡

∗ 𝑠𝑆,𝑡 +

𝑇𝑗,𝑡 − 𝑇𝑆,𝑡
𝑇𝐿,𝑡 − 𝑇𝑆,𝑡

𝑆𝑈 𝑆
=
𝑃̂𝑗,𝑡

𝐷(𝑟, 𝜆, 𝜔, 𝑡) = 𝑒−(𝑟+𝜆−𝜔)𝑡
(
)
𝛿𝜆
1 − 𝑒−(𝑟+𝜆−𝜔)𝑡 ,
𝑅(𝑟, 𝜆, 𝜔, 𝛿, 𝑡) =
𝑟+𝜆−𝜔

𝑇2,𝑡 − 𝑇𝑗,𝑡
𝑇2,𝑡 − 𝑇1,𝑡

∗ 𝑠1,𝑡 +

𝑇𝑗,𝑡 − 𝑇1,𝑡
𝑇2,𝑡 − 𝑇1,𝑡

𝑆𝐿𝐵,𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑
𝑆𝑈 𝑆
𝑂̂ 𝑗,𝑡 = 𝑃𝑗,𝑡
− 𝑃̂𝑗,𝑡
.

(33)
[
]
We calculate the ESG premium by estimating 𝐸𝑡𝑃 1{𝐺𝑗 >𝐾 } and
[
] 𝑇𝑗 𝑗
inserting the empirical estimates 𝑂̂ 𝑗,𝑡 and 𝐸̃ 𝑡𝑃 1{𝐺𝑗 >𝐾 } into Eq. (16).
𝑗
𝑇𝑗
]
[
We provide several estimates of 𝐸𝑡𝑃 1{𝐺𝑗 >𝐾 } based on different

𝑟𝑡,𝑇𝑗,𝑡 is the 𝑇𝑗,𝑡 −𝑡-year riskfree rate at time 𝑡.5 We convert the discretelycompounded yield-to-maturity to a continuously-compounded yield-to𝑦𝑜

𝑜,𝑐𝑐
𝑗,𝑡
maturity 𝑦𝑜,𝑐𝑐
𝑗,𝑡 using the formula 𝑦𝑗,𝑡 = 𝑓𝑗 ∗ ln(1 + 𝑓𝑗 ), where 𝑓𝑗 is the
coupon frequency for bond 𝑗. The price of the ordinary synthetic bond
is then
𝑀
∑

𝐶𝑖 𝑒

𝐶
−𝑦𝑜,𝑐𝑐
𝑗,𝑡 ∗𝑡𝑖

.

𝑇𝑗

(25)

𝑑𝐺𝑡𝑗 = 𝜇𝑗 𝑑𝑡 + 𝜎𝑗 𝑑𝑊𝑡

The default intensity 𝜆̂ 𝑗,𝑡 is estimated by solving Eq. (20) for 𝜆𝑗,𝑡 ,
𝑜
𝑃̂𝑗,𝑡
=

′
̂ 𝐶
𝐶𝑖 𝐷′ (𝑟𝑡,𝑇𝑗,𝑡 , 𝜆𝑗,𝑡 , 𝑡𝐶
𝑖 ) + 𝑅 (𝑟𝑡,𝑇𝑗,𝑡 , 𝜆𝑗,𝑡 , 𝛿, 𝑡𝑀 )

𝑗

assumptions about the firm’s future ESG commitments. To provide
empirical grounding for our estimates, they are based on the firm’s
historical ESG commitment.
To estimate the firm’s historical ESG commitment, we assume that
𝐺𝑗 follows a generalized Wiener process,

𝑖=1

𝑀
∑

(32)

The implied option price is estimated as (see Eq. (8))

The yield-to-maturity of the ordinary bond is 𝑦𝑜𝑗,𝑡 = 𝑠𝑜𝑗,𝑡 + 𝑟𝑡,𝑇𝑗,𝑡 where

𝑜
𝑃̂𝑗,𝑡
=

(31)

[
]
3.2.3. ESG risk premium and estimation of 𝐸𝑡𝑃 1{𝐺𝑇 >𝐾}

(24)

∗ 𝑠2,𝑡 .

(30)

𝜔̂ 𝑗,𝑡 is the sustainium at time 𝑡 of the bond issuer, and the sustainium
𝑆𝑈 𝑆 − 𝑃̂ 𝑜 .
bond premium for SLB 𝑗 at time 𝑡 is 𝑃̂𝑗,𝑡
𝑗,𝑡

where 𝑠𝑆,𝑡 (𝑠𝐿,𝑡 ) is the yield spread of the short (long) maturity bond.
If there is not a shorter and longer maturity bond, but two bonds with
either shorter or longer maturity we extrapolate the yield spread. For
example, if there are two ordinary bonds with a maturity of 𝑇2,𝑡 > 𝑇1,𝑡 >
𝑇𝑗,𝑡 , the yield spread of the ordinary bond is
𝑠𝑜𝑗,𝑡 =

̂
̂ 𝑡𝐶 )
̂ 𝑗,𝑡 , 𝛿,
𝐶𝑖 𝐷(𝑟𝑡,𝑇𝑗,𝑡 , 𝜆̂ 𝑗,𝑡 , 𝜔̂ 𝑗,𝑡 , 𝑡𝐶
𝑖 ) + 𝑅(𝑟𝑡,𝑇𝑗,𝑡 , 𝜆𝑗,𝑡 , 𝜔
𝑀

𝑖=1

(23)

∗ 𝑠𝐿,𝑡 ,

𝑀
∑

(34)

and at time 𝑡 we observe historical observations of the factor at times
𝑡𝑗1 < 𝑡𝑗2 < ⋯ < 𝑡𝑗𝑘 < 𝑡 where 𝑡𝑗𝑖+1 − 𝑡𝑗𝑖 is one year.6 To estimate the
(
)
parameters 𝜇𝑗 and 𝜎𝑗 , we note that 𝐺𝑇𝑗 − 𝐺𝑡𝑗 ∼ 𝑁 𝜇𝑗 (𝑇 − 𝑡), 𝜎𝑗2 (𝑇 − 𝑡)
and estimate the linear regression

(26)

𝑖=1

where we use the historical recovery rate between 1987–2021 of 34.8%
̂
from Moody’s (2022) as our estimate of the recovery rate 𝛿.

𝑗
𝐺𝑡+1
− 𝐺𝑡𝑗 = 𝛽 + 𝜖𝑡+1 , 𝑡 = 𝑡𝑗1 , … , 𝑡𝑗𝑘−1 ,

3.2.2. Sustainium bond and estimation of 𝜔
We use the subset of SLBs with no option-linked cash flows to
compute the price of a synthetic bond with a sustainability premium
but no option-linked cash flows. SLBs with penalty type ‘‘Carbon Offset/Donation’’ have no options embedded and (absent other frictions
impacting the price such as liquidity) the yield-to-maturity difference

where 𝜖𝑡+1

(35)

∼ 𝑁(0, 𝜉 2 ). The parameter estimates are then

𝜇̂ 𝑗 = 𝛽̂

(36)

̂
𝜎̂ 𝑗 = 𝜉.

(37)

6
We assume an informational lag of 3 months for KPI data. This means
that KPI data for year 𝑡 − 1 will become available in April of year 𝑡. The
informational lag differs between firms/SLBs and we choose three as this is
a typical lag. The empirical results of Section 5 do not qualitatively change if
we use an informational lag of zero or six months.

5

The riskfree rate is the swap rate at time 𝑡 for the same currency and
maturity as the SLB: 𝑟𝑡,𝑇𝑗,𝑡 = 𝑦𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑
− 𝑠𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑
, where the superscript observed
𝑗,𝑡
𝑗,𝑡
refers to the actual observed yield-to-maturity and yield spread for SLB 𝑗 at
time 𝑡.
6

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.
ℎ and 𝜎
ℎ (with superscript
Based on the historical estimates 𝜇̂ 𝑗,𝑡
̂ 𝑗,𝑡
h to indicate that these are historical estimates), we make different
𝑓
𝑓
assumptions about
[ the future
] 𝜇 and
[ 𝜎 , and it is then
] straightforward
𝑗
𝑃
to calculate 𝐸̂ 𝑡 1{𝐺𝑗 >𝐾 } = 𝑃𝑡 𝐺𝑇 > 𝐾𝑗 |𝐺𝑗𝑗 . Specifically, we
𝑡𝑘

𝑗

𝑗

𝑇𝑗

Table 3
Data sources. Panel A summarizes the number of bonds covered and the total number
of observations (at both the bond-day level and the transaction level for TRACE and
Propellant) for each of the three data sources. Panel B breaks down the regional
distribution of all bond-days from each source. Panel C shows the same statistics as
Panel A, but for each individual venue in the Propellant data set. The data covers the
period from September 10, 2019, to March 4, 2024.

include three different assumptions about future firm commitment in
our empirical estimates:

Panel A: Data sources overview

• Same commitment. In this scenario we assume that the future
commitment of the firm is the same as the past, i.e. 𝜇 𝑓 = 𝜇̂ 𝑗,𝑡 and
𝜎 𝑓 = 𝜎̂ 𝑗,𝑡 , and issuing an SLB does not change the ESG behaviour
of the firm.
• Stronger commitment. In this scenario we assume that the future
commitment of the firm is stronger than in the past by assuming
that 𝜇 𝑓 = min(2𝜇̂ 𝑗,𝑡 , 0) and 𝜎 𝑓 = 𝜎̂ 𝑗,𝑡 . Issuing an SLB incentivizes
the firm’s ESG efforts through the ESG-linked cash flows in the
SLB. Even if the purely pecuniary benefits from reaching the ESG
target are modest, as the anecdotal evidence in Section 2 suggests,
a firm’s choice to issue sustainability-linked bonds may signal a
stronger commitment to sustainability. A lower ESG drift captures
this increase in effort.
• Stronger and more focused commitment. In this scenario we assume
that the future commitment of the firm is both stronger and more
focused than in the past by assuming that 𝜇𝑓 = min(2𝜇̂ 𝑗,𝑡 , 0)
and 𝜎 𝑓 = 21 𝜎̂ 𝑗,𝑡 . Here, the firm is increasing ESG efforts as well
as focussing more on making sure targets are met, for example
through increased monitoring.
[
]
Most estimates of 𝐸̂ 𝑡𝑃 1{𝐺𝑗 >𝐾 } are based on relatively few observa-

Bloomberg
TRACE
Propellant

Bloomberg
TRACE
Propellant

𝑁
∑

]
[
𝐸̂ 𝑡𝑃 1{𝐺𝑗 >𝐾 }
𝑇𝑗

𝑗=1

Bloomberg
Marketaxess
Tradeweb
LSE
Tradeecho
Tradition
Liquidnet

𝑇𝑗

𝑇𝑗

𝑗

𝑇𝑗

𝑗

EU

US

AS

Other

213,462
10,144
72,064

53,222
20,287
4864

252,507
175
1083

32,646
1946
1937

Bonds

Transactions

Bond-days

Volume (Millions)

354
339
330
298
229
41
7

83,021
66,442
110,153
7333
3801
158
12

44,257
36,330
46,425
6495
2508
52
12

65,111.84
40,534.62
76,149.16
3291.23
2249.17
201.33
11.09

To calculate transactions-based liquidity measures, we extract transactions from the TRACE database for bonds issued by FINRA-regulated
firms, typically United States dollar denominated bonds and use the
cleaning procedure described in Dick-Nielsen (2009). We augment the
TRACE data with transactions for European bonds, done through the solution provided by Propellant.digital B.V. European trading venues are
through MIFID II required to disseminate all their transactions in spirit
similar to the data collection for the TRACE database, but unlike U.S.
transactions, different venues’ data come in different formats and are
not collected in one database. Propellant provides a software solution
that collects the major trading venues’ data and allows for one homogeneous data set. Further details are provided in Appendix A.2. There
are 17,464 transactions across 8566 bond-days that are overlapping
between the TRACE and Propellant data (transactions with identical
volume and price on the same day) and to avoid double counting these
transactions, we remove the one present in the Propellant data set.

where 𝑁 is the number of targets for which we can calculate a probability at time 𝑡. Our time-𝑡 estimate of[the probability
of missing the
]
target under any of three scenarios, 𝐸̃ 𝑡𝑃 1{𝐺𝑗 >𝐾 } , is then
[
]
[
]
𝐸̃ 𝑡𝑃 1{𝐺𝑗 >𝐾 } = 0.25𝐸̂ 𝑡𝑃 1{𝐺𝑗 >𝐾 } + 0.75𝐸𝑡𝑐𝑜𝑚 .

551,837
32,552
79,948

for two ordinary bonds that both have either shorter or longer maturity.
In this case, we choose the bonds with a time-to-maturity closest to that
of the SLB and where the difference in time-to-maturity between the
two ordinary bonds is at least six months.

(38)

𝑗

Bond-days

–
354,645
270,920

Panel C: Propellant venues

tions of 𝐺𝑗 and are therefore noisy. To reduce the noise, we calculate
a shrinkage estimator as in Vasiček (1973) and Blume (1975) and
calculate in all three scenarios a common time-𝑡 probability of missing
the target as
𝐸𝑡𝑐𝑜𝑚 =

Transactions

Panel B: Regions

𝑗

𝑇𝑗

Bonds
1129
81
366

𝑗

(39)

4. Data
In this section we describe the data and Appendix provides further
details.
We restrict our sample of corporate bonds to standard fixed-rate
bonds with a time-to-maturity of at least six months.7 We collect price
and yield information on all corporate bonds from Bloomberg that are
marked as sustainability-linked until the end of our sample period,
March 4, 2024. The yield-to-maturity on SLBs is calculated using the
current coupon without using the information on potential step-up
coupons. For each SLB we look up comparable ordinary bonds (i.e. not
green, sustainable, or sustainability-linked) on Bloomberg issued by the
same company that have a maturity that is less than four years from
the SLB’s maturity and have the same currency and seniority. Every
day, we select two ordinary bonds that have available yield data and
with a maturity closest to but smaller and larger, respectively, than the
maturity of the SLB. If it is not possible to find two such bonds, we look

Table 3 shows the coverage of our three main data sources:
Bloomberg, TRACE, and Propellant. A bond-day is in the sample if
there is Bloomberg data available on that day and therefore the number
of bond-days with Bloomberg data in Panel A is equal to the total
number of bond-days. Propellant covers more bond-days and bonds
than TRACE, while bonds that TRACE covers has more transactions.
Panel B shows the number of bond-days with data in different regions
and we see that TRACE covers predominantly U.S. while Propellant
covers Europe and the coverage of the rest of the world is low.
Propellant reports the trading venue where the transaction took place
and Panel C shows that the main trading platforms are Bloomberg,
Marketaxess and Tradeweb and the three platforms have a fairly similar
share of the trading while other platforms have modest transaction
activity. Our data sample starts on September 10, 2019; the earliest
issuance date of the SLBs in our final sample.

7
Specifically, we restrict the sample to bonds that have ‘At maturity’ or
‘Callable’ as ‘Maturity Type’ in Bloomberg. For callable bonds, we include only
those bonds where the call option is a make-whole call or a fixed-price call
restricted to the last 3 months (or less) before the bond matures.

After cleaning the data, the details of which can be found in Appendix A.3, we are left with a final sample that contains 75 SLBs with
7

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.
Table 4
SLB sample. This tables shows statistics for the sample of SLBs used in the empirical
analysis. Panel A breaks down the SLBs by types of KPI. Panel B show the types of
penalties most commonly used in the structuring of SLBs. Finally, Panel C show the
distribution of the penalty size for those SLBs that have a coupon step up penalty.

# of SLBs issued

Issuance amount (USD Billions)

63
11
0
24
0
0
0

60.8
10.4
0.0
3.7
0.0
0.0
0.0

Imputed Roundtrip Cost (IRC) of Feldhütter (2012) suggest that SLBs
are more liquid than ordinary bonds: the Amihud measure and IRC
are higher and trade size is lower for ordinary bonds. The differences
are not statistically significant and the number of bond-days with
computable liquidity measures are only a fraction of all bond-days,
and different for different measures, so it is difficult to draw conclusions from trade-based liquidity measures that can only be computed
conditional on a transaction occurring.
Trade count, trading volume and bond age can be calculated on
all bond days and it is clear that SLBs are newer bonds that trade
more. The average age of SLBs in our sample is 1.144 years while it
is 5.902 years for the ordinary bonds. Given that bonds trade more
frequently when they are recently issued, it is not surprising that SLBs
trade more often (2.467 pr. day vs. 1.498 pr. day for ordinary bonds)
and that the trading volume is higher ($1.517 m pr. day vs. $0.900 m
pr. day for ordinary bonds). The differences in age and trading volume
are highly significant and it is therefore important to control for the
liquidity differences in our results. We do so by adding trade count,
volume and age as controls in our regressions (we restrict the controls
to those three liquidity measures in order not to reduce the sample
size).10

# of SLBs issued

Issuance amount (USD Billions)

5.2. Sustainium

28
21
14
0

30.6
19.4
10.8
0.0

Panel A: KPI type
# of SLBs issued

Issuance amount (USD Billions)

GHG (Greenhouse Gas)
Other
Renewables
ESG rating
Diversity
Missing info

65
20
6
3
4
0

44.1
20.0
6.8
0.6
3.4
0.0

Multiple KPIs

17

15.9

Panel B: Penalty type

Coupon step up
Cash/Redemption
Coupon step up/Down
Carbon offset/Donation
Missing info
Complex
Step down

Panel C: Step up coupon penalty

=25 BPS
<25 BPS
>25 BPS
No information

We expect SLBs to trade at higher prices than ordinary bonds issued
by the same firm, i.e. a positive SLB premium, since SLBs have potential
future additional cash flows. Part of the SLB premium may also be due
to ESG investors willing to pay a premium for ESG-friendly securities
(Pedersen et al., 2021; Pastor et al., 2021; Feldhütter and Pedersen,
2024 and others). If ESG investors’ non-pecuniary benefits accrue solely
through ownership as experimental evidence in Bonnefon et al. (2022)
suggests, the sustainium may be zero, since SLBs do not finance specific
green projects. In contrast, if investors are concerned with the actual
impact of their portfolio decisions as in Oehmke and Opp (2024) and
Moisson (2022), the sustainium might be significantly positive.
As outlined in Section 3.2.2 we estimate a bond-time sustainium for
a subset of SLBs where the penalty is in terms of donations or carbon
offset. For these bonds, there are no potential additional payments to
bond holders and therefore a yield difference between the SLB and an
𝑆 = 𝑠𝑜 − 𝑠𝑆𝑈 𝑆 , can be attributed to the ESG label
ordinary bond, 𝜔𝑆𝑈
𝑗,𝑡
𝑗,𝑡
𝑗,𝑡
itself. For these sustainium-only bonds we estimate the regression

98 associated options,8 a combined issuance amount of 52.53 billion
USD, and a total of 24,349 SLB bond-day observations spanning from
April 1, 2020, to March 4, 2024. The data sample contains 10.4% of the
total number of SLBs in the Bloomberg database and 19.2% of the total
issuance amount. We see in Table 4 that the distributions of the KPIs,
penalty types, and penalty sizes of coupon step ups in our final sample
are similar to those of all SLBs: KPIs related to greenhouse gases are the
most common KPI type and the most commonly associated penalty is a
coupon step up of 25 bps. Table 5 shows that on average the SLBs have
a time-to-maturity of 6.33 years, a coupon of 2.29 and an issuance size
of 862$ million.
5. Empirical results

𝑆
𝜔𝑆𝑈
= 𝛽𝑋𝑗,𝑡 + 𝜖𝑗,𝑡
𝑗,𝑡

In this section we discuss the pricing of SLBs. We first look at the
liquidity of SLBs as well as ordinary bonds issued by the same firm.
Then we investigate if SLBs require a premium unrelated to cash flows
for being labelled ESG and whether SLBs are mispriced. Finally, we
examine determinants of SLB prices and ESG risk premiums.

where 𝑋𝑗,𝑡 is a vector containing a constant, log(size), equity volatility, leverage, profitability, Tobin’s q, credit rating, ESG rating, and
industry-adjusted ESG rating. Appendix A.4 details the calculation of
the variables.
Table 7 shows the regression results. There are three variables
that have predictive power for the sustainium: equity volatility, credit
rating, and industry-adjusted ESG rating. In the richest specification
(6) the sustainium decreases by 1.62 bps for every rating notch. The
standard deviation of credit rating is 1.49, so a one standard deviation
improvement in rating implies an increase of 2.41 bps in the sustainium
(a higher numeric value of credit rating implies a lower credit quality).
The positive relation between the sustainium and credit quality has
the same sign as the relation between the greenium and credit quality,
see Caramichael and Rapp (2024). The table also shows that there is a
negative relation between industry-adjusted ESG rating and sustainium.
A one standard increase in industry-adjusted ESG rating implies a
2.34 bps lower sustainium (the standard deviation of industry-adjusted
ESG rating is 1.28). A potential explanation for the negative relation

5.1. Liquidity
The ease with which a corporate bond is traded affects corporate
bond prices,9 and we therefore compare the liquidity of SLBs to that of
the corresponding regular bonds. We calculate liquidity of the synthetic
ordinary bond as the weighted average liquidity of the two ordinary
bonds that are used to calculate the synthetic yield, where the weights
for the liquidity measures are the same as those used to determine the
synthetic yield.
Table 6 shows the average liquidity of SLB bonds and synthetic
ordinary bonds. The transaction-based Amihud measure, trade size and

8
There are 6 SLBs with three KPIs, 11 SLBs with two KPIs, and 58 SLBs
with one KPI.
9
See Friewald et al. (2012), Bao et al. (2011), Dick-Nielsen et al. (2012)
and Feldhütter (2012) and others.

(40)

𝑜
10
Specifically, we add log(1 + 𝐿𝑜𝑗,𝑡 ) − log(1 + 𝐿𝑆𝐿𝐵
𝑗,𝑡 ), where 𝐿𝑗,𝑡 is the weighted
average liquidity measure of the two bonds used to determine the synthetic
yield on day 𝑡 for SLB 𝑗, and 𝐿𝑆𝐿𝐵
is the SLB’s liquidity measure.
𝑗,𝑡

8

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Table 5
Summary statistics for the SLB sample. The distribution of the age, time-to-maturity, coupon, yield-to-maturity, yield spread, and issuance
amount for the final sample. There are 24,349 bond-day observations in the period from April 1, 2020 to March 4, 2024.

Age (In Years)
TTM (In Years)
Coupon
Yield-to-Maturity
Yield spread
Issuance (USD Millions)

Mean

Std

Min

p1

p25

p50

p75

p99

Max

1.14
6.33
2.29
3.57
1.22
862

0.77
2.47
1.92
2.14
0.92
514

0.00
1.46
0.00
−0.37
−0.57
67

0.02
2.01
0.00
−0.13
0.05
70

0.50
4.36
0.50
1.19
0.48
500

1.04
5.84
2.25
3.95
1.03
856

1.71
8.64
3.75
5.31
1.70
1190

3.13
11.78
7.38
7.12
3.87
2161

3.47
12.51
7.88
8.39
4.58
2300

Table 6
Bond liquidity. At the bond-day level we calculate the Amihud measure, IRC measure,
average trade size, trade count, volume, and age. The first and second columns show
the average for SLBs and a weighted average of ordinary bonds (where the weights
are the same as those in Eqs. (23)–(24)), respectively. The Amihud and IRC measures
are calculated on a daily basis as in Dick-Nielsen, Feldhütter, and Lando(2012) and we
winsorize at the 1% and 99% level. Trade count, total volume, and age are calculated
on all bond-days, while average trade size requires at least one transaction on a bondday to be computable. Additionally, for the Amihud, IRC, and trade size measures, we
use a trailing 90-day average as our final daily measure. The third column shows the
difference between the two groups on days where both groups have observations, while
the fourth shows the number of bond-day pairs with non-missing data. The parentheses
show standard errors (clustered at the bond-level) of the difference. *, **, and ***
indicate statistical significance at the 0.10, 0.05 and 0.01 level, respectively.
SLBs

Ordinary bonds

Difference

N

Amihud

0.058

0.077

9238

IRC

0.209

0.225

Trade size (Millions)

0.723

0.619

Trade count

2.467

1.498

Volume (Millions)

1.517

0.900

Age

1.144

5.902

−0.019
(0.020)
−0.015
(0.048)
0.104
(0.065)
0.969**
(0.406)
0.617***
(0.223)
−4.758***
(0.721)

The average sustainium is 1.89 bps in the sustainium-only bond
sample, 1.18 bps in the coupon-linked SLB sample, and 1.31 bps overall. Thus, the sustainium is small but positive. The sustainium is similar
in sign and magnitude as the average green bond premium of 3.37 bps
in Feldhütter and Pedersen (2024). Fig. 3 shows the time series of the
average sustainium in the complete sample including sustainium-only
and coupon-linked SLBs and we see that the sustainium is consistently
small and positive.12
5.3. SLB premium determinants
Absent frictions and the presence of ESG investors, the value of the
embedded conditional cash flows in SLBs will be determined by the
size of the cash flows, the probability of the firm missing the target
and a potential ESG risk premium. Kölbel and Lambillon (2023) find
surprisingly that there is no relation between the penalty size and
the SLB premium. If the market does not price SLBs correctly, firm
behaviour is unlikely to be aligned with investor ESG preferences.
Table 9 Panel A shows the probabilities of missing the target under
the different assumptions about the future commitment of the firm
issuing the SLB (outlined in Section 3.2.3). Here, we focus on the
subset of SLBs with ESG-linked coupons. The average probability is
between 14% and 39% and quite low for both reducing green house
gasses (GHG), 15%–37%, and non-GHG targets, 11%–41%. According
to industry reports, the historical frequency of missing targets has been
low13 and our results imply that this trend of meeting targets is due to
firms setting easy targets. These results support the concern in the ESG
market that targets ‘‘lack ambition and are too easy to meet’’ and ‘‘are
too soft’’.14
Panel B shows that the relation between the SLB premium and the
penalty size in our sample is positive and highly significant: the regression coefficient when regressing the SLB premium on penalty size is
1.05–1.17 depending on specification. Thus investors take into account
penalty sizes when pricing SLBs and higher penalties translate into

5555
10,356
24,349
24,349
24,349

between sustainium and industry-adjusted ESG rating is that for green
firms the ‘‘ESG gap’’ between ordinary bonds and SLBs is smaller as
implied by the model in Feldhütter and Pedersen (2024). Finally, a
one standard increase in equity volatility implies a 0.45 bps higher
sustainium (the standard deviation of equity volatility is 0.23).
We use regression specification (6) in Table 7 to compute a firmtime level sustainium for all firm-time observations as
̂ 𝑗,𝑡 .
𝜔̂ 𝑗,𝑡 = 𝛽𝑋

(41)

If the ranges of firm characteristics are substantially different in the full
sample compared to the sustainium-only sample, this approach would
be problematic because the approach would lead to extrapolation outside the range of the independent variables in the regression. Therefore,
Table 8 shows the distribution of the variables for the sustainium-only
sample as well as for the remaining sample where the bond coupons are
linked to ESG targets. The table shows that firms issuing sustainiumonly bonds are smaller, have better credit rating and lower ESG rating
than firms using coupon-linked SLBs. The biggest sustainium-only issuers are predominantly Japanese – SingTel, Ajinomoto, Mitsubishi,
Daiwa, Shiseido, TDK, ANA, Tokyu, Obayashi, and Asics – while the
biggest coupon-linked SLB issuers are international firms — Optus Finance, Novartis Finance, Sanofi, Enel, Analog Devices, Enbridge, Eaton,
SK Hynix, Eni, L’Oreal, Air France-KLM and General Mills. Importantly,
we see that there is significant overlap in the distribution of all firmlevel variables, validating the calculation of the sustainium using the
regression in Eq. (41).11

goals creates the wrong investor incentives, and (2) if the coupons are linked
to ESG targets, their investors may be forced to treat the overall bond as
a derivative and hence regularly mark to market the position from an SPPI
perspective (for more on SPPI see https://www.bdo.co.uk/en-gb/insights/
business-edge/business-edge-2017/ifrs-9-explained-solely-payments).
12
At the individual bond-day level, there are a number of negative sustainium observations; 32.0% of the predicted sustainium values are negative.
This is noise at the individual bond-day level that is averaged out when
aggregating in the cross section as the figure shows.
13
NatWest report that ‘‘based on our tracker of selected public
SLBs in the European and US market, 86% were on track to meet
their target at the end of 2022’’ (NatWest, April 18, 2023, ‘‘SLB
target misses aren’t necessarily a negative: it’s about the context’’,
https://www.natwest.com/corporates/insights/sustainability/slb-targetmisses-arent-necessarily-a-negative-its-about-the-context.html).
14
Reuters, November 9, 2022, ‘‘Explainer: Decoding COP27: the many
shades of green bonds’’ (https://www.reuters.com/business/cop/decodingcop27-many-shades-green-bonds-2022-11-09/) and GlobalCapital, April
4, 2023, ‘‘In defense of SLBs’’ (https://www.globalcapital.com/article/
2bhpp15s781netjeiefi8/sri/green-and-social-bonds-and-loans/in-defence-ofslbs).

11
In conversions with bond issuers, they often mention two reasons for
issuing sustainium-only bonds, (1) rewarding investors if the firm fails ESG

9

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Table 7
Sustainium determinants. There are 24 SLB bonds issued by 18 firms with 4509 bond-day observations with no option-linked cash
flows in the sample period 2020:04–2024:03. This table shows results of a( regression of the SLB premium
(in basis points) on
)
∑𝑁𝑡𝑆𝑈 𝑆
1
𝑆
𝑆𝑈 𝑆
log(1 + 𝐿𝑜𝑖,𝑗,𝑡 ) − log(1 + 𝐿𝑆𝑈
firm characteristics for this subsample. The liquidity controls are 𝑁 𝑆𝑈
𝑆
𝑖,𝑗,𝑡 ) , 𝑖 = 1, … , 3 where 𝐿𝑖,𝑗,𝑡
𝑗=1
𝑡

(𝐿𝑜𝑖,𝑗,𝑡 ) is the value of liquidity variable 𝑖 on day 𝑡 for SLB 𝑗 with no cash flow effects (ordinary bond) and the three liquidity
variables are trade count, trading volume and bond age. Standard errors clustered at the bond level are in parentheses and *, **,
and *** indicate statistical significance at the 0.10, 0.05, and 0.01 level, respectively.

Constant
Log(size)
Equity vol
Leverage
Profitability
Tobin’s q
Credit rating

(1)

(2)

(3)

(4)

(5)

(6)

17.01

8.22

7.17

20.59

9.45

10.18

(21.61)

(21.97)

(18.87)

(16.84)

(20.28)

(16.45)

1.19

1.03

1.08

1.21

1.04

1.09

(1.73)

(1.85)

(1.79)

(1.74)

(1.85)

(1.78)

1.97∗∗∗

1.95∗∗∗

2.00∗∗∗

1.92∗∗∗

1.93∗∗∗

1.94∗∗∗

(0.29)

(0.23)

(0.29)

(0.33)

(0.29)

(0.33)

−11.06

−8.39

−8.44

−11.92

−8.67

−9.13

(11.53)

(10.83)

(10.02)

(10.25)

(10.27)

(9.17)

−7.13

−4.60

−6.70

−9.41

−5.59

−9.30

(15.81)

(14.04)

(14.92)

(13.31)

(12.46)

(12.51)

−3.51

−1.13

−3.81

−3.60

−1.13

−3.95

(3.41)

(2.72)

(3.34)

(3.39)

(2.72)

(3.29)

−1.54∗∗∗

−1.23∗∗

−1.41∗∗∗

−1.74∗∗∗

−1.31∗

−1.62∗∗

(0.40)

(0.57)

(0.73)

−1.47∗∗

Industry-adj ESG rating

(0.72)

ESG rating
Liquidity controls
𝑅2
𝑁

No
0.168
4509

(0.48)

(0.65)

−1.73∗∗∗

−1.53∗

(0.62)

(0.79)

(0.68)

−1.83∗∗∗
(0.66)

−0.63

1.92

−0.60

(2.55)

(2.36)

(2.60)

(2.35)

No
0.130
4509

No
0.173
4509

Yes
0.131
4509

Yes
0.178
4509

Yes
0.172
4509

2.14

Table 8
SLB and sustainium bond issuer characteristics. There are 75 SLB bonds issued by 41 firms with 24,349 bond-day observations in the sample period
2020:04–2024:03. There are 24 SLB bonds issued by 18 firms with 4509 bond-day observations with no option-linked cash flows in the sample period
2020:04–2024:03, called sustainium bonds. The remaining SLB bonds have option-linked cash flows, called coupon-linked SLBs. This table shows the
distribution – across bond-days – of firm characteristics in the two samples. Standard errors clustered at the bond level are in parentheses and the
last column tests for a difference in means and *, **, and *** indicate statistical significance at the 0.10, 0.05, and 0.01 level, respectively.
Coupon-linked SLBs

Log(size)

Sustainium-only bonds

q5

q25

q50

q75

q95

Mean

q5

q25

q50

q75

q95

10.47

8.51

9.52

10.89

11.21

12.09

9.12

6.49

8.34

9.26

9.66

12.63

(0.16)

Equity vol

0.12

(0.35)

0.01

0.01

0.02

0.14

0.47

(0.03)

Leverage

0.47
0.14

0.11

0.41

0.50

0.59

0.68

0.02

0.05

0.07

0.10

0.22

0.32

6.92

0.01

0.01

0.01

0.01

0.02

6.07

2.30

5.60

7.90

8.80

10.00

8.60

0.02

1.65

0.39
0.20
0.10
6.69

4.00

5.40

6.30

7.20

7.40

5.52

0.00

0.23

0.33

0.57

0.77

6.00

8.00

8.00

9.00

12.00

6.68

-0.04

0.07

0.18

0.29

0.58

−0.05
(0.04)

0.01

0.01

0.01

0.01

1.10

−0.08
(0.09)

4.60

6.00

6.90

8.10

8.40

0.23
(0.50)

4.60

5.10

5.50

5.90

6.50

0.55∗∗
(0.24)

4.00

6.00

(0.35)

higher bond prices as basic financial theory implies. Furthermore, we
see that the interaction between the penalty size and the probability of
missing the target is positive in all specifications, as expected, between
1.05–1.92, and statistically significant in half of the specifications.
We also see in Panel B that equity volatility is a firm-specific characteristic that consistently has statistical significance in explaining the
SLB premium: a higher equity volatility implies a higher SLB premium.
A potential explanation is that different types of uncertainty are correlated and equity volatility is correlated with uncertainty about meeting
the target. Indeed, we find that there is a positive correlation between
equity volatility and 𝜎𝑗 in Eq. (34).15 Since 𝜎𝑗 is based on relatively
few data points and updated on an annual basis (when a new historical

0.08
(0.06)

(0.13)

(0.27)

0.01
(0.10)

(0.28)

(0.20)

Credit rating

0.02

(0.09)

(0.42)

ESG rating

0.01

(0.04)

(0.01)

Industry-adj ESG rating

0.01

(0.06)

(0.01)

Tobin’s q

0.12

1.35∗∗∗
(0.38)

(0.09)

(0.03)

Profitability

Mean diff

Mean

7.00

8.00

9.00

1.92∗∗∗
(0.44)

observation of the factor is released) while equity volatility is updated
on a daily basis, equity volatility will provide current information about
𝜎𝑗 and thus the probability of missing the target. While beyond the
scope of this paper, calculating the probability of missing the target
using information from both historical observations of the KPI as well
as current financial data is an interesting topic for future research.
5.4. Are SLBs mispriced?
The existing literature on SLBs finds that they are mispriced. Kölbel
and Lambillon (2023) conclude that the yield difference between on
ordinary bond and an SLB issued by the same issuer exceeds the
maximum potential penalty (expressed in yield) that issuers need to
pay in case the target is not reached. This implies that even if the
market prices an SLB with a probability of one of missing the target, the
SLB price is higher than that of an ordinary bond with same (ordinary
and penalty) coupons and SLBs are overpriced. In contrast (Berrada

15
Since different 𝐺𝑗 ’s have different scales, we calculate a scaled version
𝜎𝑗
as 𝜎𝑗𝑠𝑐𝑎𝑙𝑒𝑑 = log( 𝐺 −𝐾
) and the correlation in the panel of 𝜎𝑗𝑠𝑐𝑎𝑙𝑒𝑑 and equity
𝑡

volatility is 0.07 both at the KPI-level and at the bond level (where we compute
an average 𝜎𝑗𝑠𝑐𝑎𝑙𝑒𝑑 for bonds with multiple KPIs.).
10

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Table 9
SLB premium determinants. Panel A shows the average estimated probability of meeting the ESG target. ‘GHG’ is the subsample of targets that are related to green house gasses, while
𝑜
𝑆𝐿𝐵
‘non-GHG’ are all other targets. In Panel B the SLB premium is regressed on explanatory variables. The liquidity controls are log(1 + 𝑇 𝐶𝑗,𝑡
) − log(1 + 𝑇 𝐶𝑗,𝑡
), log(1 + 𝑉𝑗,𝑡𝑜 ) − log(1 + 𝑉𝑗,𝑡𝑆𝐿𝐵 ),
and log(1 + 𝐴𝑜𝑗,𝑡 ) − log(1 + 𝐴𝑆𝐿𝐵
𝑗,𝑡 ), where 𝑇 𝐶𝑗,𝑡 is the trade count, 𝑉𝑗,𝑡 is the volume, and 𝐴𝑗,𝑡 is the age for ordinary bond (superscript 𝑜) 𝑗 and SLB (superscript 𝑆𝐿𝐵) 𝑗 on day 𝑡.
Standard error clustered at the bond level are in parentheses, the number of observations in square brackets (in Panel A), and *, **, and *** indicate statistical significance at the
0.10, 0.05, and 0.01 level, respectively.
Panel A: Probability of missing target

Same
Stronger
Stronger & Focused
𝑁

All

GHG

non-GHG

0.39***
(0.01)
0.14***
(0.02)
0.14***
(0.01)
[19,840]

0.37***
(0.01)
0.16***
(0.03)
0.15***
(0.01)
[12,354]

0.41***
(0.02)
0.11***
(0.02)
0.12***
(0.02)
[7486]

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

3.56
(6.01)
1.20***
(0.33)

5.85
(5.80)

6.53
(6.18)

5.89
(6.21)

0.16
(4.95)
1.07***
(0.28)

2.05
(4.79)

2.15
(4.96)

1.57
(4.96)

Panel B: Determinants of SLB premium

Constant
Penalty size
Penalty × Prob (Same)

1.86**
(0.74)

Penalty × Prob (Stronger)

1.55**
(0.66)
1.05
(0.89)

1.08
(0.80)

Penalty × Prob (More Focused)
Log(size)
Equity Vol
Leverage
Profitability
Tobin’s q
Industry-adj ESG rating
ESG rating
Credit rating
Liquidity controls
𝑅2
𝑁

−0.08
(0.33)
0.62*
(0.32)
0.29
(1.11)
−3.11
(3.38)
−0.75
(0.65)
0.06
(0.14)
−0.38
(0.44)
−0.14
(0.20)
No
0.18
19,840

−0.14
(0.32)
0.82***
(0.32)
0.18
(1.20)
−4.97
(3.66)
−1.41
(0.78)
0.16
(0.16)
−0.60
(0.50)
−0.17
(0.19)
No
0.12
19,840

1.92
(1.23)
−0.11
(0.35)
0.89***
(0.33)
0.34
(1.32)
−5.58
(3.84)
−1.67*
(0.89)
0.17
(0.17)
−0.60
(0.52)
−0.17
(0.21)
No
0.08
19,840

−0.13
(0.34)
0.93***
(0.33)
0.48
(1.34)
−5.91
(3.93)
−1.71*
(0.97)
0.20
(0.18)
−0.66
(0.54)
−0.18
(0.21)
No
0.07
19,840

Table 10
𝑜
Mispricing. Panel A shows the average estimate of the ordinary bond 𝑃𝑗,𝑡
in Eq. (11),
𝑆𝑈 𝑆
𝑆𝐿𝐵
the ‘‘sustainium bond’’ 𝑃𝑗,𝑡
in Eq. (9), and the observed bond price 𝑃𝑗,𝑡
. Panel
B shows if the SLB premium is significantly different from the upper bound of the
𝑆𝐿𝐵
𝑜
option value as well as zero (in which case 𝑃𝑗,𝑡 = 𝑃𝑗,𝑡 ). There are 19,840 bond-day
observations and standard errors are clustered at the bond-level and *, **, and ***
indicate statistical significance at the 0.10, 0.05, and 0.01 level, respectively.

𝑀𝑖𝑠𝑝𝑟𝑖𝑐𝑖𝑛𝑔𝑡 =

Mean
90.93

𝑆𝑈 𝑆
𝑃𝑗,𝑡

90.99

𝑆𝐿𝐵
𝑃𝑗,𝑡

91.51

UB - SLB price premium
Liquidity controls
N

0.58***
(0.18)
0.46***
No
19,840

−0.04
(0.29)
0.85***
(0.29)
−0.91
(1.40)
−3.39
(3.43)
−2.21**
(0.88)
0.10
(0.14)
−0.32
(0.46)
0.03
(0.20)
Yes
0.17
19,840

𝑃𝑡𝑆𝐿𝐵 − 𝑃𝑡𝑜
𝑂𝑡𝑈 𝐵

(42)

where 𝑃𝑡𝑆𝐿𝐵 is the SLB price, 𝑃𝑡𝑜 is the price of an ordinary non-ESG
bond given in Eq. (11), and 𝑂𝑡𝑈 𝐵 is the upper bound in Eq. (14). If
the mispricing measure is greater than one, the SLB price premium is
greater than the sum of all penalties and the SLB is overpriced. If the
measure is less than zero, the SLB premium is negative and the SLB is
underpriced. For values between zero and one there is no mispricing.
Table 10 Panel A shows summary stats for the variables used in
calculating the mispricing measure. The average ordinary bond price is
90.93 while the average sustainium-only bond price is 90.99 (i.e. an average sustainium of 1.28 bps in yield space documented in Section 5.2

Panel B: Mispricing test
SLB price premium

−0.06
(0.29)
0.76***
(0.29)
−1.03
(1.31)
−2.83
(3.27)
−1.85**
(0.74)
0.06
(0.13)
−0.28
(0.42)
0.01
(0.19)
Yes
0.19
19,840

et al., 2022) find that SLBs trade at lower prices than ordinary bonds
on average, i.e. SLBs are underpriced on average.16
We revisit these conflicting results by relying on a mispricing measure similar to that proposed by Berrada et al. (2022). For a given bond
at time 𝑡 the measure is given as

Panel A: Average prices

𝑜
𝑃𝑗,𝑡

−0.01
(0.29)
0.58**
(0.29)
−0.86
(1.30)
−1.17
(3.09)
−1.25*
(0.67)
−0.03
(0.11)
−0.09
(0.38)
0.03
(0.19)
Yes
0.24
19,840

1.87*
(1.11)
−0.03
(0.30)
0.81***
(0.30)
−1.05
(1.40)
−3.08
(3.35)
−2.15***
(0.82)
0.07
(0.13)
−0.25
(0.43)
0.05
(0.20)
Yes
0.17
19,840

−0.01
(0.15)
1.04***
Yes
19,840

16

11

Berrada et al. (2022) also finds that a subset of SLBs are overpriced.

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Table 11
ESG risk premium. Panel A shows the average ESG risk premium given in Eq. (16). ‘GHG’ is the subsample of targets that are related to green house gasses, while ‘non-GHG’
are all other targets. If an SLB has multiple targets, it is included in the GHG sample if all options are GHG related, else it is included in the non-GHG sample. Panel B shows
regressions with the ESG risk premium on the lefthand side. The credit rating variables measures the bond’s credit rating and takes the value 1 for AAA, 2 for AA+, 3 for AA, …
𝑜
𝑆𝐿𝐵
, 21 for C. The liquidity controls are log(1 + 𝑇 𝐶𝑗,𝑡
) − log(1 + 𝑇 𝐶𝑗,𝑡
), log(1 + 𝑉𝑗,𝑡𝑜 ) − log(1 + 𝑉𝑗,𝑡𝑆𝐿𝐵 ), and log(1 + 𝐴𝑜𝑗,𝑡 ) − log(1 + 𝐴𝑆𝐿𝐵
𝑗,𝑡 ), where 𝑇 𝐶𝑗,𝑡 is the trade count, 𝑉𝑗,𝑡 is the volume, and
𝐴𝑗,𝑡 is the age for ordinary bond (superscript 𝑜) 𝑗 and SLB (superscript 𝑆𝐿𝐵) 𝑗 on day 𝑡. Standard error clustered at the bond level are in parentheses, the number of observations
in square brackets (in Panel A), and *, **, and *** indicate statistical significance at the 0.10, 0.05, and 0.01 level, respectively. Regressions (1) and (4), (2) and (5), and (3) and
(6) use the ESG premium as calculated with the same, stronger, and stronger & focused commitment assumptions, respectively.
Panel A: ESG risk premium

Same
Stronger
Stronger & Focused
𝑁

All

GHG

non-GHG

−0.22
(0.19)
−0.41**
(0.20)
−0.42**
(0.20)
[19,840]

0.03
(0.17)
−0.14
(0.18)
−0.15
(0.18)
[12,354]

−0.63
(0.41)
−0.85**
(0.41)
−0.86**
(0.41)
[7486]

Panel B: Determinants of the ESG risk premium

Constant
VIX
Log(size)
Equity Vol
Leverage
Profitability
Tobin’s q
Industry-adj ESG rating
ESG rating
Credit rating
Liquidity controls
𝑅2
𝑁

(1)

(2)

(3)

(4)

(5)

(6)

−7.57
(6.52)
2.01
(1.31)
0.25
(0.36)
−0.75**
(0.35)
−0.88
(1.30)
5.73
(4.09)
1.06
(0.84)
−0.26
(0.18)
0.74
(0.56)
0.14
(0.22)
No
0.08
19,840

−7.17
(6.77)
1.89
(1.34)
0.22
(0.37)
−0.77**
(0.36)
−0.94
(1.34)
5.81
(4.14)
1.16
(0.87)
−0.25
(0.18)
0.71
(0.56)
0.13
(0.23)
No
0.08
19,840

−7.12
(6.77)
1.94
(1.35)
0.22
(0.37)
−0.77**
(0.36)
−0.96
(1.35)
5.80
(4.13)
1.16
(0.88)
−0.25
(0.18)
0.71
(0.56)
0.13
(0.23)
No
0.08
19,840

−2.99
(5.18)
1.97
(1.34)
0.17
(0.30)
−0.67**
(0.31)
0.58
(1.38)
3.10
(3.53)
1.57**
(0.79)
−0.15
(0.14)
0.38
(0.46)
−0.08
(0.21)
Yes
0.18
19,840

−2.39
(5.40)
1.86
(1.35)
0.13
(0.31)
−0.68**
(0.31)
0.60
(1.43)
3.08
(3.57)
1.69**
(0.81)
−0.14
(0.14)
0.34
(0.46)
−0.10
(0.21)
Yes
0.19
19,840

−2.34
(5.40)
1.91
(1.35)
0.13
(0.31)
−0.68**
(0.31)
0.58
(1.43)
3.08
(3.56)
1.69**
(0.81)
−0.15
(0.14)
0.34
(0.46)
−0.10
(0.21
Yes
0.19
19,840

translates into 6 bps in price space). The SLBs have a price that is on
average $0.58 higher for a face value of $100 than an ordinary bond.
We test if there is mispricing in Table 10 Panel B. The table
shows that without liquidity controls the average SLB price premium is
significantly higher than zero and significantly below the upper bound.
The SLB price premium reduces when controlling for bond liquidity,
but the conclusion that there is no statistical evidence for mispricing
remains.
Fig. 4 shows the mispricing measure over time. The figure shows
that there are periods in 2022–2023 where the mispricing measure is
less than zero, but the underpricing is short and statistically insignificant. In the last part of the sample, the mispricing measure is slightly
greater than one, but again the distance to the mispricing bound of one
is statistically insignificant. Overall, we find no evidence that SLBs are
mispriced.
Why are our results different from the existing literature? First,
Berrada et al. (2022) and Kölbel and Lambillon (2023) focus on pricing
of SLBs in the primary market, while we focus on pricing in the
secondary market. Second, and perhaps more importantly, our matching procedure is different from theirs. Kölbel and Lambillon (2023)
compare the yield-at-issuance of an SLB with the yield-at-issuance with
an ordinary bond issued by the same firm with the closest issue date,
maturity and issue size. On average, the issuance date of the SLB is 528
days later than the ordinary bond in their sample and this difference is
likely to introduce systematic noise due to changes in macro-economic
variables such as interest rates and macro-economic uncertainty. For
example, the average issuance date of the ordinary bonds in their
matched sample is March 2020 – when Covid shocked markets – while

the average issuance date of the SLBs is September 2021, a significantly
more calm period. This may explain why they find a ‘‘free lunch’’,
i.e. that the prices of SLBs are so high that on average the mispricing
measure is higher than one. Berrada et al. (2022) discount SLB cash
flows without the penalty with sector curves estimated using bonds
with the same rating issued by firms in the same industry and find
that on average SLB prices are lower, i.e. a mispricing measure lower
than zero. Within a rating category there is a wide range of yields and
the sector curve yield might therefore not reflect the yield of the SLB
issuer with sufficient accuracy, leading to a noisily estimated mispricing
measure. In contrast, our approach carefully matches the secondary
market SLB yield with an interpolated yield from non-SLB bonds with
similar maturity from the same issuer on the same day, leading to more
precise estimates.
5.5. ESG risk premium
The SLBs in our sample span a range of distinct ESG targets and
some may command a risk premium. Since targets related to emission
of greenhouse gasses are most common we separate them into GHG and
non-GHG. It is not clear if there is a GHG risk premium and if so what
sign it is expected to have. On one hand emissions of GHGs contribute
to global warming and if there is a global lack of coordination in
reducing GHGs, emissions increase more than expected resulting in
increased risk of states with low consumption due to climate disasters.
In this case, the embedded options in SLBs are a hedge against climate
risk because the firm is more likely to miss the target in such bad states
of the world, leading to extra bond cash flows, and SLBs have a negative
12

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Fig. 3. Yield sustainium. A raw sustainium is estimated by calculating the yield difference between the yield of non-SLBs and the yield on a subset of SLBs with the feature that
their coupon is not tied to the issuing firm reaching a sustainability target (instead the firm donates money to sustainability-linked causes). For that sample the raw sustainium
is regressed on firm-level characteristics and a predicted sustainium is computed for all firms using the regression coefficients. The graph shows the monthly average predicted
sustainium for months with at least four bonds in the sample period with a 95% confidence band using standard errors clustered at the bond level.

risk premium. On the other hand high economic activity may result in
large emissions of GHGs which in turn make it more likely that the
SLB option ends in the money. Here, the option pays of in a good state
of the world – in terms of consumption – and investors may require a
positive risk premium.17
Since we are interested in the risk premium related to cash flow risk,
we estimate the risk premium as the expected value of the optional cash
flows minus the market price of those cash flows as outlined in Section 3.2.3. Table 11 Panel A shows the average ESG risk premium and
we see that the point estimates are mostly negative, and statistically
significant in some specifications, consistent with the embedded option
being a hedge against ESG risk. However, when we focus on SLBs with
GHG targets, the average risk premium is statistically insignificant and
the sign is not consistently negative, suggesting that the negative risk
premium is not due to hedging of climate risk. For non-GHG SLBs the
risk premium is significantly negative in some specifications. The nonGHG targets include a range of different ESG areas and this suggests
that ESG risks unrelated to climate change are priced.18
Turning to determinants of the risk premium, Panel B shows that
there is no significant relation between the ESG risk premium and
risk premiums in general — as measured through the VIX. The only
firm characteristics that have significant explanatory power for the risk

premium across specifications is equity volatility and a higher equity
volatility implies a more negative ESG risk premium.
6. Conclusion
A major issue in global financial markets is how to speed up the shift
to a greener and more socially inclusive economy. Aligning financial
incentives of companies with ESG incentives is a critical component
of the solution, and sustainability-linked bonds (SLBs) have recently
emerged as a class of securities that can support such alignment.
Because SLB cash flows are directly linked to achieving future ESG
goals, they encourage issuing companies to take ESG-conscious actions.
Financial market practitioners, regulators, NGOs and academics are
concerned that SLBs do not work as intended. Firms may chose easy targets that reflect ‘‘business-as-usual’’ and the ESG-related option element
may be difficult to price and the bonds overpriced. If this is the case,
SLBs will not work as intended and may even hinder firms’ transition
to a greener economy. We provide a flexible theoretical framework
for pricing SLBs that includes credit risk, investor preferences for
sustainable securities, the likelihood that the firm will fulfil the target
and the penalty size in order to analyse these important concerns.
SLB cash flows are identical to cash flows of an ordinary fixed-rate
bond plus ESG-linked cash flows that only pay out if a combination
of ESG targets are not reached. Absence of mispricing requires that the
value of the ESG-linked cash flows is greater than zero but less than the
sum of potential cash flows. Empirically, we find that SLBs on average
satisfy these ‘‘no-mispricing’’ bounds, in contrast to existing literature.
Also, we find that the value of the ESG option embedded in SLBs is
strongly related to the size of the penalty. Overall, our empirical results
indicate no mispricing.

17

See Giglio et al. (2021) for an extensive review.
Besides those mentioned in Section 2, examples include number of electric
vehicle charging points installed in managed infrastructure (Abertis), reduction
in the amount of packaging placed on the market (Carrefour), increasing
amount of recycled plastic usage (Hera), increase patient outreach/access
(Novartis), and reducing industrial water withdrawal intensity (Suzano).
18

13

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.

Fig. 4. Mispricing. The figure shows the time series variation of the mispricing measure for the SLB premium. On each day in the sample where we have at least ten observations
we compute the mispricing measure as the average SLB premium on that day divided by the average upper bound on the same day and the figure shows the time series variation.

We also find that firms set targets that are easy to reach: the average
probability of meeting the target in our sample period is 61%–86%. Furthermore, we find that investors are willing to accept a 1–2 bps lower
yield due to SLBs ESG label, providing new empirical evidence showing
that impact investing matters for asset prices. Finally, we estimate the
ESG premium as the expected value of the potential penalty minus the
extracted market price. The ESG premium is negative, and statistically
significant under some assumptions, providing evidence that SLBs can
be used as financial hedges against ESG risk.

A.2. Propellant
The Propellant data used in the paper covers transactions from:
Bloomberg, London Stock Exchange, Marketaxess, Tradeecho,
Tradeweb, Tradition, and Liquidnet. We clean the Propellant data the
following way:
1. Multiple amended trades (‘AMND’ = True) point to the same
‘ORIGINAL_TRANSACTION_IDENTIFICATION_CODE’, so we
only keep the last amended trade for a given
‘ORIGINAL_TRANSACTION_IDENTIFICATION_CODE’ and drop
any amended trades without one.
2. Drop trades without any ‘TRADING_DATE_AND_TIME’ and
‘PRICE’ information.
3. Drop cancelled trades (‘CANC’ = True).
4. Drop all observations that are not in the percentage of par price
format
(‘PRICE_NOTATION’ ≠ ‘PERC’).
5. Drop entries with extreme prices (below 10 and above 1000).
These are mostly due to wrong price information due to a
misplaced decimal point.
6. There is no volume cap in the Propellant data set, however, since
there is a volume cap on TRACE data of 5,000,000, we impose
the same cap on the Propellant data for comparability.

CRediT authorship contribution statement
Peter Feldhütter: Writing – review & editing, Writing – original
draft, Formal analysis. Kristoffer Halskov: Writing – review & editing,
Writing – original draft, Formal analysis. Arthur Krebbers: Writing –
review & editing, Writing – original draft.
Declaration of competing interest
The authors have nothing to disclose.
Data availability
Pricing of Sustainability-Linked Bonds Dataset (Reference data) (Mendeley Data)

Table A.1 below shows the amount of transactions that are removed
at each step of the cleaning process described above.

Appendix. Data
In this Appendix we discuss in more detail how we clean the data.

A.3. Final sample

A.1. Bloomberg

To arrive at the final sample used in our empirical analysis, we first
discard all SLB bond-days after the bond’s first option target date. Next,
we remove SLB bonds from the sample if there are less than 20 bondday observations for the bond. Also, we discard a bond-day if we are
not able to calculate the price of an ordinary bond (𝑃𝑗,𝑡 ), the price of a
𝑆𝑈 𝑆 ), and – for the SLBs with ESG-linked coupons –
sustainium bond (𝑃𝑗,𝑡
]
∑ ∑ 𝑁𝑗 𝑗 𝑃 [
the physical option value 𝐾
𝑆 𝐸 1{𝐺𝑇 >𝐾} 𝐷(𝑟𝑡,𝑇 , 𝜆𝑡 , 𝜔𝑡 , 𝑡𝑗𝑖 ). In
𝑗=1
𝑖=1 𝑖 𝑡

Bloomberg has several data sources available and we prioritize the
data sources in the order: ‘CBBT’, ‘BGN’, ‘BMRK’, and ‘BVAL’. That is,
for a given bond-day, we extract price and yield spread information
from CBBT, and if there is none, we try BGN, and so on. We use
Bloomberg’s I-spread as yield spread, which uses the relevant swap rate
in the same currency as the bond when calculating the spread.

𝑗

14

Journal of Financial Economics 162 (2024) 103944

P. Feldhütter et al.
Table A.1
Cleaning process of the Propellant data set. This table shows the number of transactions
that are removed at each step of the cleaning process, as well as how many transactions
remain afterwards. The description of each step can be found in the text.
Cleaning step

# of transactions removed

# of transactions remaining

Uncleaned data
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6

–
2723
65,199
4891
9479
188
–

382,766
380,043
314,844
309,953
300,474
300,286
300,286

8. Industry-Adjusted
ESG Rating:
Numerical
demeaned) ESG rating extracted from MSCI.
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particular, this implies that we can compute the firm characteristics
𝑋𝑗,𝑡 in Eq. (29) on day 𝑡 for the firm issuing bond 𝑗 and we have
at least three historical
observations
of the ESG factor such that we
[
]
can calculate 𝐸𝑡𝑃 1{𝐺𝑇 >𝐾} . For sustainium-only bonds, we require that
𝑗

we can compute the firm characteristics 𝑋𝑗,𝑡 in Eq. (29) on day 𝑡 for
the firm issuing bond 𝑗. Finally, we exclude the bond with Bloomberg
ticker ‘BS422627 Corp’ because the bond prices in Bloomberg are not
consistent with the reported yield-to-maturity.
A.4. Calculation of firm characteristics
Since we are dealing with a sample of global firms, we use Compustat to gather both price and accounting data. This requires finding
the unique GVKEY of each firm in our sample, which has been done
manually. All accounting data has been lagged 3 months to avoid
look-ahead bias. Furthermore, all accounting data have been converted
to USD by following the ‘‘Currency Translation’’ guide provided by
Compustat. The following list details the calculation of the eight firm
characteristics used in Section 5 of the paper:
1. Log(Size): log(𝐸𝑖𝑡𝑀 ), where 𝐸𝑖𝑡𝑀 is the market value of equity
calculated as ‘‘Common Shares Outstanding ’’ times ‘‘Price - Close Daily’’ for firm 𝑖 at time
√ 𝑡.∑
21
1
2
2. Equity Volatility:
𝑡=1 (𝑟𝑖𝑡 − 𝑟̄𝑖 ) , where 𝑟𝑖𝑡 is the equity
21
return of firm 𝑖 at time 𝑡 and 𝑟̄𝑖 is the average equity return
over the past 21 days for firm 𝑖. Returns are calculated using the
daily prices from Compustat, adjusted for dividends and stock
buybacks/issuance/splits.
3. Leverage:

𝑆 +𝐷𝐿
𝐷𝑖𝑡
𝑖𝑡
𝑆 +𝐷𝐿
𝐸𝑖𝑡𝑀 +𝐷𝑖𝑡
𝑖𝑡

, where 𝐷𝑖𝑡𝑆 and 𝐷𝑖𝑡𝐿 is ‘‘Debt in Current

Liabilities’’ and ‘‘Long-Term Debt - Total’’, respectively.
𝑅 −𝐶
4. Profitability: 𝑖𝑡𝐴 𝑖𝑡 , where 𝑅𝑖𝑡 , 𝐶𝑖𝑡 , and 𝐴𝑖𝑡 is ‘‘Revenue - Total’’,
𝑖𝑡

‘‘Cost of Goods Sold’’, and ‘‘Assets - Total’’, respectively.
5. Tobin’s Q: Defined as

𝐸𝑖𝑡𝑀 +𝐿𝑀
𝑖𝑡
𝐸𝑖𝑡𝐵 +𝐿𝐵
𝑖𝑡

(industry

, where 𝐸 and 𝐿 refer to the

equity and liabilities values of the firm, respectively, while the
superscripts 𝑀 and 𝐵 indicates the market and book values,
respectively. Because we do not have data on the total market
𝐵
value of a firm’s liabilities, we let 𝐿𝑀
𝑖𝑡 = 𝐿𝑖𝑡 . The book value of
𝐵
equity, 𝐸𝑖𝑡 , is calculated as ‘‘Stockholder’s Equity’’ plus ‘‘Deferred
Taxes and Investment Tax Credit ’’ minus ‘‘Preferred/Preference
Stock (Capital) - Total’’. Missing values of ‘‘Stockholder’s Equity’’
and ‘‘Preferred/Preference Stock (Capital) - Total’’ are set to 0
and equity book values below 0 are set to 0. The book value
of liabilities, 𝐿𝐵
𝑖𝑡 , is ‘‘Liabilities - Total’’. Finally, the variable is
scaled by dividing with 100.
6. Credit Rating: Extracted manually from Bloomberg and converted to a numerical value such that a higher number corresponds to a lower credit rating, i.e. 𝐴𝐴𝐴 = 1, 𝐴𝐴+ = 2, . . . ,
𝐶 = 21.
7. ESG Rating: Numerical ESG rating extracted from MSCI. Values
are between 0 and 10 with a higher number corresponding to a
more green and sustainable firm.
15


==> JFE02 - Business groups and the incorporation of firm-specific shocks into stock prices.txt <==
Journal of Financial Economics 139 (2021) 852–871

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Business groups and the incorporation of ﬁrm-speciﬁc shocks
into stock prices ✩
Mara Faccio a,b,c,d, Randall Morck b,c,d,e, M. Deniz Yavuz a,∗
a

Purdue University, Krannert School of Management, 403W. State Street, West Lafayette, IN 47907, United States
Asian Bureau of Finance and Economics Research, NUS Business School, BIZ 2 Storey 4, #04-05 1 Business Link 117592, Singapore
c
European Corporate Governance Institute, c/o the Royal Academies of Belgium, Palace of the Academies, Rue Ducale 1 Hertogsstraat,
1000 Brussels, Belgium
d
National Bureau of Economic Research, 1050 Massachusetts Ave, Cambridge MA 02138, United States
e
University of Alberta, Alberta School of Business, 4-20K Business Building, Edmonton, AB T6G 2R6, Canada
b

a r t i c l e

i n f o

Article history:
Received 3 December 2019
Accepted 12 February 2020
Available online 11 October 2020
JEL classiﬁcation:
G14
G15
G32
G34
M41

a b s t r a c t
Firm-speciﬁc information has a damped effect on business group-aﬃliated ﬁrms’ stock
prices. Such ﬁrms’ idiosyncratic stock returns are less responsive to idiosyncratic commodity price shocks than are the idiosyncratic returns of otherwise similar unaﬃliated ﬁrms
in the same country and commodity-sensitive industry. Using global commodity shocks
means we assess responses to common idiosyncratic shocks of the same magnitude, frequency, and observability. Further identiﬁcation follows from difference-in-difference tests
exploiting successful and matched exogenously failed control block transactions. We conclude that business group ﬁrms’ stock prices provide less ﬁrm-speciﬁc information to capital providers and managers.
© 2020 Elsevier B.V. All rights reserved.

Keywords:
Business groups
Incorporation of ﬁrm-speciﬁc information
Economic growth

1. Introduction
✩

We thank participants at the 2019 Arizona State University (ASU)
Sonoran Winter Finance Conference, Ball State University, Cambridge
Judge Business School, Copenhagen Business School, Erasmus University
Rotterdam, George Mason University, INSEAD, KU Leuven, Louisiana State
University, Maastricht University, the 2019 Mitsui Conference at the University of Michigan, Northeastern University, Politecnico School of Management, Purdue University, Surrey Business School, Tilburg University,
Università Bocconi, the University of Birmingham Business School, the
University of British Columbia, the University of Illinois at Chicago, University of Lugano, and Zhongnan University of Economics Law Wenlan
School of Business, as well as Heitor Almeida (discussant), George Aragon,
Susan Feinberg, Radhakrishnan Gopalan, Jeff Pontiff, and Kelly Shue for
comments and earlier discussions. We thank Mitch Johnston, Chen Zhaojing and Shrijata Chattopadhyay for excellent research assistance.
∗
Corresponding author.
E-mail addresses: mfaccio@purdue.edu (M. Faccio), rmorck@ualberta.ca
(R. Morck), myavuz@purdue.edu (M. Deniz Yavuz).

https://doi.org/10.1016/j.jﬁneco.2020.09.005
0304-405X/© 2020 Elsevier B.V. All rights reserved.

A fundamental role of the stock market is to incorporate
ﬁrm-speciﬁc (idiosyncratic) information into stock prices
(Grossman, 1976), which provide feedback to ﬁrms’ managers and capital providers (Bond et al., 2012) so that their
capital allocation decisions are more economically eﬃcient
(Tobin, 1984). We ﬁnd that business groups damp this
stock-price feedback mechanism because investors’ expectations about intra-group risk sharing and transfers confound stock price responses to idiosyncratic shocks.1 Given
that the eﬃciency of capital allocation and productivity
growth are impaired when stock prices move less idiosyn-

1
We deﬁne business groups as collections of listed ﬁrms under common control through equity blocks.

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

cratically (Wurgler, 20 0 0; Durnev et al., 2004a), our results
suggest that more businesses belonging to groups could
damp the eﬃciency of capital allocation and productivity
growth in an economy.
We hypothesize that business group member ﬁrms’
stock prices incorporate less ﬁrm-speciﬁc information because investors expect intragroup risk-sharing and resource transfers. Business groups, which are ubiquitous
around the world, can spread risk across their member ﬁrms (Hoshi et al., 1990, 1991; Friedman et al.,
2003; Khanna and Yafeh, 2005; Gopalan et al., 2007) and
can shift resources from member ﬁrms with excess free
cash ﬂow to low-earnings ﬁrms with unﬁnanced profitable investments (Almeida and Wolfenzon, 2006a), fund
private beneﬁts for their top insiders (Johnson et al.,
20 0 0; Bertrand et al., 20 02), or prop up ill-run aﬃliates
(Morck and Nakamura, 1999). Investors, expecting business
groups to behave in any or all of these ways, would rationally expect idiosyncratic shocks to have less impact on
the share price of a group aﬃliate than on the share price
of an otherwise comparable unaﬃliated ﬁrm.
Ascertaining whether or not business groups cause their
member ﬁrms’ share prices to move less idiosyncratically is a diﬃcult econometric challenge because idiosyncratic shocks to different ﬁrms vary in frequency, magnitude, and observability. One would ideally like to observe
the responses of group-aﬃliated and unaﬃliated ﬁrms to
the same shock. This is what we do by introducing a
novel methodology that focuses on how shocks to global
commodity prices are incorporated into stock prices of
ﬁrms in the same commodity-sensitive industries. These
shocks are observable by all market participants; affect all
commodity-sensitive ﬁrms in the same country and industry with the same magnitude, permanence, and frequency;
and are measured prior to any risk sharing, propping, or
tunneling activities.
Our identiﬁcation strategy relies on matching commodities to industries and, thus, to ﬁrms. We do this
in three main ways. The ﬁrst approach uses statistically
estimated out-of-sample sensitivities of stocks in U.S.
industries to commodity shocks, emulating the Rajan and
Zingales (1998) methodology for ﬂagging external ﬁnancesensitive sectors. The major advantage of the statistical
method is that it gauges the sensitivity of stocks in
an industry to commodity price-related shocks through
all possible channels, including supply and demand effects, linkages to untraded commodities, or other factors
(Anderson and Danthine, 1981). The second approach, constrained statistical matches, selects commodity-industry
links that best satisfy the criterion of the statistical method
subject to the requirement that the matched industry also
be a direct user or producer of the commodity in the Bureau of Economic Analysis (BEA) input-output (I-O) tables.
The third approach simply links industries to commodities
that constitute large fractions of their inputs or outputs in
the BEA input-output tables. Because business groups are
relatively unimportant in the US (La Porta et al., 1999a;
Masulis et al., 2011), our use of U.S. data as benchmarks
for the statistical method and constrained statistical
method mitigates attenuation bias due to group-aﬃliated
ﬁrms possibly being less responsive to commodity shocks

that would result if we used groups’ domestic country
data instead. The third method sidelines this problem
by focusing on commodity inputs and outputs instead of
estimating sensitivities in sample.
Our main ﬁnding is that the idiosyncratic returns of
business group-aﬃliated ﬁrms are less responsive to idiosyncratic commodity price shocks than are the idiosyncratic returns of unaﬃliated ﬁrms after controlling for
time-varying country-industry level latent variables. The
results are not driven by ﬁrm-level observable characteristics such as hedging, diversiﬁcation across industries, a
ﬁrm’s equity ownership of other ﬁrms, leverage, size, or
research and development (R&D) activity. The results are
robust to battery of tests.2
Further identiﬁcation follows from difference-indifference tests exploiting changes in group aﬃliation, control block acquisitions, and failed control block bids. When
previously unaﬃliated ﬁrms become group-aﬃliated, their
stocks become less sensitive to commodity price shocks.
Likewise, when previously aﬃliated ﬁrms cease to be
group-aﬃliated, their stocks become more sensitive to
such commodity price shocks. Further identiﬁcation tests
preclude potential selection problems in control block
transactions by comparing successful control block acquisitions with matched control block bids that failed for
exogenous reasons (Seru, 2014), and reaﬃrm our results.
We also show that when a group aﬃliate in a
commodity-sensitive sector is hit by a commodity price
shock, the stocks of the group’s other aﬃliates in sectors not sensitive to that commodity react to the shock
nonetheless. These results are consistent with investors expecting risk sharing or income shifting within business
group ﬁrms to spread ﬁrm-speciﬁc stock return volatility
associated with idiosyncratic commodity shocks across afﬁliates.
Group aﬃliation attenuates share price responses to
commodity shocks, so it may well attenuate share price
responses to other ﬁrm-speciﬁc shocks and increase stock
price synchronicity across all the ﬁrms in the business
group. Attenuated ﬁrm-speciﬁc shocks should increase a
stock’s co-movement with its market, measured by its market model R2 . Firm-level tests show business group aﬃliates’ stocks co-moving more with their markets than do
otherwise similar unaﬃliated ﬁrms’ stocks. This is consistent with our results generalizing to other idiosyncratic
shocks, i.e. investor’s expectations of intra-group transactions confounding the effects of other idiosyncratic shocks
on stock prices.
We contribute to the literature in several ways. First,
the novel methodology we develop, tracking the responses
of investors to the same idiosyncratic commodity shock,
could have broader applications. An important feature of
this shock is that it is globally determined, observed by
all investors and, unlike commonly used accounting measures, unaffected by ex-post actions, such as wealth transfers. We posit that differences in group ﬁrms’ stock price
responses to these idiosyncratic shocks could provide a
2
We vary industry-commodity matching, business group aﬃliate identiﬁcation, regression speciﬁcations, samples and the asset pricing model
used in calculation of idiosyncratic returns.

853

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Fig. 1. Stock return co-movement, economic development, and the importance of business groups.
The R2 s are from Morck et al. (2013), averaged across 1995–2010. Gross domestic product (GDP) per capita, from the International Monetary Fund’s
World Economic Outlook dataset [https://www.imf.org/external/pubs/ft/weo/2019/02/weodata/index.aspx] is in current US dollars and is averaged across
all sample years. The country abbreviations are from the same dataset. Fraction of group-aﬃliated observations (incidence of business groups) is from
Table 1. The sample contains 40 countries that are in Morck et al. (2013) and in Table 1.

measure of investors’ expectation about the internal operations of business groups with different structures, in different economic conditions, or in eras or countries with different laws or regulations.
Second, the results highlight a salient consequence to
engaging in activities such as risk sharing, income shifting, and propping: damping the feedback that stock prices
provide to managers and shareholders about each individual group ﬁrm’s investment decisions and opportunities. Business groups may arise to substitute group-level
centrally planned resource allocation for stock market directed resource allocation in countries whose stock markets work poorly (Khanna and Yafeh, 2007). However, our
results show a feedback effect: expected resource allocation at the business group-level damps individual stock
price reactions to ﬁrm-speciﬁc events, making stock prices
less informative as guides to ﬁrm-level resource allocation.
Business groups can thus be a cause as well as a consequence of impaired information ﬂow in the stock market.
Third, we show business group prevalence to be a complementary explanation, in addition to others surveyed
by Morck et al. (2013), of market-level stock synchronicity. Our ﬁrm-level tests aﬃrm a causal role for business
groups in damping ﬁrm-speciﬁc stock price movements.
Fig. 1 shows that stock returns are more synchronous in
economies where more ﬁrms are group-aﬃliated.
Fourth, we causally link two seemingly unrelated ﬁndings in the literature. Stock prices move less idiosyncratically in lower income economies (Morck et al., 20 0 0) and
business groups are also more prominent in lower income economies (R. La Porta et al., 1999b; Fogel, 2006;
Khanna and Yafeh, 2007; Masulis et al., 2011). This pattern
is evident in Fig. 1 as well, but income levels could proxy

for any number of factors associated with both stock return synchronicity and the prevalence of business groups.
Our study connects these two lines of research by showing
that business group aﬃliation causes stock prices to react
less to idiosyncratic shocks.
In summary, group ﬁrms’ stocks moving less than do
the stocks of otherwise similar unaﬃliated ﬁrms on the
same commodity price shock event can be viewed as
each individual group ﬁrm’s stock price providing less
ﬁrm-speciﬁc feedback to capital providers and managers
(Bond et al., 2012). Business groups can be a secondbest response to high capital market information and
transactions costs (Khanna and Yafeh, 2007). However,
our ﬁndings show that business groups can also exacerbate such costs by confounding the incorporation of
idiosyncratic information into group ﬁrms’ stock prices,
which can reduce the value and, therefore, the production of ﬁrm-speciﬁc information (Veldcamp, 2006),
creating a lock-in effect. Given that idiosyncratic information incorporated into stock prices correlates
highly with economy-level eﬃciency of capital allocation (Wurgler, 20 0 0), business groups could trap an
economy in a state of ineﬃcient capital allocation. We
posit that business groups could help explain the stability
of the middle income trap (Rajan and Zingales, 2004;
Almeida and Wolfenzon, 2006b; Eichengreen et al., 2013),
in which many economies’ growth slows and stalls
after a ﬁrst generation of large businesses rises, an issue of ﬁrst-order importance in ﬁnancial and economic
development.
Section 2 describes the data and methods of isolating
commodity shocks and identifying commodity-sensitive industries. Section 3 presents the baseline results associating
854

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

business group aﬃliation with reduced stock price sensitivity to commodity shocks. Section 4 explains causal inference and Section 5 discusses robustness. Section 6 discusses economy level implications and Section 7 concludes.

ﬁed as a government, corporation, or investment fund is
presumed to be an individual.
Firms whose controlling shareholder is a government entity are dropped from the sample because soft
budget constraints of state-owned enterprises (SOEs)
(Kornai, 1986) could affect the link between their fundamentals and stock returns. SOEs’ public shareholders could
anticipate bailouts to smooth earnings ﬂuctuations, and
natural monopoly SOEs could pass shocks to consumers,
partially immunizing shareholders. SOE shares’ reactions
thus can resemble those of group aﬃliates even if the SOEs
are not formal aﬃliates of state-controlled groups of listed
ﬁrms, such as existed in Austria and Italy until recently and
remain important in China.
We classify a ﬁrm as group-aﬃliated if its controlling
shareholder is a corporation, if its controlling shareholder
is an individual who controls at least one other ﬁrm in
our sample, or if the ﬁrm itself is the controlling shareholder of at least one other ﬁrm in our sample. All other
ﬁrms, including those controlled by investment funds, are
designated as unaﬃliated. This classiﬁcation algorithm follows prior studies (e.g. Faccio et al., 2001; Bae et al., 2002;
Bertrand et al., 2002; Baek et al., 2006; Masulis et al., 2011)
in deﬁning business groups as collections of separate legal
entities under common control through equity blocks.
To identify controlling shareholders who own control blocks in multiple ﬁrms in the sample, the
names of controlling shareholders are matched by
Levenshtein (1965) distance: the minimum number of
single character edits (excluding punctuation, multiple
consecutive spaces, and spaces at the beginning or at
the end) required to change one name into the other,
normalized by the length of the shorter name. If the
Levenshtein distance between two names is 20% or less,
the algorithm infers a match. The algorithm allows for
minor name variations that exact matching would miss,
but it is far from perfect.
False and missed matches are inevitable. The vagaries
of languages and the complexities of control chains (see
Almeida et al., 2011) combined with a relatively stringent
(20%) threshold likely leave missed matches predominating. Our approach misses group aﬃliates controlled via
multiple control chains that sum to over 20% if each fall

2. Data and methodology
Several steps are involved in the construction of our
sample. First, we identify group-aﬃliated ﬁrms. Next, we
calculate idiosyncratic components of stock returns and idiosyncratic components of commodity shocks. Finally, we
identify which industries (and, hence, ﬁrms) should be
sensitive to shocks to the prices of key commodities using
three methods of matching.
2.1. Group aﬃliation
Ownership data for publicly traded ﬁrms worldwide are
from three sources: Worldscope for 1993 through 2009,
Thomson Reuters Ownership for 2005 through 2012, and
Datastream Asset-4 Universe for 2002 through 2013.3 For
an economy to be included in our sample, it must have
at least 50 publicly traded ﬁrms for which we have ownership data at any time during the entire sample period. This
leaves a sample of 43 economies.
Each of these data sources provides the name and the
cash ﬂow (i.e., ownership) rights of each ﬁrm’s largest
shareholder. We presume that the largest blockholder
has a controlling stake if her ownership stake in the
ﬁrm is at least 20%. This cut-off is also employed by La
Porta et al. (1999b) to infer control.4 Using this relatively
high ownership threshold minimizes problems due to
cross-economy differences in the precise threshold that
triggers ownership disclosure. Our data provide ownership
stakes, not voting control stakes, which depend on control
enhancement devices such as dual-class shares, golden
shares, reserved board seats, or pyramiding via unlisted afﬁliates. This almost certainly leads to misclassifying some
group aﬃliates as unaﬃliated and, therefore introduces an
attenuation bias, i.e., biasing point coeﬃcient estimates on
measures of group aﬃliation towards zero.
Controlling shareholders are classiﬁed as governments,
corporations, investment funds or individuals (including
families), using lists of words and abbreviations commonly found in the names of each sort of entity.
Faccio et al. (2011) provide a list of terms commonly found
in the names of government shareholders (in various languages), and Faccio and O’Brien (2020) supply an analogous list for corporate entities. For example, a controlling
shareholder whose name contains the term “Ltd,” or its
equivalent in another language, is presumed to be a corporation, and a controlling shareholder whose name contains
the term “municipal” is presumed to be a government entity. Investment funds are ﬂagged using an analogous list
we develop for this purpose. Terms such as “fund” identify
investment funds.5 Any controlling shareholder not classi-

tual funds [e.g., Sweden (Högfeldt, 2005)], or other institutional investment funds. In recent years, increasing numbers of US ﬁrms have investment funds as common equity blockholders (Gilje, Gormley and Levit,
2018). The Investment Companies Act of 1940 proscribes US investment
companies from intervening in listed ﬁrms’ management decisions except
as shareholders operating via channels legally open to shareholders, so
the effects we explore are less likely to be evident in such cases. Disputed
ﬁndings (e.g., Rock and Rubinfeld., 2017; Schmalz, 2018) nonetheless associate common institutional investor ownership with coordinated corporate strategies, notably price ﬁxing. To avoid counting US exchange-traded
funds or investment funds as controlling shareholders in deﬁning business groups, common blockholders are screened for English terms associated with institutional investors. This presumes that English terms ﬂag
US-based institutional investors and miss those based in other countries.
Robustness tests (not shown) that retain investment companies associated with a business family (using a list of keywords such as “family,”
“estate,” etc.) as common controlling shareholders for the purpose of detecting business groups yields results (not shown) similar to those in the
tables. The list of words used to identify investment funds of business
families is available upon request.

3

All three datasets have been discontinued.
Robustness tests in Section 5.2 use a 15% ownership threshold.
5
In some countries, business families control business groups via pension funds [e.g., Brazil (Perkins, Morck and Yeung, 2014)], closed-end mu4

855

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

below that threshold as well as those controlled via control enhancement devices. This further potential misclassiﬁcation of group aﬃliates as unaﬃliated also adds attenuation bias to the tests. An opposite problem arises if we
misidentify targets in the process of being acquired or divisions in the process of being divested as group aﬃliates.
This is a potentially more serious problem in economies,
such as the US, with more merger and divestiture activity.6
Our procedure yields 55,671 unique ﬁrms and 390,186
ﬁrm-years of ownership data. Table 1, Panel A, summarizes
ﬁrm-year observations classiﬁed as group-aﬃliated versus unaﬃliated, by economy. Consistent with prior studies, business groups are prevalent around the world, and
more prevalent in some economies than others. For example, group-aﬃliated ﬁrms account for large fraction of
ﬁrms in Chile, Hong Kong, Italy, and Peru, but lower
fractions of ﬁrms in Canada, Taiwan, the United Kingdom, and the United States. Stulz (2005) shows how
the percentage of shares held by control block holders
varies across economies. Although presence of a control
blockholder does not imply business group aﬃliation, the
Stulz (2005) ranking of economies by percentage of shares
held by blockholders is consistent with our ranking by the
prevalence of business groups: Canada, Taiwan, the United
Kingdom, and the United States rank low, while Chile and
Peru rank high.

Compared with unaﬃliated ﬁrms, group-aﬃliated ﬁrms
are on average smaller, more leveraged, less invested in
R&D, more diversiﬁed, and less actively hedging. Our tests
thus must allow for these differences between groupaﬃliated and unaﬃliated ﬁrms in contrasting their responses to idiosyncratic shocks.
2.3. Firm-speciﬁc shocks
For each ﬁrm, Datastream weekly (Wednesday-toWednesday) total returns are used. These include price
changes and dividends and are adjusted for stock splits,
reverse splits, and stock dividends. Stocks that trade
for fewer than 12 weeks during our sample period are
dropped, as are ﬁrm-week observations with three or more
missing daily returns in the week. Following prior literature, in particular Jin and Myers (2006), we use a version
of the international capital asset pricing model (CAPM) to
deﬁne ﬁrm-speciﬁc shocks. For the sake of transparency,
we like to avoid changing methodology. However, in robustness tests, we consider an alternative asset pricing
model based on the Fama and French (2015) global 5factor model.
Firm-speciﬁc shocks are the residuals from separate regressions for each ﬁrm in the sample period:

ri,t =αi +

2.2. Firm-level control variables

2 




β1,i,t+l rm,t+l +β2,i,t+l rUS,t+l +eUS,m,t+l +εi,t .

l=−2

(1)

Table 1, Panel B, summarizes the means of key ﬁrmlevel characteristics across group-aﬃliated and unaﬃliated
ﬁrms. The panel reports statistics both from the entire
sample and from the sample excluding US ﬁrms. We report both because in some tests we exclude US ﬁrms. Firm
diversiﬁcation is minus one times the Herﬁndahl Index
of the ﬁrm’s industrial focus, measured using Datastream
annual segment-level revenues in up to ten product segments, so a value of minus one indicates an undiversiﬁed
ﬁrm.7 Leverage is book value of total debt divided by book
value of total assets. Hedging activity is an indicator variable equal to 1 if Datastream reports that the ﬁrm discloses ﬁnancial data associated with hedging or derivative
usage: Comprehensive Income Hedging Gain/Loss, Unrealized Valuation Gains/Losses Hedges/Derivatives, Derivative
Assets Current, Derivative Liabilities Current, Derivative Assets Non-Current, and Derivative Liabilities Non-Current.
The proxies for ﬁrm size, market capitalization in millions
of US dollars and total assets in thousands of US dollars,
enter the regressions as logs. R&D activity is R&D expenses
over total assets. If R&D expenses are missing, R&D spending is presumed insubstantial and set to zero.

The explained variable, ri,t , is the total return of ﬁrm
i’s stock in week tin the local currency. The explanatory
variables are rm , t + l , the stock market return of economy
m (where ﬁrm i’s stock trades) in local currency, rUS,t+l is
the US stock market return (in US dollars), and eUS,m(i ),t+l is
the return from buying US dollars at the beginning of the
week and selling at the end of the week in m’s domestic currency. Including leads and lags, l,of −2,−1, 0, 1, and
2 weeks for the explanatory variables accounts for differences in time zones, illiquidity, and nonsynchronous trading. The residual, εi,t , is the ﬁrm-speciﬁc shock of stock iin
week t. We focus on how shocks to the idiosyncratic component of stock returns, εi,t , react to idiosyncratic shocks
to commodity prices.
2.4. Idiosyncratic commodity shocks
We construct economy-speciﬁc idiosyncratic commodity price shocks by considering how different commodities’ prices can affect different economies’ fundamentals
differently. For example, an oil price increase can have a
more widespread impact across all sectors in a heavily oil
export-dependent economy, such as Norway, than a more
diversiﬁed economy such as Germany.
Datastream provides daily price indexes for major commodities, whose prices are globally determined, starting in
1993.8 Tables 2 and 3 list these and their Datastream iden-

6
Many instances of listed US ﬁrms holding equity blocks exceeding 20% in other listed ﬁrms could be corporate control transactions in
progress. Acquirers often begin with toehold acquisitions followed by bids
for all the target’s shares (Betton, Eckbo and Thorburn, 2009). Lasting toeholds exist, for example between ﬁrms undertaking a joint venture, but
the stakes are typically far smaller than 20% and do not indicate common
control (Ouimet, 2013).
7
If segment-level sales are unreported we assume the ﬁrm’s sales are
in one segment.

8
Commodities such as natural gas, whose pricing is subject to segmented markets problems, are excluded from the sample.

856

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Journal of Financial Economics 139 (2021) 852–871

Table 1
Group-aﬃliated ﬁrms.
The Panel A tabulates the count of ﬁrm-year observations in our ﬁnal ownership sample during 1993–
2013. Panel B reports mean characteristics of group-aﬃliated and unaﬃliated ﬁrms averaged across all
available ﬁrm-year observations. We classify ﬁrms as group-aﬃliated if they satisfy one of the following
criteria: the controlling shareholder is a corporation (with the exclusion of investment funds), the controlling shareholder is an individual who controls at least one other ﬁrm in our sample, or the ﬁrm itself
is the controlling shareholder of at least one other ﬁrm in our sample. Firms are otherwise classiﬁed as
unaﬃliated ﬁrms. State-owned enterprises are excluded from the sample. Market size and total assets are
in millions of US dollars.
Panel A: Incidences and fractions of group-aﬃliated ﬁrm-year observations, by economy
Economy name

Unaﬃliated
ﬁrm-year

Group-aﬃliated
ﬁrm-year

Total

Fraction of
group-aﬃliated
observations

Australia
Austria
Belgium
Brazil
Canada
Chile
China
Croatia
Denmark
Egypt
Finland
France
Germany
Greece
Hong Kong
India
Indonesia
Ireland
Israel
Italy
Japan
Jordan
Kuwait
Malaysia
Mexico
Netherlands
New Zealand
Norway
Peru
Philippines
Poland
Russian Federation
Singapore
South Africa
South Korea
Spain
Sweden
Switzerland
Taiwan
Thailand
Turkey
United Kingdom
United States

14,847
533
1115
2069
19,601
735
6661
280
2330
508
1358
7674
6718
1893
5493
9751
2252
866
2427
1468
36,392
700
518
6251
922
1947
910
1647
424
897
1612
1091
3965
2804
9026
1361
3252
2475
9549
2824
1385
29,987
73,582

4292
606
1206
1544
3687
1713
7519
339
513
189
545
4718
5290
464
6817
4730
1284
245
1467
1871
16,110
294
362
4770
346
729
385
1086
526
883
925
905
4035
2062
4117
1256
1186
1322
834
1284
951
5203
9476

19,139
1139
2321
3613
23,288
2448
14,180
619
2843
697
1903
12,392
12,008
2357
12,310
14,481
3536
1111
3894
3339
52,502
994
880
11,021
1268
2676
1295
2733
950
1780
2537
1996
8000
4866
13,143
2617
4438
3797
10,383
4108
2336
35,190
83,058

0.22
0.53
0.52
0.43
0.16
0.70
0.53
0.55
0.18
0.27
0.29
0.38
0.44
0.20
0.55
0.33
0.36
0.22
0.38
0.56
0.31
0.30
0.41
0.43
0.27
0.27
0.30
0.40
0.55
0.50
0.36
0.45
0.50
0.42
0.31
0.48
0.27
0.35
0.08
0.31
0.41
0.15
0.11

Total

282,100

108,086

390,186

0.28

Panel B: Mean characteristics of group-aﬃliated and unaﬃliated ﬁrm-year observations
All economies

All economies except US

Firm characteristic

Groupaﬃliated

Unaﬃliated

Groupaﬃliated

Unaﬃliated

Diversiﬁcation
Leverage
Hedging activity
Market size
Total assets
R&D activity

−0.77
0.23
0.17
1049
3048
0.02

−0.80
0.21
0.19
1596
6324
0.05

−0.75
0.23
0.17
1048
3081
0.01

−0.78
0.21
0.18
1349
6448
0.02

857

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 2
Commodity-industry matches using the statistical and the constrained statistical methods.
The table displays the commodities matched to industries using the statistical method (Column 3) and the constrained statistical methods (Column 6). In
Column 4, “all” refers to all SIC four-digit industries classiﬁed under the FF-30 industry in the same row. To determine the matches we use out-of-sample
US ﬁrms that are in the lowest quartile of stock market capitalization at the beginning of each month in each industry. The following commodities, which
are priced globally, and return series that are available in Datastream are considered: Gold (GOLDBLN), Silver (SILVERH), Aluminum (LAHCASH), Copper
(LCPCASH), Nickel (LNICASH), Zinc (LZZCASH), Lead (LEDCASH), Tin (LTICASH), Crude oil (CRUDWTC), Corn (CORNUS2), Wheat (WHEATSF), Lumber (LUMRLF1), Feeder cattle (CFCINDX), Lean hog index (CLHINDX), Cotton (COTTONM), Soybean (SOYBEAN), Cacao (COCINUS), Coffee (COFDICA), Sugar (WSUGDLY).
FF = Fama and French; SIC = Standard Industrial Classiﬁcation.
(1)
FF-30
industry

(2)
FF-30 industry description

(3)
Statistical
method:
matched
commodity

(4)
SIC four-digit
industries

(5)
SIC four-digit industry description

(6)
Constrained
statistical
method:
matched
commodity

1

Food products

None

100–199
200–299
2010–2019
2040–2046
2050–2059
2060–2063
2095

Agriculture production - crops
Agriculture production – Livestock
Meat Products
Flour and other grain mill
Bakery products
Sugar and confectionery
Roasted coffee

4
8

Recreation
Healthcare, medical
equipment,
pharmaceutical products
Construction and
construction materials
Steel works (metals) etc.
Fabricated products and
machinery
Precious metals,
non-metallic, and
industrial metal mining

Feeder cattle
Feeder cattle

Corn
Feeder Cattle
Feeder Cattle
Wheat
Wheat
Sugar
Coffee
None
None

None

2400–2439

Lumber and wood products

Lumber

Silver
Feeder cattle

All

Gold

1020–1029
1030–1039
1050–1059
1040–1049
All others
All

11
12
13
17

19
21
22

Petroleum and natural gas
Communication
Personal and business
services
Business equipment
Transportation
Wholesale
Retail

23
25
26
27

Crude oil
Feeder cattle
Crude oil
Crude oil
Feeder cattle
Lead
Feeder cattle

5210–5219

tiﬁers. Following Gorton and Rouwenhorst (2004), commodity returns are changes in spot prices. Economy-level
commodity shocks are the residuals from separate regressions of the form Eq. (2) for each commodity economy
pair:
rc,m,t = αc +

2 




β1,c,t+l rm,t+l + β2,c,t+l rUS,t+l +eUS,m,t+l



Silver
None
Copper ores
Lead and zinc ores
Bauxite & aluminum ore
Gold and silver ores

Lumber & building materials

Copper
Zinc
Aluminum
Gold
Gold
Crude oil
None
None
None
None
None
Lumber

hypothesis is that group aﬃliation could damp the observable effects of commodity shocks on share prices. Three alternative methods of matching industries to commodities
are employed to circumvent this problem.
2.5.1. Statistical method
The statistical method reapplies the methodology of
Rajan and Zingales (1998), who use US data to estimate external ﬁnance dependence across industries in the US and
infer that the same industries are apt to require external
ﬁnancing elsewhere. We likewise use US data for out-ofsample benchmarks in tests using this methodology, to estimate commodity price dependence across industries in
the US and infer that the same industries are commodity
price sensitive in other economies, too.
Following Rajan and Zingales (1998) in using US data
to identify industry-commodity matches has several advantages. First, because business groups are relatively
rare in the US (La Porta et al., 1999b; Villalonga and
Amit, 2009; Masulis et al., 2011), group aﬃliation is relatively less likely to damp the observable effects of commodity shocks on share prices there. US industries’ com-

+ εc,m,t .

l=−2

(2)
The explained variable rc , m , t is commodity c’s weekly
(Wednesday-to-Wednesday) return in economy m’s local
currency at time t. The explanatory variables are as in [1].
The idiosyncratic shock to commodity c’s price change in
economy min week t is the residual, εc,m,t .
2.5. Identifying industry-commodity matches
Our tests require identifying industries that are sensitive to shocks to the price of each commodity. In-sample
estimation of these sensitivities is problematic because our
858

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 3
Commodity-industry matches using the Bureau of Economic Analysis (BEA) data.
The table lists industries at the input-output (I-O) six-digit code level matched with commodities by utilizing the 2002 industry
commodity use table from the BEA website (https://www.bea.gov/industry/benchmark- input- output- data). Primary industries are
in italics.
I-O six-digit
industry code
31161A
111,335
1113A0
112,120
115,000
31151A
1121A0
311,514
316,100
311,410
311,513
111,200
311,520
112A00
311,320
311,920
311,210
311,615
112,300
311,221
311,830
311,119
311,111
1111B0
313,240
111,920
313,100
314,110
486,000
213,112
325,182
221,200
114,100
311,700
481,000
324,121
324,110
325,130
561,700
324,191
325,181
213,111
335,991
325,310
211,000
324,199
324,122
325,910
2122A0
335,911
331,419
33131A
332,430
312,110
331,314
331,520
336,212
33131B
331,420
335,920
331,411
337,110
32121B

Industry deﬁnition

Matching
commodity

Animal (except poultry) slaughtering, rendering, and processing
Tree nut farming
Fruit farming
Dairy cattle and milk production
Support activities for agriculture and forestry
Fluid milk and butter manufacturing
Cattle ranching and farming
Dry, condensed, and evaporated dairy product manufacturing
Leather and hide tanning and ﬁnishing
Frozen food manufacturing
Cheese manufacturing
Vegetable and melon farming
Ice cream and frozen dessert manufacturing
Animal production, except cattle and poultry and eggs
Chocolate and confectionery manufacturing from cacao beans
Coffee and tea manufacturing
Flour milling and malt manufacturing
Poultry processing
Poultry and egg production
Wet corn milling
Tortilla manufacturing
Other animal food manufacturing
Dog and cat food manufacturing
Grain farming
Knit fabric mills
Cotton farming
Fiber, yarn, and thread mills
Carpet and rug mills
Pipeline transportation
Support activities for oil and gas operations
Carbon black manufacturing
Natural gas distribution
Fishing
Seafood product preparation and packaging
Air transportation
Asphalt paving mixture and block manufacturing
Petroleum reﬁneries
Synthetic dye and pigment manufacturing
Services to buildings and dwellings
Petroleum lubricating oil and grease manufacturing
Alkalies and chlorine manufacturing
Drilling oil and gas wells
Carbon and graphite product manufacturing
Fertilizer manufacturing
Oil and gas extraction
All other petroleum and coal products manufacturing
Asphalt shingle and coating materials manufacturing
Printing ink manufacturing
Gold, silver, and other metal ore mining
Storage battery manufacturing
Primary smelting & reﬁning of nonferrous metal (excluding copper and aluminum)
Alumina reﬁning and primary aluminum production
Metal can, box, and other metal container (light gauge) manufacturing
Soft drink and ice manufacturing
Secondary smelting and alloying of aluminum
Nonferrous metal foundries
Truck trailer manufacturing
Aluminum product manufacturing from purchased aluminum
Copper rolling, drawing, extruding, and alloying
Communication and energy wire and cable manufacturing
Primary smelting and reﬁning of copper
Wood kitchen cabinet and countertop manufacturing
Engineered wood member and truss manufacturing

Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Feeder cattle
Lean hog index
Cacao
Coffee
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Corn
Cotton
Cotton
Cotton
Cotton
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Crude oil
Gold
Gold
Gold
Aluminum
Aluminum
Aluminum
Aluminum
Aluminum
Aluminum
Aluminum
Copper
Copper
Copper
Lumber
Lumber

(continued on next page)

859

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Journal of Financial Economics 139 (2021) 852–871

Table 3 (continued)
I-O six-digit
industry code

Industry deﬁnition

321,100
321,999
33721A
322,110
113A00
321,920
321,992
337,122
321,219
321,910
32121A
113,300
212,230
1111A0
311,225
31122A
1119B0
311,910
311,940
311,313
1119A0
31131A

Sawmills and wood preservation
All other miscellaneous wood product manufacturing
Wood television, radio, and sewing machine cabinet manufacturing
Pulp mills
Forest nurseries, forest products, and timber tracts
Wood container and pallet manufacturing
Prefabricated wood building manufacturing
Non-upholstered wood household furniture manufacturing
Reconstituted wood product manufacturing
Wood windows and doors and millwork
Veneer and plywood manufacturing
Logging
Copper, nickel, lead, and zinc mining
Oilseed farming
Fats and oils reﬁning and blending
Soybean and other oilseed processing
All other crop farming
Snack food manufacturing
Seasoning and dressing manufacturing
Beet sugar manufacturing
Sugarcane and sugar beet farming
Sugar cane mills and reﬁning

modity price sensitivities are thus a useful out-of-sample
benchmark, against which to gauge how business group
aﬃliation could dampen commodity price-sensitivity in
economies in which business groups are important. Second, US stock prices appear to incorporate more ﬁrmspeciﬁc information (broadly deﬁned) than do stocks in
most other economies (Bartram et al., 2012). Third, because
the US has, on average, more listed ﬁrms per industry, US
data provide more precise point estimates.
Firm-level US data are from Compustat and the Center
for Research in Security Prices. Using 30 Fama and French
(FF-30) industries ensures a large number of ﬁrms in each
industry to estimate industry sensitivity to commodities.
Firms that hedge commodity risk can exhibit a lower sensitivity to commodity shocks. However, smaller US ﬁrms
are less likely to hedge (Nance et al., 1993; Geczy et al.,
1997; Carter et al., 2006; Rampini et al., 2014). We therefore use the smallest quartile (by market capitalization) of
US ﬁrms in each industry at the beginning of each month
to match industries to commodities.
Each US industry is matched to one commodity by assessing how sensitive ﬁrm-speciﬁc return shocks in an industry are to idiosyncratic shocks in the prices of different
commodities. This is accomplished by estimating the following three sets of equations:

∀ ﬁrms i, ri,t = αi +

2 



βi,t+l rUS,t+l + εi,t ,

(3)

2 



βc,t+l rUS,t+l + εc,US,t ,

l=2

(4)
and

∀ industries j, εi( j ),t = α j +

19 



βc, j εc,US,t + τi,t .

Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Lumber
Zinc
Soybean
Soybean
Soybean
Wheat
Wheat
Wheat
Sugar
Sugar
Sugar

Eqs. (3) and (4) adapt Eqs. (1) and (2) to US ﬁrms.
Eq. (5), which runs pooled regressions for each industry
j, explains residuals εi,t from Eq. (3) with contemporaneous residuals ε c ( US ), t from Eq. (4). That is, Eq. (5) explains
variation in the ﬁrm-speciﬁc shocks in week t stock return
of small US ﬁrms i in industry j with variation in the US
economy-speciﬁc idiosyncratic components of the return
to holding commodity c that week. The τi,t are regression
residuals in Eq. (5). A tighter link between commodity c
and industry j is inferred from a more statistically signiﬁcant loading βc, j in the regression Eq. (5) for that industry.
We require a minimum threshold of three for the absolute value of the t-statistic of the loading βc, j and then select the commodity-industry pair with the highest absolute
t-statistic among these as a potential match. We then run
a univariate second pass regression analogous to Eq. (5) –
namely, ε i , t = β c , j ε c ( US ), t + τ i , t – for the potential match.
We declare a match between industry j and commodity c
only if the commodity’s coeﬃcient has the same sign as
in the ﬁrst pass regression and the t-statistic in this second pass regression also exceeds three in absolute value.
This extra step is done to cull false matches due to multicollinearity (no false matches are identiﬁed).
The major advantage of the statistical method is that
it gauges an industry’s sensitivity to commodity prices
through all possible channels. For example, a shock to oil
prices could affect the auto industry by affecting input
prices (supply shock) or consumer preferences as to the
type of car (demand shock). The commodity matches identiﬁed with this procedure could proxy for the prices of
goods that affect an industry, but for which no global commodity market exists (Anderson and Danthine, 1981), other
fundamental shocks that affect an industry, substitutes for
industry’s main product, or other such factors. In all such
cases, the industry-commodity match is valid for our analysis as long as the shock to the matched commodity is a

l=−2

∀ commodities c, rc,US,t = αc +

Matching
commodity

(5)

c=1

860

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

good proxy for the unobserved fundamental shock to the
matched industry.
The major disadvantages of statistical matching are that
type one and type two errors inevitably arise, missing genuine matches and declaring spurious matches. Spurious or
missed matches are likely to induce attenuation bias in the
tests that follow. We therefore test whether industry commodity matches are valid out-of-sample (see Section 3).
The third Column of Table 2 reports the industrycommodity matches detected using the statistical method.
Some matches are intuitive, such as that between the Precious metals, non-metallic, and industrial metal mining industry and Gold and between the Petroleum and natural
gas industry and Crude oil. Others link seemingly unrelated industries and commodities, such as Fabricated products and machinery, and Feeder cattle. Closer investigation
provides economic intuition for some of these. For example, farm equipment is included in the Fabricated products
and machinery industry. Regardless, validating matches intuitively is subject to ex post justiﬁcation bias. We therefore take the matches as determined by the data.
We supplement tests using this approach with tests
using matches based on a constrained statistical matching method and on Bureau of Economic Analysis (BEA)
input-output tables that list industries direct dependence
on commodities.

2.5.3. BEA method
An alternative and qualitatively different approach uses
Bureau of Economic Analysis (BEA) input-output tables.
These list every industry’s use of inputs produced by every other industry for approximately 56 thousand industry
pairs in the US. This matching method is not statisticalbased and, thus, avoids noise-driven matches and mismatches. However, it does not capture all possible channels
through which commodity price shocks could affect an industry. For example, an increase in oil prices can boost the
proﬁts of coal mines, which produce a substitute for oil but
do not use much oil as input.
To employ the BEA matching method, we begin by determining a set of basic commodity-linked industries by
identifying industries that produce each given commodity
or use it as their predominant input. For example, Cotton
farming is linked to the commodity Cotton; Cattle ranching
and farming to Feeder cattle; Petroleum reﬁneries to Crude
oil; and so on. We declare these base industries matched
to that commodity.
We then identify industries that depend on a commodity by summing each industry’s inputs from the base industries that are already linked to the commodity. If at
least 10% of an industry’s inputs are from industries already linked to the commodity, we match that industry to the same commodity. For example, the base industries matched to Crude oil provide 22% of the inputs
of Asphalt shingle and coating materials manufacturing,
so we also match that industry to Crude Oil. We repeat
this matching process for two additional rounds, increasing the threshold for declaring a match to 20% in the second and 30% in third round because the number of industries matched to each commodity increases prior to each
round.9 Table 3 lists the 86 matches of (six-digit I-O classiﬁcation) industries to commodities.10

2.5.2. Constrained statistical method
The statistical method generates statistically highly
signiﬁcant matches between some industries and commodities that perhaps are not directly related. If these
commodities capture genuine supply and demand, crossindustry, or latent factor effects, the method is useful. If
these matches are false positives, tests using them suffer
from attenuation bias.
The modiﬁed statistical method is designed to mitigate any such bias. This method uses the same algorithm
as the statistical matching method, but it adds the requirement that the commodity and industry be directly
related. This retains the matches between Petroleum and
natural gas and Crude oil, and between Precious metals
and Gold, but drops several matches with Feeder cattle
and adds matches at ﬁner [four-digit Standard Industrial
Classiﬁcation (SIC)] industry levels between industries and
commodities they directly produce or consume. We verify that, in the univariate second pass regression analogous to Eq. (5), the t-statistic of the loading βc, j on commodity shocks exceeds three in absolute value for the additional industry-commodity matches introduced in this
way. This adds matches between Roasted coffee and Coffee,
Meat products and Feeder cattle, Lumber and wood products and Lumber etc. The sixth Column of Table 2 reports
industry-commodity matches determined by this method.
The constrained statistical matching method potentially
mitigates concerns about noise-driven matches and mismatches, but it reduces the sample size by 74% because
fewer ﬁrms end up in industries matched to a commodity. This could give rise to issues related to power in regressions. Therefore, we view this method as a robustness
test.

3. The incorporation of idiosyncratic commodity shocks
into stock prices
Eq. (6) tests whether or not group-aﬃliated ﬁrms’ stock
returns incorporate idiosyncratic information differently
vis-à-vis unaﬃliated ﬁrms. Following Jin and Myers (2006),
we employ a variant of Fama-MacBeth estimation, which
Petersen (2009) ﬁnds appropriate in panel regressions explaining abnormal returns. The regressions explain weekly
shocks to ﬁrm-speciﬁc stock returns with idiosyncratic
components of weekly shocks to the prices of matched
commodities, calculated separately for each economy:

 
 
εi,t = b1 εc( j )m,t sgn βc, j + b2 Gi,t + b3 Gi,t εc( j ),m,t sgn βc, j
+

N


bv Xi,t + δ j,m + ui, j

(6)

v=4
9
Alternative thresholds and additional rounds of matching generate
similar results (unreported). We stop at the third round because a fourth
adds only two matches.
10
A concordance table provided by the BEA matches its I-O industry
classiﬁcation system with the North American Industry Classiﬁcation System (NAICS), and a second concordance table provided by the US Bureau
of the Census links NAICS industries to the SIC system available in Datastream.

861

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

The explained variable εi,t is the ﬁrm-speciﬁc shock to
the return of stock i in week t from Eq. (1). The ﬁrst explanatory variable, εc( j ),m,t is the idiosyncratic commodity
shock εc,m,t to country m from Eq. (2) that is matched to
ﬁrm i’s industry j. Multiplying the idiosyncratic component
of commodity shock by sgn(βc, j ),which is one or minus
one as βc, j in Eq. (5) is positive or negative, respectively,
sgnensures that expected sign of b1 is positive regardless of
whether shocks to the price of commodity caffect industry jpositively or negatively.11 If ﬁrm i’s industry j is not
matched with any commodity c, the ﬁrm is dropped from
the sample. The second explanatory variable is an indicator
variable, denoted Gi,t , set to one if ﬁrm iis group-aﬃliated
at time t and to zero otherwise.
In some speciﬁcations, we include ﬁrm-speciﬁc control
variables, Xi , t and industry-economy ﬁxed effects, denoted
δ j , m , based on 30 Fama-French industries. Industryeconomy ﬁxed effects subsume all latent factors with
variation at the industry, economy, or industry-economy
level. Moreover, the estimates in the tables are the means
of week-by-week Fama-MacBeth regressions, so the coeﬃcients of the industry-economy ﬁxed effects take
different values each week, effectively leaving the regressions subsuming all time-varying industry-, economy-,
and industry-economy-level latent factors as well. In this
context, Fama-MacBeth estimation has the advantage of
mitigating potential bias due to cross-sectional correlation
in the ﬁrm-speciﬁc stock returns. The dependent variables
are estimated idiosyncratic returns and so ought not to be
autocorrelated. To err on the side of underestimating signiﬁcance levels, we allow for any potential autocorrelation
in the ﬁrm-speciﬁc stock returns by assessing the significance of the means of the coeﬃcients in Eq. (6) using
Newey-West t-statistics, adjusted for four-week lags.
The coeﬃcient b1 can be estimated if industry-economy
ﬁxed effects are not introduced. A positive and signiﬁcant coeﬃcient for b1 implies that, on average, commodities are correctly matched to industries. The coeﬃcient of
interest in Eq. (6) is b3 , the sign-adjusted interaction of
the commodity shock measure εc( j ),m,t with the group afﬁliation indicator, Git . A negative and signiﬁcant b3 implies
that group-aﬃliated ﬁrms exhibit a muted response to
economy-speciﬁc commodity shocks as compared with unaﬃliated ﬁrms.
Table 4 summarizes the main regression results. Regressions 1 and 2 use the variant of εc( j ),m,t calculated in
Eq. (2) and matched to industries using the statistical method. Regressions 3 and 4 use the variant of
εc( j ),m,t matched to industries using the constrained statistical method, and Regressions 5 and 6 use the variant
of εc( j ),m,t matched to industries using the BEA matching
method. Regressions 2, 4, and 6 include industry-economy
ﬁxed effects.
In Regressions 1, 3 and 5, the coeﬃcient b1 on the commodity shock measure is positive and statistically significant. These out-of-sample tests aﬃrm that, on average,
all three industry-commodity matching procedures suc-

cessfully identify commodity shocks relevant to the ﬁrmspeciﬁc shocks. The coeﬃcient b1 in Regression 1 links a 1
percentage point idiosyncratic shock to commodity prices
to a 5 basis points idiosyncratic shock to the stock prices
of unaﬃliated ﬁrms.
The key coeﬃcient of interest is b3 ,on the interaction
of the commodity shock measure with the group aﬃliation indicator. This is negative and statistically signiﬁcant
in all speciﬁcations, indicating a muted incorporation of
commodity shocks into the idiosyncratic stock returns of
group-aﬃliated ﬁrms on average. The interaction coeﬃcient in Regression 1 links a 1 percentage point shock to
commodity prices to a 3 (5.82 – 2.46 = 3.36) basis point
shock to the ﬁrm-speciﬁc stock returns of group-aﬃliated
ﬁrms. This is about 40% less than the shock to unaﬃliated
ﬁrms’ share prices, and the difference between the two is
highly statistically signiﬁcant across all speciﬁcations. The
regressions in Table 4 demonstrate a statistically and economically signiﬁcant damping of the impact of idiosyncratic commodity price shocks on the idiosyncratic return
of group-aﬃliated ﬁrms relative to unaﬃliated ﬁrms.
4. Identiﬁcation of group aﬃliation as the culprit
The results show that group-aﬃliated ﬁrms’ stocks are
less responsive to a given economy-speciﬁc commodity
shock than are unaﬃliated peer ﬁrms in the same economy, industry, and time. The primary vulnerability of the
ﬁndings in Table 4 that remains is that group-aﬃliated
and unaﬃliated ﬁrms could differ along other ﬁrm-level
dimensions, some perhaps unobservable given data constraints. This section presents tests designed to mitigate
these concerns.
4.1. Mitigating omitted variables
Table 1, Panel B, shows group-aﬃliated and unaﬃliated
ﬁrms differing from each other in diversiﬁcation, leverage,
hedging activity, size, and R&D activity. We therefore next
include these control variables to mitigate concerns that
group aﬃliation could be proxying for these other differences in ﬁrm characteristics.
A ﬁrm diversiﬁed across industries can exhibit a
muted response to a commodity shock that affects only
some of its industry segments. We also control for each
ﬁrm’s leverage. The stock prices of more leveraged ﬁrms
are plausibly more sensitive to shocks. Group-aﬃliated
ﬁrms could hedge commodity risk more aggressively
to shield the wealth of their controlling block holders
(Tufano, 1996). We proxy for hedging activity in two ways.
One is a hedging indicator set to 1 if Datastream reports
that the ﬁrm has ﬁnancial accounts related to hedging or
derivative usage. The second is ﬁrm size, reﬂecting prior
ﬁndings showing that larger ﬁrms employ more extensive
hedging strategies (Nance et al., 1993; Geczy et al., 1997;
Carter et al., 2006; Rampini et al., 2014). The log of market capitalization or log of total assets proxies for ﬁrm
size. We also control for each ﬁrm’s R&D spending each
year. R&D-intensive ﬁrms’ valuations are thought to depend more on future growth opportunities than on current
conditions (and shocks that primarily affect current cash

11
The sign of βc, j is similarly calculated using the regression speciﬁcation Eq. (5) for the BEA matched industry-commodity pairs.

862

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 4
Incorporation of idiosyncratic information into stock prices.
The Table reports mean coeﬃcients from Fama-MacBeth cross-section regressions, run separately for each of 1095 weeks. Industries are matched to commodities using the statistical matching in Regressions 1 and 2, modiﬁed statistical matching in Regression 3 and 4 and Bureau of Economic Analysis (BEA)
matching in Regressions 5 and 6. US ﬁrms are excluded from the sample in the ﬁrst 4 regressions as they are used to identify the industry-commodity
links. US ﬁrms are included in the sample in Regressions 5 and 6. The dependent variable is the weekly idiosyncratic stock return in local currency, measured from Wednesday to Wednesday. Coeﬃcients are multiplied by one hundred. The numbers in parentheses are p-values. Signiﬁcance levels of means
of coeﬃcients from weekly cross-sectional regressions are adjusted for potential autocorrelation using Newey-West methodology with 4 lags. Boldface
indicates coeﬃcients signiﬁcant at 10% or better in two-tailed tests.
Statistical Matching
Explanatory variable

(1)

(2)

Constrained Statistical Matching
(3)

(4)

BEA Matching
(5)

5.82
(0.00)

Group-aﬃliated ﬁrm

0.06
(0.01)

0.06
(0.00)

0.14
(0.00)

0.09
(0.01)

0.04
(0.14)

0.02
(0.51)

Idiosyncratic
commodity return ∗
group-aﬃliated ﬁrm

−2.46

−1.84

−1.85

−1.91

−1.64

−1.90

(0.01)

(0.04)

(0.02)

(0.07)

(0.03)

(0.03)

Intercept
Economy ∗ industry
ﬁxed effects
Firm ∗ week
observations

7.11
(0.00)

(6)

Idiosyncratic
commodity return

−0.03
(0.29)

2.54
(0.00)

−0.09
(0.06)

−0.04
(0.18)

No

Yes

No

Yes

No

Yes

5,767,175

5,767,175

1,491,947

1,491,947

1,057,725

1,057,725

Number of economies

42

42

42

42

43

43

Average adj. R2

0.01

0.05

0.01

0.04

0.01

0.11

ﬂows). All variables are measured annually at the prior ﬁscal year-end.
Table 5 summarizes these regressions, all of which expand Regression 2 in Table 4 by including diversiﬁcation,
leverage, R&D activity, total assets, or market capitalization and their interactions with the industry-economy speciﬁc commodity shock. Industries and commodities are
matched using the statistical matching method. Regressions 1–6 of Table 5 incorporate the new control variables
and matching interactions one pair at a time, and Regression 7 includes them all. No interaction is statistically signiﬁcant in Regressions 1–6, and some interactions are signiﬁcant in Regression 7. More important, the interaction
between the group aﬃliation indicator and the commodity shock measure remains uniformly negative and statistically signiﬁcant. This suggests that omitting these ﬁrmlevel characteristics in the previous analyses cannot explain group-aﬃliated ﬁrms’ muted stock price responses to
commodity shocks.
Clearly, the tests in this section cannot mitigate all
potential concerns about sources of confounding variation. The conclusions are subject to the caveat that groupaﬃliated and unaﬃliated ﬁrms could differ along other dimensions that are unobservable due to data limitations.

ter the ﬁrms’ status as group-aﬃliated changes (the treatment group). These changes are contrasted against contemporaneous changes in sensitivities of ﬁrms’ stock prices
to commodity price shocks for ﬁrms whose group aﬃliation status does not change (the control group). Identiﬁcation comes from ﬁrms whose group aﬃliation status does
not change serving as a counterfactual for how treated
ﬁrms’ ﬁrm-speciﬁc stock returns would have responded
to the commodity shocks had their aﬃliation status not
changed. As in all difference-in-difference tests, the identiﬁcation assumptions are that omitted ﬁrm-level characteristics do not signiﬁcantly change around the treatment and
that the change in group aﬃliation is exogenous. Relaxing
these identiﬁcation assumptions is explored in Section 4.3.
The treatment group consists of ﬁrms that are unaﬃliated in one year and group-aﬃliated in the following year
(positive treatment ﬁrms) or aﬃliated in one year and unaﬃliated in the following (negative treatment). These tests
require that the ﬁrms we designate as treated genuinely do
change aﬃliation status. Group aﬃliation is inferred from
a ﬁrm having another ﬁrm as its controlling shareholder,
controlling another ﬁrm, or being controlled by a controlling shareholder who controls another ﬁrm. We use a 20%
minimum threshold for designating any given equity block
suﬃcient to exercise control and, thus, to make a ﬁrm a
group aﬃliate. We do not want blocks that either meet
or fail to meet the threshold brieﬂy or by small margins
to count as changes in group aﬃliation status. The treatment group therefore is restricted to ﬁrms whose group
aﬃliate status changes because the control block(s) relevant to its status change(s) by at least 5 percentage points
and whose status does not change during the prior or sub-

4.2. Changes in group aﬃliation: difference-in-difference tests
An alternative identiﬁcation strategy is based on a
difference-in-difference setting, where changes in group
aﬃliation act as the treatment. These difference-indifference tests explore how the sensitivities of ﬁrms’ stock
prices to commodity price shocks change before versus af863

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 5
Group aﬃliation versus other ﬁrm-level characteristics.
The Table revisits the mean coeﬃcients from Fama-MacBeth cross-section Regression 2 of Table 4, run separately for each of 1095 weeks but including
additional control variables and their interactions with the group aﬃliation indicator. The dependent variable is ﬁrm-speciﬁc stock return in local currency,
measured from Wednesday to Wednesday, for stocks in 42 economies. Coeﬃcients are multiplied by one hundred. Numbers in parentheses are p-values,
adjusting for time series autocorrelation of 4 weeks in successive cross-section estimates using the Newey-West methodology. Boldface indicates mean
coeﬃcients signiﬁcant at 10% or better in two-tailed tests. R&D = research and development.
Explanatory variable
Idiosyncratic commodity return
∗
group-aﬃliated ﬁrm
Idiosyncratic commodity return
∗
diversiﬁcation
Idiosyncratic commodity return
∗
leverage
Idiosyncratic commodity return
∗
hedging activity
Idiosyncratic commodity return
∗
log market size
Idiosyncratic commodity return
∗
log total assets
Idiosyncratic commodity return
∗
R&D activity
Group-aﬃliated ﬁrm
Diversiﬁcation

(1)

(2)

(3)

(4)

(5)

(6)

(7)

−1.87
(0.04)
0.94
(0.59)

−1.69
(0.06)

−1.81
(0.04)

−1.79
(0.05)

−1.86
(0.04)

−1.95
(0.03)

−1.80
(0.05)
0.51
(0.74)
−4.35
(0.04)
1.66
(0.37)
0.69
(0.09)

−28.2
(0.23)
0.06
(0.00)

−33.0
(0.17)
0.06
(0.00)
−0.06
(0.04)
0.15
(0.01)
1.66
(0.36)
−0.08
(0.00)

0.03
(0.96)

0.28
(0.60)

Yes
0.05

Yes
0.06

−3.01
(0.15)
1.58
(0.37)
0.66
(0.13)
0.20
(0.57)

0.06
(0.00)
−0.01
(0.81)

Leverage

0.06
(0.00)

0.06
(0.00)

0.06
(0.00)

0.05
(0.00)

0.19
(0.00)
−0.03
(0.31)

Hedging activity

−0.07
(0.00)

Log market size

−0.02
(0.05)

Log total assets
R&D activity
Economy∗ industry ﬁxed effects
Average adj. R2

Yes
0.05

Yes
0.05

Yes
0.05

sequent two-year periods. This effectively excludes, from
the treatment group, ﬁrms attached to their groups due to
stakes varying around the threshold because such ﬂuctuations could reﬂect seasoned equity issues, share buybacks,
stock dividends, or share creation associated with stock options, not genuine changes in group aﬃliation status. The
data exclude ﬁrms that either list or delist within the same
windows because differences in betas cannot be calculated
for these ﬁrms.
We use propensity scores matching to match each
treatment ﬁrm with a control ﬁrm, whose group aﬃliation status does not change, within the same industry,
economy, and year using the nearest neighbor matching
(Abadie et al., 2004) by ﬁrm size, leverage, R&D over assets, and commodity beta in the prior year. If no match is
available from the same country-industry-year, we default
to a global match from the same industry-year. We require differences in propensity scores to be within the 0.05
range. Positively and negatively treated ﬁrms are matched
separately. Matching is done with replacement to preclude
the order of the observations from affecting the results.
Commodity betas for each treatment ﬁrm and control
ﬁrm are estimated with respect to the industry-matched
commodity return for each year. This entails estimating a
variant of Regression Eq. (5) separately for each ﬁrm. The

Yes
0.05

Yes
0.05

explained variable is ﬁrm-level idiosyncratic return shocks
and the explanatory variable is the idiosyncratic shock to
the commodity matched with the ﬁrm’s industry. Firms
with fewer than 24 weeks of data are dropped from the
sample, and betas are symmetrically winsorized at the 5%
level to mitigate the impact of outliers. First differences in
the commodity betas of each ﬁrm are calculated. The tests
then focus on the difference-in-difference between treatment and control ﬁrms’ commodity betas.
These difference-in-difference tests, summarized in
Table 6, align with the ﬁndings in Tables 4 and 5. Group
aﬃliation mitigates the sensitivity ﬁrm-speciﬁc stock returns to industry-speciﬁc commodity price shocks. The
commodity beta of unaﬃliated ﬁrms that become aﬃliated (positively treated ﬁrms) on average falls signiﬁcantly,
by −3.96 (p-value = 0.00), and the commodity beta of
their nearest neighbor ﬁrms, whose group aﬃliation does
not change, remains constant on average. The commodity beta of aﬃliated ﬁrms that become unaﬃliated (negatively treated ﬁrms) on average rises signiﬁcantly, by 2.88
(p-value = 0.07), and the average commodity beta of their
nearest neighbor ﬁrms displays a statistically insigniﬁcant
decline of −0.45. The difference-in-difference point estimate for negatively treated ﬁrms is a statistically signiﬁcant 3.33 (p-value = 0.08). Because the ﬁrst differences of
864

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 6
Firms changing group aﬃliation status.
The table reports a difference-in-difference analysis of changes in the sensitivity of ﬁrm-speciﬁc stock returns to commodity
price shocks. The treatment group consists of ﬁrms experiencing a change in aﬃliation status between year t-1 and year
t + 1, by either becoming group-aﬃliated (positive treatment) or ceasing to be aﬃliated with a business group (negative
treatment). Group aﬃliates have a controlling shareholder with a block of 20% or more; unaﬃliated ﬁrms do not. Block
acquisitions or sales that change a ﬁrm’s group aﬃliation status must be for at least 5% of the ﬁrm’s shares. The ﬁrm’s
group aﬃliation must be stable going forward 1 year. The difference is the sensitivity of ﬁrms’ ﬁrm-speciﬁc stock returns to
commodity shocks after the change in group aﬃliation status minus that before the change in status. The matched group
contains ﬁrms that did not experience a change in group aﬃliation status and that are in the same economy-industry
selected using the nearest neighbor matching on total assets, leverage, research and development expenses divided by total
assets and commodity beta in the year prior to the event. The sample covers all economies. Coeﬃcients are multiplied by
one hundred. When both positive and negative treated observations are pooled, the difference-in-difference coeﬃcients of
negatively treated observations are multiplied by −1. Industry-commodity matching is by statistical method. The left hand
side variable is winsorized at the 5% level. Boldface indicates coeﬃcients signiﬁcance at 10% or better in two-tailed tests.
Commodity beta (sensitivity of ﬁrm-speciﬁc stock returns to
commodity price shocks)
Treatment

Compared groups

Positive treatment
(unaﬃliated
transition to
aﬃliated)

Treated (transition) ﬁrms

Negative treatment
(aﬃliated
transition to
unaﬃliated)
Pooled treatment
(positive treatment
and sign-inverted
negative
treatment)

Matched ﬁrms
Number of observations
Treated (transition) ﬁrms
Matched ﬁrms
Number of observations
Treated (transition) ﬁrms

12 Months
Before

12 Months
After

Difference

Difference-indifference

7.46
(0.00)
6.65
(0.00)
2,855
6.35
(0.00)
6.34
(0.00)
2,302

3.50
(0.00)
6.46
(0.00)
2,855
9.22
(0.00)
5.89
(0.00)
2,302

−3.96
(0.00)
−0.19
(0.89)
2,855
2.88
(0.07)
−0.45
(0.76)
2,302
−3.47
(0.00)
0.09
(0.93)
5,157

−3.76
(0.03)

Matched ﬁrms
Number of observations

treated ﬁrms are always in the predicted direction and statistically signiﬁcant, while those of the nearest neighbor
ﬁrms are statistically insigniﬁcant, the results are driven
by the changes in treated ﬁrms, not changes in the control
group.
Pooling positively and negatively treated ﬁrms (after
multiplying negatively treated ﬁrms’ differences in commodity beta by minus one) generates a highly statistically
signiﬁcant difference-in-difference estimate of about −3.57
(p-value = 0.00).
Thus, shocks to the ﬁrm-speciﬁc returns of groupaﬃliated ﬁrms that become unaﬃliated are more sensitive
to commodity price shocks, and shocks to the ﬁrm-speciﬁc
returns of unaﬃliated ﬁrms that become aﬃliated are less
sensitive to commodity price shocks.

2,855
3.33
(0.08)

2,302
−3.57
(0.00)

5,157

(unsuccessful) acquisition attempts that failed for plausibly exogenous reasons. If control block targets are selected
in anticipation of changes in their sensitivity to commodity
risk, instead of group aﬃliation being the cause of those
changes, changes would be evident in the sensitivity to
commodity risk also among targets of unsuccessful acquisition attempts.
Control block acquisition attempts recorded in the
Thomson One database are merged with our ownership
data. We require that the bidder seek to own at least 20%
of the target’s shares after the transaction and that the target be classiﬁed as unaﬃliated in the year prior to the
bid. Instances of ﬁrms purchasing their own shares are
dropped.
The treatment group consists of target ﬁrms that are
unaﬃliated prior to the acquisition announcement, become
group-aﬃliated as a result of a successful acquisition, and
continue to be publicly traded so their commodity betas
can be estimated after the acquisition. The last requirement is especially important in this context because acquisitions in most economies entail acquiring a suﬃcient
block of stock to exercise effective control and are not bids
for all of the target ﬁrm’s shares as is generally the case in
the US.
The control group consists of targets that are unaﬃliated prior to the acquisition announcement, remain unaﬃliated because the acquisition attempt failed due to a plausibly exogenous reason, and continue to be publicly traded
after the failed acquisition attempt. Acquisition bids that

4.3. Placebo tests exploiting failed merger and acquisition
transactions
Identiﬁcation in Section 4.2 relies on the assumption
that ﬁrms become aﬃliated or unaﬃliated for exogenous
reasons. If changes in group aﬃliation status are endogenous, a sample selection bias problem arises. The results
would be also consistent with, for example, groups taking on ﬁrms that are expected to become less sensitive
to commodity shocks and divesting ﬁrms expected to become more sensitive to commodity shocks. One approach
to mitigating such concerns follows Seru (2014) in comparing successful control block acquisition attempts with
865

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 7
Targets of successful control block bids versus bids that failed due to plausibly exogenous reasons.
The table reports a difference-in-difference analysis of changes in the sensitivity of ﬁrm-speciﬁc stock returns to commodity
price shocks. The treated group consists of targets of successful control block acquisitions, in which targets were unaﬃliated
in the year prior to the bid announcement, which left the acquirer owning 20% or more of the target’s shares after the
transaction. The matched group consists of targets of similar bids that failed for plausibly exogenous reasons. The targets
were unaﬃliated in the year prior to the bid announcement and the acquirer sought to own at least 20% of the target’s
shares after the transaction. Firms in the matched group are selected using nearest neighbor matching criteria based on
total assets, leverage, research and development expenses divided by total assets, and commodity beta in the year prior to
the acquisition or failed acquisition attempt, and are, when possible, from the same economy-industry-year as each target of
successful bid. The sample covers all economies. Industry-commodity matching is by the statistical method. Coeﬃcients are
multiplied by one hundred. The dependent variable is winsorized at the 5% level. Boldface indicates coeﬃcients signiﬁcance
at 10% or better in two-tailed tests.
Commodity beta (sensitivity of ﬁrm-speciﬁc stock returns to
commodity price shocks)
Treatment

Compared groups

Positive
treatment
(unaﬃliated
transition to
aﬃliated)

Treated (successful
transition) ﬁrms
Matched (unsuccessful
transition) ﬁrms
Number of observations

12 Months
Before

12 Months
After

Difference

Difference-indifference

4.99
(0.00)
4.70
(0.00)
5284

0.61
(0.71)
6.97
(0.00)
5284

−4.38
(0.02)
2.28
(0.01)
5284

−6.65
(0.00)

failed due to plausibly exogenous reasons consist of acquisition attempts, as reported in Thomson One, that failed
because of intervention by regulatory bodies (Savor and
Lu, 2009; Seru, 2014; Faccio and Hsu, 2017), court decisions (Seru, 2014; Faccio and Hsu, 2017), employee opposition, or unexpected adverse market-wide conditions [e.g.,
the 20 07–20 09 ﬁnancial crisis, the 1997 Asian ﬁnancial
crisis, etc., as in Seru (2014)]. Acquisition bids that failed
due to ﬂuctuations in commodity prices are excluded, as
are takeovers that failed because a rival bidder acquired a
control block. The latter are excluded because the rival’s
takeover is included in the treatment group. The reasons
behind the failure of each given transaction are determined
based on the deal description in Thomson One, Capital IQ,
and newspapers articles in Factiva and Lexis-Nexis.
In these tests, identiﬁcation follows from the targets
of unsuccessful acquisition attempts (placebo treatment
ﬁrms) serving as counterfactuals for how successfully acquired targets’ (treatment ﬁrms’) sensitivities to commodity shocks would have changed had they not been acquired.
As in Section 4.2, we use propensity score matching to
pair targets of successful acquisitions with targets of unsuccessful acquisitions within the same economy, industry
and year (if possible) using the nearest neighbor matching
(Abadie et al., 2004) with total assets, leverage, R&D expenses as a fraction of total assets and commodity beta in
the prior year as covariates. If no match is available from
the same country, we default to a global match from the
same industry-year. As before, the matching is done with
replacement.
Commodity betas with respect to industry-matched
commodities are estimated for treatment and control ﬁrms
over the 52 weeks before and 52 weeks after the takeover
announcement date, excluding the announcement week.
Firms with fewer than 24 weeks of observations are
dropped and betas are winsorized at the 5% level.
As Table 7 shows, the results of the tests based on
takeover attempts that failed for plausibly exogenous rea-

5284

sons do align with those in Tables 4 and 5. Firm-speciﬁc
stock returns become signiﬁcantly less sensitive to commodity shocks after a ﬁrm becomes aﬃliated with a business group following a successful takeover, in contrast to
control ﬁrms that remain unaﬃliated after a takeover attempt that failed for plausibly exogenous reasons. These
tests mitigate the concern that our previous results are due
to self-selection.
4.4. Within-group risk sharing
If a commodity shock to a one group ﬁrm is diffused
across the group, other ﬁrms in the group would appear
sensitive to the shock. Tests for this second-hand commodity shock sensitivity must therefore focus on business
groups containing one or more ﬁrms in industries sensitive
to a given commodity and one or more ﬁrms in industries
insensitive to that commodity. These tests are best illustrated by a simple example. Consider a business group of
three ﬁrms: Firm F1 in an industry sensitive to commodity C1 ; ﬁrm F2, in an industry sensitive to commodity C2 ;
and ﬁrm F3, in an industry insensitive to any commodities.
One set of tests explores whether F1 is sensitive to C2 , F2
is sensitive to C1 , and F3 is sensitive to both C1 and C2 .
We employ a variant of the Fama-MacBeth regressions
of Eq. (6):

 


εi,t = b1 εc( j ),m,t sgn βc, j + b2 ε¬c( j ),m,t sgn β¬c, j + ui,t .

(7)
As in Eq. (6), the explained variable εi,t is the ﬁrmspeciﬁc shock to the return of stock i in week t from
Eq. (1). Unlike in Eq. (6), where the explanatory variable
εc( j ),m,t was idiosyncratic shock to the price of commodity cmatched to i’s industry jin its economy min week t,
in Eq. (5)the explanatory variable of interest, ε ¬c ( j ), m , t , is
shock to the price of a commodity ¬c(j) which is not c ( j ),
but a different commodity matched to the industry of another ﬁrm in ﬁrm i’s group. As in Eq. (6), sgn(β ¬c , j ) is one
or minus one as β ¬c , j is positive or negative, respectively,
866

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 8
Within-Group Transmission of Commodity Shocks.
The table tests whether a ﬁrm’s stock price reacts to commodity shocks to other ﬁrms within the same business group that matches with a commodity other than the ﬁrm’s own matched commodity. For this exercise
we use a sample of ﬁrms that belong to the same business group, i.e. have a common controlling shareholder,
such that at least two ﬁrms of the group are in our sample and at least one of the ﬁrms matches with a different commodity than matched commodities of other group ﬁrms. In Regression 4, we include only cases that a
group ﬁrm’s industry beta does not statistically signiﬁcantly load on the commodity shocks in regression(5);
i.e., we require the absolute value of t-statistics of beta to be less than 0.5 when commodities are entered individually. The dependent variable is the weekly idiosyncratic stock return in local currency, measured from
Wednesday to Wednesday. Coeﬃcients are multiplied by one hundred. The numbers in parentheses are pvalues. Estimation is by weekly Fama-MacBeth regressions in Regressions 1–3 and monthly in Regression 4.
In regression 4 low number of observations results in few extreme coeﬃcients when Fama-Macbeth regressions are run for each week. In this case, the average coeﬃcient of idiosyncratic commodity shocks to other
group ﬁrms is 6.2 and p = 0.04. We adjust standard errors for time series autocorrelation of 4 weeks using
the Newey-West methodology. Boldface indicates coeﬃcients signiﬁcance at 10% or better in two-tailed tests.
Shocks

All (1)

All (2)

Top 25% shocks
to other group
ﬁrms (3)

Non-sensitive
industry-commodity
pairs (4)

Idiosyncratic Commodity
Shocks to Other Group Firms

0.86
(0.04)

0.70
(0.10)

1.12
(0.02)

2.52
(0.08)

Intercept

−0.01
(0.44)

3.80
(0.00)
−0.01
(0.59)

2.60
(0.11)
−0.02
(0.33)

−0.01
(0.84)

Firm ∗ week observations
Average adj. R2

735,014
0.01

735,014
0.02

188,636
0.02

39,943
0.00

Own idiosyncratic commodity
shocks

and inverts the sign of the explanatory variable if the industry loads negatively on its matched commodity.
With no risk sharing across groups, shocks to the industries of a ﬁrm’s fellow group aﬃliates would not affect its own shares and the regression coeﬃcient b2 in
Eq. (7) would be zero. If group-level risk sharing or income
shifting are important, b2 would be signiﬁcantly positive.
Table 8 summarizes Fama-MacBeth regressions of
Eq. (7). Regression 1 considers ﬁrm’s reaction to all commodities that affect the industries of its fellow group ﬁrms
but do not affect the ﬁrm’s own industry. The coeﬃcient
of b2 is statistically signiﬁcant and its point estimate, 0.86
is about 25% of the main coeﬃcient in Regression 1 of
Table 4, which is 3.36. These point estimates indicate that
a second-hand commodity shock, affecting the industry of
one or more of a ﬁrm’s fellow group aﬃliates, moves its
stock by about 25% as much as does a commodity shock to
the ﬁrm’s own industry.
Commodity shocks are on average positively correlated,
and even if a ﬁrms’ industry does not match with the other
group ﬁrms’ commodity a positive coeﬃcient could ensue
as a result of this correlation. Regression 2 of Table 8 controls for the shocks to ﬁrms’ own matched commodity.
The coeﬃcient of b2 is now 0.7 and barely statistically signiﬁcant at 10%. Second-hand commodity shocks should
stand out more clearly if the shocks they echo are larger.
To restrict our analysis to severe second-hand commodity
shocks, we sort commodity shocks by their absolute values
for each economy and retain only the top quartile of these
for each economy. Regression 3 repeats the test with this
sample. The coeﬃcient b2 increases to 1.1 and becomes statistically signiﬁcant at the 2% level. More severe commodity shocks to a ﬁrm’s fellow group aﬃliates thus tend to

affect its own share price more. This indicates that grouplevel risk sharing intensiﬁes in response to more intense
commodity shocks to a group member ﬁrm.
Finally, a group aﬃliate not matched to a commodity could show a stock return response if its industry is
somewhat sensitive to that commodity, but not sensitive
enough to meet the t-statistic greater than three threshold
for matching in Eq. (5). Such a high threshold makes sense
for our other tests, where misattributing commodity sensitivity to an industry that is not commodity-sensitive must
be avoided. In these tests, we instead need to avoid falsely
classifying a sector as commodity-insensitive. To address
this concern, we focus on ﬁrms in industries that do not
statistically signiﬁcantly load on any commodity shocks in
Eq. (5) by requiring the absolute value of t-statistics of beta
to be less than 0.5 for the ﬁrms’ industry and commodity to be included in the test in Regression 1 of Table 8.
Results are displayed in Regression 4.12 The coeﬃcient on
other group ﬁrm shock is 2.5 and is statistically signiﬁcant
with a p-value of 0.08.
Overall, we ﬁnd a statistically signiﬁcant, albeit attenuated, effect in the idiosyncratic stock returns of group ﬁrms
to shocks to other ﬁrms within the same business group.
This is consistent with shocks being spread across ﬁrms in
the same group.

12
In this test the total number of observations is less than 40 thousand,
which corresponds to about 36 observation per week. We use monthly
regressions, instead of weakly, to mitigate concerns related to running
cross-sectional regressions with few observations. When we run FamaMacbeth regressions at the weekly level, we obtain a coeﬃcient of 6.2,
which is statistically signiﬁcant with p-value=0.04.

867

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 9
Robustness tests.
We repeat the test in Regression 2 of Table 4 using alternative methods and samples. Regression 1 modiﬁes the statistically matching as described in
Section 5.1. Regression 2 drops group-aﬃliated ﬁrms that control other ﬁrms in the sample. Regression 3 uses a 15% threshold to presume control, and
Regression 4 excludes Japan and the UK from the sample. These two economies have the largest number of observations in the sample that already excludes
the US. Regression 5 limits the time period to the latest 10 years. Regression 6 uses panel data regression instead of Fama-MacBeth regressions. Regression
7 uses local market returns and Fama-French global 5 factors to estimate the idiosyncratic component of stock and commodity returns. Coeﬃcients were
multiplied by one hundred. The numbers in parentheses are p-values. When we use Fama-MacBeth regressions, we adjust the standard errors for time
series autocorrelation of 4 weeks using the Newey-West methodology. Boldface indicates coeﬃcients signiﬁcance at 10% or better in two-tailed tests.
Explanatory variable

Statistical and
economic
signiﬁcance
(1)

Group ﬁrms
at bottom of
ownership
pyramid (2)

15%
threshold
for control
(3)

Exclude
Japan and UK
(4)

Time eriod:
2003–2013
(5)

Panel
regression
(6)

Fama-French
Five-factor
model (7)

Group-aﬃliated Firm

0.07
(0.00)
−1.29
(0.05)

0.06
(0.00)
−1.81
(0.05)

0.06
(0.00)
−2.22
(0.02)

0.06
(0.02)
−2.40
(0.04)

0.07
(0.00)
−1.85
(0.07)

0.04
(0.00)
−0.98
(0.00)

0.02
(0.27)
−2.48
(0.01)

Yes

Yes

Yes

Yes

Yes

Yes

Yes

6624,689
42
1095

5755,866
42
1095

5753,487
42
1095

4180,231
40
1095

4864,415
42
574

5767,175
42
1095

5781,727
42
1095

Idiosyncratic commodity return
group-aﬃliated ﬁrm

∗

Economy ∗ industry ∗ time ﬁxed
effects
Firm ∗ week observations
Number of economies
Number of weeks

5. Robustness tests

5.2. Diversiﬁcation through share ownership

We run a number of robustness tests using the speciﬁcation in Regression 2 of Table 4. If the coeﬃcient of
the interaction between group aﬃliation and idiosyncratic
commodity shock measure is negative and signiﬁcant at
the 10% level, then we say the tests generate results that
are qualitatively similar to those in Table 4.

We have controlled for ﬁrms with sales diversiﬁed
across industries. Firms that are at the top of the business
groups pyramids could be diversiﬁed if the ﬁrms in which
they hold stakes operate in different industries. As a result, ﬁrms at the top of pyramids could be less sensitive
to commodity shocks. To mitigate this concern, we repeat
our main test using only ﬁrms that are at the bottom of a
pyramid. To do this, we drop group aﬃliates that control
other ﬁrms in the sample. Regression 2 in Table 9 shows
that our results continue to hold when we focus on ﬁrms
that are at the bottom of the business group pyramid.

5.1. Alternative method of matching commodities with
industries

5.3. Alternative ways of identifying business groups
An alternative to matching based on statistical signiﬁcance considers economic signiﬁcance as well. The statistical matching method assumes that a more statistically signiﬁcant loading βc, j on commodity c implies a tighter link
between the commodity and industry j. A plausible variant of the statistical method infers a tighter link if the
economic impact of a shock to a commodity price, deﬁned as the standard deviation of shocks to that commodity multiplied by the point estimate βc, j , is the tightest.
This approach matches an industry to the commodity with
the highest economic impact, assessed in this way, whose
loading βc, j also has a t-statistic exceeding three in absolute value and retains the same sign in the second step
single regressions as in the ﬁrst step multivariate regression, as deﬁned in the description of the statistical matching method. While new matches emerge, most intuitive
matches remain (the list of matches are available upon request). For example, the Petroleum and natural gas industry remains matched with the commodity Crude oil because that commodity has both the most statistically signiﬁcant and most economically important loading for stock
returns in that industry. Regression 1 of Table 9, using
matches determined by this method, generates results that
are qualitatively similar to those in Table 4.

Our main tests in Table 4 use a 20% threshold for designating a ﬁrm’s largest shareholder as its controlling shareholder. Using a relatively high stake can under-identify
group-aﬃliated ﬁrms if smaller stakes suﬃce to lock in
control if other equity is diffusely held and small shareholders do not vote at shareholder meetings. Erroneously
classifying some group-aﬃliated ﬁrms as unaﬃliated introduces attenuation bias in our tests. To explore the sensitivity of our tests to this concern, we construct an alternative
version of the group aﬃliation indicator variable, Grou pi,t ,
reclassifying controlling shareholders as those with stakes
exceeding 15% and then reassessing group as described in
Section 2.1. Regression 3 in Table 9, shows that this change
yield results qualitatively similar to those in Table 4. 13
5.4. Alternative samples
Our results are not driven by a few economies or extreme observations. For example, Regression 4 in Table 9,
13
The number of observations drops slightly when the 15% threshold
is used because the number of ﬁrms identiﬁed as controlled by governments, which are dropped from the sample, increases.

868

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

which is also based on the statistical matching, shows that
dropping Japan and the UK (the US is again excluded),
which have the largest number of observations, yields
qualitatively similar results.
Qualitatively similar results are ensued after winsorizing ﬁrm-speciﬁc stock returns and economy-speciﬁc commodity returns at 1% (unreported).
We have roughly 20 years of ownership data in the
sample. Ownership data coverage becomes wider in the
latter 10 years. Fama-MacBeth regressions give equal
weights to every time period regardless of the number of
observations. Dropping the initial 10 years of data and repeating our tests using only the 2003–2013 period yields
results, summarized in Regression 5 of Table 9, that are
qualitatively similar to those in Table 4.

prices in general could co-move more in economies where
business groups are more important. Therefore, we explore
whether ﬁrm- and economy-level stock price co-movement
correlates with the incidence of business groups.
To do this, we deﬁne the co-movement of ﬁrm i’s stock
return with its market return in year tto be



Yi,t = log

R2i,t
1 − R2i,t



(8)

where R2i,t is the regression R-squared statistic of Eq. (1) run
on weekly returns for each ﬁrm in each year. The logistic
transformation Eq. (8), which follows Morck et al. (20 0 0),
generates a variable with a roughly normal distribution
and that is more positive for stocks whose shares more
closely track market returns and more negative for stocks
whose prices move more idiosyncratically.
We then run regressions explaining Yi,t with ﬁrmlevel group aﬃliation controlling for economy-level variables shown elsewhere to correlate with stock return comovement: log gross domestic product (GDP) per capita
(Morck et al., 20 0 0), property rights (Morck et al., 20 0 0),
and accounting standards (Jin and Myers, 2006).14
Table 10 displays Fama-MacBeth regressions of Yi,t on
these explanatory variables. We use Newey-West estimator
with 10 year lags to adjust for persistence in country-level
variables. As in prior studies, log GDP per capita attracts
a negative coeﬃcient across all speciﬁcations and is uniformly signiﬁcant. Property rights enters insigniﬁcantly if
alongside other variables but are signiﬁcant when included
alone (not reported). These results accord with the prior
literature.
The primary variable of interest, Group Aﬃliation, attracts a positive and signiﬁcant coeﬃcient in all speciﬁcations. Group-aﬃliated ﬁrms’ stock returns have signiﬁcantly higher co-movement with their markets or, in other
words, less idiosyncratic volatility as a fraction of total
volatility than do unaﬃliated ﬁrms.
These ﬁndings suggest that more pervasive business
group aﬃliation should be added to the list of economy characteristics associated with greater stock return co-movement. Fig. 1, Panel C, conﬁrms this pattern, with economy level co-movement measure from
Morck et al. (2013) on the vertical axis and the fraction of
observations that are from group aﬃliates, from Table 1, on
the horizontal axis. Stocks in countries with more groupaﬃliated ﬁrm observations have statistically signiﬁcantly
(p=0.09) higher economy-level stock return co-movement.
The considerable scatter around the positive correlation
line leaves abundant room for other mechanisms. However,
our difference-in-difference ﬁndings, especially those using failed control block bids, aﬃrm a direction of causation
at the ﬁrm-level: Business group aﬃliation damps idiosyncratic stock return volatility, which in return causes share
price co-movement. Firm-level data on business groups
causing attenuated commodity shock-related ﬁrm-speciﬁc
stock return volatility thus provide new economic intu-

5.5. Alternative regression speciﬁcation
We employ Fama-MacBeth estimation following Jin and
Myers (2006) and the Petersen (2009) ﬁnding that this
approach is appropriate in panel regressions explaining
abnormal returns. An alternative is to run panel regressions controlling for country ∗ industry ∗ time ﬁxed effects
and double-cluster at the country ∗ industry and businessgroup level. Regression 6 in Table 9 shows that the coeﬃcient of Idiosyncratic commodity return ∗ Group-aﬃliated
ﬁrm is negative and statistically signiﬁcant although the
coeﬃcient is −0.98, which is slightly smaller than the
corresponding coeﬃcients estimated by Fama-MacBeth regressions.
5.6. Alternative asset pricing model
Because we seek to test whether idiosyncratic shocks
are incorporated differently into the stock prices of groupaﬃliated ﬁrms versus non-aﬃliated ones, we focus on the
relation between idiosyncratic shocks to stock returns and
idiosyncratic shocks to commodity prices with respect to
the international version of CAPM developed by Jin and
Myers (2006) to provide such a variance decomposition.
A priori, we do not expect the Jin and Myers international CAPM to result in biased estimations of idiosyncratic shocks for group-aﬃliated versus unaﬃliated ﬁrms.
Nonetheless, testing whether results are affected by the
choice of the particular asset pricing model is useful.
We use a global version of the Fama and
French (2015) ﬁve-factor model, changing speciﬁcations (1)
and (2) to include local market returns and Fama-French
global ﬁve factors on the right-hand side in estimating
idiosyncratic component of ﬁrm and commodity returns,
respectively. Regression 7 in Table 9 shows that the coeﬃcient of Idiosyncratic commodity return ∗ Group-aﬃliated
ﬁrm is negative, slightly larger in magnitude than in
Regression 2 in Table 4 and highly statistically signiﬁcant.
6. Business groups and R-squared around the world
We interpret the tests above as evidence that business group aﬃliation damps ﬁrm-speciﬁc shocks associated with commodity price changes. If business group afﬁliation similarly buffers other ﬁrm-speciﬁc shocks, share

14
GDP per capita is from the World Bank WDI data set. Property rights
index data are from the Heritage Organization website 2013 index of economic freedom. Accounting standards are from La Porta et al. (1998).

869

M. Faccio, R. Morck and M. Deniz Yavuz

Journal of Financial Economics 139 (2021) 852–871

Table 10
R-squared around the world.
The dependent variable is a logistic transformation of the R-squared to Y =
R2
log( 1−R
2 )from annual ﬁrm-level regressions based on equation [1]. Results summarizes Fama-MacBeth regressions for each year, adjusting for time series autocorrelation over 10 years using the Newey-West methodology. Numbers in
parentheses are p-values. Boldface indicates coeﬃcients signiﬁcance at 10% or
better in two-tailed tests. GDP = gross domestic product.
Explanatory variable

(1)

Log GDP per capita

−0.14
(0.03)

(2)

(3)

(4)

0.09
(0.02)

−0.13
(0.03)
0.06
(0.02)

Intercept

0.82
(0.20)

−0.62
(0.00)

0.74
(0.21)

−0.15
(0.01)
0.08
(0.00)
0.00
(0.94)
0.00
(0.17)
0.57
(0.10)

Number of ﬁrm ∗ years
Average adj. R2

321,875
0.02

321,875
0.01

321,875
0.02

299,276
0.02

Group-aﬃliated ﬁrm
Property rights
Accounting standards

ition to explain, partially at least, economy-level patterns
in stock return co-movement.

Where markets expect more extensive resource and risk
shifting across group aﬃliates, their stock prices provide
less information feedback to corporate decision makers
and capital providers (Bond et al., 2012). That is, by responding to capital market imperfections with more active hierarchical allocation, business groups further impair
this important information transmission role of the stock
market. Business groups thus could lock in ineﬃcient capital allocation (Wurgler, 20 0 0; Durnev et al., 2004), possibly contributing to the stalled economic growth of middleincome countries, the middle income trap (Rajan and Zingales, 2004; Eichengreen et al., 2013).

7. Conclusions
We use global shocks to commodity prices to ascertain whether business groups’ activities, such as risk
sharing and internal transfers, cause the stock prices of
group-aﬃliated ﬁrms to be less responsive to idiosyncratic
shocks. Using global shocks to commodity prices allows us
to exclude explanations of different responses being due
to differences of shock frequency, magnitude, and observability across ﬁrms. We ﬁnd that business group member
ﬁrms’ stocks are less sensitive to commodity shocks than
are otherwise similar unaﬃliated ﬁrms’ stocks at the same
time, in the same economy, and in the same commoditysensitive industry. Difference-in-difference tests exploiting successful and matched exogenously failed control
block transactions also conﬁrm our results. Further tests
show damped ﬁrm-speciﬁc volatility more generally in the
stocks of business group aﬃliates, linking cross-economy
differences in overall stock return co-movement to differences in the prevalence of business groups.
Business groups, as a second-best hierarchical allocation mechanism (Coase, 1937) in response to ineﬃcient
ﬁnancial and other markets (Morck, Wolfenzon and Yeung, 2005; Khanna and Yafeh, 2007), allocate capital internally within the group (Almeida and Wolfenzon, 2006b;
Morck et al., 2011). Internal capital markets can also be
used to maximize business groups’ controlling shareholders’ private beneﬁts (Bertrand et al., 2002), for example, by
siphoning off group member ﬁrms’ ﬁrm-speciﬁc abnormal
earnings (Jin and Myers, 2006). The extent to which business group aﬃliates’ share price responses to commodity
price shocks are attenuated relative to unaﬃliated ﬁrms’
share price responses can be a useful empirical variable for
measuring the extent to which investors expect business
groups to shift resources and risk across their aﬃliates. We
welcome research using shock sensitivity to better discern
how business groups are governed.

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==> JFE03 - ESG-efficient frontier.txt <==
Journal of Financial Economics 142 (2021) 572–597

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Responsible investing: The ESG-eﬃcient frontier ✩
Lasse Heje Pedersen a,b,c,∗, Shaun Fitzgibbons a, Lukasz Pomorski a
a
b
c

AQR Capital Management, Two Greenwich Plaza, Greenwich, CT 06830, USA
Copenhagen Business School, Solbjerg Plads 3:A5, DK-2000 Frederiksberg, Denmark
Centre for Economic Policy Research (CEPR), London, UK

a r t i c l e

i n f o

Article history:
Received 7 October 2019
Revised 24 January 2020
Accepted 26 February 2020
Available online 9 November 2020
JEL classiﬁcation:
D62
G11
G12
G23
M14
Q5

a b s t r a c t
We propose a theory in which each stock’s environmental, social, and governance (ESG)
score plays two roles: (1) providing information about ﬁrm fundamentals and (2) affecting
investor preferences. The solution to the investor’s portfolio problem is characterized by an
ESG-eﬃcient frontier, showing the highest attainable Sharpe ratio for each ESG level. The
corresponding portfolios satisfy four-fund separation. Equilibrium asset prices are determined by an ESG-adjusted capital asset pricing model, showing when ESG raises or lowers
the required return. Combining several large data sets, we compute the empirical ESGeﬃcient frontier and show the costs and beneﬁts of responsible investing. Finally, we test
our theory’s predictions using proxies for E (carbon emissions), S, G, and overall ESG.
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords:
Portfolio choice
ESG
Socially responsible investing
Impact investing
Sustainable investing
CSR
Carbon
Governance

✩
We are grateful for helpful comments from Marcin Kacperczyk (the
referee), Antti Ilmanen, Ronen Israel, and Dan Villalon as well as seminar participants at Copenhagen Business School, and The Future of Investing Conference at London Business School. We are very thankful to Alice
Zhao for her excellent research assistance. AQR Capital Management is a
global investment management ﬁrm, which may or may not apply similar investment techniques or methods of analysis as described herein. The
views expressed here are those of the authors and not necessarily those
of AQR. Pedersen gratefully acknowledges support from FRIC Center for
Financial Frictions (grant no. DNRF102).
∗
Corresponding author at: Copenhagen Business School, Solbjerg Plads
3:A5, DK-20 0 0 Frederiksberg, Denmark.
E-mail address: LHP.ﬁ@cbs.dk (L.H. Pedersen).

1. Introduction
Asset owners and portfolio managers overseeing trillions of dollars seek to incorporate environmental, social,
and governance (ESG) considerations into their investment
process.1 Meanwhile, investors have little guidance in how
to incorporate ESG in portfolio choice and, worse, opinions
1
For example, the 2018 Global Sustainable Investment Review reports
over $30 trillion invested with explicit ESG goals as of the beginning
of 2018. The 2017–2018 annual report of the Principles for Responsible

https://doi.org/10.1016/j.jﬁneco.2020.11.001
0304-405X/© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/)

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

differ dramatically across academics and practitioners
about whether ESG will help or hurt their performance.
Some argue that ESG considerations must necessarily
lower expected returns (e.g., Hong and Kacperczyk, 2009),
and others argue that the “outperformance of ESG strategies is beyond doubt” (Financial Times, 2017).2
To reconcile these opposing views, we develop a theory that illuminates both the potential costs and beneﬁts of ESG-based investing. Our theory explains how the
increasingly widespread adoption of ESG affects portfolio
choice and equilibrium asset prices. Further, we estimate
the magnitude of these effects empirically.
Our conclusions are ﬁvefold. (1) Theoretically, we show
that an investor optimally chooses a portfolio on the ESGeﬃcient frontier. (2) The portfolios that span the frontier
are all combinations of the risk-free asset, the tangency
portfolio, the minimum-variance portfolio, and what we
call the ESG-tangency portfolio (four-fund separation). (3)
Equilibrium asset returns satisfy an ESG-adjusted capital
asset pricing model (CAPM), showing when higher ESG assets have lower or higher equilibrium expected returns. (4)
We estimate the costs and beneﬁts of responsible investing
via the empirical ESG-eﬃcient frontier based on environmental (E) and governance (G) measures and show how
ESG screens can have surprising effects. (5) We test the
theory’s equilibrium predictions using four ESG proxies,
providing a rationale for why certain ESG measures predict
returns positively (some aspects of governance) and others
negatively (non-sin stocks, a measure of S) or close to zero
(low carbon emissions, an example of E, and commercial
ESG measures).
We consider three types of investors. Type-U (ESGunaware) investors are unaware of ESG scores and simply
seek to maximize their unconditional mean-variance utility. Type-A (ESG-aware) investors also have mean-variance
preferences, but they use assets’ ESG scores to update
their views on risk and expected return. Type-M (ESGmotivated) investors use ESG information and also have
preferences for high ESG scores. In other words, M investors seek a portfolio with an optimal trade-off between
a high expected return, low risk, and high average ESG
score. While optimizing across three characteristics (risk,
return, ESG) can seem challenging, we show that the investor’s problem can be reduced to a trade-off between
ESG and Sharpe ratio. In other words, risk and return can
be summarized by the Sharpe ratio.
Speciﬁcally, for each level of ESG, we compute the
highest attainable Sharpe ratio (SR). We denote this connection between ESG scores and the highest SR by the
ESG-SR frontier, as seen in Fig. 1, Panel A. The ESG-SR
frontier is a useful way to illustrate the investment opportunity set when people care about risk, return, and
ESG. This frontier depends only on security characteristics;

that is, it is independent of investor preferences. Hence,
an investment staff can ﬁrst mechanically compute the
frontier and then the investment board can choose a
point on the frontier based on the board’s preferences.
Further, investors with the same information should agree
on the frontier even if they prefer different portfolios on
the frontier. This separation property resembles that of the
standard mean-variance frontier, which also depends only
on security characteristics, so investors can mechanically
compute the frontier and then choose their portfolio’s
placement on the frontier based on risk aversion.
To understand why the ESG-SR frontier is humpshaped, consider ﬁrst the tangency portfolio known from
the standard mean-variance frontier, shown in Fig. 1, Panel
B. This tangency portfolio has the highest SR among all
portfolios, so its ESG score and SR deﬁne the peak in
the ESG-SR frontier. Further, the ESG-SR frontier is humpshaped because restricting portfolios to have any ESG score
other than that of the tangency portfolio must yield a
lower maximum SR, as illustrated in Panel B.
Type-A investors choose the portfolio with the highest
SR, that is, the tangency portfolio using ESG information
in Fig. 1, Panel A. Type-M investors have a preference for
higher ESG, so they choose portfolios to the right of the
tangency portfolio, on the ESG-eﬃcient frontier. Choosing
portfolios below or to the left of the eﬃcient frontier is
suboptimal because, in this case, the investor can improve
one or both of the ESG score and the SR, without reducing the other. Nevertheless, type-U investors may choose
a portfolio below the frontier, because they compute the
tangency portfolio while ignoring the security information
contained in ESG scores (they condition on less information). Type-M investors with a small preference for ESG
choose a portfolio just to the right of peak with nearly
the maximum SR (higher than the SR achieved by typeU in the example depicted in Fig. 1), and type-M investors
with strong preferences for ESG choose portfolios on the
far right of the ESG-eﬃcient frontier (possibly with lower
Sharpe ratios than U investors).
We also derive the equilibrium security prices and
returns. We show that expected returns are given by an
ESG-adjusted CAPM, as seen in Fig. 2. When there are
many type-U investors and when high ESG predicts high
future proﬁts, we show that high-ESG stocks deliver high
expected returns.3 This is because high-ESG stocks are
proﬁtable, yet their prices are not bid up by type-U investors, leading to high future returns. When the economy
has many type-A investors, then these investors bid up
the prices of high-ESG stocks to reﬂect their expected
proﬁts, thus eliminating the connection between ESG
and expected returns. Further, if the economy has many
type-M investors, then high-ESG stocks actually deliver
low expected returns, because ESG-motivated investors are
willing to accept a lower return for a higher ESG portfolio.

Investments, a proponent of ESG supported by the United Nations, states
that its signatories manage close to $90 trillion in assets.
2
See also Edmans (2011, p. 621), who ﬁnds that “certain socially responsible investing (SRI) screens may improve investment returns,” and
Nagy et al. (2015, p. 3), who ﬁnd that portfolios that incorporate ESG as
an investment signal “outperformed the MSCI World Index over the sample period while also increasing their ESG proﬁle.”

3
High-ESG ﬁrms are more proﬁtable if such ﬁrms beneﬁt from being less wasteful, having more motivated employees, being better governed, or having customers who are willing to pay a higher price for
their products. See also the literature on corporate social responsibility,
e.g., Baron (2009), Benabou and Tirole (2010), Hart and Zingales (2017),
and Oehmke and Opp (2020).

573

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Fig. 1. Environmental, social, and governance (ESG)–eﬃcient frontier and relation to mean-variance frontier. Panel A shows the ESG-SR frontier; that is,
the maximum Sharpe ratio (on the y-axis) that can be achieved for all portfolios with a given ESG score (on the x-axis). The peak of the ESG-SR frontier is
the Sharpe ratio (SR) of the standard tangency portfolio. Investors who care about both SR and ESG should choose a frontier portfolio to the right of this
portfolio, on the ESG-eﬃcient frontier. Panel B shows the standard mean-variance frontier and the corresponding standard tangency portfolio (denoted “all
assets”). The slope of the line from the risk-free rate to the tangency portfolio is the maximum SR. Panel B also shows the mean-variance frontier built
exclusively for portfolios with a certain ESG score, s̄. This frontier is a hyperbola that lies inside (i.e., to the right of) the standard hyperbola, and it has its
own tangency portfolio with corresponding Sharpe ratio SR(s̄ ). This Sharpe ratio deﬁnes a point on the ESG-SR frontier: {s̄, SR(s̄ )}.

574

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Fig. 2. Environmental, social, and governance–adjusted capital asset pricing model (ESG-CAPM).

To illustrate how the theory can be used in practice and
investigate its testable implications, we consider empirical
proxies for E, S, G, and overall ESG. As a measure of E (i.e.,
how green a company is), we compute each company’s
carbon intensity. As a measure of S, we use the sin stock
indicator deﬁned as in Hong and Kacperczyk (2009). As a
measure of G, we compute how (un)aggressive a company
is in its accounting choices based on the accruals in the
ﬁnancial statements (Sloan, 1996). As a measure of overall
ESG, we use the aggregate ESG score produced by MSCI, a
leading provider of ESG ratings.
We begin by empirically estimating the ESG-eﬃcient
frontier for some of these ESG proxies. The shape of the
empirical frontier naturally depends on whether ESG predicts returns. Hence, we consider a frontier for a proxy that
predicts returns in our sample (G) and one that does not
(E). Given that G predicts returns, both beneﬁts and costs
accrue to ESG investing using this proxy. Starting with the
beneﬁt of ESG information, we ﬁnd that the maximum SR
that incorporates this ESG proxy is about 12% higher than
the maximum SR that ignores such information (corresponding to the vertical difference between the two tangency portfolios in Fig. 1, Panel A). For the cost of ESG
preferences, doubling the average ESG score relative to the
level that maximizes the SR leads to a reduction in SR of
only 3%.
When we estimate the ESG-SR frontier using E (carbon),
we ﬁnd little ex post improvement to the Sharpe ratio of
an investor who incorporates such information in her portfolio decision. The frontier is still useful, however, because

it shows the SR cost of tilting toward a less carbon intensive portfolio, a cost that is empirically small even for a
signiﬁcant reduction in carbon. In summary, these frontiers
show a responsible investor’s opportunity set, quantifying
the costs and beneﬁts of using ESG in investing.
We also study a common way of incorporating ESG into
a portfolio: restricting the investment universe by removing the assets with the weakest ESG scores. We ﬁnd a
seemingly counterintuitive result that investors who screen
out assets with the worst ESG characteristics may build
optimal portfolios that have lower aggregate ESG scores
than portfolios of investors who do not impose ESG-type
restrictions. This happens because unconstrained investors
can short poor ESG assets to hedge out risks or to ﬁnance larger positions in high-ESG assets. Not surprisingly,
limiting the breadth of the investment universe detracts
from ﬁnancial outcomes as well. The ESG-SR frontier for
investors who screen out poor ESG stocks is strictly dominated by the unconstrained frontier.
Finally, we carry out a series of theory-motivated empirical tests that help explain how the four ESG proxies
we consider correlate with returns. To help explain why
our measure of G predicts returns, we ﬁrst show that this
aspect of governance positively predicts future proﬁtability. We also observe some increase in investor demand for
stocks of this type, but not to the point of making them
more expensive compared with other stocks. In fact, stocks
with attractive G trade at relatively cheaper Tobin’s q. So,
G could predict returns in our sample because investors
did not fully appreciate that G predicts proﬁtability. Our

575

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Journal of Financial Economics 142 (2021) 572–597

measure of S (not being a sin stock) predicts returns negatively as shown by Hong and Kacperczyk (2009), although
the statistical signiﬁcance is limited in our tests. To understand why, we show that this measure of S predicts proﬁts
negatively and high S is associated with stronger investor
demand. Finally, we ﬁnd that our two remaining proxies,
E (carbon intensity) and overall ESG (from MSCI), correlate
positively with investor demand and high valuations. These
proxies do not have a statistically signiﬁcant link to returns
in our data, perhaps because of the much shorter sample
periods.
We contribute to the literature both theoretically
and empirically. A growing theoretical literature on ESG
follows Merton (1987) and assumes that ESG-sensitive
investors refuse to hold certain assets. For example,
Heinkel et al. (2001), Luo and Balvers (2017), and
Zerbib (2020) show that, in equilibrium, such market segmentation leads to higher expected returns to non-green
companies.
Besides allowing such segmentation, we explicitly
model many assets characterized by ESG scores in addition
to the standard risk-return characteristics.4 Based on this
general setting, we derive several interesting properties of
the solution to the portfolio problem with parallels to the
classic Markowitz solution, including the novel result that
the ESG-SR frontier characterizes the solution, under certain conditions. Further, we show when ESG should predict
returns positively or negatively in equilibrium.
Empirically, our research bridges the gap between papers arguing that ESG hurts performance and those arriving at the opposite conclusion. The former group, based
on the segmentation theories, is supported by empirical literature showing that sin stocks (alcohol, tobacco,
and gaming, which can be seen as a poor S in ESG)
generate positive abnormal returns (Hong and Kacperczyk, 2009). The sin premium parallels the ﬁnding of
Baker et al. (2018) that “green municipal bonds are issued at a premium to otherwise similar ordinary bonds.”
Papers in the latter group show that stocks with good
governance (the G in ESG) generate positive abnormal returns (Sloan, 1996; Gompers et al., 2003) as do stocks
with higher employee satisfaction (part of the S of ESG)
(Edmans, 2011). Our model and empirical results help explain these opposing ﬁndings. We submit that ESG is a
positive return predictor if ESG is a positive predictor of
future ﬁrm proﬁts and the value of ESG is not fully priced
in the market. Further, the model predicts that this rela-

tion can be weakened with ESG becoming a neutral return predictor when most investors see the value in ESG
and even ﬂips sign, with ESG becoming a negative predictor of returns, when investors are willing to accept lower
returns for more responsible stocks. So, according to our
model, the results of Hong and Kacperczyk (2009) arise
because their measure of sin stocks (belonging to the industries related to alcohol, tobacco, and gaming) is associated with low investor demand, while the ESG measures
of Gompers et al. (2003) and Edmans (2011) are related to
higher ﬁrm proﬁts in a way that the market has not fully
appreciated.5
Our paper is also linked to the economic theories of
discrimination: taste-based discrimination (Becker, 1957)
and statistical discrimination (Phelps, 1972). Indeed, ESG
scores play a dual role in our model because ESG affects
investor preferences both directly (a kind of taste-based
discrimination) and indirectly because ESG scores are informative of risk and expected returns (a form of statistical discrimination). In equilibrium, the interplay between
these two dimensions allows for a variety of potential outcomes. This ﬂexibility is important, because the empirical
literature suggests that the link between ESG and returns
is not trivial. Certain ESG measures predict returns positively while others predict negatively, which highlights the
need for a theoretical framework that allows for a similar
ﬂexibility in outcomes, with testable predictions of when
each applies.
2. Portfolio choice with ESG: the ESG-eﬃcient frontier
2.1. Model: Markowitz meets sustainability goals
We examine an investor’s problem of choosing a portfolio of n risky assets and a risk-free security. The riskfree return is r f , and the risky assets have excess returns collected in the vector of random variables denoted
by r = (r 1 , .., r n ) . The assets have an ESG scores given by
s = (s1 , .., sn ) .
We consider three types of investors. Type-U investors
are uninterested or unaware of ESG scores. They take expected excess returns to be E (r ) with risk given by the
variance-covariance matrix, var(r ). Type-A (ESG-aware) investors use ESG scores to update their views on risk and
expected return. They use assets’ expected excess return,
μ = E(r|s ), conditional on the ESG information s, and the
conditional variance-covariance matrix of excess returns
 = var(r|s ).6 Type-M (ESG-motivated) investors use ESG
information and also have preferences for high ESG scores.
The portfolio problem for U and A investors has the stan-

4
In our model, ESG-motivated investors have a preference for stocks
with high ESG, but, mathematically, these investors’ utility could in principle capture a preference for any security characteristic. The only other
models of this form with many assets that we are aware of are provided
by Fama and French (2007), who consider a model of investor “taste”,
Baker et al. (2018), who consider a model in which some investors prefer green bonds, and Pastor et al. (2019) and Zerbib (2020), who consider ESG scores. These papers assume that the relevant characteristic,
e.g., ESG, has a linear effect on utility, essentially changing expected returns, whereas we consider more general ESG preferences. Further, these
papers do not derive the ESG-SR frontier or our other theoretical results,
except the ﬁnding that the preferred assets could have lower expected returns in equilibrium. See also Gollier and Puget (2014) and Friedman and
Heinle (2016), who consider a single risky asset to study issues related to
corporate engagement of responsible investors.

5
Bebchuk et al. (2013) ﬁnd that the return predictability associated
with the governance indicator of Gompers et al. (2003) has disappeared,
conjecturing an explanation based on investor learning. We ﬁnd that the
governance metric of Sloan (1996) based on accruals has continued to
predict returns post-publication.
6
An active debate is ongoing about whether ESG has an effect on
valuations and, even more so, whether it is relevant to future risks or
returns. For example, Flammer (2015) and Kruger (2015) provide supportive evidence for valuations and returns, and Dunn et al. (2018),
Ilhan et al. (2018), and Hoepner et al. (2019) show that ESG correlates
with risks.

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Journal of Financial Economics 142 (2021) 572–597

dard Markowitz solution, so we focus here on the solution
for type-M investors. Section 3 discusses equilibrium asset
prices with all three types of investors.
Investor M starts with a wealth of W and chooses a
portfolio of risky assets, x = (x1 , .., xn ) , where xi is the
fraction of capital invested in security i or, said differently,
the investor buys xiW dollars’ worth of security i. The investor’s utility depends on her future wealth and the ESG
characteristics of the portfolio. Given her portfolio choice,
the investor’s future wealth is





 = W 1 + r f + x r .
W

security. The tangency portfolio is the portfolio that maximizes the Sharpe ratio, namely, the expected excess return divided by the standard deviation of excess returns. To
generalize this idea, we consider the maximum SR for each
level of ESG score. The maximum SR that can be achieved
with an ESG score of s̄ is denoted the ESG-SR frontier,
SR(s̄ ):



SR(s̄ ) =

(1)

The investor seeks to maximize her utility U over

ﬁnal wealth W and average ESG score, s̄ = xx 1s , given the
extended mean-variance framework





 |s −
U =E W

γ̄
2





 |s + W f (s̄ ).
V ar W






= W 1 + r f + x μ −

γ̄
2

γ 
2

x x + f

xs
x 1

max x μ −
x∈X

γ 
2

x x + f

  
xs
x 1

,

(6)

This expression means that the investor’s problem can
be thought of as ﬁrst choosing the best portfolio given a
level of risk σ and an ESG score s̄ and then maximizing
over σ and s̄. The former problem is solved by choosing
the portfolio with the highest SR for the given ESG score (a
more detailed proof is given in the Appendix), which yields

(3)





max max SR(s̄ )σ −

where γ = γ̄ W is the relative risk aversion. Hence, by
dropping constant terms, the utility maximization problem
is



max
x
s.t. x 1 = 1
and x s = s̄

⎫⎤
⎪
⎪
⎪
⎢
⎪
⎥
⎪
⎢
⎪
⎬⎥


⎢
⎥
γ
max ⎢
max
max
x μ −
σ 2 + f (s̄ ) ⎥
⎥.
2
s̄ ⎢ σ ⎪
⎪
x∈X
⎢
⎪
⎪
⎥
⎪
⎪

⎪
⎪⎦
⎣
⎪
⎪
s.t. s̄ = xx 1s
⎪
⎪
⎩ 2
⎭
σ = x  x

xs
x 1
,

=



x μ
.
√
x  x

⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨

⎡

  

  



In order to use this deﬁnition of the highest Sharpe for
each ESG level, we ﬁrst rewrite the utility maximization
problem Eq. (4) as

(2)

W 2 x  x + W f



(5)

Here, γ̄ is the absolute risk-aversion parameter and
f : R → R ∪ {−∞} is the ESG preference function.7 The ESG
preference function depends on the average ESG score
among the risky asset positions (i.e., s̄ is the weighted sum
of ESG scores, scaled by the total position in risky assets,
x 1), meaning that the investor gets no ESG utility from
investing in the risk-free asset. We consider more general
ESG preference functions in Section 2.4. The overall utility
can be written as

U = W 1 + r f + x μ −

max
x∈X

s.t. s̄ = xx 1s

x μ
√
x  x

σ

s̄

γ
2


σ 2 + f (s̄ ) .

(7)

The optimal level of risk is given by σ = SR(s̄ )/γ . Inserting this risk level and simplifying the expression results in Proposition 1.

(4)

Proposition 1 (ESG-SR trade-off). The investor should choose
her average ESG score s̄ to maximize the following function of
the squared Sharpe ratio and the ESG preference function f :

where the set of feasible portfolios is X = {x ∈ Rn |x 1 > 0},
that is, all long-biased portfolios (generalized sets of allowed portfolios are discussed in Section 2.3). We consider
portfolios that invest at least as much long as short because deﬁning the overall ESG characteristic for a portfolio
that is short overall is diﬃcult, but, in principle, the framework can be applied more generally.





max (SR(s̄ ) )2 + 2γ f (s̄ ) .
s̄

(8)

This proposition shows how investors optimally trade
off ESG and Sharpe ratios. Not surprisingly, ESG affects the
optimal portfolio choice, given that ESG is in the utility
function, but the interesting result here is that we can analyze this trade-off using a part that depends only on securities [the ESG-SR frontier, SR(s̄ )] and another part that
depends only on preferences [2γ f (s̄ )]. In other words, just
like the standard Markowitz theory is powerful because
the mean-variance frontier can be computed independent
of preference parameters and then decisions about what
portfolio to pick are based on risk aversion, the ESGSR frontier can be computed independent of preferences
and then the investor can decide in the end where on
the frontier to place herself. Put differently, the ESG-SR
frontier summarizes all security-relevant information. The
investor’s problem is to ﬁrst place herself on the ESGSR frontier and then decide on the amount of risk. This
method works because investors care about the average

2.2. Solution: ESG-SR frontier
We now solve an ESG-motivated investor’s portfolio
problem. Because the objective function depends on the
ESG scores, s, the optimal portfolio depends on these
scores.
In a standard mean-variance analysis, the investor optimally combines the tangency portfolio with the risk-free
7
Economists generally hesitate to add arguments to the utility function
because this ﬂexibility means that almost any outcome can be justiﬁed,
but, here, we simply formalize the intentions of investors who control
trillions of dollars, as discussed in the Introduction. We allow that the
ESG preference function takes the value −∞ to capture screens, as discussed in Section 2.3.

577

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Journal of Financial Economics 142 (2021) 572–597

minimum-variance portfolio,  −1 1, and the ESG-tangency
portfolio,  −1 s.
The optimal portfolio looks the same as the standard
Markowitz solution, except that the expected excess returns μ have been adjusted. In other words, the optimal
portfolio can be found as follows. The investor ﬁrst compute ESG-adjusted expected returns, μ + π (s − 1s̄ ), in the
sense that each stock’s expected excess return is increased
if its ESG score si is above the desired average score s̄; otherwise, it is lowered. The amount of adjustment depends
on the scaling parameter π , or the strength of the preference for ESG.8 Next, the investor compute the optimal
portfolio found in the standard way, that is, multiplying by
1
−1
γ  . Therefore, all investors, regardless of their risk aversion and ESG preferences, should choose a combination of
four portfolios (or funds): the risk-free asset, the standard
tangency portfolio, the minimum variance portfolio, and
the portfolio that we call the ESG-tangency portfolio. The
ESG-tangency portfolio is the tangency portfolio if we replace the expected excess returns with the ESG scores.

ESG, which does not change when the investor chooses the
risk level in the second step by choosing her cash holding. If investors care about total ESG, x s, instead of average
ESG, then the investor’s problem cannot be summarized as
the ESG-SR frontier, which also shows that our frontier results are not trivial.
Understanding the ESG-SR frontier shows how differences in risk aversion and differences in ESG preferences
can be distinguished. If a group of investors have no direct
preferences for ESG ( f ≡ 0) but differ in their risk aversion γ , then all these investors should invest in the same
portfolio of risky assets (i.e., with the same Sharpe ratio
and average ESG score), but the more risk tolerant should
put a larger fraction of their wealth in this portfolio (i.e.,
own less cash instruments). If a group of investors have
the same risk aversion but differ in their ESG preferences,
then investors with stronger ESG preferences should buy
a portfolio with lower SR, but higher average ESG score.
Interaction effects also exist. If a group of investors care
equally about ESG but differ in their risk aversion, then
an investor with higher risk aversion not only puts more
money in the risk-free asset, but she also tilts her portfolio
toward higher ESG and lower SR. Mathematically, this behavior is due to the fact that the second term in Eq. (8) is
γ f (s̄ ), and, economically, this interaction is due to the fact
that SR matters less when an investor is more risk averse
(because she knows that she will take less risk anyway), so,
in relative terms, ESG becomes more important. More generally, observing an investor’s portfolio of risky assets and
its placement on the ESG-SR frontier is revelatory about
γ f (s̄ ); observing the investor’s cash position (or leverage),
about the risk aversion γ .
We next characterize how the maximum Sharpe ratio depends on the ESG score. We use the notation cab =
a  −1 b ∈ R for any vectors a, b ∈ Rn .

2.3. Example: how investors choose portfolios using the
ESG-SR frontier
Fig. 3, Panel A, illustrates how the ESG-motivated investor M chooses her portfolio using the ESG–Sharpe ratio
frontier. For every ESG level, she ﬁnds the portfolio with
the highest SR. One way to think about this step is that
the investor computes a standard mean-variance frontier
for all portfolios with this level of ESG as illustrated in
Fig. 1, Panel B. Then, the investor computes the maximum
Sharpe ratio as the slope of the line that goes from the
risk-free security to the tangency portfolio (again, based
only on portfolios with this ESG level). The investor collects all these Sharpe ratios and plots them against the ESG
levels as seen in Fig. 3, Panel A. The Appendix further explains the connection between the standard mean-variance
frontier and the ESG-SR frontier.
Panel A also shows investor M’s indifference curves.
These curves slope down because investor M likes high
Sharpe ratios and high ESG scores and can trade off one
versus the other to remain indifferent about all portfolios
on each indifference curve. Investor M’s utility is maximized at the point where her indifference curve is tangent
to the ESG-SR frontier. This solution is not the global maximum of the Sharpe ratio, as the investor optimally chooses
a higher level of ESG to satisfy her nonﬁnancial preference
for ESG.
This solution contrasts with that of our ESG-aware investor A, depicted in Fig. 3, Panel B. Investor A also considers ESG information to build a better forecast of returns
but does not have any direct (nonﬁnancial) preference for
ESG. That is, he would tilt toward portfolios with high ESG
(or, for that matter, with low ESG) only in as much as they
help maximize the investment outcome. This means that
the investor has horizontal indifference curves, illustrating that his preference depends only on the Sharpe ratio.

Proposition 2 (ESG-SR frontier). The maximum Sharpe ratio,
SR(s̄ ), that can be achieved with an ESG score of s̄ is



SR(s̄ ) =


cμμ −

csμ − s̄c1μ

2

css − 2s̄c1s + s̄2 c11

.

(9)

The maximum Sharpe ratio across all portfolios is
√
SR(s∗ ) = cμμ , which is attained with an ESG score of s∗ =
csμ /c1μ . Increasing the ESG score locally around s∗ leads to
nearly the same Sharpe ratio, SR(s∗ + ) = SR(s∗ ) + o(),
∗
because the ﬁrst-order effect is zero, dSRds(s ) = 0.
We next consider the nature of the optimal portfolio
weights for an ESG-aware investor.
Proposition 3 (four-fund separation). Given an average ESG
score s̄, the optimal portfolio is

x=

1

γ

 −1 (μ + π (s − 1s̄) )

(10)

as long as x 1 > 0, where

π=

c1μ s̄ − csμ
.
css − 2c1s s̄ + c11 s̄2

(11)

The optimal portfolio is therefore a combination of
the risk-free asset, the tangency portfolio,  −1 μ, the

8
When π = 0, portfolio choice simpliﬁes to the traditional meanvariance optimization.

578

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Journal of Financial Economics 142 (2021) 572–597

Fig. 3. ESG–eﬃcient frontier and investor indifference curves. This ﬁgure shows examples of an ESG–Sharpe ratio frontier (solid line) and an investor’s
indifference curves (dashed lines). Panel A draws an ESG-motivated investor’s indifference curves. This type-M investor’s utility increases in both the
Sharpe ratio and the ESG score of her portfolio, yielding a trade-off illustrated by the downward-sloping indifference curves. Panel B draws an ESG-aware
investor’s indifference curves, which are horizontal because this type of investor does not derive direct utility from ESG.

579

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Journal of Financial Economics 142 (2021) 572–597

We can also imagine that this investor considers the ESG–
Sharpe ratio frontier but would always choose the portfolio
with the highest possible Sharpe.
Finally, investor U solves a standard mean-variance optimization just like investor A, except that U computes potentially different estimates of risk and expected returns.
We illustrate this when we estimate the empirical ESG-SR
frontier in Section 4.2.

of risk. This speciﬁcation has the advantage that it also
works for long-short portfolios with x 1 = 0 and it retains
much of the tractability of the speciﬁcation considered earlier.
The generalized ESG preference function can capture
screens by having e(x, s ) = −∞ for all portfolios, where
xi = 0 for any security with si < 0.2. A screen can be seen
as an extreme version of nonlinear preferences across the
stocks’ ESG scores. In other words, an investor perhaps
does not view a portfolio of three stocks with ESG scores
of (0.1, 0.8, 0.9) the same as one with (0.6, 0.6, 0.6) even
if they have the same average, because the former has one
very low-ESG stock. Instead of capturing this idea with a
screen, a less extreme (and still tractable) version would be

2.4. Generalized ESG preferences
Some investors use screens to help implement their
ESG views. For example, an investor can screen out any
stock with a low ESG score, for example, si < 0.2. The
previous analysis naturally holds for the subset of nonscreened stocks. We can also incorporate such screens
more directly by changing the set of allowed portfolios to
X = {x ∈ Rn |x 1 > 0, ∀i xi = 0 if si < s∗}. Zerbib (2020) also
models screens combined with ESG preferences and empirically analyzes their effects.
Some investors prefer to exclude short positions, which
can be captured by X = {x ∈ Rn+ }, or both short positions and screened stocks X = {x ∈ Rn+ |∀i xi = 0 if si < s∗ }.
Investors can achieve a better risk-return trade-off if they
allow shorting, and shorting low-ESG stocks could be consistent with ESG preferences.9 Hence, investors can require
that their position in low-ESG stocks be zero or negative,
that is, X = {x ∈ Rn |x 1 > 0, ∀i xi ≤ 0 if si < s∗}. For any of
these restrictions, we can use the following result because
all these portfolio sets are cone-shaped. We say that X is
cone-shaped if x ∈ X implies that ax ∈ X for all a > 0 (said
differently, X depends only on x/x 1).



e(x, s ) = e1 xx 1s − e2

x diag( s1 , ..., s1 )x
1

(x 1 )2

n

, where e1 , e2 ∈ R are pa-

rameters. Here, the utility is more penalized if the investor
has a stock with an ESG score close to zero. In any event,
the investor can still think in terms of an ESG-SR frontier
as seen from Proposition 5.
Proposition 5 (generalized ESG-SR frontier). If the investor
has generalized ESG preferences e(x, s ), then the investor’s
problem is



max
ē


(SR(ē ) )2
+ ē ,
2γ

(12)

where SR(ē ) is the maximum Sharpe ratio for a given level of
ESG utility:



SR(ē ) =

Proposition 4 (ESG-SR frontier with screens). The conclusion
of Proposition 1 continues to hold for any cone-shaped X.10

max
x∈X
s.t. ē = e(x, s )



x μ
.
√
x  x

(13)

Finally, the theory can also work if each security has
a multidimensional ESG score (e.g., one score for environmental concerns, another for social, and a third for governance, with investors having preferences over such combinations).
Having characterized the solution to the ESG-aware
portfolio problem in a variety of cases, we note that such a
solution exists under certain conditions.11 Instead of going
into theoretical details, the empirical Section 4.2 shows the
practical applicability of the framework.

We can consider even more general ESG utility functions of the form e(x, s ) : X × Rn → R ∪ {−∞}, where X ⊆
Rn is a cone-shaped set of allowed portfolios. We assume
that the ESG utility function is homogeneous of degree
zero with respect to portfolios, that is, e(ax, s ) = e(x, s ) for
any a > 0. This is a natural assumption because it means
that the cash holding does not affect the ESG utility. For
example, the portfolio x = (0.2, 0.2) means that 20% of assets are put in each risky asset and the rest, 60%, is in cash,
and the portfolio 2x = (0.4, 0.4) means that twice as much
money is put in the same portfolio of risky assets, leaving
only 20% in cash. Homogeneity means that the same ESG
utility results because the risky portfolio is the same. This
homogeneity is what allows the investor to ﬁrst focus on
the optimal combination of the Sharpe ratio and portfoliolevel ESG score and then decide on the amount of risk.

One interesting example is e(x, s ) = f ( √ x s ), where

3. Equilibrium asset pricing with ESG
3.1. ESG-adjusted CAPM
Having solved the Markowitz problem with ESG investors, we next endogenously derive security prices and
returns. We consider an overlapping-generations (OLG)
economy in which, at time t, security prices are pt =
( p1t , .., pnt ) and excess returns from time t − 1 to t are
rt = (rt1 , .., rtn ) . The exogenous variables are the ESG scores

x x

the investor cares about how much ESG she gets per unit
9
In the approach based on the average ESG score, the optimal portfolio can include short positions, and this approach gives the investor
credit if the short positions have lower ESG scores than the long ones.
Fitzgibbons et al. (2018) argue that ESG-sensitive investors should be willing to short low-ESG stocks.
10
The deﬁnition [Eq. (4)] of the SR function must depend on the same
set of allowed portfolios, X.

11
A suﬃcient condition for existence is that the ESG preference function
f is continuous, we consider a compact space of ESG levels, s̄ ∈ [smin , smax ],
and for all such ESG levels, the portfolio x in Eq. (10) satisﬁes x 1 > 0. In
this case, for any s̄, an optimal portfolio is given in Eq. (10) with a resulting objective function Eq. (8) that is continuous in s̄, and any continuous
function attains its maximum on a compact space.

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Journal of Financial Economics 142 (2021) 572–597

s, the risk-free rate r f , the security dividend payoffs vt =
(vt1 , .., vtn ) , and the shares outstanding of each stock, normalized to one. We denote the total market dividend by
vtm = vt1 + . . . + vtn and assume that dividends are independent and identically distributed (i.i.d.) over time. We model
the informational value of ESG scores as E(vt |s ) = μ
ˆ +

λ(s − sm ), where sm = i mi si is the weighted-average
ESG

score of the market portfolio, mi = pi / j p j is the weight
of the market portfolio in stock i, and the parameter λ ∈ R
determines how informative ESG scores are for future profits. A positive λ means that more ESG friendly ﬁrms are
also more proﬁtable on average, and a negative λ has the
reverse interpretation.
Recall that the economy has three types of investors.
Type-U investors do not use ESG information at all: They
have no preference for ESG (i.e., their ESG preference function is fU ≡ 0 ), and they ignore the informational value of
ESG signals s, assuming that the best forecast of future dividends is the unconditional mean μ
ˆ = E(v ) and payoff risk
ˆ = var(v ). ESG-aware type-A investors also
is taken to be 
do not enjoy ESG utility ( fA ≡ 0 ), but they exploit ESG to
update their views on securities, using μ̄ = E(v|s ) as the
¯ = var(v|s ) to capture payoff risk.
expected payoff and 
ESG-motivated type-M investors use ESG information and
have a preference for a high average ESG score. A new generation of investors appears each time period, with type-U
investors born with wealth W U and similarly for types A
and M, and the aggregate wealth is W = W U + W A + W M .
Investors live for one period, and market clearing requires
that the total demand for shares from all young investors
equals the shares outstanding.
We are looking for equilibrium prices pt and excess
returns rt and start by noticing that these are related as

rti =

vti + pit
pit−1

− 1 − rf.

of the same type. If all investors ignore ESG (i.e., all are
type-U), then we are back to a standard CAPM equilibrium. All investors hold the unconditional tangency portfolio, that is, the portfolio that maximizes SR relative to their
information set, which ignores ESG. The tangency portfolio equals the market portfolio, and each security’s expected excess return is driven by its unconditional market beta, β i =

investor who understands that ESG scores are informative can exploit this insight. Proposition 6 characterizes the
equilibrium.

Proposition 6. If all investors are ESG-unaware, i.e., of type-U
(W A = W M = 0 ), then any security i has steady-state equilibrium price
i

p =

vti

pi



μˆ i − Wγ cov vi , vm
rf

.

(15)

Unconditional expected excess return obeys the standard
unconditional CAPM:

 

E rti = β i E (rtm ),

(16)

but conditional expected returns are given by





E rti |s = β i E (rtm ) + λ

si − sm
.
pi

(17)

This proposition provides several intuitive results. First,
the price [Eq. (15)] of any ﬁrm’s equity is given by
its expected cash ﬂow payoff (μ
ˆ i ) less a risk premium
γ
i
m
[ W cov(v , v )], discounted by the risk-free rate. Second,
expected excess returns [Eq. (16)] are driven by market betas from the perspective of an investor who ignores ESG
scores. Third, from the perspective of an investor who uses
ESG scores, Eq. (17) shows that stocks returns have alphas relative to the CAPM that depend linearly on ESG.
If a high-ESG score is indicative of a high future proﬁt,
that is, if λ > 0, then stocks with ESG scores above average have higher conditional expected returns than those
with below-average ESG scores. This is in line with the
empirical ﬁndings such as those of Gompers et al. (2003),
who show that an ESG-type metric (governance) earns
CAPM alphas.13 Market prices adjust when more investors
are aware that this type of information could be relevant.
At the extreme, all market participants incorporate it into
their decision, as in the case that we consider next.
Suppose that all investors use ESG signals, but without ESG preferences (i.e., all are ESG-aware of type-A). In
this case, we get a conditional CAPM equilibrium, and investors can no longer proﬁt from using the informational
value of ESG scores because this information is already incorporated into prices. This theoretical prediction is in line
with the empirical ﬁnding of Bebchuk et al. (2013), who argue that market participants have gradually learned about
the usefulness of governance and have impounded it into
prices. Consequently, they show that the measures from
Gompers et al. (2003) do not predict abnormal returns
out-of-sample.

(14)

We focus on the steady-state equilibrium in which
prices (and expected returns) are constant, pt = p for all
t. In such an equilibrium, excess returns are simply given
by rti =

cov(rti ,rtm )
. What is new here is that a (small)
var(rtm )

− r f , and the return variance is driven by divi-

dend risk as prices are constant. Such a steady-state equilibrium exists because, over time, dividends are i.i.d., ESG
scores are constant, and the wealth of different investor
types is constant. If we did not make these assumptions,
each security price would depend on its current ESG score
and the current investor ESG sentiment (as summarized
by the total πt from Proposition 3), leading to interesting
dynamics. For example, a security’s return variance would
suddenly also depend on the risk of changes in the overall ESG investor sentiment, changes in the stock’s own ESG
score, changes in how ESG predicts dividends (e.g., because
of changes in customer demand for green products), and
the covariances of all shocks. Here we focus on the steady
state for simplicity.12
Let us consider equilibrium implications of the model,
starting with the simplest cases in which all investors are
12
Pastor et al. (2019) consider a simpliﬁed three-period model with ESG
risk, deriving an interesting two-factor model in which required returns
depend on the covariance with the market and an ESG factor.

13
The model is also consistent with λ < 0, when ESG is in conﬂict with
ﬁnancial outcomes (e.g., when corporations engage in charity).

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Journal of Financial Economics 142 (2021) 572–597

Finally, suppose that all investors use ESG in their signals and in their identical ESG preferences (i.e., all type-M).
Such ESG preferences change the equilibrium in an interesting way. To derive this equilibrium, we ﬁrst note that
returns [Eq. (14)] can be written in vector form as

rt = diag

1
pi

vt − r f ,

cost of capital encourages high-ESG ﬁrms to make real
investments because, using this low discount rate, more
projects would have a positive net present value. While
we do not explicitly model ﬁrm decisions to invest in ESG,
this insight helps explain why ﬁrms can choose to increase
their corporate investment in ESG or why ﬁrms with a
stronger ESG proﬁle could realize higher growth than ﬁrms
with relatively weaker ESG. Recent papers emphasizing
the effect of ESG investment on corporate decisions include Albuquerque et al. (2018), Landier and Lovo (2020),
Oehmke and Opp (2020), and Pastor et al. (2019).
If all types of investors exist, then several things can
happen. If a security has a higher ESG score, then, everything else equal, its expected return can be higher or
lower. A higher ESG score increases the demand for the
stock from type-M investors, leading to a higher price and,
therefore, a lower required return, as seen in Proposition 7.
Companies with poor ESG scores that are down-weighted
by type-M investors would have lower prices and higher
cost of capital.
Furthermore, the force that can increase the expected
return is that the higher ESG could be a favorable signal
of ﬁrm fundamentals, and, if many type-U investors ignore
this, the fundamental signal perhaps would not be fully
reﬂected in the price, as seen in Proposition 6. Whether
favorable ESG characteristics signal good proﬁtability (e.g.,
good governance leading to a well-run company or a social
company with happy productive employees) or low profitability (e.g., a company spending shareholders’ money on
charities that employees and customers do not appreciate)
is an empirical question; that is, the sign of λ is an empirical question. Further, it is an empirical question whether
the force of Proposition 6 or 7 is stronger, that is, the extent to which ESG information is incorporated into prices
and the extent to which ESG-investors’ demand pressure
affects required returns.
Finally, we can consider the effect of an increasing
adoption of ESG investing over time (i.e., an increasing
fraction of ESG-motivated investors or a stronger ESG
preference among them). A future increase in ESG investing would lead to higher prices for high-ESG stocks,
corresponding to a larger π in the model (as seen in
Proposition 7). If these ﬂows are unexpected (or not fully
captured in the price for other reasons), then high-ESG
stocks would experience a return boost during the period
of this repricing of ESG. If these ﬂows are expected, then
expected returns should not be affected.

(18)

where diag( 1i ) means the diagonal matrix with elements
p

( p11 , . . . , p1n ). Any investor clearly wants to maximize the
SR for the chosen ESG score. Further, in equilibrium,
all investors must choose the market portfolio, which
must therefore maximize for SR among all portfolios
with an ESG equal to that of the market, sm . Based on
Proposition 3, any investor buys the following portfolio:

x=

1

γ

 

 

¯ −1 diag pi
diag pi 



1

f
m
μ̄
−
r
+
π
s
−
1
s
.
(
)
i

× diag

p

(19)

The total wealth invested in each stock is W x, where
W is the aggregate wealth, and the total dollar supply
is p because shares outstanding are normalized to one.
Hence, the equilibrium condition is p = W x. (We derive
the equilibrium in the Appendix.) All investors hold the
market portfolio in this equilibrium with only type-M
investors (everyone cannot be more ESG friendly than
the average). Nevertheless, a security’s required return is
affected by its ESG as well as its conditional market beta,

β̄ i =

cov(rti ,rtm |s)
, as seen in Proposition 7.
var(rtm |s )

Proposition 7 (ESG-CAPM). If all investors are ESG-motivated
of type-M (W U = W A = 0 ), then any security i has
equilibrium price

pi =



μˆ i + λ si − sm − Wγ cov(vi , vm |s )


,
r f − π si − sm

(20)

where sm is the ESG score of the market portfolio and the corresponding π is given by Eq. (11). The equilibrium conditional
expected excess return is given by





E (rti |s ) = β̄ i E (rtm |s ) − π si − sm .

(21)

If all investors are ESG-aware of type-A (W U = W M = 0 ),
the same conclusions hold with π = 0.
This proposition shows that equilibrium asset prices are
different when all investors derive utility from ESG (typeM) relative to an economy dominated by investors who
ignore ESG (as in Proposition 6). With such ESG-motivated
investors, the price of any ﬁrm’s equity depends on its ESG
score in two ways. First, the ESG score affects the expected
cash ﬂow as seen in the numerator of Eq. (20). Second,
a higher ESG score lowers the discount rate used in the
denominator, thus increasing the price. Turning to the
implications for returns in Eq. (21), the ﬁrm’s cost of capital is given by the standard conditional CAPM expression
[β̄ i E (rtm |s )] adjusted for whether the ESG score is above or
below that of the market. In other words, the ﬁrm’s cost
of capital is lower if its ESG score is higher or, equivalently, the ﬁrm can issue shares at higher prices. This low

3.2. Testable predictions of the theory
To summarize, the theory makes the following predictions:
1. The trade-off between risk, expected returns, and ESG
can be summarized by the ESG-SR frontier.
2. Using ESG information can increase the investor’s SR by
improving the ESG-SR frontier.
3. Given the investor’s information set, investors with
stronger ESG preferences (or higher risk aversion)
choose portfolios with higher ESG scores and
(marginally) lower SR.
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Journal of Financial Economics 142 (2021) 572–597

4. Even investors with preferences for the average ESG
score optimally choose portfolios with positions (long
or short) in almost any security (as opposed to standard
models of taste-based discrimination that imply stricter
segregation).
5. ESG investors choose a combination of four portfolios (or funds): the risk-free asset, the standard tangency portfolio, the minimum-variance portfolio, and
the ESG-tangency portfolio.
6. A security with a higher ESG score has
a. A higher demand from ESG investors, which lowers
the expected return;
b. Different expected future proﬁts, which can increase
the expected return if the market underreacts to
this predictability of fundamentals; and
c. Stronger ﬂows from investors, which can increase
the price in the short term.

vestors). We start with a one-period economy with a riskfree rate of r f = 3% and n = 10 risky assets, which we
think of as equity sectors. The ﬁnal payoff of each asset
is vi = μ̄ + f + ε i , where μ̄ = 1 is the expected payoff, f is
a common shock, and ε i is an idiosyncratic shock, where
both shocks have zero means and volatilities σ f = σε =
0.15. Each asset has a supply of shares of zi = 1n = 10% so

that the market portfolio has payoff vm = i zi vi = μ̄ + f +
 1 i
i nε .
One of the assets is brown, and the others are green.
Type-M investors buy b = 30% of the shares outstanding of
green stocks and 0% of brown stocks. This screening approach is more extreme than the ESG-integration approach
that we focus on elsewhere, but it provides a simple example of how much prices change for a given change in
demand. The market is cleared by type-A investors, who
have risk aversion of γ = 3 and wealth W A = 1 (equal to
the expected future value of the market).
The difference in expected returns of brown-versusgreen assets is E (r brown ) − E (r green ) = 0.23% in equilibrium,
as shown in the Appendix. In a one-period model, this difference in required returns corresponds to a small differ-

Many of these predictions are qualitative in nature, but
it is interesting to considering the quantitative effects of
ESG on returns (predictions 6.a and 6.b). Starting with
6.b (corresponding to Proposition 6), we empirically estimate how different ESG measures predict future earnings
(see Section 4.4). This provides an estimate of λ in the
model. Speciﬁcally, we run a regression of the form

vti

i
At−1

brown

ence in prices of only ppgreen − 1 = −0.2%. With many time
periods, a permanent difference in required returns can
have a large price effect. To see this, recall from the Gordon Growth Model (GGM) that P = D/(k − g), where k is
the required return and g is growth. GGM implies that

=

i
i
λst−1
+ controls + εti , where At−1
is assets. We empirically

scale earnings by assets (instead of just using earnings
as in the model) so that our variables are more stationary, but we can link the results to the model as follows.
If this predictability is not already incorporated in prices,
then the effect of expected returns for an investor exploitvti

i
ing this effect should be Et (rti |st−1
) = Et ( i
i
i
Et (vti /At−1
|st−1
)
i
pit−1 /At−1

− rf =

pt−1

i
λst−1
i
pit−1 /At−1

D
1
P
∂P 1
1
=−
=−
=− .
2 P
∂k P
k
−
g
D
(k − g )

So, with a price-dividend ratio of DP = 30, a permanent
difference in required returns of ∂ k = 0.23% is associated
with a meaningful price difference of ∂PP = − DP ∂ k = −30 ×
0.23% = −7%.

i
− r f |st−1
)=

− r f . To make this concrete,

we can use the estimates from Table 1 (explained in more
detail in Section 4.4). For example, one of the strongest
predictors of future proﬁts is our proxy for governance,
which has λ = 0.061 in Table 1, Panel B, Regression 5.
Coupled with the average price-to-asset of

pit−1

4. Empirical results
4.1. ESG measures and data

of 1.5 in

As ESG is a broad umbrella term, we consider four
proxies that capture different ESG aspects, possibly followed by different investor clienteles. Our goal is not to
run a horse race between them, but rather to present a
discussion of how different elements of ESG can be priced
in the market and an illustration of how our theory guides
empirical tests for investors who want to incorporate some
ESG metric into their portfolios.

i
At−1
i
of st−1

our sample, this means that an increase
of 0.22
(equivalent to moving from the 10th to the 90th percentile
of this variable) could elevate returns by 0.0611.×5 0.22 =
0.89%. This calculation takes into account only the value
of the earnings at time t; that is, prices are assumed
constant in steady state. If prices also adjust, then the
effect could be larger. To capture this effect, note that,
when the economy is not in steady state, returns are
given by rti =
pi

vti + pit
pit−1

pt−1

1. A measure of E: low carbon intensity. As a measure
of how green a company is (the E in ESG), we compute its carbon intensity (CO2 ), deﬁned as the ratio
of carbon emissions in thousands of tons over sales
in millions of dollars. Carbon emissions can be measured in different ways, but we use the sum of scope
1 carbon emissions (a ﬁrm’s direct emissions, e.g., from
the ﬁrm’s own fossil fuel usage) and scope 2 carbon
emissions (indirect emissions from purchased energy,
e.g., electricity). We do not include scope 3 emissions
(other indirect emissions) because they are rarely reported by companies and are at best noisily estimated

− 1 − r f , so an additional effect comes
pi /vti

i
from Et ( i t |st−1
) = Et ( i t

i
At−1

vti

i
i
i
pt−1 /vt−1
vt−1
At−1

Ai

i
i
|st−1
) = vit−1 λst−1
,
t−1

where we assume that price-earnings ratios stay constant.
So, with

i
At−1
i
vt−1

(22)

= 3.2, which is the median of assets-to-gross

proﬁts in our data, this return effect would be 3.2 ×
0.061 × 0.22 = 4.3%.
Finally, we consider the quantitative effect of ESG demand (prediction 6.a, corresponding to Proposition 7, but
here looking at ESG demand from some, but not all, in583

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Journal of Financial Economics 142 (2021) 572–597

and inconsistent across different data providers (e.g.,
Busch et al., 2018). We negate the CO2 variable so that
higher values indicate better ESG (less carbon intensive, greener companies). These data are obtained from
Trucost and are available from January 2009 through
March 2019.
2. A measure of S: non–sin stock indicator. Stocks in certain sin industries are shunned by some ESG-conscious
investors, for example, tobacco, gambling, and alcohol (related to the S in ESG). We consider a non–sin
stock indicator, taking the value of zero for sin stocks
and the value of one otherwise, so that higher values
indicate better ESG. Sin industries are deﬁned as in
Hong and Kacperczyk (2009), and this indicator is
available for our longest sample, January 1963 through
March 2019.
3. A measure of G: low accruals. We use a measure of
governance that can be computed over a long sample
period based on accounting information. We look at
each ﬁrm’s accruals over assets with a sample period
spanning January 1963 through March 2019. Accruals are essentially accounting income for which the
related cash has not yet been received.14 We negate
accruals so that higher values indicate better ESG. The
idea, coming from the accounting literature, is that
low accruals indicate that a ﬁrm is conservative in
its accounting of proﬁts (e.g., Sloan, 1996) and better
governed companies tend to adopt more conservative
accounting processes (e.g., Kim et al., 2012). Research
shows companies that are subject to Securities and
Exchange Commission enforcement actions tend to
have abnormally high accruals prior to such actions
(e.g., Richardson et al., 2006) and companies with
high accruals have a higher likelihood of earnings
restatements (e.g., Richardson et al., 2002).
4. A measure of overall ESG: MSCI ESG scores. One of the
most widely used ESG scores by institutional investors
is computed by MSCI, and our sample for this variable
is from January 2007 through March 2019.15 The MSCI
score is a comprehensive assessment of each company’s
ESG proﬁle. We use the top-level ESG score that summarizes each company’s E, S, and G characteristics, on
an industry-adjusted basis, as a numerical score from
zero (worst ESG) to ten (best ESG).

4.2. Empirical ESG-SR frontier
To compute the ESG–Sharpe ratio frontier implied by
our theory, investors must ﬁrst choose their investment
universe and compute risk and expected returns. We consider monthly returns of stocks in the Standard & Poor’s
(S&P) 500 index, which makes the analysis conservative
in the sense that we focus on a liquid and realistic investment universe with high data coverage, ruling out that
our results are driven by microcap stocks. To compute
risk (i.e., the variance-covariance matrix of the S&P 500
stocks), we assume that all investors use Barra’s US Equity risk model (Barra USE3L model), an industry standard
for use in portfolio management.17 ESG-unaware investors
and ESG-aware investors compute expected returns in different ways. U investors focus on the general equity risk
premium and the traditional value factor, book-to-market,
while A investors also use ESG information.18
To compute the annualized expected return of any stock
i in any month t, U investors use

EtU (ri,t+1 ) = MKT t + bmi,t BMt ,

(23)

where MKT t is the equity risk premium, bmi,t is stock
i’s cross-sectional book-to-market z-score (i.e., the stock’s
book-to-price ratio minus the cross-sectional mean, divided by the cross-sectional standard deviation), and BMt
is the return premium of the value factor. For each factor,
the return premium at time t is its constant Sharpe ratio, multiplied by its volatility as estimated using the Barra
model. Details on the estimation method are given in the
Appendix.
Similarly, A and M investors compute the annualized
expected return of stock i as

EtA (ri,t+1 ) = MKT t + bmi,t BMt + si,t ESGt ,

(24)

where si,t is the stock’s ESG score at time t and ESGt is
the return premium of the ESG factor, based on one of
the proxies listed in Section 4.1. The ESG score si,t is computed as the cross-sectional z-score of the raw ESG metric. Because a stock’s ESG score si is normalized as a crosssectional z-score, we get the intuitive interpretation that
an ESG score of zero means an average stock in terms of
the ESG measure, a score of two means that the stock has
ESG characteristics two standard deviations better than the
average stock, and so on. For a portfolio, the average ESG

score is computed as in the theory Section 2.1, s̄ = xx 1s ,
which provides a similar intuition for long-only portfo-

We merge these data sets with the XpressFeed database
for stock returns and market values, the Compustat
database to compute ﬁrm fundamentals, institutional holdings from 13f holdings reports (as aggregated by Thomson
Reuters), signed order ﬂow computed from intraday data,
and the risk model of Barra US Equity (USE3L) that is used
in the computation of the empirical EGS eﬃcient frontier.16

available between January 1993 and December 2012. We thank Tarun
Chordia for kindly making these variables available to us.
17
Estimating the covariance matrix is not a contribution of this paper,
so we use a third-party risk model for convenience. For details about
the risk model, see Barra documentation, available, for example, at http:
//www.alacra.com/alacra/help/barra_handbook_US.pdf.
18
We design our empirical setup to be as simple as possible, with a
single non-ESG factor, value. Of course, investors may consider other factors as well. In such cases, we would expect similar patterns to those
discussed here, although including or not including ESG could matter relatively less for investment outcomes. Unless ESG has meaningfully better
performance or diversiﬁcation properties than other factors, we would expect that as one adds more factors, the optimal weight on ESG, and its
incremental impact, to decrease.

14
We measure accruals as in Sloan (1996): (change in current assets minus change in cash) minus (change in current liabilities minus change in
debt included in current liabilities minus change in taxes payable) minus
(depreciation and amortization expense).
15
The MSCI website states that, as of August 2018, “MSCI ESG Research
is used by 46 of the top 50 asset managers and over 1,200 investors
worldwide” (https://www.msci.com/esg-ratings, accessed July 7, 2019).
16
The variables related to signed order ﬂow are deﬁned as in
Chordia et al (2002) and Chordia and Subrahmanyam (2004) and are

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Journal of Financial Economics 142 (2021) 572–597

lios, but long-short portfolios can in principle attain an unbounded range of ESG scores.
Using the above methodology, we compute the ESG-SR
frontiers for two ESG proxies: E and G. We do not build the
frontier for S because this proxy is binary (sin or non-sin),
which corresponds to screening (something we consider in
Section 4.3). For brevity, we leave out the frontier for overall ESG because it resembles the E frontier.
Starting with the ESG-SR frontier for the environmental proxy based on CO2 emissions, Fig. 4 shows the frontier both from the perspective of ESG-unaware and ESGaware investors (solid and dashed lines, respectively). Further, we distinguish what we call the ex ante perceived
frontier (Panel A) and the realized frontier (Panel B). For
the former, each month, the investor computes risk and expected returns as deﬁned previously and then derives the
ESG-SR frontier and the corresponding frontier portfolios.
Panel A simply shows the time series average of these perceived frontiers. The ex post frontiers in Panel B show the
realized Sharpe ratios of these portfolios.
The two ESG-SR frontiers in Panel A are close together,
suggesting that the environmental proxy we use here is
not very helpful in explaining average returns. This is also
conﬁrmed by the fact that the two frontiers peak around
a carbon score of zero, suggesting that the typical stock
in investor’s A and B tangency portfolio is about average
in its emissions footprint (we further conﬁrm this in the
regression framework in Section 4.6). This ﬁnding is even
more striking when looking at Panel B: The two frontiers
sit on top of each other, meaning that the realized Sharpe
ratios of the portfolios on the two frontiers are essentially
identical for any given level of carbon intensity.
The ESG-SR frontier remains useful even when the ESG
proxy is a weak predictor of returns (as is the case in
Fig. 4). For example, the frontier can be used to quantify
the trade-off faced by type-M investors, who are willing to
sacriﬁce some of the Sharpe ratio to improve their portfolios’ ESG proﬁle. In the context of Panel B, such ESGmotivated investors seek portfolios with less carbon emissions (greener portfolios). Moving two units to the right
from the tangency portfolio (i.e., moving toward greener
portfolios, so that the typical stock in the portfolio is two
standard deviations greener) reduces the optimal Sharpe
ratio by about 3%. This modest reduction in SR could be an
acceptable price to pay for some ESG-motivated investors
for such a large reduction in CO2 . Pushing further toward
greener portfolios is increasingly costly; for example, moving from the peak to the portfolio score four units greener
reduces the Sharpe ratio by about 10%.
Fig. 5 presents the ex ante and ex post frontiers, built
similarly as in Fig. 4, but using our governance proxy.
These frontiers are interesting because the frontiers for the
ESG-unaware differ signiﬁcantly from those of the ESGaware investor. This difference arises because our G proxy
predicts returns in our sample (as discussed further in Section 4.6). To understand Fig. 5, Panel A, note that the ESGunaware investor U maximizes the Sharpe ratio for the
ESG score of 0.25, meaning that a typical stock in her
portfolio is close to average for this ESG measure. This
near-neutrality to ESG is not surprising because the U investor uses information only on book-to-market ratios, and

any exposure to G happens incidentally through the weak
correlation between book-to-market and G. Moreover, the
frontier is relatively symmetric in the neighborhood of
zero, meaning that this investor perceives the cost of targeting a positive G score to be similar to the cost of targeting a same-magnitude negative tilt on ESG. For example,
targeting a G score two standard deviations higher than
optimal (i.e., moving from 0.25 to 2.25) lowers investor
U’s perceived Sharpe ratio by about 9% and targeting a G
score two standard deviations lower than optimal (–1.75)
degrades the perceived Sharpe ratio by 7%.
The ESG-aware investor’s perceived frontier looks very
different, as seen in Fig. 5, Panel A. The frontier peaks at a
G score of 2.25; that is, for the ESG-aware investor, maximizing the Sharpe ratio means targeting a portfolio with
a signiﬁcantly higher G score than the market. Moreover,
the frontier is clearly asymmetric, in a way that suggests
that decreasing a portfolio’s G score would be meaningfully more costly to the Sharpe ratio than increasing it. For
example, a two standard deviation increase from the optimal point (2.25 to 4.25) reduces the Sharpe ratio by about
3%. The penalty for a similar move in the opposite direction (2.25 to 0.25) is three times as high, 9%.
The perceived frontiers in Fig. 5, Panel A, intersect because forcing a negative ESG score is seen as more costly
by investor A than by investor U given that A takes into
account that G positively predicts returns. The two curves
cross at a G score of approximately zero, which is also intuitive. At this point, the optimal portfolio is essentially the
same for both investors because none of them can get exposure to the G score that they disagree about.
Finally, Panel B of Fig. 5 shows the realized Sharpe ratios of the portfolios that underlie the frontiers in Panel A.
A’s (ex post) realized frontier is similar to A’s ex ante perceived frontier, because the ESG score that drives the frontier is explicitly incorporated into A’s returns forecast and
because our model of ex ante risk and expected returns
captures well the ex post realized returns.
U’s realized frontier in Panel B has a different shape
than U’s perceived frontier in Panel A because U ignores
that G predicts returns. The realized ESG-SR frontier looks
fairly similar to that of investor A for ESG scores close
to zero because their portfolios are more similar in that
range. U’s frontier is otherwise below because, for any ESG
target, investor U chooses a portfolio with a suboptimal
trade-off between market exposure, value, and G.
Fig. 5, Panel B, shows the costs and beneﬁts of using
ESG investing based on governance. The beneﬁt of using
G information can be measured by looking at the realized
SR of the ESG-aware investor, which is 11% higher than the
realized SR of the ESG-unaware investor (ex ante, in Fig. 5,
Panel A, it is 12% higher). The cost of an ESG-motivated
investor’s preferences can be measured as the reduction in
SR that occurs when targeting an even higher ESG score
than that of an A investor.
4.3. Impact of restrictions: screening out the worst ESG
stocks
Our empirical application has so far allowed investors
to deploy their capital in unconstrained portfolios, going
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Journal of Financial Economics 142 (2021) 572–597

Fig. 4. Empirical ESG–eﬃcient frontier using carbon emissions as a proxy for E. We estimate the ESG–Sharpe ratio frontier for Standard & Poor’s
(S&P) 500 stocks, with returns driven by valuation (measured by each stock’s book-to-market ratio) and a proxy for E (measured by each stock’s CO2
emissions-to-sales ratio). The ﬁgure shows annualized maximum Sharpe ratios attainable for each level of ESG constraint. The ESG-unaware investor U
(dashed line) solely utilizes book-to-market to estimate expected returns. The ESG-aware investor A (solid line) uses both book-to-market and a measure
of governance (the G in ESG) based on accruals to estimate expected returns. Panel A presents the perceived frontier, built using the ex ante estimates
from each investor. Panel B presents the ex post frontier using the realized Sharpe ratios of the portfolios from Panel A.

long and short any stock in the investment universe. Also
of interest is to consider realistic constraints faced by many
ESG-sensitive investors. Among such constraints, undoubtedly the most popular one is screening out stocks with
the weakest ESG characteristics (i.e., removing such stocks
from the investable universe). Fig. 6 shows how the ESG-SR
frontier is affected by screens using the governance-related

proxy we utilize in Fig. 5. Fig. 6 shows three different frontiers: one for the unconstrained investor A (exactly as in
Fig. 5, Panel A), another obtained when the investor removes the 10% of stocks with the lowest ESG characteristics, and a third frontier with a 20% screen.
The ﬁrst observation is perhaps the most obvious: Constraints reduce a portfolio’s expected performance. Not sur-

586

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Fig. 5. Empirical ESG–eﬃcient frontier using accruals as a proxy for G. We estimate the ESG–Sharpe ratio frontier for Standard & Poor’s (S&P) 500 stocks,
with returns driven by valuation (measured by each stock’s book-to-market ratio) and ESG (measured by each stock’s accruals-to-assets ratio, a measure
related to governance). The ﬁgure shows annualized maximum Sharpe ratios attainable for each level of ESG constraint. The ESG-unaware investor U
(dashed line) solely utilizes book-to-market to estimate expected returns. The ESG-aware investor A (solid line) uses both book-to-market and a measure of
governance (the G in ESG) based on accruals to estimate expected returns. Panel A presents the perceived frontier, built using the ex ante estimates from
each investor. Panel B presents the ex post frontier using the realized Sharpe ratios of the portfolios from Panel A.

prisingly, the frontier with the 10% screen is strictly below
the unconstrained one, and the frontier with a 20% screen
is lower still. This means that, for any desired level of the
ESG score, the maximum attainable Sharpe ratio is lower
in a screened universe than in the unrestricted one.
What is perhaps more interesting is the magnitude by
which the Sharpe ratio decreases. To benchmark the reduction, a useful rule of thumb is that, under certain assumptions, the Sharpe ratio is approximately linear in the square
root of investment breadth (e.g., Grinold and Kahn, 1995).
This implies that a 10% (20%) reduction in breadth should

lower the Sharpe ratio roughly by 5% (10%). The reductions are roughly the magnitudes of the decrease for ESG
scores below about –0.5. The penalty is about half as small
closer to the ESG score of zero, perhaps because around
that value the optimal portfolio does not invest in extremely weak ESG stocks (or, presumably, in extremely
strong ESG stocks). For the values of ESG score meaningfully above zero, the magnitude of the penalty is sharply
higher than what could be inferred from the square root
of breadth rule of thumb. For example, removing the 20%
of stocks with the lowest ESG reduces the Sharpe ratio by
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Journal of Financial Economics 142 (2021) 572–597

Fig. 6. The Impact of screening on the ESG–eﬃcient frontier. This ﬁgure shows an ESG-aware investor’s perceived ESG–Sharpe ratio frontier (solid line; the
same as the solid line in Fig. 5, Panel A) as well as two frontiers for an investor who allows herself to use only a screened investment universe: removing
10% of stocks with the lowest ESG scores (dashed line) or removing 20% of stocks (dotted line). The ESG proxy used here is G, based on negated accruals
scaled by assets.

over 25% when the investor seeks to achieve high portfolio
ESG scores, due in part to the beneﬁts of shorting low-ESG
stocks.
A related ﬁnding from Fig. 6 is that the portfolio with
the highest Sharpe ratio (the tangency portfolio) has a
lower ESG score when the worst ESG stocks are removed.
The unconstrained investor A optimizes the Sharpe ratio
at the portfolio ESG score of 2.25. After removing 10% of
weakest ESG stocks, the Sharpe ratio is maximized at the
ESG score of 1.5; after removing 20%, the optimum is an
ESG score of one.
This ﬁnding is surprising since it means that investors
who exclude low-ESG assets from their investment universes may optimally build portfolios with lower ESG
scores than investors who allow for such low-ESG assets.
The intuition behind this ﬁnding is that low-ESG assets
are effectively funding sources, allowing the unconstrained
investor to short them to build larger long positions in
high-ESG securities. Moreover, low-ESG assets can be useful hedging instruments for high-ESG assets and could help
the investor improve the Sharpe ratio of the overall portfolio, potentially by increasing their investment in highESG securities. With screening, the investor may optimally
choose not to take such a large position in high-ESG assets.

A reports results based on the accounting rate of returns, deﬁned as the return on net operating assets as
in Richardson et al. (2006) and Panel B based on gross
proﬁtability over assets, deﬁned as revenue minus cost
of goods sold over total assets as in Novy-Marx (2013).
In both panels, these ﬁrm fundamentals are measured 12
months after the ESG variables. For each of our four ESG
proxies deﬁned in Section 4.1, we present two speciﬁcations, one based on a pooled sample with month ﬁxed
effects and with standard errors clustered at the ﬁrm level
and the other using the Fama-MacBeth procedure with
Newey-West standard errors. We also control for ﬁrm beta,
size, and book-to-market, although these control variables
are not critical for our results.
Regressions 1 and 2 in Table 1 use our E proxy. Negated
carbon emissions predict higher accounting returns in
Panel A but are insigniﬁcant predictors of gross proﬁtability in Panel B. We conclude that our E proxy perhaps
is not robustly related to fundamentals. We ﬁnd somewhat mixed results for our S proxy. The negative estimates
in Regressions 3 and 4, in both panels, indicate that sin
stocks have relatively stronger future fundamentals, consistent with Blitz and Fabozzi (2017), but these estimates are
only borderline signiﬁcant. Regressions 7 and 8 show that
the overall ESG score from MSCI is positively related to future fundamentals, but with statistical signiﬁcance only in
Panel B.
The results are the strongest for our governance proxy
(based on low accruals) in Regressions 5 and 6. In Panel
A, the highly statistically signiﬁcant also have a large economic magnitude. A one standard deviation increase in
negated accruals predicts a corresponding increase of 0.02
in the accounting rate of returns, or 20% of its average level
of 0.1. This ﬁnding opens up the possibility, which we conﬁrm later, that accruals contain information about future
fundamentals that may not be fully priced into the market
(similar to ﬁndings of Richardson et al., 2006). The cor-

4.4. Does ESG predict future fundamentals?
A necessary condition for ESG-type information to
generate positive abnormal returns is that it correlates
with future fundamentals.19 To test for this possibility,
we relate our ESG proxies to future fundamentals. We
consider two measures of fundamentals in Table 1. Panel
19
ESG could lead to price increases even without a fundamentals channel if investor demand for ESG characteristics goes up. This is perhaps
more likely over short periods and does not lead to a consistent return
premium over the long term.

588

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Table 1
Does environmental, social, and governance (ESG) score predict ﬁrm proﬁts?
This table reports the regression of future proﬁtability on current ESG scores, where proﬁtability is measured 12 months into the future. Proﬁtability is
computed as the accounting return (return on net operating assets, RNOA) in Panel A and as gross proﬁt over assets in Panel B. We consider four ESG
metrics [E (negated CO2 intensity), S (a non–sin stock indicator), G (negated accruals over assets), and overall ESG (using MSCI ESG scores)] and three
control variables (market beta, the logarithm of market capitalization, and the logarithm of the book-to-price ratio). The estimation method is either a
pooled regression with month ﬁxed effects (pooled) or Fama-MacBeth (FM). Robust t-statistics are in parentheses and are clustered at the stock level in
pooled regressions or adjusted using a Newey-West weighting scheme in Fama-MacBeth regressions.
Panel A: Predicting RNOA
RNOA (t + 12)

Dependent variable

E (low CO2)

(1)

(2)

0.006∗ ∗ ∗
(4.91)

0.006∗ ∗ ∗
(7.34)

S (non-sin)

(3)

(4)

−0.008∗
(−1.94)

−0.006∗ ∗ ∗
(−2.88)

G (low accruals)

(5)

(6)

0.208∗ ∗ ∗
(23.26)

0.193∗ ∗ ∗
(28.64)

ESG (MSCI)
Beta
Ln market cap
Ln(P/B)
RNOA(t)
Constant

(7)

(8)

0.0001
(0.24)
−0.040∗ ∗ ∗
(−4.40)
0.006∗ ∗ ∗
(4.89)
0.038∗ ∗ ∗
(11.94)
0.734∗ ∗ ∗
(61.25)
0.001
(0.06)

−0.068∗ ∗ ∗
(−17.90)
0.011∗ ∗ ∗
(12.45)
0.014∗ ∗ ∗
(6.72)
0.763∗ ∗ ∗
(88.59)
0.020∗ ∗ ∗
(2.78)

−0.068∗ ∗ ∗
(−10.24)
0.011∗ ∗ ∗
(23.91)
0.015∗ ∗ ∗
(6.98)
0.765∗ ∗ ∗
(97.48)
0.021∗ ∗
(2.32)

−0.064∗ ∗ ∗
(−33.77)
0.015∗ ∗ ∗
(32.71)
0.027∗ ∗ ∗
(22.59)
0.710∗ ∗ ∗
(167.53)
−0.005
(−0.95)

−0.067∗ ∗ ∗
(−20.69)
0.015∗ ∗ ∗
(26.55)
0.028∗ ∗ ∗
(22.01)
0.707∗ ∗ ∗
(118.95)
0.003
(0.47)

−0.060∗ ∗ ∗
(−31.79)
0.014∗ ∗ ∗
(30.14)
0.028∗ ∗ ∗
(23.73)
0.725∗ ∗ ∗
(169.65)
−0.019∗ ∗ ∗
(−6.59)

−0.062∗ ∗ ∗
(−19.43)
0.014∗ ∗ ∗
(26.85)
0.028∗ ∗ ∗
(22.11)
0.720∗ ∗ ∗
(128.80)
−0.009
(−1.56)

0.0001
(0.15)
−0.052∗ ∗ ∗
(−11.62)
0.008∗ ∗ ∗
(6.54)
0.026∗ ∗ ∗
(9.27)
0.756∗ ∗ ∗
(63.53)
0.002
(0.19)

239,440
0.708
Pooled

239,440
0.712
FM

1374,620
0.631
Pooled

1374,620
0.631
FM

1354,499
0.636
Pooled

1354,499
0.635
FM

116,130
0.723
Pooled

116,130
0.727
FM

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

−0.002
(−0.89)

−0.003∗
(−1.79)

0.061∗ ∗ ∗
(7.66)

0.070∗ ∗ ∗
(14.46)
0.001∗ ∗ ∗
(3.02)
−0.015∗ ∗ ∗
(−3.30)
−0.001∗ ∗
(−2.24)
0.006∗ ∗ ∗
(8.58)
0.948∗ ∗ ∗
(177.07)
0.028∗ ∗ ∗
(3.51)
171,284
0.892
FM

Number of observations
R-squared
Estimation method
Panel B: Predicting proﬁtability

Gross proﬁt over assets (t + 12)

Dependent variable

E (low CO2)

−0.005
(−0.96)

∗

−0.006
(−1.79)

S (non-sin)
G (low accruals)

−0.022∗ ∗ ∗
(−4.89)
−0.005
(−1.43)
0.036
(1.32)
1.026∗ ∗ ∗
(25.35)
0.019∗ ∗ ∗
(3.11)

−0.014∗ ∗
(−2.29)
−0.004∗ ∗
(−2.37)
0.038∗ ∗
(2.25)
1.017∗ ∗ ∗
(63.36)
0.010
(1.13)

−0.025∗ ∗
(−2.38)
−0.001
(−1.39)
0.012
(1.53)
0.978∗ ∗ ∗
(49.31)
0.028∗ ∗ ∗
(7.32)

−0.013∗ ∗ ∗
(−5.91)
−0.002∗ ∗ ∗
(−3.84)
0.014∗ ∗ ∗
(3.42)
0.980∗ ∗ ∗
(132.34)
0.023∗ ∗ ∗
(7.92)

−0.009∗ ∗ ∗
(−5.15)
−0.001∗
(−1.85)
0.002∗ ∗
(2.21)
0.960∗ ∗ ∗
(160.64)
0.020∗ ∗ ∗
(8.73)

−0.008∗ ∗ ∗
(−3.59)
−0.001∗ ∗ ∗
(−4.13)
0.002∗ ∗ ∗
(3.34)
0.960∗ ∗ ∗
(252.59)
0.023∗ ∗ ∗
(7.91)

0.001∗ ∗
(2.49)
−0.017∗ ∗ ∗
(−6.98)
−0.001∗
(−1.93)
0.006∗ ∗ ∗
(4.83)
0.954∗ ∗ ∗
(102.37)
0.026∗ ∗ ∗
(5.26)

361,540
0.087
Pooled

361,540
0.684
FM

1877,268
0.267
Pooled

1877,268
0.686
FM

1521,202
0.712
Pooled

1521,202
0.747
FM

171,284
0.866
Pooled

ESG (MSCI)
Beta
Ln market cap
Ln(P/B)
GPOA(t)
Constant
Number of observations
R-squared
Estimation method

responding regressions in Panel B replicate the result for
gross proﬁtability. Again, higher G scores predict an increase in future proﬁtability, but this time by a relatively
smaller amount. A one standard deviation move of accruals is associated with a 0.006 move in gross proﬁtability,
or about 2% of its average level of 0.3.

The results for the G proxy are robust to a variety
of controls. For example, differences could exist in accruals across industries, but the addition of industry dummy
variables to Regression 5 does not change the coeﬃcient (it
slightly increases from 0.208 to 0.209, with a t-statistic of
22.6 versus 23.3). Similarly, running the regressions with-

589

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Journal of Financial Economics 142 (2021) 572–597

out controls for ﬁrm size, book-to-market, or beta, or without date ﬁxed effects, has little effect on the result. Lastly,
a strong positive effect exists on accounting returns and on
proﬁtability even 24 or 36 months after we measure accruals. We conclude that there is strong evidence that accruals
correlate with future proﬁtability.

whether an ESG variable should help or hurt returns. For
the full picture, one also needs to analyze investor demand
for ESG. In this section, we consider institutional ownership, trading activity, and signed order ﬂow to capture investors’ interest in owning or purchasing a given stock.
Table 2, Panel A, uses a similar setup as Table 1 to
predict institutional holdings (in percent, using 13f data)
based on ESG metrics three months earlier (where the lag
chosen to ensure that the ESG variables are known before
we observe institutional holdings) and our usual controls.

4.5. Does ESG predict investor demand?
As we explain in the theory section, correlation with
future fundamentals is not enough in itself to determine

Table 2
Does environmental, social, and governance (ESG) score predict investor demand?
This table reports the regression of investor demand on measures of ESG. Investor demand is measured as institutional ownership (obtained from 13f
reports, led by three months) in Panel A, trading activity (log number of trades in the next month) in Panel B, and signed order ﬂow (dollar buy volume
over total dollar volume) in Panel C. The ESG proxies and control variables are as in Table 1. The estimation method is either a pooled regression with
month ﬁxed effects (pooled) or Fama-MacBeth (FM). Robust t-statistics are in parentheses and are clustered at the stock level in pooled regressions or
adjusted using a Newey-West weighting scheme in Fama-MacBeth regressions.
Panel A: Predicting institutional ownership
Institutional holdings (t + 3)

Dependent variable

E (low CO2)

(1)

(2)

2.206∗ ∗ ∗
(3.37)

2.284∗ ∗ ∗
(14.65)

S (non-sin)

(3)

(4)

6.128∗ ∗
(2.43)

7.037∗ ∗ ∗
(11.50)

G (low accruals)

(5)

(6)

1.060
(0.74)

3.208∗ ∗ ∗
(2.98)

Ln market cap
Ln(P/B)
Constant

Number of observations
R-squared
Estimation method

(8)

0.420∗ ∗ ∗
(6.98)
5.512∗ ∗ ∗
(11.27)
−1.265∗ ∗ ∗
(−2.67)
1.642∗ ∗ ∗
(9.22)
82.049∗ ∗ ∗
(18.45)
180,326
0.083
FM

5.774∗ ∗ ∗
(8.50)
10.079∗ ∗ ∗
(50.48)
−0.321
(−1.20)
−10.649∗ ∗ ∗
(−6.77)

5.912∗ ∗ ∗
(21.96)
10.057∗ ∗ ∗
(108.99)
−0.354∗ ∗ ∗
(−5.08)
−10.400∗ ∗ ∗
(−17.28)

5.698∗ ∗ ∗
(14.13)
9.662∗ ∗ ∗
(62.30)
−1.759∗ ∗ ∗
(−11.05)
−17.176∗ ∗ ∗
(−6.40)

6.905∗ ∗ ∗
(20.76)
9.691∗ ∗ ∗
(64.95)
−1.264∗ ∗ ∗
(−8.39)
−19.342∗ ∗ ∗
(−18.11)

1.610∗ ∗ ∗
(3.37)
9.599∗ ∗ ∗
(53.67)
−2.282∗ ∗ ∗
(−13.90)
−3.402∗ ∗ ∗
(−3.00)

3.038∗ ∗ ∗
(11.91)
9.650∗ ∗ ∗
(85.18)
−1.931∗ ∗ ∗
(−13.83)
−5.076∗ ∗ ∗
(−9.55)

0.343∗ ∗
(2.55)
6.371∗ ∗ ∗
(7.05)
0.846∗ ∗ ∗
(3.32)
1.136∗ ∗ ∗
(3.86)
62.372∗ ∗ ∗
(24.56)

378,623
0.454
Pooled

378,623
0.450
FM

962,867
0.470
Pooled

962,867
0.424
FM

737,865
0.475
Pooled

737,865
0.422
FM

180,326
0.033
Pooled

ESG (MSCI)
Beta

(7)

Panel B: Predicting number of trades
ln #trades (t + 1)

Dependent variable
(1)
E (low CO2)

(2)

(3)

−0.063
(−3.46)

−0.061
(−0.97)

S (non-sin)
G (low accruals)

0.282∗ ∗ ∗
(3.44)

ESG (MSCI)
Beta
Ln market cap
Ln(P/B)
Constant
Number of observations
R-squared
Estimation method

(4)

∗∗∗

1.382∗ ∗ ∗
(29.97)
0.898∗ ∗ ∗
(67.04)
−0.003
(−0.16)
−0.415∗ ∗ ∗
(−2.95)

0.936∗ ∗ ∗
(43.48)
0.709∗ ∗ ∗
(111.50)
−0.062∗ ∗ ∗
(−7.13)
−0.071
(−0.85)

0.940∗ ∗ ∗
(43.56)
0.724∗ ∗ ∗
(108.31)
−0.085∗ ∗ ∗
(−9.80)
−0.178∗ ∗ ∗
(−3.05)

0.004
(0.61)
0.989∗ ∗ ∗
(21.81)
0.642∗ ∗ ∗
(37.60)
−0.075∗ ∗ ∗
(−4.12)
2.519∗ ∗ ∗
(13.37)

49,264
0.737
Pooled

312,487
0.886
Pooled

263,217
0.892
Pooled

28,703
0.647
Pooled
(continued on next page)

590

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Table 2
Continued.
Panel C: Predicting signed order ﬂow
Buy volume/total volume (t + 1)

Dependent variable
(1)
E (low CO2)

(2)

(3)

(4)

−0.069∗ ∗ ∗
(−4.07)

S (non-sin)

0.321
(1.27)
0.767∗
(1.95)

G (low accruals)

0.271∗ ∗ ∗
(4.63)
0.079∗ ∗ ∗
(4.11)
0.019
(0.79)
48.874∗ ∗ ∗
(238.71)

1.593∗ ∗ ∗
(19.20)
0.740∗ ∗ ∗
(30.86)
0.280∗ ∗ ∗
(8.20)
44.105∗ ∗ ∗
(139.66)

1.588∗ ∗ ∗
(17.47)
0.769∗ ∗ ∗
(28.03)
0.249∗ ∗ ∗
(6.62)
44.206∗ ∗ ∗
(207.70)

−0.015∗
(−1.67)
0.097∗
(1.75)
−0.106∗ ∗ ∗
(−4.55)
−0.023
(−0.87)
51.086∗ ∗ ∗
(225.45)

49,318
0.011
Pooled

313,711
0.122
Pooled

264,242
0.121
Pooled

28,736
0.166
Pooled

ESG (MSCI)
Beta
Ln market cap
Ln(P/B)
Constant
Number of observations
R-squared
Estimation method

Table 3
Environmental, social, and governance (ESG) score and valuation.
We regress each ﬁrm’s valuation ratio (the logarithm of price-to-book)
on the contemporaneous ESG score, controlling for the market beta. The
ESG proxies are as in Table 1. Robust t-statistics are in parentheses and
are clustered at the stock level in these pooled regressions.

Institutional investors (whose interest we measure using
13f ﬁlings) seem to incorporate ESG when forming their
portfolios. All four ESG proxies correlate positively with institutional holdings. The economic effect of these variables
is noticeable. For example, a one standard deviation increase in E (negated CO2 intensity) is associated with increased institutional ownership of 1.3% in favor of greener
ﬁrms. The corresponding number is 0.3%–1.3% for G and
0.6%–0.8% for overall ESG. As for our binary S proxy, a
move from a sin stock to a non-sin stock implies an increase in holdings of 6%–7%.
Panels B and C in Table 2 consider measures of trading
activity (logarithm of the number of trades) and signed order ﬂow (the fraction of dollar volume that is attributable
to buys). For brevity, we report only pooled regressions
with date ﬁxed effects. The results are perhaps most intuitive for accruals, where both the number of trades and the
fraction of buys increase when this ESG proxy improves.
For the other three metrics, evidence is not as straightforward. The number of trades seems to decrease for stocks
with low carbon intensity and for non-sin stocks. For the
former proxy, we also see a decrease in the fraction of
buys.

Dependent variable

Ln(P/B)
(1)

E (low CO2)

(2)

(3)

S (non-sin)

0.020
(0.30)
−0.470∗ ∗ ∗
(−11.59)

G (low accruals)

0.338∗ ∗ ∗
(21.13)
0.514∗ ∗ ∗
(27.37)

0.058∗ ∗ ∗
(8.25)
−0.348∗ ∗ ∗
(−8.56)
1.245∗ ∗ ∗
(21.81)

2120,679 1708,222
0.073
0.077
Pooled
Pooled

203,502
0.046
Pooled

ESG (MSCI)
Beta
Constant
Number of observations
R-squared
Estimation method

(4)

0.086∗ ∗ ∗
(7.25)

−0.449∗ ∗ ∗ 0.402∗ ∗ ∗
(−16.39) (28.48)
1.391∗ ∗ ∗ 0.366∗ ∗ ∗
(38.32)
(5.48)
427,857
0.050
Pooled

4.6. Does ESG predict valuation and future returns?
should be more expensive and have lower future returns
than stocks with good G. To assess these predictions, we
consider valuations (Tobin’s q) and risk-adjusted returns in
Tables 3 and 4.
Table 3 shows how the ESG proxies correlate with
the logarithm of the price-to-book ratio. Because our
interest here is how much the market is willing to pay
for ESG characteristics, we analyze the relation between
contemporaneous valuation and ESG proxies. We control
for market beta, but we naturally omit the previously
used control variables that are related to valuation by
construction (i.e., size and book-to-market).

The ﬁndings so far suggest that at least some ESG proxies (e.g., G) robustly correlate with future fundamentals.
At the same time, some evidence exists that investors tilt
their portfolios toward stocks with more attractive G. As
we show in the theory section, the interplay between the
two effects could lead to a return premium or discount,
depending on which effect is stronger. The prediction is
perhaps easier to make relative to the proxies for E, S,
and overall ESG, for which we ﬁnd less correlation to future fundamentals and stronger investor demand. Hence,
the theory suggests that stocks with good E, S, or ESG
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Journal of Financial Economics 142 (2021) 572–597

Table 4
Does environmental, social, and governance (ESG) score predict returns?
This table reports the performance of high-ESG minus low-ESG portfolios. For each month, we sort stocks into portfolios based on quintiles of their ESG
scores (deﬁned as in Table 1). We then compute the return over the following month of the quintile with the best ESG scores minus that with the lowest
scores. Stocks are equal weighted in Panel A and value weighted in Panel B. We report the portfolios’ excess return, one-factor capital asset pricing model
(CAPM) alpha, three-factor alpha that also controls for the Fama-French (FF) factors related to size and value, ﬁve-factor alpha that further controls for the
FF factors related to proﬁtability and investment, and six-factor alpha that also controls for momentum (Mom), annualized and in percentages. t-statistics
are reported in parentheses.

Panel A: Equal-weighted returns
Average excess return
CAPM alpha
Three-factor (FF) alpha
Five-factor (FF) alpha
Six-factor (FF + Mom) alpha
Panel B: Value-weighted returns
Average excess return
CAPM alpha
Three-factor (FF) alpha
Five-factor (FF) alpha
Six-factor (FF + Mom) alpha

E
(low CO2 )

S
(non-sin)

G
(low accruals)

ESG
(MSCI)

5.15%
(1.59)
7.02%∗ ∗
(2.09)
5.03%
(1.63)
5.98%∗
(1.92)
5.12%∗
(1.73)

0.50%
(0.35)
−0.42%
(−0.30)
0.06%
(0.05)
1.28%
(0.94)
1.03%
(0.74)

7.84%∗ ∗ ∗
(4.41)
7.87%∗ ∗ ∗
(4.39)
7.30%∗ ∗ ∗
(4.03)
8.85%∗ ∗ ∗
(4.91)
8.71%∗ ∗ ∗
(4.76)

0.38%
(0.28)
1.29%
(1.00)
0.74%
(0.60)
0.28%
(0.22)
0.27%
(0.22)

4.88%∗
(1.89)
4.13%
(1.52)
3.02%
(1.14)
4.71%∗
(1.85)
4.33%∗
(1.72)

−3.04%∗ ∗
(−2.07)
−4.12%∗ ∗ ∗
(−2.85)
−3.69%∗ ∗
(−2.58)
−0.20%
(−0.15)
−0.36%
(−0.26)

3.01%∗ ∗
(2.30)
4.00%∗ ∗ ∗
(3.12)
3.22%∗ ∗ ∗
(2.64)
3.32%∗ ∗ ∗
(2.76)
3.07%∗ ∗
(2.52)

0.02%
(0.01)
1.34%
(0.70)
0.84%
(0.45)
−0.58%
(−0.31)
−0.59%
(−0.32)

folio decisions (in Section 4.2, our application was for simplicity, limited to the market factor and the value factor).
For the E and overall ESG proxies, we ﬁnd little or weak
evidence of abnormal returns. Over our sample period, less
carbon intense companies seem relatively outperformed
based on the point estimate, but this effect is signiﬁcant
only at the 10% level. Bolton and Kacperczyk (2019) ﬁnd
a carbon premium in returns but show that it disappears
in richer speciﬁcations, for example, when they control for
industry composition.
Finally, we ﬁnd some evidence for the sin premium, as
in Hong and Kacperczyk (2009). Because we consider a
spread portfolio long in non-sin stocks (higher ESG) and
short sin stocks (lower ESG), a sin return premium would
be reﬂected as a negative alpha estimate. We ﬁnd point
estimates of a sin premium up to 4% a year with valueweighted returns, but the estimate is small and insignificant with equal-weighted returns and when we control
for the ﬁve-factor or six-factor models (with both equaland value-weighted returns), consistent with ﬁndings of
Blitz and Fabozzi (2017). Our results are weaker than those
of Hong and Kacperczyk (2009), possibly because of differences in methodology and in sample period.20 We compare
sin stocks with the whole universe of non-sin stocks, while
Hong and Kacperczyk (2009) compare sin stocks with the
closest peers that do not suffer from the sin stigma, that
is, a different set of control stocks.

Regression 1 in Table 3 suggests that prices of stocks
with strong E scores (i.e., stocks with low carbon intensity, green stocks) are relatively higher than brown stocks’
prices. This is consistent with the relatively higher demand
from investors that we show earlier. A similar pattern is revealed when using the overall ESG metric (from MSCI) in
Regression 4. In contrast, we ﬁnd no signiﬁcant difference
in valuations between sin and non-sin stocks when using
our S proxy in Regression 2.
Perhaps most interesting is Regression 4, suggesting
that G (low accruals) is not priced by the market. In fact,
we ﬁnd low valuation ratios for stocks with high G scores
despite the stronger forecasted proﬁtability. This opens up
the possibility that such stocks generate attractive returns,
which is something we conﬁrm below.
Table 4 shows the return predictability of the ESG proxies. Based on each of our four ESG proxies, we sort stocks
into quintiles (in the case of the sin or non-sin indicator,
into two portfolios) each month and then form a portfolio
that goes long the best ESG stocks and short the worst ESG
stocks. Table 4 presents the resulting performance for both
the equal-weighted and value-weighted portfolios, controlling for a variety of asset pricing factors.
The portfolio based on G has highly signiﬁcant returns. The economic magnitude of this effect is substantial: 7% a year for the equal-weighted and 3% a year for
the value-weighted portfolio, even after controlling for the
ﬁve Fama and French (2015) factors augmented with momentum. This ﬁnding reinforces our conclusion that G, or
at least the particular aspect of governance we proxy for
here over our sample, can be useful even for investors who
already use multiple other investment factors in their port-

20
The last years in our sample are particularly diﬃcult for sin stocks.
Tobacco companies posted historically weak results. For example, the
MSCI World Tobacco index under-performed the cap-weighted benchmark
in each of 2016, 2017, and 2018, by about 1%, 9%, and 28%, respectively.

592

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

5. Conclusion: ethical, saintly, and guiltless investing

Gompers et al. (2003)] and in practitioner journals (e.g.,
Nagy et al., 2015). This heterogeneity results in a range
of possible equilibria depending on the relative importance of each investor type, leading to a relation between
ESG and expected returns that is positive, negative, or
neutral.
We test the empirical predictions of the theory using a range of ESG proxies that reﬂect different aspects
of our model and that can represent different clienteles
of investors. Our proxy G has historically offered ESG investors guiltless saintliness, perhaps because good G predicts strong future fundamentals, while attracting modest investor demand, leading to relatively cheap valuations and positive returns. Our proxies for E, S, and overall ESG are weaker predictors of future proﬁts, and investor demand appears stronger for these proxies, which
could help explain the higher valuations of stocks that
score well on these metrics and the low or insigniﬁcant
returns.
In conclusion, we think that our model provides a useful framework for responsible investment that we hope
will be useful both for future research on the costs and
beneﬁts of ESG investing and for ESG applications in
investments practice.

Investors increasingly incorporate ESG views in their
portfolios. Said simply and with a twist on the meaning
of ESG, many investors want to own ethical companies in
a saintly effort to promote good corporate behavior, while
hoping to do so in a guiltless way that does not sacriﬁce
returns.
Investors must realistically evaluate the costs and beneﬁts of responsible investing, and we hope that our framework is a useful way to conceptualize and quantify these
costs and beneﬁts. We show that a responsible investor’s
decision can be conceptualized by the ESG-eﬃcient frontier, a graphical illustration of the investment opportunity
set. The beneﬁt of ESG information can be quantiﬁed as
the resulting increase in the maximum Sharpe ratio (relative to a frontier based on only non-ESG information). The
cost of ESG preferences can be quantiﬁed as the drop in
Sharpe ratio when choosing a portfolio with better ESG
characteristics than those of the portfolio with maximum
Sharpe.
In addition to its practical appeal, the ESG-eﬃcient
frontier is based on a rigorous theoretical framework. We
explicitly derive the frontier and the corresponding set of
optimal portfolios. The optimal portfolios are spanned by
four funds, one of which captures stocks’ ESG scores. This
framework can be viewed as a theoretical foundation for
what is called ESG integration, meaning that ESG characteristics are used directly in portfolio construction (not as
screens).
Empirically, we ﬁnd that when ESG is proxied for by a
measure of governance based on accruals, the maximum
SR is achieved for a relatively high level of ESG. Increasing the ESG level even further leads to only a small reduction in SR, implying that ethical goals can be achieved
at a small cost. When we impose realistic constraints on
the portfolio, we see a downward shift in the ESG-SR frontier. This is an expected outcome, because imposing constraints reduces the maximum Sharpe ratio that one can
attain for any given ESG score. More surprisingly, screens
that remove the lowest ESG assets from the investment
universe can lead investors who maximize their Sharpe ratio to choose a portfolio with lower ESG scores than those
chosen by unconstrained investors who allow investments
in low-ESG assets. This result highlights nuances in optimally incorporating ESG into portfolio construction and
suggests improvements to traditional approaches based on
simple screening.
Turning to equilibrium asset prices, we derive an ESGadjusted CAPM, which helps describe market environments
that make ESG scores predict returns positively or negatively. To our knowledge, our model is the ﬁrst to explicitly
model heterogeneity in how investors use ESG information. We allow for investors to have preferences over ESG
and for the possibility that investors ﬁnd investment intelligence from ESG information. We argue that this feature
is realistic, because not only do we observe large assets
under management deployed with ESG in mind (e.g., the
2018 Global Sustainable Investment Review), but ESG also is
increasingly discussed as a potential alpha signal, both in
academic outlets [going back to at least Sloan (1996) and

Appendix
A.1. Relation between the ESG-SR frontier and the
mean-variance frontier
Fig. 1 shows how the ESG-SR frontier is related to the
standard mean-variance frontier. What follows is a sketch
of the math behind the graph. Consider ﬁrst the frontier
among portfolios with a certain ESG score. To see that
this is a hyperbola, minimize the variance x  x for all
portfolios with a given expected return, x μ = μ̄, portfolio weights that sum to one, x 1 = 1, and a given ESG score
x s = s̄. The solution to this minimization problem is linear in the expected return, μ̄, which means that the corresponding variance is quadratic in μ̄, showing that the frontier is a hyperbola when plotted in the usual way (mean,
standard deviation).
The hyperbola for a given ESG score clearly lies inside
the standard hyperbola, because minimizing the variance
among all portfolios must provide a result that is at least
as small as minimizing over the subset with a given ESG
score. In fact, the two hyperbolas touch in a single point.
To see why, recall that the standard mean-variance frontier is spanned by two portfolios. In other words, there exist portfolios x1 , x2 such that the frontier consists of portfolios of the form ax1 + (1 − a )x2 , where a runs from −∞
to ∞. Because x1 and x2 have different ESG scores generically, all frontier portfolios have different ESG scores. Further, for each ESG score, exactly one frontier portfolio has
this score, so this is where the two hyperbolas touch each
other.
Finally, given that the hyperbola for a given ESG scores
lies inside the standard frontier, then the Sharpe ratio of
its tangency portfolio must be lower than the overall tangency portfolio (except in the single case when they are
the same).
593

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

A.2. Example in Section 3.2

where Xt is a matrix of all securities’ factor exposures, Ft+1
is a vector of factor returns, and t+1 are the idiosyncratic
shocks. For investor U, Xt is an N × 2 matrix in which the
ﬁrst column is a vector of ones and the second contains
the book-to-market z-scores. For investor A, Xt is an N × 3
matrix in which the ﬁrst two columns are the same and
the third column is a vector of ESG z-scores. Even though
investors U and A use different factor models (i.e., different
Xt and Ft+1 ), we use the same notation for simplicity.
The factor returns Ft+1 are unobserved, but they can be
estimated as follows. Each time period, we run a crosssectional regression of stock returns on their characteristics and note that the regression coeﬃcients are the factor
returns. Speciﬁcally, we run a generalized least squares regression each period of stock-level returns on stock-level
characteristics, using the Barra risk model to obtain an estimate of the residual covariance matrix, t = var( t+1 ),
which yields the following estimated factor returns

With prices p, the demand of type-A investors is

x=

1

γ

 

 

¯ −1 diag pi
diag pi 

1

diag

pi


μ̄ − 1 − r f . (25)

The demand in dollars is W0A x. In equilibrium, this dollar demand must equal the supply in dollars, net of what
the type-M investors buy, diag( pi )z̄. Here, z̄i = 1n for the
brown asset and z̄i = 1n (1 − b) for the green assets (because M investors have bought the remaining nb shares
outstanding for green assets). Hence, we have the equilibrium condition

z̄ =

W0A

γ



 
¯ −1 μ̄ − 1 + r f p ,

(26)

which implies that

p=

μ̄ − Wγ A ¯ z̄
0

1 + rf

.



Fˆt+1 = XtT t−1 Xt

(27)

¯ =
Using that the variance-covariance matrix is 

pgreen =

0

1 + rf

Etj (rt+1 ) = Xt Etj (Ft+1 ),

= 0.918

(33)

which means that we need to estimate expected factor rej
turns, Et (Ft+1 ). The simplest way to do this is to assume
j

and

p

(32)

factor-mimicking portfolio weights, i.e., Fˆt+1 = θt rt+1 .
Finally, we need to compute expected returns:

(28)

brown

Xt t−1 rt+1 .

Here, we can interpret θt := (XtT t−1 Xt )−1 XtT t−1 as the

σ f2 11 + σε2 I,



μ̄ − Wγ A σ f2 (1 − b + b/n) + (1 − b)σε2 /n

−1 T

=



μ̄ − Wγ A σ f2 (1 − b + b/n) + σε2 /n
0

1 + rf

that Et (Ft+1 ) is constant over time and then estimate the
factor premiums as the sample average of factor returns.
This simple method does not work well empirically, however, because it leads, for example, to perceived and realized ESG-SR frontiers that differ signiﬁcantly even for investor A. This problem arises because investors have an incentive to choose extreme portfolios when the perceived
risk is time-varying (i.e., sometimes very low) while the
perceived expected return is constant.
A more realistic speciﬁcation is to assume that each factor k has a time-varying risk and a constant Sharpe raj
k ) = σ F,k SRF,k . The volatility of each factor, σ F,k ,
tio, Et (Ft+1
t
t
can be computed based on the factor-mimicking portfolio

= 0.916. (29)

The corresponding excess returns are E (r green ) =
μ̄
− 1 − r f = 5.88% and E (r brown ) = brown
− 1 − rf =
pgreen
μ̄

p

6.11%. (Excluded stocks are often highly correlated because
they tend to share similar characteristics, e.g., belong to
the same industry. We capture this effect by considering
a small number of assets, n = 10, each representing a
sector. Alternatively, one can consider a large number of
individual stocks and include industry factors in addition
to the market-wide risk and idiosyncratic risk).

weights and the overall risk model, σtF,k =

nally, we estimate SRF,k as the realized full-sample Sharpe
k /σ F,k .
ratio of the volatility-scaled factor returns, Fˆt+1
t

A.3. Estimating the empirical ESG-eﬃcient frontier
As discussed in Section 4.2, we model expected returns
as linear functions of factor exposures. For instance, investor U estimates expected returns as

EtU (ri,t+1 ) = MKT t + bmi,t BMt ,

A.4. Proofs
Proof of Proposition 1. Consider the problem of maximizing the return given a level of risk σ and an ESG score s̄:

(30)



where MKT t is the equity risk premium, bmi,t is stock i’s
cross-sectional book-to-market z-score, and BMt is the return premium of the factor-mimicking value factor, and
similarly for investor A, who also includes an ESG factor.
To show how we estimate these models, it is helpful to
write them in a general way that captures either investor
type. We ﬁrst show how we model the vector of realized
returns, rt+1 , and then later we turn to the expected rej
turns, Et (rt+1 ), for investor j ∈ {U, A}. Realized returns follow a standard factor model:

rt+1 = Xt Ft+1 +

t+1 ,

T

θtk t (θtk ) . Fi-

γ



max
x μ −
σ 2 + f (s̄ ) .
2
x

s.t. s̄ = xx 1s
2

σ = x x

(34)

Clearly, maximizing the expected return for given level
of σ and s̄ is achieved by maximizing the Sharpe ratio for
that σ and s̄. Further, the resulting Sharpe ratio is the same
for all levels of σ . To see why, suppose that x1 is the optimal solution for (σ1 , s̄ ) and x2 is the optimal solution
for (σ2 , s̄ ). We can scale x2 as σ1 /σ2 x2 to have a volatility

(31)
594

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

of σ1 , and this scaled portfolio still has the same average
ESG score, s̄. Given that x1 has the highest expected return
among such portfolios,

SR(x1 ) =

x1 μ

≥

σ1

σ1 
σ2 x2 μ

σ1

=

x2  μ

= SR(x2 ).

σ2

The maximum Sharpe ratio clearly is attained by the
tangency portfolio, which is proportional to  −1 μ. This
portfolio has the ESG score and Sharpe stated in the proposition. This result can also be derived by differentiating
the SR(s̄ ) with respect to s̄ and considering the ﬁrst- and
second-order conditions (there are two solutions to the
ﬁrst-order condition). 

(35)

The symmetric argument shows that the opposite inequality also holds, so SR(x1 ) = SR(x2 ) = SR(s̄ ).
Let us solve the problem explicitly. If we rewrite the
ﬁrst constraint as x s˜ = 0, where s˜ = s − 1s̄, and introduce
Lagrange multipliers π and θ , then the solution is characterized by the ﬁrst-order condition

0 = μ + π s˜ − θ  x,

Proof of Proposition 3. We have from the proof of
Proposition 1 that x = θ1  −1 (μ + π s˜). Further, from the

proofs of Propositions 1–2, we know that θ = σ1 SR(s̄ ) and
σ = SR(s̄ )/γ . Combining these yields x = γ1  −1 (μ + π s˜),
where we recall that s˜ = s − 1s̄. 

(36)

Proof of Propositions 4–5. These results follow based on
arguments analogous to those in the ﬁrst part of the proof
of Proposition 1 using that, for any x ∈ X and a > 0, we
have ax ∈ X and e(ax, s ) = e(x, s ). The optimization problem can be written as

meaning that the optimal portfolio is given by

x=

1

θ

 −1 (μ + π s˜).

(37)



Both constraints clearly bind, and the ﬁrst one yields

1
0 = s˜  −1 (μ + π s˜).

(38)

θ

x∈X

s˜  −1 μ
(s − 1s̄)  −1 μ
π = −  −1 = −
s˜  s˜
(s − 1s̄)  −1 (s − 1s̄)
c1μ s̄ − csμ
.
css − 2c1s s̄ + c11 s̄2

(39)

The second constraint yields

σ2 =

1

θ2

(μ + π s˜)  −1 (μ + π s˜).

(40)

Using the ﬁrst constraint, we can simplify as

σ2 =

1

θ2



μ  −1 (μ + π s˜),



θ=

σ


cμμ −

csμ − c1μ s̄



2

css − 2c1s s̄ + c11 s̄2

.

p=

(42)

SR(s̄ ) = σ θ =

!



=

cμμ −

in

the

proof

css − 2c1s s̄ + c11 s̄

1
pi


μ̄ − r f + π (s − 1sm ) .

#

"

p = diag

of

1



r f − π si − sm



(47)



γ
μ̄ − ¯ 1 ,

(48)

W

which proves Eq. (20) stated in the proposition. To translate this result to expected excess returns, we multiply
both sides by diag( 1i ), yielding
p

.
2

(46)

Solving this equation for the vector of prices p yields

μ  −1 (μ + π s˜)

2
csμ − c1μ s̄



p

(43)

equations

 

 

W ¯ −1 
1=
 μ̄ − diag pi (r f − π (s − 1sm )
γ

 
W ¯ −1 
=
 μ̄ − diag(r f − π si − sm p .
γ

Proof of Proposition 2. The maximum Sharpe ratio for a
given ESG score s̄ is the Sharpe ratio of the optimal portfolio given in the proof of Proposition 1:

two

γ

 

¯ −1 diag pi
diag pi 

This condition can be simpliﬁed by multiplying both
sides by diag( 1i ):

2

μ x μ  −1 (μ + π s˜)
SR(s̄ ) =
=
.
σ
σθ

W

× diag

yields (SR2(γs̄)) + f (s̄ ). Multiplying by 2γ gives the result
[Eq. (8)] in the proposition. 

last

⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨

Proof of Propositions 6–7. For Proposition 7, the equilibrium condition with all investors of type-M is

This shows explicitly that we can write the optimal
portfolio as x = σ v, where the vector v depends only on
the exogenous parameters and s̄, that is, not on σ .
Finally, as seen in Eq. (7), the optimal level of
risk is given by σ = SR(s̄ )/γ . Inserting this risk level

Using the
Proposition 1,

⎡

(41)

implying that the second Lagrange multiplier is

1

2

x  x + e(x, s )

⎫⎤
⎪
⎪
⎪
⎢
⎪
⎥
⎪
⎢
⎪⎥
⎬


⎢
⎥
γ 2
= max ⎢
max
max
x μ −
σ + ē ⎥
⎢
⎥
σ
2
ē
⎪
⎪
x∈X
⎢
⎪
⎪⎥
⎪
⎪
⎪
⎪
⎣
⎦
⎪
⎪
s.t. ē = e(x, s )
⎪
⎪
⎩ σ 2 = x  x
⎭


γ 2 
= max max σ SR(ē ) −
σ + ē
σ
2
ē


2
(SR(ē ) )
= max
+ ē
(45)
2γ
ē

So, the ﬁrst Lagrange multiplier is

=



γ 

max x μ −

1

1 = diag

(44)

595

pi

#

"

diag

1



r f − π si − sm





μ̄ −

γ ¯ 
 1 , (49)

W

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

and rearrange to obtain

i

 f

diag r − π s − s


m

= diag

Journal of Financial Economics 142 (2021) 572–597

 1 
pi


γ
μ̄ − ¯ 1 .
W

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The vector of expected excess returns μ thus is given
by

1
μ = diag i μ̄ − r f
p
1
 

γ
¯ 1 − diag π si − sm .
=
diag i 
W

(51)

p

The expected excess return of the market portfolio
i

( 1p p ) is given by



μ

m

= 1 diag

pi
1 p


μ

 i 
 

γ

¯ 1 − 1 diag p diag π si − sm .
1


W (1 p)
1p

=

(52)
That is,

 
γ 1 p

μ =
m

W

var(r |s ) − π (s − s ) =
m

m

m

 
γ 1 p
W

var(r m |s ),
(53)

where we use the deﬁnition of the ESG score of the market sm = 11 p p s. The expected excess return of security i

can be written as μi = zi  μ using the i’th unit vector zi =
(0, . . . , 0, 1, 0, . . . , 0), that is,

μi =
=

γ
W

1

zi  diag

 
γ 1 p
W

pi

 

¯ 1 − zi  diag π si − sm




cov(ri , r m |s ) − π si − sm .

(54)

Combining with the expression above for μm , we get



μi = β̄i μm − π si − sm .

(55)

Finally, when all investors are of type-A and choose
the tangency portfolio, we have π = 0, which is seen from
Proposition 3 and the expression for π .
For Proposition 6, similar calculations show that prices
are given by

p=

1
rf



μˆ −

γ ˆ 
1

(56)

W

and returns by the unconditional CAPM. Conditional expected returns are given by


 

 i  E vi s

 μˆ i + λ si − sm


f
E r |s =
− 1+r =
− 1 + rf .
i
i
p

p

(57)
Using the expression for the price,





 i  Wγ cov vi , vm + λ si − sm
E r |s =
pi

 i m

cov r , r
λ si − sm
m
=
E (r ) +
,
var(r m )
pi
where covi(v ,v ) = cov(r i , r m ) and
i

m

p ( 1 p)

γ ( 1 p )
W

(58)

E (r )
= var
(r m ) . 
m

596

L.H. Pedersen, S. Fitzgibbons and L. Pomorski

Journal of Financial Economics 142 (2021) 572–597

Nagy, Z., Kassam, A., Lee, L., 2015. Can ESG Add Alpha?. MSCI Inc, New
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==> JFE04 - Market expectations of a warming climate.txt <==
Journal of Financial Economics 142 (2021) 627–640

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Market expectations of a warming climateR
Wolfram Schlenker a,b,∗, Charles A. Taylor a
a
b

School of International and Public Affairs, Columbia University, 420 West 118th Street, New York, NY 10027, USA
National Bureau of Economic Research (NBER), 1050 Massachusetts Ave., Cambridge, MA 02138, USA

a r t i c l e

i n f o

Article history:
Received 21 February 2020
Revised 14 July 2020
Accepted 30 August 2020
Available online 24 April 2021
JEL classiﬁcation:
D84
Q02
Q54
Keywords:
Market expectations
Belief formation
Weather markets
Climate change

a b s t r a c t
We compare prices of ﬁnancial derivatives whose payouts are based on future weather
outcomes to CMIP5 climate model predictions as well as observed weather station data
across eight cities in the US from 2001 through 2020. Derivative prices respond both to
short-term weather forecasts for the next two weeks and longer-term warming trends. We
show that the long-term trends in derivative prices are comparable to station-level data
and climate model output. The one exception is February in the northeastern US, where
ﬁnancial markets price in a polar vortex-induced cooling effect, a recent scientiﬁc ﬁnding
that was not present in the older CMIP5 climate output. When looking at the spatial and
temporal heterogeneity in trends, futures prices are more aligned with climate model output than observed weather station trends, suggesting that market participants closely align
their expectations with scientiﬁc projections rather than recent observations.

1. Introduction
Scientists overwhelmingly agree that the climate is
changing because of human activity. The American Association for the Advancement of Science (2006) reported
that “the scientiﬁc evidence is clear: global climate change
caused by human activities is occurring now.” But public
opinion in the US remains mixed. As of 2016, less than half
of Americans believed that the earth is getting warmer due
to human activity, a number that has not budged much
since the Pew Research Center started asking the question

R
We are grateful to Siqi He for extracting the futures data from
Bloomberg Terminals. This work was supported by the U.S. Department
of Energy, Oﬃce of Science, Biological and Environmental Research Program, Earth and Environmental Systems Modeling, MultiSector Dynamics,
Contract No. DE-SC0016162.
∗
Corresponding author at: School of International and Public Affairs,
Columbia University, 420 West 118th Street, New York, NY 10027, USA.
E-mail address: wolfram.schlenker@columbia.edu (W. Schlenker).

https://doi.org/10.1016/j.jﬁneco.2020.08.019
0304-405X/© 2021 Elsevier B.V. All rights reserved.

© 2021 Elsevier B.V. All rights reserved.

in 2006.1 Views on climate change vary greatly across geography, political aﬃliation, educational status, and economic sector (Leiserowitz et al., 2017; Howe et al., 2015).
Politicians in the US have questioned the evidence on climate change, with some famously calling it an “elaborate
hoax.”
Given the divergent beliefs about climate change, debate persists about the accuracy of global climate models
and the extent to which agents incorporate these projections into their actions. We address these issues by examining how market participants update their expectations about climate over time. The Chicago Mercantile Exchange (CME) offers futures contracts for eight cities on
two main weather products: cooling degree days (CDDs),
which measure how much cooling is necessary during
hot temperatures in summer, and heating degree days
(HDDs), which measure how much heating is required
during cold temperatures in winter. The payoffs from

1
https://www.pewresearch.org/science/2016/10/04/
public- views- on- climate- change- and- climate- scientists/.

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

these contracts depend on observed temperatures over the
course of a month. The contracts are traded before the
month in which the weather is realized and thus provide
a direct measure of the market’s view on the expected
climate.
First, we show that the futures market capitalizes
weather shocks, that is, deviations from climate averages,
in the two weeks leading up to such unexpected weather
deviations. This is consistent with Dorﬂeitner and Wimmer (2010) and the more general ﬁnding that for horizons
beyond 8–10 days, “the nature of temperature dynamics
simply makes any point forecast of temperature unlikely to
beat the climatological forecast at long horizons, because
all point forecasts revert fairly quickly to the climatological forecast” (Campbell and Diebold, 2005, p.12). Futures
prices several weeks before the start of a month should reﬂect expectations about a month’s weather before the outcomes can be known.
Second, we ﬁnd that market expectations, as measured
by futures prices when weather outcomes are unknown,
have been changing at the same annual rate as temperature projections in the CMIP5 archive, the latest repository
in which various climate modeling groups made predictions for 2006 onward. The time trend also aligns with the
observed annual change from weather station data. All ﬁnd
signiﬁcant warming as shown by an increase in CDDs in
summer and a decrease in HDDs in winter. Climate models’
predictions have materialized, especially on average, validating model projections.
Third, the futures market closely follows advances in
the climate literature. When we regress the trend in futures prices for each airport and contract month observed
over our sample period on the observed trend at the
weather station as well as climate projections, the latter
has the most explanatory power. Further, the futures market seems to price in recent climatological advances that
were not available in the CMIP5 archive and have not been
detectable in weather station observations. Recent research
predicts that a shift in the jet stream will reduce late winter temperatures in the northeastern US via an increase in
cold air from the Arctic (i.e., a polar vortex). Likewise, the
futures market has shown a signiﬁcant increase in HDDs in
February. Together this suggests that market participants
are taking into account both global climate model output
and the latest research rather than simply projecting forward past time trends.
Finally, we present evidence in the Online Appendix
how oceanic oscillations like El Niño-Southern Oscillation
(ENSO) affect temperatures over the medium term across
the eight cities in our sample. Employing LASSO regressions to select relevant oceanic oscillation indices, we ﬁnd
that removing these large-scale effects reduces the year-toyear variability in observed weather but does not change
the time trend. The observed warming trend is hence not
driven by oceanic drivers of natural variability in temperatures but rather by increased greenhouse gas emissions.
In addition to contributing to the literature on the impact of climate change on ﬁrms and ﬁnancial markets, our
ﬁndings have relevance to climate adaptation. Economists
have estimated the beneﬁts and costs from a changing
climate (Auffhammer, 2018). Many of the recent micro-

level estimates relate outcomes of interest to random exogenous year-to-year weather ﬂuctuations to obtain unbiased damage estimates (Dell et al., 2014). While random
and exogenous year-to-year variation is preferable from a
statistical perspective, adaptation to a permanent change
in climate might mitigate some of the weather sensitivity
that is observed in response to unknown random weather
shocks. Agents should undertake adaptation investments
in response to anticipated permanent shifts in the climate
that are either unproﬁtable or infeasible for a one-time unknown weather shock. However, before agents can adapt,
they ﬁrst must form a belief about the extent to which
the climate is changing, if at all. This paper suggests that
agents, at least those participating in weather markets,
have been actively updating their beliefs about the extent
and geography of warming.
Our paper adds to several strands of literature. The ﬁrst
examines the impact of weather ﬂuctuations and climate
change on the corporate sector and ﬁnancial markets. Corporate earnings of several economic sectors are sensitive to
temperature ﬂuctuations (Addoum et al., 2020), and understanding the extent to which ﬁnancial markets are pricing
in climate change risks has implications for ﬁnancial stability (Carney, 2015). Some papers ﬁnd that the stock market
underreacts to the impact of predictable climatic trends on
ﬁrms’ proﬁtability and valuation (Hong et al., 2019), while
others show that real estate market and municipal bonds
do price in sea level rise (Bernstein et al., 2019) and agricultural land markets capitalize climate change expectations (Severen et al., 2018). Weather derivatives can provide a useful hedge against such ﬂuctuations as well as a
direct measure of the market’s expectation of future climate.
Second, studies have emphasized how climate policies
designed to limit emissions can affect ﬁrm proﬁtability.
Anttila-Hughes (2016) ﬁnds that energy company valuations respond to extreme events that may be evidence of
climate change. Meng (2017) shows how the stock market incorporates changes in the likelihood of US carbon
regulation as measured by betting markets. Limiting emissions may render a fossil fuel company’s marginal or most
costly reserves worthless if they can no longer be extracted
(McGlade and Ekins, 2015). Thus, expectations about future
climate policies that are themselves related to observed
cliamte trends are key to the energy sector’s proﬁtability
and will be reﬂected in ﬁnancial markets.
Third, another strand of the literature focuses on how
agents adjust their behavior in response to environmental forecasts (Rosenzweig and Udry, 2014; Neidell, 2009).
Shrader (2020) ﬁnds that ﬁshermen update their beliefs
using El Niño medium-range weather forecasts to make
optimal ﬁshing decisions. Before El Niño forecasts were
available, the cost of weather shocks was much higher
because ﬁsheries could not adapt. On the other hand,
Burke and Emerick (2016) ﬁnd that changes in agricultural
yields in response to observable long-term temperature
trends are not signiﬁcantly different from yield changes in
response to random weather shocks. Some authors have
modeled how market participants learn about and adapt to
changing weather conditions. For example, Kala (2019) examines how Indian farmers dependent on monsoon pre628

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

cipitation update their beliefs. Twitter reactions show that
people become habituated to extreme weather events as
they become more frequent (Moore et al., 2019).
Similarly, public opinion surveys ask respondents to
self-report their beliefs, which also seem driven by recent weather events, especially extremes. Many studies
have shown that people’s beliefs about climate change
are strongly inﬂuenced by recent local weather conditions
(Myers et al., 2013; Deryugina, 2013; Akerlof et al., 2013;
Li et al., 2011; Zaval et al., 2014). Observed periods of cooling can translate into climate skepticism (Kaufmann et al.,
2017). It is also possible that agents hold differing private
and public beliefs about climate change, especially if certain views on climate change are perceived as more expedient.
What is common across much of the literature on climate change expectations is that researchers infer climate
beliefs indirectly by backing them out from observed indirect actions or by relying on stated responses. We add
to this literature by using a different revealed preference
approach to measure beliefs about climate change by analyzing ﬁnancial derivatives whose value directly depends
on expected weather. This allows us to observe the evolution of market expectations on warming by looking at the
price of futures contracts that are linked to future weather
outcomes.

ﬁrms offering bespoke weather-based hedging services to
market participants.
The ﬁnal settlement price of the futures contract is
based on the respective weather station HDDs or CDDs index for the month as reported by MDA Federal Information
Systems, Inc. Each degree day in a contract has a payout
multiplier of $20. For example, if a customer buys one July
CDDs contract for 300 CDDs, the cost would be $6,000. If
the realized cumulative CDDs for the month of July settled
at 330 degree days, the clearance value would be $6,600,
and the trader would reap a proﬁt of $600 ($20 times the
increase of 30 degree days). Trading volume generally increases in the two weeks prior to the start of a contract
month, with lower trade volume more than two weeks before the start of the contract month.
The weather contracts are based on cumulative HDDs
and CDDs in a given month. These are indexed to 65◦ F
(18 ◦ C), the temperature considered the most comfortable
for humans, on average, and a common standard for utility
companies because cooling and heating systems tend to be
turned on above and below that level, respectively. For example, a mean daily temperature of 85◦ F would count as
20 CDDs. These daily degree days are then summed over
the course of the contract month.
CDDs measure by how much daily average temperatures Tad at airport a on day d exceed 65◦ F and thus require cooling, hence the name cooling degree days. The exact formula to derive CDDam for month m is obtained by
summing over all days d (m ) of the month:

2. Data
We ﬁrst describe the ﬁnancial data before discussing
the weather and climate data.

CDDam =



max{Tad − 65, 0}.

(1)

d (m )

2.1. Financial data

Likewise, HDDs measure by how much and for how long
temperature fall below 65◦ F and thus require heating. The
exact formula to derive HDDam is

Weather futures contracts are traded on the CME. The
products were ﬁrst launched in the fall of 2001 and became fully operational for the ﬁrst full year in 2002.
Contracts are available for eight geographically distributed
cities across the US over our sample period 2001–2020.
Each city is linked to a speciﬁc weather station in the city
at one of the airports. These are Atlanta (ATL), Chicago
O’Hare (ORD), Cincinnati/Northern Kentucky (CVG), DallasFort Worth (DFW), Las Vegas (LAS), Minneapolis-Saint Paul
(MSP), New York LaGuardia (LGA), and Sacramento (SAC).
The location across the US is displayed in Online Appendix
Fig. A1. In the past more cities had weather markets, but
trading in several cities was halted due to a lack of liquidity, while at the same time new cities like Portland and
Tokyo were launched as recently as 2019. Therefore, we focus on the eight US cities for which contracts were consistently available through spring 2020.
The main participants in the weather market are insurance companies and ﬁrms seeking to offset weather risk.
For example, an energy company may sell an HDDs contract to mitigate the risk of lower demand for heating oil
due to a mild winter. Likewise, a citrus company may purchase an HDDs contract to mitigate the risk of a winter
freeze. The other market participants are speculators who
take contract positions based on their expectations of future weather. More generally, volumes in this market decreased in recent years due to the entry of reinsurance

HDDam =



max{65 − Tad , 0}.

(2)

d (m )

For our baseline analyses, we use end-of-day daily futures prices obtained from Bloomberg terminals. Prices are
carried forward in the absence of market activity. For example, if there is a recorded trade on June 17 at a price
of 300 CDDs for the July contract, followed by no trade
on June 18, the Bloomberg data will show a price of 300
again. Unfortunately, the volume data only include contracts traded via the exchange and not private over-thecounter block trades (Dorﬂeitner and Wimmer, 2010),2 and
it is missing for most days. Some data cleaning was necessary because of “sticky ﬁngers,” for example, sudden price
jumps by a factor of 10. The exact adjustments are listed
in Online Appendix Section A1.
The raw daily data we downloaded from the Bloomberg
terminals are displayed in Fig. 1 for the two airports with
the highest volume in CDDs: LGA and DFW. We pick two
2
Due to the illiquidity of the weather market, we cannot guarantee
that contracts were actually traded on days where the settlement price
provided by CME does not change. To ensure that only traded prices were
considered, we sometimes exclude time periods where the settlement
price never changes, but the results are robust to the inclusion/exclusion
of these days.

629

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Fig. 1. Futures prices around maturity The graphs display the time series of futures prices around maturity. Day 0 is the end of the month on which the
weather derivative is based; for example, day 0 for a June contract is June 30. The top row is for New York LaGuarida airport (LGA), and the bottom row for
Dallas-Fort Worth (DFW). The left column shows CDDs for July, while the right columns show HDDs for December. Years are color coded as shown in the
bottom legend. Price series that are ﬂagged for quality issues are shown as dashed lines instead of solid lines. The gray-shaded area shows the period over
which we average futures prices in our baseline speciﬁcation to derive market expectations, which is four weeks before the start of the month. Contracts
for the remaining airports and months are shown in Online Appendix Fig. A2.

representative months: the left column shows CDDs in July,
while the right column shows HDDs contracts for December. Contracts for the remaining airports and months are
shown in Online Appendix Fig. A2. Each graph displays the
annual prices series for roughly two-and-a-half months.
Day 0 is the last day of the month on which the contract is based. Both the end of the month and the beginning of the month are indicated by vertical dashed black
lines. The temporal extent ranges from 70 days prior to
the end of the contract month (roughly 40 days prior to
start of the contract month) to 10 days past the end of the
contract month. Years are color coded from blue (2001) to
red (2020). Prices generally do not move past the end of
the contract month (day 0) as all information has been revealed. Most price volatility occurs one to two weeks prior
to the start of the contract month and within the contract
month. There are limited price changes more than two
weeks before the start of the contract month, as limited
information on weather shocks is revealed that the market could incorporate that far out. These ﬂat prices depict
market expectations of the climate before annual weather
shocks are realized.
The main ﬁnding of our paper is clearly visible in the
raw data: looking at futures prices a month before the start
of the contract month (i.e., the left side of each graph), we
see how prices for CDD contracts in the left column are

generally drifting upward over the years (color coded from
blue to red), indicating an upward shift in the required
amount of cooling as it gets hotter. By the same token,
the right column shows prices for HDD contracts drifting
downward over the years, indicating a downward shift in
the expected amount of heating required.
While we do not have reliable volume data for the
Bloomberg terminal time series, Online Appendix Fig. A3
displays the fraction of days there has been a price change
for the two-months period ranging from one month prior
to the contract month to the contract month itself. It
shows how the number of day-to-day price changes increase from 2001 to 2010, a likely indication that trading
volume is picking up, before declining again until 2020.
The decrease in volume is the reason that some of the
original contract cities are no longer offered.
We contacted the CME and obtained volume data for
the subset of the contracts shown in Online Appendix
Fig. A4. Note the reduction in the number of lines representing contracts relative to Fig. 1, our baseline data set
from Bloomberg. We display volume data for this subset
in Online Appendix Table A1. Panel A shows volume by
year. It is increasing from the start of weather derivatives
in 2002 to 2008, when sales for winter and summer contracts combined topped US$ 2 billion per year. Volume declines between 2008 and 2016, before another uptick in ac-

630

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

tivity since 2017. Panel B aggregates the volume data by
airport. Volume is highest in both CDDs and HDDs for LGA
with a combined trading value of US$3.9 billion. The second largest value for CDDs is for DFW, and for HDDs at
ORD. The smallest value is for Sacramento at US$ 0.2 billion. The combined traded value over all airports and years
for this subset of the data (and hence a lower bound) exceeds US$10 billion, a large enough amount to ensure that
the market should eﬃciently incorporate weather information.

any given point (i.e., weather station) if there is spatial heterogeneity. For example, a city’s airport located close to a
mountain might have a different temperature than that of
the surrounding area when averaged over the entire grid.
We observe strong seasonality: more CDDs in the summer, and more HDDs in the winter. As expected, northerly
cities (Chicago, Minneapolis, New York) have relatively
more HDDs and less CDDs, while southerly cities (Atlanta,
Dallas, Las Vegas) have less HDDs and more CDDs. Across
the eight cities, there are very few occurrences of HDDs in
the summer months and CDDs in winter months, which is
why HDDs futures contracts are not traded in summer and
CDDs contracts are not traded in winter.
Online Appendix Fig. A6 plots the price of each weather
derivative at the end of the contract month against the realized weather at the underlying weather station. The output closely follows the 45-degree line, demonstrating that
the market is active enough to ensure weather outcomes
are fully priced in by contract close and that there are no
arbitrage opportunities.

2.2. Weather data
We pair the futures data with weather data: both
weather station observations at the location associated
with each contract as well as gridded climate model projections.
For station data, we obtained the ID of the airport
weather station underlying each contract and downloaded
daily minimum and maximum temperatures from the
National Oceanic and Atmospheric Administration’s FTP
server. We then computed the daily mean by averaging the
minimum and maximum temperature before calculating
the degree days for the 65◦ F bound as given in Eqs. (1) and
(2) above.
Climate projections were taken from the Coupled Model
Comparison Project (CMIP) repository, which asks various
modeling groups to simulate changing temperatures under
comparable assumptions. We rely on the 5th round CMIP5
archive where these groups predicted climate trends from
2006 onwards. We obtain daily values from NASA NEXGDDP, a data set of 21 models that were spatially downscaled to a common 0.5◦ grid and select the grid cell in
which the weather station is located. NASA NEX-GDDP has
data for two scenarios. Representative Concentration Pathway (RCP) 4.5 assumes an additional energy ﬂux of 4.5 W
per meter square. This is a moderate warming scenario in
which greenhouse gas emissions are reduced and radiative
forcing stabilizes such that the global mean temperature
increases by 1.8 ◦ C (3.2◦ F) by 2100. Note there is large spatial heterogeneity, and warming in the US is usually projected to be higher than the global average by a factor of
roughly two. RCP8.5, on the other hand, simulates major
warming where emissions continue to rise such that there
will be additional radiative forcing of 8.5 W per square
meter resulting in a global mean temperature increase of
3.7 ◦ C by 2100. In the short term of our study period
(2001–2020), however, both models give similar projections. The models are predicted to diverge further toward
the end of the century as carbon emissions accumulate
over time.
Online Appendix Fig. A5 shows box plots for the number of CDDs and HDDs by month for the eight cities
with weather futures contracts. The red line displays the
weather station data, and the blue line shows the climate
model data. Both use data from 1950 to 2005, which was
the historical baseline period in the CMIP5 archive. There
is close alignment in the mean values as well variance
around the means in both data sets. Recall that the climate
models predict average temperature over the entire grid,
and hence might differ from the observed temperature at

3. Empirical analysis
We start by analyzing the timing of when futures
prices capitalize weather shocks in Section 3.1. Forecasting and prediction skill of weather (short term) and
climate (medium to long term) are closely connected
(Auffhammer et al., 2013). Climate models build on a foundation of short-term weather dynamics, and the same underlying physical laws apply to the predictions of both
weather and climate models. If market participants are accurately updating their longer-term beliefs based on climate warming trends, it would be expected that they
also accurately update their short-term beliefs based on
weather forecasts. The long-term trends are examined in
Section 3.2.
3.1. Capitalization of short-term weather shocks
Weather forecasts are widespread and freely available.
There has been a sustained improvement in weather forecasting across all prediction ranges over recent decades.
Bauer et al. (2015) present forecasting skill over time for
weather anomalies, deﬁned as deviations from the average
climate; for example, it is 10◦ F hotter today than what it is
normally this time of the year. A score of one indicates that
the forecasting model explains 100% of the year-to-year
anomaly, while a score of zero implies it cannot explain
anything more than what is expected from the average
conditions for the season.3 A 3-day forecast has improved
from a skill of 80% in 1981 to 98% in 2014. On the other
hand, a 10-day forecast (not offered in 1981) increased
from 30% in 1995 to 45% in 2014. Thus we would expect an
inverted U-shape in terms of the impact of weather shocks
on futures prices since long-term forecasts beyond 10 days
3
The score is deﬁned as 1 minus the ratio of the root mean squared error in the full weather forecast model relative to the root mean squared
error of a baseline model that just predicts the average climatology. The
authors state that “Values greater than 60% indicate useful forecasts,
while those greater than 80% represent a high degree of accuracy.”

631

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

have quickly diminishing value and since very short-term
forecasts should have already been incorporated into prices
given their certainty, aligning with Dorﬂeitner and Wimmer (2010) who ﬁnd that weather forecasts only inﬂuence
futures prices up to 11 days into the future. After this
point, using the average outcome as prediction is just as
good. As such, anticipated changes in weather around one
week out should have the largest impact on current prices
in an eﬃcient market.
To test this, we estimate when weather shocks capitalize into futures prices for the eight airports in our sample. In a ﬁrst step, we remove the seasonality to obtain
weather shocks (anomalies), that is, deviations from the
average value that a rational market participant should expect. Speciﬁcally, we regress daily average temperature Tad
at airport a on day d on a constant αa as well as ﬂexible spline that is a function f of the day of the year.4
We also include a linear time trend γa in the year y(d ) as
the weather might be warming over time. The regression
equation is

Tad = αa + βa f (d ) + γa y(d ) + ad .

One particularity about this regression is that while temperature data is available every day, prices are only available on trading days. As a result, the coeﬃcient β1 is for
the sum of all weather shocks after the previous close and
today’s weather. All other βτ use the weather on a single day, which is τ − 1 days past the current close for
leads (τ > 0) and τ days before the previous close for lags
(τ < 0 ).7 The coeﬃcient β0 is normalized to be zero.
In line with the discussion on forecasting skill, future
weather shocks should be capitalized into prices when
>
weather forecasts can predict them, so we expect β
τ
0 for the next two weeks τ ∈ [1, 14]. After that point,
weather forecasts become unreliable and not better than
the average climate (Campbell and Diebold, 2005). Past
weather is already known to market participants and
 should be zero for τ < 0.
hence the β
τ
The left panel of Fig. 2 shows individual coeﬃcient es with the expected hump-shaped pattern. The
timates β
τ
black line shows the point estimates with the 95% conﬁdence band added in gray. As expected, past weather
shocks have no effect on futures prices, while coeﬃcients
for the next two weeks are generally positive as weather
shocks get anticipated by the market and priced in prior
to realization. Beyond day τ = 14, the coeﬃcients become
insigniﬁcant again as weather forecasts beyond this time
period are generally not better than the average climatology for the location. The right panel of Fig. 2 makes this
point more visible by plotting the cumulative sum of coτ 
eﬃcients relative to τ = 0; that is
k=1 βk for τ > 0 and
−1 
β
for
τ
<
0
.
The
cumulative
sum
of coeﬃcients for
k=τ k
negative τ show no trend and the 95% conﬁdence band includes zero. On the contrary, the line increases from 0 to
1 over the next two weeks as 100% of weather shocks get
capitalized into the futures price. The curve ﬂattens around
14 days into the future as weather forecasts become unreliable.
Online Appendix Fig. A8 splits the regression into HDDs
and CDDs and ﬁnds very similar relations. The one exception is that the coeﬃcient estimate β−1 is positive for
CDDs, which measure required cooling on the previous
day. This is not surprising as the daily maximum, which
is crucial for the amount of required cooling, is generally
observed in the late afternoon after the market closes and
hence would not get priced in until the next day.
One can invert the estimated relation to obtain how
futures prices predict future weather. We can also run
the opposite regression for illustrative purposes: do price
changes in the futures market predict future weather
shocks. In other words, are price changes a reliable
weather forecast? We run the following inverse regression
problem:

(3)

 f (d ) is shown
The estimated seasonality for each airport β
a

in Online Appendix Fig. A7. Years are color coded to show
the linear trend over time. The annual increase has not
been uniform; for example, Las Vegas warmed faster than
Sacramento as there is a large distance between the red
line (2020) and the blue line (2001). The weather shock
on day d is simply the observed number of degree days
D(Tad ) minus the degree days that would be expected at
the predicted average
climate according to the seasonality
5
regression D T
ad .
In a second step, we then regress the change in futures
prices  pcd for contract c on day d, that is, the difference
between the closing price to that of the previous close,
on lags and leads of daily degree day shocks 
Dc[d+τ ] =





D(Tc[d+τ ] ) − D(T
c[d+τ ] ) for days that fall within the con-

tract month.6

 pcd = αc +

21


τ =−7



βτ D(Tc[d+τ ] ) − D(T
c[d+τ ] ) + cd .

(4)

4
To address leap years, we normalize the start of the year on January
1st to equal zero and the end of the year on December 31st to equal
one. The ﬁve knots of the restricted cubic spline are at 0.05, 0.27, 0.50,
0.72, and 0.95. This will give us four variables for the phase of the year
f (d ). We force the seasonality on December 31st to equal January 1st to
guarantee continuity by running a constraint regression.
5
While degree days are a nonlinear transformation when temperatures
cross the truncation point at 65◦ F, the truncation is rarely observed; that
is average daily temperatures are generally above 65◦ F in the summer and
below 65◦ F in the winter. See Online Appendix Fig. A5 that shows there
are very few HDDs in the summer and CDDs in the winter. Expected degree days are close to degree days at the expected temperature. We obtain similar results whether we ﬁt the seasonality separately for HDDs
and CDDs or jointly for average temperature. We focus on the latter to
estimate one unique seasonality rather than two separate regressions for
summer and winter.
6
A contract c speciﬁes how many degree days will be observed at airport a in month m of year y, for example, CDDs in June 2015 at LaGuardia
airport. For a June contract, the weather shocks for days d + τ that are
outside the month of June are set to zero as the price of a June contract
is solely based on weather in June.

τ1 


D(Tc[d+τ ] ) − D(T
c[d+τ ] ) = αc + β  pcd + cd .

(5)

τ =τ0

7
For example, if day d is a Monday, β1 includes the sum of the degree day shocks for Saturday, Sunday, and Monday; β2 is the degree days
shock on Tuesday; β3 is the degree day shock on Wednesday, etc. On the
other hand, β−1 is the degree day shock on the previous Friday.

632

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Fig. 2. Capitalization of weather shocks This ﬁgure displays the results from a distributed lag model. Daily futures price changes  pcd for contract c on
Dc[d+τ ] , that is, the difference compared to the average climate on day d + τ . The regression
day d are regressed on 21 leads and 7 lags of weather shocks 

 for the weather shock on
D
equation is  p = α + 21 β 
+  and uses 49,019 observations. The left graph shows the estimated coeﬃcient β
cd

c

τ =−7

τ

c[d+τ ]

τ

cd

a particular lead/lag τ . Negative values of τ on the horizontal axis indicate weather occurring on an earlier day (in the past), while positive values depict
τ 
weather at a future date. The right graph shows
k=1 βk , the cumulative sum of coeﬃcients from day 0 onwards for positive values of the horizontal
−1 
axis and k=τ βk , the cumulative sum of coeﬃcients before day 0 for negative values of the horizontal axis. The regression pools CDD contracts in June–
September and HDD contracts for November–March. The estimated coeﬃcients for leads τ > 1 and lags τ ≤ −1 are on the weather shock for one day, but
the coeﬃcient shown for τ = 1 is for the sum of shocks from today to the previous close given that futures are not traded every day.

The regression results are shown in Online Appendix Table A2. Each entry is from a single regression of the sum
of future weather shocks τ0 − τ1 days into the future on
today’s price change in the weather derivative. Different
rows vary the time period τ0 − τ1 . The ﬁrst column pools
all airports, and the remaining eight columns run the regression by airport. We ﬁnd that price changes predict
weather shocks over the next two weeks, especially days
4–11, the sweet spot of weather forecasts, but cannot predict weather shocks more than two weeks in advance.8
The coeﬃcient on weather shocks three weeks into the future (15–21 days) is not signiﬁcant.

Balancing these two tradeoffs, our baseline model uses
average futures prices pamy of contract c for airport a
in month m of year y. The average price is taken the
fourth week (28-22 days) prior to the start of a contract
month, for example, the average price between June 3,
and June 9, 2015 for a July 2015 CDDs contract in Atlanta.
This ensures that prices reﬂect future expectations and not
contemporaneous weather as conﬁrmed in the previous
section.
3.2.1. Linear time trends
In the baseline we pool four summer months (June–
September) in the CDDs regression and ﬁve winter months
(November–March) in the HDDs regression. We ﬁt a simple
linear trend in the year y after including airport-by-month
ﬁxed effects αam , for example, a ﬁxed effect for June contracts in Atlanta. We cluster the error terms for a particular
month m as they might be subject to the same common
weather shock.

3.2. Capitalization of long-term weather trends
We now turn to our main analysis of market expectations of climate change. With weather futures, we must
be careful to separate price changes driven by short-term
weather forecasts and those reﬂecting longer-term market
beliefs on warming. Some shocks are partially forecastable
over the course of months based on oceanic-atmospheric
phenomena like ENSO or the North Atlantic Oscillation
(NAO). Ideally, we would use futures prices quoted well before the contract’s delivery month. However, for the same
reason that weather is challenging to forecast far in advance, trading does not pick up until close to the contract
delivery month, and early dated prices may not be representative of the market’s true expectation given the illiquidity.

pamy = αam + β y + amy .

(6)

Table 1 shows the predicted annual change β in column
(1a). Panel A shows that, on average, prices increased by
$2.4 per year for each of the four summer months, June to
September, or $10 per year for the combined four-month
period. This annual increase is statistically signiﬁcant at
the 1% level. Since our data set spans 20 years, the price
for a CDD contract increased by roughly $50 since 2001
for each of the monthly summer contracts. Recall that the
payout of the weather derivatives has a multiple of 20, so a
price increase of $50 implies a change in payout by $1,0 0 0
over our sample period. Panel B shows that the price for
a HDD contract declined, on average, by $1 per year, or $5
for the ﬁve-month span from November to March. It is signiﬁcant at the 5% level.
Columns (b)-(d) replicate an equivalent analysis using the weather station and climate model data. The dependent variable is no longer the futures price pamy but

8
The regression should be considered with caution as the reverse
regression problem can lead to biased coeﬃcients. In the climate literature, the width of tree rings is often taken as a temperature
proxy for past temperatures before weather stations were available. As
Auffhammer et al. (2015) point out, weather inﬂuences tree rings. Running the inverse regression where temperature is regressed on tree rings
will lead to biased coeﬃcients and predictions with artiﬁcially low variance.

633

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Table 1
Linear time trends in degree days.

Trend
Observations

Trend
Observations

Trend
Observations
Data
Years

(1a)

(1b)

(1c)

2.432∗∗∗
(0.160)

2.998∗∗∗
(0.887)

2.286∗∗∗
(0.169)

522

522

522

1.000∗∗
(0.415)

2.081
(1.723)

1.662∗∗∗
(0.354)

676

676

1.719∗∗∗
(0.384)

1.856
(1.731)

(1d)

(2a)

Panel A: CDDs June–September
2.774∗∗∗
2.148∗∗∗
(0.174)
(0.330)
522

222

Panel B: HDDs November–March
1.854∗∗∗
1.175∗∗
(0.370)
(0.573)

676

676

322

(2b)

(2c)

(2d)

2.676∗∗∗
(0.772)

2.167∗∗∗
(0.173)

2.432∗∗∗
(0.160)

576

576

522

1.677
(1.524)

1.734∗∗∗
(0.314)

1.000∗∗
(0.415)

760

760

676

1.643∗∗∗
(0.329)

1.719∗∗∗
(0.384)

Panel C: HDDs November–March (excluding February in Northeast)
1.527∗∗∗
1.710∗∗∗
2.224∗∗∗
1.610
(0.362)
(0.336)
(0.478)
(1.529)

604

604

604

604

281

684

684

604

Futures
Common

Station
Common

RCP4.5
Common

RCP8.5
Common

Futures
Traded

Station
All

RCP4.5
All

RCP8.5
All

This table reports the estimated annual increase/decrease in degree days β . Each entry is from a separate regression where degree days Damy at airport a
for month m in year y are regressed on airport-by-month ﬁxed effects as well as a linear time trend: Damy = αam + β y + amy . Panel A regresses CDDs for
the summer months June–September, while Panels B and C use HDDs for November–March. Panel C excludes February for the four northeastern airports
in Online Appendix Fig. A1. The data set ranges from winter 20 01/20 02 through winter 2019/2020. Columns (a) uses the average futures price pamy four
weeks before the start of each contract month, for example, the average price between May 4, and May 10, for a June contract. Columns (b) uses observed
station-level data for the month, while columns (c) and (d) use climate model projections in the NASA NEX-GDDP database under the RCP4.5 and RCP8.5
scenarios for the month. Columns (1a)-(1d) estimate the trends for a consistent set of observations where futures data are available. Columns (2a)-(2d)
conduct sensitivity checks to the included years. Columns (2a) exclude contracts where the price did not change during the fourth week preceding the
contract month. Columns (2b)-(2d) include all years even if futures data are not available. Stars indicate signiﬁcance levels: ∗ 10%, ∗∗ 5%, ∗∗∗ 1%.

the number of degree days at the weather station or climate grid. Columns (1b)-(1d) hold the set of observations constant and only include months with available futures price data. Column (1b) uses the observed degree
days for the contract month from the underlying station
data as the dependent variable. The observed trends (annual changes) are larger in magnitude with an increase of
three CDDs per year during the summer and a decrease
of two HDDs during the winter. The standard errors are
much larger given the greater year-to-year swings stemming from random weather ﬂuctuations. As a result, trends
in observed weather are not signiﬁcantly different from
those anticipated by the futures market as shown in column (1a). The smaller standard errors for futures prices
relative to the station-level data also suggest that we are
correctly measuring longer-term market expectations and
not just annual weather realizations, which are much noisier. Columns (1c) and (1d) show average trends per month
in the NASA NEX-GDDP data set averaged across the 21 climate models for the RCP4.5 and RCP8.5 scenarios, respectively.
While columns (1a)-(1d) intentionally keep the set of
city-year observations constant, columns (2a)-(2d) replicate the analysis with different subsets of the data. First,
to address concerns about market illiquidity, column (2a)
excludes observations where there was no price change
in the week over which prices are averaged, that is, the
fourth week prior to the start of the contract month in
our baseline speciﬁcation. This exclusion reduces the sample size by roughly half but results in point estimates of
similar magnitude to those in column (1a). The time trends
are statistically different from zero and not statistically different than the estimates in column (1a). The reduction in

observations in column (2a) can be explained by the fact
that we are taking average prices over the fourth week
prior to the start of the contract month, a period when
limited information about the eventual weather outcome
is available beyond the climate normals. We hence do not
expect many price changes, which happen when new information gets incorporated. Nevertheless, it is reassuring
that the time trends are similar whether there is a price
change (and hence update) or not. Second, to address concerns about the endogeneity of this market, for example,
if contracts are traded more in particularly cold or hot
years as ﬁrms realize they need a hedge, columns (2b)(2d) use all available months with weather station and climate model data (even if no futures price data existed) and
again ﬁnd very similar annual changes to those in columns
(1b)-(1d).
So far we have pooled all months of a season as
well as each airport into a single regression. Online Appendix Tables A3 and Table A4 relax this assumption to
examine heterogeneity by geography and month. Each table presents the pooled results from Panels A and B of
Table 1 in the top row of the corresponding panel for reference. Online Appendix Table A3 allows time trends to
differ by airport while still pooling all summer or winter
months, and Online Appendix Table A4 allows time trends
to differ by month while still pooling all airports. We observe some differences by airport; for example, in column
(1a) the futures market predicts warming in Las Vegas
above the national average in both winter and summer,
and below-average warming in Chicago and Sacramento
in the summer, all at the 1% signiﬁcance level. All significant time trends have the same sign as the national analysis, that is, more CDDs in the summer and fewer HDDs
634

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Table 2
Sensitivity of linear trend to when expectations are taken.

Trend
Observations

Trend
Observations

(1)

(2)

2.451∗∗∗
(0.147)

2.428∗∗∗
(0.142)

520

522

-0.905∗∗
(0.408)

-0.900∗∗
(0.405)

672

676

(3)

(4)

Panel A: CDDs June–September
2.432∗∗∗
2.385∗∗∗
(0.160)
(0.189)
522

522

Panel B: HDDs November–March
-1.000∗∗
-1.224∗∗∗
(0.415)
(0.431)
676

676

Panel C: HDDs November–March (exl. Feb in NE)
-1.719∗∗∗
-1.908∗∗∗
(0.384)
(0.414)

(5)

(6)

2.431∗∗∗
(0.239)

2.448∗∗∗
(0.314)

522

522

-1.356∗∗∗
(0.482)

-1.628∗∗
(0.697)

676

676

-2.077∗∗∗
(0.465)

-2.202∗∗∗
(0.727)

-1.656∗∗∗
(0.371)

-1.642∗∗∗
(0.363)

Observations

600

604

604

604

604

604

Airport FE
Weeks prior

Yes
6

Yes
5

Yes
4

Yes
3

Yes
2

Yes
1

Trend

This table shows a sensitivity analysis of column (1a) of Table 1, now column (3), to the time window over which futures prices are averaged to evaluate
expectations. The last row displays how many weeks prior to the start of the contract month the futures prices are averaged over, ranging from one to six
weeks. Stars indicate signiﬁcance levels: ∗ 10%, ∗∗ 5%, ∗∗∗ 1%.

in the winter, although the winter time trends sometimes
become insigniﬁcant, especially in the northeastern subset
of airports (CVG, LGA, MSP, ORD).9 In column (1b), none of
the time trends in weather station data differ signiﬁcantly
by airport, although they are estimated with more noise
due to the large year-to-year variability. In columns (1c)(1d), the climate models show below-average warming in
Sacramento in the RCP4.5 data. In summary, while there
are small differences, there does not seem to be a systematic signiﬁcant difference by airport.
The story is different when examining heterogeneity
by month in Online Appendix Table A4. Futures prices
show a signiﬁcant positive annual increase for February
HDDs, suggesting an expectation of colder temperatures.
It is highly signiﬁcant at the 1% level. This ﬁnding is primarily driven by regional heterogeneity. Online Appendix
Fig. A10 shows time trends per month after separating
the eight airports into a northeastern quadrant (CVG, LGA,
MSP, ORD) and the remaining four (ATL, DFW, LAS, SAC)
in the south and southwest. The February cooling trend
(positive increase in HDDs) is only observed for the northeastern quadrant in the futures data. Since we are splitting
the sample further, the estimated time trends become less
precisely estimated, but February cooling is neither supported by recent weather observations nor climate runs in
the CMIP5 archive. All other winter months either show
a signiﬁcant negative time trend or an insigniﬁcant time
trend in HDDs.
The futures market may be incorporating recent information about a shift of the polar vortex that was not available at the time of CMIP5. Recent studies suggest that
melting ice sheets destabilize the jet stream, leading to
an increased frequency of stable weather patterns bringing
cold arctic air to Europe and North America (Francis and

Vavrus, 2015). (Zhang et al., 2016, p.1094) conclude that
the “Arctic polar vortex shifted persistently towards the
Eurasian continent and away from North America in February over the past three decades. [... ] Our analysis reveals
that the vortex shift induces cooling over some parts of the
Eurasian continent and North America which partly offsets
the tropospheric climate warming there in the past three
decades.” Kim et al. (2014, p.1) note that “the mechanism
that links sea-ice loss to cold winters remains a subject of
debate,” so it remains an active topic of research.
One crucial paper for our analysis is Charlton and
Polvani (2007), who more generally examine a phenomenon called stratospheric sudden warming (SSW) and
its relation to the troposphere, speciﬁcally the polar vortex. The authors note that “given the prominent role of
SSW events, it is somewhat surprising that relatively few
attempts have been made to establish a comprehensive climatology of SSWs. [p. 450]” The authors proceed to do so
in two accompanying articles in the Journal of Climate in
2007 and operationalize how SSW events in January and
February in the stratosphere can inﬂuence weather in the
troposphere.10 A fully rational market would incorporate
this new ﬁnding, an issue we return to in the next section
where we present nonlinear trends and ﬁnd an uptick in
the 20 07–20 08 winter immediately following publication.
Before we do so, Panel C row of Table 1 replicates the
analysis for HDDs from Panel B after excluding February

10
The authors write: “A useful analogy might be drawn at this point
with the atmosphere-ocean system: in the same way as understanding
and successfully modeling the El Niño-Southern Oscillation phenomenon
is of primary importance for the atmosphere-ocean system, understanding and successfully modeling stratospheric sudden warming events is
of primary importance for the stratosphere-troposphere system. [p.450]”
ENSO similarly allows a weather forecast with a lead time of more than
four weeks; that is the futures data might be picking up relevant information of how a year’s weather is shifting. Online Appendix Section A2
ﬁnds that oceanic indices like El Niño are not a major factor of the observed warming trend.

9
The winter time trend for Sacramento is also insigniﬁcant, although it
is less traded than other contracts and the summer time trend was also
closer to zero.

635

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Fig. 3. Nonlinear time trends in futures prices and weather This ﬁgure estimates nonlinear time trends using restricted cubic splines in time (knots at
20 03, 20 08, 2013, and 2018) on the residuals, which are obtained by subtracting airport-by-month ﬁxed effects βam among the eight airports and four
summer months (June–September) in the left graph or eight airports and ﬁve winter months (November–March) in the right graph, excluding February for
the four northeastern airports. The green line uses futures prices four weeks before the start of the contract month. The red line shows the results for the
observed weather station data. The blue lines use climate model output from NASA NEX-GDDP. In each case we subtract the average for the airport and
month (i.e., airport-by-month ﬁxed effect). The horizontal axis reports the year a season ends, winter 20 01/20 02 is recorded as 2002. The 95% conﬁdence
bands are added as shaded areas. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

contracts for the four northeastern airports. While the exclusion has very limited effect on the estimated annual decrease in monthly HDDs for the regression using weather
station data or climate model outputs in columns (b)-(d),
it changes the coeﬃcient on the annual decrease in futures
prices in column (a), making it much more closely aligned
with the annual changes in observed weather and climate
model output.
We present a ﬁnal sensitivity check of the observed futures price trends to the window over which the prices are
averaged in Table 2. Our baseline uses prices that are averaged over the fourth week prior to the start of the contract month. Prices at this point are mostly stable as shown
in Fig. 1 because new information on the annual shocks
are not yet available. The six columns in Table 2 replicates the analysis by averaging anywhere between one to
six weeks prior to the start date of the contract month.
The time trend on CDDs in Panel A is completely insensitive to the chosen time window and very stable around
an additional 2.4 CDDs per year for each of the summer
months. The time trend on HDDs in Panel B and Panel
C are very similar whether we average prices six, ﬁve, or
four weeks in advance of the start of the contract month.
There is a slight uptick as we get closer to the start date of
the contract month, suggesting an even larger annual decline, although the difference is not signiﬁcant given the
larger standard errors. The overall robustness of the relation across the time periods supports the idea that markets expected a consistent increase in the need for cooling
in the summer and a decrease in the need for heating in
the winter.

ble trends.11 The lines in green, red, blue, and cyan correspond to the variables listed in columns (1a)-(1d) of
Table 1 (Panel A for CDDs and Panel C for HDDs), respectively, that is, residuals from the weather futures prices,
weather station outcomes, and climate projections under
RCP4.5 and RCP8.5.
The futures prices and climate model output show a
steady upward trend in CDDs and a downward trend in
HDDs. The trends on the weather station data (red lines)
are less smooth for both cooling and heating, partly because of the noisiness inherent in year-to-year swings in
weather realizations that are larger than predicted average
outcomes in the other data sets. For example, the winter
2017/2018 was especially warm, leading to a sharp drop in
HDDs for that year. There also seems to be a short-term
plateau in the observed warming trend around 2010, but
the long-term effects over the 20-year period are similar
across data sets. For both cooling and heating, the green
lines showing futures price trends closely follow the cyan
and blue lines of the climate model projections and not the
red lines. This suggests that beliefs are not myopically updated based on recently observed weather but are rather
tied to the smooth warming trend projected by climate
models and observed in longer-term station data.
In the previous section we found a statistically signiﬁcant cooling trend in February futures prices for the four
northeastern airports. To show this, we again relax the
linearity assumption in Fig. 4 and plot the residuals of
February prices four weeks before the start of the contract month after removing airport ﬁxed effects. We then
add a trend line using the same restricted cubic splines in

3.2.2. Nonlinear trends
Fig. 3 relaxes the linearity assumption of the time trend
and instead plots a semiparametric regression of the residuals after removing airport-by-month ﬁxed effects αam in
Eq. (6) to account for different average monthly climates
(i.e., June in Atlanta is hotter than June in Minneapolis).
We use restricted cubic splines to allow for more ﬂexi-

11
The spline knots are at 20 03, 20 08, 2013 and 2018. Online Appendix
Fig. A11 presents locally weighted lowess regression of the same residuals. Speciﬁcally, we apply STATA’s lowess command to the annual average of the residuals. We ﬁrst average the monthly residuals per year
since a locally weighted regression with several observations in the same
year would need to arbitrarily pick which of the month to include in the
local average. The point estimates are similar to the spline regression,
which we use going forward because they allow us to construct conﬁdence bands.

636

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Fig. 4. Nonlinear time trend in February futures at northeastern airports This ﬁgure estimates nonlinear time trends using restricted cubic splines in time
(knots at 20 03, 20 08, 2013, and 2018) on the residuals of February contracts among the four airports in the northeastern quadrant in Online Appendix
Fig. A1. Residuals are obtained after removing airport ﬁxed effects and are displayed for the four airports. The solid line uses futures prices four weeks
before the start of the contract month. The 95% conﬁdence band is added as shaded area. (For interpretation of the references to color in this ﬁgure legend,
the reader is referred to the web version of this article.)

To test this, we estimate time trends βam that are airport and month speciﬁc instead of the common trend β
used in Eq. (6):

time as well as the 95% conﬁdence band. We observe an
almost linear uptick in residuals between 2007 and 2012,
which is consistent with the publication of Charlton and
Polvani (2007) a study in the premier climatology journal
that presents a novel comprehensive climatology to predict
the “polar vortex.” While we cannot be sure of when the
market became aware of various ﬁndings in the scientiﬁc
literature, it is striking that starting around 2007, February
becomes the only month where the futures markets predicts a cooling in the short term that eventually diminishes
as anthropogenic warming becomes dominant.

pamy = αam + βam y + amy .

(7)

We run this model with futures price data to obtain βam ,
s , and the cliobserved weather station data to obtain βam
f

4.5 and RCP8.5
mate model output under RCP4.5 to obtain βam

8.5 ).12 In a second step we then regress the esto obtain βam
timated time trend in the futures data on the other trends:
f
s
4. 5
8. 5
βam
= α0 + αs βam
+ α4.5 βam
+ α8.5 βam
+ am .

3.2.3. Comparing spatial and temporal heterogeneity
The previous section has shown that the market incorporated a unique subseasonal cooling dynamic for part
of the US. We extend this type of analysis further by examining whether the observed heterogeneity in the time
trend mostly aligns with climate model output or observed
station-level trends. This allows us to contrast whether futures markets reﬂect knowledge about climate model projections or simply assume the continuation of observed
time trends. While all data sets show similar average time
trends, the spatial and temporal heterogeneity varies.
Intuitively, if traders rely mostly on recent observed
trends, we would expect that airports and/or contract
months that show larger than average warming in the
station-level data between November 2001 and March
2020 would also have larger than average annual changes
in futures prices as well. On the other hand, if market
participants mostly respond to climate model projections,
we would observe the distribution of time trends to more
closely align with what is observed in the climate model
output.

(8)

If market participants are just incorporating the average for
each airport-by-month, we would only expect the constant
α0 to be signiﬁcant, as it picks up the common average. On
the other hand, if futures prices incorporate the observed
heterogeneity in time trends found in the station-level data
or climate model output, we would expect αs , α4.5 , or α8.5
to be signiﬁcant.
It should be noted that it is much harder to predict spatial heterogeneity in warming than it is to predict average
trends because of all the localized feedback loops of the
climate system. The average trend is given by a simple balance of energy calculation. For example, if one increases
the burner under a pot of water, the average temperature
will increase, but it is much harder to predict where this
12
We use all monthly observations from November 2001-March 2020 in
the station and climate model data, even if the futures data is not available. Since the weather station data are more variable (it measures actual
outcomes versus averages among climate models), we include as many
observations as possible in order not to unfairly penalize the station-level
data by making the time trend more variable.

637

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Table 3
Comparing spatial and temporal heterogeneity in trends.
(1a)
Trend at weather station

(1b)

∗∗∗

0.628
(0.155)

0.501∗∗∗
(0.126)

Trend in NEX-GDDP: RCP8.5

-0.037
(0.049)
0.158
(0.192)

Trend in NEX-GDDP: RCP8.5
Observations

0.716∗∗∗
(0.155)

Panel C: Years 2011–2020
-0.046
-0.062
(0.046)
(0.056)
-0.034
(0.186)
0.730∗∗∗
(0.162)

∗∗

Trend in NEX-GDDP: RCP4.5

72

72

Panel A: All years
0.135
0.302∗∗∗
(0.113)
(0.100)
0.432
(0.474)
0.066
(0.392)

0.346
(0.167)

0.175
(0.260)

Trend in NEX-GDDP: RCP8.5

(2a)

Panel B: Years 2006–2020
-0.014
-0.130∗∗
(0.058)
(0.065)
0.098
(0.295)
0.457∗∗∗
(0.166)

-0.056
(0.054)

Trend in NEX-GDDP: RCP4.5

Trend at weather station

(1d)

0.251∗∗
(0.101)

Trend in NEX-GDDP: RCP4.5

Trend at weather station

(1c)

72

72

68

(2b)

(2c)

(2d)

0.666∗∗∗
(0.120)

0.137
(0.105)
0.627
(0.426)
0.080
(0.376)

0.400∗∗
(0.172)

-0.107∗
(0.063)
0.262
(0.323)
0.415∗∗∗
(0.153)

0.733∗∗∗
(0.166)

-0.062
(0.052)
-0.033
(0.188)
0.737∗∗∗
(0.168)

68

68

∗∗∗

0.840
(0.137)

0.422
(0.318)

0.159
(0.197)

68

This table examines spatial and temporal heterogeneity in various data sources. A separate linear time trend βam is ﬁt for each month and airport:
f
s
on the trend in the weather station data βam
as well as the trends in the
Damy = αam + βam y + amy . We then regress the trend in the futures data βam

4.5
8.5
, βam
by NASA NEX-GDDP RCP4.5 and RCP8.5, respectively. Columns (1a)-(1d) include all months (November–March for HDDs
climate model output βam
and June–September for CDDs). Columns (2a)-(2d) exclude February for the four northeastern airports. Panels vary the years over which the time trends
are estimated. Stars indicate signiﬁcance levels: ∗ 10%, ∗∗ 5%, ∗∗∗ 1%.

extra energy will show up and how it will spread across
the volume of water. Similarly, changes in wind patterns
might lead to higher warming in some areas while reducing it in others (Hsiang and Kopp, 2018). February cooling
due to the polar vortex over eastern North America goes
hand-in-hand with higher-than-expected warming in the
Arctic. Cooling in East Coast cities does not refute that the
globe is warming, which it is in total, but rather reﬂects
the uncertainty on where the extra energy manifests as jet
streams shift.
The results are given in Table 3. Columns (a)-(c) include
each estimated time trend in the weather/climate data
one at a time, while columns (d) jointly include all three.
Columns (1a)-(1d) include all 72 airport-month combinations of the 8 airports and 9 months: June–September for
CDDs in the summer and November–March for HDDs in
the winter. Columns (2a)-(2d) exclude February for the
four northeastern airports for a total of 68 observations.
Panel A pools all observations from November 2001–
March 2020 in the estimation of the βam . The coeﬃcient
on the climate model output in columns (b) and (c) is
consistently larger than for the heterogeneity actually observed in the weather station data over the same period. When we include all three in column (d), they are
no longer individually signiﬁcant given the high degree
of multicollinearity, but climate model output under the
RCP4.5 scenario has the largest point estimate.
Panel B and Panel C limit the observations to 2006–
2020 and 2011–2020, respectively, in the calculation of the
trends βam . The reason is twofold: ﬁrst, climate models in
the CMIP 5 archive used 1950–2005 as the baseline to cal-

ibrate their models. By limiting the data to a period past
2005, the model should predict completely out of sample. Note, however, that we are using the actual observed
s , so the
climate trends from the weather station data βam
climate model would simply incorporate some of the information that is in the station-level data. Since it took
climate modeling groups several years to run the models
before they were posted, Panel C further limits the time
window to after 2010. Second, the pace of global warming slowed between 1998–2012 and then picked up again
around 2012.
Both Panel B and C show that the spatial heterogeneity
in trends in the futures data is better aligned with the heterogeneity in the climate model output rather than with
the trend at the underlying weather station. For this subinterval of accelerated warming, the heterogeneity found in
RCP8.5 is a better predictor than RCP4.5. On the one hand,
this is not surprising as the early 20 0 0s mostly relied on
climate projections from the Intergovernmental Panel on
Climate Change (IPCC) fourth assessment report that did
not include RCP8.5. On the other hand, as we have argued
above, the futures market was quick to pick up on scientiﬁc advances related to the polar vortex. Since the IPCC
reports are based on published studies, much of the underlying theory might have also been available to interested
parties in the early 20 0 0s. We lack a credible proxy for
when information is received by the market, so we cannot
directly test when market participants update their view
on which climate model to follow.
It is noteworthy that across all the time periods considered in Panels A-C, the heterogeneity in the futures
638

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

Fig. 5. Predicted change in degree days in climate models This ﬁgure shows nonparametric time trends by airport averaged over the 21 climate models in
the NASA NEX-GDDP database. The y-axis gives the predicted average change in monthly CDDs or HDDs. The top row shows the results for the change in
monthly CDDs in the summer (June–September) and the bottom row for the change in monthly HDDs in the winter (November–March). The left column
uses the predictions under the RCP4.5 scenario, while the right column uses RCP8.5. Speciﬁcally, a nonparametric lowess regression is ﬁt to the annual
average of the monthly residuals after removing airport-by-month ﬁxed effects.

price trends more closely mirror climate models than the
eventual weather realizations. Combined with the uptick in
February futures prices that is not supported by stationlevel observations, we conclude that market participants
are using climate models, or some related source of information, to update their beliefs on future weather rather
than just projecting forward historical trends. Moreover,
as Online Appendix Section A3 shows, previous warming trends in the early part of the 20th century have
plateaued, and simply forecasting that past trends will continue rather than using climate model projections would
be a risky endeavor for investors.
Warming trends are predicted to diverge further out
in the future as shown in Fig. 5, which displays climate
model output through 2100. We again remove airport-bymonth ﬁxed effects and then average the residuals over the
four summer months (June–September) or the ﬁve winter months (November–March). The top row again shows
CDDs, while the bottom row shows HDDs. The left column
shows nonparametric warming paths under the RCP4.5
scenario, while the right column uses RCP8.5. For example,
the reduction in HDDs in Minneapolis under the RCP8.5
scenario (bottom right graph) is almost twice as large as
for Atlanta.

that are consistent with climate model projections. We ﬁnd
the market has been accurately pricing in a warming climate and that this began occurring at least since the early
20 0 0s when the weather futures markets were formed.
The market also seems to price in recent scientiﬁc ﬁndings like the polar vortex that can lead to February cooling
over the eastern US, an effect neither present in the CMIP5
archive nor detectable in recent weather station observations.
Our ﬁndings have direct implications for ﬁrms and ﬁnancial markets. Recent studies have highlighted how the
valuations of companies and entire industries are sensitive to weather ﬂuctuations and climate change risk. Since
eﬃcient and proﬁt-maximizing behavior requires an accurate assessment of predicted warming, weather markets can provide companies with pertinent information
on future weather and climate trends as well as a hedge
against potential lost proﬁt. Relatedly, our ﬁndings may
have relevance to climate adaptation. Adaptation requires
that agents form beliefs about the extent to which the climate is changing. This paper suggests that agents, at least
those participating in weather markets, have been updating their beliefs that summers are getting hotter and winters colder.
There are policy implications of our ﬁndings, especially
since some politicians still question the existence and extent of climate change. The observed annual trend in futures prices shows that the supposedly eﬃcient ﬁnancial
markets agree that the climate is warming. To date, climate models have been very accurate in predicting warming trends observed across the US. While we cannot be

4. Conclusion
To the best of our knowledge, this paper is the ﬁrst to
use a direct measure of climate change expectations as derived from weather-based futures contracts. The evidence
shows that ﬁnancial markets incorporate warming trends
639

W. Schlenker and C.A. Taylor

Journal of Financial Economics 142 (2021) 627–640

sure that the market believes warming to be human induced, per se, anyone doubting climate change can attempt
to proﬁt from that belief by betting against the observed
warming trend. The price of a summer month CDD contract, for example, has increased by roughly $50 over the
20-year sample period. Since the payout of the ﬁnancial
derivative has a multiplier of 20, this implies an additional
$1,0 0 0 in value is on the table per contract. When money
is on the line, it is hard to ﬁnd parties willing to bet
against the scientiﬁc consensus.

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==> JFE05 - Do investors care about carbon risk.txt <==
Journal of Financial Economics 142 (2021) 517–549

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Do investors care about carbon risk? ✩
Patrick Bolton a,b, Marcin Kacperczyk a,b,∗
a
b

Columbia University, Imperial College London, CEPR, and NBER, United States
Imperial College London and CEPR, United Kingdom

a r t i c l e

i n f o

Article history:
Received 21 October 2019
Revised 24 September 2020
Accepted 23 October 2020
Available online 14 May 2021
JEL classiﬁcation:
G12
G23
G30
D62

a b s t r a c t
We study whether carbon emissions affect the cross-section of US stock returns. We ﬁnd
that stocks of ﬁrms with higher total carbon dioxide emissions (and changes in emissions)
earn higher returns, controlling for size, book-to-market, and other return predictors. We
cannot explain this carbon premium through differences in unexpected proﬁtability or
other known risk factors. We also ﬁnd that institutional investors implement exclusionary
screening based on direct emission intensity (the ratio of total emissions to sales) in a few
salient industries. Overall, our results are consistent with an interpretation that investors
are already demanding compensation for their exposure to carbon emission risk.
© 2021 Elsevier B.V. All rights reserved.

Keywords:
Carbon emissions
Climate change
Stock returns
Institutional investors

1. Introduction
Many studies seek to explain the cross-sectional pattern of stock returns based on exposures to aggregate risk
factors such as size and book-to-market ratios, or ﬁrmspeciﬁc risk linked to observable ﬁrm characteristics. One

✩
We thank Jawad Addoum, Franklin Allen, Eric Bouyé, Kent Daniel,
Charles Donovan, Elyse Douglas, Gerry Garvey, Lukasz Pomorski, Ailsa
Roell, Zacharias Sautner, Gireesh Shrimali, Michela Verardo, Jeff Wurgler,
and the referee for helpful suggestions. We also appreciate comments
from seminar participants at Blackrock, EFA Conference, IESE, Newcastle
University, the New Frontiers in Investment Research conference, NHH
Bergen, NYU Law Roundtable on Climate Disclosure, UBS, University of
Cardiff, and University College Dublin. We are grateful to Trucost for giving us access to their corporate carbon emissions data, and to Jingyu
Zhang for very helpful research assistance. This project has received funding from the European Research Council (ERC) under the ERC Advanced
Grant programme (grant agreement No. 885552 Investors and Climate
Change).
∗
Corresponding author.
E-mail addresses: pb2208@columbia.edu (P. Bolton), mkacperc@ic.
ac.uk (M. Kacperczyk).

https://doi.org/10.1016/j.jﬁneco.2021.05.008
0304-405X/© 2021 Elsevier B.V. All rights reserved.

variable that has so far been missing from the analysis is
corporate carbon emissions. This omission may be for historical reasons, as concerns over global warming linked to
carbon dioxide (CO2 ) emissions from human activity have
only recently become salient. But, both the evidence of rising temperatures and the renewed policy efforts to curb
CO2 emissions raise the question of whether carbon emissions represent a material risk for investors that is reﬂected in the cross-section of stock returns and portfolio
holdings.
Two major developments, in particular, suggest that this
may be the case. First, the Paris COP 21 climate agreement of December 2015, with 195 signatories committing
to limit global warming to well below 2 °C above preindustrial levels. Second, the rising engagement of the ﬁnance industry with climate change, largely as a result
of the call to non-governmental actors to join the ﬁght
against climate change at the COP 21. Institutional investors are increasingly tracking the greenhouse gas emissions of listed ﬁrms and forming coalitions such as Climate
Action 100+ to engage with companies to reduce their

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

carbon emissions.1 More and more asset owners are following the lead of the Church of England Pension Fund,
whose stated goal is “to demonstrate transparently that it
has delivered on its commitment to be aligned to the Paris
Agreement.”2
Even if the US has pulled out of the Paris Agreement
under the Trump administration, and even if the commitments of the other remaining signatories are only partially
credible, major curbs in CO2 emissions are likely to be introduced over the next decade. Primarily affected by these
curbs are the companies with operations generating high
CO2 emissions, or with activities linked to companies in
the value chain that have high CO2 emissions. In light of
these developments, one would expect to see the risk with
respect to carbon emissions to be reﬂected in the crosssection of stock returns. Yet, considerable skepticism remains, not least in the US where the Trump administration had worked to upend regulations that limit CO2 emissions. For example, Darren Woods, ExxonMobil’s CEO, recently declared that “Individual companies setting targets
and then selling assets to another company so that their
portfolio has a different carbon intensity has not solved the
problem for the world.” And that ExxonMobil was “taking
steps to solve the problem for society as a whole and not
try and get into a beauty competition.”3
The lack of consensus among institutional investors
around climate change naturally raises the possibility that
carbon risk may not yet be reﬂected in asset prices. To ﬁnd
out, in this paper we systematically explore whether investors demand a carbon risk premium by looking at how
stock returns vary with CO2 emissions across ﬁrms and industries. We undertake a standard cross-sectional analysis,
asking whether carbon emissions affect cross-sectional US
stock returns.
There are several ways in which one might expect CO2
emissions to affect stock returns. First, since CO2 emissions are tied to fossil-fuel energy use, returns are affected
by fossil-fuel energy prices and commodity price risk. Relatedly, ﬁrms with disproportionately high CO2 emissions
may be exposed to carbon pricing risk and other regulatory
interventions to limit emissions. The ﬁrms that are most
reliant on fossil energy are also more exposed to technology risk from lower-cost renewable energy. Forwardlooking investors may seek compensation for holding the
stocks of disproportionately high CO2 emitters and the associated higher carbon risk they expose themselves to, giving rise to a positive relation in the cross-section between
a ﬁrm’s own CO2 emissions and its stock returns. We refer
to this as the carbon risk premium hypothesis.
An interesting question is whether carbon emissions
are perceived to be a systematic risk factor and whether
the carbon risk premium is tied to loadings on this risk

factor. Carbon emissions could be a systematic risk factor if
expected regulatory interventions to curb emissions apply
uniformly to all emissions. For example, if a large federal
carbon tax were to be introduced, this would be a systematic shock affecting all companies with signiﬁcant emissions. Alternatively, most regulatory interventions could be
introduced in a piecemeal way at the state, industry, and
municipal level. Similarly, technological improvements in
the use of renewable energy could be mostly targeted to
particular operations or sectors. In this case, one would not
expect carbon emissions to be a systematic risk factor.
A second hypothesis is that ﬁnancial markets are pricing carbon risk ineﬃciently and the risk associated with
carbon emissions is underpriced. Carbon risk may not be
fully integrated by most investors, who by force or habit
look at future cash-ﬂow projections through local thinking
à la Gennaioli and Shleifer (2010), ignoring unrepresentative information about global warming and its attendant
risks. To be sure, the cash-ﬂow scenarios commonly used
by ﬁnancial analysts do not directly refer to carbon emissions and their possible future repricing. A recent study by
In et al. (2019) on a different sample than ours ﬁnds that a
portfolio that is long stocks of companies with low carbon
emissions and short stocks of companies with high emissions generates positive abnormal returns. We refer to this
hypothesis as the market ineﬃciency, or carbon alpha, hypothesis. An important question we explore is whether ﬁnancial markets underprice carbon risk (after controlling
for other known risk factors, industry, and ﬁrm characteristics) to the point that responsible investors, who care
about carbon emissions and climate change, could be “doing well by doing good.”
A third hypothesis is that the stocks of ﬁrms with high
emissions are like other “sin stocks”; they are shunned by
socially responsible, or ethical, investors to such an extent
that the spurned ﬁrms present higher stock returns. A key
question in this respect is how investors identify the ﬁrms
to be divested from. Do they look at carbon emissions at
the ﬁrm level, or do they pigeonhole ﬁrms into broader
categories such as the industry they operate in? Even socially responsible investors that care about climate change
may use sparse models (à la Gabaix, 2014) and not look
much beyond industry categorizations, such as the energy
and electric utility sectors, which produce a disproportionate share of CO2 emissions. Prominent divestors like the
Rockefeller Brothers Fund, for example, who have pledged
to divest from fossil fuel companies, largely focus on energy companies that extract coal and oil from tar sands.4
We refer to this as the divestment hypothesis.
A pioneer in producing company-level CO2 emissions
data is the Carbon Disclosure Project (CDP).5 It has been
joined by other leading providers of carbon data, including MSCI ESG Research and Trucost, among others.6 While
more and more institutional investors make use of the
data, it is not known how much individual companies’
stock returns are actually affected by the availability of

1

See http://www.climateaction100.org/.
Statement made by Adam Matthews, the fund’s director of ethics and
engagement. The Church of England Pension Fund is co-chairing the IIGCC
initiative.
3
Quoted in Exxon CEO Calls Rivals’ Climate Targets a ‘Beauty Competition’ by Kevin Crowley, Bloomberg News, March 5, 2020, https://
www.bnnbloomberg.ca/exxon- ceo- calls- rivals- climate- targets- a- beautycompetition-1.1400957.
2

4

See https://www.rbf.org/mission- aligned- investing/divestment.
See http://www.cdp.net/en- US/Pages/About- Us.aspx.
6
See https://www.msci.com/climate- change- solutions and https://
www.trucost.com/policy- academic- research.
5

518

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

these more granular CO2 emissions data to ﬁnancial analysts. Our study relies on the Trucost EDX data, which
cover around 10 0 0 listed companies since ﬁscal year 2005,
and over 2900 listed companies in the US since ﬁscal year
2016. We match these data with the FactSet returns and
balance sheet data for all US-listed companies from 2005
to 2017.
Carbon emissions from a company’s operations and
economic activity are typically grouped into three different
categories: direct emissions from production (scope 1), indirect emissions from consumption of purchased electricity, heat, or steam (scope 2), and other indirect emissions
from the production of purchased materials, product use,
waste disposal, outsourced activities, etc. (scope 3). The
scope 3 category in turn is separated into upstream and
downstream indirect emissions. The data on scope 1 and
scope 2 emissions are widely reported. Scope 3 emissions
on the other hand are estimated using an input-output
matrix. Although scope 3 emissions are the most important component of companies’ emissions in a number of
industries (e.g., automobile manufacturing), they have not
been reported by companies until recently.
Our main broad ﬁnding is that carbon emissions signiﬁcantly affect stock returns. For all three categories of
emissions, we ﬁnd a positive and statistically signiﬁcant
effect on ﬁrms’ stock returns. We designate the higher
returns associated with higher emissions as a carbon premium. We estimate how this carbon premium is related
to three different measures of corporate emissions: 1)
the total level of emissions; 2) the year-by-year change
in emissions; and 3) emission intensity, which measures
carbon emissions per unit of sales. A striking result is
that the carbon premium is related to the level of (and
to changes in) emissions, but not to emission intensity.
One reason why the premium is tied to total emissions
is that regulations limiting emissions are more likely to
target activities where the level of emissions is highest.
For example, in its planned climate stress test, the Bank of
England focuses only on large ﬁrms and measures risk in
terms of required reductions in the level of emissions (see
the 2021 biennial exploratory scenario on the ﬁnancial
risks from climate change (Bank of England discussion
paper, 2019)). Similarly, since technological change generally involves a ﬁxed cost, renewable energy is more
likely to displace fossil fuels in ﬁrms where returns to
scale are highest. Another consideration is that since
emission intensity is a ratio, it is likely to be a noisier
metric of carbon risk exposure. Two ﬁrms with identical
emission intensities may vary substantially in their levels
of emissions. Indeed, this is what we ﬁnd: the correlation
coeﬃcient between the level of scope 1 emissions and
emission intensity is 0.6, and signiﬁcantly less for scope 2
and scope 3. Nevertheless, it is somewhat surprising that
we ﬁnd no premium associated with emission intensity
since emission-intensive ﬁrms might well be the ﬁrst to
become unproﬁtable should the carbon price rise. Investors
would then demand a premium for holding these ﬁrms.
Interestingly, there is also a signiﬁcant carbon premium
associated with the year-to-year growth in emissions. As
one would expect, we ﬁnd that the level of emissions is
highly persistent. Hence, emission levels reﬂect a long-run

risk exposure with respect to carbon emissions. Changes
in emissions, in turn, reﬂect short-run effects; how much
worse, or better, carbon risk gets. Of course, changes in
emissions could also indicate changes in earnings, but we
control for this effect by adding the company’s return on
equity, sales growth, and earnings growth, among our independent variables.
The carbon premium is economically signiﬁcant: A onestandard-deviation increase in respectively the level and
change of scope 1 emissions leads to a 15-bps and 26-bps
increase in stock returns, or respectively a 1.8% and 3.1%
annualized increase. In addition, a one-standard-deviation
increase in the level and change of scope 2 emissions leads
to respectively a 24-bps and 18-bps increase in stock returns, or a 2.9% and 2.2% annualized increase. Finally, a
corresponding one-standard-deviation increase in the level
and change of scope 3 emissions increases stock returns
by 33 bps and 31 bps per month, or 4.0% and 3.8% on
an annual basis. Importantly, ﬁrms with higher emissions
generate higher returns, after controlling for size, book-tomarket, momentum, other well-recognized variables that
predict returns, and ﬁrm characteristics, such as the value
of property, plant & equipment (PPE), and investment over
assets.
Other things equal, a carbon premium is the reﬂection
of a lower investor demand for stocks of companies associated with high emissions. In equilibrium, this lower
demand translates into a lower stock price, and possibly
also lower holdings of high-emission stocks by some categories of investors. Following Hong and Kacperczyk (2009),
we explore to what extent companies with high carbon
emissions are treated like “sin stocks” by institutional investors. We ﬁnd that, in aggregate, institutional investors
do hold a signiﬁcantly smaller fraction of companies with
high scope 1 emission intensity, but they are not underweight companies with high levels of emissions. When we
disaggregate by investor categories (mutual funds, insurance companies, banks, pension funds, and hedge funds),
we ﬁnd that insurance companies, pension funds, and mutual funds are underweight scope 1 emission intensity.
The negative ownership effect of moving from high to low
scope 1 emission-intensity ﬁrms is economically large and
accounts for about 15%−20% of the cross-sectional variation in the ownership variable. This ﬁnding is in line with
the rise in the sustainable investment movement and the
popular negative exclusionary screening investment strategy followed by funds with an environmental, social, and
governance (ESG) tilt.7
We ﬁnd that divestment is only based on scope 1 emission intensity. This is true both in aggregate and for each
institutional investor category. Essentially, institutional investors have been applying exclusionary screens (or not)
solely on the basis of scope 1 emission intensity. Even
more remarkable, we ﬁnd that when we exclude the in-

7
See Krueger, Sautner, and Starks (2020). Also, according to the
Global Sustainable Investment Review 2018, negative/exclusionary screening is the largest sustainable investment strategy globally, representing
$19.8 trillion of assets under management. http://www.gsi-alliance.org/
wp-content/uploads/2019/03/GSIR_Review2018.3.28.pdf.

519

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Journal of Financial Economics 142 (2021) 517–549

dustries with the highest CO2 emissions (oil & gas, utilities,
and motor industries), there is no signiﬁcant exclusionary
screening at all by institutional investors. In other words,
the exclusionary screening is done entirely in these salient
industries; in all other industries, there is no signiﬁcant divestment. Overall, these ﬁndings lead us to reject the divestment hypothesis. First, although there is signiﬁcant divestment by institutional investors, it is not directly linked
to an effect on stock returns. Institutional investor portfolios are signiﬁcantly underweight ﬁrms with high scope 1
emission intensity, but stock returns are not affected signiﬁcantly by emission intensity.
Our ﬁnding that stock returns are positively related to
the level (and changes) of carbon emissions is largely consistent with the view that investors are pricing in a carbon
risk premium at the ﬁrm level. This result contradicts the
carbon alpha hypothesis, whereby investors holding a portfolio long stocks of companies with low carbon emissions
and short stocks of companies with high emissions generates positive abnormal returns. Garvey et al. (2018) and
In et al. (2019) suggest that portfolios that sort stocks by
emission intensity (going long stocks with low intensity
and short stocks with high intensity) generate a positive
alpha. In contrast, we ﬁnd that there is no signiﬁcant effect of carbon intensity on stock returns. Our study differs
in two important respects from theirs. First, we cover a different time period and sample of ﬁrms. Second, we control
for industry, ﬁrm characteristics, and known risk factors,
while neither of these studies includes all of these controls. Controlling for industry signiﬁcantly affects the results. Also, in contrast to In et al. (2019), we analyze the
effects of carbon emissions for each scope category separately, thereby avoiding double counting.
Another important ﬁnding is that the carbon premium
has only materialized recently. We show that if we look
back to the 1990s by imputing the 2005 cross-sectional
distribution of total emissions to the 1990s, there is no signiﬁcant carbon premium, consistent with the view that investors at that time likely did not pay as much attention to
carbon emissions. However, if we apply the same analysis
to our sample period, by imputing the 2017 cross-sectional
distribution of emissions back throughout our sample period, we ﬁnd that there is a highly signiﬁcant carbon premium.
To summarize, investors seem to take a somewhat
schizophrenic attitude to carbon emissions. On the one
hand, institutional investors clearly want to take a proactive approach by divesting from industries with high CO2
emissions. On the other hand, this categorical exclusionary screening approach only partially addresses the carbon
risk issue. Indeed, investors price in a carbon emission risk
premium at the ﬁrm level in all industries even though divestment is concentrated in the industries with the highest
CO2 emissions (oil & gas, utilities, and transportation industries). If there is one general lesson that emerges from
our analysis it is that carbon risk cannot just be reduced to
a fossil fuel supply problem. It is also a demand problem.
Once one factors in both the supply and demand aspects,
all companies in all sectors are exposed to various degrees
to carbon emissions risk. A coarse exclusionary approach
focusing only on the energy and utility sectors misses the

full extent of the problem investors face. Accounting for
carbon risk is also required on the demand side, which inevitably involves the careful tracking of emissions at the
ﬁrm level in all sectors.
Our study is related to a rapidly growing literature on
climate change and ﬁnancial markets. An early study by
Matsumura, Prakash, and Vera-Munoz (2014) of S&P 500
ﬁrms between 2006 and 2008 looks at the effects of direct carbon emissions on ﬁrm value, and the effects of
voluntary public disclosure of emissions (through CDP) on
ﬁrm value. They ﬁnd that higher emissions are associated with lower ﬁrm values, but that voluntary disclosure mitigates the negative valuation effect of emissions.
Relatedly, Chava (2014) looks at the effects of environmental concerns, as reﬂected in KLD ratings, on ﬁrms’
cost of capital. He ﬁnds that ﬁrms that derive substantial revenues from the sale of coal or oil, as reﬂected in
a KLD rating, are associated with a higher implied cost
of capital. In an extensive survey of institutional investors,
Krueger et al. (2020) also ﬁnd that institutional investors
believe that carbon emissions represent a material risk.
Among their responses, institutional investors also say that
they do not believe that there is substantial underpricing
of carbon risk. Andersson et al. (2016) propose a carbon
risk hedging strategy for passive investors based on low
carbon indexes.
More recently, Ilhan et al. (2020) ﬁnd that carbon emissions increase downside risk as reﬂected in out-of-themoney put option prices. Hsu et al. (2019) look at the
effects of environmental pollution on the cross-section of
stock returns. They ﬁnd that highly polluting ﬁrms are
more exposed to environmental regulation risk and command higher average returns. Engle et al. (2020) construct an index of climate news through textual analysis of The Wall Street Journal and other media and show
how a dynamic portfolio strategy can be implemented
that hedges risk with respect to climate change news.
Görgen et al. (2019) construct a carbon-risk factor and estimate a carbon beta for ﬁrms. Monasterolo and De Angelis (2019) explore whether investors demand higher risk
premia for carbon-intensive assets following the COP 21
agreement.
Other related studies explore the asset pricing consequences of greater material risks linked to climate events
and global warming. Hong et al. (2019) ﬁnd that the rising drought risk caused by climate change is not eﬃciently
priced by stock markets. Several studies examine climate
change and real estate prices. Baldauf et al. (2020) ﬁnd
little evidence of declining prices as a result of greater
ﬂood risk due to sea level rise. Bakkensen and Barrage
(2017) ﬁnd that climate risk beliefs in coastal areas are
highly heterogeneous and that rising ﬂood risk due to climate change is not fully reﬂected in coastal house prices.
Bernstein et al. (2019) ﬁnd that coastal homes vulnerable
to sea-level rise are priced at a 6.6% discount relative to
similar homes at higher elevations. However, in a related
study, Murﬁn and Spiegel (2020) ﬁnd no evidence that sea
level rise risk is reﬂected in residential real estate prices.
Finally, Giglio et al. (2018) use real estate pricing data to
infer long-run discount rates for valuing investments in climate change abatement.
520

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Journal of Financial Economics 142 (2021) 517–549

products, and end-of-life treatment of sold products.9 According to CDP’s 2016 Climate Change Report, most scope
3 emissions are concentrated in two categories: purchased
goods and services (around 44%) and use of sold products
(around 48%).10 The Greenhouse Gas Protocol provides detailed guidance on how to identify a company’s most important sources of scope 3 emissions and how to calculate
them. For purchased goods and services, this basically involves measuring inputs, or “activity data,” and applying
emission factors to these purchased inputs that convert activity data into emissions data. The upstream scope 3 data
from Trucost that we use is constructed using an inputoutput model that provides the fraction of expenditures
from one sector across all other sectors of the economy.
This model is extended to include sector-level emission
factors, so that an upstream scope 3 emissions estimate
can be determined from each ﬁrm’s expenditures across all
sectors from which it obtains its inputs (see Trucost, 2019).
Downstream scope 3 emissions caused using sold products can also be estimated and are increasingly reported
by companies. Trucost has recently started assembling this
data, but we were not able to include it our study.
Because they are easier to measure, and because disclosure requirements are stricter, data on scope 1 and
scope 2 have been more systematically reported and accurately estimated. As Busch et al. (2018) show, there is very
little variation in the reported scope 1 and 2 emissions
data across the data providers. Correlations in the reported
scope 1 (scope 2) data average 0.99 (0.98), across the ﬁve
providers CDP, Trucost, MSCI, Sustainalytics, and Thomson
Reuters.11 However, when it comes to estimated scope 1
and scope 2 emissions (when reported data are missing),
the correlations drop to 0.79 and 0.63, respectively for the
three providers, Trucost, MSCI, and Sustainalytics, that offer these estimates. Finally, only two data providers, Trucost and ISS ESG, provide estimates of scope 3 emissions.
The Trucost EDX database we use in our main analysis reports all three scopes of carbon emissions in units of tons
of CO2 emitted in a year. We report the summary statistics
of the emissions variables in Panel A of Table 1.
The average ﬁrm in our sample produces 1.97 million
tons of scope 1 emissions, and is tied to 1.72 million tons
of scope 3 emissions. The quantity of scope 2 emissions is
relatively smaller, at 342,0 0 0 tons of CO2 equivalent. Notably, the median number is the largest for scope 3 emissions, as almost all companies in our sample are tied to
a signiﬁcant quantity of such emissions. The scope 1, 2,
and 3 measures are in units of tons of CO2 and normalized using the natural log scale. We also report annual
growth rates in each emission measure. To mitigate the
impact of outliers, we winsorize all growth measures at
the 2.5% level. The carbon intensity of a company is expressed as tons of CO2 equivalent divided by the com-

The remainder of the paper is organized as follows.
In Section 2, we describe the data and provide summary
statistics. We discuss the results in Section 3. Concluding
remarks are in Section 4.
2. Data and sample
Our primary database covers the 2005–2017 period and
is largely a result of matching two data sets by Trucost
and FactSet in the US. Trucost provides information on corporate carbon and other greenhouse gas emissions. FactSet provides data on stock returns, corporate fundamentals,
and institutional ownership. We performed the matching
using ISIN as a main identiﬁer. In some instances, in which
ISIN was not available to create a perfect match, we relied
on matching based on company names (after standardizing
the company names in FactSet and Trucost we match the
names with a similarity score of one). Finally, when there
are multiple subsidiaries of a given company, we used the
primary location as a matching entity. The ultimate matching produced 3421 unique companies out of 3481 companies available in Trucost. Among the 60 companies we
were not able to match, more than half are not exchange
listed and the remaining ones are small. Hence, we believe our data cover almost the entire universe of companies with available emission data.
2.1. Data on corporate carbon emissions
Firm-level carbon emissions data are assembled by
seven main providers: CDP, Trucost, MSCI, Sustainalytics,
Thomson Reuters, Bloomberg, and ISS. All these providers
follow the Greenhouse Gas Protocol that sets the standards for measuring corporate emissions.8 More and more
companies disclose their greenhouse gas emissions, and
most large corporations report their emissions to CDP.
Other providers rely on the CDP data and supplement it
with other sources. Emissions can be measured directly
at the source or more commonly by applying conversion
factors to energy use. The Greenhouse Gas Protocol distinguishes between three different sources of emissions:
scope 1 emissions, which cover direct emissions over one
year from establishments that are owned or controlled by
the company; these include all emissions from fossil fuel
used in production. Scope 2 emissions come from the generation of purchased heat, steam, and electricity consumed
by the company. Scope 3 emissions are caused by the
operations and products of the company but occur from
sources not owned or controlled by the company. These include emissions from the production of purchased materials, product use, waste disposal, and outsourced activities.
In some sectors, like automobile manufacturing, by far
the most important component of their emissions is the
aggregation of all their scope 3 emissions. The Greenhouse
Gas Protocol distinguishes between 15 different categories
of scope 3 emissions, including purchased goods and services, capital goods, upstream & downstream transportation and distribution, waste generated in operations, business travel, employee commuting, processing & use of sold
8

9

See http://ghgprotocol.org/standards/scope- 3- standard.
See CDP 2016 Climate Change Report “Tracking Progress on Corporate
Climate Action.”
11
More than 6,300 companies worldwide answered CDP’s climate
change questionnaire in 2018. Of these, 76% disclosed scope 1 emissions,
68% scope 2 emissions, and 38% scope 3 emissions (see https://www.cdp.
net).
10

See https://ghgprotocol.org.
521

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 1
Summary statistics.
This tables reports summary statistics (averages, medians, and standard deviations) for the variables used for the six sets of regressions. The sample
period is 2005–2017. Panel A reports the emission variables. Panel B reports the cross-sectional return variables. RET is the monthly stock return; LOGSIZE
is the natural logarithm of market capitalization (in $ million); B/M is the book value of equity divided by market value of equity; ROE is the return on
equity; LEVERAGE is the book value of leverage deﬁned as the book value of debt divided by the book value of assets; MOM is the cumulative stock return
over the one-year period; INVEST/A is the CAPEX divided by book value of assets; HHI is the Herﬁndahl index of the business segments of a company with
weights proportional to revenues; LOGPPE is the natural logarithm of plant, property & equipment (in $ million); BETA is the CAPM beta calculated over
the one year period; VOLAT is the monthly stock return volatility calculated over the one year period. Panel C reports the time-series variables. MKTRF
is the monthly return on the value-weighted stock market net of the risk free rate; HML is the monthly return on the portfolio long value stocks and
short growth stocks; SMB is the monthly return on the portfolio long small-cap stocks and short large-cap stocks; MOM is the monthly return on the
portfolio long 12-month stock winners and short 12-month past losers; CMA is the monthly return of a portfolio that is long on conservative investment
stocks and short on aggressive investment stocks; BAB is the monthly return of a portfolio that is long on low-beta stocks and short on high-beta stocks;
LIQ is the liquidity factor of Pastor and Stambaugh; NET ISSUANCE is the monthly return of a portfolio that is long on high-net-issuance stocks and short
on low-net-issuance stocks. Net issuance for year t is the change in the natural log of split-adjusted shares outstanding from the ﬁscal yearend in t-2 to
the ﬁscal yearend in t-1; IDIO VOL is the monthly return of a portfolio that is long on low idiosyncratic volatility stocks and short on high idiosyncratic
volatility stocks. Panel D reports the ownership variables. IOi,t is the fraction of the shares of company i held by institutions in the FactSet database at
the end of year t. IO is calculated by aggregating the shares held by all types of institutions at the end of the year, and then dividing this amount by
shares outstanding at the end of the year. IO_BANKS is the ownership by banks; IO_INSURANCE is the ownership by insurance companies; IO_INVESTCOS
is the ownership by investment companies (e.g., mutual funds); IO_ADVISERS is the ownership by independent investment advisers; IO_PENSIONS is the
ownership by pension funds; IO_HFS is the ownership by hedge funds. PRINVi,t is the inverse of ﬁrm i’s share price at the end of year t; TOT VOLATi,t is the
standard deviation of daily stock returns for company i over the one-year period; VOLUMEi,t is the average daily trading volume (in $million) of stock i over
the calendar year t; NASDAQi,t is an indicator variable equal to one if a stock i is listed on NASDAQ in year t, and zero otherwise; SP500i,t is an indicator
variable equal to one if a stock i is part of the S&P 500 Index in year t, and zero otherwise.

Variable

Mean

Median

Std. Dev.

10.55
10.52
12.31
0.08
0.14
0.09
1.92
0.34
1.58
2.12
1.04
0.75
0.71

10.47
10.66
12.46
0.03
0.05
0.06
0.15
0.18
0.98
0.16
0.58
0.06
0.47

2.95
2.36
2.25
0.36
0.45
0.24
5.88
0.46
1.59
6.45
1.31
2.29
0.68

1.14
8.25
0.50
0.24
0.15
0.05
9.76
0.82
6.22
1.10
0.10
0.02
0.01

1.08
8.25
0.39
0.22
0.11
0.03
11.32
1.00
6.34
1.05
0.08
0.03
0.00

10.84
1.57
0.41
0.18
0.45
0.05
21.23
0.24
2.26
0.44
0.06
0.30
0.43

0.70
0.00
0.07
0.07
0.02
0.49
0.15
0.51
−0.18

1.06
−0.22
0.04
0.36
−0.06
0.74
0.38
0.55
0.03

4.08
2.57
2.26
4.53
1.39
2.66
3.59
1.65
5.27

76.84
0.10
0.35
18.19
43.94
3.40
10.87
0.05
0.10
0.44
0.30
0.37

82.93
0.07
0.13
18.37
46.11
3.51
7.73
0.03
0.08
0.21
0.00
0.00

22.22
0.16
3.11
8.64
15.39
2.31
10.04
0.11
0.06
0.56
0.46
0.48

Panel A: Emission variables
Log (Carbon Emissions Scope 1 (tons CO2 e))
Log (Carbon Emissions Scope 2 (tons CO2 e))
Log (Carbon Emissions Scope 3 (tons CO2 e))
Growth Rate in Carbon Emissions Scope 1 (winsorized at 2.5%)
Growth Rate in Carbon Emissions Scope 2 (winsorized at 2.5%)
Growth Rate in Carbon Emissions Scope 3 (winsorized at 2.5%)
Carbon Intensity Scope 1 (tons CO2 e/USD m.)/100 (winsorized at 2.5%)
Carbon Intensity Scope 2 (tons CO2 e/USD m.)/100 (winsorized at 2.5%)
Carbon Intensity Scope 3 (tons CO2 e/USD m.) /100 (winsorized at 2.5%)
Carbon Intensity Direct (winsorized at 2.5%)/100
Carbon Intensity Indirect (winsorized at 2.5%)/100
GHG Direct Impact Ratio (winsorized at 2.5%)
GHG Indirect Impact Ratio (winsorized at 2.5%)
Panel B: Cross-sectional return variables
RET (%)
LOGSIZE
B/M (winsorized at 2.5%)
LEVERAGE (winsorized at 2.5%)
MOM (winsorized at 0.5%)
INVEST/A (winsorized at 2.5%)
ROE (winsorized at 2.5%, in%)
HHI
LOGPPE
BETA
VOLAT (winsorized at 0.5%)
SALESGR (winsorized at 0.5%)
EPSGR (winsorized at 0.5%)
Panel C: Time-series variables
MKTRF (in%)
HML (in%)
SMB (in%)
MOM (in%)
CMA (in%)
BAB (in%)
LIQ (in%)
NET ISSUANCE (in%)
IDIO VOL (in%)
Panel D: Ownership variables
IO (in%)
IO_BANKS (in%)
IO_INSURANCE (in%)
IO_INVESTCOS. (in%)
IO_ADVISERS (in%)
IO_PENSIONS (in%)
IO_HFS (in%)
PRINV (winsorized at 0.5%)
VOLAT (winsorized at 0.5%)
VOLUME (in $million) (winsorized at 2.5%)
NASDAQ
SP500
522

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 2
Stock characteristics by emission calculation.
The table reports the sample means of the main variables over the
2005–2017 period. All variables are deﬁned in Table 1. Imputed includes
all ﬁrms for which Trucost estimates the levels of emissions. Direct includes all ﬁrms for which data is directly available.
Calculation Method

Imputed

Direct

SCOPE 1 TOT
SCOPE 2 TOT
SCOPE 3 TOT
SCOPE 1 INT
SCOPE 2 INT
SCOPE 3 INT
RET (%)
LOGSIZE
B/M
LEVERAGE
MOM
INVEST/A
ROE
HHI
LOGPPE
BETA
VOLAT
SALESGR (%)
EPSGR (%)

1,366,013
264,203
1,433,741
211.76
35.89
158.11
1.00
8.22
0.50
0.24
0.15
0.05
9.88
0.84
6.19
1.13
0.10
1.67
1.53

5,954,876
957,827
4,057,516
588.91
68.26
197.92
1.09
9.64
0.48
0.27
0.13
0.05
14.89
0.72
8.03
1.04
0.07
−0.16
0.25

emissions are positively correlated. Yet, the coeﬃcients are
relatively small. Similarly, the level of scope 1 emissions is
obviously positively correlated with scope 1 emission intensity, but the size of the coeﬃcient is only 0.6, reﬂecting
the fact that two ﬁrms with the same scope 1 intensity
may have very different levels of emissions. A large ﬁrm,
with high emissions, can have the same emission intensity
as a small ﬁrm. The low correlation between levels and intensity is even more pronounced for scope 2 (0.24) and
scope 3 (0.27). In Panel B, we also report the autocorrelation coeﬃcients for the different measures of emissions.
Emission levels for all three categories are highly persistent, with an autocorrelation coeﬃcient of 0.977 for scope
1, 0.955 for scope 2, and 0.967 for scope 3. Interestingly,
the year-to-year growth in emissions also has some persistence, especially for scope 3 emissions. As for the emission
intensity variables they are, not surprisingly, also highly
persistent as sales are highly persistent.
We also analyze the average values of all three emission
sources over time. Fig. 1 and Table 4 present the results. As
one might expect, there is a steady decline in scope 1 and
scope 3 emissions at the ﬁrm level over time as a result
of energy eﬃciency improvements, technological innovations, and an increase in the reliance on renewable energy
sources. There is a sharp decline in scope 1 emissions from
2015 to 2016. However, this mainly reﬂects the addition by
Trucost of many smaller ﬁrms to the sample in 2015, as
can be seen in Fig. 2. The addition of all these ﬁrms to the
sample also explains why total scope 3 emissions sharply
increase from 2015 to 2016, and why total scope 1 emissions remain ﬂat even though per-ﬁrm emissions decline.
All these results are further conﬁrmed by the numbers in
Panels A and B of Table 4; averages for all ﬁrms in our
sample are in Panel A while those conditioned on the presence in the sample prior to 2015 are in Panel B. We can see
that when we drop the new ﬁrms added in 2016 from the
sample, the averages for 2016 and 2017 are very close to
the numbers in 2015. While we still observe some decline
in scope 1 emissions, there is no such decline in scope 2
and scope 3 emissions. If anything, the numbers for scope
3 emissions go up, although not by much.
We note that ﬁrms with signiﬁcant emissions are represented in a wide range of industries. In Table 5, we
present the distribution of ﬁrms in our sample with respect to the six-digit Global Industry Classiﬁcation (GIC 6).
Banks, biotech, and oil & gas are the most represented industries, with each one having more than 150 ﬁrms.12 In
Table 6, we provide a list of industries with the highest
and the lowest intensity of emissions. Power, electric, and
multi-utility industries produce the most scope 1 emissions, while consumer ﬁnance, thrifts and mortgages, and
capital markets are the cleanest. The ranking is somewhat
different when we classify industries with respect to their
scope 2 and scope 3 emissions. Metals and mining, electric utilities, and construction materials are the three most
scope 2 emission-intensive industries (the cleanest industries mimic those based on scope 1 classiﬁcation). In turn,

pany’s revenues in million US dollar units, also winsorized
at the 2.5% level. The average (unwinsorized) scope 1 intensity in our sample equals 265.26 tons/million, while the
intensities for scope 2 and scope 3 are 39.64 tons/million
and 164.22 tons/million, respectively. The EDX database
also provides information on whether the emissions data
was reported or estimated, which allows us to do a sensitivity analysis and determine how the results are affected
by the exclusion of the estimated data. We describe how
the data breaks down into ﬁrms with reported and estimated emissions data in Table 2. As Matsumura, Prakash,
and Vera-Munoz (2014) note, ﬁrms that do not report their
emissions are typically smaller (and therefore have smaller
emissions) and are less proﬁtable. But in other respects,
ﬁrms that report their emissions have similar characteristics to those that do not. In particular, their stock returns,
volatility, leverage, book-to-market ratios, capital expenditures, and betas are very similar.
We also report alternative measures Trucost provides,
in particular: i) CARBON DIRECT, which adds three additional greenhouse gas to the GHG Protocol scope 1 measures; ii) CARBON INDIRECT, which covers a slightly broader
set of emissions by the direct suppliers to a company than
scope 2; iii) GHG DIRECT, measured in US dollars, which
covers all direct external environmental impacts of a company. Trucost applies a monetary value to GHG emissions
quantities, which represents the global average damage of
each environmental impact; and iv) GHG INDIRECT, which
covers indirect supply chain environmental impacts. These
are estimated impacts based on Trucost’s environmental
impact models. Again, these are reported in US dollars and
represent the global average damages of each environmental impact.
How correlated are these different emission variables?
We report the cross-correlations in Panel A of Table 3.
As one would expect, the levels of all three categories of

12
Some ﬁrms in this table are classiﬁed into multiple industries; hence,
the total number of ﬁrms in the table (3917) exceeds the number of
unique ﬁrms in our sample (3421).

523

P. Bolton and M. Kacperczyk

Table 3
Carbon emissions: correlations.
The sample period is 2005–2017. Panel A presents the cross-correlations among emission variables. Panel B presents the coeﬃcients from estimating the AR(1) model for various measures of emissions. All
regressions include year-month ﬁxed effects. We cluster standard errors at ﬁrm and year dimensions. The emission variables are deﬁned in Table 1. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Cross-correlations

SCOPE 1 TOT
SCOPE 2 TOT
SCOPE 3 TOT
SCOPE 1 INT
SCOPE 2 INT
SCOPE 3 INT

SCOPE 1 TOT

SCOPE 2 TOT

SCOPE 3 TOT

SCOPE 1 INT

SCOPE 2 INT

SCOPE 3 INT

1.00
0.39
0.51
0.60
0.05
0.21

1.00
0.75
0.03
0.24
0.09

1.00
0.03
0.02
0.27

1.00
0.10
0.25

1.00
0.10

1.00

Panel B: Autocorrelations
VARIABLES
LOG (SCOPE 1 TOT)t-1

(1)
LOG (SCOPE 1)

(2)
LOG (SCOPE 2)

(3)
LOG (SCOPE 3)

(4)

(5)

(6)

SCOPE 1

SCOPE 2

SCOPE 3

(7)
SCOPE 1 INT

(8)
SCOPE 2 INT

0.977∗ ∗ ∗
(0.003)

524

0.955∗ ∗ ∗
(0.005)

LOG (SCOPE 2 TOT)t-1

0.967∗ ∗ ∗
(0.004)

LOG (SCOPE 3 TOT)t-1

SCOPE 1t-1

0.045∗
(0.021)

SCOPE 2t-1

0.025
(0.015)

SCOPE 3t-1

0.190∗ ∗ ∗
(0.047)

0.946∗ ∗ ∗
(0.012)

SCOPE 2 INTt-1
SCOPE 3 INTt-1
0.281∗ ∗ ∗
(0.033)

0.573∗ ∗ ∗
(0.052)

0.475∗ ∗ ∗
(0.046)

0.057∗ ∗ ∗
(0.001)

0.106∗ ∗ ∗
(0.002)

0.053∗ ∗ ∗
(0.003)

0.065∗ ∗ ∗
(0.013)

0.026∗ ∗ ∗
(0.004)

0.969∗ ∗ ∗
(0.021)
0.031
(0.033)

Year/month F.E.

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Observations
R-squared

156,446
0.972

156,374
0.945

156,578
0.975

122,686
0.014

122,602
0.020

122,794
0.085

156,578
0.962

156,578
0.850

156,578
0.964

Journal of Financial Economics 142 (2021) 517–549

0.945∗ ∗ ∗
(0.005)

SCOPE 1 INTt-1

Constant

(9)
SCOPE 3 INT

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

food products, metals and mining, and construction materials are the three most scope 3 emission-intensive industries. Internet software and services, health care technologies, and software are the three least emission-intensive
industries. The Trucost industry classiﬁcation is ﬁner than
the GIC six-digit classiﬁcation. Given that we control for
industry a natural question is how sensitive the results are
to the classiﬁcation itself. The classiﬁcation in theory could
be so ﬁne that it includes only one ﬁrm in each industry or
so coarse that it includes all ﬁrms in one industry. Adding
industry ﬁxed effects would be meaningless under these
polar classiﬁcation systems. As a robustness check, we also
perform our analysis under the GIC classiﬁcation and report the results in Table A.4 in the Appendix.
Finally, we observe not only substantial variation in the
growth rates of emissions across different industries, but
also signiﬁcant variation in the rates of all three categories
of emissions across ﬁrms within the same industry. Fig. 3
displays the time series plots of the average cross-sectional
standard deviations of emission growth rates across all
ﬁrms (Panel A) and across all ﬁrms within a given GIC 6
industry (Panel B). Even though the scale of the variation
in Panel A is larger than that in Panel B, there is still a
signiﬁcant dispersion in emissions in Panel B. Moreover,
the standard deviation in carbon emission growth rates is
very stable over time. In particular, the standard deviation
did not signiﬁcantly change following the addition of new
ﬁrms to the sample in 2015.
2.2. Variables in cross-sectional return regressions
Our empirical analysis of stock returns employs a
monthly measure of returns as a dependent variable. In
our cross-sectional return regressions, the dependent variable RETi,t is the monthly return of an individual stock i
in month t. Our return data primarily comes from FactSet,
but for a small subset of delisted ﬁrms, we replace the return data with delisting-adjusted values from Compustat.
Finally, we remove observations with returns greater than
100% to mitigate the impact of outliers. The number of excluded ﬁrm/month observations is 109 and its exclusion
does not materially affect our results. However, using unrestricted returns data would be problematic as the data, for
example, include four observations with monthly returns
greater than 10,0 0 0%.
Our control variables are deﬁned as follows: LOGSIZEi,t
is the natural logarithm of ﬁrm i’s market capitalization
(price times shares outstanding) at the end of year t; B/Mi,t
is ﬁrm i’s book value divided by its market capitalization
at the end of year t; LEVERAGE is the book leverage of the
company; ROEi,t is the ﬁrm’s earnings performance, given
by the ratio of ﬁrm i’s net yearly income divided by the
value of its equity; MOMi,t is the average of the most recent 12 months’ returns on stock i, leading up to and including month t-1; INVEST/A represents the ﬁrm’s capital
expenditures divided by the book value of its assets; HHI
is the Herﬁndahl concentration index of ﬁrms with respect
to different business segments, based on each segment’s
revenues; LOGPPE is the natural logarithm, of the ﬁrm’s
property, plant, and equipment; BETAi,t is the market beta
of ﬁrm i in year t, calculated over the one year period

Fig. 1. Carbon emissions: time series summary.
The data source is Trucost and the data sample period is 2005–2017. Panels A and B present average ﬁrm emissions (in tons of CO2 equivalent
to revenues in $ million). The emissions are broken down into scope 1,
scope 2, and scope 3 emissions. In Panel B, GHG Direct and GHG Indirect
are impact ratios expressed as a percentage of costs in revenues (in $ million). Carbon direct and Carbon indirect are intensities expressed in tons of
CO2 equivalent to revenues in $ million. Panels C and D present the total
emissions (across all ﬁrms) per year.

525

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 2. Carbon emissions: sample selection.
The data source is Trucost. The ﬁgure presents the number of ﬁrms with valid emission data over the 2005–2017 period.

Table 4
Carbon emissions over time.
The table reports the cross-sectional averages of scope 1, scope 2, and scope 3 levels and intensity variables over the 2005–2017 period. Panel A considers
a full sample of ﬁrms. Panel B is restricted to a sample of ﬁrms that existed prior to 2016. The emissions variables are deﬁned in Table 1.
Panel A: Full sample
Year

SCOPE 1 TOT

SCOPE 2 TOT

SCOPE 3 TOT

SCOPE 1 INT

SCOPE 2 INT

SCOPE 3 INT

2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017

2,697,225
2,775,999
2,893,335
3,147,450
2,482,940
2,655,585
2,639,823
2,417,298
2,223,849
2,255,386
2,161,598
883,498
809,277

335,402
379,869
410,656
683,294
385,670
400,848
440,716
431,992
398,491
425,080
419,362
184,335
176,805

2,414,925
2,229,797
2,281,158
2,750,231
1,907,531
1,987,772
2,217,712
2,222,692
2,046,741
1,979,578
1,783,537
858,982
935,203

411.16
373.64
341.57
308.70
334.35
339.68
305.06
308.23
335.82
281.89
273.32
154.25
139.29

37.55
39.17
37.38
39.75
41.41
40.47
40.20
39.57
39.22
54.37
56.79
33.66
33.88

229.79
205.90
193.13
164.33
184.06
173.56
169.39
160.65
159.69
152.26
150.77
139.00
145.53

Year

SCOPE 1 TOT

SCOPE 2 TOT

SCOPE 3 TOT

SCOPE 1 INT

SCOPE 2 INT

SCOPE 3 INT

2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017

2,697,225
2,775,999
2,893,335
3,147,450
2,482,940
2,655,585
2,639,823
2,417,298
2,223,849
2,255,386
2,161,598
1,993,060
1,922,550

335,402
379,869
410,656
683,294
385,670
400,848
440,716
431,992
398,491
425,080
419,362
404,850
404,904

2,414,925
2,229,797
2,281,158
2,750,231
1,907,531
1,987,772
2,217,712
2,222,692
2,046,741
1,979,578
1,783,537
1,874,254
2,149,459

411.16
373.64
341.57
308.70
334.35
339.68
305.06
308.23
335.82
281.89
273.32
269.09
243.38

37.55
39.17
37.38
39.75
41.41
40.47
40.20
39.57
39.22
54.37
56.79
45.78
44.95

229.79
205.90
193.13
164.33
184.06
173.56
169.39
160.65
159.69
152.26
150.77
167.35
176.12

Panel B: Legacy sample

526

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 5
Industry representation by number of ﬁrms.
The table reports the distribution of unique ﬁrms in our sample with regard to GIC 6 industry classiﬁcation. Total represents the total number of ﬁrms
in our sample. The sample period is 2005–2017.
GIC 6

Industry Name

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
Total

Energy Equipment & Services
Oil, Gas & Consumable Fuels
Chemicals
Construction Materials
Containers & Packaging
Metals & Mining
Paper & Forest Products
Aerospace & defense
Building Products
Construction & Engineering
Electrical Equipment
Industrial Conglomerates
Machinery
Trading Companies & Distributors
Commercial Services & Supplies
Professional Services
Air Freight & Logistics
Airlines
Marine
Road & Rail
Transportation Infrastructure
Auto Components
Automobiles
Household Durables
Leisure Products
Textiles, Apparel & Luxury Goods
Hotels, Restaurants & Leisure
Diversiﬁed Consumer Services
Media
Distributors
Internet & Direct Marketing Retail
Multiline Retail
Specialty Retail
Food & Staples Retailing
Beverages
Food Products
Tobacco
Household Products
Personal Products
Health Care Equipment & Supplies
Health Care Providers & Services
Health Care Technology
Biotechnology
Pharmaceuticals
Life Sciences Tools & Services
Banks
Thrifts & Mortgage Finance
Diversiﬁed Financial Services
Consumer Finance
Capital Markets
Mortgage Real Estate Investment Trusts (REITs)
Insurance
Internet Software & Services
IT Services
Software
Communications Equipment
Technology Hardware, Storage & Peripherals
Electronic Equipment, Instruments & Components
Semiconductors & Semiconductor Equipment
Diversiﬁed Telecommunication Services
Wireless Telecommunication Services
Media
Entertainment
Interactive Media & Services
Electric Utilities
Gas Utilities
Multi-Utilities
Water Utilities
Independent Power and Renewable Electricity Producers
Equity Real Estate Investment Trusts (REITs)
Real Estate Management & Development

# of Firms

527

75
164
81
17
21
47
12
46
32
36
54
16
118
40
69
42
15
13
27
31
5
43
8
64
21
41
95
38
83
8
45
17
110
27
17
57
9
12
15
109
77
20
203
87
34
260
61
28
37
92
22
111
100
102
150
47
34
82
103
34
15
49
22
29
42
17
30
13
17
184
35
3917

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 6
Carbon emission production by industry.
Panel A reports the top 10 of GIC 6 industries in terms of average emission production (scope 1, scope 2, scope 3). Panel B reports the bottom 10 of GIC
6 industries in terms of average emission production (scope 1, scope 2, scope 3). The sample period is 2005–2017. The emission variables are expressed in
tons of CO2 e.
Panel A: Largest emissions (avg.)
GIC 6

Scope 1

GIC 6

Scope 2

GIC 6

Scope 3

69
65
18
67
6
2
17
4
7
3

33,300,000
30,700,000
17,600,000
17,200,000
6,343,545
6,302,663
4,316,221
3,827,648
3,286,922
3,280,770

34
23
6
3
7
60
12
38
32
2

2,163,081
2,094,174
1,749,360
1,475,783
1,375,637
1,219,956
1,014,037
994,783
825,501
820,777

23
36
37
12
35
2
34
38
6
22

18,700,000
11,800,000
6,847,386
6,575,213
6,106,099
6,049,237
5,882,429
4,313,762
3,580,245
3,285,134

Panel B: Smallest emissions (avg.)
GIC 6

Scope 1

GIC 6

Scope 2

GIC 6

Scope 3

47
50
46
49
64
51
53
55
42
16

601
6767
6965
7469
7649
8770
8898
9132
11,657
17,895

47
42
19
16
43
50
51
66
45
46

1756
11,824
21,798
22,653
24,606
35,404
36,013
39,177
44,082
45,627

47
51
68
42
71
70
16
46
28
43

15,193
27,069
41,182
64,097
84,764
102,300
114,132
116,073
145,311
151,772

using daily data; VOLATi,t is the standard deviation of returns based on the past 12 months of monthly returns;
SALESGRi,t is the dollar change in annual ﬁrm revenues normalized by last month’s market capitalization; EPSGRi,t is
the dollar change in annual earnings per share, normalized by the ﬁrm’s equity price. To eliminate the impact
of outliers, we winsorize B/M, LEVERAGE, and INVEST/A at
the 2.5% level, and MOM, VOLAT, SALESGR, and EPSGR at the
0.5% level. We report the summary statistics of these variables in Panel B of Table 1.
The average ﬁrm’s monthly stock return is 1.14%, with
a standard deviation of 10.84%. The average ﬁrm has a
market capitalization of $13 billion, with a median value
of $3.8 billion. The average book-to-market ratio is 0.50,
while the average book leverage is 24%. The average market beta is 1.10, slightly more than that of the market.

gressive investment stocks. BAB is the monthly return of a
portfolio that is long on low-beta stocks and short on highbeta stocks; LIQ is the liquidity factor of Pastor and Stambaugh; NET ISSUANCE is the monthly return of a portfolio
that is long on high-net-issuance stocks and short on lownet-issuance stocks. Net issuance for year t is the change
in the natural log of split-adjusted shares outstanding from
the ﬁscal yearend in t-2 to the ﬁscal yearend in t-1; IDIO
VOL is the monthly return of a portfolio that is long on low
idiosyncratic volatility stocks and short on high idiosyncratic volatility stocks. We present the summary statistics
for the various portfolio returns in Panel C of Table 1.
The average market risk premium in our sample is 0.7%
per month. Other factors with relatively high risk premia
are net issuance and BAB. Somewhat atypically, the value
factor return in our sample is equal to 0%. Similarly, the
momentum factor generates a mere 0.07% per month, and
the volatility factor has a negative return of −0.18% per
month.

2.3. Variables in the time series return regressions
The variables for our time series regressions are deﬁned as follows: MKTRFt is the monthly return of the CRSP
value-weighted portfolio in month t, net of the risk-free
rate; SMBt , HMLt , MOMt, and CMAt are well-known portfolio return series downloaded from Ken French’s website:
SMB is the monthly return of a portfolio that is long on
small stocks and short on large stocks; HML is the monthly
return of a portfolio that is long on high book-to-market
stocks and short on low book-to-market stocks; MOM is
the monthly return of a portfolio that is long on past oneyear return winners and short on past one-year return
losers; CMA is the monthly return of a portfolio that is
long on conservative investment stocks and short on ag-

2.4. Variables in divestment regressions
Our institutional ownership regression variables are:
IOi,t , which is the fraction of the shares of company i
held by institutions in the FactSet database at the end of
year t. IO is calculated by aggregating the shares held by
all types of institutions at the end of the year, and then
dividing this value by the number of shares outstanding
at the end of the year. We further decompose the institutional ownership with respect to subgroups of owners. IO_BANKS is the ownership by banks; IO_INSURANCE
is the ownership by insurance companies; IO_INVESTCOS
528

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 3. Standard deviation of carbon emission growth rates.
The data source is Trucost. Panel A presents the cross-sectional standard deviation of ﬁrm-level emissions. Panel B presents the cross-sectional standard
deviation of ﬁrm level emissions within GIC-6 industries, all averaged across all the industries in a given year. All emissions are broken down into scope
1, scope 2, and scope 3, over the 2005–2017 period. The emission levels are measured in millions of tons of CO2 equivalent and are winsorized at the 1%
level.

is the ownership by investment companies (e.g., mutual
funds); IO_ADVISERS is the ownership by independent investment advisers; IO_PENSIONS is the ownership by pension funds and IO_HFS is the ownership by hedge funds.
Even though the total institutional ownership captures the
intensive margin only, the range of disaggregated ownership variables varies from 0% to 100% (as long as the
total institutional ownership in the data has a positive
value).

The control variables in the ownership regressions include PRINVi,t , which is the inverse of ﬁrm i’s share price
at the end of year t; VOLATi,t is the standard deviation of
monthly stock returns for ﬁrm i over the one-year period;
VOLUMEi,t is the average daily trading volume (in $million)
of stock i over the calendar year t. NASDAQi,t is an indicator variable equal to one if a stock i is listed on NASDAQ in
year t, and zero otherwise; SP500i,t is an indicator variable
equal to one if a stock i is part of the S&P 500 Index in

529

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

year t, and zero otherwise. We report the summary statistics for these variables in Panel D of Table 1.
The average IO is 0.77, and the cross-sectional standard
deviation of IO is 0.22. In other words, in a typical year,
a typical ﬁrm has about 77% of its shares held by institutional investors, and the standard deviation of institutional
ownership in a typical cross-section is 22%. Among the different institutional owners, independent advisers are the
biggest holders, with an average stock’s ownership equal
to 43.9%, followed by investment companies with an average 18.2% ownership. Banks and insurance companies,
in turn, are the smallest institutional owners. The average
daily stock return volatility in our sample is 10% or annualized 158.7%. The average daily stock volume is $440,0 0 0.
Finally, about 30% of stock-month observations are companies listed on NASDAQ, and 37% observations are ﬁrms
from the S&P 500 Index.

lated to LOGSIZE. However, scope 1 and scope 3 emission
intensities are weakly negatively related to LOGSIZE. The
level of emissions is also signiﬁcantly associated with high
book-to-market ratios, high tangible capital (PPE), highly
levered ﬁrms, and ﬁrms with high growth in sales and
earnings. On the other hand, the level of emissions is lower
for ﬁrms with high capital expenditures, although these
growth ﬁrms are associated with high increases in emissions. Interestingly, only diversiﬁcation (HHI) and tangible
capital signiﬁcantly affect emission intensity.

3.2. Evidence on cross-sectional returns
For all three categories of emissions, we relate in turn
the level of companies’ emissions, the year-to-year growth
in emissions, and the companies’ emission intensity to
their corresponding stock returns in the cross-section.
We ﬁrst estimate the following cross-sectional regression
model using pooled OLS:

3. Results
We begin our analysis by investigating the determinants
of scope 1, scope 2, and scope 3 emissions. We then turn to
the evaluation of the carbon return premium in the crosssection of stocks. We next explore the time-series properties of the cross-sectional carbon premium with respect
to well-known risk factors. Finally, we consider the divestment hypothesis by looking at institutional ownership patterns.

RE Ti,t = a0 + a1 LOG (T OT Emissions )i,t
+ a2Control si,t−1 + μt + εi,t ,

(1)

where RE Ti,t measures the stock return of company i in
month t and Emissions is a generic term alternately standing for SCOPE 1, SCOPE 2, and SCOPE 3 emissions. The
vector of controls includes a host of ﬁrm-speciﬁc variables known to predict returns, such as LOGSIZE, B/M,
ROE, LEVERAGE, MOM, INVEST/A, HHI, LOGPPE, BETA, VOLAT,
SALESGR, and EPSGR.13 We also include year/month ﬁxed
effects. We cluster standard errors at the ﬁrm and year levels. Our coeﬃcient of interest is a1 .
We report the results in Table 8, Panel A. Column 1
shows the results for SCOPE 1; column 2 for SCOPE 2, and
column 3 for SCOPE 3. For all three categories of emissions,
we ﬁnd a positive and statistically signiﬁcant effect on
ﬁrms’ stock returns. The effect is also economically signiﬁcant: a one-standard-deviation increase in SCOPE 1 leads to
a 13-bps increase in stock returns, or 1.5% annualized, and
a one-standard-deviation increase in SCOPE 2 leads to a 23bps increase in stock returns, or 2.8% annualized. Finally, a
one-standard-deviation increase in SCOPE 3 increases stock
returns by 30 bps per month, or 3.6% annualized.
Since emissions tend to cluster signiﬁcantly within speciﬁc industries, a question of interest is whether the ﬁrmspeciﬁc differences can be attributed to industry-speciﬁc
effects. To examine this possibility, we additionally include
industry-ﬁxed effects using the Trucost industry classiﬁcation. The results presented in columns 4 to 6 are quite
striking. Including industry effects signiﬁcantly strengthens the cross-sectional dispersion of returns due to carbon emissions. In fact, the economic signiﬁcance increases
by anywhere between 70% and 280% relative to the model
without industry effects.
We also plot the time series of the cumulative values
of the unadjusted and industry-adjusted carbon premia in

3.1. Determinants of carbon emissions
Since emissions are not reported by all companies, one
basic issue to explore ﬁrst is how companies that do report
their emissions compare with non-reporting companies. To
assess the quantitative differences on the extensive margin, we compare various ﬁrm-level characteristics for the
reporting and non-reporting ﬁrms. We describe basic summary statistics of the two categories of ﬁrms in Table A.1
of the Appendix. As one might expect, we ﬁnd that larger
ﬁrms are more likely to report their emissions. Also, ﬁrms
with lower book-to-market ratios and higher book leverage
are more likely to report emissions. At the same time, the
two groups of ﬁrms do not differ signiﬁcantly in terms of
their stock returns or investment levels.
Next, we assess the differences in emission levels, yearby-year changes, and emission intensities across ﬁrms using a regression framework. Our dependent variables are
levels, changes, and intensities of scope 1, scope 2, and
scope 3. Since there is little theory that can guide us on
what determines the level of carbon emissions, especially
with regard to their different sources, we include a host of
ﬁrm-level variables, comprising LOGSIZE, B/M, ROE, LEVERAGE, INVEST/A, HHI, LOGPPE, SALESGR, and EPSGR. To reﬂect
the possibility that ﬁrm-level emissions could concentrate
across ﬁrms and over time, we cluster standard errors at
the ﬁrm and year levels. Standard errors in all panel regressions become signiﬁcantly smaller in alternative speciﬁcations that cluster at the ﬁrm, industry, time, or industry
and time levels. We present the results in Table 7.
Not surprisingly, all three categories of emission levels,
and changes in emissions, are signiﬁcantly positively re-

13
HHI, SALESGR, and EPSGR are measured as of time t to reﬂect the fact
that all three may have a nontrivial contemporaneous effect on the level
of emissions at time t.

530

P. Bolton and M. Kacperczyk

Table 7
Determinants of carbon emissions.
The sample period is 2005–2017. The dependent variables are natural logarithm of total emissions, percentage change in total emissions, and carbon intensity. All variables are deﬁned in Table 1. We report
the results of the pooled regression with standard errors clustered at the ﬁrm level and year (in parentheses). All regressions include year-month ﬁxed effects and industry-ﬁxed effects. ∗ ∗ ∗ 1% signiﬁcance;
∗∗
5% signiﬁcance; ∗ 10% signiﬁcance.
(2)
LOG (SCOPE 2)

(3)
LOG (SCOPE 3)

(4)

(5)

(6)

SCOPE 1

SCOPE 2

SCOPE 3

(7)
SCOPE 1 INT

(8)
SCOPE 2 INT

(9)
SCOPE 3 INT

0.438∗ ∗ ∗
(0.036)
0.464∗ ∗ ∗
(0.060)
0.006∗ ∗ ∗
(0.001)
0.531∗ ∗
(0.196)
−2.026∗ ∗ ∗
(0.489)
−1.044∗ ∗ ∗
(0.119)
0.376∗ ∗ ∗
(0.036)
0.237∗ ∗ ∗
(0.059)
0.137∗ ∗
(0.049)

0.571∗ ∗ ∗
(0.032)
0.555∗ ∗ ∗
(0.059)
0.006∗ ∗ ∗
(0.001)
0.625∗ ∗ ∗
(0.188)
−1.950∗ ∗ ∗
(0.460)
−0.569∗ ∗ ∗
(0.081)
0.372∗ ∗ ∗
(0.037)
0.190∗ ∗
(0.062)
0.146∗ ∗
(0.049)

0.572∗ ∗ ∗
(0.022)
0.562∗ ∗ ∗
(0.054)
0.007∗ ∗ ∗
(0.001)
0.574∗ ∗ ∗
(0.162)
−2.457∗ ∗ ∗
(0.432)
−0.499∗ ∗ ∗
(0.063)
0.317∗ ∗ ∗
(0.023)
0.231∗ ∗
(0.077)
0.144∗ ∗
(0.050)

0.026∗ ∗ ∗
(0.008)
−0.033∗ ∗
(0.015)
−0.002∗ ∗ ∗
(0.000)
0.026
(0.020)
0.676∗ ∗ ∗
(0.145)
0.014
(0.021)
−0.033∗ ∗ ∗
(0.005)
0.311∗ ∗ ∗
(0.042)
−0.005
(0.008)

0.026∗ ∗ ∗
(0.008)
−0.038
(0.021)
−0.002∗ ∗ ∗
(0.001)
0.010
(0.030)
0.706∗ ∗ ∗
(0.132)
−0.024
(0.024)
−0.034∗ ∗ ∗
(0.006)
0.343∗ ∗ ∗
(0.041)
−0.011
(0.012)

0.027∗ ∗ ∗
(0.006)
−0.041∗ ∗
(0.017)
−0.001∗ ∗ ∗
(0.000)
0.019
(0.023)
0.530∗ ∗ ∗
(0.117)
0.023∗ ∗
(0.008)
−0.030∗ ∗ ∗
(0.006)
0.320∗ ∗ ∗
(0.030)
0.001
(0.006)

−0.118∗
(0.063)
−0.003
(0.107)
−0.002
(0.002)
0.364
(0.230)
−0.586
(1.161)
−2.185∗ ∗ ∗
(0.497)
0.127∗ ∗ ∗
(0.042)
−0.085
(0.070)
0.009
(0.038)

0.002
(0.006)
0.003
(0.010)
−0.000
(0.000)
0.002
(0.030)
−0.067
(0.153)
0.009
(0.030)
0.025∗ ∗ ∗
(0.007)
−0.019∗ ∗
(0.007)
0.006∗ ∗
(0.003)

−0.021∗ ∗
(0.009)
0.000
(0.013)
0.000
(0.000)
−0.056∗
(0.030)
−0.446∗ ∗
(0.201)
−0.260∗ ∗ ∗
(0.062)
0.026∗ ∗ ∗
(0.007)
0.010
(0.024)
−0.002
(0.006)

Year/month F.E.
Industry F.E.

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Observations
R-squared

189,187
0.899

189,115
0.849

189,283
0.905

156,506
0.150

156,410
0.136

156,578
0.320

189,283
0.786

189,283
0.650

189,283
0.935

LOGSIZE
B/M
ROE
LEVERAGE
531

INVEST/A
HHI
LOGPPE
SALESGR
EPSGR

Journal of Financial Economics 142 (2021) 517–549

(1)
LOG (SCOPE 1)

Variables

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 8
Carbon emissions and stock returns.
The sample period is 2005–2017. The dependent variable is RET. All variables are deﬁned in Table 1. We report the results of the pooled regression
with standard errors clustered at the ﬁrm and year level (in parentheses). All regressions include year-month ﬁxed effects. In the regressions for columns
4 through 6, we additionally include industry-ﬁxed effects. Panel A reports the results for the natural logarithm of total ﬁrm-level emissions; Panel B
reports the results for the percentage change in carbon total emissions; Panel C reports the results for carbon emission intensity. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5%
signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
Variables
LOG (SCOPE 1 TOT)

(1)

(2)

(3)

(4)

0.043∗ ∗
(0.023)
0.098∗ ∗
(0.042)

LOG (SCOPE 2 TOT)

(5)

(6)

0.164∗ ∗ ∗
(0.036)
0.167∗ ∗ ∗
(0.048)

−0.140
(0.163)
0.460
(0.260)
−0.559∗
(0.272)
0.321
(0.276)
−2.218
(1.740)
0.010∗
(0.005)
0.032
(0.110)
−0.015
(0.100)
0.059
(0.131)
0.978
(3.571)
0.692
(0.429)
0.592∗ ∗
(0.234)

−0.184
(0.167)
0.469
(0.266)
−0.579∗
(0.280)
0.348
(0.272)
−1.914
(1.794)
0.009
(0.005)
−0.026
(0.112)
−0.027
(0.088)
0.023
(0.131)
0.674
(3.415)
0.688
(0.430)
0.589∗ ∗
(0.231)

0.135∗ ∗
(0.046)
−0.193
(0.165)
0.444
(0.258)
−0.498∗
(0.274)
0.338
(0.274)
−1.587
(1.838)
0.008
(0.005)
0.137
(0.101)
−0.045
(0.090)
0.047
(0.130)
0.749
(3.506)
0.672
(0.420)
0.575∗ ∗
(0.232)

Year/month F.E.
Industry F.E.

Yes
No

Yes
No

Yes
No

Yes
Yes

Yes
Yes

Yes
Yes

Observations
R-squared

184,288
0.203

184,216
0.204

184,384
0.204

184,288
0.206

184,216
0.206

184,384
0.206

(4)

(5)

(6)

LOG (SCOPE 3 TOT)
LOGSIZE
B/M
LEVERAGE
MOM
INVEST/A
ROE
HHI
LOGPPE
BETA
VOLAT
SALESGR
EPSGR

−0.302∗
(0.148)
0.656∗ ∗
(0.234)
−0.699∗ ∗ ∗
(0.177)
0.284
(0.291)
0.277
(2.111)
0.009∗
(0.004)
0.130∗
(0.072)
0.020
(0.058)
0.045
(0.148)
0.622
(3.290)
0.679
(0.412)
0.637∗ ∗
(0.231)

−0.327∗
(0.154)
0.642∗ ∗
(0.229)
−0.712∗ ∗ ∗
(0.171)
0.294
(0.290)
0.267
(2.126)
0.009∗
(0.004)
0.052
(0.073)
0.019
(0.058)
0.040
(0.147)
0.501
(3.285)
0.686
(0.412)
0.636∗ ∗
(0.233)

0.312∗ ∗ ∗
(0.071)
−0.410∗ ∗
(0.163)
0.562∗ ∗
(0.224)
−0.790∗ ∗ ∗
(0.167)
0.301
(0.290)
0.699
(2.082)
0.007∗
(0.004)
0.111
(0.071)
−0.017
(0.057)
0.063
(0.146)
0.549
(3.269)
0.648
(0.407)
0.615∗ ∗
(0.227)

Panel B: Growth rate in total emissions
Variables

(1)

SCOPE 1

0.641∗ ∗ ∗
(0.153)

SCOPE 2

(2)

0.627∗ ∗ ∗
(0.144)
0.345∗ ∗
(0.125)

SCOPE 3
LOGSIZE
B/M
LEVERAGE
MOM
INVEST/A
ROE
HHI
LOGPPE
BETA

(3)

−0.023
(0.110)
0.391
(0.232)
−0.433∗
(0.217)
0.204
(0.265)
−2.508
(1.820)
0.009∗ ∗
(0.004)
−0.143
(0.154)
−0.006
(0.058)
0.109

−0.013
(0.112)
0.388
(0.233)
−0.414∗
(0.216)
0.217
(0.268)
−2.244
(1.848)
0.009∗ ∗
(0.004)
−0.112
(0.153)
−0.015
(0.057)
0.119

0.321∗ ∗
(0.120)
1.203∗ ∗ ∗
(0.318)
−0.037
(0.111)
0.410∗
(0.226)
−0.441∗
(0.213)
0.166
(0.267)
−2.638
(1.867)
0.009∗ ∗
(0.004)
−0.162
(0.151)
0.006
(0.060)
0.106

532

−0.107
(0.114)
0.771∗ ∗
(0.257)
−0.794∗ ∗ ∗
(0.213)
0.160
(0.264)
−0.620
(2.326)
0.008∗ ∗
(0.003)
−0.072
(0.098)
0.053
(0.041)
0.155

1.186∗ ∗ ∗
(0.314)
−0.099
−0.121
(0.115)
(0.117)
0.764∗ ∗
0.789∗ ∗ ∗
(0.257)
(0.246)
−0.785∗ ∗ ∗
−0.799∗ ∗ ∗
(0.217)
(0.214)
0.175
0.124
(0.266)
(0.264)
−0.463
−0.807
(2.291)
(2.341)
0.008∗ ∗
0.009∗ ∗
(0.003)
(0.003)
−0.056
−0.089
(0.097)
(0.102)
0.045
0.066
(0.041)
(0.044)
0.166
0.145
(Continued on next page)

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 8
(Continued)
Panel B: Growth rate in total emissions
Variables

(1)

(2)

(3)

(4)

(5)

(6)

(0.165)
1.853
(4.240)
0.459
(0.447)
0.573∗ ∗
(0.247)

(0.165)
2.004
(4.226)
0.544
(0.454)
0.573∗ ∗
(0.246)

(0.168)
1.800
(4.274)
0.280
(0.430)
0.568∗ ∗
(0.250)

(0.158)
1.373
(4.072)
0.463
(0.429)
0.641∗ ∗
(0.263)

(0.157)
1.504
(4.075)
0.549
(0.434)
0.641∗ ∗
(0.263)

(0.162)
1.341
(4.107)
0.284
(0.402)
0.636∗ ∗
(0.266)

Year/month F.E.
Industry F.E.

Yes
No

Yes
No

Yes
No

Yes
Yes

Yes
Yes

Yes
Yes

Observations
R-squared

153,051
0.218

152,955
0.218

153,123
0.218

153,051
0.221

152,955
0.221

153,123
0.222

(4)

(5)

(6)

VOLAT
SALESGR
EPSGR

Panel C: Emission intensity
Variables
SCOPE 1 INT

(1)

(2)

(3)

−0.010
(0.012)

SCOPE 2 INT

0.005
(0.006)
0.145
(0.121)

SCOPE 3 INT

0.081
(0.074)

−0.154
(0.169)
0.456
(0.264)
−0.545∗
(0.264)
0.332
(0.277)
−1.953
(1.815)
0.010∗
(0.005)
−0.139
(0.137)
0.034
(0.099)
0.047
(0.131)
1.027
(3.512)
0.709
(0.435)
0.600∗ ∗
(0.234)

−0.133
(0.159)
0.470
(0.269)
−0.558∗
(0.269)
0.321
(0.279)
−2.047
(1.823)
0.010∗
(0.005)
−0.069
(0.113)
0.010
(0.087)
0.045
(0.131)
0.978
(3.527)
0.714
(0.432)
0.600∗ ∗
(0.232)

0.055
(0.033)
−0.124
(0.164)
0.479∗
(0.258)
−0.532∗
(0.263)
0.317
(0.279)
−1.916
(1.867)
0.010∗
(0.005)
0.028
(0.082)
0.006
(0.093)
0.051
(0.131)
1.028
(3.563)
0.712
(0.427)
0.600∗ ∗
(0.232)

Year/month F.E.
Industry F.E.

Yes
No

Yes
No

Yes
No

Yes
Yes

Yes
Yes

Yes
Yes

Observations
R-squared

184,384
0.203

184,384
0.203

184,384
0.203

184,384
0.206

184,384
0.206

184,384
0.206

LOGSIZE
B/M
LEVERAGE
MOM
INVEST/A
ROE
HHI
LOGPPE
BETA
VOLAT
SALESGR
EPSGR

−0.229
(0.142)
0.732∗ ∗
(0.244)
−0.608∗ ∗ ∗
(0.195)
0.282
(0.292)
−0.041
(2.123)
0.010∗ ∗
(0.004)
−0.032
(0.074)
0.081
(0.065)
0.035
(0.148)
0.577
(3.296)
0.718
(0.414)
0.660∗ ∗
(0.235)

−0.230
(0.141)
0.732∗ ∗
(0.243)
−0.606∗ ∗ ∗
(0.195)
0.282
(0.292)
−0.037
(2.127)
0.010∗ ∗
(0.004)
−0.043
(0.072)
0.079
(0.064)
0.034
(0.148)
0.558
(3.297)
0.719
(0.413)
0.660∗ ∗
(0.236)

0.048
(0.075)
−0.229
(0.142)
0.732∗ ∗
(0.244)
−0.603∗ ∗ ∗
(0.196)
0.281
(0.291)
−0.022
(2.134)
0.010∗ ∗
(0.004)
−0.030
(0.067)
0.080
(0.066)
0.036
(0.148)
0.572
(3.300)
0.717
(0.413)
0.661∗ ∗
(0.235)

We ﬁnd again a positive and statistically signiﬁcant effect
of the growth in emissions on stock returns. Interestingly,
controlling for industry makes almost no difference when
it comes to the effect of the growth in emissions. To
allay any concern that our results may be driven by the
correlation between emissions and size, we provide additional robustness tests in which we estimate univariate
regression models with respective emission variables only,
and regressions with emissions and size only. The results,
reported in Table A.2 of the Online Appendix indicate that
size is an important control when one considers the level
of total emissions as a regressor but it is not as important
in the model with the growth rate of emissions. Note

Fig. 4. Because different emission variables have different
supports, we express the magnitudes in terms of unit standard deviation of each variable at each cross-section in
time, so that all plots of the cumulative effect show comparable numbers in terms of economic signiﬁcance. As can
be seen in the ﬁgure, there are large positive cumulative
returns for all measures of total emissions. The economic
magnitudes of the effect become even larger once we factor in differences in industry exposures.
We next estimate the same cross-sectional regression model (1) replacing the level of emissions (LOG
(Emissions TOT)) with the year-to-year growth in emissions
((Emissions)). The results are reported in Table 8, Panel B.
533

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 4. Carbon cumulative return premia: level effect.
Figures show the cumulative values of carbon premia estimated from the cross-sectional regressions of monthly returns on the natural logarithm of the
level of scope 1, scope 2, and scope 3 emissions. The regressions include the same set of controls as in Table 7. Panel A shows the plots for the model
without industry ﬁxed effects, while Panel B shows the results with industry-ﬁxed effects as additional control. The data source is Trucost and the sample
period is 2005–2017.

lated to the growth in emissions in Fig. 5. All measures of
emissions exhibit a steady rate of increase in the carbon
premium over time.
Finally, we estimate the cross-sectional regression
model in (1) for emission intensities. We report the results
in Table 8, Panel C. There is no signiﬁcant effect of emission intensity on returns for any of the three categories
of emissions, whether we control for industry or not. The
cumulative effect of emission intensity on the carbon pre-

also that ROE has a signiﬁcant positive effect on stock
returns under this speciﬁcation (it is insigniﬁcant in the
speciﬁcation with emission levels). We attribute this to
the fact that ﬁrms with high emission growth likely also
have higher earnings, which could result in higher stock
returns (to the extent that the higher earnings outcome is
unanticipated).
We also plot the time series of the cumulative values
of the unadjusted and industry-adjusted carbon premia re534

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 5. Carbon cumulative return premia: change effect.
Figures show the cumulative values of carbon premia estimated from the cross-sectional regressions of monthly returns on the percentage changes (year
over year) of scope 1, scope 2, and scope 3 emission levels. The regressions include the same set of controls as in Table 7. Panel A shows the plots for the
model without industry ﬁxed effects, while Panel B shows the results with industry-ﬁxed effects as additional control. The data source is Trucost and the
sample period is 2005–2017.

mium, presented in Fig. 6, is also quite weak, with the exception of scope 2 for which we observe a slightly positive
trend. Overall, these results reveal that there is a significant carbon premium with respect to the level of emissions, reﬂecting ﬁrms’ long-run risk exposure to carbon
emissions, and a premium with respect to the growth in
emissions, which capture the more short-term evolution of
ﬁrms’ risk exposure to future emissions.
One open question with our analysis above is that we
use carbon emission data in year t to explain monthly returns over the same year t. This could conceivably introduce a look-ahead bias. That is, under this speciﬁcation we
might unwittingly relate stock returns for some months
in year t to emission data that might not yet have been
available to investors. To address this question, we undertake the following robustness check. We relate monthly

stock returns with a lag of respectively 0 to 12 months
between the time when emissions are reported and the
month when returns are realized.
Another interpretation of the results with lagged returns is that investors have limited attention and do not
immediately absorb new information about carbon emissions at the ﬁrm level (Kacperczyk et al., 2016). In that
case, carbon emissions for year t will be gradually reﬂected
in returns over the year. An additional consideration is that
investors obtain information about carbon emissions from
multiple sources that are not all available at the same time.
For example, a lot of ﬁrms disclose their emissions ﬁrst
to the CDP, data which then is merged into and combined
with other sources by Trucost. Different information that is
likely to be highly correlated with other information (given
that all providers use the same data collection protocols)
535

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 6. Carbon cumulative return premia: intensity effect.
Figures show the cumulative values of carbon premia estimated from the cross-sectional regressions of monthly returns on the carbon intensity of scope 1,
scope 2, and scope 3 emissions. The regressions include the same set of controls as in Table 7. Panel A shows the plots for the model without industry ﬁxed
effects, while Panel B shows the results with industry-ﬁxed effects as additional control. The data source is Trucost and the sample period is 2005–2017.

becomes available at different times. This is another reason why carbon emissions are only gradually reﬂected in
stock returns.
We report the results in Table A.3. A remarkable pattern emerges from this analysis. Panel A1 reports the results for LOG (SCOPE 1 TOT). The coeﬃcient is statistically
signiﬁcant for the ﬁrst month (without industry ﬁxed effects), remains signiﬁcant at the 5% level until month 6
(with industry ﬁxed effects), and is insigniﬁcant thereafter.
Not surprisingly, it takes time for information about emis-

sions to be reﬂected in stock prices, but eventually (after
six months or so) this information appears to be fully absorbed. Essentially the same pattern is observed for the
level of scope 2 and scope 3 emissions (with a somewhat
faster (slower) integration of scope 2 (scope 3) emission
information into stock prices), as the results in Panels A2
and A3 show. The same pattern is present for the growth
in total emissions, as can be seen in panels B1, B2, and B3.
However, emission intensity is nearly always insigniﬁcant,
as we report in Panels C1, C2, and C3. The only visible ex536

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Fig. 7. Carbon intensity and institutional ownership: cumulative effect.
Figures show the cumulative values of the coeﬃcient of emission intensity estimated from the cross-sectional regressions of monthly ﬁrm-level institutional
ownership on scope 1, scope 2, and scope 3 emissions intensity. The regressions include the same set of controls as Table 11. Panel A shows the plots for
the full sample, Panel B shows the results for the sample of ﬁrms excluding salient industries (GIC 19, 20, 23), Panel C shows the results for the sample
of ﬁrms excluding the same salient industries and also ﬁrms that are added to the sample post 2015. The data source is Trucost and the sample period is
2005–2017.

537

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 9
Carbon emissions and stock returns net of earnings returns.
The sample period is 2005–2017. The dependent variable is RET net of daily return realized on the earnings announcement day. All variables are deﬁned
in Table 1. We report the results of the pooled regression with standard errors clustered at the ﬁrm and year level (in parentheses). All regressions include
year-month ﬁxed effects. In the regressions for columns 4 through 6, we additionally include industry-ﬁxed effects. Panel A reports the results for the
natural logarithm of total emissions; Panel B reports the results for the percentage change in carbon total emissions; Panel C reports the results for carbon
emission intensity. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
Variables
LOG (SCOPE 1 TOT)

(1)

(2)

(3)

0.044∗
(0.024)

(4)

0.088∗ ∗
(0.040)

LOG (SCOPE 2 TOT)

(5)

(6)

0.152∗ ∗ ∗
(0.031)
0.150∗ ∗ ∗
(0.044)
0.121∗ ∗
(0.047)

LOG (SCOPE 3 TOT)

0.279∗ ∗ ∗
(0.067)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

184,288
0.220

184,216
0.221

184,384
0.220

184,288
0.223

184,216
0.223

184,384
0.223

(4)

(5)

(6)

Panel B: Growth rate in total emissions
Variables

(1)

SCOPE 1

0.552∗ ∗ ∗
(0.137)

SCOPE 2

(2)

(3)

0.532∗ ∗ ∗
(0.131)
0.288∗ ∗
(0.111)

0.266∗ ∗
(0.108)

SCOPE 3

0.896∗ ∗
(0.313)

0.882∗ ∗
(0.316)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

153,051
0.235

152,955
0.236

153,123
0.235

153,051
0.239

152,955
0.239

153,123
0.239

(4)

(5)

(6)

Panel C: Emission intensity
Variables
SCOPE 1 INT

(1)

(2)

(3)

−0.008
(0.011)

SCOPE 2 INT

0.004
(0.007)
0.155
(0.124)

0.079
(0.068)

SCOPE 3 INT

0.050
(0.032)

0.029
(0.071)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

184,384
0.220

184,384
0.220

184,384
0.220

184,384
0.223

184,384
0.223

184,384
0.223

ception is scope 1 emission intensity, which is signiﬁcant
at the 5% level in month 6 in the model with industry ﬁxed
effects. We conclude from this analysis that our results are
not biased by a look-ahead effect.
Another possible explanation is that ﬁrms with higher
emissions have also been exposed to unexpected positive
value shocks. We explore this hypothesis by analyzing returns that strip out the effect of earnings surprises. Speciﬁcally, we subtract from the monthly stock returns the component that is realized on earnings announcement days
and re-estimate the regression model in (1) with the adjusted returns. We report the results in Table 9 for the
level of total emissions (Panel A), for the growth rate of
emissions (Panel B), and for emission intensity (Panel C).
We ﬁnd no signiﬁcant differential effect of earnings an-

nouncements on the carbon premium. Stocks with higher
levels and growth rates of emissions still have higher returns, and emission intensity is still insigniﬁcant.
3.3. Carbon premium and risk factors
Is the carbon premium linked to traditional risk factors?
To answer this question, we estimate the following timeseries regression model using monthly data:

a1,t = c0 + cFt + εt ,

(2)

where a1,t is the carbon return premium estimated from
the cross-sectional Fama-MacBeth regression in Eq. (1); F
is a set of factor-mimicking portfolios that includes MKTRF, HML, SMB, MOM, CMA, BAB, LIQ, NET ISSUANCE, and
538

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

IDIO VOL. These factors have been widely used in many
studies of asset prices. There are also economic reasons
to believe that they could be meaningfully related to our
carbon factor. Speciﬁcally, the ﬁrst ﬁve factors correspond
to the classic framework of Fama and French. In light of
our results reported above, ﬁrm-level emissions are related
to ﬁrm size and to ﬁrms’ growth opportunities; hence
we include both the SMB and HML factors. The investment factor, CMA, controls for any differences in investments across ﬁrms. The market and momentum factors
are standard controls in all time-series regressions. The
BAB factor controls for the possibility that high carbon risk
ﬁrms may be exposed to margin investments. The liquidity factor controls for possible differences in market liquidity among ﬁrms with different levels of carbon emissions,
which could arise if some ﬁrms are not as actively traded
as others due to ESG norm-based reasons. The net-issuance
factor controls for any variation in capital structure and
market timing by ﬁrm managers. Finally, the idiosyncratic
volatility factor controls for the possibility that the measure of risk we capture may be idiosyncratic in nature. We
calculate the standard errors of the coeﬃcients using the
Newey-West procedure with 12 lags to account for autocorrelation in error terms. Our coeﬃcient of interest is c0 ,
which measures the residual carbon premium, controlling
for other risk/style factors.
Panel A in Table 10 shows the results for the carbon
premium related to total emissions. In the odd columns,
we report the unconditional carbon premium as a benchmark. In the even columns, we report results from regressions that add various factors MKTRF, HML, SMB, MOM,
CMA, BAB, LIQ, NET ISSUANCE, and IDIO VOL. Comparing the
odd and even columns for the respective scope categories
of emissions, we ﬁnd that the carbon premium remains
statistically and economically signiﬁcant after we adjust for
differential factor exposures. However, the economic size
of the premium is about 10%−20% smaller in magnitude.
Overall, the regression intercepts from the cross-sectional
return regressions are both economically and statistically
signiﬁcant in the presence of various risk factors.
Panel B shows the results for the carbon premium related to the growth rate in total emissions. We ﬁnd again
that the set of standard risk factors cannot explain the average value of the carbon premium for any of the emissions categories. This time, however, the difference in magnitudes across speciﬁcations is much smaller. Panel C gives
the results for emission intensity. Whether unconditionally
or conditionally on the risk factors, we ﬁnd no signiﬁcant
carbon premium.
Overall, our time-series regression results show that the
carbon premium cannot be explained by known risk factors. This result reinforces the ﬁnding in Section 3.2 that
the level of carbon emissions contains independent information about the cross-section of average returns.

carbon emissions by institutional investors implementing a
sustainable investment policy. To the extent that some investors may shun companies with high carbon emissions,
risk sharing would be limited, and idiosyncratic risk could
be priced (e.g., Merton, 1987; Hong and Kacperczyk, 2009).
If the extent of such divestment is high, one would expect
to see signiﬁcant pricing effects.
We test this possibility by looking at the portfolio holdings of institutional investors. Formally, we estimate the
following pooled regression model:

IOi,t = d0 + d1 Emission j,t + d2Control s j,t + εi,t .

(3)

We consider ownership effects based on carbon intensity, the measure that is most aligned with explicit
mandates imposed by socially sensitive asset managers. In
the Online Appendix, Table A.4, we also present the results
for the less commonly used measures of total emissions
and growth in emissions. As these results conﬁrm, these
variables have no signiﬁcant impact on institutional investor portfolios. The vector of controls includes LOGSIZE,
PRINV, B/M, MOM, BETA, VOLAT, VOLUME, NASDAQ, and
SP500. All regressions include year/month ﬁxed effects.
Also, carbon emissions tend to vary geographically, due
to resource-driven ﬁrm locations. It is thus possible that
the geographic location may also interact with ownership
incentives. We test this idea by including in the ownership
regression state ﬁxed effects determined by the ﬁrm headquarters’ locations (in even columns). Our coeﬃcient of
interest is d1 , which measures the degree of avoidance of
ﬁrms with greater carbon emissions. We cluster standard
errors at the industry and year levels.
In Panel A of Table 11, we report the results for the aggregate institutional ownership measure. Columns 1 and 2
show the results for SCOPE 1 INT, respectively without and
with state ﬁxed effects. Both coeﬃcients are negative and
statistically signiﬁcant at the 5% level. The economic effect
of the divestment is relatively modest: a one-standarddeviation increase in SCOPE 1 leads to approximately a
1.3-percentage-point decrease in aggregate institutional
ownership, which is about 6.3% of the cross-sectional standard deviation in ownership. In contrast, the coeﬃcients
are statistically insigniﬁcant for SCOPE 2 INT and SCOPE 3
INT, indicating that the exclusionary screens institutional
investors apply in constructing their portfolios are entirely
based on SCOPE 1 INT.
The institutional investor world pools a number of different constituencies with possibly different investor pressures. We conjecture that certain institutions, such as insurance companies, investment advisers, or pension funds,
are more likely to face investor pressure, and thus they
avoid high-emission companies, as opposed to mutual
funds and hedge funds who are natural arbitrageurs. We
test this hypothesis formally by dividing the institutional
investors’ universe into six categories: banks, insurance
companies, investment companies, independent advisers,
pension funds, and hedge funds. For each category, we
obtain their stock-level institutional ownership and estimate the regression model in (3) for each of them separately. Panel B reports the results broken down by investor category. We observe a strong cross-sectional variation in the ownership patterns. Insurance companies, in-

3.4. The divestment hypothesis
An important possible explanation for the observed carbon premium could be under-diversiﬁcation resulting from
divestment and exclusionary screening of stocks with high
539

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

vestment advisers, and pension funds tend to hold less of
the high scope 1 emission companies. At the same time,
we observe positive, though weaker, ownership effects for
banks, investment companies, and hedge funds, consistent with these groups being natural arbitrageurs. The di-

vestment effects are economically large. A movement in
SCOPE 1 INT from one standard deviation below the mean
to one standard deviation above the mean, corresponding
to a spread between low and high-emission ﬁrms leads
to a reduction in ownership by 21%, 5%, and 4% of the

Table 10
Can the carbon premium be explained by risk factors?
The sample period is 2005–2017. The dependent variable is the monthly carbon premium estimated each period using a cross-sectional return regression.
All variables are deﬁned in Table 1. We report the results of the time-series regression with standard errors adjusted for autocorrelation with 12 lags using
Newey-West test (in parentheses). Panel A reports the results for the natural logarithm of contemporaneous total emissions; Panel B reports the results for
the percentage change in carbon emissions; Panel C reports the results for carbon emission intensity. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
LOG (SCOPE 1 TOT)
Variables

LOG (SCOPE 2 TOT)

(1)

(2)

(3)

(4)

0.058∗ ∗
(0.026)

−1.176
(0.714)
−6.020∗ ∗ ∗
(1.598)
−0.331
(0.887)
0.399
(0.559)
0.086∗ ∗ ∗
(0.028)
0.772
(0.824)
2.658∗ ∗ ∗
(0.768)
1.250
(1.015)
1.566∗ ∗
(0.723)
0.053∗ ∗
(0.023)

Constant
Industry adj.
Adj. R2
Observations

No
0.001
156

No
0.331
156

MKTRF
HML
SMB
MOM
CMA
BAB
LIQ
NET ISSUANCE
IDIO VOL

LOG (SCOPE 3 TOT)
(5)

(6)

0.085∗ ∗
(0.037)

3.298∗ ∗ ∗
(1.084)
−4.284∗ ∗
(1.759)
1.184
(2.858)
−3.853∗ ∗
(1.721)
0.053
(0.036)
0.303
(1.749)
0.816
(1.135)
−1.603
(2.207)
0.986
(1.332)
0.070∗ ∗ ∗
(0.027)

0.103∗ ∗ ∗
(0.035)

3.429∗ ∗
(1.357)
−6.444∗ ∗
(2.537)
1.539
(1.840)
−3.580∗ ∗ ∗
(1.281)
0.116∗ ∗ ∗
(0.036)
1.581
(1.681)
3.094∗ ∗ ∗
(1.016)
0.376
(2.352)
0.414
(1.319)
0.065∗ ∗
(0.027)

No
0.001
156

No
0.335
156

No
0.001
156

No
0.247
156

(3)

(4)

(5)

(6)

1.559∗ ∗ ∗
(0.237)

8.303
(8.965)
−17.483∗ ∗
(7.113)
−23.109∗
(13.738)
9.171
(8.912)
−0.468∗ ∗ ∗
(0.168)
11.861
(8.199)
9.512∗
(4.847)
15.976
(13.211)
16.111
(11.811)
1.424∗ ∗ ∗
(0.250)

No
0.001
144

No
0.290
144

Panel B: Growth rate in total emissions

SCOPE 1
Variables

SCOPE 2

SCOPE 3

(1)

(2)

Constant

0.640∗ ∗ ∗
(0.089)

4.847
(5.605)
−8.427∗ ∗
(3.853)
−15.284∗ ∗
(6.419)
3.223
(4.704)
−0.159∗
(0.087)
−8.919∗ ∗ ∗
(3.255)
0.808
(2.495)
4.702
(5.262)
3.851
(6.820)
0.643∗ ∗ ∗
(0.120)

0.435∗ ∗ ∗
(0.065)

−2.463
(2.516)
−5.897∗
(3.362)
−9.960∗
(5.667)
3.703
(2.727)
−0.153∗ ∗ ∗
(0.058)
2.396
(2.036)
−1.343
(2.342)
1.724
(4.821)
6.477∗
(3.474)
0.463∗ ∗ ∗
(0.063)

Industry adj.
Adj. R2
Observations

No
0.001
144

No
0.107
144

No
0.001
144

No
0.178
144

MKTRF
HML
SMB
MOM
CMA
BAB
LIQ
NET ISSUANCE
IDIO VOL

(continued on next page)

540

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 10
(continued)
Panel C: Emission intensity
SCOPE 1 INT
Variables

(2)

−0.006
(0.008)
No
0.001
156

−0.793∗ ∗ ∗
(0.177)
−0.927∗ ∗ ∗
(0.315)
−1.027∗ ∗
(0.519)
0.855∗ ∗ ∗
(0.214)
0.001
(0.007)
0.302
(0.391)
0.229
(0.297)
0.445
(0.304)
0.333
(0.293)
−0.004
(0.007)
No
0.413
156

MKTRF
HML
SMB
MOM
CMA
BAB
LIQ
NET ISSUANCE
IDIO VOL
Constant
Industry adj.
Adj. R2
Observations

SCOPE 2 INT

(1)

SCOPE 3 INT

(3)

(4)

0.121
(0.102)
No
0.001
156

1.790
(2.810)
−6.181
(4.340)
−9.486
(6.371)
−1.195
(2.970)
0.008
(0.101)
−4.055
(3.961)
0.372
(2.942)
−6.006
(5.742)
8.908∗ ∗ ∗
(3.069)
0.181∗
(0.097)
No
0.135
156

(5)

(6)

0.018
(0.027)
No
0.001
156

0.820
(0.880)
−4.063∗ ∗
(1.635)
−0.722
(1.214)
−0.449
(0.597)
0.039
(0.031)
−0.645
(0.915)
2.608∗ ∗ ∗
(0.800)
−0.139
(1.159)
0.424
(0.723)
0.012
(0.028)
No
0.104
156

are oil & gas (GIC = 2), utilities (GIC = 65–69), and
transportation (GIC = 19, 20, and 23). It is therefore natural to wonder whether our results are disproportionately
driven by these sectors, and whether our cross-sectional
carbon premium would become signiﬁcantly smaller if we
exclude these industries from our analysis.
In Table 12, we report the results for the subset of
ﬁrms, excluding the sectors mentioned above. Panel A reports the results for total emissions, Panel B for the growth
rate in emissions, and Panel C for emission intensity. Compared with the results in Table 8, we observe that, if
anything, excluding these salient sectors strengthens the
results on the ﬁrm-level carbon premium. These ﬁndings
imply that there is a coarser categorization of companies
by investors within the salient industries, where returns
are less sensitive to differences in emissions across ﬁrms.
In Table 13, we report the results on institutional
ownership when the salient high-CO2 industries are excluded. Consistent with Gabaix (2014), we ﬁnd that coarse
industry-level categorization drives our divestment results.
Indeed, there is no signiﬁcant divestment in the other industries. This is true in the aggregate as well as for the different categories of investors. It is as if investors decided
to reduce their exposure to certain industries by divesting from some ﬁrms but holding on to the best in class
in terms of scope 1 emission intensity in those industries.
In Table A.5 of the Online Appendix, we provide additional
evidence on this result with respect to levels and changes
in emissions. We do not observe any divestment based
on levels of emissions, but some divestment based on the

cross-sectional standard deviation of ownership for investment advisers, insurance companies, and pension funds,
respectively. In particular, given its large aggregate shares
of stock holdings, the effect through investment advisers
could lead to signiﬁcant pricing effects. In sharp contrast
to the results for SCOPE 1 INT, we observe that (with the
exception of banks loading up positively on SCOPE 3 INT)
all coeﬃcients for the different investor types are small
and statistically insigniﬁcant, which suggests that institutional investors do not seem to discriminate between
stocks with regard to their scope 2 and scope 3 emission
intensities.
Overall, institutional investors do signiﬁcantly divest
from ﬁrms associated with high SCOPE 1 INT. They do not
screen companies based on the level of their emissions (or
growth in emissions), even though the carbon premium
is associated with these variables. They prefer to screen
ﬁrms based on how eﬃciently they use fossil fuel energy
and do not seem to be concerned about reducing their exposure to the level of carbon emissions per se. We conclude from these ﬁndings that, unlike for “sin” stocks (as
shown by Hong and Kacperczyk, 2009), limited risk sharing caused by divestment cannot alone explain why we observe a return premium for companies with higher levels
(and growth) of emissions.
3.5. Coarse categorization
It is often pointed out that only a handful of industries produce the most signiﬁcant fraction of carbon emissions.14 The typical salient industries that are mentioned

production, 30% from transport, and 11% from industrial production
(see https://www.iea.org/media/statistics/Energy_and_CO2_Emissions_in_
the_OECD.pdf).

14

For instance, in a 2016 report, the International Energy Agency estimates that 39% of CO2 emissions come from electricity and heat
541

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 11
Carbon emissions and institutional ownership.
The sample period is 2005–2017. The dependent variable in Panel A is IO. The dependent variables in Panel B, Panel C, and Panel D are IO_BANK,
IO_INSURANCE, IO_INVESTCOS, IO_ADVISERS, IO_PENSIONS, and IO_HFS. Panels A-D present the result for contemporaneous measures of emission intensity.
Panel B presents the results for SCOPE 1, Panel C presents the results for SCOPE 2, and Panel D presents the results for SCOPE 3. All variables are deﬁned
in Table 1. We report the results of the pooled regression with standard errors clustered at the industry and year level (in parentheses). All regressions
include year-month ﬁxed effects. In Panel A, the regressions for columns 2, 4, and 6 additionally include state-ﬁxed effects. All regressions in Panels B-D
include state ﬁxed effects. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Aggregate ownership (Emission intensity)
Variables

(1)

(2)

(0.085)

(0.083)

SCOPE 2 INT

(3)

(4)

−0.383
(1.621)

−0.381
(1.610)

SCOPE 3 INT
LOGSIZE
PRINV
MOM
B/M
BETA
VOLAT
VOLUME
NASDAQ
SP500
Year/month F.E.
State ﬁxed effect
Observations
R-squared

(5)

(6)

−0.130
(0.581)
1.850
(1.706)
−37.200∗ ∗ ∗
(6.476)
−1.858∗
(0.856)
−1.216
(1.549)
9.695∗ ∗ ∗
(1.388)
4.532
(12.565)
−4.582∗ ∗
(1.626)
−1.292
(1.505)
1.510
(2.095)

2.078
(1.510)
−29.353∗ ∗ ∗
(5.614)
−1.453
(0.937)
−1.165
(1.423)
9.123∗ ∗ ∗
(1.508)
−7.617
(14.257)
−4.427∗ ∗ ∗
(1.400)
−1.159
(1.467)
2.559
(2.120)

1.847
(1.702)
−37.098∗ ∗ ∗
(6.448)
−1.792∗
(0.876)
−0.890
(1.602)
9.470∗ ∗ ∗
(1.459)
4.118
(12.827)
−4.612∗ ∗
(1.636)
−1.529
(1.700)
1.711
(2.093)

2.096
(1.484)
−29.333∗ ∗ ∗
(5.611)
−1.542
(0.895)
−1.533
(1.366)
9.332∗ ∗ ∗
(1.421)
−6.867
(13.550)
−4.379∗ ∗ ∗
(1.422)
−0.875
(1.431)
2.418
(2.122)

1.859
(1.678)
−37.161∗ ∗ ∗
(6.392)
−1.871∗ ∗
(0.823)
−1.205
(1.541)
9.705∗ ∗ ∗
(1.375)
4.770
(11.939)
−4.568∗ ∗
(1.650)
−1.255
(1.638)
1.508
(2.088)

0.094
(0.550)
2.104
(1.499)
−29.308∗ ∗ ∗
(5.640)
−1.544
(0.920)
−1.498
(1.339)
9.300∗ ∗ ∗
(1.430)
−7.095
(14.024)
−4.389∗ ∗ ∗
(1.378)
−0.751
(1.303)
2.394
(2.129)

Yes
No

Yes
Yes

Yes
No

Yes
Yes

Yes
No

Yes
Yes

170,701
0.121

160,406
0.166

170,701
0.118

160,406
0.162

170,701
0.118

160,406
0.162

Panel B: Disaggregate ownership
Variables
SCOPE 1 INT
SCOPE 2 INT
SCOPE 3 INT
Controls
Year/month F.E.
State ﬁxed effect
Observations

(1)
Banks

(2)
Insurance

(3)
Invest. Cos.

(4)
Advisers

(5)
Pensions

(6)
Hedge Funds

0.001∗ ∗
(0.000)
0.009
(0.006)
0.004∗
(0.002)

−0.011∗
(0.005)
−0.253
(0.144)
−0.021
(0.071)

0.026
(0.022)
−0.139
(0.406)
0.038
(0.115)

−0.258∗ ∗ ∗
(0.056)
−0.156
(0.992)
0.052
(0.409)

−0.009∗
(0.004)
0.049
(0.097)
0.028
(0.030)

0.033
(0.028)
0.108
(0.441)
−0.230
(0.151)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

160,406

160,406

160,406

160,406

160,406

160,406

growth of scope 2 and scope 3 emissions. This divestment
is particularly strong for pension funds.

2005 and estimate the carbon premium over this decade
and compare this premium to the one obtained over
our sample period, when similarly imputing back carbon
emissions based on the levels of emissions in 2017. Both
tests offer complementary views on the role of changing
investors’ attention. The ﬁrst test allows us to assess the
short-term impact of changing attention, while the second
test is more suited for the long-term changes in attention.
The Paris Agreement possibly raised both the awareness
of risks tied to carbon emissions and the prospect of regulatory interventions to limit carbon emissions. One could
therefore expect that the carbon risk premium would increase after 2015 following the Paris Agreement. We test

3.6. Investor awareness
The carbon premium in stock returns could also be
affected by the changing awareness of investors about carbon risk. In particular, one would expect that periods with
greater climate change awareness would have a higher
carbon premium. We evaluate this hypothesis in two ways.
First, we compare the estimated carbon premium before
and after the Paris Agreement in 2015. Second, we impute
carbon emissions in the 1990s based on their levels in
542

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 12
Carbon emissions and stock returns: excluding salient industries.
The sample period is 2005–2017. The dependent variable is RET. All variables are deﬁned in Table 1. We report the results of the pooled regression
with standard errors clustered at the industry level (in parentheses). The sample excludes companies in the oil and gas (gic=2), utilities (gic=65–69),
and transportation (gic=18, 19, 23) industries All regressions include year-month ﬁxed effects. In the regressions for columns 4–6, we additionally include
industry-ﬁxed effects. Panel A reports the results for the natural logarithm of total emissions; Panel B reports the results for the percentage change in
carbon emissions; Panel C reports the results for carbon emission intensity. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
Variables
LOG (SCOPE 1 TOT)

(1)

(2)

(3)

∗∗

(4)

0.072
(0.025)

(6)

0.177
(0.044)
∗∗

LOG (SCOPE 2 TOT)

(5)

∗∗∗

0.227∗ ∗ ∗
(0.057)

0.097
(0.039)
0.117∗ ∗
(0.048)

LOG (SCOPE 3 TOT)

0.324∗ ∗ ∗
(0.074)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

164,094
0.213

164,166
0.213

164,190
0.213

164,094
0.216

164,166
0.216

164,190
0.216

(4)

(5)

(6)

Panel B: Growth rate in total emissions
Variables

SCOPE 1

(1)

(2)

(3)

∗∗∗

∗∗∗

0.657
(0.151)

SCOPE 2

0.630
(0.142)
∗∗∗

0.438∗ ∗ ∗
(0.112)

0.463
(0.117)

SCOPE 3
Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

1.480∗ ∗ ∗
(0.321)
Yes
Yes
No

Observations
R-squared

135,522
0.230

135,570
0.230

135,594
0.230

(1)

(2)

Yes
Yes
Yes

Yes
Yes
Yes

1.456∗ ∗ ∗
(0.322)
Yes
Yes
Yes

135,522
0.233

135,570
0.233

135,594
0.233

(4)

(5)

(6)

Panel C: Emission intensity
Variables
SCOPE 1 INT

(3)

−0.012
(0.016)

0.004
(0.016)

SCOPE 2 INT

0.154
(0.102)

0.150
(0.112)

SCOPE 3 INT
Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

0.054
(0.035)
Yes
Yes
No

Observations
R-squared

164,190
0.213

164,190
0.213

164,190
0.213

this hypothesis by estimating the regression model in (1)
on the two sub-periods: 2005–2015, and 2016–2017.15 We
report the results in Table 14. We ﬁnd that indeed the premium associated with all three categories of emissions is
larger during the 2016–2017 subperiod, especially for scope
1 and scope 2. This could be seen as evidence that investors care more about carbon risk following the Paris
Agreement. However, an important caveat is that our sample increases after 2015, so that the difference in returns
pre and post Paris could be attributed to the new ﬁrms
that were added to our sample. We explore this possibility

Yes
Yes
Yes

Yes
Yes
Yes

0.160∗
(0.078)
Yes
Yes
Yes

164,190
0.216

164,190
0.216

164,190
0.216

in the Online Appendix and indeed ﬁnd in Table A.6 that
the increase in return premium is mostly due to the addition of the new ﬁrms. We ﬁnd that when we exclude the
new ﬁrms, the carbon premium becomes insigniﬁcant in
the two years following the Paris Agreement. The insignificance of the carbon premium does not necessarily mean
that carbon risk is no longer priced after the Paris Agreement in 2015; it could be due to a weak statistical power
given how noisy returns tend to be.
We further explore the cross-sectional variation of the
effect of the Paris Agreement by examining whether the
awareness that the Paris Agreement raised had a differential effect on the returns of ﬁrms with different exposures
to carbon policy risk. We measure the exposures using
our three measures of ﬁrm-level emissions. Our treatment

15
To enhance the statistical robustness of our results, we now cluster
standard errors at the ﬁrm and year-month levels.

543

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Journal of Financial Economics 142 (2021) 517–549

Table 13
Carbon emissions and institutional ownership: excluding salient industries.
The sample excludes companies in the oil & gas (gic=2), utilities (gic=65–69), and transportation (gic=18, 19, 23) industries. The sample period is
2005–2017. Panel A presents the results for aggregate ownership for contemporaneous carbon intensity measures, Panel B for disaggregated ownership.
All variables are deﬁned in Table 1. We report the results of the pooled regression with standard errors clustered at the industry and year level (in
parentheses). All regressions include year-month ﬁxed effects. In Panel A, the regressions for columns 2, 4, and 6, the regressions additionally include
state-ﬁxed effects. All regressions for Panel B results include state ﬁxed effects. ∗ ∗ ∗ 1%; ∗ ∗ 5%; ∗ 10% signiﬁcance.
Panel A: Aggregate ownership
Variables
SCOPE 1 INT

(1)

(2)

−0.015
(0.094)

−0.007
(0.104)

SCOPE 2 INT

(3)

(4)

−0.565
(1.968)

−0.525
(2.024)

SCOPE 3 INT
Controls
Year/month F.E.
State ﬁxed effect
Observations
R-squared

(5)

(6)

0.421
(0.538)

0.246
(0.568)

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
No

Yes
Yes
Yes

152,799
0.126

143,337
0.169

152,799
0.126

143,337
0.169

152,799
0.127

143,337
0.170

(1)

(2)

(3)

(4)

(5)

(6)

Banks
0.001∗
(0.000)
0.006
(0.006)
0.004∗
(0.002)

Insurance
−0.013
(0.012)
−0.298∗
(0.164)
−0.015
(0.077)

Invest. Cos.
−0.059
(0.041)
−0.320
(0.487)
0.063
(0.125)

Advisers
−0.060
(0.078)
−0.224
(1.252)
0.436
(0.376)

Pensions
0.009
(0.010)
0.051
(0.124)
0.041
(0.031)

Hedge Funds
0.114
(0.068)
0.261
(0.523)
−0.282
(0.170)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

143,337

143,337

143,337

143,337

143,337

143,337

Panel B: Disaggregate ownership

Variables
SCOPE 1 INT
SCOPE 2 INT
SCOPE 3 INT
Controls
Year/month F.E.
State ﬁxed effect
Observations

sample is the subset of ﬁrms in the largest quartile of the
distribution of ﬁrms sorted by the size of their carbon
emission as of the end of 2014. We match these ﬁrms
with a control group of ﬁrms with similar characteristics identiﬁed by two different techniques: the nearest
neighbor and the Mahalanobis distance. The matching
characteristics we use are the same as those we include in
our return regressions. We report the results based on the
nearest neighbor matching in Table 15. The results based
on Mahalanobis matching are qualitatively similar.
To validate the quality of our matching, in Table A.7,
we show, as an example, the balance test for the matched
samples of treatment and control ﬁrms based on the scope
1 emission levels. We ﬁnd that the two samples are not
very different from each other along many ﬁrm-level dimensions. Notable exceptions are market capitalization,
book-to-market ratio, return on equity, and property plant
and equipment for which the differences are statistically
signiﬁcant, though not economically large. Importantly, the
differences in market capitalization and PPE are expected
given that the treatment sample is based on the size of
ﬁrm emissions, which are strongly correlated with both
characteristics. Next, we compare the returns of ﬁrms in
the treatment and control groups in the one-year period
around the Paris Agreement of December 2015. Formally,
we estimate the following difference-in-differences regres-

sion model:

RE Ti,t = e0 + e1 T REAT ∗ AF T E R j,t + e2Control si,t
+ e3 μi + e4 μt + εi,t ,

(4)

where TREAT is a generic indicator variable taking the
value one for ﬁrms in the treatment sample and zero for
ﬁrms in the control sample, and AFTER is an indicator
variable equal to zero for the period 2015/05–2015/11 and
equal to one for the period 2015/12–2016/05. We also include ﬁrm and year-month ﬁxed effects in the regression.
We estimate this model separately for each scope and
emission measure. In the regressions, the sorts correspond
to each scope measure, which then separately identify each
individual treatment variable. Our coeﬃcient of interest is
e1 , which measures the differential effect of the change on
ﬁrms with high emissions and ﬁrms with low emissions.
In Panel A of Table A.7, we present the results for the
level of total emissions. We ﬁnd a strong and positive
effect on returns based on scope 1 emissions, but no
signiﬁcant effects for the other two scopes of emissions.
The effect is economically large, implying that the Paris
Agreement resulted in an average increase in returns of
more than 10.6% over the six-month period. In Panel B, we
show the results based on changes in emissions. While the
magnitudes of the results for scope 1 and scope 3 based
on the model with industry ﬁxed effects are fairly large

544

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 14
Carbon emissions and stock returns: sub-periods.
The sample period is 2005–2017. The dependent variable is RET. All variables are deﬁned in Table 1. We report the results of the pooled regression with
standard errors clustered at the ﬁrm and year/month level (in parentheses). All regressions include year-month ﬁxed effects and industry-ﬁxed effects. We
report the results for the natural logarithm of contemporaneous total emissions in Panel A; the results for the growth rate in ﬁrm emissions in Panel B;
and the results for emission intensity in Panel C. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
2005–2015
Variables
LOG (SCOPE 1 TOT)

(1)

2016–2017

(2)

(3)

0.127∗ ∗ ∗
(0.037)

(4)

0.127∗ ∗ ∗
(0.042)

LOG (SCOPE 2 TOT)

(5)

(6)

0.205∗ ∗
(0.075)
0.233∗ ∗
(0.087)
0.265∗ ∗ ∗
(0.086)

LOG (SCOPE 3 TOT)

0.340∗ ∗ ∗
(0.107)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

121,694
0.268

121,622
0.269

121,778
0.269

62,594
0.115

62,594
0.115

62,606
0.115

Panel B: Growth rate in total emissions
2005–2015
Variables

(1)

SCOPE 1

0.610∗ ∗ ∗
(0.161)

SCOPE 2

2016–2017

(2)

(3)

(4)

(5)

(6)

0.629∗ ∗
(0.249)
0.265∗ ∗ ∗
(0.097)

0.459∗ ∗
(0.193)

SCOPE 3

1.259∗ ∗ ∗
(0.355)

1.032∗ ∗
(0.436)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

108,888
0.278

108,804
0.279

108,948
0.279

44,163
0.089

44,151
0.089

44,175
0.089

Panel C: Emission intensity
2005–2015
Variables
SCOPE 1 INT

(1)

2016–2017

(2)

(3)

0.005
(0.007)

SCOPE 2 INT

(4)

(5)

(6)

0.010
(0.019)
0.091
(0.094)

0.117
(0.125)

SCOPE 3 INT

0.030
(0.091)

0.040
(0.087)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

121,778
0.268

121,778
0.268

121,778
0.268

62,606
0.114

62,606
0.114

62,606
0.114

(between 3.7% and 4.5%), they are statistically insigniﬁcant. In Panel C, we present the results based on carbon
intensity. Surprisingly, we ﬁnd a strong negative coeﬃcient
for scope 3 emissions. The effects for the other two scopes
are small and insigniﬁcant. Overall, these results on the
differential cross-sectional effects of the Paris Agreement
are broadly consistent with our other results but their
statistical signiﬁcance is relatively small. Again, one of
the reasons could be the relatively small statistical power
of the tests, as returns are generally quite noisy. Another
reason could be that the salient effects, such as Paris

Agreement, take a longer time to materialize in investors’
beliefs.
To offer a longer-term perspective on the changing investors’ beliefs, we exploit the fact that climate change
and carbon emissions were not yet salient issues in the
1990s. It is only in the last two decades, with the accumulation of CO2 in the atmosphere and the repeated recordbreaking temperatures, that climate change has turned into
a widespread concern. This naturally raises the question of
whether stock returns were already affected by corporate
carbon emissions in the 1990s. If information about ﬁrm545

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 15
Paris Agreement and stock returns: difference-in-differences estimation.
The dependent variable is RET. Our treatment sample is the subset of ﬁrms in the largest quartile of the distribution of ﬁrms sorted by the size of their
carbon emission as of the end of 2014. We match these ﬁrms with a control group of ﬁrms with similar characteristics identiﬁed by the nearest neighbor
method. The matching characteristics we use are the same as those in our return regressions. TREAT is a generic indicator variable taking the value one for
ﬁrms in the treatment sample and zero for ﬁrms in the control sample, and AFTER is an indicator variable equal to zero for the period 2015/05–2015/11
and equal to one for the period 2015/12–2016/05. We estimate this model separately for each scope and emission measure. In the regressions, the sorts
correspond to each scope measure which then separately identify each individual treatment variable. We also include ﬁrm and year-month ﬁxed effects
in the regression. All variables are deﬁned in Table 1. Standard errors (in parentheses) are clustered at the ﬁrm and year/month level. All regressions for
columns 4–6 include industry-ﬁxed effects. We report the results for the natural logarithm of contemporaneous total emissions in Panel A; the results for
the growth rate in ﬁrm emissions in Panel B; and the results for emission intensity in Panel C. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5% signiﬁcance; ∗ 10% signiﬁcance.
Panel A: Total emissions
Variables
TREAT1∗ AFTER

(1)

(2)

(3)

(4)

10.615∗ ∗ ∗
(1.175)

TREAT2∗ AFTER

(5)

(6)

10.705∗ ∗ ∗
(1.200)
−1.783
(5.861)

−1.681
(5.821)

∗

−8.917
(6.081)

TREAT3 AFTER

−8.782
(6.127)

Controls
Firm F.E.
Year/month F.E.
Industry F.E.

Yes
Yes
Yes
No

Yes
Yes
Yes
No

Yes
Yes
Yes
No

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Observations

5452

6604

6604

5452

6604

6324

(4)

(5)

(6)

Panel B: Growth rate in total emissions
Variables
TREAT1∗ AFTER

(1)

(2)

(3)

0.438
(4.426)

TREAT2∗ AFTER

4.425
(3.373)
−3.712
(3.541)

0.361
(2.592)

∗

TREAT3 AFTER
Controls
Firm F.E.
Year/month F.E.
Industry F.E.
Observations

0.396
(4.338)
Yes
Yes
Yes
No
5764

Yes
Yes
Yes
No
5706

Yes
Yes
Yes
No
5901

3.671
(3.927)
Yes
Yes
Yes
Yes
5764

Yes
Yes
Yes
Yes
5706

Yes
Yes
Yes
Yes
5901

(4)

(5)

(6)

Panel C: Emission intensity
Variables
TREAT1∗ AFTER

(1)

(2)

(3)

2.825
(5.876)

TREAT2∗ AFTER

2.855
(5.994)
−0.016
(5.344)

∗

0.021
(5.417)
∗∗∗

−7.749∗ ∗ ∗
(2.128)

−7.614
(2.070)

TREAT3 AFTER
Controls
Firm F.E.
Year/month F.E.

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Industry F.E.
Observations

No
4540

No
4853

No
4736

Yes
4540

Yes
4853

Yes
4736

level emissions was scarce and/or investors did not pay
attention to carbon risk, one would expect that the pricing effects we identify between 2005 and 2017 would be
much smaller back then. Given that our carbon emissions
data begins in 2005, we cannot evaluate this hypothesis directly. However, we can impute back the unobserved emissions data for each ﬁrm in the 1990s from the values we
observe later on. In other words, since emission levels are
highly autocorrelated and the cross-sectional variation in
emissions is stable over time (see Fig. 3), it seems reasonable, as a ﬁrst pass, to assume that the cross-sectional vari-

ation of emissions in the 1990s tracks closely that observed
in our data.
Speciﬁcally, we make the assumption that each ﬁrm
with stocks trading during the 1990s has an emission intensity equal to the ﬁrst oﬃcially reported value in the
2005–2017 period. We then collect the time-series information on each company’s revenues for the 1990–1999 period and impute the total value of emissions for each ﬁrm
by taking the product of the emission intensity coeﬃcient
and the ﬁrm’s time-varying sales. We thus obtain a panel
of imputed total corporate emissions for 1990–1999. We
546

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

Table 16
Carbon emissions and stock returns (imputed emissions).
The sample period is 1990–1999. The dependent variable is RET. All variables are deﬁned in Table 1. We report the results of the pooled regression with
standard errors clustered at the ﬁrm and year level (in parentheses). All regressions include year-month ﬁxed effects. In the regressions for columns 4
through 6, we additionally include industry-ﬁxed effects. The total level of emissions is imputed using the earliest observed level of emission intensity
for each ﬁrm for the period 2005–2017 (in Panel A) and for 1990–1999 (in Panel B) and scaling it by respective revenue values. ∗ ∗ ∗ 1% signiﬁcance; ∗ ∗ 5%
signiﬁcance; ∗ 10% signiﬁcance.
Panel A: (2005–2017)
Variables
LOG (SCOPE 1 TOT)

(1)

(2)

(3)

∗∗∗

(4)

0.097
(0.024)

(6)

0.291
(0.046)
∗∗∗

LOG (SCOPE 2 TOT)

(5)

∗∗∗

0.336∗ ∗ ∗
(0.065)

0.186
(0.043)

0.245∗ ∗ ∗
(0.043)

LOG (SCOPE 3 TOT)

0.585∗ ∗ ∗
(0.127)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

161,122
0.199

161,062
0.200

161,313
0.200

161,122
0.203

161,062
0.203

161,313
0.204

(1)

(2)

(4)

(5)

(6)

Panel B: (1990–1999)
Variables
LOG (SCOPE 1 TOT)

(3)

−0.037
(0.034)

LOG (SCOPE 2 TOT)

0.082
(0.078)
0.033
(0.045)

0.236
(0.134)

LOG (SCOPE 3 TOT)

0.318∗
(0.162)

0.005
(0.059)

Controls
Year/month F.E.
Industry F.E.

Yes
Yes
No

Yes
Yes
No

Yes
Yes
No

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

59,878
0.149

59,878
0.149

59,878
0.149

59,878
0.156

59,878
0.156

59,878
0.156

do exactly the same for emissions over our sample period.
That is, we take the emission intensity coeﬃcient for 2017
and impute back total emissions over the 2017–2005 sample period by multiplying this coeﬃcient with the ﬁrm’s
sales year by year. This latter imputation has the additional
beneﬁt of adding imputed emissions to our sample for all
the new ﬁrms added to our sample in 2016 and provides
another robustness check of our ﬁndings.
Next, we estimate the regression model in (1) using the
imputed emission values for both time periods and report
the results in Table 16. The process of imputation is not
suitable to obtain the variation in emission growth rates
since changes in emissions would vary one to one with
changes in revenues. We have therefore considered an alternative model in which we have ﬁxed the growth rates at
the ﬁrst available reported value and used it for all dates
in the 1990–1999 period. The results from this estimation,
available upon request, indicate that again the carbon premium is insigniﬁcant. The results in Panel A for the period
of our sample indicate that this imputation works and that
there is a signiﬁcant carbon premium associated with the
imputed level of emissions for all three scope categories.
Notably, the magnitude of the results is even stronger than
for the reported emission data. In contrast, the results in
Panel B for the 1990s indicate that there was no signiﬁcant
carbon premium over this period. This ﬁnding is consistent
with the quite plausible view that investors did not yet in-

ternalize carbon risk over this time period, but began to do
so in the last two decades, as reporting on climate change,
the effects of global warming, technological progress in renewable energy, and political action to curb carbon emissions intensiﬁed.
3.7. Robustness
We have explored a number of alternatives that provide
insight on the effects we document. We report the speciﬁc
tables in the Online Appendix. Below, we brieﬂy summarize the main ﬁndings in these tables.
First, we estimate the carbon premium excluding the
period of the ﬁnancial crisis, which we deﬁne as the period
from August 2007 to July 2009. The reason for excluding
the ﬁnancial crisis is that during this period the level of
emissions is artiﬁcially low because of the crisis and stock
returns are highly volatile. As a result, the relation between
stock returns and carbon emissions may be distorted by
the observations from the crisis period. Broadly, we ﬁnd
in Table A.8 that excluding the crisis period does not affect
our results in a major way.
Second, we explore the robustness of our results to the
alternative GIC 6-digit industry classiﬁcation. How much
does this alternative classiﬁcation affect changes in the estimates when industry ﬁxed effects are included? Again,
the results, reported in Table A.9, are broadly similar to
547

P. Bolton and M. Kacperczyk

Journal of Financial Economics 142 (2021) 517–549

those obtained under the ﬁner Trucost industry classiﬁcation. Third, we exclude the salient industries from our
analysis of the carbon premium pre and post Paris Agreement. The results are reported in Table A.10. If anything,
the increase in the size of the premium is more pronounced in the non-salient industries (with the exception,
possibly, of scope 3 emissions).
Fourth, we split the sample into two categories of ﬁrms,
those that report their emissions and those for which
emissions are estimated, and contrast how the carbon premium varies across the two categories. The results are reported in Table A.11. The coeﬃcient for the level of scope
1 emissions is slightly smaller and slightly less signiﬁcant
for ﬁrms that disclose their emissions than for ﬁrms that
do not. This is not entirely surprising given that, other
things equal, ﬁrms are more likely to disclose their emissions if their performance on that dimension is better. Alternatively, ﬁrms that go out of their way to disclose may
also have taken steps to reduce their emissions.16 Overall,
the carbon premium is larger and more signiﬁcant for the
ﬁrms that do not disclose their emissions for all categories
of emissions and for both emission levels and the growth
in emissions (with one exception for scope 3 emission
levels).
Fifth, we estimate the premium associated with the
level and intensity of all three categories of emissions
added up together. This is to facilitate comparison with
the results in Garvey et al. (2018) and In et al. (2019). As
one might expect based on our results for the disaggregated emissions, there is a highly signiﬁcant premium associated with the level of emissions, but not with emission
intensity. The results are presented in Table A.12. Sixth,
we also report how institutional investor portfolios are not
underweight companies with high levels of emissions (or
high growth rates) in Table A.4. If anything, institutional
investors load up on scope 2 and scope 3 emission levels. This could be a mechanical effect of their exclusionary
screening policies based on scope 1 emission intensity.
Seventh, we further report how institutional investor
portfolios are affected by the level of emissions in the
companies they hold outside the salient industries tied to
fossil fuels. We report the results in Table A.5. Interestingly, institutional investor portfolios load up on all three
scope emission levels in the non-salient industries. Again,
this is likely the consequence of institutional investors’ exclusionary screening in the salient industries. If they hold
less in these industries, they must hold more in other industries. Table A.13 also reports the exposure to emission
levels of institutional investors’ portfolios in the salient industries. Here we observe that their portfolios do not exhibit a signiﬁcant tilt away from or into ﬁrms with high
emission levels (with the exception of scope 3 emissions,
where they are signiﬁcantly underweight).

Eighth, we explore how sensitive the carbon premium
is to the addition of other ﬁrm characteristics besides size.
Table A.2 reports the results. It turns out that, controlling
for other ﬁrm characteristics such as B/M, PPE, leverage,
etc. matters. Without these controls, there is no signiﬁcant
premium associated with the level of emissions; however,
the growth in emissions remains highly signiﬁcant). Note
also that when we add industry ﬁxed effects, adding size
as a control or not affects results, with a signiﬁcant premium associated with the level of scope 1 emissions appearing only when we control for size.
Ninth, we check the robustness of our ownership regressions with respect to outliers using the natural logarithm transformation. The results, in Table A.14, indicate
that there is no signiﬁcant difference compared to our
baseline results in Table 8. Tenth, we estimate the carbon
premium on only the subset of ﬁrms for which we have
carbon emission data before 2016. The results are reported
in Table A.15. Although the size of the premium is a little
smaller, it is broadly in line with the one estimated on the
full sample.
4. Conclusion
How is climate change affecting stock returns? This is
a fundamental question for the burgeoning ﬁeld of climate
change and ﬁnance. It is also a fundamental question for
policy makers who are seeking to enlist investors in the
ﬁght against climate change. We address this question
by undertaking a cross-sectional stock returns analysis,
with carbon emissions as a ﬁrm characteristic, and ﬁnd
robust evidence that carbon emissions signiﬁcantly and
positively affect stock returns. There is a straightforward
link between climate change mitigation and the reduction
in carbon emissions. Whether through the production of
their goods and services, or through the use of their products, ﬁrms are differentially affected by policies to curb
carbon emissions and by renewable-energy technology
shocks. Our evidence suggests that investors are discerning
these cross-sectional differences and are pricing in carbon
risk. We also ﬁnd that the carbon premium cannot be explained through a sin stock divestment effect. Divestment
takes place in a coarse way in a few industries such as oil
and gas, utilities, and automobiles, and is entirely based
on scope 1 emission intensity screens. Notably, we ﬁnd
no carbon premium associated with emission intensity.
Moreover, outside the salient industries where all the
divestment takes place, we ﬁnd a robust, persistent, and
signiﬁcant carbon premium at the ﬁrm level for all three
categories of emission levels and growth rates.
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==> JFE06 - ESG rating uncertainty.txt <==
Journal of Financial Economics 145 (2022) 642–664

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Sustainable investing with ESG rating uncertaintyR
Doron Avramov a,∗, Si Cheng b, Abraham Lioui c, Andrea Tarelli d
a

Interdisciplinary Center (IDC), Herzliya, Israel
Chinese University of Hong Kong, Hong Kong
EDHEC Business School and EDHEC & Scientiﬁc Beta Research Chair, Nice, France
d
Catholic University of Milan, Milan, Italy
b
c

a r t i c l e

i n f o

Article history:
Received 9 February 2021
Revised 26 June 2021
Accepted 25 July 2021
Available online 17 September 2021
JEL classiﬁcation:
G11
G12
G24
M14
Q01

a b s t r a c t
This paper analyzes the asset pricing and portfolio implications of an important barrier
to sustainable investing: uncertainty about the corporate ESG proﬁle. In equilibrium, the
market premium increases and demand for stocks declines under ESG uncertainty. In addition, the CAPM alpha and effective beta both rise with ESG uncertainty and the negative ESG-alpha relation weakens. Employing the standard deviation of ESG ratings from six
major providers as a proxy for ESG uncertainty, we provide supporting evidence for the
model predictions. Our ﬁndings help reconcile the mixed evidence on the cross-sectional
ESG-alpha relation and suggest that ESG uncertainty affects the risk-return trade-off, social
impact, and economic welfare.
© 2021 Elsevier B.V. All rights reserved.

Keywords:
ESG
Rating uncertainty
Portfolio choice
Capital asset pricing model

1. Introduction
The global ﬁnancial market has experienced exponential growth in sustainable investing, an investment approach that considers environmental, social, and gover-

R
Bill Schwert was the editor for this article. We especially thank an
anonymous referee for insightful comments and suggestions. We also
thank Bill Schwert, Yakov Amihud, Marcin Kacperczyk, Lubos Pástor, Lasse
Heje Pedersen, Luke Taylor, seminar participants at Catholic University of
Milan, Ben-Gurion University of the Negev, Bar-Ilan University, Bocconi
University, and EDHEC Business School, and conference participants at the
2021 North American and European Summer Meetings of the Econometric Society for useful comments and discussions. We are solely responsible for any remaining errors.
∗
Corresponding author.
E-mail
addresses:
doron.avramov@idc.ac.il
(D.
Avramov),
sicheng@cuhk.edu.hk (S. Cheng), abraham.lioui@edhec.edu (A. Lioui),
andrea.tarelli@unicatt.it (A. Tarelli).

https://doi.org/10.1016/j.jﬁneco.2021.09.009
0304-405X/© 2021 Elsevier B.V. All rights reserved.

nance (ESG) factors in portfolio selection and management.
Since the launch of the United Nations Principles for Responsible Investment (PRI) in 2006, the number of signatories has grown from 734 in 2010 to 1384 in 2015 and 3038
in 2020, with total assets under management of US$21 trillion in 2010, US$59 trillion in 2015, and US$103 trillion in
2020.1 In line with the increasing concerns about global
warming, BlackRock CEO Larry Fink wrote in a recent annual letter that climate change will force businesses and
investors to shift their strategies, leading to a “fundamental
reshaping of ﬁnance” and “signiﬁcant reallocation of capital.”2
As the ESG objective is becoming a primary focus in asset management, the reallocation of capital has major im1

See, https://www.unpri.org/pri.
See,
https://www.blackrock.com/corporate/investor-relations/larryﬁnk- ceo- letter.
2

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

alpha relation is, hence, negative.4 Accounting for ESG uncertainty, the equilibrium alpha increases with ESG uncertainty and the ESG-alpha relation weakens.
We move on to empirically test the model implications
using U.S. common stocks from 2002 to 2019. We collect
ESG ratings from six major rating agencies, namely, Asset4 (Reﬁnitiv), MSCI KLD, MSCI IVA, Bloomberg, Sustainalytics, and RobecoSAM. We employ the average (standard
deviation of) ESG ratings across rating agencies to proxy
for the ﬁrm-level ESG rating (ESG uncertainty). Consistent
with existing studies, we conﬁrm that there are substantial variations across different rating providers, while the
average rating correlation is 0.48. The variations are quite
persistent throughout the entire sample period.
We ﬁrst examine how the ESG rating and uncertainty
affect investor demand. To better capture the demand from
ESG-sensitive investors, we consider three distinct types
of institutions: norm-constrained institutions, hedge funds,
and other institutions. Norm-constrained institutions, such
as pension funds as well as university and foundation endowments, are more likely to make socially responsible
investments compared to hedge funds or mutual funds
that are natural arbitrageurs (Hong and Kacperczyk, 2009).
We ﬁrst conﬁrm that norm-constrained institutions display
preferences for greener ﬁrms. Consistent with the model
prediction, we ﬁnd that in the presence of uncertainty
about the ESG proﬁle, ESG-sensitive investors lower their
demand for risky assets. For instance, among the high-ESGrating portfolios, norm-constrained institutions hold 22.8%
of the low-uncertainty stocks but only 18.1% of the highuncertainty stocks, indicating a 21% decline. The results are
particularly strong among high-ESG stocks, suggesting that
rating uncertainty matters the most for ESG-sensitive investors in their ESG investment. Notably, even with growing ESG awareness, their demand for green assets has continued to diminish with rating uncertainty over the past
decade. In addition, while hedge funds invest more in lowESG stocks, rating uncertainty plays a similar role in discouraging stock investment.
We next examine the cross-sectional implications of
ESG uncertainty. We ﬁrst sort stocks into quintile portfolios
based on their ESG uncertainty. Within each uncertainty
group, we further sort stocks into quintile portfolios according to their ESG ratings. We ﬁnd that the ESG rating
is negatively associated with future performance among
stocks with low ESG uncertainty, providing empirical support for the predictions of Pástor et al. (2021a), who rely
on deterministic ESG scores. For instance, brown stocks
outperform green stocks by 0.59% per month in raw return and 0.40% per month in CAPM-adjusted return. However, in the presence of ESG uncertainty, our model shows
that the ESG-alpha relation can be nonlinear and ambiguous. Indeed, we demonstrate empirically that the negative
return predictability of ESG ratings does not hold for the
remaining ﬁrms. The results are robust to adjusting returns
for alternative risk factors and controlling for ﬁrm characteristics in Fama and MacBeth (1973) regressions.

plications for portfolio decisions and asset pricing. However, ESG investors often confront a substantial amount of
uncertainty about the true ESG proﬁle of a ﬁrm. In the absence of a reliable measure of the true ESG performance,
any attempt to quantify it needs to cope with incomplete
and opaque ESG data and nonstructured methodologies. A
meaningful illustration of uncertainty about the ESG score
is the pronounced divergence across ESG rating agencies.3
While such uncertainty could be an important barrier to
sustainable investing, to date, little attention has been devoted to the role of ESG uncertainty in portfolio decisions
and asset pricing.
This paper aims to ﬁll this gap by analyzing the equilibrium implications of ESG uncertainty for both the aggregate market and the cross section. To pursue this
task, we consider brown-averse agents who extract nonpecuniary beneﬁts from holding green stocks, following
Pástor et al. (2021a). We ﬁrst study the aggregate market
through a mean-variance setup that consists of the market
portfolio and a riskless asset. Due to uncertainty about the
ESG proﬁle, equities are perceived to be riskier. In addition,
the demand for equities consists of two components: (1)
the usual demand when ESG preferences are muted and
(2) a demand for a pseudo-asset with a positive payoff for
a green market and a negative payoff for a brown market
as well as volatility that evolves from uncertainty about
the market ESG score. Aggregating these components, we
show that the overall demand for equities falls due to ESG
uncertainty, even when the market is green.
We then formulate the market premium in equilibrium.
While the higher risk due to ESG uncertainty essentially
commands a higher market premium, there is an offsetting
force when the market is green because ESG investors extract nonpecuniary beneﬁts from holding green stocks. The
ultimate implications of ESG preferences with uncertainty
for the market premium are thus inconclusive. When the
market is green neutral, however, the equity premium rises
with ESG uncertainty. For perspective, when ESG uncertainty is not accounted for and the market is green (green
neutral), the market risk does not change, the demand for
risky assets rises (does not change), and the market premium drops (does not change) relative to ESG indifference.
We further derive a CAPM representation in which both
alpha and the effective beta vary with ﬁrm-level ESG uncertainty. The effective beta differs from the CAPM beta
in the following way. While the CAPM beta is based on
the covariance and variance of actual returns, the effective beta reﬂects the notion that both the market and individual stock returns are augmented by a random ESGbased component, which is positive for a green asset and
negative otherwise. Thus, the effective beta is based on
the covariance and variance of ESG-adjusted returns. Regarding alpha, when ESG uncertainty is not accounted for,
the CAPM alpha exclusively reﬂects the willingness to hold
green stocks due to nonpecuniary beneﬁts, and the ESG-

3
Berg et al. (2020) report that the average correlation among six major rating providers is only 0.54. They also ﬁnd that, even when the categories of attributes considered for the evaluation of a ﬁrm’s ESG proﬁle
are ﬁxed, raters largely disagree on the measurement of these granular
characteristics.

4

643

See, e.g., Heinkel et al. (2001) and Pástor et al. (2021a).

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

Finally, we calibrate the model for plausible values of
market volatility and risk aversion. The investment universe consists of a riskless asset and the market portfolio. Our calibration considers two types of agents who observe the returns on investable assets. One type of agents
accounts for ESG preferences with uncertainty in assessing the risk-return proﬁle of the optimal portfolio, while
the other type is ESG indifferent. Accounting for ESG uncertainty signiﬁcantly reduces the demand for the market portfolio and the certainty equivalent rate of return of
ESG-sensitive agents. The calibration results reinforce the
notion that ESG uncertainty could negatively, and significantly, affect the risk-return trade-off, social impact, and
economic welfare.
This paper contributes to several strands of the literature. First, we explicitly account for uncertainty about the
ESG proﬁle in equilibrium asset pricing for both the aggregate market and the cross section. Prior work has focused on investors’ ESG preferences (e.g., Heinkel et al.,
2001; Pástor et al., 2021a), while our model predictions
and calibration results highlight the importance of considering ESG uncertainty when analyzing sustainable investing. Speciﬁcally, the perceived equity risk increases with
ESG uncertainty, while the demand for equity falls. ESG
uncertainty also affects the market premium in aggregate,
as well as the CAPM alpha and effective beta in the cross
section.
Second, we contribute to the growing literature on
the cross-sectional return predictability of the ESG proﬁle.
Prior studies show weak return predictability of the overall ESG rating (e.g., Pedersen et al., 2021) and mixed evidence based on different ESG proxies (e.g., Gompers et al.,
20 03; Hong and Kacperczyk, 20 09; Edmans, 2011; Bolton
and Kacperczyk, 2020). Our contribution is to propose that
ESG uncertainty could tilt the ESG-performance relation
and serve as a potential mechanism to explain the opposing ﬁndings. We show that ESG ratings are negatively
associated with future performance when there is little
uncertainty and that the ESG-performance relation could
be insigniﬁcant or positive when uncertainty increases.
Thus, the sin premium (Hong and Kacperczyk, 2009) and
carbon premium (Bolton and Kacperczyk, 2020) could
be attributed to the notion that sin stocks (i.e., companies involved in producing alcohol, tobacco, and gaming) and carbon emissions are clearly deﬁned and thus
subject to minimal uncertainty among investors. On the
other hand, other ESG proﬁles could be more challenging to measure or rely on nonstandardized information
and methodologies, thereby displaying more uncertainty
and mixed evidence on return predictability. A recent work
by Pástor et al. (2021b) further highlights the distinction
between ex ante expected returns and ex post realized
returns, and shows that U.S. green stocks outperformed
brown stocks during the last decade, due to unexpectedly strong increases in environmental concerns. While our
model is static in nature and formulates expected returns,
we also conﬁrm that our ﬁndings are stronger in the pre2011 period. This suggests that the equilibrium outcome
over longer horizons could be even stronger than the full
sample evidence we report, due to the unexpected outcomes realized over the last decade.

To the extent that ESG uncertainty will decrease with a
better understanding of a ﬁrm’s true ESG proﬁle, our work
enriches academic and policy discussions in that context.
Despite the rapid growth in the sustainable investing and
ESG data markets,5 the comparability of ESG information
remains a critical issue. Due to the lack of standards governing the reporting of ESG information, it is not a trivial task to compare the ESG data of two different companies (Amel-Zadeh and Serafeim, 2018). In addition, the
construction of ESG ratings is nonregulated, and methodologies can be opaque and proprietary, leading to substantial divergence across data providers (e.g., Mackintosh,
2018; Berg et al., 2020). Our ﬁndings imply that the lack
of consistency across ESG rating agencies makes sustainable investing riskier and hence reduces investor participation and potentially hurts economic welfare. This has important normative implications. For instance, it would be
useful for policy makers to establish a clear taxonomy of
ESG performance and uniﬁed disclosure standards for sustainability reporting. It would be especially instructive to
identify which investments are really green. Doing so could
mitigate ESG uncertainty, thus reducing the cost of equity
capital for green ﬁrms, leading to higher social impact.
Our study of the equilibrium implications of ESG uncertainty owes a debt to the innovative setup developed
by Pástor et al. (2021a), although our focus is different.
Pástor et al. (2021a) comprehensively analyze the equilibrium implications of sustainable investing and conduct an
analysis of welfare and social impact. They also account
for the possibility that ESG investors can disagree about a
ﬁrm’s ESG proﬁle and analyze cases in which the market
is green neutral or green. Notably, in their setup, the ESG
score is certain because investors are dogmatic about their
ESG perceptions and can observe each other’s perceived
ESG values. Relative to their important work, we study the
implications of uncertainty about the corporate ESG proﬁle. In particular, the investors in our model agree that the
ESG scores are uncertain and they also agree on the underlying distribution of the uncertain scores. The empirical
proxy for uncertainty is the dispersion, or disagreement,
across raters. We show that ESG uncertainty affects the equity premium, investor’s demand for risky assets, economic
welfare, and the alpha and beta components of stock returns.
The remainder of this paper is organized as follows.
Section 2 presents the model. Section 3 describes the
data and the main variables used. Section 4 empirically
examines how ESG ratings and uncertainty affect investor demand and cross-sectional return predictability.
Section 5 calibrates the model and explores its quantitative implications. The conclusion follows in Section 6.
2. ESG and market equilibrium
The theory section develops the economic setup. We
start with a single risky asset, i.e., the market portfolio,
and a riskless asset. We derive the optimal portfolio and
5
The estimated spending on ESG data was US$617 million in 2019
and could approach US$1 billion by 2021. See, http://www.opimas.com/
research/547/detail/.

644

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

discuss the implications of uncertainty about the ESG proﬁle for the market premium and welfare. The single-asset
setup is then extended to consider multiple risky assets.
We analyze the implications of ESG uncertainty for the demand of individual stocks, derive an asset pricing model
for the cross section of stock returns, and discuss incremental effects of ESG uncertainty on the alpha and beta
components of returns.

be positive. In particular, if the agent learns that the market ESG score is higher than previously thought (i.e., ˜g,M
is positive), the price that he would be willing to pay for
the market will be revised upward (positive ˜M ), while a
downward price revision applies for a score lower than
previously thought.7
Observe from Eq. (3) that the investment in the riskless
asset does not contribute to the portfolio’s ESG proﬁle, as
perceived by the agent. This is because the riskless asset
is implicitly assumed to be green neutral. As ESG scores
are ordinal in nature, the choice of considering the riskless
asset as a reference level does not imply loss of generality. In addition, to capture the ESG beneﬁts and costs from
investing in the market, we allow the market portfolio to
depart from green neutrality.
The agent picks x, attempting to maximize the expected
value of preferences in Eq. (3). The ﬁrst-order condition
suggests that the optimal portfolio in the presence of ESG
uncertainty is given by

2.1. One risky asset
Consider a single-period economy in which an optimizing agent trades at time 0 and liquidates the position at
time 1. Let r˜M denote the random rate of return on the
market portfolio in excess of the riskless rate, r f , and let
g˜M denote the true, but unobservable, ESG score of the
market portfolio.6 We model the excess market return and
the ESG score as

r˜M = μM + ˜M ,

(1)

g˜M = μg,M + ˜g,M ,

(2)

x∗ =

where E (r˜M ) = μM is the expected market excess return,
E (g˜M ) = μg,M is the expected value of the market ESG
score, and ˜M and ˜g,M are zero-mean residuals. We assume that the residuals obey a bivariate normal distribution with σM , σg,M , and ρg,M denoting the standard deviation of return, the standard deviation of ESG score, and the
correlation between residuals, respectively.
It is assumed that the agent knows the joint distribution of return and the ESG score as well as the underlying parameters. In the empirical analysis that follows, μg,M
and σg,M are proxied by the average and standard deviation of ESG ratings across six major data vendors, respectively. From an investor’s perspective, a higher σg,M indicates more disagreement among ESG raters and hence
more uncertainty about the true ESG proﬁle of the market.
Following Pástor et al. (2021a), we consider an optimizing agent who derives nonpecuniary beneﬁts from holding stocks based on their ESG characteristics. Moreover,
preferences are formulated through the exponential utility
(CARA) function





˜

˜ 1 , x = −e−AW1 −BW0 xg˜M ,
V W





1 μM + bμg,M

γ

2
σM,U

,

(4)

where b = AB , γ = AW0 stands for the relative risk aversion,
2
2 + b2 σ 2 + 2bσ σ
and σM,U
= σM
M g,M ρg,M is the variance of
g,M
return, as perceived by the agent. Henceforth, b is referred
to as brown aversion for brevity. The ex ante market vari2 , is no longer equal to σ 2 because, with ESG unance, σM,U
M
certainty, the risky asset is perceived to be a package of
two distinct securities. The ﬁrst delivers the market excess
return r˜M , while the second reﬂects exposure to ESG uncertainty and yields bg˜M . The latter component can be interpreted as investing b units in a pseudo-asset that pays g˜M
per unit. As b increases, i.e., when the ratio between brown
aversion and risk aversion increases, the ESG component
becomes more meaningful in investment decisions. A suf2
2 is that the brown aversion
ﬁcient condition for σM,U
≥ σM
and the correlation between market return and ESG score
are nonnegative (i.e., b ≥ 0 and ρg,M ≥ 0). As noted earlier,
these conditions are likely to be satisﬁed.
In what follows, we consider a positive market premium (i.e., μM > 0), which is plausible in the presence
of risk aversion. The brown-aversion assumption is sensible for ESG-perceptive investors. Additionally, to distill the
incremental effects of ESG uncertainty, we consider two
benchmark cases. In the ﬁrst, the agent is ESG indifferent, and in the second, preference for ESG is accounted for,
while the ESG proﬁle is known for certain. The latter case
is studied by Pástor et al. (2021a) in a multiple-security
setup.
Equation (4) presents the optimal stock position in the
presence of uncertainty about the ESG proﬁle. Stock investment is thus driven by the relative risk aversion, γ , and
the price of risk of the portfolio that yields r˜M + bg˜M . To
give perspective on the optimal equity demand, consider
the case that incorporates ESG preferences but excludes
uncertainty. Then, the perceived volatility of the stock return is still σM . Conforming to intuition, the demand for

(3)

˜ 1 = W0 1 + r f + xr˜M is the terminal wealth, W0 is
where W
the initial wealth, x is the fraction of wealth invested in
the risky asset, A stands for the agent’s absolute risk aversion, and B characterizes the nonpecuniary beneﬁts that
the agent derives from stock holdings. Positive (negative)
B indicates that the agent extracts beneﬁts from holding
green (brown) stocks. Hence, B can be interpreted as the
absolute brown aversion. In the following, we make the
sensible assumption of a nonnegative brown aversion (B ≥
0). Slightly departing from Pástor et al. (2021a), we formulate preferences for ESG to be wealth-dependent. Then, the
expression BW0 represents the relative brown aversion.
In the presence of brown aversion, the correlation between residuals in Eqs. (1) and (2), ρg,M , is assumed to
6
Consistent with static setups, we do not formulate intertemporal preferences; hence, the riskless rate is exogenously speciﬁed.

7

645

We thank the referee for suggesting this avenue.

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664
2
μUM = γ σM2 − bμg,M + γ (σM,U
− σM2 ).

stocks rises as b rises and the market is green. Essentially,
stocks are more attractive to a green-loving agent.
When ESG uncertainty is accounted for, however, this
intuition is no longer binding. To illustrate, consider two
limiting cases. In the ﬁrst, b grows with no bound. The investor then avoids equities, i.e., lim γ1
b→∞

μM +bμg,M
= 0. Simi2
σM,U

larly, when ESG uncertainty rises with no bound, the demand for stocks evaporates. Thus, both increasing brown
aversion and increasing uncertainty translate into increasing equity risk. In the presence of ESG uncertainty, a
brown-averse agent could substantially reduce stock investing, even when the market is green, on average.
Moving beyond the two limiting cases, we further examine portfolio tilts in the presence of ESG uncertainty. For
that purpose, we rewrite the optimal portfolio as

x∗ =

1 μM
1 μg,M
+ b
γ σM2 γ σM2
−

1 μM + bμg,M

γ

σM2


b2


2
σg,M
σM σg,M ρg,M
+
2
b
.
2
2
σM,U
σM,U

(5)

The ﬁrst term on the right-hand side of Eq. (5) describes the benchmark case of ESG indifference. Preferences for ESG generate the second and third terms. The
term γ1

bμg,M

σM2

corresponds to the second benchmark case

U

that SR
=
SRI

with ESG preferences when the ESG proﬁle is known for
certain. It suggests that as b rises, the demand for the risky
asset rises and portfolio tilt intensiﬁes. The third term
purely reﬂects the incremental effect of ESG uncertainty.
The ratio

tainty to the total, ex ante, market variance. Additionally,
in the presence of a positive correlation between market
return and the ESG proﬁle, the agent employs the market
portfolio to hedge against risk evolving from ESG uncerσ σ ρg,M
tainty, as captured by the hedge ratio M g,M
. Hence,
2

μNM − μIM = −bμg,M ,
 2

μUM − μIM = γ σM,U
− σM2 − bμg,M .

σM,U

μNM = γ σM2 − bμg,M ,

(7)

(9)
(10)

The no-uncertainty case is associated with a negative
ESG incremental premium when the market is green and
the agent is brown-averse, while the incremental premium
is zero when the market is green neutral. In addition,
it is evident from Eq. (10) that the market premium increases with ESG uncertainty. Collectively, with ESG uncertainty, the incremental premium is positive when the market is green neutral. Otherwise, with a green market and a
brown-averse agent, the sign of the incremental premium
is inconclusive due to the conﬂicting forces.
The single-security economy establishes a solid benchmark in which to comprehend the more complex multiasset setup to be developed later in the text. While the
cross-sectional ESG-alpha relation is negative when ESG
uncertainty is not accounted for, the single-security case
provides the ﬁrst clue that (1) the risk premium increases
with ESG uncertainty, and (2) the risk premium of a green
stock could exceed that of a brown stock in the presence
of ESG uncertainty. Taken together, the ESG-alpha relation
in the cross section can be subject to conﬂicting forces.
Up to this point, we have considered a single-agent
economy for ease of exposition. In what follows, to assess
the welfare implications of ESG uncertainty in the aggregate and to study the multi-asset economy, we extend the

the incremental effect of ESG uncertainty on stock investing (captured by the third term) is negative.8
In addition, when the market is green neutral (i.e.,
μg,M = 0) and when the ESG proﬁle is known for certain,
stock investing is unaffected relative to ESG indifference. In
contrast, when the market is green neutral and ESG uncertainty is accounted for, participation in the equity market
is discouraged, relative to both benchmark cases.
We now turn to analyzing the equilibrium implications
of ESG preferences with uncertainty. It is assumed that, in
equilibrium, the representative agent’s wealth is fully invested in the market portfolio. Thus, equalizing the optimal
stock allocation in Eq. (4) to 1 yields the market premium.
The market premiums for the cases of ESG indifference (I),
ESG preference with no uncertainty (N), and ESG preference with uncertainty (U) are given by

(6)

2
σM,U
bμ
− g,M
. The ﬁrst term is greater than one
σM2
γ σM2

and reﬂects the increase in perceived equity risk. The second captures the decrease in the market premium due to
the nonpecuniary beneﬁts from ESG investing.
In the presence of ESG preferences, the market risk premium thus incorporates an ESG incremental premium that
can be deﬁned as

2
σg,M
stands for the contribution of ESG uncer2
σM,U

μIM = γ σM2 ,

(8)

Retaining the assumptions of a green market and a
brown-averse agent, the market premium diminishes relative to Eq. (6), as captured by the second term in Eq. (7).
This is because, as implied by Pástor et al. (2021a) in
a multi-asset context, an agent who extracts nonpecuniary beneﬁts from holding green stocks is willing to compromise on a lower risk premium relative to an ESGindifferent agent. If the market is green neutral, the second
term disappears; hence, the equity premium is unchanged
even when ESG preferences are accounted for.
Further accounting for uncertainty in Eq. (8), there are
two conﬂicting forces. On the one hand, the agent extracts
nonpecuniary beneﬁts from holding the green market, a
force leading to diminished market premium. On the other
hand, the market is perceived to be riskier; thus, it commands a higher market premium, as formulated in the
third term of Eq. (8). The overall effect is inconclusive. If
the market is green neutral, the equity premium increases
relative to both benchmark cases due to the increasing risk
channel.
The same conﬂicting forces apply to the equilibrium
Sharpe ratio (the slope of the capital allocation line) when
accounting for ESG uncertainty, SRU , relative to ESG indifference, SRI . Given market return volatility, σM , it follows

8
In the case where μM + bμg,M is negative, the ESG uncertainty effect
on stock investing goes the opposite way. This requires the interaction of
extreme brown aversion along with an extreme brown market.

646

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

framework to account for multiple heterogeneous agents.
Thus, consider I agents indexed by i = 1, . . . , I, who differ
in their initial wealth Wi,0 , absolute risk aversion Ai , and
absolute brown aversion Bi . Market clearing requires that
I
Wi,0
∗
i=1 wi xi = 1, where wi = W0 is the fraction of agent i’s
initial wealth relative to aggregate wealth. With heterogeneous agents, the market premium equivalent to Eq. (8) is
given by
2
μUM = γM σM,U
− bM μg,M,U ,

where γM = I
bM =
I

−1
i=1 wi γi bi

γM−1

γM−1

−1 −2
i=1 wi γi σi,U
I

μg,M,U =

1

−1
i=1 wi γi

I

Proposition 1. The optimal portfolio strategy of investor i is
given by

X ∗i =

is the aggregate risk aversion,

is the perceived aggregate variance, and

bi →∞

μg,M is the perceived aggregate

ESG uncertainty grows with no bound for all stocks, economic agents avoid stocks altogether. Third, in intermediate cases, uncertainty about ESG proﬁles nonlinearly intervenes in formulating the optimal portfolio, through the inverse of i,U , and tends to reduce the demand for both
green and brown stocks.
To highlight the incremental implications of ESG uncertainty for portfolio selection, we rewrite Eq. (14) as

ESG score. Online Appendix A.1 provides details.
The changing cost of equity capital due to ESG preferences has implications for economic welfare and social impact. For instance, Pástor et al. (2021a) show that when the
market is green, the lower cost of equity capital could trigger increasing capital investment and social impact. In our
setup, a green representative ﬁrm would be harmed by the
higher cost of equity capital induced by ESG uncertainty,
which could trigger adverse effects on capital investment
and social impact. In the calibration experiment described
in Section 5.1, we comprehensively analyze the utility loss
attributable to ESG uncertainty. We also calibrate the market premium, as well as equity demand and welfare for
two types of agents: the ﬁrst is indifferent to ESG, while
the other is ESG perceptive and recognizes the uncertainty
about the sustainability proﬁle.

X ∗i =

We move on to formulate an economy populated with
I optimizing agents, N risky assets, and a riskless asset. We
aim to derive an asset pricing model for the cross section
of equity returns in the presence of ESG uncertainty, while
we also extend the analysis of portfolio selection.
We model the excess returns and ESG scores on N assets as

g˜ = μg + ˜ g ,

(13)


 1 

−1
μr + bi μg + i μr + bi μg ,
r
γi
γi

(15)

−1
λr −1 −1
λg −1 r μg
r μr
i
+
b

,
i
i
−1
−1
γi
γi
1  r μ r
1 r μg

(16)

1

 2




−1
where i = −−1
bi g + 2bi rg −1
IN + b2i g + 2bi rg −1
r
r
r
and IN stands for the N × N identity matrix.
The ﬁrst term of the optimal portfolio coincides with
the strategy in Pástor et al. (2021a) (Eq. (4)). The second
term is exclusively attributable to ESG preferences with
uncertainty about the sustainability proﬁle. Interestingly, in
the presence of heterogeneous agents, the ESG uncertainty
term precludes fund separation because the incremental
portfolio, evolving from ESG uncertainty, is agent speciﬁc.
In particular, consider the alternative decomposition of
the optimal portfolio:

2.2. A multi-asset economy

(12)

(14)

This portfolio strategy is the multi-asset version of
Eq. (4). It suggests that in the presence of ESG preferences, investors perceive asset excess returns to be the
sum of (1) N stock excess returns r˜ and (2) N returns on
pseudo-assets yielding bi g˜ . Several implications are in order. First, inﬁnitely brown-averse agents act as if they were
inﬁnitely risk averse, as, in the presence of ESG uncertainty, lim X ∗i = 0. Second, in another extreme case when

(11)

r˜ = μr + ˜ r ,



−1
i,U μr + bi μg ,

where i,U = r + b2i g + 2bi rg is the covariance matrix of
r˜ + bi g˜ .

2
is the aggregate brown aversion, σM,U
=

−1 −2
i=1 wi bi γi σi,U
−1 σ −2
bM γM
M,U

1

γi

X ∗i =

λr = 1 −1
r μr ,
−1
−1
2
bi r g + 2bi r rg .
where

λg = 1 −1
r μg ,

and

i = I N +

The decomposition shows that each optimizing agent
holds three portfolios: (1) a riskless asset, (2) the maximum Sharpe ratio portfolio in the risk-return space, and
(3) the maximum Sharpe ratio portfolio in the risk-ESG
space. Note that ESG uncertainty affects the demand for
risky assets through the N × N matrix i , which enters
both risky asset portfolios. If all agents have the same bi ,
then the matrix i is common to all agents and, therefore, a three-fund separation results. Otherwise, the two
risky portfolios are agent speciﬁc and, hence, fund separation does not apply in the setup of heterogeneous agents
with ESG uncertainty.

where μr is an N-vector of expected excess returns and μg
is an N-vector of expected ESG scores. The residuals from
both equations are assumed to obey a 2N-variate normal
distribution. The N × N covariance matrices of returns and
ESG ratings are denoted by r and g , respectively, while
rg is the N × N cross-covariance matrix between r˜ and g˜
with diagonal elements that are assumed to be positive.
Similar to Eq. (3), the agent maximizes an exponen


˜ i,1 , X i = −e−AiW˜ i,1 −BiWi,0 X i g˜ , where
tial utility function, V W


˜ i,1 = Wi,0 1 + r f + X  r˜ is the terminal wealth and X i is
W
i

the N-vector of portfolio weights per investor i.
Proposition 1 describes the optimal portfolio in the
presence of multiple risky assets. The proof is in Online
Appendix A.2.

2.3. CAPM with ESG uncertainty
The next two propositions illustrate the cross-sectional
asset pricing implications of ESG preferences, ﬁrst exclud647

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

ing and then accounting for ESG uncertainty. The proofs
are in Online Appendices A.3 and A.4.

Proposition 3. With ESG uncertainty, the equilibrium expected
excess returns of the risky assets are formulated as





μr = βμM + βe f f − β μM − bM μg,U − βe f f μg,M,U ,

Proposition 2. Excluding ESG uncertainty, the equilibrium expected excess returns of the risky assets are given by





μr = βμM − bM μg − βμg,M ,

(18)
2 −b μ
where μM = γM σM,U
M g,M,U is the equilibrium market

(17)

r X M
is the N-vector of the equilibrium CAPM
σM2
M,U X M
beta, βe f f =
is the N-vector of effective beta, and
2
σM,U

premium, β =

2 −b μ
where μM = γM σM
M g,M is the equilibrium market pre2 = X  X
mium, σM
r
M is the market return variance, β =
M

I

−1 −1
i=1 wi γi i,U
−1
i=1 wi γi

r X M
is the N-vector of market beta, μg,M = X M μg is the agσM2

−1
M,U =

gregate market greenness, X M = i=1 wi X i is the N-vector of
aggregate market positions in risky assets, γM is the aggregate risk aversion, and bM is the aggregate brown aversion.

trix of ESG-adjusted perceived asset returns. μg,U =

I

I

is the inverse of the covariance maB M μg
bM

is

the perceived aggregate ESG scores of individual assets, where

I
−1
−1
−1
BM = ( Ii=1 wi γi−1 −1
i=1 wi γi bi i,U , and μg,M,U =
i,U )

X M μg,U is the perceived aggregate market ESG score. Online
Appendix A.4 displays simpliﬁed expressions for asset pricing
with ESG uncertainty assuming homogeneous agents.

In the absence of ESG uncertainty, the expected excess
return expression in Eq. (17) is identical to that derived
by Pástor et al. (2021a), with the slight modiﬁcation that
the market can depart from green neutrality. Expected returns are affected by ESG preferences through (1) the modiﬁed market premium and (2) the alpha component that
stands for excess return unexplained by βμM . Alpha depends on the effective ESG score, i.e., the difference between the ﬁrm’s own ESG score and the market ESG score
multiplied by the stock’s beta. A numerical example is useful to illustrate. Assume a stock with β = 1.2 and μg,M = 2.
As long as the ESG score is below 2.4, the stock has a positive alpha even when the stock is green. The threshold
value 2.4 reﬂects zero alpha, while alpha turns negative if
the ESG score goes above the threshold. For instance, if the
ESG score is 3 (2), the effective ESG score is 0.6 (−0.4), and
alpha is negative (positive). Altogether, as long as the market is not green neutral, it is not the ﬁrm’s own ESG score
that dictates the sign and magnitude of alpha. Instead, it is
the effective ESG score.
In the presence of ESG preferences and certainty about
the ESG proﬁle, the beta measuring exposure to total market risk, β, coincides with the CAPM beta. This is because,
as noted earlier, the perceived return on any security is
equal to the sum of (1) the actual return and (2) the
pseudo-asset return that is proportional to the ESG score,
while the ESG score is nonrandom. Thus, in the absence of
ESG uncertainty, the covariance and variance terms used to
deﬁne beta are unchanged. With uncertainty, the ESG score
is random; hence, the resulting beta is no longer identical
to the standard CAPM beta.
As proposed by Pástor et al. (2021a), in the absence of
ESG uncertainty, equilibrium expected returns compensate
for exposure to (1) the market risk factor and (2) an ESGbased factor. When ESG uncertainty is in play, fund separation no longer results; thus, expected returns cannot be
represented through a multifactor model. Instead, we propose a CAPM-type representation, in which expected excess returns are expressed as the sum of two components:
the ﬁrst reﬂects the exposure to the market factor, while
the second is a nonzero alpha that stands for (1) nonpecuniary beneﬁts from ESG investing and (2) an additional
risk premium attributable to ESG uncertainty. The following proposition explains the equilibrium expected returns
with ESG uncertainty, which is the core of our analysis.

The expected excess return expression in Eq. (18) modiﬁes the no-uncertainty case in Eq. (17) by replacing the
market beta with the effective beta. Thus, it is the effective
beta that is priced in the cross section of equity returns. To
give perspective on the notion of effective beta, note that
the perceived return on an arbitrary asset still consists of
two components: (1) the actual return and (2) b times the
ESG score of that asset. Because ESG scores for the market
and individual assets are random, both the covariance and
variance terms, used to deﬁne beta, depart from the standard return-based counterparts. The effective beta is based
on ESG-adjusted returns. Collectively, expected excess returns on N risky assets are formulated as the sum of three
terms. The ﬁrst term reﬂects exposure to market risk, as in
the standard CAPM. Then, the difference between the effective beta and the market beta gives rise to the second
term. The third term accounts for the uncertainty-adjusted
effective ESG scores, analogously to Eq. (17) but using the
effective beta instead.
To provide further intuition on the beta-pricing speciﬁcation, we consider a simpliﬁed case in which agents
have homogeneous preferences (γ and b are equal across
agents). The effective beta can then be represented as

βe f f =

2
b2 σg,M
σM2
2bσrg,M
β
+
βg +
βrg ,
2
2
2
σM,U
σM,U
σM,U

where βg =

(19)

g X M
 X
2
2 + b2 σ 2 +
, βrg = σrg M , and σM,U
= σM
2
g,M
σg,M
rg,M

2bσrg,M . The effective beta is a weighted average of (1) the
CAPM beta, β; (2) the ESG uncertainty beta, βg ; and (3)
the ESG-return cross-covariance beta, βrg . The ESG uncertainty beta represents the comovement between the asset’s own ESG uncertainty and the market ESG uncertainty.
The cross-covariance beta represents the asset’s contribution to the aggregate ESG-return cross covariance, σrg,M .
The weights in Eq. (19) reﬂect the relative contributions to
the perceived market return variance, i.e., the actual return,
the ESG component, and the cross-covariance component.
The asset’s effective beta coincides with its market beta
if preferences for ESG are muted (b = 0) or if the market is
not subject to ESG uncertainty (σg,M = σrg,M = 0). To provide more intuition about the dependence of the effective
648

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

beta on ESG uncertainty, consider the case in which the
covariance matrix of ESG uncertainty, g , is diagonal with
elements σg,2 j ( j = 1, . . . , N), while rg is diagonal with elements σrg, j . The effective beta of asset j can be written as

βe f f , j =

b2 σ 2 X j σ 2
σM2
2bσrg,M X j σrg, j
β j + 2g,M 2 g, j +
.
2
2
σrg,M
σM,U
σM,U σg,M
σM,U

2.4. Demand and expected return in a two-asset economy
In particular, to gain additional intuition about the demand for multiple risky assets and their equilibrium expected returns, it is useful to consider a simpliﬁed economy consisting of two risky assets (along with a riskless
asset), both green and brown. In that economy, expected
excess returns are denoted by μr,green for the green stock
and μr,brown for the brown, the corresponding ESG scores
are μg > 0 and −μg , the variances of the ESG scores are
σg,2green and σg,2brown , and the correlation between the scores
is assumed to be zero. Asset returns are assumed to be uncorrelated with identical variance denoted by σr2 . Finally,
ESG scores are assumed to be positively correlated with
returns of the same asset, with covariances denoted by
σrg,green and σrg,brown . The expressions below follow from
Propositions 1 and 3. Online Appendix A.5 provides further
details.
The two-asset optimal strategy is formulated as

(20)

Given positive market weights in equilibrium, X j > 0,
the effective beta increases with the asset’s own ESG uncertainty, σg,2 j , and with the covariance between ﬁrm’s ESG
and return, σrg, j , while it does not depend on the mean
ESG score. Interestingly, as long as the aggregate ESG uncertainty is nonzero, a positive market beta asset with
certain ESG proﬁle (σg, j = σrg, j = 0) has an effective beta
σM2
2 β j , which is lower than the market beta
σM,U

equal to

β j . This is because the asset contributes to the aggre-

gate return-based risk, but not to the aggregate ESG uncertainty.
We next analyze alpha variation with ESG uncertainty in the case of homogeneous agents. Combining
Eqs. (18) and (19), we show in Online Appendix A.4 that
the CAPM alpha can be expressed as

α=

 2



 2bσrg,M 


βg − β +
βrg − β
2
σ
σM,U




× μM + bM μg,M − bM μg − βμg,M .
b σ

2
g,M
2
M,U

αj =

2
b σg,M



X j σg,2 j



− βj

2
2
σM,U
σg,M


× μM + bM μg,M

+

2bσrg,M



X j σrg, j

σrg,M


− bM μg, j − β j μg,M .
2
σM,U

μr,green + bi μg
1
,
γi σr2 + b2i σg,2green + 2bi σrg,green

(23)

Xi,∗brown =

μr,brown − bi μg
1
.
γi σr2 + b2i σg,2brown + 2bi σrg,brown

(24)

The optimal portfolio illustrates that, for ESG-sensitive
agents (bi > 0), demand falls with higher ESG uncertainty
but rises with higher ESG scores. The notion is that when
targeting an ESG level, uncertainty about the precise ESG
proﬁle should be accounted for. As in the single-asset
setup, the effect of ESG uncertainty is ampliﬁed by the
positive correlation between return and the ESG score. For
ESG-indifferent agents (bi = 0), the demand for green and
brown stocks is equal to the mean-variance demand when
ESG preferences are excluded.
We next formulate expected excess returns in equilibrium. We denote the fraction and brown aversion of ESGsensitive investors by wESG and bESG > 0, while the corresponding parameters of ESG-indifferent agents are wIND =
1 − wESG and bIND = 0. Assuming that all agents have the
same relative risk aversion γ , expected excess returns on
the green and brown assets are formulated as

(21)

The second term on the right-hand side of Eq. (21) is identical to that in Eq. (17) when ESG uncertainty is excluded.
The ﬁrst term represents the incremental effect of ESG uncertainty and is further analyzed below. For ease of interpretation, we assume again that g and rg are diagonal.
Then, it follows that

 2

Xi,∗green =



− βj
(22)

Given positive market portfolio weights in equilibrium,
X j > 0, the asset alpha increases with ESG uncertainty, σg,2 j .
Likewise, alpha increases with the asset ESG-return cross
covariance, σrg, j . Additionally, in the presence of aggregate
ESG uncertainty, a positive market beta asset with zero effective ESG score (μg, j − β j μg,M = 0) and with certain ESG
proﬁle has a negative alpha because its effective beta in
Eq. (20) is smaller than its market beta, as noted earlier.
We have shown that both alpha and the effective
beta rise with ESG uncertainty. The analysis is based on
the simplifying assumption of homogeneous brown-averse
agents. Relaxing the homogeneity assumption, alpha and
beta variations with ESG uncertainty appear quite complex
to analyze analytically. However, in the calibration developed in Section 5.2, we consider heterogeneous agents in
a two-asset economy (both brown and green) and show
that, even then, alpha and the effective beta do increase
with ESG uncertainty. Below, we provide further analytical
results for the two-asset economy for ease of interpretation.



σ2
σ
βgreen γ σM2 1 + b2ESG g,σgreen
+ 2bESG rg,σgreen
− wESG bESG μg
2
2
r
r


μr,green =
,
2
σ
σ
1 + (1 − wESG ) b2ESG g,σgreen
+ 2bESG rg,σgreen
2
2
r
r
(25)



σ2



σ
βbrown γ σM2 1 + b2ESG g,σbrown
+ 2bESG rg,σbrown
+ wESG bESG μg
2
2
r
r


μr,brown =
,
2
σg,brown
σrg,brown
2
1 + (1 − wESG ) bESG σ 2 + 2bESG σ 2
r
r

(26)
where βgreen and βbrown are the equilibrium CAPM betas.
In the limiting case where wESG = 0 or bESG = 0, all agents
are ESG indifferent and equilibrium expected excess re2 and β
2
turns boil down to βgreen γ σM
brown γ σM . In the opposite extreme, where wESG = 1, expected return diminishes
with the ESG score and rises with ESG uncertainty. The latter force can magnify the required return to the extent that
649

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

a green asset could, possibly, deliver higher return than a
brown asset.
Otherwise, in the intermediate case in which both ESGsensitive and ESG-indifferent agents populate the economy, the expected return difference between the brown
and the green assets diminishes with ESG uncertainty. To
see why, consider two assets with identical beta (βgreen =
βbrown = β ) and ESG uncertainty (σg,green = σg,brown = σg
and σrg,green = σrg,brown = σrg ). The expected return gap
(also the alpha gap) is given by

μr,brown − μr,green =

2wESG bESG μg



σ2

σ

1 + (1 − wESG ) b2ESG σg2 + 2bESG σrg2
r

2019. Our sample begins in 2002, as we require ESG ratings from at least two data vendors.

3.2. Main variables
We focus on the overall ESG rating from each data
provider, i.e., “ESG Combined Score” from Asset4, “ESG
Rating” from MSCI IVA, “ESG Disclosure Score” from
Bloomberg, “Sustainalytics Rank” from Sustainalytics, and
“RobecoSAM Total Sustainability Rank” from RobecoSAM.11
For MSCI KLD data, we construct an aggregate ESG rating
by summing all strengths and subtracting all concerns (e.g.,
Lins et al., 2017; Berg et al., 2020).
ESG rating agencies can differ in terms of their sample coverage and rating scale. In the Online Appendix, we
report the number of U.S. common stocks covered by each
data vendor over time. In addition, Asset4, Bloomberg, Sustainalytics, and RobecoSAM apply a scale from 0 to 100,
MSCI IVA uses a seven-tier rating scale from the best (AAA)
to the worst (CCC), and the MSCI KLD rating ranges from
−11 to +19 in our sample. Panel B further demonstrates
that requiring a common sample covered by all data vendors could signiﬁcantly reduce the sample size and shorten
the sample period. Therefore, we focus on pairwise ESG
rating disagreement and then average across all rater pairs.
Note that the ESG uncertainty in our model is motivated by
the fundamental diﬃculty and lack of consensus in measuring and interpreting the true ESG proﬁle. The disagreement among ESG raters is largely due to the lack of consensus on the scope and measurement of ESG performance
(Berg et al., 2020), and, as a result, investors cannot reliably observe the ﬁrm’s true ESG proﬁle and are exposed
to uncertainty in their sustainable investment. Hence, we
employ the disagreement among ESG raters as a proxy
for uncertainty about a ﬁrm’s ESG proﬁle and label such
disagreement ESG uncertainty to be consistent with the
model terminology.
Speciﬁcally, we obtain 14 rater pairs from the six data
providers.12 To achieve comparability across rating agencies, we proceed as follows. For each rater pair-year, we
sort all stocks covered by both raters according to the
original rating scale of the respective data provider and
calculate the percentile rank (normalized between zero
and one) for each stock-rater pair. Then, for each stock,
we compute the pairwise rating uncertainty as the sample standard deviation of the ranks provided by the two
raters in the pair. Speciﬁcally, let g j,t,A and g j,t,B denote
the ESG rank for stock j in year t from raters A and B, respectively. The pairwise rating uncertainty is calculated as

.

r

(27)
When all agents are ESG sensitive (wESG = 1 and bESG >
0), the difference in expected returns is independent of
ESG uncertainty and equal to 2bESG μg . In other words, controlling for ESG uncertainty and beta, the expected return
gap between the brown and the green assets is ﬁxed, reﬂecting the nonpecuniary beneﬁts from holding green assets. The return gap is nonexistent when either bESG = 0 or
wESG = 0, as all agents are ESG indifferent.
Otherwise, when ESG preferences are heterogeneous,
the expected return gap monotonically decreases with σg2
and σrg .9 This suggests that ESG uncertainty could weaken
the negative ESG-performance relation, as the asset demand of ESG-sensitive agents diminishes, which, in turn,
implies lower aggregate nonpecuniary beneﬁts from ESG
investing. In the limit, when ESG uncertainty grows with
no bound, the expected return gap between green and
brown assets approaches zero.
3. Data
3.1. Data sources
Our sample consists of all NYSE/AMEX/Nasdaq common
stocks with share codes 10 or 11; daily and monthly stock
data are obtained from the Center for Research in Security Prices (CRSP). We collect ESG rating data from six
data vendors, including Asset4 (Reﬁnitiv), MSCI KLD, MSCI
IVA, Bloomberg, Sustainalytics, and RobecoSAM. These data
providers represent the major players in the ESG rating
market, and their ratings are widely used by practitioners
as well as in a growing number of academic studies (e.g.,
Eccles and Stroehle, 2018; Berg et al., 2020; Gibson et al.,
2021).
Quarterly and annual ﬁnancial statement data come
from the Compustat database. Analyst forecast data come
from the Institutional Brokers’ Estimate System (I/B/E/S).
We also acquire quarterly institutional equity holdings
from the Thomson-Reuters Institutional Holdings (13F)
database.10 The full sample period ranges from 2002 to

agers with more than $100 million U.S. dollars under discretionary management. All holdings worth more than $20 0,0 0 0 U.S. dollars or 10,0 0 0
shares are reported in the database.
11
Although the Bloomberg ESG disclosure score measures the extent of
disclosure of ESG-related data by a company, it is positively associated
with ESG quality due to the largely voluntary nature of ESG disclosure
requirements (López-de-Silanes et al., 2020).
12
There are 14 (instead of 15) rater pairs because MSCI KLD data are
only available until 2015, while RobecoSAM data start in 2016, as shown
in the Online Appendix.

9
The no-uncertainty case leads to μr,brown − μr,green = 2bM μg , where
bM = wESG bESG .
10
The institutional ownership data come from money managers’ quarterly 13F ﬁlings with the U.S. Securities and Exchange Commission (SEC).
The database contains the positions of all institutional investment man-

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Journal of Financial Economics 145 (2022) 642–664

|g j,t,A√−g j,t,B | .13 For perspective, a company that is ranked by

equity returns, we construct 25 equity portfolios independently sorted on the ESG rating and rating uncertainty, and
report the average ESG rating, ESG rating uncertainty, and
monthly return.
In addition, we examine the market ESG uncertainty
throughout the sample period, as well as the time trend in
ESG uncertainty at the market and individual stock level.
While ESG data vendors do not provide a direct assessment for the market ESG proﬁle, we evaluate the valueweighted ESG score of the U.S. market by using ﬁrm-level
ratings per the different vendors. To preserve comparability across data vendors, we rely on the same pairwise measures used at the single-stock level.15 For each stock-rateryear, we average the percentile ranks corresponding to the
speciﬁc rater across all rater pairs covering this stock. For
each rater-year, we then value-weight ﬁrms’ ESG average
percentile ranks to obtain a rater-speciﬁc market-level ESG
rating. Finally, for each year, using all rater-speciﬁc market
ESG ratings, we evaluate the aggregate market-level ESG
rating and rating uncertainty as the pairwise mean and
standard deviation across raters.
In Fig. 1, the top graph plots the time-series of the market ESG ratings corresponding to each data vendor, and we
observe signiﬁcant dispersion across vendors. The bottom
graph shows the time-series of market ESG uncertainty, as
well as the equal- and value-weighted average of stocklevel ESG uncertainty. Stock-level ESG uncertainty, on average, diminishes during the ﬁrst half of the sample, as
the number of raters increases and their coverage widens.
Stock-level uncertainty remains stable in the second subperiod. Focusing on the market, as ESG ratings are correlated across ﬁrms and vendors, the evidence indicates
that the market ESG uncertainty does consistently prevail
throughout the entire sample period. This further supports
our intuition that ESG uncertainty could play an important
role in asset pricing.

2

two data providers at the 33rd and 59th percentiles would
generate a rating uncertainty of 0.18.
Finally, we compute the ﬁrm-level ESG rating uncertainty as the average pairwise rating uncertainty across
all rater pairs. Similarly, we compute the pairwise average rank and then average across all rater pairs to obtain
the ﬁrm-level ESG rating. Notably, the pairwise measure
has the advantage of maximizing the use of available rating information while still preserving comparability across
raters, despite the difference in their sample coverage.14
In addition, investors may not have access to all six data
vendors; therefore, the average pairwise rating level and
rating uncertainty provide an approximate assessment for
the perceived ESG proﬁle and rating uncertainty among investors. As a robustness check, we also consider alternative
proxies for ESG rating (ESGALL ) and rating uncertainty (ESG
UncertaintyALL ) using all ESG ratings from all raters (instead
of rater pairs), without requiring common coverage, at a
given point in time. The Online Appendix provides a detailed deﬁnition for each variable.
In the Online Appendix, we present the pairwise ESG
uncertainty and correlation of ESG ratings. The average correlation across all rater pairs is 0.48 and ranges from 0.25
to 0.71. MSCI KLD and MSCI IVA exhibit the lowest correlation and the highest rating disagreement with other raters,
and the average correlation is 0.38 and 0.34, respectively.
On the other hand, ratings provided by Sustainalytics and
RobecoSAM are more correlated with those of other raters,
and the average correlation is 0.59 and 0.56, respectively.
Our ﬁndings are largely consistent with the existing literature and echo the growing concerns related to the lack of
agreement across ESG rating agencies (e.g., Chatterji et al.,
2016; Amel-Zadeh and Serafeim, 2018; Berg et al., 2020;
Gibson et al., 2021).
The Online Appendix also reports the summary statistics for the stock-level data used in the paper. We report
the mean, standard deviation, median, and quantile distribution of the annual ESG rating and ESG rating uncertainty
and other stock characteristics. The average ESG rating is
0.46, and the ESG rating uncertainty is 0.18. In addition, to
study the demand for risky assets and the cross section of

13

4. Investor demand, stock return, and alpha
4.1. Investor demand
We start with the ﬁrst testable hypothesis generated from the model, i.e., investor demand for risky
assets increases with the ESG score, consistent with
Pástor et al. (2021a), while it diminishes with ESG
rating uncertainty, as formulated in Proposition 1 and
Eqs. (23) and (24). We rely on institutional ownership
as a proxy for the demand for ESG investment, as
Krueger et al. (2020) ﬁnd that institutional investors incorporate ESG when forming their portfolios. While retail investors could still have ESG preference, it is highly costly to
obtain and analyze the ESG information, especially when
even the most specialized raters do not agree, on average, on the ﬁrm ESG proﬁle. Due to the complex nature
of ESG investment, retail investors often rely on ﬁnancial
institutions to achieve their ESG target, thereby making in-

To illustrate, consider two ratings g1 and g2 . The pairwise rating un-

(g1 − g1 +2 g2 ) +(g2 − g1 +2 g2 ) = |g1√−g2 | .
2−1
2
2

certainty is given by

2

14
Unlike standard economic measures that are cardinal and can be directly compared, ESG scores are ordinal in nature. Thus, ESG scores are
sensitive to the sample coverage considered by the particular data vendor. As shown in the Online Appendix, ESG rating agencies differ in
their sample coverage; the stand-alone rank (e.g., 90th percentile) provided by one rater may not be directly comparable to the corresponding ﬁgure from another rater if, for instance, one rater covers, on average, more green ﬁrms. To ensure comparability across all vendors covering a stock, a proper experiment for determining the stock-level average ESG rating and rating uncertainty is to narrow down the focus to
only those stocks jointly covered by all vendors. This experiment, however, could considerably shrink the sample, which reﬂects the coverage
intersection of all vendors providing a rating for the stock. In contrast,
the pairwise measure requires only a minimal set of restrictions on common coverage and, hence, allows us to explore the richness in ESG ratings
provided by each data vendor, while still preserving comparability across
vendors.

15
In unreported analysis, we conﬁrm that the alternative measurement
method described above (ESGALL and ESG UncertaintyALL ) provides similar
results.

651

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

Fig. 1. Market ESG ratings and ESG uncertainty, and average stock-level ESG uncertainty.
The top graph shows the time-series of the market ESG score obtained from each data vendor, as well as the mean ESG rating across data vendors.
The bottom graph shows the time-series of market ESG uncertainty, as well as the equal- and value-weighted average of stock-level ESG uncertainty.
Section 3.2 provides details on the construction of the variables.

type 5), following Abarbanell et al. (2003).16 We follow
Hong and Kacperczyk (2009) to consider types 1, 2, and 5
as norm-constrained institutions. Our data on hedge fund
holdings are constructed by matching the 13F institutional
holdings with a manually collected list of the names of
hedge fund companies.17 The remaining institutions are
mostly mutual funds.18
The analysis proceeds as follows. At the end of each
year t, we independently sort stocks into quintile portfolios based on their ESG rating and rating uncertainty to
generate 25 (5 × 5) portfolios. The low- (high-) ESG-rating
and ESG-rating-uncertainty portfolios comprise the bottom
(top) quintile of stocks based on the ESG rating and ESG
rating uncertainty, respectively. For each type of institution, we compute the average institutional ownership in

stitutional ownership a reasonable source for investigating the ESG demand. For instance, Hartzmark and Sussman (2019) show that once Morningstar published sustainability ratings for mutual funds, there was a massive
shift of fund ﬂows from low-sustainability funds to highsustainability ones. A recent study on Robinhood investors
also shows that retail investors do not respond to ESG disclosures (Moss et al., 2020).
To test the model predictions based on ESG-sensitive
investors, it is also critical to account for the heterogeneity
among institutions, as they are subject to different social
norm pressures and apply various strategies to make socially responsible investments. For instance, pension funds,
universities, religious organizations, banks, and insurance
companies are more norm-constrained than hedge funds
or mutual funds that are natural arbitrageurs (Hong and
Kacperczyk, 2009). We therefore consider three distinct
groups: norm-constrained institutions, hedge funds, and
other institutions. Speciﬁcally, we disaggregate the 13F institutional holdings based on institution type, including
bank trust (type 1), insurance company (type 2), investment company (type 3), independent investment advisor
(which includes hedge funds, type 4), and others (including corporate/private pension funds, public pension funds,
university and foundation endowments, and miscellaneous,

16
We thank Brian Bushee for making the institutional investor classiﬁcation data available via his website: https://accounting-faculty.wharton.
upenn.edu/bushee/.
17
We thank Vikas Agarwal for generously sharing the data. A detailed
description of the hedge fund list is provided by Agarwal et al. (2013).
18
While mutual funds and hedge funds are increasingly subject to social
norm pressures, as shown by the rapid growth of ESG investment, some
could still prioritize ﬁnancial returns at the cost of lower ESG standard.
However, this remains an empirical question that we directly test.

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Journal of Financial Economics 145 (2022) 642–664

Table 1
Institutional ownership of portfolios sorted by ESG rating and uncertainty.
At the end of year t, stocks are independently sorted into quintiles according to their ESG ratings and ESG rating uncertainty to generate 25 (5 × 5)
portfolios. The low- (high)-ESG-rating and ESG-rating-uncertainty portfolios comprise the bottom (top) quintile of stocks based on the ESG rating and ESG
rating uncertainty, respectively. For each of the 25 portfolios, we compute the average institutional ownership in each quarter in year t + 1 and rebalance
the portfolios at the end of year t + 1. Panel A reports the time-series averages of quarterly institutional ownership of norm-constrained institutions for each
of the 25 portfolios and the average difference in institutional ownership between high- and low-ESG-rating portfolios (“HML-R”), as well as between highand low-ESG-rating-uncertainty portfolios (“HML-U”). Panels B and C report similar statistics for average ownership of hedge funds and other institutions,
respectively. The Online Appendix provides a detailed deﬁnition for each variable. Newey-West adjusted t-statistics are shown in parentheses. Numbers
with “∗ ”, “∗ ∗ ”, and “∗ ∗ ∗ ” are signiﬁcant at the 10%, 5%, and 1% levels, respectively.
Panel A: Norm-constrained institutions
ESG rating

ESG uncertainty
Low

2

3

4

High

HML-U

t-stat

All

Low
2
3
4
High

0.170
0.185
0.189
0.211
0.228

0.183
0.192
0.215
0.211
0.236

0.187
0.207
0.210
0.211
0.238

0.178
0.209
0.212
0.215
0.225

0.179
0.184
0.191
0.211
0.181

0.009
−0.001
0.002
0.000
−0.047∗ ∗ ∗

(0.80)
(−0.23)
(0.40)
(0.04)
(−2.73)

0.177
0.195
0.200
0.211
0.230

HML-R

0.058∗ ∗ ∗
(10.21)

0.053∗ ∗ ∗
(12.00)

0.050∗ ∗ ∗
(8.33)

0.047∗ ∗ ∗
(8.51)

0.002
(0.08)

2

3

4

High

0.053∗ ∗ ∗
(11.39)

Panel B: Hedge funds
ESG rating

ESG uncertainty
Low

Low
2
3
4
High

0.157
0.143
0.153
0.148
0.127

0.157
0.147
0.144
0.144
0.124

0.160
0.155
0.144
0.140
0.128

0.156
0.153
0.149
0.142
0.128

0.130
0.149
0.153
0.141
0.119

HML-R

−0.031∗ ∗ ∗
(−6.14)

−0.033∗ ∗ ∗
(−8.15)

−0.032∗ ∗ ∗
(−6.30)

−0.029∗ ∗ ∗
(−5.57)

−0.011
(−1.25)

2

3

4

High

HML-U
∗∗∗

−0.027
0.006
−0.000
−0.006∗
−0.008

t-stat

All

(−3.70)
(1.31)
(−0.08)
(−1.96)
(−1.33)

0.157
0.149
0.150
0.142
0.127
−0.030∗ ∗ ∗
(−8.06)

Panel C: Other institutions
ESG rating

ESG uncertainty
Low

Low
2
3
4
High

0.347
0.343
0.370
0.382
0.363

0.367
0.374
0.373
0.375
0.368

0.357
0.387
0.371
0.378
0.363

0.363
0.390
0.384
0.369
0.357

0.317
0.354
0.360
0.360
0.328

HML-R

0.016
(1.28)

0.001
(0.13)

0.006
(0.59)

−0.005
(−0.37)

0.011
(0.35)

each quarter in year t + 1 for each of the 25 portfolios,
and rebalance the portfolios at the end of year t + 1. We
report the time-series averages of quarterly institutional
ownership for each of the 25 portfolios and the average
difference in institutional ownership between high- and
low-ESG-rating portfolios (“HML-R”) as well as between
high- and low-ESG-rating-uncertainty portfolios (“HMLU”). The standard errors in all estimations are corrected
for autocorrelation using the Newey and West (1987)
method.
We tabulate the results in Table 1, with Panel A for
the stock ownership from norm-constrained institutions,
Panel B for hedge funds, and Panel C for other institutions. Several ﬁndings are worth noting in Panel A. First,
as expected, norm-constrained institutions are in favor of
greener ﬁrms. For instance, they hold 17.7% of the brown
stocks (i.e., stocks in the bottom ESG rating quintile), while

HML-U
∗∗

−0.030
0.010
−0.011
−0.022∗ ∗ ∗
−0.035

t-stat

All

(−2.57)
(1.43)
(−1.66)
(−3.25)
(−1.63)

0.356
0.370
0.368
0.370
0.363
0.007
(0.71)

they hold 23.0% of the green stocks (i.e., stocks in the top
ESG rating quintile), indicating a 30% increase. Second, the
ownership gap between low- and high-ESG-rating portfolios attenuates when rating uncertainty increases. When
uncertainty is low, green stocks display 5.8% higher institutional ownership than brown stocks, while the ownership gap declines to an insigniﬁcant 0.2% when rating uncertainty is high. More importantly, this pattern is due to
a decline in the demand for green ﬁrms when ESG uncertainty is high, and the difference is statistically significant and economically meaningful. For instance, among
the high-ESG-rating portfolios, norm-constrained institutions hold 22.8% of the low-uncertainty stocks but only
18.1% of the high-uncertainty stocks, indicating a 21% decline. In line with our working hypothesis, demand for
green ﬁrms from norm-constrained institutions diminishes
with ESG rating uncertainty, suggesting that rating uncer-

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D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

tainty matters the most for ESG-sensitive investors in their
ESG investment (i.e., green stocks).19
Panel B reports similar statistics for hedge fund ownership. Hedge funds invest more in brown stocks on average,
e.g., they hold 15.7% of the brown stocks, but only 12.7% of
the green stocks.20 The ownership gap between low- and
high-ESG-rating portfolios tends to diminish as ESG rating
uncertainty rises. For high-uncertainty stocks, the ownership gap is no longer signiﬁcant. Unlike the case of normconstrained institutions, rating uncertainty mostly affects
hedge fund holdings for brown stocks. For instance, within
the lowest rating group, hedge funds hold 15.7% of the
low-uncertainty stocks, but 13.0% of the high-uncertainty
stocks, indicating a 17% decline. Despite the different incentives for hedge funds to implement sustainable investment, we continue to ﬁnd that the rating uncertainty matters the most for investors in their preferred investment
universe.
As shown in Panel C, we do not ﬁnd strong ESG preference among other institutions. Conditional on the level
of ESG rating, we ﬁnd evidence that rating uncertainty reduces investor demand, while the economic magnitude is
much smaller than in the previously discussed subsamples
for norm-constrained institutions and hedge funds.
Overall, our ﬁndings support the model prediction that,
for ESG-sensitive investors, demand for risky assets increases with the ESG score but diminishes with ESG rating uncertainty. Our ﬁndings suggest that, although institutional investors are likely to be more sophisticated
and have access to privileged information, the uncertainty
about corporate ESG proﬁle remains an important barrier
to their investment. This could further limit their capacity to engage in ESG issues and improve the ESG performance of the ﬁrm (e.g., Dimson et al., 2015; Dyck et al.,
2019; Chen et al., 2020; Krueger et al., 2020). As more institutions seek sustainable investing, it is likely that ESGinduced investor demand will play an even more prominent role in the future.

We assess return predictability using a conventional
portfolio sort. In particular, at the end of each year t,
we sort stocks into quintile portfolios based on their ESG
rating uncertainty. Within each rating uncertainty group,
we further sort stocks into quintile portfolios according to
their ESG ratings and generate 25 (5 × 5) portfolios.21 The
low- (high)-ESG-rating and ESG-rating-uncertainty portfolios comprise the bottom (top) quintile of stocks based on
the ESG rating and ESG rating uncertainty, respectively. For
each of the 25 portfolios, we compute the value-weighted
return in each month in year t + 1 and rebalance the portfolios at the end of year t + 1. Within each quintile of portfolios sorted by ESG rating uncertainty, we also implement
the zero-cost trading strategy by taking long positions in
the bottom quintile of stocks (lowest ESG rating) and selling short stocks in the top quintile (highest ESG rating).
The payoff of the long-short investment strategy is computed as the low (bottom quintile) minus high (top quintile) portfolio return (“LMH-R”), indicating the return predictability of ESG ratings after controlling for rating uncertainty. We then report the time-series averages of monthly
returns for each of the 25 portfolios and the long-short
strategy.
In addition to raw portfolio returns, we report riskadjusted returns from (1) the CAPM, i.e., only adjusting
for the market factor (MKT, deﬁned as the excess return on the value-weighted CRSP market index over the
one-month Treasury bill rate); (2) the Fama-French-Carhart
four-factor model (FFC), consisting of the market factor
(MKT), the size factor (SMB, deﬁned as small minus big
ﬁrm return premium), the book-to-market factor (HML, deﬁned as the high book-to-market minus the low book-tomarket return premium) (Fama and French, 1993), and the
Carhart (1997) momentum factor (MOM, deﬁned as the
winner minus loser return premium); and (3) the FamaFrench six-factor model (FF6), consisting of the market factor (MKT), the size factor (SMB), the book-to-market factor (HML), the proﬁtability factor (RMW, deﬁned as the robust minus weak return premium), the investment factor
(CMA, deﬁned as the conservative minus aggressive return
premium), and the momentum factor (MOM) (Fama and
French, 2018).22 The standard errors in all estimations
are corrected for autocorrelation using the Newey and
West (1987) method.
Table 2 reports the results, with Panel A for raw return and Panel B for CAPM-adjusted return. In the interest
of brevity, we tabulate the results of FFC-adjusted return
and FF6-adjusted return in the Online Appendix and only
discuss the main ﬁndings in this subsection. Several ﬁndings are worth noting. First, the ESG rating is negatively associated with future performance among stocks with low
rating uncertainty, and the long-short portfolio return is
signiﬁcant at 0.59% per month. Brown stocks (i.e., stocks
in the bottom ESG rating quintile) continue to outperform

4.2. Cross-sectional return predictability
In line with Pástor et al. (2021a), our model predicts a negative relation between the ESG rating and
CAPM alpha when there is no uncertainty in ESG ratings (Proposition 2). Negative return predictability stems
from nonpecuniary beneﬁts from holding green stocks.
However, the ESG-alpha relation is less clear in the presence of ESG uncertainty due to the conﬂicting forces
of the uncertainty-adjusted stock beta and ESG rating
(Proposition 3).
19
Perhaps not surprisingly, investor demand is less affected among
other ESG rating groups, as such investment may not be entirely ESGdriven; hence, the rating uncertainty plays a lesser role in asset allocation
decisions.
20
Note that hedge funds can take both long and short positions, hence
the long position per se may not fully reﬂect the ESG preference of hedge
funds. Unreported results examine the net hedge fund ownership, deﬁned
as the hedge fund ownership minus the short interest, where the short
interest is computed as the number of shares held short scaled by the
number of shares outstanding (Jiao et al., 2016). The net hedge fund ownership is 10.3% for brown stocks and 9.4% for green stocks.

21
We employ a conditional sort to better control for rating uncertainty,
while an independent sort yields similar ﬁndings, as shown in the Online
Appendix.
22
We thank Kenneth French for making the common factor returns
available via his website: https://mba.tuck.dartmouth.edu/pages/faculty/
ken.french/data_library.html.

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Journal of Financial Economics 145 (2022) 642–664

Table 2
Performance of portfolios sorted by ESG rating and uncertainty.
At the end of year t, stocks are ﬁrst sorted into quintiles according to their ESG rating uncertainty. Within each ESG rating uncertainty group, stocks are
further sorted into quintiles according to their ESG ratings to generate 25 (5×5) portfolios. The low- (high)-ESG-rating and ESG-rating-uncertainty portfolios
comprise the bottom (top) quintile of stocks based on the ESG rating and ESG rating uncertainty, respectively. For each of the 25 portfolios, we compute
the value-weighted return in each month in year t + 1 and rebalance the portfolios at the end of year t + 1. Panel A reports the time-series averages of
monthly returns for each of the 25 portfolios, as well as for the investment strategy of going long (short) the low- (high)-ESG-rating stocks (“LMH-R”). The
column “All” reports similar statistics for portfolios sorted by ESG ratings only. The row “All” reports returns for portfolios sorted by ESG uncertainty only,
as well as the investment strategy of going long (short) the high (low) ESG-uncertainty stocks (“HML-U”). In Panel B, portfolio returns are further adjusted
by the CAPM. The Online Appendix provides a detailed deﬁnition for each variable. Newey-West adjusted t-statistics are shown in parentheses. Numbers
with “∗ ”, “∗ ∗ ”, and “∗ ∗ ∗ ” are signiﬁcant at the 10%, 5%, and 1% levels, respectively.

ESG rating

Panel A: Return

Panel B: CAPM-adjusted return

ESG uncertainty

ESG uncertainty

Low

2
∗∗∗

3
∗∗∗

4

High

∗∗

∗∗

All
∗∗

Low
∗∗

2

3

4

High

All

∗

1.235
(2.95)
1.245∗ ∗ ∗
(3.36)
1.096∗ ∗ ∗
(2.69)
0.730∗ ∗
(2.09)
0.642∗
(1.97)

1.113
(2.99)
1.026∗ ∗ ∗
(2.84)
0.965∗ ∗ ∗
(2.83)
0.695∗
(1.81)
0.842∗ ∗
(2.53)

0.767
(1.98)
1.093∗ ∗ ∗
(3.30)
1.050∗ ∗ ∗
(2.86)
1.105∗ ∗ ∗
(2.90)
0.855∗ ∗ ∗
(3.06)

0.875
(2.30)
1.043∗ ∗ ∗
(2.74)
1.104∗ ∗ ∗
(2.89)
1.019∗ ∗ ∗
(2.96)
1.184∗ ∗ ∗
(3.62)

0.760
(2.32)
1.095∗ ∗ ∗
(2.91)
0.949∗ ∗ ∗
(3.15)
0.990∗ ∗ ∗
(2.68)
0.854∗ ∗ ∗
(2.81)

0.923
(2.58)
0.963∗ ∗ ∗
(2.85)
1.021∗ ∗ ∗
(3.11)
1.017∗ ∗ ∗
(3.42)
0.805∗ ∗
(2.57)

0.168
(0.93)
0.187
(1.16)
0.040
(0.23)
−0.192
(−1.24)
−0.230∗
(−1.95)

0.064
(0.40)
0.076
(0.38)
−0.031
(−0.20)
−0.389∗ ∗ ∗
(−3.28)
−0.063
(−0.55)

−0.311
(−1.82)
0.115
(0.77)
0.002
(0.02)
0.108
(0.55)
−0.012
(−0.10)

−0.141
(−0.89)
0.042
(0.29)
0.064
(0.46)
0.040
(0.34)
0.245∗
(1.83)

−0.101
(−0.58)
0.151
(0.77)
0.079
(0.42)
0.006
(0.03)
−0.001
(−0.01)

−0.101
(−0.84)
−0.008
(−0.07)
0.053
(0.64)
0.095
(1.32)
−0.095
(−1.49)

LMH-R

0.594∗ ∗ ∗
(2.72)

0.271
(1.30)

−0.088
(−0.39)

−0.309
(−1.43)

−0.094
(−0.42)

0.118
(0.78)

0.398∗
(1.86)

0.128
(0.58)

−0.299
(−1.25)

−0.387∗
(−1.75)

−0.100
(−0.42)

−0.006
(−0.04)

ESG rating

ESG uncertainty
3

4

High

HML-U

3

4

High

HML-U

0.071
(0.84)

0.226∗
(1.67)

Low
2
3
4
High

Low
All

ESG uncertainty

2
∗∗

0.753
(2.31)

∗∗∗

0.875
(2.61)

∗∗∗

0.935
(3.07)

∗∗∗

1.083
(3.28)

∗∗∗

0.940
(3.29)

0.187
(1.40)

green stocks (i.e., stocks in the top ESG rating quintile) after adjusting for risk exposures, i.e., the long-short portfolio yields a CAPM-adjusted (FFC-adjusted, FF6-adjusted)
return of 0.40% (0.46%, 0.50%) per month.23
Second, the negative return predictability of ESG ratings
no longer holds for the remaining ﬁrms and even turns
positive in some cases. For perspective, we also consider
a univariate portfolio sort based on ESG ratings and report
similar statistics in the column titled “All”. The ESG rating
does not predict stock returns for the full sample, which is
consistent with the existing literature showing weak return
predictability of the overall ESG rating (e.g., Pedersen et al.,
2021) and mixed evidence based on different ESG proxies
(e.g., Gompers et al., 2003; Hong and Kacperczyk, 2009;
Edmans, 2011; Bolton and Kacperczyk, 2020). The empirical evidence that ESG uncertainty can nontrivially interact
with the ESG-performance relation is also consistent with
Eq. (27). Our results further highlight the importance of
rating uncertainty, as it not only affects investor demand
but also has meaningful asset pricing implications, i.e., the
negative ESG-alpha relation only exists among stocks with
low rating uncertainty. The lack of consistency across ESG
rating agencies could be a barrier for investors who have to

Low

2
∗∗

−0.155
(−1.98)

−0.090
(−1.20)

−0.003
(−0.04)

∗

0.120
(1.72)

balance information on ESG scores and uncertainty when
making portfolio decisions.
Additionally, we consider a univariate portfolio sort
based on ESG uncertainty and report the results in the
row titled “All”. Consistent with the model prediction, as
shown in Eq. (22), we ﬁnd that when ESG uncertainty is in
play at the market level, stocks with low ESG uncertainty
carry a negative and statistically signiﬁcant CAPM alpha of
−0.16% per month. As shown in the Online Appendix, the
result is also robust to FFC-adjusted and FF6-adjusted returns. Furthermore, returns are increasing in ESG uncertainty, although the patterns are not always monotonic.
For instance, the high-minus-low ESG uncertainty portfolio (“HML-U”) shows a monthly CAPM alpha of 0.23% that
is statistically signiﬁcant at the 10% level, supporting the
model prediction that CAPM alpha increases with ESG rating uncertainty. Collectively, our ﬁndings support the prediction that brown stocks outperform green stocks only
in the absence of rating uncertainty, and ESG uncertainty
could tilt this relation via conﬂicting forces, as illustrated
in Proposition 3.
As a robustness check, we perform regression analysis to further control for other ﬁrm characteristics. Specifically, we estimate the following monthly Fama and MacBeth (1973) regression:

Perfi,m = α0 + β1 ESGi,m−1 + β2 ESGi,m−1

23

As our model is derived in market equilibrium, it is based on one
market factor. However, the economic magnitude and statistical signiﬁcance in FFC-adjusted and FF6-adjusted returns reinforce our conclusion
that accounting for rating uncertainty can be useful even for investors
who use multiple investment factors in their portfolio decisions.

× Low ESG Uncertaintyi,m−1

+ β3 Low ESG Uncertaintyi,m−1


+ β4 M i,m−1 + ei,m ,
655

(28)

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

Table 3
ESG rating, uncertainty, and stock returns.
This table presents the results of the following monthly Fama-MacBeth regressions, as well as their corresponding Newey-West adjusted t-statistics:


Perfi,m = α0 + β1 ESGi,m−1 + β2 ESGi,m−1 × Low ESG Uncertaintyi,m−1 + β3 Low ESG Uncertaintyi,m−1 + β4 M i,m−1 + ei,m ,
where Perfi,m refers to the excess return (models 1 to 4) or CAPM-adjusted return (models 5 to 8) of stock i in month m, ESGi,m−1 refers to the ESG rating,
Low ESG Uncertaintyi,m−1 refers to a dummy variable that takes a value of one if the ESG rating uncertainty is in the bottom quintile across all stocks in
that month and zero otherwise. The vector M stacks all other control variables, including the Log(Size), Log(BM), 6M Momentum, Log(Illiquidity), Gross
Proﬁtability, Corporate Investment, Leverage, Log(Analyst Coverage) and Analyst Dispersion. The Online Appendix provides a detailed deﬁnition for each
variable. Numbers with “∗ ”, “∗ ∗ ”, and “∗ ∗ ∗ ” are signiﬁcant at the 10%, 5%, and 1% levels, respectively.
Stock returns regressed on lagged ESG rating and uncertainty
Excess return

ESG

CAPM-adjusted return

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Model 7

Model 8

0.002
(0.01)

0.098
(0.65)

0.139
(0.91)

−0.044
(−0.59)
−0.021
(−0.19)
0.275
(0.50)

0.591
(0.46)

0.111
(0.77)
0.019
(0.18)
0.105
(0.20)
0.103∗ ∗
(2.17)
0.355∗
(1.83)
−0.005
(−0.08)
−0.034
(−0.73)
−0.174
(−1.40)
−0.828∗ ∗ ∗
(−4.37)
−0.555
(−0.31)

0.162
(0.77)
−0.254∗ ∗
(−2.26)
0.125∗ ∗
(2.20)
−0.044
(−0.60)
−0.024
(−0.21)
0.276
(0.50)

2.281∗
(1.70)

0.199
(1.03)
−0.223∗
(−1.75)
0.109
(1.38)
−0.038
(−0.29)
0.008
(0.12)
0.194
(0.42)
0.056
(1.03)
0.180
(1.00)
0.037
(0.50)
−0.037
(−0.79)
−0.019
(−0.14)
−0.539∗ ∗ ∗
(−2.71)
1.775
(1.09)

0.042
(0.23)

−0.100
(−1.28)
0.001
(0.01)
0.336
(0.70)

0.062
(0.33)
−0.163∗
(−1.91)
0.114∗
(1.86)
−0.101
(−1.30)
−0.001
(−0.01)
0.335
(0.69)

0.533
(0.42)

0.301
(1.65)
−0.312∗ ∗
(−2.36)
0.114
(1.61)
0.111
(0.77)
0.017
(0.17)
0.111
(0.21)
0.103∗ ∗
(2.15)
0.359∗
(1.85)
−0.007
(−0.09)
−0.034
(−0.73)
−0.175
(−1.41)
−0.831∗ ∗ ∗
(−4.37)
−0.614
(−0.34)

283,671
0.048

254,873
0.082

272,728
0.043

245,451
0.076

272,728
0.045

245,451
0.078

ESG × Low ESG Uncertainty
Low ESG Uncertainty

Constant

2.309∗
(1.71)

−0.036
(−0.27)
0.009
(0.14)
0.188
(0.40)
0.056
(1.00)
0.178
(0.99)
0.037
(0.49)
−0.037
(−0.78)
−0.019
(−0.15)
−0.536∗ ∗ ∗
(−2.67)
1.800
(1.09)

Obs
R-squared

283,671
0.045

254,873
0.080

Log(Size)
Log(BM)
6M Momentum
Log(Illiquidity)
Gross Proﬁtability
Corporate Investment
Leverage
Log(Analyst Coverage)
Analyst Dispersion

where Perfi,m refers to the excess return or CAPM-adjusted
return of stock i in month m, ESGi,m−1 refers to the ESG
rating, and Low ESG Uncertaintyi,m−1 refers to a dummy
variable that takes a value of one if the ESG rating uncertainty is in the bottom quintile across all stocks in that
month and zero otherwise. The vector M stacks all other
control variables, including Log(Size), Log(BM), 6M Momentum, Log(Illiquidity), Gross Proﬁtability, Corporate Investment,
Leverage, Log(Analyst Coverage) and Analyst Dispersion. The
parameter of interest is β2 . Since the model predicts a negative ESG-performance relation when there is no rating uncertainty, we should see a negative value of β2 . The Online Appendix provides a detailed deﬁnition for each variable. We also report Newey and West (1987) adjusted tstatistics.
We tabulate the results in Table 3, with models 1 to
4 for excess return and models 5 to 8 for CAPM-adjusted
return. As expected, the ESG rating does not predict stock
returns for the full sample. More importantly, the ESG rating is negatively associated with future stock performance
when rating uncertainty is low. This relation is signiﬁcant across all regression speciﬁcations after controlling for
other potential sources of uncertainty about corporate ESG

proﬁles and disagreement on ﬁrm fundamentals, such as
analyst dispersion. Overall, we conﬁrm the early results in
the portfolio sort and provide supporting evidence for the
ESG-augmented CAPM after considering rating uncertainty.
4.3. Additional analysis and robustness checks
Given the rapid growth in sustainable investing during
the last decade (e.g., GSIA, 2018; PRI, 2020), we next assess how our ﬁndings evolve over time. We then conduct
robustness checks using an alternative proxy for ESG rating
and rating uncertainty.
We divide the full sample into two subperiods, 2003–
2010 and 2011–2019, and repeat the main analysis. Table 4
has a layout similar to Table 1, in which Panels A, B, and
C show the results for the norm-constrained institutions,
hedge funds, and other institutions, respectively. First,
we conﬁrm that for all three types of institutions, their
preference for green assets increases over time. Normconstrained institutions hold 12.3% of the brown stocks
(i.e., stocks in the bottom ESG rating quintile), while they
hold 19.2% of the green stocks (i.e., stocks in the top ESG
rating quintile) in the post-2011 period, indicating a 56%
656

Panel A: Norm-constrained institutions

ESG rating

2003–2010

2011–2019

ESG uncertainty

ESG uncertainty

Low

2

3

4

High

Low
2
3
4
High

0.234
0.238
0.244
0.262
0.271

0.239
0.250
0.266
0.265
0.276

0.243
0.257
0.258
0.255
0.277

0.238
0.264
0.261
0.265
0.266

0.262
0.244
0.251
0.269
0.195

HML-R

0.037∗ ∗ ∗
(8.58)

0.037∗ ∗ ∗
(8.60)

0.034∗ ∗ ∗
(6.87)

0.028∗ ∗ ∗
(7.18)

−0.067
(−1.67)

HML-U

t-stat

0.028
0.006
0.007
0.007
−0.076∗ ∗

(1.59)
(0.76)
(1.09)
(1.06)
(−2.41)

All

Low

2

3

4

High

0.239
0.251
0.255
0.264
0.273

0.114
0.138
0.140
0.166
0.190

0.133
0.140
0.170
0.163
0.200

0.137
0.163
0.168
0.172
0.203

0.124
0.160
0.167
0.170
0.188

0.105
0.130
0.137
0.161
0.168

0.034∗ ∗ ∗
(12.78)

0.076∗ ∗ ∗
(20.93)

0.068∗ ∗ ∗
(21.05)

0.065∗ ∗ ∗
(10.36)

0.064∗ ∗ ∗
(11.55)

0.063∗ ∗ ∗
(10.22)

3

4

High

HML-U
∗

−0.009
−0.008
−0.003
−0.006
−0.022∗ ∗ ∗

t-stat

All

(−1.77)
(−0.93)
(−0.54)
(−0.71)
(−3.65)

0.123
0.145
0.151
0.165
0.192

D. Avramov, S. Cheng, A. Lioui et al.

Table 4
Institutional ownership of portfolios sorted by ESG rating and uncertainty: Subsample analysis.
At the end of year t, stocks are independently sorted into quintiles according to their ESG ratings and ESG rating uncertainty to generate 25 (5 × 5) portfolios. The low- (high)-ESG-rating and ESG-ratinguncertainty portfolios comprise the bottom (top) quintile of stocks based on the ESG rating and ESG rating uncertainty, respectively. For each of the 25 portfolios, we compute the average institutional ownership
in each quarter in year t + 1 and rebalance the portfolios at the end of year t + 1. Panel A reports the time-series averages of quarterly institutional ownership of norm-constrained institutions for each of the 25
portfolios and the average difference in institutional ownership between high- and low-ESG-rating portfolios (“HML-R”), as well as between high- and low-ESG-rating-uncertainty portfolios (“HML-U”). We divide
the full sample into two subperiods, and report results for 2003–2010 on the left and 2011–2019 on the right. Panels B and C report similar statistics for average ownership of hedge funds and other institutions,
respectively. The Online Appendix provides a detailed deﬁnition for each variable. Newey-West adjusted t-statistics are shown in parentheses. Numbers with “∗ ”, “∗ ∗ ”, and “∗ ∗ ∗ ” are signiﬁcant at the 10%, 5%, and
1% levels, respectively.

0.069∗ ∗ ∗
(27.30)

Panel B: Hedge funds
657

ESG rating

2003–2010

2011–2019

ESG uncertainty

ESG uncertainty

Low

2

3

4

High

0.133
0.117
0.104
0.093
0.086

0.128
0.110
0.114
0.100
0.087

0.136
0.115
0.115
0.096
0.090

0.127
0.119
0.106
0.098
0.088

0.097
0.107
0.112
0.091
0.066

HML-R

−0.047∗ ∗ ∗
(−13.62)

−0.041∗ ∗ ∗
(−7.73)

−0.046∗ ∗ ∗
(−7.20)

−0.039∗ ∗ ∗
(−13.21)

−0.030∗ ∗ ∗
(−3.17)

t-stat
∗∗∗

−0.036
−0.010∗ ∗
0.008
−0.002
−0.020∗ ∗

(−4.08)
(−2.39)
(1.55)
(−1.00)
(−2.13)

All

Low

2

0.129
0.113
0.111
0.096
0.088

0.179
0.166
0.196
0.196
0.163

0.183
0.180
0.170
0.183
0.157

0.181
0.189
0.169
0.178
0.162

0.182
0.184
0.187
0.182
0.162

0.160
0.187
0.189
0.186
0.166

−0.042∗ ∗ ∗
(−12.15)

−0.016∗ ∗ ∗
(−3.08)

−0.026∗ ∗ ∗
(−6.31)

−0.019∗ ∗ ∗
(−5.25)

−0.019∗ ∗
(−2.56)

0.006
(0.51)

3

4

High

HML-U
∗

−0.019
0.021∗ ∗ ∗
−0.008
−0.009∗
0.003

t-stat

All

(−1.97)
(5.08)
(−1.65)
(−1.81)
(0.78)

0.181
0.182
0.184
0.183
0.162
−0.019∗ ∗ ∗
(−5.68)

Panel C: Other institutions

ESG rating

2003–2010

2011–2019

ESG uncertainty

ESG uncertainty

Low

2

3

4

High

Low
2
3
4
High

0.385
0.387
0.394
0.375
0.357

0.389
0.409
0.385
0.383
0.367

0.384
0.401
0.377
0.388
0.361

0.414
0.407
0.384
0.367
0.353

0.356
0.379
0.363
0.351
0.291

HML-R

−0.028∗ ∗
(−2.13)

−0.023
(−1.67)

−0.023∗ ∗
(−2.23)

−0.061∗ ∗ ∗
(−5.46)

−0.065
(−1.36)

HML-U
−0.029
−0.008
−0.031∗ ∗ ∗
−0.024∗ ∗
−0.066

t-stat
(−1.54)
(−0.97)
(−6.31)
(−2.64)
(−1.57)

All

Low

2

0.390
0.396
0.376
0.370
0.360

0.314
0.304
0.349
0.388
0.369

0.347
0.343
0.362
0.369
0.370

0.333
0.374
0.365
0.368
0.365

0.317
0.374
0.385
0.372
0.361

0.283
0.331
0.356
0.369
0.361

−0.029∗ ∗ ∗
(−3.34)

0.055∗ ∗ ∗
(10.32)

0.023∗ ∗ ∗
(3.35)

0.032∗ ∗ ∗
(3.62)

0.044∗ ∗ ∗
(4.56)

0.078∗ ∗ ∗
(5.44)

HML-U
∗∗

−0.031
0.027∗ ∗ ∗
0.007
−0.019∗ ∗
−0.008

t-stat

All

(−2.42)
(3.11)
(1.02)
(−2.19)
(−1.09)

0.327
0.347
0.361
0.370
0.366
0.039∗ ∗ ∗
(9.84)

Journal of Financial Economics 145 (2022) 642–664

Low
2
3
4
High

HML-U

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

increase. For perspective, they hold 14% more green stocks
than brown stocks in the pre-2011 period. While hedge
funds invest more in brown stocks during both periods,
they hold 33% less green stocks in the pre-2011 period
and only 10% less green stocks in the post-2011 period. Interestingly, other institutions exhibit a shift in ESG preference over time, i.e., from brown-loving to green-loving.
They hold 7% less green stocks in the pre-2011 period, but
12% more green stocks in the post-2011 period.
Second, for norm-constrained institutions, demand for
green ﬁrms diminishes with ESG rating uncertainty in both
periods, while the effect is stronger in the pre-2011 period. Among the green stocks, norm-constrained institutions hold 27.1% (19.0%) of the low-uncertainty stocks, but
19.5% (16.8%) of the high-uncertainty stocks, in the pre2011 (post-2011) period, indicating a 28% (12%) decline.
It is possible that the rising popularity of sustainable investing also incentivizes institutional investors to invest in
ESG research and even create internal rating tools (e.g.,
Mooney, 2019), partially mitigating the negative effect of
rating uncertainty. Overall, our ﬁndings conﬁrm that even
with growing ESG awareness, the demand for green assets
diminishes with ESG rating uncertainty for ESG-sensitive
investors.
When there is no uncertainty in ESG ratings, our model
predicts a negative relation between the ESG rating and
expected CAPM alpha due to the nonpecuniary beneﬁts of
holding green stocks. However, Pástor et al. (2021a,b) show
that green assets have higher realized alphas when investors’ tastes for green holdings shifted unexpectedly during the last decade. As a result, we expect our ﬁndings
to be stronger in the pre-2011 period, which provides a
cleaner setting in which to analyze the equilibrium expected returns of stocks.
Table 5 has a layout similar to Table 2, with Panel A
for raw return and Panel B for CAPM-adjusted return. As
expected, the ESG rating is negatively associated with future performance among stocks with low rating uncertainty in the pre-2011 period, yielding a signiﬁcant longshort portfolio return (“LMH-R”) of 1.12% (t-stat=3.06) per
month and CAPM-adjusted return of 0.96% (t-stat=2.81)
per month. Consistent with our model prediction, the negative ESG-CAPM alpha relation does not hold for the remaining ﬁrms. A univariate portfolio sort based on ESG uncertainty further conﬁrms that CAPM alpha increases with
ESG rating uncertainty, i.e., the high-minus-low ESG uncertainty portfolio (“HML-U”) shows a monthly CAPM alpha of
0.42% (t-stat=2.04) in the pre-2011 period.
In contrast, we do not ﬁnd a negative return predictability of ESG ratings across all ESG-rating-uncertainty
portfolios or a positive ESG uncertainty-CAPM alpha relation in the post-2011 period. Our ﬁndings in both subperiods remain unchanged for FFC- and FF6-adjusted return,
as reported in the Online Appendix. Note that our results
should not be interpreted to mean that ESG rating uncertainty no longer matters in the future. Instead, the equilibrium outcome over longer horizons could be even stronger
than the full sample evidence we report, due to the unexpected outcomes realized over the last decade.
Next, we conduct robustness checks by using alternative deﬁnitions of ESG rating and rating uncertainty. Specif-

ically, for each rater-year, we sort all stocks covered by this
rater according to the original rating scale and calculate
the percentile rank (normalized between zero and one) for
each stock. The ﬁrm-level ESG rating is deﬁned as the average rank across all raters (labelled ESGALL ), and the ESG rating uncertainty is deﬁned as the standard deviation of the
ranks provided by all raters (labelled ESG UncertaintyALL ).
As noted earlier, this method can entail some bias due to
the lack of comparability across vendors.
We repeat our main analysis using the alternative proxy
for ESG rating and rating uncertainty, and present the results in the Online Appendix. First, we conﬁrm that normconstrained institutions have a strong preference for green
assets in general, while they display a lower demand for
green ﬁrms when ESG uncertainty is high. For instance,
among the high-ESG-rating portfolios, norm-constrained
institutions hold 23.4% of the low-uncertainty stocks, but
only 15.5% of the high-uncertainty stocks, indicating a 33%
decline. As a result, green stocks no longer attract more
norm-constrained institutional investors than brown stocks
when rating uncertainty is high.
Moving to cross-sectional stock returns, our ﬁndings are
largely consistent with the model prediction that the ESG
rating is negatively associated with future performance
among stocks with low rating uncertainty. The long-short
portfolio return (FFC-adjusted return, FF6-adjusted return)
is signiﬁcant at 0.52% (0.35%, 0.35%) per month. While the
CAPM-adjusted return is not statistically signiﬁcant, the
magnitude is sizable at 0.31% per month. Unreported results show that the long-short portfolio yields a return of
1.05% per month and a CAPM-adjusted (FFC-adjusted, FF6adjusted) return of 0.87% (0.75%, 0.73%) per month in the
pre-2011 period, all statistically signiﬁcant at the 5% or 1%
level. We further conﬁrm that ESG rating is negatively associated with CAPM-adjusted return when rating uncertainty is low, after controlling for other ﬁrm characteristics. In short, our main results are robust to the alternative
deﬁnitions of ESG rating and rating uncertainty.
5. Calibration
As ﬁnal experiments, we calibrate the model to study
the general equilibrium implications of ESG rating uncertainty for the market premium, the cross section of stock
returns, economic welfare, and equity demand. Following
Pástor et al. (2021a), we consider ESG-indifferent (IND)
and ESG-sensitive (ESG) agents. The former group does not
derive utility from ESG externalities (i.e., bIND = 0), while
the utility of the latter positively depends on the market ESG score and negatively depends on rating uncertainty, through bESG > 0. Speciﬁcally, we assume that 20%
of the agents have ESG preferences, while the remaining fraction consists of ESG-indifferent agents. Hence, ESGsensitive agents are not the vast majority in the economy,
yet they account for a substantial fraction.24
The ESG parameters, bESG , μg,M , σg,M , ρg,M , and the
stock-level counterparts of μg,M , σg,M , and ρg,M are unknown. In the data section above, we describe ways to map
24
In unreported results, we conﬁrm that a larger fraction of ESGsensitive investors leads to stronger implications of ESG uncertainty.

658

Panel A: Return

ESG rating

2003–2010

2011–2019

ESG uncertainty

ESG uncertainty

Low

2

3

4

High

All

Low

2

3

4

High

All

1.427∗
(1.86)
1.235∗
(1.83)
0.944
(1.26)
0.497
(0.86)
0.309
(0.52)

0.845
(1.35)
0.973
(1.44)
1.014∗
(1.74)
0.502
(0.73)
0.346
(0.57)

0.528
(0.77)
0.955∗
(1.75)
0.919
(1.43)
0.928
(1.29)
0.524
(1.08)

0.949
(1.43)
0.984
(1.53)
1.157∗
(1.74)
0.763
(1.22)
1.205∗ ∗
(2.05)

0.667
(1.23)
0.902
(1.34)
0.879∗
(1.70)
1.108∗
(1.91)
0.619
(1.18)

0.773
(1.23)
0.957
(1.64)
0.764
(1.33)
0.976∗
(1.87)
0.420
(0.75)

1.065∗ ∗ ∗
(2.93)
1.254∗ ∗ ∗
(3.61)
1.231∗ ∗ ∗
(3.53)
0.937∗ ∗
(2.52)
0.937∗ ∗ ∗
(3.36)

1.351∗ ∗ ∗
(3.25)
1.073∗ ∗ ∗
(3.42)
0.921∗ ∗
(2.55)
0.868∗ ∗
(2.40)
1.283∗ ∗ ∗
(5.14)

0.980∗ ∗
(2.52)
1.215∗ ∗ ∗
(3.19)
1.166∗ ∗ ∗
(3.20)
1.262∗ ∗ ∗
(4.15)
1.150∗ ∗ ∗
(3.98)

0.809∗ ∗
(2.00)
1.096∗ ∗ ∗
(2.68)
1.057∗ ∗ ∗
(2.80)
1.247∗ ∗ ∗
(4.43)
1.166∗ ∗ ∗
(3.78)

0.842∗ ∗
(2.26)
1.266∗ ∗ ∗
(3.55)
1.011∗ ∗ ∗
(2.94)
0.884∗
(1.92)
1.062∗ ∗ ∗
(3.38)

1.056∗ ∗ ∗
(2.92)
0.968∗ ∗ ∗
(2.79)
1.249∗ ∗ ∗
(3.83)
1.054∗ ∗ ∗
(3.62)
1.147∗ ∗ ∗
(4.26)

LMH-R

1.119∗ ∗ ∗
(3.06)

0.499∗
(1.78)

0.004
(0.01)

−0.256
(−0.74)

0.048
(0.12)

0.353
(1.45)

0.127
(0.59)

0.068
(0.23)

−0.170
(−0.70)

−0.357
(−1.22)

−0.220
(−0.87)

−0.091
(−0.50)

ESG rating

ESG uncertainty
Low

2

3

4

High

HML-U

Low

2

3

4

High

HML-U

0.482
(0.81)

0.533
(0.87)

0.666
(1.25)

1.011∗
(1.70)

0.832∗
(1.71)

0.350
(1.51)

0.994∗ ∗ ∗
(3.50)

1.180∗ ∗ ∗
(4.41)

1.174∗ ∗ ∗
(3.97)

1.146∗ ∗ ∗
(3.92)

1.037∗ ∗ ∗
(3.35)

0.043
(0.31)

Low
2
3
4
High

659

All

D. Avramov, S. Cheng, A. Lioui et al.

Table 5
Performance of portfolios sorted by ESG rating and uncertainty: Subsample analysis.
At the end of year t, stocks are ﬁrst sorted into quintiles according to their ESG rating uncertainty. Within each ESG rating uncertainty group, stocks are further sorted into quintiles according to their ESG ratings
to generate 25 (5×5) portfolios. The low- (high)-ESG-rating and ESG-rating-uncertainty portfolios comprise the bottom (top) quintile of stocks based on the ESG rating and ESG rating uncertainty, respectively.
For each of the 25 portfolios, we compute the value-weighted return in each month in year t + 1 and rebalance the portfolios at the end of year t + 1. Panel A reports the time-series averages of monthly returns
for each of the 25 portfolios, as well as for the investment strategy of going long (short) the low- (high)-ESG-rating stocks (“LMH-R”). The column “All” reports similar statistics for portfolios sorted by ESG
ratings only. The row “All” reports returns for portfolios sorted by ESG uncertainty only, as well as the investment strategy of going long (short) the high (low) ESG-uncertainty stocks (“HML-U”). We divide the
full sample into two subperiods, and report results for 2003–2010 on the left and 2011–2019 on the right. In Panel B, portfolio returns are further adjusted by the CAPM. The Online Appendix provides a detailed
deﬁnition for each variable. Newey-West adjusted t-statistics are shown in parentheses. Numbers with “∗ ”, “∗ ∗ ”, and “∗ ∗ ∗ ” are signiﬁcant at the 10%, 5%, and 1% levels, respectively.

ESG uncertainty

Panel B: CAPM-adjusted return

ESG rating

2003–2010

2011–2019

ESG uncertainty

ESG uncertainty
2

3

4

High

All

Low

2

3

4

High

All

0.568∗ ∗
(1.99)
0.397∗ ∗
(2.00)
0.088
(0.32)
−0.192
(−0.86)
−0.391∗ ∗
(−2.06)

0.058
(0.27)
0.172
(0.56)
0.259
(1.14)
−0.348∗
(−1.70)
−0.403∗ ∗
(−2.29)

−0.284
(−0.91)
0.236
(0.98)
0.133
(0.79)
0.109
(0.26)
−0.159
(−0.80)

0.162
(0.68)
0.222
(1.18)
0.358∗
(1.89)
−0.049
(−0.25)
0.461∗
(1.98)

0.011
(0.04)
0.175
(0.55)
0.237
(0.81)
0.381∗
(1.82)
−0.030
(−0.12)

−0.006
(−0.03)
0.218
(1.45)
0.034
(0.25)
0.243∗ ∗
(2.34)
−0.294∗ ∗ ∗
(−2.92)

−0.147
(−0.67)
0.023
(0.09)
0.061
(0.27)
−0.264
(−1.22)
−0.070
(−0.56)

0.022
(0.10)
0.086
(0.32)
−0.344∗
(−1.89)
−0.408∗ ∗ ∗
(−2.94)
0.310∗ ∗ ∗
(3.02)

−0.376∗
(−1.95)
−0.083
(−0.54)
−0.169
(−1.09)
0.178
(1.49)
0.110
(1.02)

−0.433∗ ∗
(−2.14)
−0.162
(−0.79)
−0.228
(−1.14)
0.204
(1.27)
0.052
(0.32)

−0.262
(−1.17)
0.098
(0.43)
−0.158
(−0.71)
−0.418
(−1.23)
−0.037
(−0.23)

−0.224
(−1.52)
−0.259∗ ∗
(−2.06)
0.019
(0.17)
−0.035
(−0.37)
0.093∗
(1.83)

LMH-R

0.959∗ ∗ ∗
(2.81)

0.460
(1.60)

−0.126
(−0.30)

−0.299
(−0.85)

0.041
(0.10)

0.289
(1.12)

−0.077
(−0.31)

−0.288
(−1.06)

−0.486∗
(−1.88)

−0.486
(−1.62)

−0.225
(−0.81)

−0.317∗
(−1.74)

ESG rating

ESG uncertainty
2

3

4

High

HML-U

Low

2

3

4

High

HML-U

0.181
(1.33)

∗∗

0.048
(0.79)

0.027
(0.32)

−0.107
(−1.07)

−0.029
(−0.19)

2
3
4
High

Low
All

∗

−0.238
(−1.87)

ESG uncertainty

∗∗

−0.255
(−2.35)

−0.068
(−0.45)

∗

0.243
(1.93)

0.419
(2.04)

−0.077
(−0.95)

∗

0.117
(1.74)

Journal of Financial Economics 145 (2022) 642–664

Low
Low

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

ESG ratings into scores for individual securities, and the
market-level ESG rating follows through aggregation. The
resulting quantities are not on the scale of equity returns
and are ordinal in nature. In particular, a higher ESG rating indicates a greener stock, while a higher standard deviation among raters amounts to greater ESG uncertainty.
Thus, stock-level and market-level ratings, as well as measures of rating uncertainty, can comfortably be used to assess the model implications through cross-sectional regressions and portfolio sorts. In the calibration experiments
that follow, we choose ESG parameters that conform to
payoffs on pseudo-assets, as formulated in the theory section.25 Further details are provided below.

i.e., the nonpecuniary beneﬁts from holding the green market versus aversion to ESG uncertainty. For ESG-sensitive
agents, we consider two values for brown aversion, namely,
bESG is equal to 1 or 2. When the market is green, both
cases generate an ESG return of 1% and 2% per year, respectively. When the market is green neutral, brown aversion is not mapped into the incremental expected return.
We also consider two values for the correlation between
ESG and market return, ρg,M , namely, 0 and 0.5. The zerocorrelation is a benchmark case that reﬂects the lower
bound on the implications of ESG uncertainty. The positive
correlation is sensible, as described in the theory section.
Finally, the market ESG uncertainty, σg,M , ranges between
0 and 0.04.26
Panel A of Fig. 2 describes the green-neutral market
case, with solid lines representing the case of ρg,M = 0
and dashed lines corresponding to ρg,M = 0.5. The limiting case of bESG = 0 represents the departure point, at
which all agents are indifferent to the market ESG proﬁle. In that case, it follows that (1) the equilibrium market
2 = 6.50%,
premium equals the ESG-indifference value, γ σM
regardless of the level of ESG uncertainty; (2) both agent
types hold the market portfolio (x∗ESG = x∗IND = 1); and (3)
the agents perceive the same certainty equivalent excess

5.1. Market premium, welfare, and equity demand
The analysis for the aggregate market is based on an
economy that consists of the market portfolio and a riskless asset (in zero net supply). The market volatility parameter employed in the calibration is σM = 15.19%, which
is the annual estimate from monthly U.S. market returns,
spanning the period from July 1963 through December
2019. Then, employing the sample estimate for the equity
premium (6.5%), we obtain γ = 2.81, following Eq. (6). Two
remarks are in order. First, while our sample for individual
stocks starts in 2002, due to limited data for ESG ratings,
the possibility of using longer return histories from the aggregate to sharpen estimates builds on Pástor and Stambaugh (2002). In addition, expected market return is endogenous in our setup, while the sample estimate is used
to set the risk aversion parameter.
We evaluate the equilibrium market premium on the
basis of Eq. (11) for the multiple-agent case. The market demand and the certainty equivalent return from investment differ across agent types. In particular, based on
Eq. (4), the optimal market demand for agent i is x∗i =
1 μM +bi μg,M

γi

2
σi,U

σ2

return (CE ESG = CE IND = γ 2M = 3.25%).
When bESG > 0, the ESG agents are sensitive to the market rating uncertainty. Then, the perceived market variance
2
2 .27 This force leads to an increasing
σM,U
is higher than σM
equilibrium market premium, and more so for higher values of bESG , σg,M , and ρg,M .
As a result, the two types of agents have different certainty equivalent return and demand for the market portfolio. On the one hand, the IND agents are not sensitive
2
2
to ESG uncertainty (σIND
,U = σM ). Thus, they beneﬁt from
the higher equilibrium market premium, which translates
into a higher certainty equivalent return and a levered position in the market portfolio (x∗IND > 1). On the other hand,
the ESG agents are more sensitive to ESG uncertainty than
2
2 ). Thus, their certainty
the aggregate market (σESG
> σM,U
,U
equivalent return and their demand for the market portfolio decline with increasing values of bESG , σg,M , and ρg,M .
We next quantitatively assess the economic cost of ESG
uncertainty, as perceived by ESG agents. The cost is represented by a diminishing certainty equivalent return relative to σg,M = 0. When ρg,M = 0 and ESG uncertainty σg,M
is set to 0.02 (0.04), the utility loss is 0.03% (0.13%) per
year for bESG = 1 and 0.13% (0.47%) for bESG = 2. Consider-

2 = σ 2 + b2 σ 2 + 2b σ σ
, where σi,U
i M g,M ρg,M . In
M
i g,M

addition, as derived in Online Appendix A.6, the certainty
equivalent excess return for agent i is given by CE i =
1
2γi




μM +bi μg,M 2
. Both the market demand and the cerσi,U

tainty equivalent return increase in the perceived market
premium and diminish in the perceived market variance.
For ESG-sensitive agents, the perceived certainty equivalent
return increases with the market ESG score, while the perceived variance rises with ESG uncertainty and the correlation between the market ESG score and market return.
The effect of ESG rating uncertainty is stronger for higher
values of bi and ρg,M .
To make the analysis suﬃciently comprehensive, we
run calibration experiments for multiple scenarios. First,
we consider both green-neutral (μg,M = 0) and green
(μg,M = 0.01) markets. The ESG implications of the former
case are exclusively attributed to ESG uncertainty. The latter case involves the two conﬂicting forces noted earlier,

26
Empirically, the magnitude of ESG uncertainty is comparable to the
scale of differences in ESG scores. For instance, considering the summary
statistics of our data set from the Online Appendix, the quartile deviation of ESG ratings is 0.14. The values of ESG uncertainty are of the same
order of magnitude as differences in ESG scores: the median ESG uncertainty is 0.16, while the 90th percentile is 0.33. Similarly, for calibration,
we consider values of ESG uncertainty that conform to ESG levels: a green
(brown) asset has a mean ESG score of 0.01 (−0.01), and ESG uncertainty
is of the order of 0.01 and multiples.
27
As we derive in Online Appendix A.1, the perceived aggregate mar2
, is a harmonic weighted average of the market variket variance, σM,U
2
2
ances perceived by the agents, which in our example are σM,
IND = σM and
2
2
2
2
2
2
σM,
ESG = σM + bESG σg,M + 2bESG σM σg,M ρg,M . It follows that σM,IND < σM,U <

25
In our model, the g = 0 case reﬂects green neutrality. Having this reference point, all the model implications are invariant to a multiplicative
scaling of ESG ratings and rating uncertainty, as long as the brown aversion parameter is also scaled such that the pseudo return, bg, remains
unchanged.

2
σM,
ESG .

660

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

Fig. 2. Equilibrium equity premium, certainty equivalent return, and market demand.
This ﬁgure shows the equilibrium market premium (μM ), the certainty equivalent excess return for ESG-sensitive (CE ESG ) and ESG-indifferent (CE IND ) agents,
the optimal market participation (x∗ESG and x∗IND ), and their variation with the market ESG uncertainty, σg,M . The relative risk aversion, γ , is 2.81, and the
market volatility, σM , is 15.19%. ESG-sensitive agents represent a fraction of wESG = 20% of the population and have a brown aversion bESG = {0, 1, 2}.
ESG-indifferent agents represent wIND = 80% of the population and have a brown aversion bIND = 0. The correlation between the market return and the
ESG score, ρg,M , is 0 (solid lines) or 0.5 (dashed lines). Panel A focuses on a green-neutral market (μg,M = 0), while Panel B describes a green market
(μg,M = 0.01). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)

661

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

ing ρg,M = 0.5 instead, the corresponding ﬁgures are 0.26%
(0.55%) for bESG = 1 and 0.55% (1.08%) for bESG = 2. The calibrated utility loss accounts for a nontrivial proportion of
the overall certainty equivalent excess return when compared to the benchmark case of no uncertainty, i.e., 3.25%.
Therefore, from the perspective of ESG agents, ESG uncertainty leads to signiﬁcant utility loss.
When the market is green neutral, preferences for ESG
essentially reduce welfare because the only effect that
comes into play is aversion to ESG uncertainty. Departing from a green-neutral market, the nonpecuniary beneﬁts from holding green stocks intervene, and more so for
higher values of brown aversion and market ESG score.
Panel B of Fig. 2 describes the green-market case, with
solid lines corresponding to ρg,M = 0 and dashed lines to
ρg,M = 0.5. In the absence of ESG uncertainty (σg,M = 0)
and when bESG > 0, the equilibrium market premium diminishes with bESG . This translates into a lower certainty
equivalent return and market demand for IND agents, who
confront a lower market premium but do not extract nonpecuniary beneﬁts from holding the green market. In contrast, ESG agents extract nonpecuniary beneﬁts from the
positive market ESG tilt, which leads to a higher certainty
equivalent return and higher market demand for increasing
values of bESG .
As the parameter σg,M captures the trade-off between
the two conﬂicting forces of ESG preferences, we derive a
break-even value of σg,M when the utility loss of ESG uncertainty entirely offsets the beneﬁts from holding green
stocks. When ρg,M = 0 and bESG is 1 (2), the welfare beneﬁts of a green market perceived by ESG agents vanish,
due to ESG uncertainty, for σg,M = 9.9% (7.2%), well above
reasonable values. However, a positive correlation between
market return and ESG rating ampliﬁes the effects of ESG
uncertainty. When ρg,M = 0.5 and bESG is 1 (2), the threshold σg,M is much lower at 4.9% (4.3%).
The market premium is also subject to the two conﬂicting forces, i.e., the negative ESG premium due to the green
market versus the positive contribution due to ESG uncertainty. When ρg,M = 0 and bESG is 1 (2), the two forces are
equal for σg,M = 6.0% (4.2%), while if ρg,M = 0.5 and bESG is
1 (2), the threshold σg,M is at 2.1% (1.9%).
Overall, we reinforce the notion that ESG uncertainty
increases the market premium, as well as reduces the economic welfare for ESG-sensitive investors and discourages
their participation in the stock market.

sumed that βgreen = βbrown = 1, and the idiosyncratic annualized return volatility is 20% for both assets. As σM =
15.19%, the total stock return volatility is 25.12%.28 We
consider a positive correlation between return and ESG
score for each asset, setting ρg,M = ρrg,green = ρrg,brown =
0.5. The off-diagonal elements in g and rg are assumed
to be zero.
Fig. 3 illustrates how the expected excess return, the
CAPM alpha, and the effective beta vary with ESG uncertainty for green and brown assets (σg,green and σg,brown ).
The solid lines represent the green asset while dashed
lines represent the brown asset. We consider a marketwide ESG uncertainty, σg,M , equal to 0.01 for the left
graphs and 0.02 for the right graphs. Starting from the
benchmark case of ESG indifference (bESG = 0), the expected excess return for both assets is equal to the market
premium, 6.50%, while the alpha is zero and the effective
beta coincides with the unit market beta.
Considering ESG-sensitive agents (bESG > 0), the positive ESG score of a green asset is associated with
lower expected return and alpha in equilibrium, as in
Pástor et al. (2021a). The effect is stronger for larger values of bESG . In addition, expected return rises with ESG uncertainty. Thus, in the presence of the conﬂicting forces of
ESG score (negative effect on alpha) and ESG uncertainty
(positive effect on alpha), a green asset with high ESG
uncertainty could have higher expected return and alpha
than a brown asset with low ESG uncertainty. For instance,
when σg,M = 0.01, σg,green = 0.10, and bESG = 1 (bESG = 2),
the green asset displays an expected excess return of 6.78%
(7.09%) and an alpha of 0.20% (0.42%). To compare, when
the ESG proﬁle of the brown asset is known for certain, its
expected excess return is 6.70% (6.90%) and alpha is 0.11%
(0.23%).
The σg,green = 0 case merits further analysis. The zerouncertainty asset does not contribute to the aggregate
ESG uncertainty; thus, its effective beta is lower than the
unit market beta, per Eq. (19), and the effect is stronger
when brown aversion and market-wide ESG uncertainty
are higher. For instance, when σg,M = 0.01, the effective
beta is 0.987 (0.974) for bESG = 1 (bESG = 2). When σg,M =
0.02, the effective beta is 0.974 (0.950) for bESG = 1 (bESG =
2). The diminished effective beta relative to the market
beta induces a negative contribution to alpha and expected
return.
As demonstrated in Eq. (20), the effective beta does not
depend on the mean ESG score. Consequently, green and
brown assets have the same effective beta for identical levels of ESG uncertainty. The effective beta increases with
ESG uncertainty and can rise above the unit market beta,
and the effect is stronger for higher values of brown aversion.
Finally, as long as the green and the brown assets have
the same ESG uncertainty, the performance difference between brown and green assets (both expected return and

5.2. Cross section of expected returns, alpha, and effective
beta
We next calibrate the cross section of expected return,
the CAPM alpha, and the effective beta in equilibrium, all
of which are formulated in Section 2.3.
To distill cross-sectional implications of ESG uncertainty, we focus on the green-neutral market described
in Section 5.1. At the stock level, we consider green and
brown assets, with mean ESG scores μg,green = 0.01 and
μg,brown = −0.01. Thus, for the green asset, ESG agents perceive an incremental ESG return equal to 1% per year for
bESG = 1 and 2% per year for bESG = 2. The corresponding
return ﬁgures are negative for the brown asset. It is as-

28
2
, is given by
The total return variance of the green asset, σgreen
2
βgreen
σM2 + σid2 ,green , where σid,green is the idiosyncratic volatility. For βgreen =
1, σM = 15.19%, and σid,green = 20%, it follows that σgreen = 25.12%. The
2
. The covariance between returns is βgreen βbrown σM2 =
same applies to σbrown
(15.19% )2 , corresponding to a correlation ρgreen,brown = 36.59%.

662

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

Fig. 3. Two-asset pricing equilibrium: Expected stock return, alpha, and effective beta.
Considering the green-neutral market described in Fig. 2, Panel A, for green (solid lines) and brown (dashed lines) assets, this ﬁgure displays the equilibrium
expected excess stock return, (μr,green and μr,brown ), the CAPM alpha, (αgreen and αbrown ), the effective beta, (βe f f ,green and βe f f ,brown ), and their variation with
ESG uncertainty, σg,green , σg,brown . The mean ESG scores of the two assets are μg,green = 0.01 and μg,brown = −0.01. The market betas of the two assets
are βgreen = βbrown = 1, while their idiosyncratic return volatility is equal to 0.2. The correlation between return and the same-asset ESG score is ρg,M =
ρrg,green = ρrg,brown = 0.5. The graphs on the left describe a market-wide ESG uncertainty that is equal to σg,M = 0.01, while the right plots display results
for σg,M = 0.02. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)

alpha) diminishes with increasing ESG uncertainty. Consider, for instance, σg,M = 0.01. As the ESG uncertainty increases from 0 to 0.10, the difference in expected return
(μr,brown − μr,green ) decreases from 0.40% to 0.23% when
bESG = 1, and from 0.80% to 0.29% when bESG = 2. Similar patterns apply to alpha. Such calibration results follow
from Eq. (27).
The overall evidence from the calibration indicates that
ESG uncertainty has meaningful implications for expected
return, alpha, and effective beta. Notably, both alpha and

the effective beta increase with ESG uncertainty. Moreover,
the alpha gap between brown and green assets diminishes
with ESG uncertainty.
6. Conclusion
We comprehensively analyze the equilibrium implications of ESG rating uncertainty for portfolio choice and asset pricing. Starting with the market portfolio as the single
risky asset, we show that rating uncertainty leads to higher
663

D. Avramov, S. Cheng, A. Lioui et al.

Journal of Financial Economics 145 (2022) 642–664

perceived market risk, higher market premium, and lower
investor demand. Next, we consider multiple risky assets
and heterogeneous economic agents and derive an ESGaugmented CAPM for the cross section of stock returns. In
particular, we propose that ESG uncertainty could tilt the
ESG-CAPM alpha relation and serve as a potential channel
to explain the mixed evidence in prior studies.
We empirically test the model implications and provide
supporting evidence. First, ESG rating uncertainty reduces
investor demand for stocks, especially for ESG-sensitive investors (i.e., norm-constrained institutions) in their ESG investment (i.e., green stocks). Second, brown stocks outperform green stocks only when rating uncertainty is low,
and the negative return predictability of ESG ratings does
not hold for the remaining ﬁrms. We then calibrate the
model to assess its quantitative implications in the presence of rating uncertainty. The analysis reinforces the notion that ESG uncertainty could affect investors’ demand,
the risk-return trade-off, and reduce economic welfare for
ESG-sensitive agents.
Our ﬁndings echo the growing concerns regarding the
lack of consistency of ESG information disclosure and ratings provided by different rating agencies. In the presence
of rating uncertainty, investors are less likely to make ESG
investments and actively engage in corporate ESG issues.
This could increase the cost of capital for green ﬁrms and
further limit their capacity to make socially responsible investments and generate real social impact. As the amount
of sustainable investing is expected to keep growing, the
overall impact will become even more striking. Viewed
from this perspective, our results provide a conservative
assessment of rating uncertainty.
Our evidence suggests that it would be useful for policy
makers to establish a clear taxonomy of ESG performance
and uniﬁed disclosure standards for sustainability reporting. It would be especially instructive to identify which investments are really green. Doing so could mitigate ESG
uncertainty, thus reducing the cost of equity capital for
green ﬁrms, leading to higher social impact.
Our paper also suggests avenues for future research.
While existing work studying equilibrium with ESG focuses
on a single-period environment, it would be natural to extend ESG equilibrium to multiperiod dynamic setups. Then,
the market ESG can display time variation, which would
give rise to an incremental asset pricing factor. It would
also be instructive to account for investors’ learning about
the ESG proﬁle of a ﬁrm. These and other topics in dynamic asset pricing are left for future research.

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==> JFE07 - Big Three and corporate carbon emissions.txt <==
Journal of Financial Economics 142 (2021) 674–696

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

The Big Three and corporate carbon emissions around the
world ✩
José Azar a, Miguel Duro b, Igor Kadach b, Gaizka Ormazabal c,∗
a

IESE Business School, School of Economics and Business, University of Navarra & CEPR, Avenida Pearson 21, Barcelona 08034, Spain
IESE Business School, Avenida Pearson 21, Barcelona 08034, Spain
c
IESE Business School, CEPR & ECGI, Avenida Pearson 21, Barcelona 08034, Spain
b

a r t i c l e

i n f o

Article history:
Received 14 July 2020
Revised 26 October 2020
Accepted 17 November 2020
Available online 24 May 2021
JEL classiﬁcations:
G15
G23
G30
M41

a b s t r a c t
This paper examines the role of the “Big Three” (i.e., BlackRock, Vanguard, and State Street
Global Advisors) on the reduction of corporate carbon emissions around the world. Using
novel data on engagements of the Big Three with individual ﬁrms, we ﬁnd evidence that
the Big Three focus their engagement effort on large ﬁrms with high CO2 emissions in
which these investors hold a signiﬁcant stake. Consistent with this engagement inﬂuence
being effective, we observe a strong and robust negative association between Big Three
ownership and subsequent carbon emissions among MSCI index constituents, a pattern
that becomes stronger in the later years of the sample period as the three institutions
publicly commit to tackle Environmental, Social, and Governance (ESG) issues.
© 2021 Elsevier B.V. All rights reserved.

Keywords:
Climate change
Carbon emissions
ESG
Big three
Shareholder activism
Institutional ownership

1. Introduction
✩
We thank Eloy Lanau, Christopher Nance, Vicent Peris, Sergio Ribera,
and Claudia Serra for their excellent research assistance. We also thank
participants at the 7th International Symposium on Environment and Energy Finance Issues, the Reﬁnitiv seminar on recent advances in CSR research, the 1st UZH Young Researcher Workshop on Climate Finance (University of Zurich), the 18th Paris December Finance Meeting, the ESSEC
Amundi Chair Webinar, and the EAA Virtual Annual Congress for helpful comments and suggestions. This paper has also beneﬁted from comments by an anonymous referee, Marco Ceccarelli (discussant), Madison
Condon, Alon Kalay, Steven Ongena, Shiva Rajgopal, Alex Wagner, Olivier
David Zerbib (discussant), and seminar participants at Bocconi University, Columbia Business School, ESSEC Business School, Luiss Guido Carli
University, and Universidad Autonoma de Barcelona. Gaizka Ormazabal
thanks the “Cátedra de Dirección de Instituciones Financieras y Gobierno
Corporativo del Grupo Santander,” the BBVA Foundation (2016 grant “Ayudas a Investigadores, Innovadores, y Creadores Culturales”), the Marie

https://doi.org/10.1016/j.jﬁneco.2021.05.007
0304-405X/© 2021 Elsevier B.V. All rights reserved.

This paper studies the role of the “Big Three” (i.e.,
BlackRock, Vanguard, and State Street Global Advisors) on
the reduction of carbon emissions around the world. In
Curie and Ramon y Cajal Fellowships, and the Spanish Ministry of Science and Innovation, grant ECO2015–63,711-P. Miguel Duro acknowledges
ﬁnancial assistance from research projects ECO2016–77,579-C3–1-P and
PID2019–111143GB-C31, funded by the Spanish Ministry of Economics, Industry, and Competitiveness, and the Ministry of Science and Innovation,
respectively. Igor Kadach acknowledges ﬁnancial assistance from research
grant ECO2017–84,016-P, funded by the Spanish Ministry of Science, Innovation, and Universities.
∗
Corresponding author.
E-mail addresses: jazar@iese.edu (J. Azar), mduro@iese.edu (M. Duro),
ikadach@iese.edu (I. Kadach), gormazabal@iese.edu (G. Ormazabal).

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

recent years, there has been an increasing popular demand
that these large investors pressure the companies in their
portfolios to curb their greenhouse gas (GHG) emissions,
and the leaders of the Big Three have made public statements about their intention to do so.1 However, whether
the effort of the Big Three to reduce corporate carbon
emissions is meaningful and/or effective remains an open
empirical question.
Our analysis focuses on the Big Three to shed light
on the recent debate about the role of these investors in
the economy (Bebchuk and Hirst, 2019b; Coates, 2019;
Fisch et al., 2020). The current interest in the Big Three
responds to the unique combination of characteristics of
these investors. The ﬁrst of these characteristics is their
size; they manage an enormous (and growing) amount
of investments. While widely diversiﬁed, the large monetary value of the pool of assets managed by the Big
Three often results in large stakes in their portfolio ﬁrms,
which makes them likely pivotal voters (Bebchuk and
Hirst, 2019b; Griﬃn, 2020). This gives the Big Three an
inﬂuential role and facilitates their engagement with
portfolio companies (Fichtner et al., 2017; Fisch et al.,
2020). The second distinctive characteristic of the Big
Three is that most of the investment vehicles sponsored
by these investors are passively managed index funds and
exchange-traded funds (ETFs).
Beyond possible altruistic reasons, the Big Three could
have several economic incentives to engage with ﬁrms
on environmental issues. One potential motivation is that
these large investors believe that reducing CO2 emissions
increases the value of their portfolio. As suggested by survey evidence (Krueger et al., 2020), a nontrivial number of
institutional investors believe climate risks have ﬁnancial
implications for their portfolio ﬁrms and the risks have
already begun to materialize, particularly regulatory risks.
The validity of this concern is supported by recent empirical research on the pricing implications of climate risk.2

The Big Three could also push ﬁrms to reduce CO2
emissions to attract or retain investment clients that are
sensitive toward environmental concerns (Barzuza et al.,
2021). As explained by prior literature, prosocial behavior has several sources: (i) altruism, (ii) direct ﬁnancial
incentives, (iii) building social image, and (iv) social pressure (e.g., Ariely et al., 2009; Lacetera and Macis, 2010;
DellaVigna et al., 2012). Given the recent proliferation of
socially responsible investing, being perceived as environmentally conscious could help the Big Three to attract
investors’ money.
To empirically analyze the potential effect of the Big
Three on corporate carbon emissions around the world, we
use two novel data sets. We obtain carbon emission data
for a wide cross-section of ﬁrms between 2005 and 2018.
We complement these data with information on Big Three
engagements with individual ﬁrms, which we hand-collect
from recent public disclosures of these fund sponsors. Our
data indicate that, on average, these large funds engage
annually with a number of ﬁrms (e.g., from 7/1/2018 to
6/30/2019, BlackRock held personal meetings with directors and executives of 1458 ﬁrms). When we explore the
determinants of the probability of such engagements, we
ﬁnd corroborating evidence that ﬁrms with higher CO2
emissions are more likely to be the target of Big Three
engagements. We also ﬁnd that the Big Three focus their
engagements on large ﬁrms (i.e., ﬁrms with a potentially
larger effect on global carbon emissions) and on ﬁrms in
which these large investors have a more substantial stake
(i.e., ﬁrms in which the Big Three are more inﬂuential).
Next, we explore whether Big Three engagements
are followed by a reduction in CO2 emissions. We start
by testing whether there is an association between Big
Three ownership in a given ﬁrm and that ﬁrm’s CO2
emissions. We ﬁnd a negative and signiﬁcant association
for MSCI ﬁrms; a one standard deviation increase in
Big Three holdings in a given ﬁrm is associated with a
reduction of approximately 2% in corporate CO2 emissions. The association is concentrated in cases where the
Big Three hold a signiﬁcant stake in a given company,
namely in cases where the Big Three are likely to be more
inﬂuential.
The negative relation between Big Three ownership
and carbon emissions is robust to a battery of additional
tests. First, we use speciﬁcations based on changes in
the values of the variables. Second, we focus on nonnegligible changes (more than 1% increase) on the levels
of Big Three ownership. Third, we add a wide range
of ﬁxed effects, including year, industry, country, ﬁrm,
country-by-year, industry-by-year, size-decile-by-year, and
country-by-industry-by-year ﬁxed effects.
We also explore cross-sectional and time-series variation in the previously documented patterns. Tellingly, we
observe that the above-mentioned negative association is
more pronounced for higher values of the probability that
the Big Three engages with the ﬁrm on environmental
issues (such probability is measured in accordance with
our previous tests). Consistent with an increasing popular
demand that these large investors pressure the companies
in their portfolios to curb emissions, we ﬁnd that the
pattern is stronger in the later years of the sample period.

1
BlackRock’s vice chairman Phillip Hildebrand and global head of impact investing Deborah Winshell stated in a report by the asset manager
that “[i] nvestors can no longer ignore climate change. Some may question
the science behind it, but all are faced with a swelling tide of climaterelated regulations and technological disruption” (BlackRock, 2016). More
recently, BlackRock CEO Larry Fink, in his 2020 annual letter addressed
CEOs and their companies stating that: “climate change is almost invariably the top issue that clients around the world raise with BlackRock
[…]. In the near future—and sooner than most anticipate—there will be a
signiﬁcant reallocation of capital” (https://www.blackrock.com/corporate/
investor-relations/larry-ﬁnk-ceo-letter).
2
Recent literature in ﬁnance highlights the importance of climate risks
for institutional investors. First, some papers provide evidence that environmental policies lower downside risk (Hoepner et al., 2019; GibsonBrandon and Krueger, 2018). Second, institutional investors can reduce
overall portfolio risk by incorporating climate criteria into their investment processes (Jagannathan et al., 2018). Modern asset pricing models
emphasize climate risks as a long-run risk factor (Bansal et al., 2017) and
the importance of environmental pollution in the cross-section of stock
returns (Bolton and Kacperczyk, 2019; Hsu et al., 2019). Archival literature corroborates these conclusions by showing that extreme weather is
reﬂected in stock and option market prices (Kruttli et al., 2019). At the
industry level, Addoum et al., (2019) show that extreme temperatures affect earnings; (Chava, 2014; Ghoul et al., 2018) show that ﬁrms can lower
their cost of capital and increase value by improving their environmental policies; and (Ginglinger and Moreau, 2019) show that greater climate
risk leads to lower ﬁrm leverage.

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J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Critically, the association becomes stronger as each of the
three institutions increases its commitment to deal with
environmental issues (which we measure based on Big
Three’s public disclosures).
To further sharpen identiﬁcation, we exploit the yearly
reconstitution of the indexes Russell 10 0 0 and Russell
20 0 0. For companies that are around the 10 0 0/20 0 0 cutoff,
the ﬁnal assignment to the index is relatively random, and
the inclusion in the Russell 20 0 0 Index likely increases Big
Three ownership (a number of funds sponsored by the Big
Three track the Russell indexes). We ﬁnd that the changes
in Big Three ownership driven by the inclusion in this
index are followed by lower subsequent CO2 emissions.
Our paper contributes to the burgeoning literature
on climate risk. One strand of this literature studies
the effect of climate risk on ﬁrm value. For example, Bansal et al. (2017) study climate risk as a longrun risk factor, and Bolton and Kacperczyk (2019) and
Hsu et al. (2019) study climate risk in the cross-section
of stock returns. In contrast with the view that environmental issues are too remote and uncertain to have a
meaningful economic effect, this literature generally ﬁnds
substantial price and real effects of climate risk. That
said, these papers also ﬁnd evidence of mispricing and
behavioral responses to environmental concerns.
Other recent studies examine whether and how institutions react to climate risk. Some of these papers
provide empirical evidence that investors take into account climate risk considerations in their investment
portfolio decisions (e.g., Hoepner et al., 2019; GibsonBrandon and Krueger, 2018).3 However, the evidence on
how institutional investors engage with their portfolio
companies on climate risk matters is relatively scant. The
available evidence is limited to studies using data from
a single fund (Dimson et al., 2015; Dimson et al., 2018)
and survey data (e.g., McCahery et al., 2016; Krueger et al.,
2020). Similar to our paper, (Dyck et al., 2019) use a
wide international sample of ﬁrms and ﬁnd a positive
association between institutional ownership and corporate
environmental scores (measured by ASSET4 E&G scores).
Our study differs from this literature in that we analyze
the role of the Big Three (rather than that of institutional
ownership in general) on CO2 emissions (rather than on
environmental scores).4 These are important distinctions;
the Big Three have unique characteristics and play an
important—yet controversial—role in the economy, and

environmental scores could reﬂect “greenwashing” rather
than actual environmental improvements.
This paper also adds to the nascent literature on large
indexers. The spectacular growth of the volume of assets
of these institutions in recent years has spurred a debate on the role of the Big Three in the economy (e.g.,
Bebchuk and Hirst, 2019b; Coates, 2019; Fisch et al., 2020).
While acknowledging the advantages of index fund investing in terms of diversiﬁcation and lower management
fees, recent academic work has raised some concerns
about the Big Three, including anticompetitive effects
(Azar et al., 2016; Azar et al., 2018; Anton et al., 2018)
and concerns related to pricing eﬃciency and trading
behavior (Coates, 2019). More related to our research
question, Bebchuk and Hirst (2019a) argue that index
funds underinvest in stewardship and defer excessively to
the preferences and positions of corporate managers. In
contrast, other authors argue that fund sponsors compete
not only on fees but also on returns (e.g., Fisch et al.,
2020). Moreover, recent research suggests that passive
investors have meaningful monitoring incentives when it
comes to cross-cutting issues such as sustainability and
certain aspects of corporate governance in which large
investors can exploit economies of scale and that do not
require a signiﬁcant investment in ﬁrm-speciﬁc monitoring
(e.g., Appel et al., 2016; Gormley et al., 2020).5
We add to this important debate by studying a
dimension of high social relevance: the reduction of
carbon emissions. This dimension of the debate is not
without controversy; for example, the fact that the Big
Three have provided relatively little voting support to
shareholder proposals related to climate issues is sometimes interpreted as evidence that these investors do
not contribute to the global effort to reduce corporate
carbon emissions (see Online Appendix OB for a detailed
discussion).
The evidence in this paper should also be relevant
for those who view GHG emissions as a market failure
(Stern, 2008; Stavins, 2011). Since a full-scale regulatory
solution to the emissions externality problem faces severe
coordination frictions across countries, corporate governance is regarded as an alternative way of addressing
climate change. In particular, large diversiﬁed institutions
are increasingly viewed as catalysts in driving ﬁrms to
reduce their carbon emissions (Andersson et al., 2016;
OECD, 2017).
The remainder of the paper is organized as follows.
In Section 2, we develop the hypothesis that the Big
Three can induce ﬁrms to reduce carbon emissions. In
Section 3, we describe the sample construction and measurement choices. In Section 4, we analyze engagements
of the Big Three with ﬁrms. Results on the association
between the Big Three and carbon emissions are discussed
in Section 5. In Section 6, we conduct additional tests.
Section 7 concludes.

3
Hoepner et al. (2019) and Gibson-Brandon and Krueger (2018) show
that better environmental policies are related to lower downside and
overall portfolio risk. In a similar spirit, Jagannathan et al. (2018) show
that investors can reduce portfolio risk by incorporating climate criteria
into their investment processes, and Ramelli et al. (2018) provide evidence that investors react to political events related to ﬁrms’ climate
strategies.
4
Three other recent papers empirically analyze the Big Three.
Bebchuk and Hirst (2019b) provide descriptive evidence of the growth of
these institutions during recent years. Fichtner et al. (2017) analyze proxy
vote records and ﬁnd that the Big Three use coordinated voting strategies
and hence follow a centralized corporate governance strategy, which generally consists in voting with management. Gormley et al. (2020) focus on
the role of Big Three on gender diversity.

5
In light of this research, Online Appendix OA provides a detailed discussion on the Big Three’s incentives to engage with portfolio ﬁrms.

676

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

2. Hypothesis development

employees exclusively focused on stewardship. We offer
some considerations in this regard. To begin, there is an
ongoing debate about the impact of index investors, and
several recent papers suggest that the net beneﬁt from
monitoring could be greater than suggested by the previous criticisms (e.g., Appel et al., 2016; McCahery et al.,
2016; Fisch et al., 2020). Moreover, according to a recent
report by Morningstar, the top active fund families have
even smaller stewardship teams, report fewer private
engagements, and exhibit voting behavior similar to that
of the Big Three (Morningstar, 2017). Recent research also
suggests that passive investors have meaningful incentives
to monitor cross-cutting issues such as sustainability and
certain aspects of corporate governance, as monitoring
these issues requires relatively less ﬁrm-speciﬁc research
(i.e., it is less costly) than monitoring mergers and acquisitions or board membership (e.g., Appel et al., 2016;
Gormley et al., 2020). Finally, the stewardship team is
larger than it might seem at ﬁrst sight, as this team
works in conjunction with thousands of fund managers
around the world. A signiﬁcant number of these investment professionals are in charge of active funds and can
thus provide valuable feedback on portfolio ﬁrms (see
Online Appendix OA for a more detailed discussion on the
monitoring costs and beneﬁts of the Big Three).6

2.1. The Big Three’s incentives to reduce carbon emissions
Corporate externalities such as CO2 emissions are commonly viewed as societal costs that are caused by corporations but are not internalized by ﬁrms’ shareholders and
managers. Under this view, shareholders (and managers)
would have no incentive to reduce corporate externalities.
However, it is plausible that large and diversiﬁed asset
managers—unlike undiversiﬁed ones—internalize at least
some of the costs from CO2 emissions and therefore would
beneﬁt from a reduction in CO2 emissions across portfolio
ﬁrms. Theoretically, this idea is supported by early models
showing that diversiﬁed shareholders could internalize
some externalities from their portfolio companies (e.g.,
Hansen and Lott, 1996; Hartford, 1997). These externalities
potentially include both direct damages to ﬁrm assets
from climate change and more indirect costs such as social
stigma and the risk that public environmental concerns
trigger regulation. In the case of the effect of CO2 emissions on the value of indexers’ portfolios, this possibility
is supported by recent literature showing that climate
change can affect ﬁrm valuations (Brinkman et al., 2008).
These institutions’ direct ﬁnancial incentives to promote
value-increasing strategies can be quite high in spite of
the low percentage fees, because of the large dollar value
of their investments (e.g., Lewellen and Lewellen, 2020).
Thus, to the extent that large indexers hold stable portfolios of a large number of corporate securities, if corporate
emissions contribute signiﬁcantly to climate-related systematic risk, reducing carbon emissions can make large
indexers better off.
Recent survey evidence on investors’ attitude toward
climate risk provides support for the idea that investors
believe that reducing carbon emissions pays off. For example, based on a survey of a large number of investment
managers, (Krueger et al., 2020) conclude that institutional
investors believe climate risks have ﬁnancial implications
for their portfolio ﬁrms and that the risks have already
begun to materialize.
Even if index managers did not believe that climate
risk alone has a substantial impact on portfolio value, the
Big Three could push for a reduction of CO2 emissions
to attract or retain investment clients that are sensitive
toward environmental concerns. Lack of response to the
social demand that the Big Three play a role in the reduction of carbon emissions could result in outﬂows from the
Big Three to asset managers perceived to be more socially
and environmentally responsible. Indeed, recent evidence
suggests investors value sustainability beyond pecuniary
motives (e.g., Riedl and Smeets, 2017; Hartzmark and Sussman, 2019) and that mutual funds compete for climateconscious investment ﬂows (Ceccarelli et al., 2020).
The incentives of the Big Three to reduce CO2 emissions
could be called into question on the grounds that most
of the investment vehicles sponsored by the Big Three are
passively managed, and passive investors have relatively
weak incentives to invest in ﬁrm-speciﬁc monitoring
(Bebchuk and Hirst, 2019a). This concern is seemingly
supported by the relatively modest number of Big Three

2.2. How can the inﬂuence of the Big Three result in lower
CO2 emissions?
Shareholders usually inﬂuence ﬁrm behavior through
three mechanisms: selling (or not buying) the stock, exercising voting rights, and engaging with management and
voicing their concerns. While index funds usually do not
“vote with their feet” (they hold the stock of the company
as long as the ﬁrm is included in the index tracked by
the fund), large indexers can be highly inﬂuential on
corporate decision-making.7 The reason is that these large
institutions often hold a substantial percent of the shares
of their portfolio companies and can thus be pivotal
voters in control contests, activist campaigns, and mergers
(Coates, 2019). Moreover, the support of the Big Three
can be important in director elections.8 To the extent
6
The Big Three offer a large number of actively managed funds. For example, 27% of BlackRock’s assets under management (i.e., USD $2 trillion)
is in actively managed funds (BlackRock, 2019a), which makes BlackRock
one of the largest active asset managers on the market. To facilitate coordination among fund managers and the investment stewardship team,
BlackRock has built a proprietary database, Aladdin® Research, where
employees introduce the key points from any engagement with portfolio
companies (BlackRock, 2020). BlackRock refers to this notion of cooperation on ﬁrm monitoring as “stewardship ecosystem” (BlackRock, 2020).
7
In the third quarter earnings release in 2019 BlackRock stated,
“of the assets we manage, 50% are equity assets, and of these, 92%
are index and 8% active. The index assets closely track market indexes created by others, which means whether we like a company
or not—including its management, its strategy, its products—we will
still hold it in these portfolios. This is quite different than actively
managed portfolios that can express displeasure by ‘voting with their
feet’ and selling the stock. Given this long-term perspective, our investment stewardship activities are focused on maximizing long-term
shareholder value” (see https://ir.blackrock.com/ﬁles/doc_news/archive/
4a1e3da1- e31d- 4295- a0e8- 96eed78aeef2.pdf).
8
While directors usually obtain a large majority of votes, losses in voting support undermine directors’ professional standing and induce direc-

677

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

that these situations are relatively common, disregarding
explicit requests from the Big Three can be costly for ﬁrm
managers and directors.
The Big Three could also exert inﬂuence over managers
without explicit engagements. By making public statements, the Big Three can communicate their preferences
to thousands of portfolio companies without having to
engage with each company’s management individually.
For example, BlackRock often sends letters to each of
the most carbon-intensive companies in their portfolio
asking them to disclose climate risks (BlackRock, 2018).
Firms’ managers and/or directors could respond to such
public demands to obtain the support of Big Three in key
voting items. For example, according to Condon (2020),
at Exxon’s 2017 annual meeting, the company’s largest
shareholder, BlackRock, voted against the reelection of two
board members in protest of a “nonengagement” policy
that precluded directors from talking to shareholders
about the company’s strategic response to climate change.
Following the vote, Exxon reconsidered its opposition to
climate risk disclosure and permitted directors to meet
with shareholders going forward.
Furthermore, the Big Three can indirectly induce a
reduction in CO2 emissions by promoting governance
structures that make ﬁrms more responsive to investors
(e.g., Gordon and Pound, 1993; Carleton et al., 1998;
Appel et al., 2016). These governance structures could
make corporate managers more responsive to the recent
demands of all investors (not just the Big Three) to take
climate risks seriously.
While reducing carbon emissions is usually costly,
ﬁrms could curb emissions through relatively eﬃcient
and nondisruptive product and process improvements. In
particular, companies could rebalance their product mix
based on their carbon emissions and/or reduce the amount
of input materials (e.g., Starbucks recently introduced a
strawless cold drink lid). In addition, ﬁrms could improve
their logistics to reduce transportation-related emissions,
switch energy sources (e.g., by moving to cleaner sources
of energy such as natural gas and wind), and/or implement CO2 capture and storage technologies (e.g., Chevron
uses such technologies to capture the emissions they ﬂare
when converting the natural gas to liqueﬁed natural gas).
Finally, ﬁrms could improve end-user energy eﬃciency
(e.g., by building weathering, turning down heating, using
LED light bulbs, and reducing redundant trips).

carbon emission data) in the period between 2005 and
2018.9 Trucost is a widely used source of ﬁrm carbon
emission data for the corporate sector (e.g., MSCI and S&P
use Trucost data in their indexes) and for international
organizations such as UNEP FI (i.e., the United Nations
Environment Program Finance Initiative). Trucost covers a
wide cross-section of ﬁrms around the world (since 2005,
this vendor has typically covered an average of 5046 ﬁrms
per year, which represent approximately 80% of global
market capitalization). Trucost collects carbon emission
data from publicly available sources. When a covered ﬁrm
does not publicly disclose its carbon emissions, Trucost
estimates a ﬁrm’s annual carbon emissions based on an
environmental proﬁling model. Appendix B provides a
description of the process followed by Trucost to assess corporate carbon emissions and an example of the
computation of a ﬁrm’s total CO2 emissions.
Several sample countries have introduced regulations
that enhance the reliability of the emissions reported by
ﬁrms to Trucost, either by mandating strict guidelines
and/or by recommending independent veriﬁcation of the
reported emissions.10 Corroborating the reliability of these
data, prior research ﬁnds a correlation of 0.99 among the
direct CO2 emissions reported by ﬁve providers, namely
CDP, Trucost, MSCI, Sustainalytics, and Thomson Reuters
(Bolton and Kacperczyk, 2019).
We obtain data on institutional ownership from the
FactSet/LionShares database. FactSet/LionShares gathers
institutional ownership for US equities from mandatory
ﬁlings with the Securities and Exchange Commission. For
stocks traded outside the US, FactSet/LionShares gathers
institutional ownership data from national regulatory
agencies and stock exchange announcements as well as
direct disclosures of mutual funds, mutual fund industry
directories, and company proxies and annual reports. We
obtain accounting and market data from Compustat Global
and Datastream/WorldScope. These data sets provide stock
price, balance sheet, and income statement information
for a large number of international ﬁrms.
Table 1 outlines the sample selection procedure. As
shown in Table 1, we depart from 55,118 ﬁrm-year observations in the Trucost data set. To be included in the
sample, we require nonmissing institutional ownership and
ﬁnancial data. We also require the ﬁrm to be incorporated
in one of the 24 countries covered by the MSCI World
Index.11 The resulting sample consists of 42,193 ﬁrm-year

3. Data, sample, and measurement

9
Carbon emission data are rarely available before 2005. The Carbon
Disclosure Project (CDP) launched the ﬁrst climate change survey in 2006,
thus enabling companies to provide standardized disclosure of emission
information.
10
For example, the “Grenelle de l’environnement” in France was addressed to all companies with over 500 employees in 2013. The French
regulation states that a company’s report must be subject to veriﬁcation by an independent third party (appointed by the executive director
or chief executive). In the UK, the reporting of direct and certain indirect emissions has been mandated from 2013, although veriﬁcation is not
mandatory.
11
To mitigate the distorting effects of outliers, we also exclude observations with extreme regression diagnostics (studentized residuals exceeding 2.5). This outlier screen removes 0.8% of the available ﬁrm-years in
the MSCI subsample and 1% of the available ﬁrm-years in the non-MSCI
subsample.

3.1. Data and sample construction
Our initial sample includes the universe of public ﬁrms
covered by Trucost (a commercial provider of corporate

tors to take corrective actions (see Cai et al., 2009; Fischer et al., 2009). In
particular, top managers and directors could lose investors’ voting support
if they fail to address environmental concerns. For example, in his 2020
letter, Larry Fink, CEO of BlackRock states that “we will be increasingly
disposed to vote against management and board directors when companies are not making suﬃcient progress on sustainability-related disclosures and the business practices and plans underlying them.”
678

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Table 1
Sample construction
This table describes the procedure to construct our sample.
Steps of the sample selection procedure:
Firms covered by Trucost from 2005 to 2018
less observations missing institutional ownership information
less observations missing accounting and market data
Final sample:
MSCI constituents
Other ﬁrms

observations, 19,224 observations corresponding to constituents of the MSCI World Index and 22,969 observations
corresponding to ﬁrms that are not included in this index.

# ﬁrm-years

# distinct ﬁrms

55,118
44,252
42,193

9,973
8,109
7,751

19,224
22,969

2,104
5,647

of 7%. This suggests that the Big Three have substantial
voting power in a number of companies around the
world (Fichtner et al., 2017). Total institutional ownership
(i.e., the sum of Big3_hldg and NonBig3_hldg) is 45% on
average, a value that is in line with prior studies on institutional ownership around the world (Bena et al., 2017).
Table 2 also shows that our sample includes a wide variety
of ﬁrms in terms of size, leverage, and proﬁtability (Panel
A) as well as country of origin and industry aﬃliation
(Panels B and C).

3.2. Measurement choices and descriptive statistics
To measure a ﬁrm’s annual carbon emissions, we deﬁne Log (CO2 ) as the logarithm of the ﬁrm’s annual GHG
emission measured in equivalents of metric tons of CO2 .
The variable measuring Big Three ownership, Big3_hldg,
is deﬁned for each ﬁrm-year as the fraction of the ﬁrm’s
equity held by the Big Three in that year. For each ﬁrmyear, we compute Big Three ownership at the parent level;
that is, we aggregate the holdings of all mutual funds of
BlackRock, Vanguard, and State Street Global Advisors in
that ﬁrm-year. Most of the Big Three’s investments in our
sample ﬁrms are held in index funds (out of the average of
4.8% of shares owned by the Big Three in the MSCI ﬁrms,
4% are owned by index funds managed by the Big Three).
NonBig3_hldg is the fraction of the ﬁrm’s equity held by
institutional investors other than the Big Three.
Our tests include a vector of ﬁrm-level control variables, Controls, deﬁned as follows. Size is the logarithm of
total assets. We include this variable to control for the volume of the ﬁrm’s business activity as well as for potential
public pressure over its environmental impact. Log (BM)
is the logarithm of the book-to-market ratio (book value
of equity divided by market value of equity). We include
this variable to control for the ﬁrm’s growth opportunities.
We also include a measure of past performance, ROA,
deﬁned as net income scaled by total assets. Leverage is
computed as the sum of the long-term debt and the debt
in current liabilities over ﬁrm’s total assets. PPE is the
ratio of property, plant, and equipment over the ﬁrm’s
total assets. We include these two variables to measure
credit constraints; more leveraged ﬁrms have to cope with
regular cash outﬂows, which could preclude ﬁnancing
of environmentally beneﬁcial investments. Conversely,
pledgeable assets support more borrowings, which in
turn allow for further investment in pledgeable assets. All
continuous control variables are winsorized at the 1 and
99 percentiles to mitigate the effect of outliers. Standard
errors are double clustered at the ﬁrm and year level (in
Section OD.2 of the Online Appendix, we repeat the tests
using alternative ways of clustering standard errors).
Table 2 presents descriptive statistics for the variables
used in our main tests. As shown in Table 2, the average
ownership by the Big Three among MSCI ﬁrms is 4.8%,
with a standard deviation of 4% and a 75th percentile

4. Engagements of the Big Three with portfolio ﬁrms
To gauge whether the Big Three can induce companies
to reduce carbon emissions, we start by analyzing these
large investors’ engagements with the ﬁrms in their portfolios. The Big Three have recently started to disclose comparable detailed data on private engagements with their
portfolio ﬁrms in investment stewardship reports (ISR).12
According to the narrative in the ISRs, most engagements go beyond sending a letter to the ﬁrm. For example,
BlackRock’s ISR states that the fund’s investment stewardship department had “substantive dialogue with the
companies listed as engaged ﬁrms.” The ISR also states
that the fund “engages companies for the following reasons: (1) to ensure that BlackRock can make well-informed
voting decisions; (2) to explain its voting and governance
guidelines; (3) to convey its thinking on long-term value
creation and sound governance practices.”
We manually collect engagement information from the
most recent ISRs published by the Big Three. We disregard
engagements by letters and include only comprehensive
engagements via calls and in-person meetings. The length
of the period covered by the ISR exhibits some variation across the three investors. BlackRock’s (2019) ISR
includes engagements from 7/1/2018 to 6/30/2019. Vanguard’s 2019 ISR includes engagements from 7/1/2018 to
12/31/2018. State Street’s 2019 ISR includes engagements
from 1/1/2018 to 12/31/2018. Vanguard and State Street
classify engagements into broad categories according to the

12
Before 2018, the disclosure of engagement data was scarce and
different across the three institutions. For example, BlackRock limited
its disclosure of engagements to summary statistics aggregated by region. In 2015, for instance, BlackRock reported that the fund conducted 90 direct engagements with its portfolio companies on environmental issues, but the identity of the companies engaged was
not revealed (see 2015 corporate governance and responsible investment report https://www.blackrock.com/corporate/literature/whitepaper/
blk- cgri- 2015- annual- vande- statistics-report.pdf).

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Journal of Financial Economics 142 (2021) 674–696

Table 2
Descriptive statistics
This table reports descriptive statistics for the variables and observations used in our tests. The sample spans from 2005 to 2018 and includes 19,224
ﬁrm-year observations in the MSCI subsample and 22,969 ﬁrm-year observations in the non-MSCI subsample. Panel A presents descriptive statistics for the
main variables used in our tests. Panel B presents descriptive statistics by country. Panel C presents descriptive statistics by industry aﬃliation. Variables
are deﬁned in Appendix A.
Panel A. Descriptive statistics of key variables
MSCI ﬁrms
Std dev

Non-MSCI ﬁrms

P25

Median

Mean

P75

Std dev

P25

Median

Mean

P75

Log(CO2 )
Big3_hldg
BlackRock_hldg
StateStreet_hldg
Vanguard_hldg
NonBig3_hldg

1.81
0.040
0.013
0.008
0.024
0.288

13.01
0.016
0.008
0.001
0.004
0.147

14.18
0.035
0.015
0.005
0.011
0.309

14.25
0.048
0.018
0.008
0.022
0.405

15.52
0.070
0.024
0.012
0.035
0.695

1.99 10.32
0.052 0.005
0.024 0.001
0.006 0.0 0 0
0.027 0.0 0 0
0.275 0.095

11.74
0.018
0.006
0.001
0.008
0.250

11.65
0.042
0.018
0.004
0.020
0.334

13.00
0.062
0.026
0.004
0.029
0.545

Controls:
Size
Log(BM)
ROA
Leverage
PPE

1.51
0.83
0.06
0.17
0.24

8.49
−1.24
0.02
0.11
0.07

9.37
−0.74
0.04
0.23
0.21

9.56
−0.83
0.05
0.24
0.27

10.45
−0.28
0.08
0.35
0.42

1.5
6.02
0.92 −1.14
0.1
0.01
0.19
0.04
0.24
0.05

6.96
−0.57
0.04
0.18
0.19

7.01
−0.67
0.03
0.21
0.25

7.91
−0.05
0.07
0.33
0.38

Mean CO2
(millions
tons)

Mean
Big3_hldg

8.00
4.21
5.20
4.06
9.18
17.09
1.56
9.20
4.72
12.08
6.00
9.23
3.97
4.69
2.13
13.93
6.41
5.86
10.26
1.39
7.29
2.40
4.21
8.05

0.02
0.03
0.02
0.03
0.03
0.03
0.02
0.02
0.02
0.02
0.03
0.01
0.02
0.07
0.02
0.02
0.02
0.03
0.01
0.02
0.01
0.02
0.02
0.09

Mean CO2
(millions
tons)

Mean
Big3_hldg

11.64
10.72
22.20
3.07
4.73
10.28
3.48
8.34
20.98
4.02
3.39
11.99
6.70
34.03
3.77
0.71
1.93

0.04
0.05
0.06
0.04
0.05
0.04
0.05
0.04
0.03
0.07
0.05
0.05
0.04
0.06
0.05
0.04
0.05

Panel B. Sample distribution by country
MSCI ﬁrms
# obs.

Austria
Australia
Belgium
Canada
Switzerland
Germany
Denmark
Spain
Finland
France
Great Britain
Greece
Hong Kong
Ireland
Israel
Italy
Japan
Netherlands
Norway
New Zealand
Portugal
Sweden
Singapore
US

105
835
146
1,019
428
597
160
328
207
863
1,252
48
422
240
83
262
4,345
297
116
67
87
331
328
6,658

% obs.

# ﬁrms

0.5
4.3
0.8
5.3
2.2
3.1
0.8
1.7
1.1
4.5
6.5
0.2
2.2
1.2
0.4
1.4
22.6
1.5
0.6
0.3
0.5
1.7
1.7
34.6

14
95
18
116
50
67
22
40
23
82
158
10
54
29
15
36
429
33
17
11
11
34
34
706

Non-MSCI ﬁrms
# obs.

% obs.

# ﬁrms

123
1,367
125
976
766
616
109
189
127
503
3,048
85
510
74
344
414
5,030
295
136
99
26
415
193
7,399

0.5
6.0
0.5
4.2
3.3
2.7
0.5
0.8
0.6
2.2
13.3
0.4
2.2
0.3
1.5
1.8
21.9
1.3
0.6
0.4
0.1
1.8
0.8
32.2

23
288
32
255
143
134
25
43
30
117
404
16
80
17
71
96
1,664
57
38
29
8
110
52
1915

# obs.

% obs.

# ﬁrms

909
797
756
294
532
559
767
1,556
383
235
2,568
573
995
592
1,457
3,269
6,727

4.0
3.5
3.3
1.3
2.3
2.4
3.3
6.8
1.7
1.0
11.2
2.5
4.3
2.6
6.3
14.2
29.3

226
165
170
86
128
133
198
402
74
53
600
126
217
112
380
825
1,752

Mean CO2
(millions
tons)

Mean
Big3_hldg

0.49
0.26
1.08
0.58
0.59
2.41
5.91
1.37
0.68
0.96
0.36
0.36
3.47
0.61
0.39
1.75
0.41
0.77
0.44
0.67
2.26
0.58
0.41
0.75

0.02
0.02
0.02
0.02
0.01
0.02
0.02
0.01
0.01
0.01
0.02
0.01
0.02
0.03
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.10

Mean CO2
(millions
tons)

Mean
Big3_hldg

1.47
0.86
1.45
0.42
0.41
1.27
0.24
0.86
1.89
0.75
0.41
2.49
1.65
4.67
0.47
0.22
0.28

0.03
0.04
0.05
0.03
0.04
0.04
0.04
0.03
0.05
0.06
0.04
0.04
0.04
0.06
0.04
0.05
0.04

Panel C. Sample distribution by industry
MSCI ﬁrms
# obs.

Food
881
Mining and minerals
412
Oil and petroleum products
1,007
Textiles, apparel & footwear
231
Consumer durables
314
Chemicals
668
Drugs, soap, perfume, tobacco
977
Construction and constr. materials
986
Steel works, etc.
340
Fabricated products
108
Machinery and business equipment
2,071
Automobiles
562
Transportation
1,159
Utilities
1,126
Retail stores
1,237
Banks, insurance, and other ﬁnancials 3,025
Other
4,120

% obs.

# ﬁrms

4.6
2.1
5.2
1.2
1.6
3.5
5.1
5.1
1.8
0.6
10.8
2.9
6.0
5.9
6.4
15.7
21.4

97
50
118
25
34
69
99
113
41
9
223
56
126
109
130
329
476

Non-MSCI ﬁrms

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Journal of Financial Economics 142 (2021) 674–696

reasons for the engagements. BlackRock simply publishes
a list of ﬁrms contacted for comprehensive engagement.
We ﬁrst analyze the descriptive statistics of these data.
In absolute terms, we observe that, during the period
covered by the ISR reports, the Big Three engage with
a relatively large number of ﬁrms; BlackRock engaged
with 1458 ﬁrms, State Street engaged with 686 ﬁrms,
and Vanguard engaged with 356 ﬁrms. In relative terms,
however, the Big Three appear to engage with a relatively
small percentage of their portfolio ﬁrms: BlackRock, State
Street, and Vanguard engage with 9%, 5%, and 3% of their
portfolio ﬁrms, respectively. The Big Three engage much
more often with ﬁrms included in MSCI World Index
than with ﬁrms not included in that index; 48% (15%) of
MSCI (non-MSCI) ﬁrms were targeted by the Big Three in
2018. In absolute terms, the number of engagements is
also substantially higher among MSCI ﬁrms than among
non-MSCI ﬁrms (625 and 275, respectively). Thus, the
Big Three appear to focus their engagement efforts on
the largest public ﬁrms in each country (the MSCI World
Index aims to cover 85% of total market capitalization
in 24 developed countries). The focus on large ﬁrms is
consistent with these ﬁrms being more inﬂuential (more
visible) and having a potentially stronger effect on climate
change.13
Next, we conduct a multivariate test on the determinants of the probability that a given ﬁrm is engaged
by each of the Big Three. For each of the Big Three,
we construct the left hand side variable as an indicator that equals one if the ﬁrm is included in the list
of engagements disclosed in 2019 ISR of one of the Big
Three institutions and zero otherwise (we refer to these
institution-speciﬁc variables as Engagement_BlackRock,
Engagement_StateStreet, and Engagement_Vanguard, respectively).14 We construct these variables for the cross-section
of our sample ﬁrms as of the start of 2018 (i.e., the ﬁrms
in the Trucost universe that meet the data requirements
described in Section 3).
The right hand side variables are deﬁned as follows.
Log (CO2 ) is the logarithm of GHG emissions, as previously
deﬁned. Big3_hldg is the fraction of the ﬁrm’s shares held
by funds managed by BlackRock, Vanguard, or State Street.
The speciﬁcation also includes a vector of controls for
ﬁrm characteristics: Size, Log (BM), ROA, Leverage, and
PPE, all of them as previously deﬁned (see Section 3 and
Appendix A for variable deﬁnitions). We also include an
indicator for whether the ﬁrm is an MSCI constituent
(MSCI_constituent).

Table 3 presents the results of estimating logit and
OLS regressions for each of the Big Three based on the
variables described above. The results reveal that the probability of Big Three engagement is higher if the target ﬁrm
exhibits higher levels of carbon emissions in the previous
year (the coeﬃcient on Log (CO2 ) is consistently positive
and statistically signiﬁcant). Table 3 also shows that, in
general, the Big Three are more likely to engage with
ﬁrms in which they are more inﬂuential (the coeﬃcients
on the three institutions’ ownership share are generally
positive and statistically signiﬁcant). The association of the
probability of engagement with Size and MSCI_constituent
is often positive and strong, which conﬁrms that the Big
Three focus their engagement efforts on MSCI constituents.
In Online Appendix OD.1, we conduct a placebo test by
constructing the dependent variables in Table 3 using
engagements that are not related to environmental issues.
The coeﬃcient on Log (CO2 ) is no longer signiﬁcant.
5. Carbon emissions and Big Three shareholdings
The previous results indicate that the Big Three selectively engage with a number of ﬁrms in their portfolio
companies on environmental issues. We next explore
whether higher ownership by these large investors is
followed by lower levels of carbon emissions.
To study the relation between Big Three ownership and
corporate carbon emissions, we estimate the following
model:

Log (CO2 )it = α + β ∗ Big3_hldgit-1 + γ ∗ NonBig3_hldgit-1
+ ∗ Controlsit-1 + τ t + δ i + ε it,
(1)
where Big3_hldg, NonBig3_hldg, and Controls are as previously deﬁned (see Section 3 and Appendix A for variable
deﬁnitions). Subindexes i and t refer to ﬁrm i and year t,
respectively. All these independent variables are measured
at the end of the prior year to avoid simultaneity bias.
τ t and δ i denote year and ﬁrm ﬁxed effects, respectively.
When estimating this model, we distinguish between constituents of the MSCI World Index and other ﬁrms, as our
results from tests of the probability of engagement (see
Table 3) suggest that the Big Three focus their monitoring
efforts on environmental issues in MSCI constituents.
Table 4 presents the results of this test. For the subsample of MSCI ﬁrms (i.e., columns 1–3), the coeﬃcient on
Big3_hldg is negative and statistically signiﬁcant, consistent
with the notion that ownership by the Big Three is associated with a subsequent decrease in CO2 emissions. The
negative association is robust to including year, industry,
country, and ﬁrm ﬁxed effects.15 That is, the association
holds both in the cross-section and in the time series and
thus is unlikely to be confounded either by time-invariant
country and industry characteristics or by the potential effect of the volume of economic activity on overall levels of
CO2 emissions. In contrast with this result, the coeﬃcient
on NonBig3_hldg is not statistically signiﬁcant, suggesting

13
Large ﬁrms emit the largest portion of corporate emissions. For
example, in 2017 the aggregate level of total CO2 emissions for our
sample of US MSCI ﬁrms is 3698 million metric tons of CO2 equivalent, which is around 70% of the total US CO2 emissions (https://www.
epa.gov/ghgemissions/inventory- us- greenhouse- gas- emissions- and- sinksfast-facts).
14
The classiﬁcation of engagements across the Big Three is not homogeneous. Vanguard includes engagements on environmental issues in the
“oversight of strategy and risks” category. State Street includes engagements on environmental issues in the “environmental/social” category.
While BlackRock does not classify engagements into categories, environmental issues are commonly included in the agenda of BlackRock’s engagements with portfolio companies (se.g., BlackRock, 2019b).

15
We deﬁne industry aﬃliations using Fama-French 38 industry
portfolios (https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_
Library/det_38_ind_port.html).

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Journal of Financial Economics 142 (2021) 674–696

Table 3
Big Three engagements with individual ﬁrms
This table presents an analysis of the determinants of the engagements of the Big Three (BlackRock, Vanguard, and State Street) with individual ﬁrms
in their portfolios. The sample is from 2018 engagement data and includes 3636 ﬁrm observations. The dependent variable Engagement_BlackRock is an
indicator variable that equals one if BlackRock engages with the ﬁrm and zero otherwise. The other two dependent variables, Engagement_StateStreet and
Engagement_Vanguard, are deﬁned in the same way for State Street and Vanguard, respectively. In the case of State Street we consider only engagements
about environmental/social issues. In the case of Vanguard we consider only engagements about “oversight of strategy and risk” (which include environmental issues). The independent variables are measured at the end of the prior year. Log (CO2 ) is the logarithm of the ﬁrm’s total GHG emissions.
BlackRock_hldg is BlackRock’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by BlackRock’s mutual funds. StateStreet_hldg and Vanguard_hldg are deﬁned in the same way for State Street and Vanguard, respectively. The control variables are deﬁned in Appendix A. t-statistics are in
parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at the 10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.
Dependent variable:
Engagement_BlackRock

Log(CO2 )
BlackRock_hldg

Engagement_StateStreet

Engagement_Vanguard

Logit
(1)

OLS
(2)

OLS
(3)

Logit
(4)

OLS
(5)

OLS
(6)

Logit
(7)

OLS
(8)

OLS
(9)

0.156∗∗∗
(5.803)
16.890∗∗∗
(8.631)

0.022∗∗∗
(5.233)
2.425∗∗∗
(7.414)

0.025∗∗∗
(3.676)
2.232∗∗∗
(5.863)

0.315∗∗∗
(5.937)

0.013∗∗∗
(5.649)

0.009∗∗
(2.355)

0.190∗∗∗
(3.791)

0.006∗∗
(2.374)

0.003
(0.671)

57.763∗∗∗
(7.382)

4.083∗∗∗
(8.231)

2.107∗∗∗
(2.944)
1.218∗∗∗
(9.453)
0.043∗∗∗
(3.857)

−0.115
(−0.458)
0.045∗∗∗
(3.941)

0.026∗∗∗
(7.112)
−0.024∗∗∗
(−4.294)
−0.002
(−0.037)
−0.058∗∗
(−2.264)
0.022
(1.298)
NO
NO

0.036∗∗∗
(7.278)
−0.014∗∗
(−2.392)
0.043
(0.821)
−0.064∗∗
(−2.446)
0.029
(1.490)
YES
YES

StateStreet_hldg

0.752∗∗∗
(6.704)

0.153∗∗∗
(8.071)

0.134∗∗∗
(6.977)

0.692∗∗∗
(2.886)

0.029∗∗∗
(2.658)

0.029∗∗
(2.489)

23.363∗∗∗
(10.227)
0.711∗∗∗
(3.013)

0.292∗∗∗
(7.360)
−0.051
(−0.849)
0.114
(0.155)
−0.826∗∗∗
(−2.892)
−0.287
(−1.523)
NO
NO

0.043∗∗∗
(6.966)
−0.009
(−0.963)
−0.111
(−1.224)
−0.139∗∗∗
(−3.165)
−0.045
(−1.565)
NO
NO

0.052∗∗∗
(6.288)
−0.015
(−1.508)
−0.132
(−1.443)
−0.105∗∗
(−2.384)
−0.017
(−0.516)
YES
YES

0.365∗∗∗
(4.823)
−0.241∗∗
(−2.298)
1.083
(0.700)
0.358
(0.685)
0.227
(0.663)
NO
NO

0.013∗∗∗
(3.715)
−0.016∗∗∗
(−2.932)
−0.036
(−0.703)
0.003
(0.120)
0.021
(1.264)
NO
NO

0.024∗∗∗
(5.017)
−0.009
(−1.632)
0.010
(0.180)
−0.004
(−0.140)
0.021
(1.085)
YES
YES

0.690∗∗∗
(9.188)
−0.320∗∗∗
(−3.027)
4.326∗∗∗
(2.671)
−0.943∗
(−1.816)
0.326
(0.992)
NO
NO

Vanguard_hldg
MSCI_constituent
Controls:
Size
Log(BM)
ROA
Leverage
PPE
Country FE
Industry FE
Pseudo R2 /R2
# obs.

0.16
3,262

0.17
3,262

0.22
3,262

0.24
3,286

0.11
3,286

that institutional ownership is generally not associated
with a decrease in carbon emissions.
Fig. 1 analyzes whether the association between Big
Three ownership and carbon emissions is concentrated in
cases in which Big Three increases to the point of holding
a signiﬁcant stake in a given company, namely in cases
in which the Big Three are likely to be more inﬂuential.
In the analysis of Fig. 1, we reestimate Eq. (1) replacing
Big3_hldg with separate indicator variables, each marking
a 1% interval of Big3_hldg values. That is, the ﬁrst indicator
variable equals one if Big3_hldg ∈ [0%, 1%] and zero otherwise, the second indicator variable equals one if Big3_hldg
∈ [1, 2%] and zero otherwise, the third indicator variable
equals one if Big3_hldg ∈ [2, 3%] and zero otherwise, and
so forth. The last indicator variable equals one if Big3_hldg
>10% and zero otherwise. We deﬁne the [0%, 1%] interval
as baseline, and thus we exclude the indicator variable for
Big3_hldg ∈ [0%, 1%]. As shown in Fig. 1, the association
between Big Three ownership and CO2 emissions becomes
signiﬁcant when the ownership of these investors crosses
the 3,4% ownership threshold. This evidence is consistent
with our conjecture that ﬁrms respond to the Big Three’s
requests to reduce emissions only when these investors
can be pivotal in key voting items.

0.14
3,286

0.29
3,323

0.12
3,323

0.16
3,323

In addition, we offer three considerations that might
help understand how the Big Three can inﬂuence ﬁrms
even though these institutions usually do not hold majority stakes. First, while the Big Three might start acquiring
a modest stake in a given company, this stake is likely
to increase in the future (among other things, because
the total volume of money invested in the mutual funds
managed by these institutions is growing signiﬁcantly).16
Second, the Big Three’s position on environmental matters
could have spillovers on other institutional investors. For
example, it is possible that some passive investors that do
not have the resources to monitor governance practices
follow the Big Three’s policies. Moreover, some environmental activists could feel encouraged to put pressure on
the ﬁrm if they observe that the Big Three are willing to
support efforts to reduce emissions. Consistent with this,
16
Bebchuk and Hirst (2019a) estimate the total inﬂows to the Big Three
from 2009 to 2018 to be more than $3 trillion, which represent 82% of the
inﬂows to all active and passive funds over that period. As a result, they
estimate that the Big Three could cast as much as 40% of the votes in S&P
500 companies within two decades. Indeed, in August of 2019, US equity
index fund assets oﬃcially surpassed their actively managed counterparts
for the ﬁrst time, reaching $4.27 trillion in total assets under management
(Griﬃn, 2020).

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Journal of Financial Economics 142 (2021) 674–696

Table 4
Big Three ownership and ﬁrms’ carbon emissions
This table presents an analysis of the association between levels of Big Three ownership and levels of total carbon emissions. The sample spans from 2005
to 2018 and includes 19,224 ﬁrm-year observations in the MSCI subsample and 22,969 ﬁrm-year observations in the non-MSCI subsample. The dependent
variable is the logarithm of CO2 (i.e., the ﬁrm’s total GHG emissions measured in equivalents of metric tons of CO2 ). The experimental variable, Big3_hldg,
is the fraction of the ﬁrm’s equity owned by mutual funds sponsored by BlackRock, Vanguard, or State Street. NonBig3_hldg is the fraction of the ﬁrms’
equity owned by funds managed by institutions other than BlackRock, Vanguard, and State Street. The control variables are deﬁned in Appendix A. Columns
(1)–(3) report results corresponding to the subsample of ﬁrms that are members of MSCI World Index. Columns (4)–(6) report results corresponding to the
subsample of ﬁrms that are not members of MSCI World Index. Both subsamples span the period from 2005 to 2018. Independent variables are measured
at the end of the prior year. Standard errors are clustered at the ﬁrm and year level. t-statistics are in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at the
10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.
Dependent variable: Log (CO2 )
MSCI
(1)
Big3_hldg
NonBig3_hldg
Controls:
Size
Log(BM)
ROA
Leverage
PPE
Country FE
Industry FE
Year FE
Firm FE
R2
# obs.

(5)

(6)

−3.44∗∗∗
(−5.76)
−0.04
(−0.25)

−1.69∗∗
(−2.27)
−0.12
(−0.74)

−1.00∗∗∗
(−2.83)
−0.07
(−0.75)

−0.76
(−1.09)
0.36∗∗∗
(3.43)

0.66
(1.41)
0.26∗∗
(2.50)

0.46
(1.60)
0.18∗∗
(2.47)

0.79∗∗∗
(42.88)
0.01
(0.55)
1.52∗∗∗
(4.55)
0.03
(0.23)
1.27∗∗∗
(8.32)
YES
YES
NO
NO

0.80∗∗∗
(42.21)
0.01
(0.30)
1.53∗∗∗
(4.65)
0.02
(0.15)
1.27∗∗∗
(8.24)
YES
YES
YES
NO

0.55∗∗∗
(13.77)
−0.02∗∗
(−2.29)
0.89∗∗∗
(5.39)
0.05
(0.69)
−0.01
(−0.08)
NO
NO
YES
YES

0.81∗∗∗
(50.85)
−0.06∗∗∗
(−3.25)
2.95∗∗∗
(14.26)
0.38∗∗∗
(3.03)
1.19∗∗∗
(12.01)
YES
YES
NO
NO

0.79∗∗∗
(54.50)
−0.06∗∗∗
(−3.16)
2.83∗∗∗
(12.89)
0.41∗∗∗
(3.29)
1.15∗∗∗
(11.54)
YES
YES
YES
NO

0.56∗∗∗
(14.96)
−0.05∗∗∗
(−4.36)
0.57∗∗∗
(6.30)
0.17∗∗
(2.22)
0.51∗∗∗
(4.38)
NO
NO
YES
YES

0.75
19,224

(2)

Non-MSCI

0.75
19,224

(3)

0.98
19,134

(4)

0.73
22,969

0.74
22,969

0.98
22,468

Fig. 1. Big Three ownership thresholds and carbon emissions. This ﬁgure reports the association between Big Three ownership thresholds and carbon
emissions. The sample spans from 2005 to 2018 and includes 19,224 ﬁrm-year observations in the MSCI subsample. We estimate Eq. (1) but replace
Big3_hldg with separate indicator variables, each marking a 1% interval of Big3_hldg values. That is, the ﬁrst indicator variable equals one if Big3_hldg ∈
[0, 1%] and zero otherwise, the second indicator variable equals one if Big3_hldg ∈ [1, 2%] and zero otherwise, the third indicator variable equals one
if Big3_hldg ∈ [2, 3%] and zero otherwise, and so forth. The last indicator variable equals one if Big3_hldg >10% and zero otherwise. We omit the ﬁrst
indicator variable, that is, the indicator variable for Big3_hldg ∈ [0, 1%]. It therefore serves as a benchmark and has a coeﬃcient value of zero (and no
conﬁdence interval). The ﬁgure plots the coeﬃcient estimates of the ten intervals together with their 95% conﬁdence limits. The dependent variable, Log
(CO2 ), the sample, control variables, and ﬁxed effects are as in Model 3, Table 4, Panel A. Filled dots (as opposed to empty dots) denote that the coeﬃcient
is statistically different from the benchmark (i.e., Big3_hldg ∈ [0, 1%]) (two-tailed, 10% level).

683

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Journal of Financial Economics 142 (2021) 674–696

Appel et al. (2019a) provide evidence that large institutional investors are crucial for the success of hedge fund
activism. Third, the inﬂuence of the Big Three could go beyond the holdings of the mutual funds sponsored by these
institutions. For example, large institutions often hold corporate debt and indirectly own corporate shares through
investment vehicles included in their family of investment
companies (e.g., pension funds and active funds, including
even hedge funds). As such, our measure of Big Three ownership is a lower bound estimate of the total amount of
claims owned directly or indirectly by these institutions (a
total amount that is not possible to measure across countries due to lack of available data).17 Taken together, these
considerations suggest that the percentage ownership of
the Big Three in a company is likely to be a conservative
estimate of the inﬂuence of these institutions in the ﬁrm.
Table 5 presents a variant of the analysis in Table 4 in
which we focus on changes rather than levels of Big
Three ownership. In Table 5, Panel A, we replace Big3_hldg
with Big3_increase, an indicator variable that equals one
if _Big3_hldg>1%. This variable identiﬁes cases in which
Big Three ownership increases meaningfully. Consistent
with Big3_increase identifying cases with relatively high
Big Three inﬂuence, the mean of Big3_hldg conditional on
Big3_increase=1 is 8%. Consistent with Table 4, Table 5,
Panel A shows that the coeﬃcient on Big3_increase is
consistently negative and signiﬁcant across speciﬁcations.
As an alternative speciﬁcation, Table 5, Panel B analyzes
the association between changes in CO2 emissions and
changes in Big Three ownership for MSCI. The dependent variable is _CO2 (t−s, t), deﬁned as the fractional
change of CO2 emissions from year t−s to year t, that is,
(CO2t −CO2t-s )/CO2t-s (s=1, …, 12). In parallel to Panel A,
the experimental variable is
_Big3_hldg (t−s−1, t−1),
deﬁned as the change in Big3_hldg from year t−s−1 to
year t−1. For consistency with the previous test, we also
include
_NonBig3_hldg (t−s−1, t−1), deﬁned as the
change in NonBig3_hldg from year t−s−1 to year t−1. The
results of Table 5, Panel B show that changes in Big Three
ownership are negatively associated with subsequent
changes in carbon emissions for MSCI ﬁrms. Panel B also
highlights that, while part of the reduction in emissions is
already observable in the subsequent year, the reduction
also extends to subsequent periods (e.g., ﬁrms might
require more than one year to implement changes, or the
changes might require some time to become effective).
To delve into the sources of our results, in Table 6
we decompose Big3_hldg into the holdings of each of
the three institutions: BlackRock_hldg, StateStreet_hldg,
and Vanguard_hldg. We also decompose NonBig3_hldg in
three ways. First, we split NonBig3_hldg into NonBig3_large
(deﬁned as the fraction of the ﬁrm’s equity held by
the largest 100 institutions other than the Big Three)
and NonBig3_small (deﬁned as the difference between
NonBig3_hldg and NonBig3_large). Second, we split Non-

Big3_hldg into NonBig3_index (deﬁned as the fraction of
the ﬁrm’s equity held by indexers other than the Big
Three) and NonBig3_nonIndex (deﬁned as the difference
between NonBig3_hldg and NonBig3_index).18 Third, we
split NonBig3_Hldg into NonBig3_LT (deﬁned as the fraction
of the ﬁrm’s equity held by long-term investors other than
the Big Three) and NonBig3_ST (deﬁned as the difference
between NonBig3_hldg and NonBig3_LT).19
As shown in Table 6, the negative association between
Big Three ownership and CO2 emissions is driven by BlackRock and State Street.20 Table 6 also reveals that there is a
negative association between CO2 emissions and non-Big
Three funds with similar characteristics: index tracking,
long term, and large. That said, Table 6 also suggests
that these associations are substantially lower than that
between CO2 emissions and Big Three ownership.
Tables 4–6 also present results for the subsample
of nonconstituents of the MSCI World Index. While in
Table 4 the coeﬃcient on Big3_hldg is not statistically
signiﬁcant for nonconstituents of the MSCI, Table 4 shows
a consistently positive coeﬃcient on NonBig3_hldg. We
offer two considerations to interpret this result. First, this
positive association is not statistically signiﬁcant in the
parallel tests of Table 5. Second, Table 6 reveals that, in
contrast to the results in the MSCI subsample, the positive
association between CO2 emissions and non-Big Three
funds in the non-MSCI subsample is driven by funds that
are not index tracking, are not long term, and are not
large. As such, one possible interpretation of the positive
coeﬃcient on NonBig3_hldg for the non-MSCI subsample
is that there is an increase in CO2 emissions preceded by
activist investors pressuring for short-term performance.
Gauging whether the potential effect of the Big Three is
large enough to meaningfully contribute to the worldwide
objective of reducing carbon emissions is an extremely
ambitious task that exceeds the scope of this paper. With
this caveat in mind, we provide some guidance to interpret
our results. In Table 4, the magnitude of the coeﬃcient
on Big3_hldg ranges from −3.44 to −1.00, depending on
the speciﬁcation. A coeﬃcient of −1.00 suggests that a

18
To identify index funds we use the variable “style” provided by FactSet. However, the investment style variable is available only for 48% of
funds in our sample; therefore, we augment the investment style classiﬁcation by using fund names. In particular, we take the list of 88 common
index benchmarks from Cremers et al. (2016) and label as indexers all
funds that refer in their names to one of these benchmarks.
19
Following Gaspar et al. (2005), we use the variable “investor
turnover,” a measure of the investment horizon of institutions, to classify institutions as either long or short term. The rationale behind this
measure is that an investor is classiﬁed as short term if it reshuﬄes its
overall portfolio frequently. Alternatively, an investor is classiﬁed as long
term if it holds its portfolio positions unchanged for a long time. Following Gaspar et al. (2013), we classify institutions with time averaged
turnover rates in the bottom 33rd percentile as long-term investors.
20
According to the data of Appendix C, Vanguard is the latest of the Big
Three in increasing signiﬁcantly its commitment to environmental issues.
In terms of the values of the commitment index constructed based on
these data, Vanguard is also the institution with the lowest values. These
patterns provide a potential explanation for the results in Table 6. That
said, we do ﬁnd a negative and signiﬁcant coeﬃcient on Vanguard_hldg
when we remove ﬁrm ﬁxed effects from the speciﬁcation (untabulated),
suggesting that Vanguard also contributes (although perhaps to a lower
degree) to the reduction of emissions.

17
Nonetheless, we also note that these other investment companies related to the Big Three act independently in environmental, social, and
governance (ESG) matters as their investment strategy could differ from
that of the mutual funds sponsored by the corresponding investment
family.

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Journal of Financial Economics 142 (2021) 674–696

Table 5
Changes in ownership
This table repeats the analysis in Table 4 using alternative speciﬁcations based on changes in ownership. Panel A replaces Big3_hldg with Big3_increase,
deﬁned as one if _Big3_hldg > 1% and zero otherwise. NonBig3_increase is deﬁned as one if _NonBig3_hldg > 1% and zero otherwise. The sample spans
from 2005 to 2018 and includes 19,224 ﬁrm-year observations in the MSCI subsample and 22,969 ﬁrm-year observations in the non-MSCI subsample. Panel
B presents results for MSCI ﬁrms using a speciﬁcation in changes. _CO2 (t−s, t) is the fractional change of CO2 emissions from year t−s to year t, that
is, (CO2t −CO2t-s )/CO2t-s (s = 1, …, 12). _Big3_hldg (t−s−1, t−1) is the change in Big3_hldg from year t−s−1 to year t−1. _NonBig3_hldg (t−s−1, t−1) is
the change in NonBig3_hldg from year t−s−1 to year t−1. Panel C repeats the analysis in Panel B for non-MSCI ﬁrms. The control variables are deﬁned in
Appendix A. Both subsamples span the period from 2005 to 2018. Independent variables are measured at the end of the prior year. Standard errors are
clustered at the ﬁrm and year level in Panel A and at the ﬁrm level in Panels B and C. t-statistics are in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at
the 10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.
Panel A. Nonnegligible changes in Big Three ownership
Dependent variable: Log(CO2 )
MSCI

Non-MSCI

(1)

(2)

(3)

(4)

(5)

(6)

Controls
Country FE
Industry FE
Year FE
Firm FE

−0.10∗∗∗
(−4.49)
−0.02
(−0.65)
YES
YES
YES
NO
NO

−0.04∗∗
(−2.52)
−0.04∗
(−2.05)
YES
YES
YES
YES
NO

−0.02∗∗∗
(−3.97)
−0.01∗
(−1.93)
YES
NO
NO
YES
YES

−0.05∗
(−1.65)
−0.02
(−1.45)
YES
YES
YES
NO
NO

−0.02
(−0.63)
−0.03∗
(−2.09)
YES
YES
YES
YES
NO

0.00
(0.33)
0.00
(0.50)
YES
NO
NO
YES
YES

R2
# obs.

0.74
19,224

0.75
19,224

0.98
19,134

0.73
22,969

0.74
22,969

0.98
22,468

Big3_increase
NonBig3_increase

Panel B. Speciﬁcation in changes (MSCI ﬁrms)
_CO2 (t−s, t)

Dependent variable:
(1)
s=1

(2)
s=2

(3)
s=3

(4)
s=4

(5)
s=5

(6)
s=6

(7)
s=7

(8)
s=8

(9)
s=9

(10)
s = 10

(11)
s = 11

(12)
s = 12

−0.78∗∗ −1.42∗ −2.68∗∗ −4.07∗∗ −3.81∗
−5.14∗∗ −4.75∗∗ −4.58∗∗ −6.76∗ −3.32∗
−4.45∗∗ −5.46∗
(−2.08) (−1.82) (−2.16) (−2.18) (−1.76) (−2.11) (−2.26) (−2.52) (−1.69) (−1.90) (−2.01) (−1.88)
_NonBig3_hldg (t−s−1, t−1)
0.20∗∗
0.07
−0.34
−0.13
−0.65∗∗ −1.48
−1.39∗
−1.97∗
−3.41
−1.31∗∗ −0.97
−1.16
(2.17)
(0.44) (−0.73) (−0.53) (−2.02) (−1.58) (−1.83) (−1.89) (−1.53) (−2.13) (−1.20) (−1.22)
YES
Controls
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
Year FE
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
YES
_Big3_hldg (t−s−1, t−1)

R2
# obs.

0.01
16,980

0.01
14,917

0.02
13,025

0.02
11,350

0.03
9824

0.04
8,390

0.07
7,072

0.11
5,856

0.07
4,699

0.16
3,620

0.20
2,595

0.17
1,631

Panel C. Speciﬁcation in changes (non-MSCI ﬁrms)
Dependent variable:

_CO2 (t−s, t)

(1)
s=1

(2)
s=2

(3)
s=3

(4)
s=4

(5)
s=5

(6)
s=6

(7)
s=7

(8)
s=8

(9)
s=9

(10)
s = 10

(11)
s = 11

(12)
s = 12

Controls
Year FE

1.31
(1.20)
0.93∗
(1.75)
YES
YES

1.46
(0.87)
1.51∗∗
(2.23)
YES
YES

1.81
(1.06)
0.75
(1.52)
YES
YES

1.00
(0.90)
1.40
(1.14)
YES
YES

5.51
(1.04)
1.96
(1.11)
YES
YES

4.83
(1.06)
1.20
(0.89)
YES
YES

−1.23
(−0.51)
0.28
(0.49)
YES
YES

−0.19
(−0.06)
0.60
(0.82)
YES
YES

2.29
(0.63)
1.51
(1.07)
YES
YES

2.31
(0.53)
2.43
(1.05)
YES
YES

0.34
(0.10)
1.95
(1.01)
YES
YES

−2.34
(−0.67)
0.55
(0.67)
YES
YES

R2
# obs.

0.01
16,964

0.03
11,765

0.04
7,638

0.03
6,237

0.03
4,982

0.04
3,953

0.09
3,306

0.09
2,714

0.09
2,162

0.08
1,613

0.08
1,165

0.14
717

_Big3_hldg (t−s−1, t−1)
_NonBig3_hldg (t−s−1, t−1)

one standard deviation increase in Big3_hldg in a given
ﬁrm is associated with a reduction of approximately 2%
in corporate CO2 emissions (the within-ﬁrm standard deviation of Big3_hldg is 2.11%). Similarly, the magnitude of
the coeﬃcient on Big3_increase in Column (3) of Table 5 is
close to −0.02, which also suggests a decrease of approximately 2% in corporate CO2 emissions. A 2% decrease
is a sizable effect when compared to current emission
reduction goals proposed by environmental initiatives. For

instance, the objective of the Regional Greenhouse Gas
Initiative (RGGI) is to reduce emission cap by 2.5% each
year from 2015 to 2020 (i.e., 12.5% in ﬁve years).21 While
among smaller, non-MSCI ﬁrms the potential effect of

21
The RGGI founded in January 2007 is a state-level emissions capping
and trading program carried out by nine northeastern US states (https:
//www.rggi.org/).

685

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Table 6
Breakdown of ownership
This table repeats the analysis in Table 4 decomposing the variables Big3_hldg and NonBig3_hldg. The sample spans from 2005 to 2018 and includes
19,224 ﬁrm-year observations in the MSCI subsample and 22,969 ﬁrm-year observations in the non-MSCI subsample. BlackRock_hldg is BlackRock’s holding
in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by BlackRock’s mutual funds. StateStreet_hldg and Vanguard_hldg are deﬁned in the same way
for the other two Big Three institutions. NonBig3_index is fraction of the ﬁrm’s equity held by indexers other than the Big Three. NonBig3_nonindex is
the difference between NonBig3_hldg and NonBig3_index. NonBig3_LT is fraction of the ﬁrm’s equity held by long-term investors other than the Big Three.
NonBig3_ST is the difference between NonBig3_hldg and NonBig3_LT. NonBig3_large isthe fraction of the ﬁrm’s equity held by large investors (top 100 by
size) other than the Big Three. NonBig3_small is the difference between NonBig3_hldg and NonBig3_large. In columns (1)–(3) the rest of the speciﬁcation is
as in column (3) of Table 4. In columns (4)–(6) the rest of the speciﬁcation is as in column (6) of Table 4. Standard errors are clustered at the ﬁrm and
year level. t-statistics are in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at the 10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.
Dependent variable: Log (CO2 )
MSCI
(1)

(2)
∗∗

−0.82
(−2.33)

Big3_hldg
BlackRock_hldg
State Street_hldg
Vanguard_hldg
NonBig3_hldg

Non-MSCI
(3)

(4)
∗∗∗

−1.10
(−3.20)

(5)
∗∗∗

−0.96
(−2.79)

∗∗∗

−1.49∗∗∗
(−2.69)
−0.06
(−0.60)

NonBig3_nonindex

(7)

(8)

0.44
(1.47)

0.42
(1.49)

0.47
(1.63)

−0.21
(−0.49)
−0.84
(−0.64)
2.00∗∗∗
(3.26)
0.18∗∗
(2.48)

−2.79
(−5.27)
−2.45∗
(−1.94)
0.62
(1.13)
−0.05
(−0.57)

NonBig3_index

(6)

0.02
(0.05)
0.17∗∗
(2.42)
−0.34∗∗∗
(−2.56)
0.14
(1.39)

NonBig3_LT
NonBig3_ST
NonBig3_large
NonBig3_small
Controls
Year FE
Firm FE

YES
YES
YES

YES
YES
YES

YES
YES
YES

R2
# obs.

0.98
19,134

0.98
19,134

0.98
19,134

−0.03
(−0.30)
0.28∗∗∗
(4.05)
−0.26∗∗
(−2.10)
0.12
(1.15)
YES
YES
YES
0.98
19,134

the Big Three on corporate CO2 emissions appears to be
insigniﬁcant, MSCI ﬁrms account for a large portion of the
market capitalization and a large part of the corporate CO2
emissions. In our sample, the 16% of the ﬁrms included
in the MSCI World Index account for 56% of the total CO2
emissions (these data correspond to 2018, the most recent
year in our sample period).
Nonetheless, some studies on climate change call for
higher magnitudes to stop global warming; according to
a recent study commissioned by the United Nations, the
global volume of GHG emissions needs to drop by 55% by
2030 (i.e., around 5% each year) to limit global warming to
1.5°.22 Moreover, an additional consideration is important
for interpreting the magnitude of our results; the estimated effect based on our results (i.e., 2%) corresponds to
the within-ﬁrm standard deviation of Big3_hldg, suggesting
that we should not expect a 2% decrease in emissions
across the board every year.

YES
YES
YES

YES
YES
YES

YES
YES
YES

0.98
22,468

0.98
22,468

0.98
22,468

0.15
(1.53)
0.20∗∗
(2.73)
YES
YES
YES
0.98
22,468

6. Sharpening identiﬁcation
An obvious concern about our previous tests is that
ﬁrms could reduce carbon emissions for reasons correlated
with the ownership of the Big Three in the company.
To the extent that our previous results are robust to
controlling for time-invariant cross-sectional variation
(our models include ﬁrm ﬁxed effects), our inferences
cannot be confounded by an omitted variable unless this
variable covaries with our key variables not only in the
cross-section but also in the time series. Nonetheless, we
conduct several tests to sharpen identiﬁcation.
6.1. Additional ﬁxed effects
Table 7 presents the results of repeating the analysis in
Tables 4 and 5 (Panel A) for the MSCI sample using a more
restrictive ﬁxed effect structure. In particular, we include
country-by-year, industry-by-year, size-decile-by-year, and
country-by-industry-by-year ﬁxed effects. As shown in
Table 7, our inferences are not sensitive to including
these additional ﬁxed effects; the coeﬃcients on Big3_hldg
and Big3_increase remain negative and signiﬁcant across

22
www.fastcompany.com/90272330/global- emissions- must- drop- 55- by2030- to- meet- climate- goals

686

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Table 7
Additional ﬁxed effects
This table repeats the analyses in Tables 4 and 5 (Panel A) for the MSCI sample including additional ﬁxed effects. The sample spans from 2005 to 2018
and includes 19,224 ﬁrm-year observations in the MSCI subsample. The control variables are as in Table 4. Standard errors are clustered at the ﬁrm and
year level. t-statistics are in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at the 10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.
Dependent variable: Log (CO2 )
Continuous variable
(1)
Big3_hldg
NonBig3_hldg

(2)
∗∗∗

−1.21
(−2.87)
−0.03
(−0.21)

(3)
∗∗∗

−1.24
(−3.78)
0.06
(0.77)

(4)
∗∗

−0.87
(−2.48)
−0.06
(−0.79)

(5)
∗∗∗

−0.98
(−2.77)
−0.08
(−0.81)

R2
# obs.

YES
YES
NO
YES
NO
NO
NO

YES
YES
NO
NO
YES
NO
NO

YES
YES
NO
NO
NO
YES
NO

0.97
19,134

0.98
19,133

0.98
19,106

0.98
19,134

_Big3_hldg > 1%

(7)

(8)

(9)

(10)

−0.53
(−1.92)
0.06
(0.87)

NonBig3_increase
NO
YES
YES
NO
NO
NO
NO

Indicator for

∗

Big3_increase

Controls
Firm FE
Year FE
Country-year FE
Industry-year FE
Size-decile-year FE
Country-industry-year FE

(6)

YES
YES
NO
NO
NO
NO
YES

−0.05∗∗∗
(−5.65)
−0.02∗∗
(−2.16)
NO
YES
YES
NO
NO
NO
NO

0.99
0.97
17,318
19,134

all models. Finally, Table 7 also includes a speciﬁcation
excluding the vector Controls. The results show that our
inferences do not hinge on any of the control variables.

−0.02∗∗∗
(−3.35)
0.00
(0.09)
YES
YES
NO
YES
NO
NO
NO
0.98
19,133

−0.02∗∗∗
(−4.06)
−0.01∗
(−1.92)
YES
YES
NO
NO
YES
NO
NO
0.98
19,106

−0.02∗∗∗
(−3.95)
−0.01∗∗
(−2.41)
YES
YES
NO
NO
NO
YES
NO
0.98
19,134

−0.01∗∗
(−2.12)
−0.00
(−0.11)
YES
YES
NO
NO
NO
NO
YES
0.99
17,318

probabilities of engagements are in the top quartile and in
the top tercile of the distribution, respectively.
As shown in Table 8, the interaction between Big3_hldg
and Big3_target is negative and signiﬁcant. The magnitude
of the coeﬃcient is larger when Big3_target is deﬁned
based on higher percentiles of the sample distribution.
These results are consistent with the association between
the Big Three and carbon emissions being more pronounced when these large funds engage with the ﬁrms’
management on environmental issues. In Online Appendix OD.3 we repeat the analysis in Table 8 using an alternative measure of Big Three’s engagement that does not
rely on the speciﬁcation in Table 3. Our inferences remain.

6.2. Cross-sectional variation in Big Three engagement
We next explore cross-sectional variation in the results in Table 4. If these results are related to Big Three
inﬂuence, we expect the pattern in Table 4 to be more
pronounced among ﬁrms with a higher probability of
being the target of Big Three engagement. As such, this
test links the analyses in Table 3 (i.e., the determinants
of the probability that the Big Three engage with the
ﬁrm) and Table 4 (i.e., the association between Big Three
holdings and carbon emissions).
In particular, we repeat the analysis in Table 4 including the interaction between Big3_hldg and Big3_target,
an indicator variable for ﬁrms with relatively higher
probability of being the target of Big Three engagements.
Speciﬁcally, Big3_target equals one if all three probabilities
of engagement corresponding to each of the Big Three as
predicted by the analysis in Table 3 are in the top quintile
of the sample distribution and zero otherwise.23 We use
the probability of engagement by each institution rather
than data on actual engagements because comparable engagement data are only available for all three institutions
in the last year of our sample period. For completeness,
we estimate two variants of this analysis redeﬁning
Big3_target as an indicator for whether all three estimated

6.3. Time variation in Big Three engagement
We analyze whether the association between Big Three
ownership and carbon emissions has evolved over time.
Fig. 2 shows results of estimating Eq. (1) by year; we plot
the coeﬃcient on Big3_hldg estimated in annual crosssectional regressions and the corresponding conﬁdence
intervals. The analysis reveals that the association between
Big Three ownership and CO2 emissions has increased
substantially over time. In fact, the association appears to
be signiﬁcant only in the most recent years. This evidence
is consistent with an increasing popular demand after the
2015 Paris Agreement that these large investors pressure
the companies in their portfolios to curb their GHG emissions, as illustrated by recent public statements by climate
activists and top executives of the Big Three.
We next explore whether this pattern is driven by a
recent increase in the Big Three’s commitment to deal
with environmental issues. We measure the commitment of each of the three institutions to improve ﬁrms’
environmental practices by constructing an index based on
seven items corresponding to three categories: (i) engage-

23
Speciﬁcally, we estimate the probability of engagement of BlackRock,
State Street, and Vanguard using models (2), (5), and (8) in Table 3. We
then code Big3_target for a given ﬁrm as one if the three estimated values
are in the top quintile of the corresponding distributions of these three
values for the sample ﬁrms.

687

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Fig. 2. Big Three ownership and carbon emissions by year. This ﬁgure reports the association between Big Three ownership and carbon emissions over
time. The sample spans from 2005 to 2018 and includes 19,224 ﬁrm-year observations in the MSCI subsample. We estimate Eq. (1) year by year and plot
the estimated coeﬃcients on Big3_hldg (point estimates) in each year, along with the corresponding 95% conﬁdence intervals. Filled dots (as opposed to
empty dots) denote that the coeﬃcient is statistically different from zero at the 10% level (two-tailed).
Table 8
Variation in the probability of Big Three engagement
This table presents an analysis of cross-sectional variation in the association between Big Three ownership and total carbon emissions based
on the probability that the Big Three engages with the ﬁrm. The sample
spans from 2005 to 2018 and includes 19,224 ﬁrm-year observations in
the MSCI subsample. The dependent variable is the logarithm of CO2 (i.e.,
the ﬁrm’s total GHG emissions measured in equivalents of metric tons
of CO2 ). Big3_hldg is the fraction of the ﬁrm’s equity owned by mutual
funds sponsored by BlackRock, Vanguard, or State Street. NonBig3_hldg is
the fraction of the ﬁrms’ equity owned by funds managed by institutions
other than BlackRock, Vanguard, and State Street. Big3_target equals one if
all three probabilities of engagement by BlackRock, State Street, and Vanguard (as predicted by the analysis in Table 3) are in the top X percentile
of the sample distribution and zero otherwise. In columns (1), (2), and
(3) X percentile is, respectively, quintile, quartile, and tercile. The control
variables are as in Table 4 (see Appendix A for deﬁnitions). The analysis
is based on the MSCI ﬁrms covered by Trucost from 2005 to 2018. Controls is as in Table 4. See Appendix A for variable deﬁnitions. Independent
variables are measured at the end of the prior year. Standard errors are
clustered at the ﬁrm and year level. t-statistics are in parentheses. ∗ , ∗ ∗ ,
and ∗ ∗ ∗ denote signiﬁcance at the 10%, 5%, and 1% levels (two-tail), respectively. Intercepts are omitted.

Appendix C for details). We label BlackRock_commitment,
StateStreet_commitment, and Vanguard_commitment the
corresponding indexes for BlackRock, State Street, and
Vanguard, respectively. We then regress total CO2 emissions on the interaction between the previous three
variables with BlackRock_target, StateStreet_target, and Vanguard_target, deﬁned as indicator variables for whether the
probability of engagement (as predicted by the analysis
in Table 3) for, respectively, BlackRock, State Street, and
Vanguard is in the top quintile over the sample period. As
shown in Table 9, Panel A, these interactions are negative
and signiﬁcant, which suggests that the increase in the Big
Three’s commitment to deal with environmental issues
during recent years is associated with a decrease in CO2
emissions.
As an alternative, corroborating analysis, we exploit the
fact that BlackRock_commitment, StateStreet_commitment,
and Vanguard_commitment increase substantially in speciﬁc years: 2017 for BlackRock, 2014 for State Street, and
2018 for Vanguard.24 As shown in Appendix C (shadowed
in gray), in these years the corresponding index increases
by 50% and reaches a value equal or higher than 4. We

Dependent variable: Log (CO2 )
Top quintile
(1)
Big3_hldg∗ Big3_target
Big3_hldg
NonBig3_hldg
Controls
Year FE
Firm FE
R2
# obs.

Top quartile
(2)

−1.80∗∗∗
(−3.29)
−0.81∗∗
(−2.30)
−0.09
(−0.91)
YES
YES
YES
0.98
19,134

Top tercile
(3)

−0.93∗∗
(−2.08)
−0.93∗∗∗
(−2.65)
−0.08
(−0.80)
YES
YES
YES
0.98
19,134

−0.77∗∗
(−2.22)
−1.05∗∗∗
(−2.83)
−0.08
(−0.80)
YES
YES
YES

24
There is anecdotal evidence associated with the data in
Appendix C corroborating that these were years of change. For example, in 2017 BlackRock states for the ﬁrst time that the environment
is an engagement priority. In that same year, BlackRock’s corporate
governance and responsible investment team grows 50% (compared to
only 10% over the period 2011-2016). Consistently, we observe that this
institution engages with more ﬁrms on environmental issues starting
in year 2017. That same year, BlackRock issues a signiﬁcantly higher
number of press releases covering environmental issues. Critically, early
in 2017, Larry Fink made strong and unprecedented public statements
on BlackRock’s commitment to ESG issues (https://www.reuters.com/
article/us-blackrock-climate-exclusive/exclusive-blackrock- vows- newpressure- on- climate- board- diversity-idUSKBN16K0CR) and in May 2017
supported the ExxonMobil climate-related shareholder proposal. In sum,
the data suggest that the year 2017 was a turning point in terms of BlackRock’s efforts to induce ﬁrms to improve their environmental practices.
Similarly, we observe that State Street’s interest toward environmental
issues increases signiﬁcantly in 2014 (https://newsroom.statestreet.
com/press-release/corporate/state-streets-corporate-responsibilityreport- highlights- philanthropy- volunt) and that of Vanguard in 2018
(https://www.ft.com/content/5dbd7d56- 1256- 11e8- 940e- 08320fc2a277).

0.98
19,134

ment with the ﬁrms, (ii) voting behavior, and (iii) public
statements. The data on each of these items is presented in
Appendix C. We deﬁne the index in a straightforward way;
we construct indicator variables based on the items in
Appendix C and add up these indicator variables. For items
1, 4, and 6, we construct an indicator variable that equals
one if the values are higher than a given threshold (see
688

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Table 9
Variation in Big Three’s commitment to the environment
This table presents an analysis of time variation in the association between Big Three ownership and total carbon emissions based on the time-varying
commitment of BlackRock, State Street, and Vanguard to tackle environmental issues. The dependent variable is the logarithm of CO2 (i.e., the ﬁrm’s total
GHG emissions measured in equivalents of metric tons of CO2 ). BlackRock_target, StateStreet_target, and Vanguard_target are, respectively, indicator variables
for whether the probability of engagement by Blackrock, State Street, and Vanguard (as predicted by the analysis in Table 3) is in the top quintile of
the distribution over the sample period. In Panel A, BlackRock_commitment, StateStreet_commitment, and Vanguard_commitment are, respectively, the timevarying commitment index of BlackRock, State Street, and Vanguard to tackle environmental issues (measured as described in Appendix C). . In Panel
B, Post_2016, Post_2013, and Post_2017 are indicator variables that equal one if the observation is after 2016, 2013, and 2017, respectively (as shown in
Appendix C, these are the years of maximum increase in BlackRock_commitment, StateStreet_commitment, and Vanguard_commitment, respectively). In Panel
A, the analysis is based on the 19,224 ﬁrm-year observations in the MSCI subsample from 2005 to 2018. In Panel B, the analysis is based on the MSCI
subsample but restricted to a window of two years around 2016, 2013, and 2017 in columns (1), (2), and (3), respectively (in column (3) only one year
is available post-2017). Controls is as in Table 4. See Appendix A for variable deﬁnitions. Independent variables are measured at the end of the prior year.
Standard errors are clustered at the ﬁrm and year level. t-statistics are in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ denote signiﬁcance at the 10%, 5%, and 1% levels
(two-tail), respectively. Intercepts are omitted.
Panel A. Whole sample period
Dependent variable: Log (CO2 )
(1)
BlackRock_target∗ BlackRock_commitment

(2)

(3)

−0.03∗∗∗
(−5.20)

StateStreet_target∗ StateStreet_commitment

−0.03∗∗∗
(−3.90)

Vanguard_target∗ Vanguard_commitment
Controls
Year FE
Firm FE

YES
YES
YES

YES
YES
YES

R2
# obs.

0.98
19,134

0.98
19,134

−0.03∗∗∗
(−3.31)
YES
YES
YES
0.98
19,134

Panel B. Short-window analysis
Dependent variable: Log (CO2 )
(1)
∗

BlackRock_target Post_2016

(2)

(3)

∗∗∗

−0.04
(−3.19)

∗

−0.03∗∗
(−2.11)

StateStreet_target Post_2013
Vanguard_target∗ Post_2017
Controls
Year FE
Firm FE

YES
YES
YES

YES
YES
YES

R2
# obs.

0.99
5,212

0.99
5,405

then focus the analysis for each of the three institutions
within the two-year window around the corresponding
change and test whether CO2 emissions decrease among
the ﬁrms with higher probability of being targeted by
that institution. As shown in Table 9, Panel B, the interactions between BlackRock_target, StateStreet_target, and
Vanguard_target with the corresponding indicators for the
years after the change (Post_2017, Post_2014, and Post_2018)
are negative and signiﬁcant. These results are also in line
with the notion that the increase in the Big Three’s commitment to deal with environmental issues is associated
with a decrease in CO2 emissions. In Online Appendix OD.4
we repeat the analysis in Table 9 using an alternative
measure of the Big Three’s commitment to deal with
environmental issues and an alternative measure of the
probability of the Big Three’s engagement. Our inferences
remain.

−0.03∗∗
(−2.28)
YES
YES
YES
0.99
3,870

6.4. Plausibly exogenous variation in Big Three ownership
We further sharpen identiﬁcation by exploiting the reconstitution of the Russell 10 0 0/20 0 0 indexes as a source
of exogenous variation in Big Three ownership. Following
prior literature (e.g., Appel et al., 2019a and others), we
exploit the yearly reconstitution of the Russell 10 0 0 and
Russell 20 0 0 indexes.25 Every year, these indexes are
formed based on end-of-May market capitalizations; the
25
This approach has been widely used in the recent ﬁnance literature to
assess the effect of passive investors on shareholder activism (Appel et al.,
2019a), ﬁrms’ corporate governance choices (Appel et al., 2016), payout
policy (Crane et al., 2016), CEO power and composition of board of directors (Schmidt and Fahlenbrach, 2017), and ﬁrm transparency and information production (Boone and White, 2015).

689

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

largest 10 0 0 companies constitute the Russell 10 0 0 (i.e.,
ﬁrms #1–10 0 0), while the next 20 0 0 ﬁrms in size are included in the Russell 20 0 0 Index (i.e., ﬁrms #10 01–30 0 0).
For companies that are around the 10 0 0/20 0 0 cutoff, the
ﬁnal assignation to the index is relatively random in the
sense that it can be determined by random variations
in market value. Because the ﬁrm-speciﬁc weight in the
index is value weighted (as a function of ﬂoat-adjusted
market capitalization as of the end of June), the position
at the top of the Russell 20 0 0 Index rather than at the
bottom of the Russell 10 0 0 Index results in a signiﬁcant
increase in the company’s weight in the index, which
triggers stock purchases by index funds tracking the
indexes.
Therefore, for each dollar invested in a passive fund
using the Russell 10 0 0 as a benchmark, very little of that
dollar will be invested in stocks at the bottom of that
index; while for each dollar invested in a passive fund
using the Russell 20 0 0 as a benchmark, a large proportion
of that dollar will be invested in stocks at the top of the
index. To the extent that the Big Three invest heavily in
funds tracking the Russell indexes, the shift from Russell
10 0 0 to Russell 20 0 0 likely increases Big Three ownership
in the ﬁrm.26
Our speciﬁcation follows the recommendations of
recent methodological papers studying the use of the
Russell index assignment as a source of exogenous variation in ﬁrms’ ownership structures (Appel et al., 2019b;
Glossner, 2018; Wei and Young, 2019; Ben-David et al.,
2019). Following Appel et al. (2019a), we conduct a 2SLS
(two-stage least squares) IV (instrumental variable) estimation including the bottom 500 stocks of the Russell
10 0 0 and top 500 stocks of the Russell 20 0 0.27

Second stage : Log(CO2 )it+1


= α + β ∗ Big3
_hldgit +
λn ∗ (ln(Mktcapit ))n
+ v ∗ ln(F loatit ) + φ1 ∗ Bandit + φ2 ∗ Russel l 20 0 0it−1
+ φ3 ∗ Bandit ∗ Russel l 20 0 0it−1 + τt + δi + ε i.

(3)

Russell2000it , the IV, is deﬁned as an indicator equal
to one if stock i is assigned to the Russell 20 0 0 Index
in year t. Mktcapit is the market capitalization of stock i
as of the end of May of year t computed following BenDavid, Franzoni, and Moussawi’s (2019) methodology to
approximate the ranking variable used by Russell to assign
stocks to indexes.28 Floatit is the ﬂoat-adjusted market
capitalization of stock i as of the end of June of year t
used by Russell to determine ﬁrm-speciﬁc index weights
(Russell resorts stocks within indexes using ﬂoat-adjusted
market capitalization measured at the end of June). Bandit
equals one if the ﬁrm’s end-of-May market capitalization
is within the banding interval and zero otherwise (see
Online Appendix OC for more details on Russell’s index
assignment procedure). Russell20 0 0it-1 equals one if the
ﬁrm is in Russell 20 0 0 in the previous reconstitution year
and zero otherwise. Finally, the speciﬁcation also includes
ﬁrm and year ﬁxed effects. We repeat the analysis using
three alternative bandwidths; we estimate Eqs. (2) and
(3) including the 50 0, 40 0, and 30 0 bottom/top stocks of
the Russell 10 0 0/20 0 0. To account for the possibility that
the effect of being included in the index on Big3_hldg is
not linear, we include polynomial controls with degree (N)
1, 2, and 3 for the ﬁrms’ market capitalization.29
Table 10, Panel A reports results of the ﬁrst-stage
estimations. Russell2000 loads with positive and highly
signiﬁcant coeﬃcients in all speciﬁcations, suggesting that
the aggregate ownership by the Big Three is almost one
percentage point higher for ﬁrms in the top of Russell
20 0 0 Index than for the other ﬁrms around the cutoff.30
Table 10, Panel B reports the results of the second-stage
estimation. The coeﬃcient on Big Three is generally negative and signiﬁcant. Compared to the average of the
estimated coeﬃcients in Table 4, the magnitude of the
coeﬃcient on Big Three ownership in Table 10 is larger.

The estimated coeﬃcient on Big3
_hldgit (which ranges

First stage: Big3_hldgit
= α + β ∗ Russell2000it + λn ∗ (ln(Mktcapit ))n
+ ν ∗ ln(Floatit ) + φ 1 ∗ Bandit + φ 2 ∗ Russell2000it-1
+ φ 3 ∗ Bandit ∗ Russell2000it-1 + τ t + δ i + ε i,
(2)

28
A common theme in the papers discussing the validity of the Russell 10 0 0/20 0 0 reconstitution as identiﬁcation strategy is that the endof-May market capitalization ranking used by Russell to determine ﬁrms’
index assignment at reconstitution is not observable to the econometrician (Appel et al., 2019b; Glossner, 2018; Wei and Young, 2019; BenDavid et al., 2019). As such, the literature uses a variety of approaches to
approximate this ranking, notably computing end-of-May market capitalization based on CRSP. In a recent paper, Ben-David et al. (2019) develop
a procedure that predicts assignment to the Russell 10 0 0/20 0 0 with signiﬁcant improvements relative to previous approaches.
29
We repeat the analysis replacing Big3_hldg with NonBig3_hldg. To the
extent that index investing is more prevalent among the Big Three than
among other investment companies, this additional analysis is a placebo
test. As shown in Online Appendix OD, Section OD.5, in this placebo test
we do not ﬁnd signiﬁcant results in either of the two stages of the estimation.
30
The strong association between Big3_hldg and Russell2000 suggests
that the “relevance condition” of the IV approach is satisﬁed. The value
of the Kleibergen-Paap F-statistic is greater than 12, which further alleviates the concern that the instrument is “weak” (uncorrelated with the
endogenous regressor).

26
Appel et al. (2019a) show that ownership by passively managed mutual funds and ETFs is about 40% higher, on average, for stocks at the
top of the Russell 20 0 0 Index relative to otherwise similar stocks at the
bottom of the Russell 10 0 0 Index. Additionally, (Appel et al., 2016) report that, on average, the ownership stakes of the three biggest passive investors are a third higher among ﬁrms at the top of the Russell
20 0 0, and each of these three institutions’ likelihood of owning more
than 5% of a ﬁrm’s shares increases by two-thirds, on average, while
their likelihood of being a top ﬁve shareholder is higher, on average, by
15%.
27
Prior literature also uses a regression discontinuity (RD) approach
around the Russell 10 0 0/20 0 0 reconstitution. Appel et al. (2019b) point
out two important limitations of the RD approach. First, it is not possible to use the sharp RD approach for sample years after 2006 (focusing
on the pre-2006 period would limit the power of our test, as our sample starts in 2005). Second, the RD approach does not provide a direct
way to quantify the effect of ﬁrms’ ownership structure on ﬁrm outcomes because the ﬁrst stage of the fuzzy RD approach does not include a measure of institutional ownership. To overcome these diﬃculties, Appel et al. (2019b) recommend an alternative approach, namely the
2SLS IV. We follow their recommendation.

690

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Table 10
Exploiting the reconstitution of the Russell 10 0 0/20 0 0
This table presents an instrumental variable (IV) 2SLS analysis of the association between ﬁrm carbon emissions and Big Three ownership. The analysis
exploits the reconstitution of the Russell 10 0 0/20 0 0 indexes. The results correspond to the estimation of the following model (Appel et al., 2019a):
First stage (Panel A): Big3_hldgit = α + β ∗ Russell2000it + λn ∗ (ln(Mktcapit ))n + ν ∗ ln(Floatit ) + φ 1 ∗ Bandit + φ 2 ∗ Russell2000it-1 + φ 3 ∗ Bandit ∗ Russell2000it-1
(1)
+ τ t + δ i + ε it,

= α + β ∗ Big3
+ φ ∗ Band ∗ Russell2000
_hldg + λn ∗ (ln(Mktcap ))n + ν ∗ ln(Float ) + φ ∗ Band + φ ∗ Russell2000
Second stage (Panel B): Log (CO )
2 it+1

+ τ t + δ i + ε it.

it

it

it

1

2

it

it-1

3

it

it-1

(2)

Big3_hldg is the fraction of the ﬁrms’ equity owned by mutual funds sponsored by BlackRock, Vanguard, or State Street. Russell2000it , the instrument, equals
one if stock i is assigned to the Russell 20 0 0 Index in year t, and zero otherwise; Mktcapit is the market capitalization of stock i as of the end of May of
year t following Ben-David et al. (2019)’s methodology; Floatit is the ﬂoat-adjusted market capitalization of stock i as of the end of June of year t used by
Russell to determine ﬁrm-speciﬁc index weights. Log (CO2 ) is the logarithm of the ﬁrm’s total GHG emissions per year measured in equivalents of metric
tons of CO2 . Bandit equals one if the ﬁrm’s end-of-May market capitalization is within the banding interval (see Online Appendix C) and zero otherwise;

equals one if the ﬁrm was in the Russell 20 0 0 Index in the previous year and zero otherwise. Big3
_hldg is the ﬁtted value of Big3_hldg
Russell20 0 0
it

it-1

from the ﬁrst-stage estimation. The model includes polynomial controls of order 1, 2, and 3. The samples in columns (1), (2), and (3) include 5643, 4371,
and 3182 ﬁrm-year observations within bandwidths of 50 0, 40 0, and 30 0 (respectively) around the threshold between Russell 10 0 0 and Russell 20 0 0 in
the years 2005–2018 (the same applies to the other two sets of columns). Panel A and B present results of the ﬁrst and second stage, respectively. Standard
errors are clustered at the ﬁrm and year level. t-statistics are reported in parentheses. ∗ , ∗ ∗ , and ∗ ∗ ∗ indicate statistical signiﬁcance at the 10%, 5%, and 1%
levels, respectively. Intercepts are omitted.
Panel A. First stage
Dependent variable: Big3_hldgt
(1)
Russell2000t
Polynomial order, N
Bandwidth
Float control
Firm FE
Year FE
Kleibergen-Paap F-stat.
R2
# obs.

(2)
∗∗∗

(3)
∗∗∗

(4)
∗∗∗

(5)
∗∗∗

(6)
∗∗∗

(7)
∗∗∗

(8)
∗∗∗

(9)
∗∗∗

0.01
(4.87)
1
500
YES
YES
YES
23.71

0.01
(5.57)
1
400
YES
YES
YES
31.08

0.01
(5.79)
1
300
YES
YES
YES
33.58

0.01
(4.80)
2
500
YES
YES
YES
23.02

0.01
(5.43)
2
400
YES
YES
YES
29.46

0.01
(5.80)
2
300
YES
YES
YES
33.61

0.01
(4.40)
3
500
YES
YES
YES
19.39

0.01
(5.35)
3
400
YES
YES
YES
28.57

0.91
5,643

0.91
4,371

0.91
3,182

0.91
5,643

0.91
4,371

0.91
3,182

0.91
5,643

0.91
4,371

0.01∗∗∗
(5.75)
3
300
YES
YES
YES
33.11
0.91
3,182

Panel B. Second stage
Dependent variable: Log (CO2 )t+1


Big3
_hdl gt
Polynomial order, N
Banding controls
Bandwidth
Float control
Firm FE
Year FE
R2
# obs.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

−6.65∗
(−1.68)
1
YES
500
YES
YES
YES

−6.86∗∗
(−2.12)
1
YES
400
YES
YES
YES

−5.34∗
(−1.80)
1
YES
300
YES
YES
YES

−6.61∗
(−1.70)
2
YES
500
YES
YES
YES

−6.85∗∗
(−2.06)
2
YES
400
YES
YES
YES

−5.34∗
(−1.80)
2
YES
300
YES
YES
YES

−6.39
(−1.63)
3
YES
500
YES
YES
YES

−6.66∗∗
(−2.03)
3
YES
400
YES
YES
YES

−5.34∗
(−1.83)
3
YES
300
YES
YES
YES

0.98
3,182

0.98
5,643

0.98
3,182

0.98
5,643

0.98
5,643

0.98
4,371

from −5.34 to −6.86) suggests that a one percentage
point increase in Big Three ownership (which is close to
its within-ﬁrm standard deviation) is associated with a
reduction of CO2 emissions of around 7%.31

0.98
4,371

0.98
4,371

0.98
3,182

7. Conclusion
This paper examines the role of the Big Three (i.e.,
BlackRock, Vanguard, and State Street Global Advisors)
on the reduction of corporate carbon emissions around
the world. Using novel data on engagements of the Big
Three with individual ﬁrms, we ﬁnd evidence that these

31
Given the local nature of the Russell 10 0 0/20 0 0 experiment, we warn
about generalizing the magnitudes of this test to the full sample. The fact

that the magnitude of the coeﬃcient on Big3
_hdl g is larger than that in
it

reduction in CO2 emissions to the extent that the Big Three are more inﬂuential among smaller ﬁrms (smaller ﬁrms cannot afford upsetting large
investors because these ﬁrms have more limited ﬁnancing opportunities).
Third, admittedly the difference in the magnitude of the coeﬃcients between Tables 4 and 10 could be partly driven by estimation error; a negative omitted variable bias in the OLS estimation or distortions in the
second-stage estimation induced by inaccuracies in the ﬁrst stage.

Table 4 is consistent with the results of similar tests in prior literature
(e.g., Ben David et al., 2018). The difference can be due to several reasons.
First, Big Three ownership is higher among US ﬁrms than among nonUS ﬁrms (the average Big Three ownership in the ﬁrms included in the
Russell 10 0 0/20 0 0 test is 12%). Second, the ﬁrms included in the Russell
10 0 0/20 0 0 test are not the largest ones (the largest ﬁrms are far away
from the switching threshold). This could result in a more pronounced
691

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

engagements are related to CO2 emissions and that the
Big Three focus their engagement efforts on large ﬁrms
in which they hold a signiﬁcant stake. We also ﬁnd that
higher ownership by the Big Three is followed by lower
carbon emissions. This pattern is stronger when the ﬁrm
is more likely to be the target of Big Three engagements
and especially so in later years of the sample period as
the Big Three increase their commitment to deal with
environmental issues.
Overall, our results are consistent with the notion that
ﬁrms under the inﬂuence of the Big Three are more likely
to reduce corporate carbon emissions. Our evidence is
particularly relevant considering that large investment
institutions are increasingly viewed as catalysts in driving
ﬁrms to reduce their carbon emissions (Andersson et al.,
2016; OECD, 2017).

Log(CO2 )
Size
Log(BM)
ROA
Leverage
PPE
Engagement_BlackRock
Engagement_StateStreet

Engagement_Vanguard

Big3_hldg
BlackRock_hldg
StateStreet_hldg
Vanguard_hldg
MSCI_constituent
NonBig3_hldg
NonBig3_index
NonBig3_nonIndex
NonBig3_LT
NonBig3_ST
NonBig3_large
NonBig3_small
Big3_target

BlackRock_target
StateStreet_target
Vanguard_target
BlackRock_commitment
StateStreet_commitment
Vanguard_commitment

The interpretation of our results is subject to at least
three caveats. First, while suggestive, our evidence is
not enough to demonstrate a causal effect of Big Three
inﬂuence on corporate CO2 emissions. Further research
is needed to establish such a causal link. Second, our
results do not speak to whether the reduction in CO2
emissions associated with Big Three ownership increases
shareholder wealth. Third, our tests do not necessarily
imply that the level of monitoring provided by the Big
Three is (net) socially optimal. We look forward to future research shedding further light on these important
issues.
Appendix A. Variable deﬁnitions

Logarithm of the total GHG emissions of the ﬁrm measured in equivalents of metric tons of CO2 .
Logarithm of the ﬁrm’s total assets.
Logarithm of the book value of common equity scaled by the market value of equity.
Net income scaled by total assets.
Total debt scaled by total assets. Total debt is the sum of long-term debt and the debt in current liabilities.
Property, plant, and equipment (PPE) scaled by total assets.
Indicator variable that equals one if BlackRock engages with the ﬁrm from July 1, 2018 until June 30, 2019 and
zero otherwise. The data include all engagements.
Indicator variable that equals one if State Street Global Advisors engages with the ﬁrm from January 1, 2018
until December 31, 2018 and zero otherwise. The data include engagements about Environmental/Social
issues.
Indicator variable that equals one if Vanguard engages with the ﬁrm from July 1, 2018 until December 31, 2018
and zero otherwise. The data include engagements about “oversight of strategy and risk” (which include
environmental issues).
Big Three’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by mutual funds managed by
BlackRock, Vanguard, or State Street Global Advisors.
BlackRock’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by BlackRock’s mutual funds.
State Street’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by State Street Global
Advisors’s mutual funds.
Vanguard’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by Vanguard’s mutual funds.
Indicator variable that equals one if the ﬁrm is an MSCI constituent and zero otherwise.
Non-Big Three’s holding in the ﬁrm, namely, the fraction of the ﬁrms’ equity owned by funds managed by
institutions other than BlackRock, Vanguard, and State Street Global Advisors.
Fraction of the ﬁrm’s equity held by indexers other than the Big Three.
Difference between NonBig3_hldg and NonBig3_index.
Fraction of the ﬁrm’s equity held by long-term investors other than the Big Three. An investor is deﬁned as a
long term if its portfolio turnover is in the bottom 33rd percentile of the distribution.
Difference between NonBig3_hldg and NonBig3_LT.
Fraction of the ﬁrm’s equity held by the largest 100 institutions by assets under management (AUM) other than
the Big Three.
Difference between NonBig3_hldg and NonBig3_large.
Indicator variable that equals one if all three probabilities of engagement by BlackRock, State Street and
Vanguard (as predicted by the analysis in Table 3) are in the top quintile of the sample distribution and zero
otherwise.
Indicator variable for whether the probability of engagement by BlackRock (as predicted by the analysis in
Table 3) is in the top quintile of the distribution over the sample period.
Indicator variable for whether the probability of engagement by State Street Global Advisors (as predicted by
the analysis in Table 3) is in the top quintile of the distribution over the sample period.
Indicator variable for whether the probability of engagement by Vanguard (as predicted by the analysis in
Table 3) is in the top quintile of the distribution over the sample period.
Time-varying index measuring BlackRock’s commitment to deal with environmental issues (see Appendix C for
details).
Time-varying index measuring State Street Global Advisors’ commitment to deal with environmental issues (see
Appendix C for details).
Time-varying index measuring Vanguard’s commitment to deal with environmental issues (see Appendix C for
details).

692

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Journal of Financial Economics 142 (2021) 674–696

Appendix B. Data on corporate carbon emissions

B.2. Example of corporate carbon emissions

B.1. Process followed by Trucost to assess corporate carbon
emissions

The table below reproduces the GHG emission amounts
reported by 3 M Co. to the Carbon Disclosure Project
(CDP). Amounts are expressed in tons and in CO2 equivalents to aid comparison.

Trucost has developed a comprehensive approach to
evaluate corporate carbon emissions. This approach employs an environmental proﬁling model that tracks 464
industries worldwide. In particular, Trucost follows four
steps (Ung et al., 2016):

Emission
Direct CO2e (Scope1)
Carbon Dioxide To Air
HFCs To Air
Dinitrogen Oxide
(Nitrous Oxide) To Air
PFCs To Air
methane to air
sulphur hexaﬂuoride to
air
Other Direct CO2e
Other Direct CO2e
First Tier Supply Chain
(Scope 3) CO2e
Purchased Electricity
(Scope 2) CO2e
Non-Electricity Supply
Chain (Scope 3) CO2e
All Other Supply Chain
(Scope 3) CO2e
Sum Of All Other Supply
Chain (Scope 3) CO2e

1. Analysis of company data: Financial information is
assessed to establish the primary business activities
of an organization. Revenues to those activities are
apportioned accordingly.
2. Mapping of company data: Using the information in
step 1, the environmental proﬁling model calculates an
organization’s direct and supply chain environmental
impacts.
3. Incorporation of disclosures and public data: The analysis incorporates reported environmental data obtained
from public sources (such as annual reports and websites). Where environmental reporting is not available,
Trucost draws on sources of proxy information (namely,
fuel use, or expenditure data), which can be converted
into emissions data. Reported ﬁgures are standardized
for consistency.
4. Company veriﬁcation process: Each analyzed company is invited to verify or reﬁne the environmental
assessment conducted by Trucost.

Total

693

Source

Quantity
Tonnes

CO2 Equivalent
(CO2e) Tonnes

CDP
CDP
CDP

3,191,764
14
108

3,288,540
3,191,764
34,045
33,586

CDP
cdp
cdp

2.69
248
0.12

21,094
5,201
2,849

PRE

–

4,892
4,892
3,977,000

CDP

–

1,690,000

TC

–

2,287,000
4,072,000

TC

–

4,072,000
11,342,431

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

Appendix C. Measurement of Big Three’s attention to environmental issues

Panel A. BlackRock
Indicator var.
Engagement
# meetings related to E
E is an engagement priority
Voting
Proxy voting guidelines include E
# votes for E proposals
Public statements
CEO letter cites E
# press releases about E
PRI signatory

1 if > 100, 0 otw.

1 if > 10%, 0 otw.

1 if > 10, 0 otw.

2011

2012

2013

2014

2015

2016

2017

2018

0
0

0
0

1
0

0
0

0
0

0
0

1
1

1
1

0
0

0
0

0
0

0
0

1
0

1
0

1
0

1
0

0
1
1

1
0
1

0
0
1

0
0
1

0
0
1

1
0
1

1
1
1

1
1
1

2011

2012

2013

2014

2015

2016

2017

2018

0
1

0
1

0
1

0
1

0
1

0
1

1
1

0
1

0
0

0
0

0
0

1
1

1
1

1
1

1
1

1
1

0
0
0

0
0
1

0
0
1

0
0
1

0
0
1

0
0
1

1
1
1

0
0
1

2011

2012

2013

2014

2015

2016

2017

2018

0
0

0
0

0
0

0
0

0
0

0
0

0
0

1
0

0
0

0
0

0
0

0
0

0
0

0
0

0
0

0
1

0
0
0

0
0
0

0
0
0

0
0
0

0
0
1

0
0
1

0
1
1

1
0
1

Panel B. State Street
Indicator var.
Engagement
# meetings related to E
E is an engagement priority
Voting
Proxy voting guidelines include E
# votes for E proposals
Public statements
CEO letter cites E
# press releases about E
PRI signatory

1 if > 100, 0 otw.

1 if > 10%, 0 otw.

1 if > 10, 0 otw.

Panel C. Vanguard
Indicator var.
Engagement
# meetings related to E
E is an engagement priority
Voting
Proxy voting guidelines include E
# votes for E proposals
Public statements
CEO letter cites E
# press releases about E
PRI signatory

1 if > 100, 0 otw.

1 if > 10%, 0 otw.

1 if > 10, 0 otw.

Panel D. Index of commitment to deal with environmental engagement (sum of above seven indicator variables)
2011
BlackRock
State Street Global Advisors
Vanguard

2
1
0

2012

2013

2014

2015

2016

2017

2018

2
2
0

2
2
0

1
4
0

2
4
1

3
4
1

6
7
2

6
4
4

Notes: “E” stands for “the environment” (which includes climate-related issues and carbon emissions).
(i) “PRI” stands for principles for responsible investment.
All data items and the index values are zero before 2011. We manually gather above information from public records of CEO letters, investment
stewardship annual reports, proxy voting and engagement guidelines, and a Factiva search on the press releases about the Big Three investors on the
main US and UK newspapers using the following keywords: “proxy voting guidelines,” “environmental shareholders proposals,” “climate risk/change,” “CEO
letter.”

694

J. Azar, M. Duro, I. Kadach et al.

Journal of Financial Economics 142 (2021) 674–696

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==> JFE08 - Sustainable investing in equilibrium.txt <==
Journal of Financial Economics 142 (2021) 550–571

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Sustainable investing in equilibriumR
Ľuboš Pástor a,c,d,e, Robert F. Stambaugh b,c, Lucian A. Taylor b,∗
a

University of Chicago, 5807 S. Woodlawn Ave., Chicago, IL 60637, USA
University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104, USA
NBER, USA
d
CEPR, United Kingdom
e
National Bank of Slovakia, Slovakia
b
c

a r t i c l e

i n f o

Article history:
Received 14 February 2020
Revised 1 May 2020
Accepted 14 May 2020
Available online 31 December 2020
JEL classiﬁcation:
G11
G12

a b s t r a c t
We model investing that considers environmental, social, and governance (ESG) criteria. In
equilibrium, green assets have low expected returns because investors enjoy holding them
and because green assets hedge climate risk. Green assets nevertheless outperform when
positive shocks hit the ESG factor, which captures shifts in customers’ tastes for green
products and investors’ tastes for green holdings. The ESG factor and the market portfolio
price assets in a two-factor model. The ESG investment industry is largest when investors’
ESG preferences differ most. Sustainable investing produces positive social impact by making ﬁrms greener and by shifting real investment toward green ﬁrms.

Keywords:
Sustainable investing
Socially responsible investing
ESG
Social impact

1. Introduction
Sustainable investing considers not only ﬁnancial objectives but also environmental, social, and governance criteria. This investment approach initially gained popularity by
imposing negative screens under the umbrella of socially
responsible investing (SRI), but its scope has expanded

R
The views in this paper are the responsibility of the authors, not the
institutions with which they are aﬃliated. We are grateful for comments
from our discussants Bernard Dumas, Harrison Hong, and Jacob Sagi,
and also from Rui Albuquerque, Malcolm Baker, George Constantinides,
Alex Edmans, Gene Fama, Sam Hartzmark, John Heaton, Ravi Jagannathan,
Ralph Koijen, Yrjo Koskinen, Stavros Panageas, Raghu Rajan, Jeff Wurgler,
and Josef Zechner; conference participants at the 2020 Spring NBER Asset
Pricing Meeting, the 2020 SFS Cavalcade, and the 2020 INSEAD Finance
Symposium; and seminar participants at the University of Chicago, University of Geneva, WU Vienna, and the National Bank of Slovakia.
∗
Corresponding author.
E-mail address: luket@wharton.upenn.edu (L.A. Taylor).

https://doi.org/10.1016/j.jﬁneco.2020.12.011
0304-405X/© 2021 Elsevier B.V. All rights reserved.

© 2021 Elsevier B.V. All rights reserved.

signiﬁcantly in recent years. Assets managed with an eye
on sustainability have grown to tens of trillions of dollars
and seem poised to grow further.1 Given this rapid growth,
the effects of sustainable investing on asset prices and corporate behavior are important to understand.
We analyze both ﬁnancial and real effects of sustainable investing through the lens of an equilibrium
model. The model features many heterogeneous ﬁrms and
agents, yet it is highly tractable, yielding simple and
intuitive expressions for the quantities of interest. The
model illuminates the key channels through which agents’
preferences for sustainability can move asset prices, tilt

1
According to the 2018 Global Sustainable Investment Review, sustainable investing assets exceeded $30 trillion globally at the start of 2018,
a 34% increase in two years. As of November 2019, more than 2600 organizations have become signatories to the United Nations Principles of
Responsible Investment (PRI), with more than 500 new signatories in
2018/2019, according to the 2019 Annual Report of the PRI.

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

portfolio holdings, determine the size of the ESG investment industry, and cause real impact on society.
In the model, ﬁrms differ in the sustainability of their
activities. “Green” ﬁrms generate positive externalities for
society, “brown” ﬁrms impose negative externalities, and
there are different shades of green and brown. Agents differ in their preferences for sustainability, or “ESG preferences,” which have multiple dimensions. First, agents derive utility from holdings of green ﬁrms and disutility from
holdings of brown ﬁrms. Second, agents care about ﬁrms’
aggregate social impact. In a model extension, agents additionally care about climate risk. Naturally, agents also care
about ﬁnancial wealth.
We show that agents’ tastes for green holdings affect
asset prices. Agents are willing to pay more for greener
ﬁrms, thereby lowering the ﬁrms’ costs of capital. Green
assets have negative CAPM alphas, whereas brown assets
have positive alphas. Consequently, agents with stronger
ESG preferences, whose portfolios tilt more toward green
assets and away from brown assets, earn lower expected
returns. Yet such agents are not unhappy because they derive utility from their holdings.
The model implies three-fund separation, whereby each
agent holds the market portfolio, the risk-free asset, and
an “ESG portfolio” whose composition depends on assets’
greenness. Agents with stronger than average tastes for
green holdings deviate from the market largely by overweighting green assets and underweighting brown ones.
Agents with weaker ESG tastes deviate in the opposite
direction, and agents with average tastes hold the market portfolio. If there is no dispersion in ESG tastes, all
agents simply hold the market. Even if all agents derive a
large amount of utility from green holdings, they nevertheless hold only the market if their ESG tastes are equally
strong, because asset prices then fully adjust to reﬂect
those tastes. For the ESG industry to exist, dispersion in
ESG tastes is necessary.
We deﬁne the “ESG factor” as a scaled return on the
ESG portfolio. We show that the ESG factor and the market portfolio together price assets in a two-factor model.
Assets’ loadings on the ESG factor, their “ESG betas,” equal
their ESG characteristics: green assets have positive ESG
betas and brown assets have negative betas. A simple version of the ESG factor is a green-minus-brown portfolio return, where both green and brown portfolios are weighted
by ESG characteristics. Assets’ CAPM alphas reﬂect exposure to the omitted, priced ESG factor. The factor has a
negative premium that comes from investors’ ESG tastes.
We interpret the ESG factor as capturing unexpected
changes in ESG concerns. These concerns can change in
two ways: customers can shift their demand for goods of
green providers, and investors can change their appreciation for green holdings. The ESG factor affects the relative performance of green and brown assets; its positive
realizations boost green assets while hurting brown ones.
If ESG concerns strengthen unexpectedly and suﬃciently,
green assets outperform brown ones despite having lower
expected returns.
To assess the model’s quantitative implications, we calibrate a setting with two types of investors: those sharing
equal concerns about ESG (“ESG investors”) and those hav-

ing no concerns (“non-ESG investors”). Given their portfolios’ green tilts, ESG investors earn lower expected returns
than non-ESG investors. The difference in expected returns
increases with λ, the wealth share of ESG investors, and
with , the maximum certain return ESG investors are
willing to forgo in exchange for investing in their desired
portfolio instead of the market. Non-ESG investors earn an
alpha that is positive and increasing in both λ and . ESG
investors earn a negative alpha whose magnitude is increasing in , concave in λ, and greatest when the dispersion in ESG tastes is greatest (i.e., λ = 0.5).
Despite earning a negative alpha, ESG investors enjoy
an “investor surplus”: they sacriﬁce less return than they
are willing to in order to hold their desired portfolio. The
reason is that equilibrium asset prices adjust to ESG tastes,
thereby pushing the market portfolio toward the portfolio desired by ESG investors. Speciﬁcally, ESG tastes make
green ﬁrms more valuable and brown ﬁrms less valuable.
The market portfolio thus moves closer to ESG investors’
desired portfolio, pushing those investors’ negative alpha
closer to zero. For example, when ESG investors have  =
4%, their alpha is at least −2%. We deﬁne investor surplus
to be the difference between alpha and −. The surplus is
always positive, ranging from /2 to .
We measure the size of the ESG investment industry by
the aggregate ESG dollar tilt away from the market portfolio. The ESG industry is largest when the dispersion in
ESG tastes is greatest. In addition, the ESG industry’s size
is reduced by the price adjustment mentioned above. For
example, suppose that the ESG industry reaches 24% of the
stock market’s value when  is 1%. Then, doubling the
strength of ESG tastes by raising  to 2% increases that
maximum industry size by less than half, to 35% of the
market’s value.
Our model implies that sustainable investing leads to
positive social impact. We deﬁne a ﬁrm’s social impact as
the product of the ﬁrm’s greenness and its scale. We show
that agents’ tastes for green holdings increase ﬁrms’ social impact through two channels. First, ﬁrms choose to
become greener, because greener ﬁrms have higher market values. Second, real investment shifts from brown to
green ﬁrms, due to shifts in ﬁrms’ cost of capital (up for
brown ﬁrms, down for green ﬁrms). We obtain positive aggregate social impact even if agents have no direct preference for it, shareholders do not engage with management,
and managers simply maximize market value.
Finally, we extend the model by allowing climate to
enter investors’ utility. Expected returns then depend not
only on market betas and investors’ tastes but also on
climate betas, which measure ﬁrms’ exposures to climate
shocks. Evidence suggests that brown assets have higher
climate betas than green assets (e.g., Choi et al., 2020; Engle et al., 2020). This difference pushes up brown assets’
expected returns in our model. The idea is that investors
dislike unexpected deteriorations in the climate. If the climate worsens unexpectedly, brown assets lose value relative to green assets (e.g., due to new government regulation that penalizes brown ﬁrms). Because brown ﬁrms
lose value in states of the world investors dislike, they are
riskier, so they must offer higher expected returns. Brown
stocks thus have positive CAPM alphas not only because of
551

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

investors’ distaste for brown holdings, but also because of
brown stocks’ larger exposures to climate risk.
Our theoretical treatment of climate risk is related to
recent empirical work on the implications of such risk for
asset prices. Hong et al. (2019) analyze the response of
food producers’ stock prices to climate risks. Bolton and
Kacperczyk (2019) conclude that investors demand compensation for exposure to carbon risk in the form of higher
returns on carbon-intensive ﬁrms. Ilhan et al. (2020) show
that ﬁrms with higher carbon emissions exhibit more tail
risk and more variance risk. Engle et al. (2020) develop a
procedure to dynamically hedge climate risk by constructing mimicking portfolios that hedge innovations in climate
news series obtained by textual analysis of news sources.
Bansal et al. (2016) identify climate change as a long-run
risk factor. Krueger et al. (2020) ﬁnd that institutional investors consider climate risk to be an important investment risk.
Besides climate risk, other aspects of ESG-related
risk have been studied. Hoepner et al. (2018) ﬁnd that
ESG engagement reduces ﬁrms’ downside risk as well
as their exposures to a downside-risk factor. Luo and
Balvers (2017) ﬁnd a premium for boycott risk. We complement these studies with a theoretical contribution. We
construct an ESG risk factor that is capable of pricing assets in a two-factor model, and we show that green and
brown assets have opposite exposures to this factor.
Prior studies report, in various contexts, that green
assets underperform brown assets. Hong and Kacperczyk (2009) ﬁnd that “sin” stocks (i.e., stocks of public
ﬁrms producing alcohol, tobacco, and gaming, which we
would classify as brown) outperform non-sin stocks. They
argue that social norms lead investors to demand compensation for holding sin stocks. Barber et al. (2021) ﬁnd
that venture capital funds that aim not only for ﬁnancial return but also for social impact earn lower returns
than other funds. They argue that investors derive nonpecuniary utility from investing in dual-objective funds.
Baker et al. (2018) and Zerbib (2019) ﬁnd that green bonds
tend to be priced at a premium, offering lower yields than
traditional bonds. Both studies argue that the premium
is driven by investors’ environmental concerns. Similarly,
Chava (2014) and El Ghoul et al. (2011) ﬁnd that greener
ﬁrms have a lower implied cost of capital. All of these results are consistent with our prediction that ESG tastes reduce green ﬁrms’ costs of capital.
Some studies ﬁnd the opposite result, that green assets outperform brown, using alternative deﬁnitions of
green and brown. Firms perform better if they are bettergoverned, judging by employee satisfaction (Edmans, 2011)
or by strong shareholder rights (Gompers et al., 2003),
or if they have higher ESG ratings in the 1992–2004 period (Kempf and Osthoff, 2007). These results are also consistent with our model as long as ESG tastes strengthen
unexpectedly over the sample period. We do not mean
to imply that we can always declare empirical success
for our model. The model clearly predicts that green assets underperform brown over a suﬃciently long period—
a period long enough that unexpected changes in ESG
tastes average to zero. We simply explain why it is

diﬃcult to distinguish ex ante versus ex post effects of ESG
concerns by looking at realized returns over periods during which ESG tastes shift. Disentangling alphas from ESG
taste shifts is a major challenge for empirical work in this
area.
Our model is also related to previous theoretical studies of sustainable investing. Heinkel et al. (2001) build an
equilibrium model in which exclusionary ethical investing affects ﬁrm investment. They consider two types of
investors, one of which refuses to hold shares in polluting ﬁrms. The resulting reduction in risk sharing increases
the cost of capital of polluting ﬁrms, depressing their investment. Albuquerque et al. (2019) construct a model in
which a ﬁrm’s socially responsible investments increase
customer loyalty, giving the ﬁrm more pricing power. This
power makes the ﬁrm less risky and thus more valuable.
Unlike these models, ours features neither a lack of risk
sharing nor pricing power; instead, the main force is investors’ tastes for holding green assets.
Fama and French (2007) argue that tastes for holding
green assets can affect prices. Baker et al. (2018) build a
model featuring two types of investors with mean-variance
preferences, where one type also has tastes for green assets. Their model predicts that green assets have lower expected returns and more concentrated ownership, and they
ﬁnd support for these predictions in the universe of green
bonds. Pedersen et al. (2021) consider the same two types
of mean-variance investors but also add a third type that
is unaware of ﬁrms’ ESG scores. This lack of awareness is
costly if ﬁrms’ ESG scores predict their proﬁts. The authors show that stocks with higher ESG scores can have
either higher or lower expected returns, depending on the
wealth of the third type of investors. They obtain four-fund
separation and derive the ESG-eﬃcient frontier characterizing the tradeoff between the ESG score and the Sharpe
ratio.
While the models in these studies share some features
with ours, we offer novel insights. We show that an ESG
factor, along with the market portfolio, prices assets in a
two-factor model. Positive realizations of this factor, which
result from shifts in customers’ and investors’ tastes, can
result in green assets outperforming brown. The size of
the ESG investment industry, as well as investors’ alphas,
crucially depend on the dispersion in investors’ ESG tastes.
ESG investors earn an investor surplus. We have a continuum of investors with multiple dimensions of ESG preferences. Including climate in those preferences results in the
pricing of climate risk. Finally, ESG investing has positive
social impact.
Positive social impact also emerges from the model of
Oehmke and Opp (2020), but through a different channel. Key ingredients to generating impact in their model
are ﬁnancing constraints and coordination among agents.
Our model does not include those ingredients, but it produces social impact nevertheless, through tastes for green
holdings. To emphasize these tastes, we do not model
shareholder engagement with management, which is another channel through which ESG investing can potentially increase market value (e.g., Dimson et al., 2015). In
our model, value-maximizing managers make their ﬁrms

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Journal of Financial Economics 142 (2021) 550–571

greener voluntarily, without pressure from shareholders,
because greener ﬁrms command higher market values.2
Our assumption that some investors derive nonpecuniary beneﬁts from green holdings has considerable
empirical support in the mutual fund literature. Mutual
fund ﬂows respond to ESG-salient information, such as
Morningstar sustainability ratings (Hartzmark and Sussman, 2019) and environmental disasters (Bialkowski and
Starks, 2016). Flows to SRI mutual funds are less volatile
than ﬂows to non-SRI funds (Bollen, 2007) and less responsive to negative past performance (Renneboog et al., 2011).
Investors in SRI funds also indicate a willingness to forgo
ﬁnancial performance to accommodate their social preferences (Riedl and Smeets, 2017).
This paper is organized as follows. Section 2 presents
our baseline model. Section 3 discusses the ESG factor.
Section 4 explores the model’s quantitative implications.
Section 5 extends the baseline model by letting agents care
about the climate, showing that climate risk commands
a premium. Section 6 examines social impact. Section 7
concludes.

˜



˜ 1i , Xi ) = −e−AiW1i −bi Xi ,
V (W

(2)

where Ai is the agent’s absolute risk aversion and bi is
an N × 1 vector of nonpecuniary beneﬁts that the agent
derives from her stock holdings. Holding the riskless asset brings no such beneﬁt. The beneﬁt vector has agentspeciﬁc and ﬁrm-speciﬁc components:

bi = di g,

(3)

where g is an N × 1 vector whose nth element is gn and
di ≥ 0 is a scalar measuring the degree of agent i’s “ESG
taste.” Agent i thus derives a nonpecuniary beneﬁt of di gn
from holding stock n. Agents with higher values of di have
stronger tastes for the ESG characteristics of their holdings. In addition to having ESG tastes, agents care about
ﬁrms’ aggregate social impact, but that component of preferences does not affect agents’ portfolio choices or asset
prices. Therefore, we postpone the discussion of that component until Section 6.3.
2.1. Expected returns

2. Model
The model considers a single period, from time 0 to
time 1, in which there are N ﬁrms, n = 1, . . . , N. Let r˜n denote the return on ﬁrm n’s shares in excess of the riskless
rate, r f , and let r˜ be the N × 1 vector whose nth element
is r˜n . We assume r˜ is normally distributed:

Due to their inﬁnitesimal size, agents take asset prices
(and thus the return distribution) as given when choosing
their optimal portfolios at time 0. To derive the ﬁrst-order
condition for Xi , we compute the expectation of agent i’s
utility in Eq. (2) and differentiate it with respect to Xi . As
we show in the Appendix, agent i’s portfolio weights on
the N stocks are

r˜ = μ + ˜ ,

Xi =

(1)

where μ contains equilibrium expected excess returns and
˜ ∼ N (0, ). In addition to ﬁnancial payoffs, ﬁrms produce
social impact. Each ﬁrm n has an observable “ESG characteristic” gn , which can be positive (for “green” ﬁrms)
or negative (for “brown” ﬁrms). Firms with gn > 0 have
positive social impact, meaning they generate positive externalities (e.g., cleaning up the environment). Firms with
gn < 0 have negative social impact, meaning they generate
negative externalities (e.g., polluting the environment). In
Section 6, we model ﬁrms’ social impact in greater detail.
There is a continuum of agents who trade ﬁrms’ shares
and the riskless asset. The riskless asset is in zero net supply, whereas each ﬁrm’s stock is in positive net supply.
Let Xi denote an N × 1 vector whose nth element is the
fraction of agent i’s wealth invested
in stock

 n. Agent i’s
˜ 1i = W0i 1 + r f + X  r˜ , where W0i is
wealth at time 1 is W
i
the agent’s initial wealth. Besides liking wealth, agents also
derive utility from holding green stocks and disutility from
holding brown stocks.3 Each agent i has exponential utility

1 −1

ai



μ+



1
bi ,
ai

(4)

where ai ≡ AiW0i is agent i’s relative risk aversion. For
tractability, we assume that ai = a for all agents. We deﬁne
ωi to be the ratio of agent i’s initial
wealth to total initial

wealth: ωi ≡ W0i /W0 , where W0 = i W0i di. Because we assume a zero aggregate position in the riskless asset, market clearing requires that wm , the N × 1 vector of weights
in the market portfolio of stocks, satisﬁes



wm =
=

i

ωi Xi di

d¯
1 −1
 μ + 2  −1 g,
a
a

(5)

d¯
a

(6)


where d¯ ≡ i ωi di di ≥ 0 is the wealth-weighted mean of
ESG tastes di across agents and ι wm = 1, with ι denoting
an N × 1 vector of ones. Note that d¯ > 0 unless the mass of
agents who care about ESG is zero. Solving for μ gives

μ = a wm − g.

Premultiplying by wm gives the market equity premium,
μm = wm μ:

2

Theoretical work on sustainable investing also includes Friedman and
Heinle (2016), Gollier and Pouget (2014), and Luo and Balvers (2017).
Bank and Insam (2017) do not mention sustainable investing, but they
model investors with preferences for other stock characteristics. Empirical work on sustainable investing includes Geczy et al. (2005), Hong and
Kostovetsky (2012), and Cheng et al. (2016), among others. For recent experimental work, see Humphrey et al. (2020). For surveys of the early
literature, see Bauer et al. (2005) and Renneboog et al. (2008).
3
We frame the discussion in terms of green and brown stocks, but our
main ideas apply more broadly to any set of green and brown assets, such
as bonds and private equity investments.

d¯
a

μm = aσm2 − wm g,

(7)

where σm2 = wm  wm is the variance of the market return.
In general, the equity premium depends on the average of
ESG tastes, d¯, through wm g, which is the overall “greenness” of the market portfolio. If the market is net green
(wm g > 0), then stronger ESG tastes (i.e., larger d¯) reduce
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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

the equity premium. If the market is net brown (wm g < 0),
stronger ESG tastes increase the premium as investors demand compensation for this brownness. For simplicity, we
assume that the market portfolio is ESG-neutral,

wm g = 0,

Both equations are derived in the Appendix. Agents
with δi > 0 accept below-market expected returns in exchange for satisfying their stronger tastes for holding green
stocks. As a result, agents whose tastes for green holdings
are weaker (δi < 0) enjoy above-market expected returns.
In departing from market holdings, all agents with δi = 0
incur higher return volatility than that of the market portfolio.

(8)

which implies that the equity premium in Eq. (7) is independent of agents’ ESG tastes. Equivalently, we could
view g as being deﬁned so that agents derive utility (disutility) from holdings that are greener (browner) than the
market. Eqs. (7) and (8) imply a = μm /σm2 . Combining this
with Eq. (6) and noting that the vector of market betas is
βm = (1/σm2 ) wm , we obtain our ﬁrst proposition.

Corollary 3. If d¯ > 0 and g = 0, agents with larger δi earn
lower expected returns.
Under the conditions of this corollary, the term in
parentheses in Eq. (11) is strictly positive. Therefore, agents
with stronger ESG tastes (i.e., larger δi ) earn lower expected returns. The effect of δi on E(r˜i ) is stronger when
the average ESG taste is stronger (i.e., when d¯ is larger),
when risk aversion a is smaller, and when g  −1 g is larger.
The low expected returns earned by ESG-sensitive
agents do not imply that these agents are unhappy. As we
show in the Appendix, agent i’s expected utility in equilibrium is given by

Proposition 1. Expected excess returns in equilibrium are
given by

d¯
a

μ = μm βm − g.

(9)

We see that expected excess returns deviate from their
CAPM values, μm βm , due to ESG tastes for holding green
stocks.

δi2

Corollary 1. If d¯ > 0, the expected return on stock n is decreasing in gn .

Xi = wm +

Proposition 2. The mean and variance of the excess return on
agent i’s portfolio are

1
a

(11)



g  −1 g ,
4

 2  −1
δi /a  g.

(14)

Proposition 3 implies three-fund separation, as each
agent’s overall portfolio can be implemented with three assets: the riskless asset, the market portfolio, and an “ESG
portfolio” whose weights are proportional to  −1 g. The

fraction

of agent i’s wealth in the riskless asset, 1 − ι Xi =
− δi /a2 ι  −1 g, can be positive or negative. The agent’s
remaining wealth is invested in stocks. Speciﬁcally, the
agent allocates a fraction φi of her remaining wealth to the
ESG portfolio and a fraction 1 − φi to the market portfolio.
To see this, note that the N × 1 vector of weights within
agent i’s stock portfolio, wi , equals the right-hand side of
Eq. (14) multiplied by 1/(ι Xi ), giving

As long as some agents care about sustainability,
Eq. (10) implies that the alphas of stocks with gn > 0 are
negative, the alphas of stocks with gn < 0 are positive, and
αn is decreasing with gn . Furthermore, the negative relation between αn and gn is stronger when risk aversion, a,
is lower and when the average ESG taste, d¯, is higher.4

Var(r˜i ) = σm2 + δi2

(13)

Proposition 3. Agent i’s equilibrium portfolio weights on the
N stocks are given by

If d¯ > 0, green stocks have negative alphas, and brown stocks
have positive alphas. Moreover, greener stocks have lower alphas.

d¯  −1
g g
a3

,

Substituting for μ from Eq. (9) into Eq. (4), we obtain
an agent’s portfolio weights:

(10)



g

2.2. Portfolio tilts and the ESG portfolio

Corollary 2. The CAPM alpha of stock n is given by

E(r˜i ) = μm − δi

−1

where V̄ is the expected utility if the agent has δi = 0. Expected utility is increasing in δi2 (note from Eq. (2) that
V̄ < 0), so the more an agent’s ESG taste di deviates from
the average in either direction, the more ESG preferences
contribute to the agent’s utility.

As long as the mass of agents who care about sustainability is nonzero, d¯ is positive, and expected returns are
decreasing in ESG characteristics. Given their ESG tastes,
agents are willing to pay more for greener ﬁrms, thereby
lowering the ﬁrms’ expected returns. Because the vector of stocks’ CAPM alphas is deﬁned as α ≡ μ − μm βm ,
Eq. (9) yields the following corollary.

d¯
αn = − gn .
a



˜ 1i ) = V̄ e− 2a2 g 
E V (W

wi =

(12)

where δi ≡ di − d¯.






 wm + δi /a2  −1 g
ι wm + δi /a2  −1 g




1

= ( 1 − φi ) w m + φi w g ,

(15)

with the fraction of agent i’s stock portfolio invested in the
ESG portfolio given by

4
Proposition 1 and its corollaries continue to hold if agents disagree
on stocks’ ESG characteristics, gn . In that case, the results hold with gn
replaced by the wealth-weighted average of agents’ perceived values of
gn , adjusted for any covariance between those perceived values and ESG
tastes. See the Appendix.

φi =
554

(δi /a2 )ι  −1 g
,
1 + (δi /a2 )ι  −1 g

(16)

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

and the N × 1 vector of weights in the ESG portfolio given
by

Corollary 4. If there is no dispersion in ESG tastes across
agents, then all agents hold the market portfolio.

1
wg =  −1  −1 g.
ι g

For example, all agents hold the market portfolio when
none of them have ESG concerns, as in the familiar CAPM.
All agents also hold the market, however, when they have
strong but equal ESG tastes. The reason is that stock prices
then fully adjust to reﬂect those tastes, again making
the market everybody’s optimal choice. Dispersion in ESG
tastes is necessary for an ESG investment industry to exist.

(17)

In the special case where ι  −1 g = 0, no agent holds the
riskless asset, and the ESG portfolio is a zero-cost position,
with5

wg =  −1 g,

(18)

and wi = Xi , so that

w i = w m + φi w g ,

2.3. Two-factor pricing with the ESG portfolio

(19)

The excess return on the ESG portfolio is r˜g = wg r˜. From
Eqs. (8) and (17) and βm = (1/σm2 ) wm , the ESG portfolio’s
market beta is zero (i.e., wg βm = 0). Premultiplying both
sides of Eq. (9) by wg gives the expected excess return on
the ESG portfolio as

with φi then deﬁned as

φi = δi /a2 .

(20)

Denote the ESG portfolio’s greenness as

gg = wg g.

d¯
a

(21)

μg = − g g ,

From Eqs. (17) and (18), gg is nonzero as long as g = 0.
Also, gg is negative if ι  −1 g < 0, but it is otherwise positive. From Eqs. (16) through (20), we see that φi has the
same sign as the product of gg and δi if the denominator of
φi in Eq. (16) is positive. From Eq. (14), this last condition
obtains if agent i invests a positive fraction of her wealth
in stocks, so that ι Xi > 0.
Therefore, for an agent with positive wealth in stocks
and δi > 0, φi is positive (negative) if gg is positive (negative). That is, such an agent in general tilts away from the
market portfolio in the direction of greenness, in that she
tilts toward the ESG portfolio when it is green and away
from it when it is brown. In contrast, agents with δi < 0
tilt away from the ESG portfolio when it is green and toward it when it is brown. From Eq. (10), the ESG portfolio’s
CAPM alpha is

d¯
a

αg = − gg ,

(23)

the same as its alpha in Eq. (22). The variance of the ESG
portfolio’s return is

σg2 =





1

ι  −1 g

2 

g  −1 g =



1

ι  −1 g



gg ,

(24)

and the covariance of its return with the N assets is

Cov(r˜, r˜g ) =



1

ι  −1 g



g.

(25)

Deﬁne the vector of simple betas with respect to r˜g as βg =
(1/σg2 )Cov(r˜, r˜g ). From Eqs. (24) and (25),

βg =

1
g.
gg

(26)

By combining Eqs. (9), (23), and (26), we relate expected
returns to betas on the market and the ESG portfolio:
Proposition 4. Expected excess returns in equilibrium are
given by

(22)

whose sign is opposite that of gg . Therefore, for the same
agents described above, those with positive (negative) values of δi have ESG-portfolio tilts that produce negative
(positive) alphas for their overall portfolios.
The ESG tilt is zero (i.e., φi = 0) for agents with average
ESG concerns, i.e., for whom di = d¯ and thus δi = 0. Those
agents hold the market portfolio. In contrast, agents who
are indifferent to ESG, for whom di = 0 and thus δi < 0,
tilt away from the market portfolio as explained above. It
is suboptimal to say, “I don’t care about ESG, so I just hold
the market.” In a world with ESG concerns, agents indifferent to ESG should tilt away from the market portfolio;
otherwise they are not optimizing. The market portfolio is
optimal for agents with average concerns about ESG but
not for those indifferent to ESG.
If all agents have identical ESG concerns, so that δi = 0
for all i, then Eqs. (16) and (20) imply a zero ESG tilt for
each agent. We thus have the following corollary.

μ = μm βm + μg βg .

(27)

As noted earlier, the ESG portfolio is zero-beta, so that
Cov(r˜g , r˜m ) = 0. Thus βm and βg are also the slope coefﬁcients in the multivariate regression of r˜ on r˜m and r˜g .
Therefore, using Eq. (27), we have a two-factor asset pricing model:
Proposition 5. Excess returns obey the regression model

r˜ = βm r˜m + βg r˜g + ν˜ ,

(28)

in which E(ν|
˜ r˜m , r˜g , βm , βg ) = 0 and all assets have zero twofactor alphas, equivalent to zero intercepts in the above regression.
From Eqs. (9), (10), and (27), the vector of CAPM alphas
is given by

In the special case considered in Section 4, in which ι  −1 g = 0 and
 has a two-factor structure, wg is proportional to g, so that the ESG
portfolio goes long green stocks and short brown stocks.
5

α = βg μg

(29)

= −(d¯/a )g.

(30)

Eqs. (29) and (30) allow alternative interpretations of α .
On one hand, Eq. (29) offers a risk-based interpretation:
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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

The elements of βg represent exposures to the risky return r˜g , and μg is the expected return accompanying a
unit of that risk. In other words, one can attribute assets’
nonzero CAPM alphas to that omitted priced risk factor.
On the other hand, the only reason that investors expose
themselves to the risk in r˜g is that they have non-average
tastes for green and brown holdings. While the popular
risk-based interpretation of factor pricing models is mechanically valid, we see here an example of how that interpretation can miss the underlying economics. The latter
are evident in Eq. (30), which reveals that the sources of α
are tastes for known characteristics, g, not aversion to an
additional fundamental risk. In Section 5, however, we extend our model to include an example of such risk, climate
shocks, and we discuss how g can also reﬂect exposures to
that risk.

practice, one can run a series of such cross-sectional regressions, period by period.
A simpler version of fˆg arises if we add the assumptions of g ι = 0 and g βm = 0; that is, if we assume that
not only the value-weighted average of gn ’s but also their
equal- and beta-weighted averages are zero (recall from
Eq. (8) that g wm = 0). In this case, g r˜e in Eq. (34) equals
g r˜, so fˆg is just a scaled (by g g) excess return on a zerocost portfolio whose weights are proportional to g. Simplifying further, fˆg is proportional to the difference between
returns on green-stock and brown-stock portfolios:

fˆg ∝ r˜green − r˜brown ,

with the weights in the green (brown) portfolio proportional to the positive (negative) elements of g.6 A popular approach to constructing traded factors (e.g., Fama and
French, 1993) is to have them be excess returns on longshort portfolios whose stock weights sum to zero. Our
model provides a formal justiﬁcation for such an approach in the context of ESG investing. However, unlike
in Fama and French (1993), stocks in our ESG factor are
weighted by their gn ’s rather than by their market capitalizations.

3. The ESG factor
We next introduce an empirically identiﬁable ESG factor, closely related to the ESG portfolio, that maintains
two-factor pricing. After discussing approaches for constructing the ESG factor, we analyze its underlying economic sources of risk. The latter analysis provides insights
into ex post versus ex ante performance of green stocks
relative to brown.

3.2. Sources of ESG factor risk
In this subsection, we extend our model from
Section 2 to identify potential sources of risk in the
ESG factor. The strength of ESG concerns can change
over time, both for investors in ﬁrms’ shares and for the
customers who buy the ﬁrms’ goods and services. If ESG
concerns strengthen, customers could shift their demands
for goods and services to greener providers (the “customer” channel), and investors could derive more utility
from holding the stocks of greener ﬁrms (the “investor”
channel). Both channels contribute to the ESG factor’s risk
in our framework.
To model the customer channel, we need to model ﬁrm
proﬁts. Let u˜n denote the ﬁnancial payoff (proﬁt in our
one-period setting) that ﬁrm n produces at time 1, for each
dollar invested in the ﬁrm’s stock at time 0. We assume a
simple two-factor structure for the N × 1 vector of these
payoffs of the form

3.1. Constructing the ESG factor
We deﬁne the ESG factor as

f˜g = (1/gg ) r˜g ,

(31)

so that the traded factor f˜g is simply the excess return on
a position in the ESG portfolio, either long or short, levered or delevered, depending on the sign and value of gg .
Using Eq. (26), we can then rewrite the two-factor model
in Eq. (28) as

r˜ = βm r˜m + g f˜g + ν˜ .

(32)

Assets’ loadings on the ESG factor, their ESG betas, are simply their ESG characteristics, g. A higher-than-expected realization of f˜g boosts the returns on green stocks and depresses those on brown ones. From Eqs. (23) and (31), the
ESG factor’s premium is negative:

E f˜g = −d¯/a.

u˜ − E0 {u˜} = z˜m βm + z˜g g + ζ˜ ,

(33)

 e

(36)

where E0 { } denotes expectation as of time 0; the random quantities z˜m , z˜g , and ζ˜ have zero means and are
 g = 0; and the elements of ζ˜
mutually uncorrelated; βm
have identical variances and are uncorrelated with each
other. The shock z˜m can be viewed as a macro output
factor, with ﬁrms’ sensitivities to that pervasive shock
being proportional to their stocks’ market betas. The shock
z˜g represents the effect on ﬁrms’ payoffs of unanticipated
ESG-related shifts in customers’ demands. These shifts
can result not only from changes in consumers’ tastes
but also from revisions of government policy. For example, pro-environmental regulations could subsidize green

One approach to constructing the ESG factor is to run a
cross-sectional regression of market-adjusted excess stock
returns, r˜e ≡ r˜ − βm r˜m , on the stocks’ ESG characteristics,
g, with no intercept. The slope from that regression is

g r˜
fˆg =  ,
gg

(35)

(34)

which from Eq. (32) has mean-zero estimation error fˆg −
f˜g = g ν˜ /g g. As N grows large, the probability limit of this
estimation error is zero as long as the covariance matrix
of ν˜ has bounded eigenvalues and the cross-sectional second moment of the elements of g is bounded below by
a positive value. The ESG factor is thus essentially just a
g-weighted average of market-adjusted stock returns. To
obtain the time series of the ESG factor’s realizations in

6

In Eq. (35), the constant of proportionality is time invariant if g g and

ι |g| both are.
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Journal of Financial Economics 142 (2021) 550–571

products, leading to more customer demand, or handicap
brown products, leading to less demand. A positive z˜g
shock increases the payoffs of green ﬁrms but hurts those
of brown ﬁrms.
To model the investor channel, we assume that the average ESG taste d¯ shifts unpredictably from time 0 to time
1. We therefore need to price stocks not only at time 0, as
we have done so far, but also at time 1, after the preference shift in d¯ occurs. To make this possible in our simple
framework, we split time 1 into two times, 1− and 1+ , that
are close to each other. We calculate prices p1 as of time
1− , by which time ESG tastes have shifted and all risk associated with u˜ has been realized. Stockholders receive u˜
at time 1+ . During the instant between times 1− and 1+ ,
these payoffs are riskless. For economy of notation, we assume the risk-free rate r f = 0.
There are two generations of agents, Gen-0 and Gen-1.
Gen-0 agents live from time 0 to time 1− ; Gen-1 agents
live from time 1− to 1+ . Gen-1 agents have identical tastes
of di = d¯1 , a condition that gives them ﬁnite utility, given
the absence of both risk and position constraints during
their lifespan. Neither a nor g change across generations. At
time 1− , Gen-0 agents sell stocks to Gen-1 agents at prices
p1 , which depend on Gen-1 ESG tastes d¯1 and the ﬁnancial
payoff u˜. This simple setting maintains single-period payoff
uncertainty while also allowing risk stemming from shifts
in ESG tastes to enter via both channels described earlier.
Given that the payoff u˜n is known at the time when
the price p1,n is computed, p1,n is equal to u˜n discounted
at the expected return implied by Eq. (9) with βm,n set to
zero:

p1,n =

u˜n
1 − gan d¯1

≈ u˜n +

gn ¯
d1 .
a

As shown in the Appendix, when N is large,

f˜ge ≈ f˜g − E0 { f˜g },

where f˜g is the ESG factor deﬁned in Eq. (31).
Eq. (41) therefore identiﬁes the two sources of risk in
the ESG factor discussed earlier: z˜g represents the customer channel while the other term represents the investor channel. While the customer channel follows closely
from the structure assumed in Eq. (36), the investor channel emerges from the equilibrium dependence of stock
prices on d¯.
The elements of f˜ge g in Eq. (40) drive a wedge between
expected and realized returns for Gen-0 agents. Suppose
that ESG concerns strengthen unexpectedly, so that f˜ge > 0.
A ﬁrm’s unexpected return in Eq. (40) is then expected to
be positive for green ﬁrms (for which f˜ge gn > 0) and negative for brown ﬁrms (for which f˜e gn < 0), because the exg

pected values of z˜m and ζ˜ are both zero. In other words,
if ˜n denotes the unexpected return for stock n, E{˜n | f˜ge >
0, gn > 0} > 0, and E{˜n | f˜e > 0, gn < 0} < 0. We thus have
g

the following proposition.
Proposition 6. Green (brown) stocks perform better (worse)
than expected if ESG concerns strengthen unexpectedly via either the customer channel or the investor channel.
As noted earlier, green stocks have lower expected returns than brown stocks. A positive realization of f˜ge , however, boosts the realized performance of green stocks while
hurting that of brown stocks. If one computes average returns over a sample period when ESG concerns strengthen
more than investors expected, so that the average of f˜e
g

(37)

over that period is strongly positive, then green stocks
outperform brown stocks, contrary to what is expected.
Furthermore, if ESG concerns strengthen via the investor
channel, making d increase, then green stocks’ alphas are
more negative at the end of the period than the beginning (see Corollary 2). In this case, past outperformance of
green stocks makes it especially likely that they will underperform in the future.
To empirically distinguish alphas from unexpected
shocks, one could use proxies for shifts in ESG tastes. Proxies for shifts in investors’ tastes could come from investor
surveys or from the ﬂows in and out of ESG-tilted funds.
Proxies for shifts in customers’ ESG tastes could come from
consumer surveys or from data on ﬁrm revenues or profitability. With such proxies, one could test whether green
stocks outperform brown ones when either type of ESG
taste strengthens unexpectedly. In addition, one could attempt to separate the effects of investors’ and customers’
tastes, because only shifts in investors’ tastes make green
stocks’ future alphas more negative after green stocks outperform.

The approximation above holds well for typical discount
rates, which are not too far from zero.7 Representing it as
an equality for all assets gives

p1 = u˜ +

1 ¯
d1 g,
a

(38)

which is the vector of payoffs to Gen-0 agents. Its expected
value at time 0 equals

E0 { p1 } = E0 {u˜} +

1
E0 {d¯1 }g.
a

(39)

Note that p1 − E0 { p1 } equals the vector of unexpected
returns for Gen-0 agents, because u˜n is the ﬁrm’s payoff per dollar invested in its stock at time 0. From
Eqs. (36) through (39), these unexpected returns are given
by

r˜ − E0 {r˜} = βm z˜m + g f˜ge + ζ˜

(40)

with

1 ¯
d1 − E0 {d¯1 } .
f˜ge = z˜g +
a
7

(41)
4. Quantitative implications

Let ρ1 ≡ u˜n − 1 and ρ2 ≡ gan d¯1 . The approximation in Eq. (37) follows

from

1+ρ1
1−ρ2

(42)

To explore the model’s quantitative implications, we
consider a special case with two types of agents: ESG investors, for whom di = d > 0, and non-ESG investors, for
whom di = 0. ESG investors thus enjoy nonpecuniary beneﬁts dg, whereas non-ESG investors receive no beneﬁts (see

ρ2 )
≈ (1 + ρ1 )(1 + ρ2 ) ≈ 1 + ρ1 + ρ2 , where we as= (1+ρ11−)(ρ1+
2
2

sume that the second-order terms ρ and ρ1 ρ2 are small enough to be
neglected. This assumption seems plausible because the magnitudes of ρ1
and ρ2 are comparable to discount rates. We rely on this approximation
in the remainder of Section 3.
2
2

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Journal of Financial Economics 142 (2021) 550–571

Rather than calibrating d, we translate it to a more easily interpreted quantity, . We deﬁne  as the maximum
rate of return that an ESG investor is willing to sacriﬁce,
for certain, to invest in her desired portfolio rather than in
the market portfolio. The sacriﬁce is greatest when there
are no other ESG investors, i.e., when λ ≈ 0, because that
is when the ESG investor’s portfolio most differs from
∗ − r∗ ,
the market portfolio. Speciﬁcally, we deﬁne  ≡ resg
m
∗ is the ESG investor’s certainty equivalent excess
where resg
∗ is
return when investing in her optimal portfolio, and rm
the same investor’s corresponding certainty equivalent if
forced to hold the market portfolio instead. Both certainty
equivalents are computed for λ = 0. In this setting,

=

4.2. ESG versus non-ESG expected portfolio returns
The difference in expected excess returns on the portfolios of the two investor types is

E{r˜esg } − E{r˜non } = −2λ,

Eq. (3)). Let λ denote the fraction of total wealth belonging
to ESG investors, so that 1 − λ is the corresponding fraction for non-ESG investors.
We further simplify the two-factor setting in Eq. (32) by
assuming that ν in Eq. (32) has a scalar covariance matrix,
η2 IN , where IN is the identify matrix. The covariance matrix of r˜ is therefore of the form

(43)

m

thogonal to market betas. We also assume equal market
weights across stocks, wm = (1/N )ι. Without loss of generality, we set (g g)/N = 1. In all calculations, we take limits
as the number of stocks, N, grows large.
4.1. Parameter values
In this simple setting there are only four parameters
whose numerical values are relevant to the initial set of
results we present: λ, a, σm , and  (deﬁned below).
We vary λ over its entire [0, 1] range. We set σm = 0.20,
roughly the historical standard deviation of the market
portfolio’s excess return. Following Eq. (7), we then set
a = μm /σm2 with μm = 0.08, roughly the market’s historical mean excess return.8
8
Identifying σm2 in Eq. (43) as the market variance is justiﬁed for large
N. If we instead denote that variance as simply σ 2 , note that the implied
variance of the market, wm  wm , is


1  2
η2
ι σ βm βm + σ f2 gg + η2 IN ι = σ 2 + ,
N
N2

noting wm βm = (1/N )ι βm = 1 and recalling

σ 2 = σm2 , the limit as N grows large.

(46)

as shown in the Appendix. Fig. 1 plots this difference as
λ goes from zero to one. The difference is zero at λ = 0,
but it declines linearly as λ increases. At λ = 1, ESG tastes
are fully reﬂected in prices, and the difference reaches its
largest magnitude. In that scenario, the difference is −2%
when  = 0.01, but it is −8% when  = 0.04. ESG investors thus earn signiﬁcantly lower returns than non-ESG
investors when the former account for a larger fraction of
wealth (larger λ) and when they have stronger ESG demands (larger ). In both scenarios, ESG tastes exert large
effects on asset prices, hurting ESG investors’ returns.
∗
The certainty equivalent returns of the two types, resg
∗
for ESG investors and rnon for non-ESG investors, are both
∗
∗
increasing in , but resg
decreases with λ whereas rnon
increases with λ, as we show in the Appendix. As λ increases, stock prices are affected more by ESG investors’
tastes, so these investors must pay more for the green
∗ need not imstocks they desire. The resulting drop in resg
ply, however, that an ESG investor is made less happy by
an increased presence of ESG investors. With the latter,
there is also greater social impact of ESG investing, as we
discuss in Section 6. The additional utility that the ESG investor derives from the greater social impact, as in Eq. (68),
can exceed the drop in utility corresponding to the lower
∗ . Non-ESG investors, on the other hand, do prefer to
resg
be lonely in their ESG tastes. A non-ESG investor is happiest when all other investors are ESG (λ = 1), because
that scenario maximizes deviations of prices from pecuniary fundamentals, which the non-ESG investor exploits
to her advantage. This investor’s preference for loneliness
in ESG tastes is even stronger if she derives utility from
social impact, because that impact is maximized when
λ = 1.

Recall that wm g = 0, which here implies ι g = 0. We
assume that β  g = 0, so that ESG characteristics are or-

σm2 =

(45)

as shown in the Appendix, along with the expressions for
∗ and r ∗ . Note that  is larger under stronger ESG tastes
resg
m
(larger d), lower risk aversion (smaller a), and a greener
ESG portfolio (larger gg ). We consider four values of :
1%, 2%, 3%, and 4% per year.

Fig. 1. ESG versus non-ESG expected portfolio return. This ﬁgure plots
the expected excess return on the portfolio of ESG investors minus the corresponding value for non-ESG investors. Results are plotted against λ, the fraction of wealth belonging to ESG investors, and
for different values of , the maximum certain return an ESG investor
would sacriﬁce to invest in her optimal portfolio instead of the market
portfolio.

 = σm2 βm βm + σ f2 gg + η2 IN .

d 2 gg
,
2a3

(44)

ι g = 0, so we simply set

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Journal of Financial Economics 142 (2021) 550–571

have nonzero alphas, due to the price impacts of ESG investors, but ESG investors hold the market, so again they
earn zero alpha. Otherwise, ESG investors earn negative alpha, which is greatest in magnitude when λ = 0.5. At that
peak, αesg = −0.5% when  = 0.01, but αesg = −2% when
 = 0.04.
Interestingly, these worst-case alphas are substantially
smaller in magnitude than the corresponding ’s. For example, when ESG investors are willing to give up a 2% certain return to hold their portfolio rather than the market
(i.e.,  = 0.02), their worst-case alpha is only −1%. The
reason is that equilibrium stock prices adjust to ESG demands. These demands push the market portfolio toward
the portfolio desired by ESG investors, thereby bringing
those investors’ negative alphas closer to zero. Through
this adjustment of market prices, ESG investors earn an
“investor surplus” in that they do not have to give up as
much return as they are willing to in order to hold their
desired portfolio.
The magnitude of this investor surplus is easy to read
from Panel B of Fig. 3, which plots αesg as a function of
. For any given value of λ, investor surplus is the difference between the corresponding solid line and the dashed
line, which has a slope of −1. The surplus increases with
 because the stronger the ESG investors feel about greenness, the more they move market prices. The relation between the surplus and λ is richer. Formally, investor surplus I ≡ αesg +  follows quickly from Eq. (48):

Fig. 2. Correlation of ESG investor’s portfolio return with the market return. The ﬁgure plots the correlation between the returns on the ESG investor’s portfolio and the market portfolio. Results are plotted against λ,
the fraction of wealth belonging to ESG investors, and for different values of , the maximum certain return an ESG investor would sacriﬁce to
invest in her optimal portfolio instead of the market portfolio.

4.3. Correlation between the ESG return and the market
return

I = [1 − 2λ(1 − λ )].

The correlation between the return on an ESG investor’s
portfolio and the return on the market portfolio is derived
in the Appendix:

ρ (r˜esg , r˜m ) = 

σm
.
σm2 + 2a (1 − λ )2


(50)

Because 0 ≤ λ ≤ 1, the value in brackets is always between
0.5 and 1, so I is always between /2 and . It reaches its
smallest value of /2 when λ = 0.5 and its largest value of
 when λ = 0 or 1. For example, when  = 0.02, I ranges
from 1% to 2% depending on λ.
Fig. 4 plots αnon as a function of λ and . Like ESG investors, non-ESG investors earn zero alpha when λ = 0 or
 = 0. However, αnon increases in both λ or . This alpha
can be as large as 8% when λ = 1 and  = 0.04. A nonESG investor earns the highest alpha when all other investors are ESG (i.e., λ = 1) and when those investors’ ESG
tastes are strong (i.e.,  is large) because the price impact
of ESG tastes is then particularly large. By overweighting
brown stocks, whose alphas are positive and large, and underweighting green stocks, whose alphas are negative and
large, the non-ESG investor earns a large positive alpha.
Given our assumptions, the differences between the alphas plotted in Figs. 3 and 4 are equal to the differences
in expected returns plotted in Fig. 1. Speciﬁcally, from
Eqs. (46) through (49), αesg − αnon = E{r˜esg } − E{r˜non }.

(47)



Fig. 2 plots the value of ρ r˜esg , r˜m as λ goes from zero
to one. The correlation takes its lowest value at λ = 0. For
 = 0.01, that value is nearly 0.9, whereas for  = 0.04,
it is just over 0.7. As  increases, indicating that ESG
investors feel increasingly strongly about ESG, those investors’ portfolios become increasingly

 different from the
market portfolio in terms of ρ r˜esg , r˜m , and this effect is
strongest
 when λ = 0. However, as λ approaches one, so
does ρ r˜esg , r˜m . When ESG investors hold an increasingly
large fraction of wealth, market prices adjust to their preferences, and all portfolios converge to the market portfolio.
4.4. Alphas and the investor surplus
The alphas of the ESG and non-ESG investors’ portfolios
are derived in the Appendix:

αesg = −2λ(1 − λ )

(48)

4.5. Size of the ESG investment industry

αnon = 2λ2 .

(49)

We deﬁne the size of the ESG investment industry by
the aggregate amount of ESG-driven investment that deviates from the market portfolio, divided by the stock market’s total value. In general, this aggregate ESG tilt is given
by

Panel A of Fig. 3 plots αesg as λ goes from zero to
one. ESG investors earn zero alpha at both extremes of
λ. Their portfolio differs most from the market portfolio when λ = 0, but all stocks have zero alphas in that
scenario, because there is no impact of ESG investors on
prices. At the other extreme, when λ = 1, many stocks



T =
559

i:di >0

ωi Ti di,

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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

Fig. 3. Alphas of ESG investors. This ﬁgure plots the alpha for the portfolio held by ESG investors as a function of λ, the fraction of wealth belonging to ESG investors, and , the maximum certain return an ESG investor
would sacriﬁce to invest in her optimal portfolio instead of the market
portfolio. Panel A plots the ESG alpha as a function of λ for four different
values of ; Panel B ﬂips the roles of λ and . The dashed line in Panel B
has a slope of −1. The differences between the solid lines and the dashed
line represent investor surplus.

Fig. 4. Alphas of non-ESG investors. This ﬁgure plots the alpha for the
portfolio held by non-ESG investors as a function of λ, the fraction of
wealth belonging to ESG investors, and , the maximum certain return
an ESG investor would sacriﬁce to invest in her optimal portfolio instead
of the market portfolio. Panel A plots the ESG alpha as a function of λ for
four different values of ; Panel B ﬂips the roles of λ and .

where

Ti =

1 
ι |wi − wm |.
2

as we show in the Appendix. The aggregate tilt depends
on the absolute values of the elements of g. To evaluate ι |g| in this quantitative exercise, we further assume that the elements of g are normally distributed
across stocks, in addition to the previous assumptions that
these elements have zero mean and unit variance 
(recall
ι g = 0 and (g g)/N = 1). Then ι |g| = NE(|gn | ) = N 2/π .
Therefore,

(52)

The aggregate ESG tilt, T , is a wealth-weighted average
of agent-speciﬁc tilts, Ti , across all agents who care at
least to some extent about ESG (i.e., di > 0). Each Ti is
one half of the sum of the absolute values of the N elements of agent i’s ESG tilt, |wi − wm |. We compute absolute values of portfolio tilts because ESG-motivated investors both overweight and underweight stocks relative
to the market. We divide by two because we do not want
to double-count: for each dollar that an agent moves into
a green stock, she must move a dollar out of another
stock.
With two types of agents, the expression for T simpliﬁes to

1
T = λ (1 − λ )
N





2aσ f2

ι |g|,


T = λ (1 − λ )



aπ σ f2

.

(54)

For this analysis, we now need to specify the value of
one additional parameter, σ f2 , the standard deviation of the
ESG factor. We set σ f = (0.2 )σm , but the effect of this parameter is easily gauged from Eq. (54). The more volatile
is the ESG factor, the more reluctant both ESG and nonESG investors are to tilt away from the market and thereby

(53)

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Journal of Financial Economics 142 (2021) 550–571

5. Climate risk
Sustainable investing is motivated in part by concerns
about climate change. Many experts expect climate change
to impair quality of life, lowering utility of the typical individual beyond what is captured by climate’s effect on
wealth. Unanticipated climate changes present investors
with an additional source of risk, which is non-traded and
only partially insurable.9 This section extends our model
from Section 2 to include climate risk.
Let C˜ denote climate at time 1, which is unknown at
time 0. We modify the utility function for individual i in
Eq. (2) to include C˜ as follows:
˜



˜

˜ 1i , Xi , C˜ ) = −e−AiW1i −bi Xi −ciC .
V (W

(55)


Let c̄ ≡ i ωi ci di, the wealth-weighted mean of climate sensitivity across agents. We assume c̄ > 0, so that agents dislike low realizations of C˜, on average. We also assume C˜
is normally distributed, and without loss of generality we
set E{C˜} = 0 and Var{C˜} = 1. Besides replacing Eq. (2) with
Eq. (55), we maintain all other assumptions from Section 2.
In principle, “climate” can be interpreted broadly, for
example, as “social climate.” However, for shocks to climate to affect asset prices, these shocks must enter the
average agent’s utility, in that c̄ > 0. This assumption is
nontrivial because individuals’ views on various social issues, such as guns and abortion, are quite heterogeneous
in practice. We emphasize the narrow interpretation of climate (“E” in ESG), for which the assumption is likely to
hold. Indeed, the correlations in ESG ratings across rating
agencies are higher for the “E” ratings than for the “S” and
“G” ratings (e.g., Berg et al., 2019).
Fig. 5. Size of the ESG industry. The ﬁgure plots the aggregate dollar size
of ESG investors’ deviations from the market portfolio (the ESG “tilt”), expressed as a fraction of the market’s total capitalization. In Panel A, results are plotted against λ, the fraction of wealth belonging to ESG investors, and for different values of , the maximum certain return an
ESG investor would sacriﬁce to invest in her optimal portfolio instead of
the market portfolio. In Panel B, results are plotted against  and for different values of λ.

5.1. Expected returns and portfolio holdings
Climate risk affects equilibrium stock returns, as shown
in the Appendix.
Proposition 7. Expected excess returns in equilibrium are
given by



d¯
2
μ = μm βm − g + c̄ 1 − ρmC
ψ,

expose themselves to the ESG factor’s risk. Higher risk
aversion (greater a) also makes them more reluctant to do
so, but they tilt more when ESG investors have stronger
tastes (greater ).
Fig. 5 plots T for different values of λ and . In Panel
A, λ goes from zero to one. At both λ = 0 and λ = 1, we
have T = 0 because all investors hold the market portfolio.
Again, we see that dispersion in ESG tastes is needed for
an ESG investment industry to exist. The maximum value
of T in Eq. (54) always occurs at λ = 0.5, the maximum of
λ(1 − λ ). In Panel B,  goes from 0 to 0.04. Larger values
of  produce larger values of T . This relation between 
and T is concave (see also Eq. (54)). For example, the ESG
industry peaks at 35% of the stock market’s value when
 = 0.02, but doubling the strength of ESG tastes (raising
 to 0.04) increases that maximum industry size by less
than half, to 50% of the market’s value. We see that the
price impact of ESG tastes weakens their impact on the
size of the ESG investment industry.

a

(56)

where ψ is the N × 1 vector of “climate betas” (slope coeﬃcients on C˜ in a multivariate regression of ˜ on both ˜m and
C˜), and ρmC is the correlation between ˜m and C˜.
Expected returns depend on climate betas, ψ , which
represent ﬁrms’ exposures to non-market climate risk. To
understand the regression deﬁning ψ , recall that ˜ is an
N × 1 vector of unexpected stock returns from Eq. (1) and
˜m is the unexpected market return. A ﬁrm’s climate beta

9
In that sense, climate risk is related to “background risk” analyzed
in prior work. Research into the risk associated with non-marketable
assets originates with Mayers (1972). Examples of non-traded systematic risk factors include human capital (Fama and Schwert, 1977), liquidity (Pástor and Stambaugh, 2003), and innovation-induced displacement
(Garleanu et al., 2012).

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Journal of Financial Economics 142 (2021) 550–571

is its loading on C˜ after controlling for the market return.
Climate betas, ψn , are likely to be related to ESG characteristics, gn , as we argue in Section 5.2.
Compared to Eq. (9), expected excess returns contain an
additional component given by the last term on the righthand side of Eq. (56). Stock n’s climate beta, ψn , enters expected return positively. Thus, a stock with a negative ψn ,
which provides investors with a climate-risk hedge, has a
lower expected return than it would in the absence of climate risk. Vice versa, a stock with a positive ψn , which
performs particularly poorly when the climate worsens unexpectedly, has a higher expected return.

as a result of stronger public pressure on institutional
investors to divest from brown assets. For example,
Choi et al. (2020) show that retail investors sell carbonintensive ﬁrms in extremely warm months, consistent with
d¯ rising in such months.
Climate shocks are thus likely to correlate negatively
with both components of the ESG factor in Eq. (41). Green
stocks, which have positive exposures to this factor, are
likely to have negative exposures to C˜. These arguments
imply a negative correlation between gn and ψn across
ﬁrms.
One can also argue that the better hedges of climate
risk are brown stocks, not green. Baker et al. (2020) assume negative climate shocks result from positive shocks
to the output of brown ﬁrms. The latter shocks translate to positive unexpected returns on those ﬁrms’ stocks,
thereby making brown stocks climate hedges. As noted
earlier, whether brown stocks or green stocks better hedge
climate risk ultimately rests on empirical evidence.
The evidence suggests that the better climate hedges
are green stocks. For example, Choi et al. (2020) show that
green ﬁrms, as measured by low carbon emissions, outperform brown ﬁrms during months with abnormally warm
weather, which the authors argue alerts investors to climate change. Engle et al. (2020) report that green ﬁrms, as
measured by high E-Scores from Sustainalytics, outperform
brown ﬁrms in periods with negative climate news. Both
studies thus show that a high-minus-low gn stock portfolio is a good hedge against climate risk, indicating that gn
is negatively correlated with ψn across ﬁrms.
In the special case where this negative correlation is
perfect, so that

Proposition 8. Agent i’s equilibrium portfolio weights on the
N stocks are given by

Xi = wm +

δi 
a2

 γ

 −1 g − i  −1 σC ,
a

(57)

where γi ≡ ci − c̄ and σC is an N × 1 vector of covariances
between ˜n and C˜.
Eq. (57), which we prove in the Appendix, implies fourfund separation. The ﬁrst three funds are the same as in
Proposition 3; the fourth one is a climate-hedging portfolio whose weights are proportional to  −1 σC . Agents with
γi > 0, whose climate sensitivity is above average, short
the hedging portfolio, whereas agents with γi < 0 go long.
The climate-hedging portfolio,  −1 σC , is a natural
mimicking portfolio for C˜. To see this, note that the N elements of  −1 σC are the slope coeﬃcients from the multiple regression of C˜ on ˜ . Therefore, the return on the
hedging portfolio has the highest correlation with C˜ among
all portfolios of the N stocks. Investors in our model hold
this maximum-correlation portfolio, to various degrees determined by their γi , to hedge climate risk. The climatehedging portfolio can tilt toward either green stocks or
brown stocks, depending on how returns on each type relate to climate shocks. The latter issue is addressed next.

ψn = −ξ gn ,

(58)

where ξ > 0 is a constant, Eq. (56) simpliﬁes to



μ = μm βm −





d¯
2
+ c̄ 1 − ρmC
ξ g.
a

(59)

Stock n’s CAPM alpha is then given by

5.2. Green stocks as climate hedges







d¯
2
αn = − + c̄ 1 − ρmC
ξ gn .
a

Ultimately the issue of whether green stocks or brown
stocks are better climate hedges is an empirical question,
because sensible economic arguments can be made either
way. The argument that green stocks should hedge climate
risk can be motivated through both channels described in
Section 3.
First, consider the customer channel. Unexpected worsening of the climate can heighten consumers’ climate
concerns, prompting greater demands for goods and services of greener providers. These demands can arise not
only from consumers’ preferences but also from government regulation. Negative climate shocks can prompt government regulations that favor green providers or penalize brown ones. For example, the new regulations
could subsidize green products and tax, or even prohibit,
brown ones. Half of the institutional investors surveyed by
Krueger et al. (2020) state that climate risks related to regulation have already started to materialize.
Second, consider the investor channel. Unexpected
worsening of the climate can strengthen investors’ preference for green holdings (i.e., increase d¯), possibly

(60)

Both terms inside the brackets are positive, so the negative
relation between αn and gn is stronger than in Corollary 2.
Greener stocks now have lower CAPM alphas not only because of investors’ tastes for green holdings, but also because of greener stocks’ ability to better hedge climate
risk. Climate risk thus represents another reason to expect
green stocks to underperform brown ones over the long
run. For the same reason, green stocks have a lower cost
of capital than brown stocks relative to the CAPM.
In this special case, two-factor pricing from
Section 3 continues to hold. Each stock has a zero alpha in the two-factor model in Eq. (32). The ESG factor
is still
 deﬁned
 as in Eq. (31), but its premium is reduced
2 ξ , as compared to Eq. (33). This reduction
by c̄ 1 − ρmC
reﬂects compensation for climate risk. The compensation
is negative because greener ﬁrms are better hedges against
this risk. The ESG factor’s premium thus has one tastebased
−d¯/a, and one risk-based component,
 component,

2 ξ.
−c̄ 1 − ρmC
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Journal of Financial Economics 142 (2021) 550–571

as long as d¯ > 0 and gn = 0. Moreover, this impact is increasing in d, decreasing in a, increasing in n , decreasing in κn ,
and decreasing in βm,n .

6. Social impact
Does sustainable investing produce real social impact?
This section explores how ﬁrms respond to the asset pricing effects from Section 2. We extend our baseline model
from that section to include ﬁrms’ choices of investment
and ESG characteristics.
We deﬁne the social impact of ﬁrm n as

Sn ≡ gn Kn ,

The intuition behind this result builds on Eq. (62),
which shows that ESG tastes lead green ﬁrms to invest
more and brown ﬁrms to invest less. That result relates
to Corollary 1, which states that ESG tastes reduce green
ﬁrms’ expected returns and hence their costs of capital.
Green ﬁrms’ lower costs of capital increase their projects’
NPVs, so green ﬁrms invest more. And vice versa, ESG
tastes increase brown ﬁrms’ costs of capital, reducing their
investment. As a result, ESG tastes tilt investment from
brown to green ﬁrms, which increases social impact for
both types of ﬁrms.
The comparative statics are also intuitive. Social impact is larger when ESG tastes are stronger (i.e., when d¯
is larger) because stronger tastes move asset prices more.
The impact is also larger when risk aversion is weaker (i.e.,
a is smaller) because less risk-averse agents tilt their portfolios more to accommodate their tastes, again resulting in
larger price effects (see Propositions 1 and 3). The impact
is larger when capital is less costly to adjust (i.e., when
κn is smaller) because more investment reallocation takes
place. The impact is also larger when ﬁrms are more productive (i.e., when n is larger) because a given change in
the cost of capital has a larger effect on investment. Finally,
the impact is larger for ﬁrms with smaller market betas
because such ﬁrms have a lower cost of capital to begin
with, so the ESG-induced change in their cost of capital is
relatively larger.
In our model, investors’ ESG tastes tilt real investment
from brown to green ﬁrms because those tastes generate
alphas, which affect the cost of capital, which in turn affects investment. There is considerable empirical support
for this mechanism. Baker and Wurgler (2012) survey studies that ﬁnd a negative relation between corporate investment and alpha. Most of these studies interpret alpha
as mispricing, whereas our study’s ESG-induced alphas do
not reﬂect mispricing. We expect ESG-induced alphas to
have an especially strong effect on investment. Whereas
mispricing is transient, ﬁrms’ ESG traits are highly persistent, which makes ESG-induced alphas highly persistent. Van Binsbergen and Opp (2019) show that when alphas are more persistent, they have stronger effects on
investment.

(61)

where Kn is the ﬁrm’s operating capital. Social impact captures the ﬁrm’s total externalities, which depend on both
the nature of the ﬁrm’s operations (gn ) and their scale (Kn ).
We consider two scenarios. In Section 6.1, we let the ﬁrm’s
manager choose Kn while taking gn as given. In Section 6.2,
we allow the manager to choose both Kn and gn . Throughout, the manager maximizes the ﬁrm’s market value at
time 0.
The extra assumptions we make here change none of
the previous sections’ predictions. Since investors are inﬁnitesimally small, they still take asset prices and ﬁrms’
ESG characteristics as given, even though ﬁrms now choose
those characteristics. Firms’ choices of Kn and gn affect
their market values, which are consistent with the expected returns derived in Section 2.
6.1. Green ﬁrms invest more, brown ﬁrms less
The ﬁrm is initially endowed with operating capital
K0,n > 0. The ﬁrm’s manager chooses how much additional
capital, Kn , to buy, while taking the ﬁrm’s ESG characteristic, gn , as given. The ﬁrm’s capital investment produces a
time-0 cash ﬂow of −Kn − κ2n (Kn )2 , where κn > 0 controls capital-adjustment costs. The ﬁrm uses capital to produce an expected gross cash ﬂow at time 1 equal to n Kn ,
where n is a positive quantity denoting one plus the
ﬁrm’s gross proﬁtability.
The optimal amount of additional capital is derived in
the Appendix:



Kn (d ) =



n

1

κn 1 + r f + μm βm,n − d gn
a

−1 .

(62)

This value is increasing in gn , indicating that greener ﬁrms
invest more, ceteris paribus.
For any ﬁrm n, agents’ ESG tastes induce social impact
equal to the difference between the ﬁrm’s actual social
impact and its hypothetical impact if agents did not care
about ESG:





Sn (d ) − Sn (0 ) = gn Kn (d ) − Kn (0 ) .

6.2. Firms become greener

(63)

We now extend the framework from Section 6.1 by allowing ﬁrm n’s manager to choose not only Kn but also
gn . The ﬁrm is initially endowed with an ESG characteristic
g0,n . The manager chooses both Kn and gn , the change
in the ﬁrm’s ESG characteristic. For example, a coal power
producer can increase its gn by installing scrubbers. Adjusting gn is costly: it reduces the ﬁrm’s time-1 cash ﬂow by a
fraction χ2n (gn )2 , where χn > 0 controls ESG-adjustment
costs.
We prove the following proposition in the Appendix.

We prove the following proposition in the Appendix.
Proposition 9. Firm n’s ESG-induced social impact is positive:

Sn ( d ) − Sn ( 0 )
=



d g2n n

aκn 1 + r f + μm βm,n − da gn



1 + r f + μm βm,n

 > 0
(64)
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Journal of Financial Economics 142 (2021) 550–571

Proposition 10. Firm n’s value-maximizing choices of ESG
adjustment and investment are

 
d
g n d ≈
aχn
 

Kn d =


1

(65)



n 1 − χ2n (gn (d ))2

κn 1 + r f + μm βm,n − d gn (d )
a


−1 ,

(66)

where gn (d ) = g0,n + gn (d ), and the approximation uses
log(1 + x ) ≈ x for small x.
Both choices are intuitive given the results from
Section 2. When d > 0, expected returns decrease in gn
(Corollary 1), so ﬁrms’ market values increase in gn . Managers who wish to maximize market value therefore make
their ﬁrms greener (i.e, gn > 0). This effect is especially
strong when risk aversion a is low because ESG characteristics then have large effects on market values. Firms also
adjust gn by more when doing so is less costly.
As in Section 6.1, ESG tastes lead green ﬁrms to invest more and brown ﬁrms to invest less. The denominator in Eq. (66) shows that ESG tastes reduce the costs
of capital for green ﬁrms, which increases their projects’
NPV and hence investment. And vice versa, ESG tastes increase brown ﬁrms’ costs of capital, reducing their projects’
NPV and investment. In addition, ESG tastes affect expected cash ﬂows in the numerator of Eq. (66). Stronger
ESG tastes induce all ﬁrms, green and brown, to adjust
their gn by more, which reduces their expected cash ﬂows,
and hence also their investment.
Agents’ ESG tastes now increase social impact not only
by tilting investment from brown to green ﬁrms, as before,
but also by making ﬁrms greener:



Fig. 6. Firm-level social impact. This ﬁgure plots Sn (d ) − Sn (0 ), the social impact induced by ESG-motivated investors, for different ﬁrms n. The
horizontal axis indicates the ﬁrm’s initial ESG characteristic, g0,n . The two
regions indicate the components of Sn (d ) − Sn (0 ) from Eq. (67). This ﬁgure uses the same parameters as the previous ﬁgures, with λ = 0.5 and
 = 0.02, as well as r f = 0.02, K0,n = 1, n = 1.2, χn = 0.5, and κn = 1.
These parameter values produce d = 0.0113, gn (d ) = 0.0113, Kn (0 ) =
0.0909, and Kn (d ) ranging from 0.0813 to 0.1007.

teristics, but it is strictly positive even for ESG-neutral
ﬁrms.
The aggregate social impact induced by ESG investors,
denoted S(d ) − S(0 ), is the sum of Sn (d ) − Sn (0 ) across
ﬁrms n. This sum can be computed from the curve in
Fig. 6. Since this curve is convex in g0,n , S(d ) − S(0 ) is
greater when there is more dispersion in ESG characteristics across ﬁrms. A larger dispersion in g0,n deepens
the cost-of-capital differentials between green and brown
ﬁrms, leading to larger investment differentials. With green
ﬁrms investing more and brown ﬁrms investing less, aggregate social impact increases.
Fig. 7 illustrates how aggregate social impact varies
with the strength of ESG preferences. We assume ﬁrms differ only in their initial ESG characteristics g0,n , which are
uniformly distributed with mean zero. The ﬁgure shows
that S(d ) − S(0 ) increases as ESG preferences strengthen,
which is intuitive. We also see that both sources of social impact from Eq. (67) grow larger as ESG preferences
strengthen. These results hold whether ESG preferences
strengthen because there are more ESG investors (Panel A)
or because ESG investors have stronger tastes (Panel B).
We have made the standard assumption that managers
maximize the ﬁrm’s market value. This assumption makes
sense if, for example, managers wish to maximize the
value of their stock-based compensation. Alternatively, a
manager could maximize shareholder welfare, which depends not just on market value but also on the ﬁrm’s ESG
characteristics (e.g., Hart and Zingales, 2017). Such behavior could result from shareholders engaging actively with
the ﬁrm, so that managers run the ﬁrm as shareholders desire (e.g., Dyck et al., 2019), or from shareholders appointing managers whose preferences match their own. Our



Sn (d ) − Sn (0 ) = g0,n Kn (d ) − Kn (0 ) + Kn (d ) gn (d ).
(67)
The ﬁrst term reﬂects the investment effect analogous
to Eq. (63). As discussed previously, when ﬁrms cannot
change their gn ’s, Kn (d ) − Kn (0 ) is positive for green
ﬁrms and negative for brown ﬁrms, making this term positive for both types of ﬁrms. When ﬁrms can change their
gn ’s, the ﬁrst term in Eq. (67) is still generally positive.
The second term reﬂects ﬁrms’ capital becoming greener.
This term is also positive since gn (d ) > 0, as implied by
Eq. (65).
Fig. 6 plots the ESG-induced social impact across ﬁrms
with different initial ESG characteristics. We see that all
ﬁrms have positive social impact. The two colored regions
indicate the two sources of social impact from Eq. (67). The
second source, from ﬁrms becoming greener, is roughly
equal across ﬁrms (top green region). The ﬁrst source,
from tilting investment toward green ﬁrms, is zero for an
ESG-neutral ﬁrm, but it is large for very green or very
brown ﬁrms, which experience the largest shifts in investment (bottom blue region). Due to this non-monotonicity,
the overall social impact induced by ESG-motivated investors is largest for ﬁrms with extreme ESG charac-

564

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

6.3. Preferences for aggregate social impact
As noted in Section 2, agents derive utility not only
from their holdings, Xi , but also from ﬁrms’ aggregate so
cial impact, S = N
n=1 Sn . We assume each agent i’s utility
is increasing in S:

˜ 1i , Xi , S ) = V (W
˜ 1i , Xi ) + hi (S ),
U (W

(68)

where hi (S ) > 0 and V is the original utility function from
Eq. (2). (The additive speciﬁcation is not needed; our results are identical if S enters utility multiplicatively.)
Proposition 11. If agents derive utility also from aggregate
social impact (Eq. (68)), all of our results in Propositions 1
through 10 and Corollaries 1 through 4 continue to hold.
The inclusion of S in the utility function does not affect any of our prior results. The reason is that inﬁnitesimally small agents take stock prices, and hence S, as given
when choosing their portfolios. When an agent tilts toward
green stocks, she generates a positive externality on other
agents via the hi (S ) term in their utility.10 Being inﬁnitesimal, though, she does not internalize any of this effect. As
the preference for S does not affect portfolio choice, it does
not affect equilibrium asset prices, real investment, or S. In
the model of Oehmke and Opp (2020), agents’ preference
for social impact does lead to impact because agents are
assumed to coordinate. In our model, agents cannot coordinate. Social impact is caused by the inclusion of Xi , not
S, in the utility function in Eq. (68).
To provide more intuition for the roles of Xi and S in
the utility function, consider why people vote in elections.
Many individuals vote because they derive utility directly
from doing so, analogous to investors deriving utility from
their holdings (Xi ) in our setting. This utility from voting
can have various sources; for example, some people enjoy
participating in a democracy, others feel a warm glow from
voting for their favorite candidate, and some might like to
tell friends they have exercised their patriotic duty. Each
individual’s utility could also depend on the election outcome (S), but that by itself is not why an individual votes.
If there are a large number of voters, the individual sees
her vote as having no effect on that component of her utility. Just as utility from voting produces an aggregate social
good (a healthy democracy), investors’ utility from their
portfolio holdings generates aggregate social impact.
More research is clearly needed on the real effects
of sustainable investing. For example, what is the relative importance of the investment channel (Kn ) and
the “become-greener” channel (gn )? What if agents care
about both social impact and climate, and the effect of the
former on the latter is uncertain? How would social impact
change if we combined the asset pricing effects we examine with direct engagement by large shareholders? We
leave these questions for future work.

Fig. 7. Aggregate social impact. The ﬁgure plots [S (d ) − S (0 )]/N, the aggregate social impact induced by ESG-motivated investors, scaled by the
number of ﬁrms. We assume√the√ﬁrms’ initial ESG characteristics g0,n are
uniformly distributed in [− 3, 3]. (These endpoints maintain g0 ι = 0
and (g0 g0 )/N = 1.) The two colored regions indicate the components of

Sn (d ) − Sn (0 ) from Eq. (67), aggregated across ﬁrms. In Panel A, results
are plotted against λ, the fraction of wealth belonging to ESG investors,
assuming  = 0.02. In Panel B, results are plotted against , the maximum certain return an ESG investor would sacriﬁce to invest in her optimal portfolio instead of the market portfolio, assuming λ = 0.5. All remaining parameter values are the same as in Fig. 6.

model arguably provides a lower bound on social impact.
Extending the model so that managers additionally care
about their ﬁrms’ ESG characteristics should produce gn
values (and hence social impact) even larger than we currently predict. Put differently, we show that ESG-motivated
investors generate social impact even without direct engagement by shareholders, and even if managers do not
care directly about ﬁrms’ ESG characteristics. Even a “selfish” manager who cares only about market value behaves
in a way that increases social impact.

10
In the presence of externalities, the competitive market solution generally differs from the social planner’s solution. For an example of a social
planner’s solution in a different setting, with interesting implications for
ESG mandates, see Hong et al. (2020).

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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571

7. Conclusion

Appendix. Proofs and derivations

We analyze both ﬁnancial and real effects of sustainable investing in a highly tractable equilibrium model. The
model produces a number of empirical implications regarding asset prices, portfolio holdings, the size of the ESG
investment industry, climate risk, and the social impact of
sustainable investing. We review those implications below.
First, ESG preferences move asset prices. Stocks of
greener ﬁrms have lower ex ante CAPM alphas, especially
when risk aversion is low and the average ESG preference is strong. Green stocks have negative alphas, whereas
brown stocks have positive alphas. Green stocks’ negative
alphas stem from two sources: investors’ tastes for green
holdings and such stocks’ ability to hedge climate risk.
Green and brown stocks have opposite exposures to an ESG
risk factor, which captures unexpected changes in ESG concerns of customers and investors. If either kind of ESG concern strengthens unexpectedly over a given period of time,
green stocks can outperform brown stocks over that period, despite having lower alphas. Stocks are priced by a
two-factor asset pricing model, where the factors are the
market portfolio and the ESG factor. A simple version of
the ESG factor is a green-minus-brown portfolio return,
where both green and brown portfolios are weighted by
ESG characteristics.
Second, portfolio holdings exhibit three-fund separation. Investors with stronger than average ESG tastes hold
portfolios that have a green tilt away from the market
portfolio, whereas investors with weaker than average ESG
tastes take a brown tilt. These tilts are larger when risk
aversion is lower. Investors with stronger ESG tastes earn
lower expected returns, especially when risk aversion is
low and the average ESG taste is high. Yet these investors
give up less return than they are willing to in order to
hold their desired portfolio. In the model extension that
adds climate risk, we obtain four-fund separation, with the
fourth fund representing a climate-hedging portfolio with
a green tilt.
Third, the size of the ESG investment industry—the aggregate dollar amount of ESG-driven investment that deviates from the market portfolio—is increasing in the dispersion of investors’ ESG preferences. With no dispersion
there is no ESG industry, because everyone holds the market.
Finally, sustainable investing generates positive social
impact in two ways. First, it leads ﬁrms to become greener.
Second, it induces more real investment by green ﬁrms
and less investment by brown ﬁrms.
While the model’s predictions for alphas have been examined empirically by prior studies, most of its other predictions remain untested, presenting opportunities for future empirical work. One challenge is that our model aims
to describe the world of the present and the future, but
not necessarily the world of the past. Although the “sin”
aspects of investing have been recognized for decades, the
emphasis on ESG criteria is a recent phenomenon. How the
model ﬁts in various time periods is another question for
empirical work.

Derivation of Eq. (4):
To compute agent i’s expected utility, we rely on Eq. (2),
˜ 1i = W0i (1 + r f + X  r˜), and the fact that r˜ is
the relation W
i
normally distributed, r˜ ∼ N (μ, ):



˜ 1i , Xi ) = E −e−AiW˜ 1i −bi Xi
E V (W







= E −e−Ai [W0i (1+r f +Xi r˜)]−bi Xi



= −e−ai (1+r f ) E e
= −e−ai (1+r f ) e
= −e

−ai Xi [r˜+ a1 bi ]



i

−ai Xi [E (r˜)+ a1 bi ]+ 12 a2i Xi Var(r˜ )Xi
i

1
1 2 

−ai (1+r f ) −ai Xi [μ+ ai bi ]+ 2 ai Xi  Xi

e

(A1)

where ai ≡ AiW0i is agent i’s relative risk aversion. Agents
take μ and  as given. Differentiating with respect to Xi ,
we obtain the ﬁrst-order condition

−ai [μ +

1
1
bi ] + a2i (2 Xi ) = 0
ai
2

(A2)

from which we obtain agent i’s portfolio weights

Xi =

1 −1

ai



μ+



1
bi .
ai

(A3)

Derivation of Eq. (5):
The nth element of agent i’s portfolio weight vector, Xi ,
is given by

Xi,n =

W0i,n
W0i

(A4)

where W0i,n is the dollar amount invested by agent i in

stock n. Let W0,n ≡ i W0i,n di denote the total amount invested in stock n by all agents. Then the nth element of
the market-weight vector, wm , is given by



W0,n
1
1
=
W0i,n di =
W0i Xi,n di
W0
W0 i
W0 i


W0i
=
Xi,n di = ωi Xi,n di.
i W0
i

wm,n =

(A5)

N
N
Note that
n=1 wm,n = 1 because
n=1 W0,n = W0 , which
follows from the riskless asset being in zero net supply.
Plugging in for Xi from Eq. (A3) and imposing ai = a, we
have



ωi Xi di
1


1
= ωi  −1 μ + bi di
a
a
i
 1



1 −1
=  μ
ωi di + 2  −1 g ωi di di

x=



i

a

i

1
d¯
=  −1 μ + 2  −1 g.
a
a

a

i

(A6)

Proof of the statement in footnote 4:
Let g˜in denote agent i’s perceived ESG characteristic of
ﬁrm n, known by all agents. Eq. (3) changes to bi = di g˜i ,
where g˜i is an agent-speciﬁc N × 1 vector containing the
values of g˜in . Eq. (5) is unchanged, with g redeﬁned as

566

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

g = ( 1/d )



Journal of Financial Economics 142 (2021) 550–571



ωi di g˜i di
i


a



= Eω [g˜i ] + Covω di /d, g˜i ,

(A7)

=−

where Eω and Covω denote the wealth-weighted expectation and covariance, respectively, across agents. The ﬁrst
term on the right-hand side of Eq. (A7) is an N × 1 vector
whose nth element is the wealth-weighted average of g˜in
across agents. The second term is a vector whose nth element is the wealth-weighted covariance between agents’
scaled ESG tastes, di /d, and perceived ESG characteristics,
g˜in . It seems plausible to assume that the second term is
a zero vector, but we do not need to make that assumption. Since Eq. (5) is unchanged, Eqs. (6) through (9) are
also unchanged.

i

i

wm +

=


=



δi 

a2

g  −1

δi  −1
wm +
g





−aXi μ − Xi bi + (a2 /2 )Xi  Xi

δ2
di δi  −1
a2 2
g  g+
σm + i 2 g  −1 g
2
2
a
2a


a2 2
1
1 2  −1
δi d − di δi + δi g  g
= −aμm +
σ +
2 m a2
2
= −aμm +

i

i

=



δi2

a

δi 

g wm +

δi
a2

wm g +

 −1 g
2

Var(r˜i ) = σ

δi2 
a4

g

−1

g

g

,

−1

g

(A14)

(A15)

in which B = [βm
trices:

βm βm



0
,
g g

0


=

σ12

0

σ22

0


.

(A16)

Inverting  using the Woodbury identity gives

1

 −1 =

δi2 
a4

−1



g], and both B B and  are diagonal ma-



g  −1 g. (A9)

σζ2

1

I−

σζ4

B B  ,

(A17)

in which  is the diagonal matrix,



Recognizing that wm  wm = σm2 and wm g = 0, we have
2
m +

δi2

 = BB + σζ2 I,

B B =

−1

a2



Derivation of Eq. (42):
The assumptions below Eq. (36), along with Eq. (40),
imply that the covariance matrix of r˜ is of the form

 g

= wm  wm +



2

noting that the bracketed term is V̄ , the agent’s expected
utility if δi = 0.

a

g  −1  wm + wm 
2

a

= V̄ e− 2a2 g 

(A8)

a

+ 4g
a

(A13)

= −e−a(1+r f ) e−a(μm − 2 σm ) e− 2a2 g 

δi

−1



δ2
a 2
σm − i 2 g  −1 g.
2
2a




d¯
μm
 wm − g
a
σm2

δi 

δi2 

g  −1 g −

δ2

 

δ
 wm + 2i  −1 g

= wm  wm +

a2

a 2
 −1
i
˜ 1i , Xi ) = −e−a(1+r f ) e−a(μm − 2 σm )− 2a2 g  g
E V (W

δi  −1
wm +
g
a2

δi d¯ 

= −a μm −

Derivation of Eq. (12):
Recall that agent i’s excess portfolio return is r˜i = Xi r˜,
where r˜ ∼ N (μ, ). Therefore,
i

(A12)

Substituting this exponent into Eq. (A1) gives

g  −1 g.

Var(r˜ ) = X   X



recalling wm g = 0 in both cases. Adding the three terms
then gives



δi d¯ 
a3

 

δ2
a2 2
σm + i 2 g  −1 g,
2
2a

=

d
δi μm
δi d
= μm − wm g + 2 2 g wm − 3 g  −1 g
a
a
a σm
= μm −

(A11)

a2 
a2
δi
δi
Xi  Xi =
wm + 2 g  −1  wm + 2  −1 g
2
2
a
a

d¯
μm βm − g
a

a2

di δi  −1
g  g,
a2

and the third is given by

Derivation of Eq. (11):
Agent i’s expected excess return is given by E(r˜i ) = Xi μ.
We take μ from Eq. (9) and express Xi in terms of wm by
subtracting Eq. (5) from Eq. (4). Recalling the assumption
wm g = 0 from Eq. (8), we obtain agent i’s expected excess
return as

E(r˜ ) = X  μ



δi
−Xi bi = − wm + 2 g  −1 [di g]

=

(A10)

θm
0

0



θg



= −1 +

1

B B
2

−1
,

σζ

(A18)

and

which is Eq. (12). We see that Var(r˜i ) > σm2 as long as δi =

θg =

0.
Derivation of Eq. (13):
The second exponent in agent i’s expected utility in Eq. (A1) contains the terms −aXi μ, −Xi bi , and
(a2 /2 )Xi  Xi . The ﬁrst of these is simply minus a times the
expression in Eq. (A8). The second is given by

σ σ

2 2
2 ζ
2 + g g

σζ

σ22

.

(A19)

Post-multiplying the right-hand side of Eq. (A17) by g and
recognizing that g βm = 0 gives



 −1 g =
567

1

−
2

σζ

θg g g
g=
σζ4



1

σζ2 + g gσ22

g.

(A20)

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 142 (2021) 550–571


a 
d
∗

resg = Xesg μ + g − Xesg
 Xesg
a
2

a 
1
λd
d
= (ι + hg) μm βm −
g + g − Xesg
 Xesg

If ι g = 0, then from Eqs. (17) through (21) and the surrounding discussion, wg = g/(ι g), and gg = (g g)/(ι g). If
ι g = 0, then wg equals the right-hand side of Eq. (A20),
and gg = (g g)/(σζ2 + g gσ22 ). In either case, (1/gg )wg =
g/(g g). The deﬁnition of f˜g in Eq. (31) implies that pre-

N

multiplying the right-hand side of Eq. (40) by (1/gg )wg ,
recalling that w β = 0, gives

goes to zero as N → ∞ if the cross-sectional second moment of the elements of g, (g g)/N, is bounded below by a
positive value for all N.

 X
2
Xesg
esg = σm +

∗
resg
= μm −

 g = 0. Therefore, using Eq. (A20),
as there, βm

 −1 g =



g=

1
η2 + Nσ f2

g.



1
η2 + Nσ f2

1
g g =
.

σ f2

(A22)

(A23)

∗
∗
resg
− rm
=

=

(A24)

1
d
1
ι + (1 − λ ) 2  −1 g = (ι + hg),
N
N
a

d=

( 1 − λ )d
,
a2 (η2 /N + σ f2 )

(A26)

( 1 − λ )d
.
a2 σ f2

( 1 − λ )2 d 2
.
2a3 σ f2

d2
,
2a3 σ f2



Xnon =

(A34)

(A35)

2a3 σ f2 .

(A36)

1
d
1
ι − λ 2  −1 g = (ι + kg),
N
N
a

(A37)

with

(A27)

λd
k=− 2 2
.
a (η /N + σ f2 )

(A38)

Similarly, the variance of the non-ESG investor’s portfolio
return for large N is

(A28)

 X
2
2 2
Xnon
non = σm + k σ f ,

which, as N grows large, converges to

h=

(A33)

Derivation of the certainty equivalent excess return of a nonESG investor (Section 4.2):
Proceeding as above, the non-ESG investor’s portfolio
weights in Eq. (A26) become

(A25)

with

h=

a 
a
w  wm = μm − σm2 .
2 m
2

and substituting for σ f2 using Eq. (A24) gives Eq. (45). The
corresponding value of d is

Therefore, using Eq. (A22), the ESG investor’s portfolio
weights in Eq. (A25) become

Xesg =

(A32)

This difference in certainty equivalents is largest when λ =
0. That largest difference, , is therefore

The portfolio weights for each type of investor follow directly from Eq. (14), with δi = (1 − λ )d for an ESG investor
and δi = −λd for a non-ESG investor:

d
Xesg = wm + (1 − λ ) 2  −1 g
a
d
Xnon = wm − λ 2  −1 g.
a

(A31)

The ESG investor’s certainty-equivalent gain from investing
as desired, versus investing in the market, is therefore

ESG portfolio has zero cost and weights wg =  −1 g as in
Eq. (18). By Eq. (A22), the ESG portfolio goes long green
stocks and short brown stocks. The greenness of the ESG
portfolio is given by

σ f2

a 2 ( 1 − λ )2 d 2
σ +
.
2 m
2a3 σ f2

∗
rm
= wm μ −

Also observe that, because ι  −1 g = 0 (recall ι g = 0), the

1
gg = wg g = g  −1 g =
.

( 1 − λ )2 d 2
.
a4 σ f2

If the ESG investor is instead constrained to hold the market portfolio, the resulting certainty equivalent excess return is given by

Using Eq. (A22) and noting g g = N, observe that for large
N,

g  −1 g =

(A30)

Combining Eqs. (A29), (A30), and (A31), we then see

Derivation of Eq. (45):
First note that  is of the same form as in Eq. (A15),
with the relabelings η2 = σζ2 , σm = σ1 , and σ f = σ2 . Also,

1
η2 + g gσ f2

2

Recall that δi for the ESG investor is (1 − λ )d, and thus
the variance of the ESG investor’s portfolio return, using
Eq. (12), is

(A21)

with ξ˜ = (g ζ˜ )/(g g). The variance of ξ˜ is σζ2 /(g g), which



a

a 
h ( 1 − λ )d
− Xesg
 Xesg .
a
2

= μm +

g m

f˜g − E0 { fg } = f˜ge + ξ˜,

a

(A39)

and a non-ESG investor’s certainty equivalent excess return
from holding her optimal portfolio is

(A29)

∗
 μ−
rnon
= Xnon

With expected utility as given by Eq. (A1), an ESG investor’s certainty equivalent excess return from holding
her optimal portfolio is

=
568

a 
X  Xnon
2 non

a 
1
λd
(ι + kg) (μm βm −
g) − Xnon
 Xnon
N
a
2

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

a 2
λ2 d2
σm + 3 2
2
2a σ f

Derivation of Eq. (56):
Modifying the earlier derivation of Eq. (4), we obtain

λ2 d2
.
2a3 σ f2

˜ 1i , Xi , C˜ ) = −e−ai (1+r f ) E e−ai Xi [r˜+ ai bi ]−ciC
E V (W

= μm −
∗
= rm
+

Journal of Financial Economics 142 (2021) 550–571



(A40)

= −e−ai (1+r f ) e

Derivation of Eq. (46):
From Eqs. (11) and (A23), the difference in expected excess returns earned by the two types of investors is

E(r˜esg ) − E(r˜non ) = −

λd2 

λd2
g  −1 g = − 3 2 .
a σf

a3

= −e

(A41)

Xi =



1
(ι + hg) σm2 βm βm + σ f2 gg + η2 IN ι
N2
1
= σm2 + η2 ,
(A42)
N

i

e

1
bi ] + a2i  Xi + ai ci σC = 0
ai

1 −1

ai



wm =
=

 w
Xesg
m

(A47)

(A48)



μ+



1
b i − c i σ C .
ai

(A49)

i

ωi Xi di

d¯
1 −1
c̄
 μ + 2  −1 g −  −1 σC
a
a
a

(A50)

which implies

 

σm Xesg  Xesg
σm
= 
.
2 2
σm2 + (1−a4λσ)2 d

d¯
a

μ = a wm − g + c̄σC .
(A43)

Substituting for d2 from Eq. (A36) gives Eq. (47).

μm = aσm2 + c̄σmC

Derivations of Eqs. (48) and (49):
Let α denote the N × 1 vector of alphas given by Eq.
(10). The alpha of the ESG investor is given by



= −λ(1 − λ ) 3 2 ,
a σf

μ=

d¯
μm − c̄σmC
 wm − g + c̄σC
a
σm2

= (μm − c̄σmC )βm −

(A44)

d¯
= μm βm − g + c̄
a

using Eqs. (A27) and (A29). Substituting for d2 from Eq.
(A36) gives Eq. (48). The wealth-weighted average alpha
must equal zero,

λαesg + (1 − λ )αnon = 0,

(A52)

where σmC ≡ Cov(˜m , C˜ ) = wm σ C . Solving Eq. (A52) for a
and substituting into the ﬁrst term on the right-hand side
of Eq. (A51) gives

1
λd
(ι + hg) − g
N
a
d2

(A51)

Premultiplying by wm , again imposing the assumption
wm g = 0, gives

f



d¯
g + c̄σC
a

σ C −

σmC
σ m ,
σm2

(A53)

noting βm = (1/σm2 )σ m = (1/σm2 ) wm . To see that the
third term on the right-hand side of Eq. (A53) is the same
as that in Eq. (56), ﬁrst observe that in the multivariate
regression of ˜ on ˜m and C˜, the N × 2 matrix of slope coeﬃcients is given by

(A45)

and applying that identity gives Eq. (49).
Derivation of Eq. (53):
Because ι Xesg = 1, ESG investors’ stock portfolio
weights, wi , are simply Xesg from Eq. (A27). Using Eqs.
(A27) and (A29), along with wm = (1/N )ι, gives



[ σ m σ C ]
=

1 
λι |Xesg − wm |
2


1 
1 1
= λι  (ι + hg) − ι
2
N
N

T =



−ai Xi [E(r˜)+ a1 bi ]+ 12 a2i Xi Var(˜ )Xi +ai ci Xi Cov(˜ ,C˜ )+ 12 ci2 Var(C˜ )

Again imposing the market-clearing condition and ai = a
gives

which equals σm2 for large N. Combining this result with
Eq. (A31) gives the correlation between the ESG investor’s
return and the market return as

σm2
σmC

σmC
σC2

1
2
σm2 σC2 − σmC

−1

σC2 σ m − σmC σC σm2 σC − σmC σ m ,

so the second column is given by



1  (1 − λ )d 
= λι 
g.
2
Na2 σ f2 



from which we obtain agent i’s portfolio weights

 w =
Xesg
m

=

˜

1
1 2 
1 2 2


−ai (1+r f ) −ai Xi [μ+ ai bi ]+ 2 ai Xi  Xi +ai ci Xi σC + 2 ci σC

−ai [μ +

Derivation of Eq. (47):
The covariance between the ESG investor’s return and
the market return, using Eq. (A27) is

 α
αesg = Xesg

1

where σC ≡ Cov(˜ , C˜ ). Differentiating with respect to Xi
gives the ﬁrst-order condition

Substituting for d2 from Eq. (A36) gives Eq. (46).

ρ (r˜esg , r˜m ) =



ψ=
(A46)

1
2
σm2 σC2 − σmC

(σm2 σC − σmC σ m ).

(A54)

Using Eq. (A54), we can rewrite the third term on the
right-hand side of Eq. (A53) as

Substituting for d from Eq. (A36), we obtain Eq. (53).
569

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor


c̄

σ C −

Journal of Financial Economics 142 (2021) 550–571

2
σm2 σC2 − σmC
ψ
2
σm


2
= c̄ 1 − ρmC
ψ

σmC
σ m
σm2

which produces Eq. (64). Comparative statics for n , βn ,
and κn follow immediately from Eq. (64). For the comparative statics for d and a, we deﬁne d˜ ≡ d/a and compute

= c̄

(A55)


∂ 
Sn ( d ) − Sn ( 0 )
˜
∂d


(1 + r f + μm βn − d˜gn ) + d˜gn
g2n n
=
κn (1 + r f + μm βn )
(1 + r f + μm βn − d˜gn )2


2
gn n
1
=
(A61)
κn (1 + r f + μm βn − d˜gn )2

recalling that σC = 1.
Derivation of Eq. (57):
Substituting for μ from Eq. (A53) into Eq. (A49) and
setting ai = a, we obtain

Xi =

1 −1

a

=

1 −1

a

=




1
a

μ + b i − c i σ C




d¯
σ
σ m
μm βm − g + c̄ σC − mC
a
σm2

1
+ b i − c i σ C

which is positive if gn = 0. Since Sn (d ) − Sn (0 ) increases in
d˜, it increases in d and decreases in a.

a

Derivation of Eqs. (65) and (66):
The ﬁrm’s value at time 0 is now

a

υn = −Kn −

μm

1
σ
 −1 βm −  −1 c̄ mC
σ m
a
σm2

d¯
1
1
di
+  −1
g − g −  −1 (ci − c̄ )σC
a

a

a

+

a

μm

1
σ
=
 −1 βm −  −1 (c̄σmC ) 2m
a
a
σm
ci − c̄ −1
1
δi
+  −1 g −
 σ C .
a
a
a
σm

Xi =

a

(A56)

σm



1
 −1 βm −  −1 μm − aσm2 βm

max −
g n

a
ci − c̄ −1
δi −1
+ 2 g−
 σ C
a
a
ci − c̄ −1
δi
= σm2  −1 βm + 2  −1 g −
 σ C
a
a
ci − c̄ −1
δi
= wm + 2  −1 g −
 σ C
a
a

(Kn )2
2


n (K0,n + Kn ) 1 − χ2n (gn )2
1 + r f + μm βn − da (g0,n + gn )

.

(A62)

The manager maximizes υn by choosing gn and Kn . The
choice of gn depends only on the third term of Eq. (A62),
and we can maximize its log. Using the approximation that
log(1 + x ) ≈ x and ignoring terms without gn , the choice
of gn simpliﬁes to

Noting from Eq. (A52) that c̄σmC = μm − aσm2 , and that
βm = 12 σ m = 12  wm , we have

μm

κn

χn
2

d
a

(gn )2 + gn .

(A63)

The ﬁrst-order condition delivers Eq. (65). Without taking
logs, the ﬁrst-order condition for Kn is

−1 − κn Kn +
(A57)



n 1 − χ2n (gn )2

1 + r f + μm βn − da gn

=0

(A64)

which delivers Eq. (66).

which is Eq. (57).
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υn = −Kn −

κn
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(Kn )2 +

n (K0,n + Kn )
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571


==> JFE09 - What do you think about climate finance.txt <==
Journal of Financial Economics 142 (2021) 487–498

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

What do you think about climate ﬁnance? ✩
Johannes Stroebel, Jeffrey Wurgler∗
Stern School of Business, New York University, New York, NY 10012, USA

a r t i c l e

i n f o

Article history:
Available online 8 August 2021
JEL classiﬁcations:
G12
G14
H43
Q54
Keywords:
Climate ﬁnance
Environment
ESG
SRI
Social discounting

a b s t r a c t
We survey 861 ﬁnance academics, professionals, and public sector regulators and policy
economists about climate ﬁnance topics. They identify regulatory risk as the top climate
risk to businesses and investors over the next ﬁve years, but they view physical risk as the
top risk over the next 30 years. By an overwhelming margin, respondents believe that asset
prices underestimate climate risks rather than overestimate them. We also tabulate opinions about the expected correlation between growth and climate change, social discount
rates appropriate for projects that mitigate the effects of climate change, most inﬂuential
forces for reducing climate risks, and most important research topics.
© 2021 Elsevier B.V. All rights reserved.

1. Introduction
The rising appreciation of the risks due to climate
change has led to a burst of research in ﬁnance. In addition to this volume, special issues on “climate ﬁnance”
have appeared, or are in progress, in at least ﬁve other
journals.1 Giglio et al. (2020) and Hong et al. (2020) survey this emerging literature. In this paper, we report the
results of a different type of survey—an anonymous, global
survey of select ﬁnancial economists, ﬁnance professionals,

✩
We thank Viral Acharya, Yakov Amihud, Stephen Brown, Shan Ge, Sabrina Howell, Anthony Lynch, and Jonathan Parker for helpful comments.
We also thank Laura Hess and Amanda Parker of the NYU Stern Development and Alumni Relations oﬃce for providing Stern graduates’ contact
information. Georgij Alekseev provided outstanding research assistance.
Finally, we are most grateful to 861 anonymous survey respondents. The
survey was deemed exempt by NYU IRB-FY2021-5655.
∗
Corresponding author.
E-mail address: jwurgler@stern.nyu.edu (J. Wurgler).
1
These include Finance Research Letters, International Review of Financial Analysis, Management Science, Review of Financial Studies, and Sustainability.

https://doi.org/10.1016/j.jﬁneco.2021.08.004
0304-405X/© 2021 Elsevier B.V. All rights reserved.

and regulators and economists in public institutions such
as central banks.
What is the value of such a survey? According to climate scientists, time is short to deﬁne research agendas
that help us manage the emerging ﬁnancial and economic
risks from climate change.2 A survey of current beliefs allows researchers to identify areas of agreement and coordinate on promising directions.
To that end, the ﬁrst notable feature of the 861 survey
responses we received was the relative uniformity of opinion on a range of important topics. This general commonality in responses extended across professional roles, geographic regions, degrees of concern about climate change,
extent of professional interest in climate ﬁnance, and year
of graduation.
Given the large sample size and consistency of responses across subgroups, the survey results offer robust

2

IPCC Special Report: “Global Warming of 1.5°C,” October 2018.

J. Stroebel and J. Wurgler

Journal of Financial Economics 142 (2021) 487–498

conclusions about respondents’ beliefs. We highlight four
of them here:

955 emails of researchers or policymakers working in their
ﬁnance-related groups.5 In total, we collected and used
11446 email addresses.
We do not imply that the relative number of email addresses gathered across these groups reﬂects the relative
importance of their views. One might be concerned that
conclusions from the pooled sample may be tilted toward
one or the other group in ways that do not reﬂect that
group’s relative knowledge or inﬂuence. For example, it is
likely that the collective pressure of ﬁnancial professionals
is more important in addressing climate change than the
role of ﬁnance academics. At a high level, however, our
analysis shows that the responses turn out to be rather
similar across most subgroups. The reader may easily compute an equally-weighted average across subgroups of interest. We present additional breakdowns in an Internet
Appendix.6
We sent a single recruitment email to each potential
survey participant, which provided the link to the Qualtrics
online survey. The survey informed respondents that we
would collect no personally identiﬁable information and
that it would take ﬁve to seven minutes to complete. We
sent the recruitment emails and collected responses in July
2021.
In total, we received 861 complete responses for an
overall response rate of 7.5%. Some 42 respondents, or
4.9% of the pooled sample, did not self-identify their occupation. There were 453 responses from faculty (response
rate = 12.7% and share of the pooled sample that selfidentiﬁed = 55%). There were 294 responses from practitioners (response rate = 4.2% and share of the pooled sample that self-identiﬁed = 36%); this segment of the sample suffered from a lack of updated email addresses, but
we are not aware of any biases introduced as a result. Finally, there were 72 responses from ﬁnancial regulators or
public-sector employees (response rate = 7.5% and share of
the pooled sample that self-identiﬁed = 9%).
Overall, and for each of these groups, the response
rates compare favorably to those of other unsolicited surveys, e.g., 9% in the CFO survey of Graham and Harvey (2001), 4.3% in the institutional investor survey of
McCahery et al. (2016), and less than 5% in the retail investor survey by Giglio et al. (2021). But any response
rate less than 100% leaves the door open to sample selection bias. In our survey, a bias is obvious: Respondents are probably more interested in climate ﬁnance than
nonrespondents. Depending on the question, this selection
bias is not entirely unhelpful, and for most questions, one

(i) Respondents are at least 20 times more likely to
believe that climate risk is currently being underestimated by asset markets as opposed to overestimated.
(ii) Respondents view regulatory risk as the top climaterelated risk for investors and ﬁrms over the next ﬁve
years, but consider physical risk the top risk over the
next 30 years.
(iii) Pressure from institutional investors is viewed as
the most powerful force for change among ﬁnancial
mechanisms. Among non-ﬁnancial mechanisms, carbon taxes and government subsidies are considered
the most potent.
(iv) Most respondents believe that realizations of climate
risk are not correlated with economic conditions.
Those who believe in a correlation were more likely
to see climate change as associated with good rather
than bad economic conditions.
We also gathered views on other subjects, such as the
social discount rate for climate change mitigation projects
and the most important research topics in climate ﬁnance going forward. We contrast the latter with actual
research trends. Finally, we note the disagreements across
subgroups on some questions, which are typically secondorder and intuitive.
We hope this survey sheds light on where climate ﬁnance is and where respondents believe it should go in
the future. We start by reviewing the survey method and
characteristics of the respondents, proceed to analyze the
responses, and then conclude. Please refer to the Internet
Appendix for additional tabulations.
2. Survey method and respondents
Our goal was to collect views about climate ﬁnance
from sophisticated researchers and practitioners around
the world. We targeted a reasonably select group of ﬁnance
academics, ﬁnance industry practitioners, and ﬁnanceoriented economists within inﬂuential regulatory or supranational institutions. These groups may consider the same
issues from different perspectives, so both the similarities
and differences in their views are interesting.
Speciﬁcally, to reach academics, we collected all available email addresses of professors of the top 100 ﬁnance departments based on research output.3 We included tenure track, adjunct, and clinical professors, for a
total of 3570 faculty email addresses. To reach practitioners, we used a sample of 6921 NYU Stern graduates working in ﬁnance.4 To reach those involved in policy, we identiﬁed 17 relevant public-sector institutions and collected

that were working in ﬁnance and received their degree between 10 and
30 years ago (the undergraduates were granted ten years to achieve a
practical familiarity with the issues involved).
5
We gathered email addresses from a range of institutions that made
researcher emails accessible on their institutional websites. The institutions are Bank of Canada, Bank of England, Bank of Korea, Deutsche Bundesbank, ECB, the Federal Reserve Banks of Boston, Chicago, Dallas, Minneapolis, New York, Philadelphia, Richmond and San Francisco, IFC, IMF,
Reserve Bank of New Zealand, and World Bank.
6
The Internet Appendix also includes results for an additional 158 respondents who were not contacted directly but instead found the survey
via Twitter and LinkedIn postings. This subsample again delivered broadly
similar responses.

3
We used the list maintained at ASU: https://apps.wpcarey.asu.edu/
ﬁn-rankings/rankings/results.cfm. The ranking was based on the total
number of articles published from 2010 through 2020 in the Journal of
Finance, Journal of Financial Economics, and Review of Financial Studies.
4
These emails were kindly provided by the NYU Stern Alumni Relations oﬃce. We requested emails of Stern MBA graduates that were working in ﬁnance and received their degree no more than 30 years ago as
well as a sample of emails of graduates of Stern’s undergraduate program

488

J. Stroebel and J. Wurgler

Journal of Financial Economics 142 (2021) 487–498

might prefer the views of those most informed over those
of an overall population. At any rate, to explore whether
such a selection might bias our results, we collect respondents’ concerns about climate change and professional interest in climate ﬁnance and examine whether responses
differ on these dimensions.
Table 1 contains summary statistics and crosstabulations of the demographic information reported
by respondents. As noted above, over half of the sample
are faculty, followed by private-sector professionals. Our
respondents’ locations tilt toward North America and
Europe. The level of climate concern across roles is similar,
with around 69% in each group expressing personal concern. The rate of concern is highest among those located
in Europe. Our survey respondents align with the general
population in this respect.7 Across roles, a majority of
participants claim some professional interest in or connection to “climate ﬁnance” (as deﬁned by the respondent),
and this rate is somewhat higher among those located in
Europe and Asia. Perhaps unsurprisingly, those individuals
who work on climate ﬁnance topics are generally more
concerned about climate change, though causality may go
both ways.
Lastly, our participants appear to skew a bit younger,
with many receiving their highest degree between 2010
and 2021. Respondents of various age ranges expressed
about the same splits in terms of concern about the climate and professional interest in climate ﬁnance.

Such transition risks can include, for example, the risk to
various businesses models in the energy and transportation sectors from increased regulation of carbon emissions.
In the pooled sample, regulatory risk was ranked a full
position higher, on average, than the second-most-cited
risk. Its perceived importance as the ﬁrst-order risk over
the coming ﬁve years is consistent across all subgroups.
The second most highly ranked short-run risk from climate change, in particular among private-sector respondents, was identiﬁed as stakeholder risk—a risk that includes changing preferences of employees and customers.
As a notable exception, public-sector professionals already
viewed physical risk as the second most important risk in
the next ﬁve years.
Over the next 30 years, however, almost all respondents judged physical risks as the most important—this
risk captures the direct risks from rising sea levels, wildﬁres, and other physical changes to the planet as a result
of climate change. One hopes the prediction is incorrect,
but physical risk was the most-cited long-term climate risk
among all subgroups except (predictably) among those relatively unconcerned about climate change. They continued
to view regulatory interventions to combat climate change
as the most important risk to businesses over the thirtyyear horizon.
3.2. Are asset markets pricing climate risks correctly?
With some understanding of the nature of climate risks
in hand, we turned to the extent to which they are currently being incorporated into asset prices. Asset markets where climate risks are often salient include the equities, real estate, and insurance markets. Indeed, a sizable literature has documented that equity markets, bond
markets, real estate markets, and derivatives markets appear to incorporate climate risk in asset prices.8 However,
little research has been done to explore whether asset
prices reﬂect climate risk to the correct degree—a question that is substantially more diﬃcult than rejecting the
null hypothesis that climate risk is not priced at all. Notable exceptions include Hong et al. (2019), who argue that
food stock prices may have underreacted to droughts, and
Shlenker and Taylor (2021), who ﬁnd that weather derivatives have marched roughly in alignment with temperature
trends over the past two decades.
Our survey reveals a substantial consensus on this
question. According to Table 3, respondents overwhelmingly believed that asset prices do not, at present, suﬃciently reﬂect climate risks. For example, those who think
that stock prices reﬂect climate risks “not enough” outnumber those who believe that stock prices reﬂect climate
risks “too much” by a factor of twenty to one (60:3 in
the pooled sample in Table 3)! With respect to real estate, the outnumbering is sixty-seven to one (67:1), and for
insurance, the outnumbering is twenty-one to one (42:2).
Respondents have highly correlated beliefs across settings:

3. Survey results
The survey consisted of ﬁve types of questions. We review them in this section.
3.1. Which climate risks are most important?
Many commentators and policymakers have made predictions about how climate change will affect businesses
and investors. But climate change involves a set of emerging risks, whereas empirical academic research usually involves historical data. Therefore, it was natural to begin the
survey with an understanding of what “climate risks” our
ﬁnance-oriented respondents are most concerned about.
Speciﬁcally, we asked respondents to rank the relative
importance of ﬁve types of risks often expressed in general discussions of climate ﬁnance (e.g., Krueger et al.,
2020; Climate-Related Market Risk Subcommittee, 2020;
Rudebusch, 2021). In addition, given that climate changes
and business responses will evolve over time, we asked
respondents to judge the importance of the various climate risks over both the next ﬁve years and the next thirty
years.
The results show a widely-held belief that the primary
climate risk over the next ﬁve years involves regulatory activity along the transition path to a low-carbon economy.
7
According to the United Nations Development Programme (UNDP)
(2021), 65% of U.S. residents believe in climate change as a global emergency. For Western Europe and North America, the number is 72%,
whereas 63% of Asia-Paciﬁc residents share this belief. The global average is 64%.

8
See, for example, Baldauf et al. (2020), Bernstein et al. (2019),
Bolton and Kacperczyk (2021), Choi et al. (2020), Engle et al. (2020),
Giglio et al. (2021), Goldsmith-Pinkham et al. (2021), Eichholtz et al.
(2019), Ilhan et al. (2021) and Painter (2020).

489

J. Stroebel and J. Wurgler
Table 1
Composition of survey respondents
The percentage breakdowns in the table are to be read in columns within blocks. For example, the share of faculty among respondents in North America is 51%, while the share of North American respondents
among faculty is 70%. The total number of respondents is 861. Not every respondent answered every question, but all questions achieved a response rate of at least 95% among respondents who ﬁnished the
survey. The table shows the distribution among respondents who answered the question of interest.
Role

Location

Climate Concern

Works in Climate
Finance

490

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

Role (%)
Faculty
Public Sector
Private Sector

55
9
36

100
0
0

0
100
0

0
0
100

51
8
40

76
12
12

60
6
34

41
9
45

55
9
35

54
7
37

57
9
34

53
8
39

Location (%)
North America
Europe
Asia
ROW

72
14
7
7

70
20
8
2

72
19
6
3

85
5
7
3

100
0
0
0

0
100
0
0

0
0
100
0

0
0
0
100

73
16
8
3

80
11
7
2

71
17
9
3

82
10
5
2

Climate Concern (%)
High
Low

69
31

70
30

73
27

68
32

67
33

77
23

69
31

76
24

100
0

0
100

78
22

56
44

Works Climate Finance (%)
Yes
No

59
41

61
39

62
38

56
44

55
45

71
29

73
27

67
33

67
33

42
58

100
0

0
100

Graduation Year (%)
< 2000
2000–2009
2010+

26
29
45

33
24
43

13
19
68

17
41
42

28
29
43

24
28
48

14
31
56

10
45
45

26
30
44

25
27
48

26
28
46

25
31
44

Journal of Financial Economics 142 (2021) 487–498

Share
Sample

J. Stroebel and J. Wurgler

Journal of Financial Economics 142 (2021) 487–498

Weitzman, 2012, 2014).9 Giglio et al. (2021) construct a
model that nests both approaches and highlights the implications for discount rates: If climate change is more costly
in good economic times, then investments to mitigate climate change pay off disproportionately in those times and
deserve a positive risk premium. On the other hand, if investments to mitigate climate change pay of largely in bad
economic times, they should be considered hedges that
command a negative risk premium.
As documented in Table 4, respondents were most
likely to state that the payoffs for projects to mitigate
climate risks would be independent of economic times.
This may reﬂect beliefs about the global nature of climate
change versus the comparatively local nature of economic
ﬂuctuations or the different horizons at which climate
and economic shocks operate. Still, respondents were three
times as likely to believe that mitigation payoffs occur
primarily in good economic times than in bad economic
times, more consistent with the Nordhous view. Asian respondents have a particularly strong belief in this covariance; this may reﬂect the salient coincidence of worsening climate and rapid growth in developing Asia in recent
decades, and the substantial contributions of coal-based
energy production in Asia to global carbon emissions.
Interestingly, we ﬁnd that respondents who are less
concerned about climate change per se (and those that
worry more about regulatory than physical climate risks)
are more likely to respond that mitigating climate change
will largely pay off in good economic times. This belief
is consistent with those respondents perceiving climate
change itself is not problematic enough to be an independent driver of economic downturns.
Many governments are now making immediate practical decisions that involve calculating the present discounted values of investments to mitigate climate risks.
We asked our survey participants to put themselves in policymaking shoes and suggest a single, suitable discount
rate for a hypothetical investment in climate-change mitigation whose beneﬁts would materialize 50 years from
now, a horizon for which private market returns are hard
to come by.10 “Beneﬁts” was phrased broadly so as to include all economic and social beneﬁts, including externalities.11 The median respondent suggested discounting an
investment with certain (risk-free) beneﬁts at 4% per year,
and suggested discounting an investment with uncertain

Those who believe climate risks are not suﬃciently reﬂected in equity markets also generally believe they are
not suﬃciently reﬂected in real estate and insurance markets.
Is this really a consensus or merely an artifact of a
sample biased toward those more concerned about climate
change? Pointing toward consensus, this belief is apparent
in every subgroup. Even respondents who have low concern about climate change themselves are far more likely
to believe that asset markets are underpricing the risks of
climate change rather than that they are overpricing them,
perhaps consistent with those respondents worrying about
potentially underpriced transition risks due to regulatory
interventions. Either the widespread belief that asset prices
and insurance markets insuﬃciently price climate risk is
way off, or these markets have a lot catching up to do.
Nevertheless, we observe a number of important differences across groups. Those individuals with a professional interest in climate ﬁnance—in other words, those
individuals with perhaps the most informed views—are
even more convinced that asset markets do not yet reﬂect climate risks accurately. When comparing across professional roles, private market participants were 22 percentage points more likely to believe that climate risks
were underpriced than academics (73% of private-sector
respondents vs. 51% of academics). In contrast, academic
researchers were more likely to believe these risks to be
accurately priced, perhaps a result of a stronger belief
among ﬁnance academics in the eﬃciency of markets.
What types of risks do individuals believe to be underpriced? Comparing answers of the same individuals across
questions, we ﬁnd that respondents who think climate
risks are not priced suﬃciently in asset markets rank the
importance of physical risk substantially higher over both
the ﬁve and thirty-year horizons.

3.3. How should investors and governments discount climate
risks?
We then turn to the normative issue of how current costs of mitigating climate risks should be traded off
against their potentially uncertain future beneﬁts. The degree to which realizations of climate risks (and, in particular, the physical realizations of climate risk) correlate with
economic conditions is an important input to this calculation for both investors and social planners since this correlation determines whether such investments should command a positive or a negative risk premium.
We ﬁrst asked respondents whether a hypothetical
climate-change mitigation project would tend to “pay off”
in good economic times, bad economic times, or independent of economic times. This was an effort to get at the covariance between realizations of climate risk and economic
activity and address a fundamental debate in the literature
on how to model climate change: As a tax on consumption which increases with economic growth and the associated carbon emissions (e.g., as in Nordhaus, 2008); or,
as a potentially disastrous event that, once realized, creates a deep economic downturn (e.g., as in Barro, 2013 and

9
Other important questions relating to how to incorporate climate
change into general equilibrium models that allow for the pricing of ﬁnancial assets is which preferences to use and how to incorporate model
uncertainty about the transmission mechanism of economic activity to
climate change (see Bansal et al., 2017; Barnett et al., 2020; Daniel et al.,
2019). Giglio et al. (2021) summarize these issues.
10
A recent exception is Giglio et al. (2015), who calculate discount
rates in the housing market over hundreds of years. See Gollier (2002),
Gollier and Weitzman (2010), Dietz et al. (2018), Giglio et al. (2021) and
Lemoine (2020) for additional discussions on discount rates in the context
of climate change mitigation.
11
In light of the various respondent types, the reader can see that our
questions had to balance simplicity with sophistication. For example, our
request for a static rate prohibited the ability to suggest a stochastic rate
or one that falls as the horizon lengthens. On the latter points, our request boils down to asking for a point estimate of a discount rate for a
“lump sum” net beneﬁt realized 50 years from now.

491

J. Stroebel and J. Wurgler

Journal of Financial Economics 142 (2021) 487–498

(i.e., expected) beneﬁts at 7% per year. The gap reﬂects a
median risk premium for investments in climate change
abatement of 3%, directionally consistent with the view
that economic conditions and climate change are positively
correlated. Implied risk premia for investments in climate
mitigation were the largest, at a median of 4%, for privatesector respondents, and the smallest, at 1%, for publicsector respondents. Directionally, risk premia were lowest
among respondents who believe that investments in climate mitigation paid off largely in bad times, though even
in this group, respondents assigned a positive risk premium on average.

reduce the implications of climate risk for the ﬁnancial
sector; see Rudebusch (2021) for a summary of some of
these efforts.
The forces for change identiﬁed by individuals correlate
in reasonable ways with their responses to other questions.
For example, respondents who believe that carbon taxes
are a particularly important force for change ranked regulatory risks as more relevant in Table 2, while respondents
who viewed customers and employees as the biggest inﬂuence also ranked stakeholder risk more strongly.
3.5. What are the most important research topics? Are
researchers working on them?

3.4. What are the biggest forces for change?

The last question asked respondents to identify the
most important research topics in climate ﬁnance. We proposed thirteen topic areas motivated by the literature and
report results in Table 6.
The topic area garnering most enthusiasm in the pooled
sample was the effects of government incentives to mitigate or adapt to climate change; such a research priority
is consistent with the previous question’s result that carbon taxes and government subsidies are among the most
important perceived forces for change. The other topic at
the top of the list was to understand the pricing of climate
risk in ﬁnancial assets. This research priority is consistent
with the earlier ﬁnding that many respondents think that
markets are currently underpricing climate risks—and indeed, we found that this research priority was particularly
strong among respondents who perceived climate risk to
be underpriced in asset markets. Public-sector policymakers and economists, many from central banks, felt that understanding the possible systemic risks generated by climate change was a critical topic for further research. Reassuringly, those with a professional interest in climate ﬁnance have the same ranking of the top four research priorities as those without such an interest.
Perhaps surprisingly, respondents did not believe that
a better understanding of climate risks in insurance markets should be a research priority, even though 30% of respondents had suggested that they had “no opinion” on
whether insurance markets accurately priced climate risks
at the moment.
How does this line up with the research actually done
at the moment? To answer this question, we analyzed all
uploaded ﬁnance publications on SSRN (that is, to the FEN
journal) within the last three years that contain “climate”
in their title or abstract in a relevant respect. We manually
classiﬁed each of these works as relating to up to three
of the topic areas. Then, we determined the relative frequency of each topic among the publications that spoke to
at least one of the research areas.
The Spearman rank correlation between topics that the
pooled set of respondents ﬁnd important and the topics
that appear in SSRN-FEN working papers is 0.85. While the
survey respondents viewed the effect of government incentives to mitigate or adapt to climate change as the most
important research topic, it is also the second most popular topic on SSRN-FEN, even though some papers on this
topic may often fall beyond traditional ﬁnance (i.e., FEN)
boundaries.

The next question asked respondents which economic
and ﬁnancial mechanisms are most promising in moving corporations to reduce their climate risk exposures
and carbon footprints. We inquired about pressures from
various ﬁnancial stakeholders, including banks and creditors, individual investors, and institutional investors; nonﬁnancial stakeholders, including customers and employees;
and policy mechanisms, including carbon taxes (and emissions trading systems which tax companies for exceeding
limits), various government subsidies, or ﬁnancial or nonﬁnancial regulation.
Table 5 indicates that the pooled sample viewed carbon taxes and institutional investors as the two most
important forces for change, with government subsidies
and pressures from customers not far behind.12 Europeans,
with the most extensive systems for pricing carbon, had
the strongest belief in carbon taxes; across roles, faculty
and public-sector policymakers and economists are the
strongest supporters. Private-sector respondents are more
skeptical of relatively hypothetical policies or mechanisms.
They viewed institutional investors and customers, whose
pressures they already face, as the two most important
forces for change.13 Despite C-suite rhetoric, not one respondent was optimistic that voluntary behavior by corporations (including, or especially, private sector respondents) would be a signiﬁcant force; at the same time, no
respondent was pessimistic enough to view meaningful
change as impossible.
Among regulatory mechanisms, academics and public
sector respondents viewed non-ﬁnancial regulation as the
more powerful tool, while our ﬁnancial market respondents believed ﬁnancial regulation to be more effective,
perhaps because those respondents are already seeing the
impact of efforts by ﬁnancial regulators to understand and
12
A mechanism here could be institutional investor preferences or
catering to sentiment that reduces the cost of capital for ﬁrms and governments pursuing green projects. See Baker et al. (2022) for evidence
from green bonds, and Pastor et al. (2021) and Pedersen et al. (2021) on
the stock market. See Flammer (2021) for negative evidence from corporate green bonds. Another direct mechanism would be institutional shareholder engagement, as in Azar et al. (2021).
13
Krueger et al. (2020) survey institutional investors about their approaches to managing climate risk, and document that many of these
investors regularly engage with portfolio companies on issues related to
climate risk, providing a second mechanism through which institutional
investors might affect ﬁrm behavior.

492

J. Stroebel and J. Wurgler
Table 2
Identifying short- and long-term climate risks
Participants were asked: “Please rank the general importance of these climate-related risks to typical businesses and investors over the next X years. [1 = Most Important; 5 = Least Important]”, where X is
either 5 or 30. Possible responses were ordered randomly. They are listed below in order of their rank in the pooled sample.
Role

Location

Climate Concern

Works in Climate
Finance

493

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

Top Risks Next 5 Years (Average Rank)
Regulatory
Stakeholder
Physical
Technological
Legal

1.9
2.9
3.1
3.4
3.6

1.7
3.0
3.3
3.4
3.6

2.1
3.2
2.8
3.1
3.8

2.1
2.7
2.9
3.6
3.6

2.0
2.9
3.0
3.5
3.7

1.8
3.0
3.4
3.1
3.6

1.7
2.7
3.6
3.5
3.5

1.8
3.2
3.1
3.3
3.6

2.0
2.9
2.9
3.4
3.8

1.7
2.9
3.7
3.4
3.3

1.9
2.9
3.1
3.4
3.7

1.9
3.0
3.1
3.5
3.5

Top Risks Next 30 Years (Average Rank)
Physical
Regulatory
Technological
Stakeholder
Legal

2.2
2.6
3.0
3.5
3.7

2.3
2.5
2.8
3.7
3.7

1.9
2.6
3.0
3.8
3.7

2.2
2.7
3.3
3.2
3.6

2.2
2.5
3.1
3.5
3.7

2.3
2.8
2.6
3.5
3.8

2.4
2.6
2.8
3.5
3.8

2.3
2.7
3.2
3.3
3.5

1.9
2.7
3.0
3.6
3.8

3.0
2.2
3.0
3.3
3.5

2.1
2.6
3.0
3.6
3.7

2.3
2.5
3.0
3.4
3.7

Journal of Financial Economics 142 (2021) 487–498

Pooled

J. Stroebel and J. Wurgler
Table 3
Current pricing of climate risks in asset markets
Participants were asked: “In the X most familiar to you, how do prices currently reﬂect climate-related risks?”, where X is either “stock markets”, “real estate markets”, or “insurance markets”. Possible responses
were ordered as below.
Role

Location

Climate Concern

Works in Climate
Finance

494

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

Pricing Stock Markets (% picked)
Too Much
Correct
Not enough
No opinion

3
21
60
16

3
26
51
20

0
19
64
17

4
13
73
10

3
22
58
17

1
18
65
16

5
8
75
12

0
19
71
10

1
12
74
13

8
40
29
24

2
16
68
14

3
27
49
20

Pricing Real Estate Markets (%)
Too Much
Correct
Not enough
No opinion

1
17
67
15

0
21
61
18

0
12
78
10

1
13
75
12

1
18
67
14

0
15
64
21

2
12
70
17

0
14
71
14

0
10
76
14

2
33
46
19

0
15
71
14

1
21
61
17

Pricing Insurance Markets (%)
Too Much
Correct
Not enough
No opinion

2
25
42
30

2
25
37
35

0
19
57
25

3
26
47
23

3
25
42
30

2
28
39
31

0
18
55
27

0
43
29
29

2
21
49
28

4
35
27
34

1
26
45
28

4
25
38
34

Journal of Financial Economics 142 (2021) 487–498

Pooled

J. Stroebel and J. Wurgler
Table 4
Covariance of climate risk with economic conditions and social discount rates
Two questions were asked involving the connection between climate risk and economic conditions. In the ﬁrst, participants were asked: “Consider an investment project that mitigates the effects of climate
change. In general, would you expect this project to pay off primarily in good economic times, primarily in bad economic times, or similarly across both good and bad economic times?” Possible responses
were ordered randomly. In the second, participants were asked: “What discount rate (in percent per year) should governments use to evaluate the certain (risk-free) beneﬁts of an investment in climate
change abatement materializing in 50 years?” and “What discount rate (in percent per year) should governments use to evaluate the uncertain expected beneﬁts of an investment in climate change abatement
materializing in 50 years?” The median discount rates and median risk premium are reported here.
Role

Location

Climate Concern

Works in Climate
Finance

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

Payoff of Climate Investment (%)
Good economic times
Bad economic times
Equally in good and bad times

32
13
55

28
16
56

40
19
40

35
8
57

33
12
55

22
19
59

43
16
41

24
10
67

28
14
58

41
12
48

33
14
53

31
12
57

Discount Rates (Median,%)
Risk-Free Investment
Climate Mitigation Investment
Risk Premium

4
7
3

3
6
3

2
4
1

5
9
4

4
7
3

2
5
3

4
5
2

5
10
6

3
6
3

4
8
5

3
6
3

4
8
4

495

Pooled

Journal of Financial Economics 142 (2021) 487–498

J. Stroebel and J. Wurgler
Table 5
Most inﬂuential forces for change
Participants were asked: “Which mechanisms do you think are most important in moving corporations to reduce their climate risk exposures and/or carbon footprints? [Choose at most three].” Possible responses
were ordered randomly, and listed below in order of their rank in the pooled sample.
Role

496

Biggest force for change (% in top-3)
Carbon Taxes
Institutional Investors
Government Subsidies
Customers
Non-ﬁnancial regulation
Financial regulation
Banks/Creditors
Employees
Individual Investors
Voluntary
Nothing will lead to change

Location

Climate Concern

Works in Climate
Finance

Pooled

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

52
48
43
41
27
22
16
6
5
0
0

59
45
44
33
34
20
12
5
5
0
0

65
37
43
35
31
21
21
4
4
0
0

37
56
42
53
15
26
20
8
5
0
0

51
47
45
42
25
22
15
6
6
0
0

59
52
39
39
35
22
15
4
1
0
0

49
53
39
29
27
24
22
10
2
0
0

33
52
29
52
38
29
10
14
14
0
0

56
51
42
40
28
24
17
6
5
0
0

42
42
47
42
24
19
13
6
5
0
0

52
51
43
38
27
26
19
5
5
0
0

50
44
44
43
28
16
10
8
5
0
0
Journal of Financial Economics 142 (2021) 487–498

Role

Location

Climate Concern

Works in Climate
Finance

497

Faculty

Public
Sector

Private
Sector

North
America

Europe

Asia

ROW

High

Low

Yes

No

SSRN Topic
Frequency

Important Research Topics (% in top-3)
Effects of gov incentives to mitigate/adapt
Pricing climate risk in ﬁnancial markets
Climate change effect on systemic risk
Real effects of SRI
New ﬁnancial instruments
GE modeling of climate change & economy
Effects of green ﬁnance on transition
Measuring asset-level climate exposure
Pricing climate risk in real estate markets
Climate risk in the insurance sector
Developing climate stress tests
Reﬁnement of ESG-type ratings
Finance address social disparities from CC

35
34
28
23
21
19
19
15
17
13
13
12
10

36
33
23
22
23
20
17
15
15
14
10
13
10

39
34
47
9
22
22
18
16
29
21
19
3
4

37
36
29
27
19
17
21
16
16
10
17
13
12

38
35
28
21
22
19
16
15
19
15
14
11
10

34
30
27
22
20
25
27
15
10
10
9
11
12

34
31
22
36
17
15
31
17
7
5
14
19
12

8
52
38
29
19
19
29
19
14
14
14
10
0

39
36
30
22
22
18
21
13
17
13
14
12
13

30
30
21
24
21
22
13
21
16
14
10
11
5

38
37
29
23
23
18
22
17
15
10
12
14
10

35
30
26
22
19
21
14
13
20
17
14
9
10

22
36
15
8
7
6
9
11
6
3
4
5
4

Correlation: Survey vs. SSRN Topic Freq.
Pearson
Spearman (rank) correlation
Kendall’s tau

.86
.85
.67

.83
.84
.64

.60
.52
.32

.86
.84
.72

.85
.78
.58

.72
.85
.67

.61
.78
.59

.67
.59
.50

.85
.77
.62

.75
.75
.59

.88
.91
.77

.75
.64
.45

Journal of Financial Economics 142 (2021) 487–498

Pooled

J. Stroebel and J. Wurgler

Table 6
Most important climate ﬁnance research topics vs. SSRN topic frequency
Participants were asked: “Which of the following research areas do you ﬁnd most important? [Choose at most three].” Possible responses were ordered randomly and listed below in order of their rank in the
pooled sample. The phrasing of options shown to respondents were: “Effects of government incentives for innovation in climate change mitigation and adaptation”; “Pricing of climate risk in ﬁnancial markets”;
“Understanding systemic risks to the ﬁnancial system from climate change”; “Real effects of socially responsible investment initiatives”; “Design of new ﬁnancial instruments to manage climate risk”; “General
equilibrium modeling of the interaction of climate risk and economy”; “Effects of green ﬁnance (e.g., green bonds) on the transition toward a sustainable economy”; “Measurement of asset-level climate risk
exposure”; “Pricing of climate risk in housing and mortgage markets”; “Understanding climate risk for the insurance sector”; “Design of climate stress test scenarios”; “Reﬁnement of ESG-type ratings”; and, “Role
of access to ﬁnance in reducing social disparities caused by climate change.” The last column shows the distribution of topic coverage by SSRN papers uploaded within the last three years. We restricted the
sample to ﬁnance papers containing the word “climate” in their abstract or title. Excluding revisions and reuploads, our sample consists of 420 publications. Papers were manually classiﬁed to belong to none,
one, or up to three of the research topics. The distribution is shown for the subset of papers that speak to at least one of the topics. The last three rows show the Pearson, Spearman (rank), and Kendall’s tau
correlation of the distribution over topics for the pooled sample and each subgroup with the SSRN topic frequency.

J. Stroebel and J. Wurgler

Journal of Financial Economics 142 (2021) 487–498

Overall, climate change’s effect on systematic risk, real
effects of socially responsible investment, new climaterelated ﬁnancial instruments such as green bonds or catastrophe bonds (see Baker et al., 2022), and a few other topics were not being pursued in proportion to their perceived
importance. Public sector respondents in particular were
disproportionately concerned about systemic risks, stress
tests, and pricing of climate risk in real estate and insurance, so their own perceptions of research needs correlated
less well with the recent work on SSRN.
Of course, many of those who post papers to SSRN are
in our sample themselves, and presumably, the topics they
ﬁnd important are the topics they write about. As a result,
it is worth reviewing the opinions of those who have no
professional interest in climate ﬁnance. The rank correlation between the SSRN-FEN topic frequency and the topicimportance percentage of the “outsiders” is 0.64, still high
but clearly lower than the 0.91 rank correlation for the “insiders.” The outsiders would like to see additional work on
climate risk pricing in real estate markets and insurance
markets as opposed to research on pricing in ﬁnancial markets or topics in green ﬁnance.

Baker, M., Bergstresser, D., Serafeim, G., Wurgler, J., 2022. The pricing and
ownership of U.S. green bonds. Annu. Rev. Financ. Econ. In press.
Bansal, R., Kiku, D., Ochoa, M., 2017. Price of Long-Run Temperature Shifts
in Capital Markets. Duke University Working Paper.
Barnett, M., Brock, W.A., Hansen, L.P., 2020. Pricing uncertainty induced
by climate change. Rev. Financ. Stud. 33, 1024–1066.
Barro, R.J., 2013. Environmental Protection, Rare Disasters, and Discount
Rates. NBER Working Paper no. 19258.
Bernstein, A., Gustafson, M.T., Lewis, R., 2019. Disaster on the horizon: the
price effect of sea level rise. J. Financ. Econ. 134, 253–272.
Bolton, P., Kacperczyk, M., 2021. Do investors care about carbon risk? J.
Financ. Econ. In press.
Choi, D., Gao, Z., Jiang, W., 2020. Attention to global warming. Rev. Financ.
Stud. 33, 1112–1145.
Climate-Related Market Risk Subcommittee, 2020. Managing Climate risk
in the U.S. Financial System. U.S. Commodity Futures Trading Commission, Washington D.D.
Daniel, K.D., Litterman, R.B., Wagner, G., 2019. Declining CO2 price paths.
Proc. Natl. Acad. Sci. 116, 20886–20891.
Dietz, S., Gollier, C., Kessler, L., 2018. The climate beta. J. Environ. Econ.
Manag. 87, 258–274.
Eichholtz, P., Steiner, E., Yonder, E., 2019. Where, when, and How Do Sophisticated Investors Respond to Flood risk?. Cornell University Working Paper.
Engle, R.F., Giglio, S., Kelly, B., Lee, H., Stroebel, J., 2020. Hedging climate
change news. Rev. Financ. Stud. 33 (3), 1184–1216.
Flammer, C., 2021. Corporate green bonds. J. Financ. Econ. this issue.
Giglio, S., Kelly, B., Stroebel, J., 2020. Climate ﬁnance. Annu. Rev. Financ.
Econ. 13. In press.
Giglio, S., Maggiori, M., Stroebel, J., Utkus, S., 2021. Five facts about beliefs
and portfolios. American Economic Review 111 (5), 1481–1522.
Giglio, S., Maggiori, M., Rao, K., Stroebel, J., Weber, A., 2021. Climate
change and long-run discount rates: evidence from real estate. Rev.
Financ. Stud. 34, 3527–3571.
Giglio, S., Maggiori, M., Stroebel, J., 2015. Very long-run discount rates. Q.
J. Econ. 130, 1–53.
Goldsmith-Pinkham, P.S., Gustafson, M., Lewis, R., Schwert, M., 2021. Sea
Level Rise and Municipal Bond Yields. Yale University Working Paper.
Gollier, C., 2002. Discounting an uncertain future. J. Public. Econ. 85,
149–166.
Gollier, C., Weitzman, M.L, 2010. How should the distant future be discounted when discount rates are uncertain? Econ. Lett. 107, 350–353.
Graham, J.R., Harvey, C.R, 2001. The theory and practice of corporate ﬁnance: evidence from the ﬁeld. J. Financ. Econ. 60, 187–243.
Hong, H., Karolyi, G.A., Sheinkman, J.A, 2020. Climate ﬁnance. Rev. Financ.
Stud. 33, 1011–1023.
Hong, H., Li, F.W., Xu, J, 2019. Climate risks and market eﬃciency. J. Econ.
208, 265–281.
Ilhan, E., Sautner, Z., Vilkov, G., 2021. Carbon tail risk. Rev. Financ. Stud.
34, 1540–1571.
Krueger, P., Sautner, Z., Starks, L.T, 2020. The importance of climate risks
for institutional investors. Rev. Financ. Stud. 33, 1067–1111.
Lemoine, D., 2020. The Climate Risk Premium: How Uncertainty Affects
the Social Cost of Carbon. University of Arizona Department of Economics Working Paper.
McCahery, J.A., Sautner, Z., Starks, L.T, 2016. Behind the scenes: the corporate governance preferences of institutional investors. J. Financ. 71,
2905–2932.
Nordhaus, W.D., 2008. A Question of Balance: Weighing the Options On
Global Warming Policies. Yale University Press.
Painter, M., 2020. An inconvenient cost: the effects of climate change on
municipal bonds. J. Financ. Econ. 135, 468–482.
Pastor, L., Stambaugh, R., Taylor, L.A, 2021. Sustainable investing in equilibrium. J. Financ. Econ. In press.
Pedersen, L.H., Fitzgibbons, S., Pomorski, L., 2021. Responsible investing:
the ESG-eﬃcient frontier. J. Financ. Econ. In press.
Rudebusch, G.D., 2021. Climate change is a source of ﬁnancial risk. FRBSF
Econ. Lett. (03) 1–6 2021.
Shlenker, W., Taylor, C.A, 2021. Market expectations of a warming climate.
J. Financ. Econ. In press.
United Nations Development Programme (UNDP) 2021. The Peoples’ climate vote. https://www.undp.org/publications/peoples- climate- vote.
Weitzman, M.L., 2012. Rare Disasters, Tail-Hedged Investments, and
Risk-Adjusted Discount Rates. NBER, p. 18496 Working Paper.
Weitzman, M.L., 2014. Fat tails and the social cost of carbon. Am. Econ.
Rev. 104, 544–546.

4. Conclusions
Scientists often describe climate change with superlatives. Urgent. Dire. Existential. The superlatives are all bad.
Encouragingly, ﬁnancial economists are devoting more and
more attention to the intersection of climate and ﬁnance.
Our survey aims to further this momentum by identifying
points of agreement, disagreement, and promising research
topics.
Our 861 anonymous respondents are selected from ﬁnance academia, the public sector, and the private sector. They are located around the world and differ in their
concern about the climate and their interest in climate
ﬁnance. Despite these differences, respondent subgroups
agreed on a majority of questions. For example, respondents tend to view regulatory risks as the most important climate risk to businesses and investors over the next
ﬁve years, but physical climate risks as the most important over the next 30 years. In addition, an order of magnitude more respondents believe that asset markets are underestimating climate risks as opposed to overestimating
them. As with other aspects of climate change, time will
tell whether these beliefs are justiﬁed.
Supplementary materials
Supplementary material associated with this article can
be found, in the online version, at doi:10.1016/j.jﬁneco.
2021.08.004.
References
Azar, J., Duro, M., Kadach, I., Ormazabal, G., 2021. The big three and corporate carbon emissions around the world. J. Financ. Econ. In press.
Baldauf, M., Garlappi, L., Yannelis, C., 2020. Does climate change affect
real estate prices? Only if you believe in it. Rev. Financ. Stud. 33,
1256–1295.

498


==> JFE10 - greenwashing justify a taxonomy for sustainable investments.txt <==
Journal of Financial Economics 163 (2025) 103954

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/finec

Sustainable finance versus environmental policy: Does greenwashing justify
a taxonomy for sustainable investments?✩
Roman Inderst a,c , Marcus M. Opp b,c,d,e ,∗
a Goethe Universität Frankfurt, Germany
b

Stockholm School of Economics, Sweden
CEPR, UK
d
ECGI, Belgium
e
FTG, USA
c

ARTICLE

INFO

Keywords:
Greenwashing
Sustainability
EU taxonomy
Sustainable Finance Disclosures Regulation
ESG funds
European Green Deal

ABSTRACT
Our paper analyzes whether a planner should design a taxonomy for sustainable investment products when
conventional tools for environmental regulation can also be used to address externalities arising from firm
production. We first show that the private market provision of ESG funds marketed to retail investors
involves greenwashing, so that a mandatory taxonomy is necessary to generate real effects of sustainable
finance. However, the introduction of such a taxonomy can only improve welfare, on top of optimally
chosen environmental regulation, if financial frictions constrain socially valuable economic activity. Otherwise,
environmental policy alone is sufficient to optimally address externalities.

1. Introduction
Next to traditional environmental policy, harnessing private financial investment is increasingly considered important for the ecological
transformation of economic activity. However, the impact of sustainable finance do date has been questioned, see e.g., Berk and van
Binsbergen (forthcoming). In particular, among policymakers, there is
a widespread concern that greenwashing (de Freitas Netto et al., 2020)
is one of the key impediments to achieving real effects of sustainable
finance.
To ensure that sustainable finance is indeed directed towards activities that have a substantial positive environmental impact, the
European Union (EU,2020) created a taxonomy as part of the Sustainable Finance Disclosure Regulation (SFDR), see Appendix D for more
details. This taxonomy has two key features. First, it defines firm activities that are considered sustainable, e.g., electricity generation from
wind power is an eligible activity, while electricity generation from
coal is not eligible. Second, to market a fund as sustainable according
to Article 9, each company in a sustainable fund’s portfolio must be EU

taxonomy-aligned. Funds that are not EU taxonomy-conform must be
sold to individual investors as “non-sustainable.”
With this background, our research questions are the following: Is
such a mandatory taxonomy needed to effectively harness investors’
desire to invest sustainably? Additionally, when and why should such
a tool be used when environmental policy tools, such as regulatory
minimum production standards or emission taxes, are also available?
Our theoretical analysis provides the following high-level insights.
Given the prevalence of warm-glow preferences for “owning” funds
with a green label, as documented by Bonnefon et al. (2019) and Heeb
et al. (2023), the market provision of sustainable investments features
a “race to the bottom” in greenwashing.1 A regulatory framework is
necessary to impact firms’ investment decisions. However, the mere
potential to generate real effects, through such a mandatory taxonomy,
is not sufficient to justify government intervention via financial regulation: In the absence of environmental policy failure, a taxonomy will
only lead to welfare improvements if financial constraints constrain

✩ Philipp Schnabl was the editor for this article. We are grateful to an anonymous referee, Bruno Biais, Alexander Guembel, Augustin Landier, Stefano Lovo,
Adriano Rampini, Pablo Ruiz-Verdu, Per Strömberg, Jean Tirole, and participants at Stanford, Duke, HEC Paris, Stockholm School of Economics, Universidad
Carlos III de Madrid, UCLA, and the Corporate Finance Theory Symposium for their helpful comments and suggestions. This project has received funding from
the Marianne and Marcus Wallenberg (MMW) foundation.
∗ Corresponding author at: Stockholm School of Economics, Sweden.
E-mail addresses: inderst@finance.uni-frankfurt.de (R. Inderst), marcus.opp@hhs.se (M.M. Opp).
1
This is consistent with widespread concerns about vague (market) standards (Berg et al., 2022) and greenwashing (de Freitas Netto et al., 2020). According
to PwC’s Asset and Wealth Management Revolution 2022 report, 71% of fund managers themselves believe that greenwashing is a common practice. Indeed,
76% simply plan to relabel existing products so they can be marketed as ESG investment products.

https://doi.org/10.1016/j.jfineco.2024.103954
Received 22 February 2024; Received in revised form 3 October 2024; Accepted 6 October 2024
Available online 23 October 2024
0304-405X/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

socially valuable economic activity. Otherwise, environmental policy
alone is sufficient to rectify inefficiencies caused by externalities.
We derive these results in a parsimonious general equilibrium production framework. Each firm can choose the scale and sustainability
of its production, i.e., costly abatement of externalities. Financing from
households, either directly or through funds, is limited by outside
financing constraints, building on Holmström and Tirole (1997).2 We
extend their model by microfounding firm payoffs in a competitive
product market, which allows us to account for consumer surplus in
the welfare analysis.
As a benchmark, we consider an economy without sustainable
investors to see how far the planner can go purely with environmental regulation: minimum standards, e.g., such as mandatory catalytic
converters, and (carbon) taxes. The planner not only cares about firms
choosing the appropriate degree of abatement but also accounts for
real activity, as determined by aggregate production. In the first-best
allocation, firms choose to abate up to the point where the marginal
cost of abatement equals the marginal social benefit, and at the optimal
aggregate output level, the marginal consumer’s reservation price just
equals the marginal social cost of production (including the externality). Now, if the planner can only avail herself of environmental policy
tools, but no direct subsidies,3 both over- and underproduction can
occur in equilibrium depending on the severity of financial constraints.
The optimum environmental policy now trades off real activity against
externalities. Environmental policy is optimally less stringent than
first-best when financial constraints bind.
We then incorporate investors with sustainability concerns into our
model. How to best capture this demand for sustainable investments
is the subject of an ongoing debate. If small household investors were
affected by externalities like global warming, but have self-interested
“homo oeconomicus” preferences, they would treat aggregate externalities as given and behave like “purely profit-motivated investors,” which
is at odds with the dramatic rise in funds with an ESG label. Instead,
studies by Bonnefon et al. (2019) or Heeb et al. (2023) show support
for investor preferences that go beyond self interest.4 In particular,
their results suggest that individual investors’ “non-pecuniary benefits
accrue through stock ownership (value alignment), not through the
actual impact (consequences) of investment decisions.”5
We build on this empirical literature and assume that a subset
of these investors derives additional non-consequentialist warm-glow
from owning “ESG funds,” which acts as an additional return (see Riedl
and Smeets (2017)).6 To capture the heterogeneity of household preferences, we assume that the intensity of this warm-glow varies across
households according to some distribution function. Since the warmglow effect resulting from a purchase of “moral satisfaction” without

any impact, see Kahneman and Knetsch (1992), we model it as a purely
decisional utility that does not (directly) enter the social planner’s
objective, as in Broccardo et al. (2022).
How does the private market respond to such preferences? As is
intuitive, the market satisfies the demand for green ESG funds by
labeling all firms as green, consistent with the blatant greenwashing
observed in practice. A “real” sustainable fund that sets more stringent
sustainability requirements cannot compete with funds that offer moral
satisfaction at lower (no) return discount. In the market equilibrium,
sustainable finance does not generate a greenium for sustainable firms
and, hence, yields no impact.
A mandatory taxonomy can prevent such a race to the bottom
by imposing a lower bar on sustainability investments of taxonomyconform firms (which may not be under-cut by private sustainability
labels). In equilibrium, a fraction of firms will meet this more stringent
sustainability requirement of the taxonomy and, in return, receive a
return subsidy (greenium) that just offsets the increased production
costs associated with abatement. The share of taxonomy-conforming
firms is determined by the fraction of retail investors whose warm
glow outweighs the necessary return sacrifice. The regulator now faces
the following trade-off. By increasing the sustainability threshold, each
abiding firm causes fewer externalities, but also requires a higher
financing subsidy to offset the higher production cost to meet the
standard. Given a downward sloping supply of sustainable capital, in
terms of the accepted return sacrifice, this leads to a smaller share of
sustainable firms in equilibrium.
However, does the prevention of greenwashing imply that introducing a taxonomy is always socially desirable if environmental policy
tools are optimally chosen? We show that the introduction of a sustainable investment category is not beneficial if firms’ internal funds are
sufficiently high so that financial constraints do not prohibit aggregate
production at the socially efficient scale. Environmental regulation
alone is sufficient.7
In contrast, with acute financial frictions, stricter environmental
regulation in isolation would exacerbate underproduction. By activating a subsidy from sustainably-oriented investors, the planner can
mitigate this trade-off between imposing a higher minimum standard
(or environmental tax) and, at the same time, inefficiently shrinking the
economy. The availability of two tools allows the planner to increase
aggregate output while keeping the weighted average social cost constant. As preferences for sustainable investment become stronger, this
favors, on the margin, an increase in the sustainability standard. Given
the time trend of preferences for sustainability in recent years, our
model predicts that optimal sustainability standards should gradually
increase over time.
Another potential rationale for a taxonomy is that environmental
policy is suboptimally lax. In this case, a taxonomy partially mitigates
environmental policy failure by inducing a fraction of firms to produce
more sustainably. However, as the taxonomy is a much less effective
tool to mitigate environmental externalities, this rationale does not
address the more fundamental question of why environmental policy
is ineffective.8 In addition to possessing less effective tools, as pointed
out by Tirole (2023) as well as Oehmke and Opp (2022), such mandate shifts of financial regulators have additional drawbacks, such as
questions of institutional conflicts and lack of policy coordination.

2
The relevance of such financial constraints for abatement investments has
been empirically documented by Bartram et al. (2022), Xu and Kim (2022),
and Lanteri and Rampini (2023).
3
As is standard on the literature on financial constraints following
Holmström and Tirole (1997), we assume that the marginal cost of public
funds (taxation distortions) is sufficiently high so that the planner cannot
remove financial constraints for all firms in the economy. Relatedly, Hoffmann
et al. (2017) analyze the optimal design of subsidized loans to finance
abatement activities in an asymmetric information environment.
4
See Moisson (2020) and Dangl et al. (2023) for how altruistic preferences
can be related to different ethical norms.
5
The specification of non-consequentialist preferences also receives support
by a large literature in environmental and resource economics that elicits
preferences. For instance, elicited willingness-to-pay frequently fails a socalled “scope test” or “adding-up test”: Subjects’ willingness-to-pay is relatively
insensitive to the actual impact of the respective scenario change, e.g., the
number of animals saved, see Boyle et al. (1994) or Desvousges et al.
(2012) for prominent studies on these effects and Kahneman (2000) for an
explanation.
6
Our qualitative results are robust to preference specifications for which
the strength of the warm-glow is also affected by impact, see Appendix C.

7
We note that this result even extends to the case in which investors have
consequentialist preferences (as long as the warm-glow from impact does not
additionally contribute to welfare).
8
Recently, Allen et al. (2023) have taken a different, positive perspective
by modeling society’s choice (through voting) over environmental policy,
comparing the outcomes when households do or do not have access to
sustainable investments. Relatedly, Döttling et al. (2024) analyzes the feedback
effects between a “one-person one-vote” political system and a “one-share
one-vote” corporate governance regime.

2

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

2. Benchmark economy

Our paper builds on a rapidly growing literature on the theory of
socially responsible investing.9 This literature consists mainly of two
strands: exclusion (following the pioneering paper by Heinkel et al.
(2001)) and impact investing,10 cf. Oehmke and Opp (forthcoming) for
a detailed comparison.11 Since we aim to model investor demand for
sustainable finance products by small retail investors, our model does
not feature large activist investors, which are studied in Chowdhry
et al. (2018), Oehmke and Opp (forthcoming), Biais and Landier (2022)
and Gupta et al. (2022). Instead, our investors are small and nonconsequentialist as in Pastor et al. (2021), but the optimal design of
a taxonomy allows the regulator to channel the aggregate supply of
sustainable finance to achieve impact.12
Our paper shares with Piccolo et al. (2022) that it considers the
interaction of socially responsible investors and endogenous product
market outcomes.13 The papers differ in their objective. The positive
analysis of Piccolo et al. (2022) focuses on the strategic interaction
of firms in a setup with market power; this effect is moot in our
competitive setting. Instead, our normative paper analyzes the rationale
for a taxonomy and its connection to environmental policy. The papers
also differ in terms of the mechanism of how sustainable finance
generates impact: While investors in Piccolo et al. (2022) influence
company decisions via ownership (control rights), our investors induce
sustainability investments via a reduction in the cost of capital for
taxonomy-conform firms.
None of the literature has addressed the two key questions of our
analysis, i.e., whether such subsidized financing is socially beneficial
in view of alternative, more direct environmental policy instruments
and how to optimally design a sustainable investment classification.14
The latter issue taps into a large theoretical literature on optimal
certification (see Bizzotto and Harstad (2023) for a recent contribution
and a detailed survey). This literature, however, typically considers the
perspective of a profit-maximizing certifier and the design of labels for
products or services when purchasers have limited information about
quality.
This paper is organized as follows. In Section 2 we introduce the
benchmark economy in which all investors care only about financial
returns and, consequently, the social planner can only avail herself of
environmental policy instruments. In Section 3 we introduce households with sustainability preferences and provide conditions under
which the introduction of a sustainable investment category is optimal
(and, if so, which threshold should be optimally chosen). Section 4
concludes. All proofs are relegated to Appendix A.

We initially analyze a benchmark economy in which all households
(investors) are purely profit-motivated. In such an economy, there is
no demand for sustainable investing and, hence, there is no scope for
a “sustainable investments” taxonomy either.
We first describe the model ingredients and objective functions
of firms, households and the regulator. Then, for given environmental
regulation, we derive the equilibrium financing and investment decisions by firms, which determines aggregate output and externalities.
This first part extends Holmström and Tirole (1997) by microfounding
firm payoffs in a competitive product market. We then characterize
optimal environmental regulation, which is the first step to answering
whether there is additional scope for “sustainable investments” and the
taxonomy from a welfare perspective.
2.1. Model primitives
Firms. The economy consists of a unit mass of profit-maximizing firms
indexed by 𝑖, each endowed with internal funds 𝐴 > 0 (which, thus,
also corresponds to aggregate internal funds).15 Firms compete in the
product market: Given individual firm output 𝑞𝑖 , each firm reaps a
1
market price of 𝑃 (𝑞) where 𝑞 = ∫0 𝑞𝑖 𝑑 𝑖 denotes aggregate output and
𝑃 satisfies the usual conditions, i.e., 𝑃 is differentiable with 𝑃 ′ < 0
and lim𝑞→∞ 𝑃 (𝑞) = 0. To focus on the effect of socially responsible
investment, we assume that sustainable production cannot ensure a price
premium in the product market.16
The production technology choice features a trade-off between profitability and sustainability 𝜃𝑖 ≤ 𝜃 max , which arises, for example, from
the costly installation of air filters and 𝜃𝑖 governing their quality. We
(
)
assume that production generates negative externality of 𝜌 𝜃 max − 𝜃𝑖
per unit of output while investment costs per unit of output are given by
( )
𝑐 𝜃𝑖 , where 𝑐 is a strictly increasing and convex function with 𝑐 ′ (0) = 0
and lim𝜃→𝜃max 𝑐 ′ (𝜃) = ∞.17 In the context of carbon emissions, one can
(
)
thus interpret 𝜃 max − 𝜃𝑖 as the firm’s carbon intensity and 𝜌 > 0 as the
social cost per unit of carbon emissions. A firm 𝑖 is carbon-neutral if
its sustainability choice satisfies 𝜃𝑖 = 𝜃 max . The total cost of production,
( )
𝑐 𝜃𝑖 𝑞𝑖 , needs to be financed by a combination of internal funds 𝐴𝑖 ≤ 𝐴
and external funds.
External financing is subject to financing frictions adopted from the
workhorse model of Holmström and Tirole (1997). Specifically, the sale
of output is only successful with probability one if the owner-manager
exerts unobservable effort. If she shirks, she obtains a per-unit private
benefit 𝐵 > 0, but with probability 𝛥𝑝 > 0 no sale occurs. As is standard
𝐵
in the literature, we assume that the agency rent 𝛥𝑝
is low enough
so that shirking is off equilibrium (see exact condition in AppendixLemma A.1).

9
See e.g., Chowdhry et al. (2018), Davies and Van Wesep (2018), Green
and Roth (forthcoming), Landier and Lovo (forthcoming), Oehmke and Opp
(forthcoming), Edmans et al. (2022), Pastor et al. (2021), Pedersen et al.
(2021), as well as Favilukis et al. (2024).
10
Laux and Mahieux (2024) analyzes how a firm optimally designs the
precision of its (climate risk) measurement and accounting system with an
eye on its bargaining perspective vis–a-vis impact investors.
11
In particular, Oehmke and Opp (forthcoming), Landier and Lovo
(forthcoming) as well as Green and Roth (forthcoming) have highlighted how
“value aligned” preferences or “narrow” investment mandates typically fail to
generate real impact. Apart from the different focus (regulation), our paper
extends (Oehmke and Opp, forthcoming) in two ways. First, we incorporate
retail investors with empirically relevant warm-glow preferences in a tractable
way. Second, firm payoffs are determined in a product market equilibrium
rather than exogenously specified, similar to Inderst and Heider (2022).
12
In contrast to Pastor et al. (2021), preferences are risk-neutral, which
ensures tractability, i.e., there is no effect on risk-premia which result from
imperfect risk-sharing.
13
Kaufmann et al. (2024) instead focus exclusively on the product market
by providing a framework to analyze competitive equilibria with rational
consequentialist consumers.
14
Biais and Landier (2022), Döttling and Rola-Janicka (2022), and Oehmke
and Opp (2022) have analyzed the interaction of environmental regulation
with the financial sector when environmental regulation is subject to a
commitment problem. There is no commitment problem in our paper.

Household investors. External funds are in abundant supply and provided by atomistic, risk-neutral households that seek to maximize their
expected net financial payoff. In addition to the investment opportunities offered by firms, households have access to a storage technology
that offers a fixed net return 𝑟0 (which is normalized to zero). This
is also the return that firms realize on assets that they do not invest
productively.

15
It is straightforward to extend the analysis to the case where firms
differ in internal funds, given that each firm is atomistic and that our main
characterization pertains to aggregate output.
16
See Hakenes and Schliephake (2021), Broccardo et al. (2022), and Piccolo
et al. (2022) for models that also consider socially responsible consumption.
17
For simplicity, we assume that firms are homogeneous (and, yet, heterogeneous sustainability choices emerge in equilibrium, see Proposition 3).
In contrast, Lanteri and Rampini (2023) analyze the implications of firm
heterogeneity in terms of financial constraints for the technology adoption of
green technologies and the composition of the capital stock.

3

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

Regulator. A key objective of our analysis is to investigate the relevance of sustainable finance and its taxonomy in the presence of
standard, environmental policy tools. Motivated by its widespread
use in practice, our main analysis considers the tool of a minimum
sustainability standard 𝜃𝑚 as the main environmental policy tool. In the
context of emissions, such regulations impose limits on the emissions
intensity, 𝜃 max − 𝜃𝑚 , for example, by requiring the use of high-quality
air filters or catalytic converters. Likewise, it can require investments
in protection against health hazards for workers or undue harm on
animals. Importantly, we show that all of our results continue to hold
if a regulator could, in addition, impose a tax 𝜏 per unit of social cost,
see Remark 1.
Given production choices 𝜃𝑖 and 𝑞𝑖 , welfare, comprises first, gross
consumer welfare; second, investment costs; and third, the externality:
𝑞
)
(
( )
(1)
𝛺=
𝑃 (𝑞)𝑑 𝑞 −
𝑞 𝑐 𝜃𝑖 𝑑 𝑖 − 𝜌 𝑞𝑖 𝜃 max − 𝜃𝑖 𝑑 𝑖,
∫
∫0
∫ 𝑖

(b) Investors decide to allocate their funds to the storage technology
and capital provision into each firm to maximize their net payoffs.
(c) Markets for capital clear.
Individual firms’ financing and production choices. Since this benchmark
economy only features profit-motivated agents, there is, for now, no
benefit from exceeding the minimum standard and all firms optimally
choose 𝜃𝑖∗ = 𝜃𝑚 . We now characterize an individual firm’s optimal
financing contracts yielding coinvestment 𝐴∗𝑖 and output 𝑞𝑖∗ .
As in Holmström and Tirole (1997), the moral hazard problem
limits outside financing capacity and output of each firm. Different
from Holmström and Tirole (1997), the optimal choices of each individual firm are affected by the financing and supply decisions of other
firms since the product market price is pinned down by the aggregate
supply of all firms 𝑞. As a result, firms only have an incentive to operate
if aggregate supply is sufficiently low so that the product price exceeds
the cost of production,
( )
𝑃 (𝑞) ≥ 𝑐 𝜃𝑚 .
(4)

which, to simplify expressions, already uses the result that shirking
is off equilibrium (see Proof of Appendix- Lemma A.1). The regulator
chooses 𝜃𝑚 as to maximize welfare in (1).
We presume that the economic activity is socially valuable, 𝛺 > 0, at
least under optimal regulation. It is, thus, necessary that the consumer
surplus on the initial unit exceeds the marginal social cost, the sum of
the marginal private investment costs 𝑐(𝜃) and externalities 𝜃 max − 𝜃 for
some 𝜃, i.e.,
[
]
𝑃 (0) > min 𝑐(𝜃) + 𝜌(𝜃 max − 𝜃) .
(A1)

In the absence of prohibitively costly (and suboptimal) environmental
( )
regulation, i.e., 𝑐 𝜃𝑚 < 𝑃 (0), the output quantity 𝑞 adjusts so that
Condition (4) is satisfied in equilibrium (see Proposition 1).
Let 𝐷𝑖 denote the promised repayment to household investors, then
incentive compatibility of effort requires that the owner’s payoff under
effort exceed the expected payoff under shirking (inclusive of private
benefits),
[
]
𝑞𝑖 𝑃 (𝑞) − 𝐷𝑖 ≥ (1 − 𝛥𝑝) 𝑞𝑖 𝑃 (𝑞) − 𝐷𝑖 + 𝐵 𝑞𝑖 .
(IC)

𝜃

Timeline. We consider the following logical sequence of events. At 𝑡 = 0
the regulator chooses the minimum production standard 𝜃𝑚 (and, as in
our extension, a tax on externalities). At 𝑡 = 1, given this regulatory
environment, firms then simultaneously choose their optimal sustain( )
ability level 𝜃𝑖 , output 𝑞𝑖 , as well as external financing 𝑐 𝜃𝑖 𝑞𝑖 − 𝐴𝑖 .
Households allocate funds to firms and the storage technology. At 𝑡 = 2,
managers choose whether to exert effort or not, and output 𝑞𝑖 is sold
at price 𝑃 (𝑞).

The investors’ participation constraint (IR) requires that outside
investors earn at least the required return 𝑟0 = 0 on their investment of
( )
𝑐 𝜃𝑖 𝑞𝑖 − 𝐴𝑖 , where 𝐴𝑖 ≤ 𝐴 denotes the insider’s coinvestment:
( )
𝐷𝑖 ≥ 𝑐 𝜃𝑖 𝑞𝑖 − 𝐴𝑖 .
(IR)
In equilibrium, the household investors’ (IR) constraint always binds
since household capital is in ample supply and investors behave competitively.
When the profitability Condition (4) holds, standard arguments
imply that it is (weakly) optimal for the firm to fully co-invest internal funds, 𝐴∗𝑖 = 𝐴. Binding (IR), the absence of shirking, and full
coinvestment imply that the firm’s gross payoff satisfies:
[
( )]
𝑈𝑖 = 𝑞𝑖 𝑃 (𝑞) − 𝑐 𝜃𝑚 + 𝐴.
(5)

First-best benchmark. Before analyzing the equilibrium outcome of the
just presented economy, it is useful to characterize first-best welfare
𝛺𝐹 𝐵 . As firms are homogeneous, first-best welfare can be characterized
using two control variables, total output 𝑞𝐹 𝐵 and a uniform standard
𝜃𝐹 𝐵 across firms. The optimal sustainability level equates, per unit of
production, the saved social cost of the externality with the marginal
increase in investment cost,
𝑐 ′ (𝜃𝐹 𝐵 ) = 𝜌.

Since individual firms take the market price as given, the objective ((5))
is linear in 𝑞𝑖 . Again by condition (4), it is then (weakly) optimal to
produce at maximal scale.
In equilibrium, an individual firm’s maximal scale is constrained
by financial frictions, as we will formally show in Corollary 2 to
Proposition 1. Maximal scale is, thus, determined by binding (IR) and
(IC) which implies that

(2)

The optimal aggregate output and market size, in turn, equates
marginal consumer surplus with marginal cost of production, comprising the externality:
𝑃 (𝑞𝐹 𝐵 ) = 𝑐(𝜃𝐹 𝐵 ) + 𝜌(𝜃 max − 𝜃𝐹 𝐵 ).

(3)

2.2. Market equilibrium
We refer to the market equilibrium as the equilibrium behavior
of private agents, firms and households, for a given regulatory environment, i.e., 𝜃𝑚 . We endogenize the optimal choice of 𝜃𝑚 in the
subsequent section. This market equilibrium is characterized by the
following conditions:

𝑞𝑖∗ = 𝑘 (𝑞) 𝐴,

(6)

where the production capacity multiplier 𝑘 (𝑞) satisfies18
1
𝑘 (𝑞) = 𝐵 [
( )] > 0.
−
𝑃
− 𝑐 𝜃𝑚
(𝑞)
𝛥𝑝

(7)

This expression is an extension of the standard multiplier in
Holmström and Tirole (1997) by incorporating product market competition. The production capacity multiplier is a decreasing function of
𝑞 because larger aggregate output pushes down product prices (and,
hence profitability). Using these optimal choices 𝜃𝑖∗ = 𝜃𝑚 , 𝐴∗𝑖 = 𝐴 and
𝑞𝑖∗ (conditional on 𝑞), the indirect utility of each firm is given by:
𝐵
𝑈𝑖∗ =
𝐴𝑘 (𝑞) .
(8)
𝛥𝑝

Definition 1. Given a minimum standard 𝜃𝑚 , a Market Equilibrium is
characterized by a co-investment, production and effort strategy for
each firm, and an investment strategy for each investor such that:
(a) Each firm 𝑖 chooses its coinvestment 𝐴𝑖 ≤ 𝐴, its technology
𝜃𝑖 ≥ 𝜃𝑚 , its output 𝑞𝑖 and its unobservable effort to maximize its
net payoff inclusive of private benefits.

18

4

( )
Corollary 2 implies that 𝑃 (𝑞) − 𝑐 𝜃𝑚 < 𝐵∕𝛥𝑝 so that 𝑘 (𝑞) > 0.

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

We now determine the aggregate output, 𝑞 = ∫ 𝑞𝑖 𝑑𝑖 that results from
the optimal behavior of individual firms.

2.3. Optimal environmental regulation
We now turn to the planner’s optimal choice of the minimum standard. Given the equilibrium characterization, the planner’s objective in
(1) simplifies to
𝑞 ∗ (𝜃𝑚 )
]
[ ( )
𝛺=
(12)
𝑃 (𝑞)𝑑 𝑞 − 𝑞 ∗ 𝑐 𝜃𝑚 + 𝜌(𝜃 max − 𝜃𝑚 ) .
∫0

Aggregate output. While each individual firm’s supply is constrained by
financial constraints, aggregate economic output, 𝑞 ∗ = ∫ 𝑞𝑖∗ 𝑑𝑖 is only
impacted by financial constraints if firms cannot jointly secure sufficient
external financing to produce the zero-profit output 𝑞̄ solving
( )
𝑃 (𝑞)
̄ = 𝑐 𝜃𝑚 .
(9)

The socially optimal choice of the single policy instrument, characterized by the first-order condition 𝑑𝑑𝜃𝛺 = 0, aims to balance deviations
𝑚
from the two separate first-order conditions for the technology and
quantity in the first-best benchmark, see (2) and (3):
| 𝑑 𝑞∗ |
( ) || 𝑑 𝜃𝑚 || [ ( ∗ )
( )
(
)]
′
𝜌 − 𝑐 𝜃𝑚 = | ( ) | 𝑃 𝑞 − 𝑐 𝜃𝑚 − 𝜌 𝜃 max − 𝜃𝑚 ,
(13)
| 𝑞∗ 𝜃 |
𝑚 |
|
|
|
where we have made explicit the dependency of equilibrium output,
( )
𝑞 ∗ 𝜃𝑚 , see Corollary 1. The left hand-side of (13) captures the socially
optimal technology choice, cf. condition (2). The right-hand side captures condition (3), which is the marginal social surplus of an additional
unit of output fixing technology 𝜃𝑚 , scaled by the semi-elasticity of
| ∗
( )|
output to environmental standards, || 𝑑𝑑𝜃𝑞 ∕𝑞 ∗ 𝜃𝑚 ||, that results from the
𝑚
|
|
feedback effect of the minimum standard on aggregate output. We
obtain:

Proposition 1 intuitively reveals that aggregate production at the
frictionless level 𝑞̄ only occurs in equilibrium if firms’ aggregate internal
funds 𝐴 are sufficiently high.
( )
Proposition 1 (Aggregate Output 𝑞 ∗ ). If 𝑃 (0) > 𝑐 𝜃𝑚 so that environmental regulation is not prohibitively costly, the economy produces 𝑞 ∗ > 0
which can be characterized as follows:
1. If aggregate internal funds 𝐴 are sufficiently small, 𝐴 < 𝑞̄𝐵∕𝛥𝑝,
financial frictions constrain aggregate output of the economy, 𝑞 ∗ < 𝑞,
̄
which solves:
( )
𝑞 ∗ = 𝐴𝑘 𝑞 ∗ .
(10)
2. If 𝐴 ≥ 𝑞̄𝐵∕𝛥𝑝, aggregate output is unaffected by financial frictions,
𝑞 ∗ = 𝑞.
̄

Proposition 2 (Environmental Regulation).If the agency problem is sufficiently strong,
𝐵
≥ 𝜌(𝜃 max − 𝜃𝐹 𝐵 ),
(14)
𝛥𝑝

The comparative results of aggregate output follow immediately.
Corollary 1. Output 𝑞 ∗ is increasing in aggregate internal funds 𝐴 (strictly
so as long as 𝐴 < 𝑞̄𝐵∕𝛥𝑝) and strictly decreasing in the minimum standard
𝜃𝑚 .

there exists a threshold for internal funds 𝐴𝐹 𝐵 such that the optimal
standard satisfies 𝜃̃𝑚 > 𝜃𝐹 𝐵 for 𝐴 > 𝐴𝐹 𝐵 and 𝜃̃𝑚 < 𝜃𝐹 𝐵 for 𝐴 < 𝐴𝐹 𝐵 . At
(
)
𝐴 = 𝐴𝐹 𝐵 , first-best welfare is achieved, i.e., 𝜃̃𝑚 = 𝜃𝐹 𝐵 and 𝑞 ∗ 𝜃𝐹 𝐵 = 𝑞𝐹 𝐵 .
𝐵
< 𝜌(𝜃 max − 𝜃𝐹 𝐵 ), the optimal standard always satisfies 𝜃̃𝑚 > 𝜃𝐹 𝐵 .
If 𝛥𝑝

Intuitively, larger aggregate internal funds increase aggregate output by mitigating the effects of external financing frictions, leading to
larger output. In contrast, a higher minimum standard increases firms’
production costs resulting in lower aggregate supply.19 We now turn to
the resulting equilibrium financing capacity and firm rents.

We first consider the case in which the agency constraints are
sufficiently strong, so that Condition (14) holds. To see the logic for
Proposition 2, set first 𝜃𝑚 = 𝜃𝐹 𝐵 . Condition (14) ensures that when
internal funds are sufficiently low (precisely, when 𝐴 < 𝐴𝐹 𝐵 ), the
economy produces output below the socially efficient scale, 𝑞 ∗ < 𝑞𝐹 𝐵 .20
Then, the marginal social surplus of an additional unit of output is
( )
(
)
strictly positive, 𝑃 (𝑞 ∗ ) − 𝑐 𝜃𝑚 − 𝜌 𝜃 max − 𝜃𝑚 > 0.
Now, suppose instead that internal funds are not scarce, so that
when 𝜃𝑚 = 𝜃𝐹 𝐵 , output expands until 𝑞 ∗ = 𝑞.
̄ As firms do not take
into account the externality, there is overproduction (from a planner
perspective), 𝑞̄ > 𝑞𝐹 𝐵 . With 𝑞 ∗ being strictly increasing (and continuous) in internal funds, there exists a unique level 𝐴 = 𝐴𝐹 𝐵 at which
𝑞 ∗ = 𝑞𝐹 𝐵 . This tension between over- and underproduction is the main
force behind the hump-shaped effect of internal funds on welfare, as
illustrated in the right panel of Fig. 1.
If the converse of (14) holds, output is always excessively high at
𝜃𝑚 = 𝜃𝐹 𝐵 , even as 𝐴 → 0, and we would find ourselves only at the part
where welfare decreases in 𝐴. Consequently, it is always optimal to set
𝜃̃𝑚 > 𝜃𝐹 𝐵 .
In the presence of two frictions – financing constraints and production externalities – one would expect one tool to be insufficient to
restore first-best. In particular, while the planner can force all firms
to choose 𝜃𝐹 𝐵 , this policy choice does not automatically ensure the
socially optimal quantity 𝑞𝐹 𝐵 since output is endogenously supplied by
profit-maximizing firms. However, as we have shown, first best welfare
𝛺𝐹 𝐵 is achieved when financial constraints are “just right,” which
stands in stark difference to canonical corporate finance models, where
financial constraints reduce total surplus as they prevent firms from
exploiting profitable investment opportunities. In the presence of social

Corollary 2 (Equilibrium Financing Capacity and Rents). For any(𝐴 >
) 0,
the equilibrium capacity multiplier, 𝑘 (𝑞 ∗ ), is finite as 𝑃((𝑞 ∗)) − 𝑐 𝜃𝑚 <
𝐵∕𝛥𝑝. Firms earn scarcity rents in equilibrium, 𝑃 (𝑞 ∗ ) > 𝑐 𝜃𝑚 ⇔ 𝑈𝑖∗ > 𝐴,
if and only if 𝐴 < 𝑞̄𝐵∕𝛥𝑝.
Thus, with endogenous product market competition, the output
quantity always adjusts so that the firms’ reward, the price 𝑃 (𝑞 ∗ ), is
never so high that firms become financially unconstrained (and (IC)
would be slack). This occurs because, in aggregate, the industry exhibits
decreasing returns to scale as the inverse demand is downward sloping.
When aggregate output is constrained by financial frictions, 𝐴 < 𝑞̄𝐵∕𝛥𝑝,
the scarcity rents imply that all firms lever up to the maximum.
Instead, when the economy produces the zero-profit output 𝑞,
̄ firms are
indifferent between producing and using the storage technology so that
𝑈𝑖∗ = 𝐴.
We finally remark on an additional feature related to the endogenous product price. When firms’ internal funds go to (zero,
) 𝐴 → 0,
𝐵
aggregate output converges to zero only if 𝑃 (0) ≤ 𝛥𝑝
+ 𝑐 𝜃𝑚 , i.e., only
if the incentive constraint binds at the highest product price. Otherwise,
when 𝐴 → 0 aggregate output converges to
(
)
( )
𝐵
𝑞min = 𝑃 −1
+ 𝑐 𝜃𝑚 ,
(11)
𝛥𝑝
which is still strictly lower than 𝑞.
̄

19
The rationale for why equilibrium output strictly decreases with a higher
minimum standard is slightly different in the two cases of Proposition 1:
When aggregate output is not constrained by financial frictions, this follows
immediately from the zero-profit condition for 𝑞 ∗ = 𝑞.
̄ Otherwise, the higher
costs of production reduce the capacity multiplier, 𝑘.

20
If the converse of (14) holds, even as 𝐴 → 0 the then strictly positive limit
𝑞min , as given by (11), strictly exceeds 𝑞𝐹 𝐵 (cf. the proof of Proposition 2).

5

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

( )
Fig. 1. Optimal minimum standard as a sole policy tool. The graph in the left panel plots the optimal minimum standard 𝜃̃𝑚 and the associated equilibrium output 𝑞 ∗ 𝜃̃𝑚
( )
𝐵
max
∗ ̃
̃
as a function of aggregate internal funds 𝐴 for the case 𝛥𝑝 ≥ 𝜌(𝜃
− 𝜃𝐹 𝐵 ). Note that the respective units on the 𝑦-axis have different scales for 𝜃𝑚 (left scale) and 𝑞 𝜃𝑚 (right
scale). The right panel plots the resulting welfare under the optimal minimum production standard 𝜃̃𝑚 . For 𝐴 = 𝐴𝐹 𝐵 , first-best welfare 𝛺𝐹 𝐵 is achieved. Financial constraints do
̄
not bind for 𝐴 ≥ 𝐴.

limit overproduction, so that 𝑞 ∗ = 𝑞𝐹 𝐵 , while at the same time setting
the minimum standard to 𝜃𝐹 𝐵 .
Intuitively, environmental policy tools work well to mitigate production externalities, but not financial frictions. Therefore, even optimal environmental policy fails to restore first-best when financial
constraints are sufficiently severe, 𝐴 < 𝐴𝐹 𝐵 . We now analyze if
sustainable finance can make a difference and whether a taxonomy is
needed.

externalities, financial constraints are thus no longer unambiguously
harmful.
We now turn to the optimal choice of 𝜃̃𝑚 , which varies with 𝐴 so
as to mitigate over- or underproduction from a social perspective. For
𝐴 < 𝐴𝐹 𝐵 , to avoid “overshrinking” the economy, the environmental
standard, solving (13), is optimally chosen to be less stringent 𝜃̃𝑚 < 𝜃𝐹 𝐵 .
For 𝐴 > 𝐴𝐹 𝐵 , to counter overproduction from a social perspective, the
optimal standard appears to be excessively stringent, 𝜃̃𝑚 > 𝜃𝐹 𝐵 (see the
(
)
left panel in Fig. 1). For 𝐴 ∈ 𝐴𝐹 𝐵 , 𝐴̄ , the economy underproduces
from a private perspective (as production is still financially profitable)
̄ financial
and overproduces from a social perspective. Once 𝐴 > 𝐴,
constraints no longer bind (at the optimal choice 𝜃̃𝑚 ), and the optimally policy no longer varies with 𝐴. The optimal minimum standard,
( )
denoted by 𝜃̄𝑚 > 𝜃𝐹 𝐵 and the realized output 𝑞 ∗ = 𝑞̄ 𝜃̄𝑚 correspond to
the optimal policy choices in an economy without financial frictions.21

3. Full model
3.1. Preferences for sustainable investing
Maintaining the assumption that there is ample supply of capital by
purely profit-motivated investors, we now incorporate investors with
sustainability preferences. These investors with concerns for sustainability are endowed with funds of size 𝐾. For ease of exposition, we
stipulate that 𝐾 is sufficiently small, so that profit-motivated investors
are needed to ensure that all firms in the economy are able to receive
financing.23
There is an active debate about how to best capture preferences for
ESG investments, both from a normative and positive perspective, in
particular regarding the question whether such investors are primarily
impact oriented or simply obtain a warm glow from owning “green
firms.”
Theoretically, if retail investors behaved like the self-interested
homo oeconomicus, they would understand that the impact of their
(infinitesimally) small investment on firm decisions and therefore aggregate emissions is zero and there would be no demand for sustainable
investment products.24 Thus, an increased concern about externalities
alone, say due to global warming, is not sufficient to explain the
large growth of sustainable investment products. Indeed Bonnefon
et al. (2019) or Heeb et al. (2023) find micro-level evidence for
preferences that depart from pure self-interest. Their results are most

Robustness under (a combined) carbon tax. We now demonstrate the
robustness of our main results under broader environmental policies.
In particular, we allow the regulator to also impose a tax 𝜏 per unit
of externality (so that the standard Pigouvian tax level would be 𝜏 =
𝜌). To avoid overburdening the reader with additional notation, we
summarize our main point upfront and relegate the formal analysis to
Appendix B.
Remark 1 (Minimum Standard and Carbon Tax).
Suppose that Condition (14) holds and the planner can use both a
minimum standard and a carbon tax. If 𝐴 < 𝐴𝐹 𝐵 , first-best welfare
cannot be attained. The optimal carbon tax is zero and the optimal
minimum standard and output are characterized by Propositions 1 and
2. If 𝐴 > 𝐴𝐹 𝐵 , first-best welfare can be achieved by setting 𝜃𝑚 = 𝜃𝐹 𝐵
and a positive tax 𝜏 > 0.
If 𝐴 < 𝐴𝐹 𝐵 , it is strictly suboptimal to impose a carbon tax because this tax eats into pledgeable income, exacerbates firms financial
constraints, and, hence leads to additional reduction in output. Therefore, the planner only uses the minimum standard as characterized by
Proposition 2.22 In contrast, if 𝐴 > 𝐴𝐹 𝐵 , the tax allows the planner to

22
The minimum standard is equivalent to a tax when tax receipts are
rebated back to firms in lump-sum fashion. Hence, tax rebates do not change
the main result that first-best cannot be achieved for 𝐴 < 𝐴𝐹 𝐵 .
23
See the proof of Proposition 3 for the exact condition.
24
See Result 1 in Oehmke and Opp (forthcoming) taking the number of
investors to infinity. Considerations for impact would either require size
or effective coordination, see Corollaries 6 and 7 in Oehmke and Opp
(forthcoming), which is impossible to achieve for retail investors.

21
The switch from binding financial constraints to non-binding constraints
causes a jump in the policy function exactly at the level of internal funds
where the planner is indifferent between causing financial constraints or not.
̄ the objective function has two global
This jump arises because, for 𝐴 = 𝐴,
maxima. See details in Proof of Proposition 2.

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Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

threshold 𝜃𝑠 .26 Following similar steps as for the derivation of (8), the
entrepreneur’s payoff would be
( )
𝐵
𝑈𝑖 𝜃𝑠 =
(15)
𝐴𝑘 (𝑞) ,
𝛥𝑝 𝑠

consistent with non-consequentialist preferences, in which investors
receive a non-pecuniary dividend from owning cleaner firms. (We
consider robustness of our results under consequentialist preferences
in Appendix C.)
Based on these observations, we consider the polar opposite of homo
oeconomicus preferences for investors with sustainability concerns in
that households experience a warm-glow boost 𝑤 per unit of investment
when owning firms with a sustainability label. The assumption that
households derive their warm glow through the respective classification
can be motivated by retail investors’ lack of information or excessive
complexity associated with a more detailed assessment. Our analysis
both considers the case when the sustainability label is provided by the
market and when this label is regulated by the taxonomy. The warm
glow implies that households are willing to accept a reduction of the
financial return by 𝑤, consistent with evidence by Riedl and Smeets
(2017). We allow for heterogeneity in the strength of the sustainability
concerns across households. That is, the warm-glow for household 𝑗,
𝑤𝑗 , is drawn from the support [0, 𝑤] with density 𝑓 (𝑤) and CDF 𝐹 (𝑤).
As in Broccardo et al., 2022, we view the warm-glow purely as a
decisional utility. As the planner’s objective remains unaffected compared to our benchmark economy, see (1), our analysis purely focuses
on the real effects of sustainable investing and the taxonomy of the
sustainability label.25 We now consider these welfare effects in two settings. First, we consider the setting where the private market, in terms
of intermediaries (or firms), provide the label. Second, we consider
a setting where the government restricts the use of the sustainability
label.

1−𝛥𝑟
can be interpreted as the outside
[
]
( )
financing multiplier for firms with a sustainability label which(incor)
porates both the return subsidy 𝛥𝑟 and the production cost 𝑐 𝜃𝑠 >
𝑐(𝜃𝑚 ).
We now obtain the following useful Lemma regarding aggregate
production.

where 𝑘𝑠 (𝑞) ∶=

𝐵
− 𝑃 (𝑞)−𝑐 𝜃𝑠 (1−𝛥𝑟)
𝛥𝑝

Lemma 1. Regardless of whether some firms choose to meet the sustainability standard 𝜃𝑠 , aggregate output 𝑞 ∗ is identical to the benchmark economy,
see characterization in Proposition 1. The equilibrium outside financing
1
multiplier of all firms is 𝑘 (𝑞) = 𝐵
.
− 𝑃 (𝑞)−𝑐 (𝜃𝑚 )]
𝛥𝑝 [
In the interesting case in which a fraction of firms produces sustainably, the logic for Lemma 1 is as follows.27 Optimality of firms’ choices
requires that the payoffs of sustainable firms and unsustainable firms
be equalized.28 Comparing the respective payoffs in (8) and (15), then
implies that the outside financing multiplier must be the same for all
firms, i.e., firms’ optimal choices imply the equilibrium condition
( )
( )
𝑘𝑠 𝑞 ∗ = 𝑘 𝑞 ∗ ≡ 𝑘∗ .
(16)
Now, given that all firms have the same outside financing multiplier
as in the benchmark economy, aggregate output is also identical to the
one in the benchmark economy.
To determine the share of output that is produced sustainably, 𝜔, we
∗
first solve for the equilibrium financing subsidy
𝛥𝑟
just outweighs
( )
( that
)
the production cost differential 𝛥𝑐 ∶= 𝑐 𝜃𝑠 − 𝑐 𝜃𝑚 > 0. Rearranging
the equilibrium condition (16) yields
𝛥𝑐
𝛥𝑟∗ =
.
(17)
𝐵
+ 𝛥𝑐
𝑃 (𝑞 ∗ ) − 𝛥𝑝

3.2. Market equilibrium
Following the structure of our equilibrium analysis in the benchmark economy, we initially analyze the behavior of firms and households given a minimum production standard 𝜃𝑚 and a “sustainability”
standard 𝜃𝑠 ≥ 𝜃𝑚 that determines the sustainability label for investments. One key outcome variable is the return subsidy 𝛥𝑟, the
greenium, that is associated with a given sustainability label 𝜃𝑠 . We
will endogenize the laissez-faire standard of the ESG label at the
very end of this Section. Section 3.3 discusses how a planner would
optimally set the standard for sustainable investments (in conjunction
with environmental policy).
The presence of sustainability-oriented investors implies the following adjustments to the equilibrium Definition 1. Equilibrium condition
1a) is still valid, but firms now have the non-trivial choice of producing
at the minimum standard 𝜃𝑚 or meeting the costlier sustainability standard 𝜃𝑠 to obtain a return subsidy 𝛥𝑟. Investor optimality, equilibrium
condition 1(b), now implies that household investor 𝑗 invests in a
“sustainable” fund if and only if 𝑤𝑗 ≥ 𝛥𝑟. Finally, the market clearing
condition requires that the supply of financing directed to firms with a
ESG label, 𝐾 (1 − 𝐹 (𝛥𝑟)), equals the demand for external financing by
firms opting to meet the standard 𝜃𝑠 .
Since investors with sustainability concerns do not have sufficient
capital to finance all firms in the economy (cf. the condition in the proof
of Proposition 3), the marginal firm in the economy always produces
at the minimum standard 𝜃𝑚 and raises financing at the storage rate
𝑟0 = 0. Hence, conditional on aggregate output 𝑞, the payoffs of firms
operating at the minimum standard are as in the benchmark economy,
see (8).
Now, if a firm wanted to raise sustainable financing at a subsidized
rate 𝑟0 − 𝛥𝑟, it would optimally choose to just meet the required

Given 𝛥𝑟∗ , we can now characterize the composition of production.
Proposition 3 (The Sustainability Subsidy and the Composition of Production).
Given 𝜃𝑚 and 𝜃𝑠 , total sustainable output is given by:
( )
𝑘∗
∗
.
(18)
𝑞𝑠 = 𝐾[1 − 𝐹 𝛥𝑟∗ ] ( )
𝑐 𝜃𝑠 𝑘∗ − 1
𝑞∗

The equilibrium share of sustainable output, 𝜔∗ ∶= 𝑞𝑠∗ , satisfies
𝑞𝑠∗
𝜔∗ =
< 1.
min {𝑞̄, 𝐴𝑘∗ }

(19)

Proposition 3 highlights that sustainable output, 𝑞𝑠∗ , is the product
of the equilibrium supply of sustainable capital, 𝐾[1 − 𝐹 (𝛥𝑟∗ )], and a
term that reflects leverage as well as the cost of sustainable production.
While the distribution of investor preferences 𝐹 and the sustainability
threshold 𝜃𝑠 do not affect aggregate output 𝑞 ∗ , they have compositional
implications for production, i.e., the fraction of firms that produce
sustainably versus the ones that produce at the minimum standard. This
characterization yields unambiguous comparative statics, which shed
more light on the underlying economic forces.
We first analyze the effect of a trend in ESG demand by retail
investors.

26
Since exceeding 𝜃𝑠 only results in higher production costs, but entails no
benefits, it is optimal to not exceed the threshold.
27
If no firm produces sustainably, then all firms just raise financing like in
the benchmark economy and the result immediately follows.
28
Producing at threshold 𝜃𝑠 cannot results in lower payoffs since all firms
have the option to produce at the minimum standard 𝜃𝑚 . It cannot result
in higher payoffs either since all firms would otherwise want to produce
sustainably (but there is not enough capital to do so).

25
If instead the warm glow was part of the objective function, a
sustainability label would be trivially beneficial, even absent any real effect.

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Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

Corollary 3. An increase in the amount of capital held by investors with
sustainability concerns 𝐾 or a First-Order Stochastic Dominance shift in
𝐹 (𝑤) increase the share of sustainable investment 𝜔∗ , while the financing
subsidy 𝛥𝑟∗ remains unchanged.

not necessarily rule out that a significant fraction of investors has
preferences for sustainability. We note that this result can even emerge
under consequentialist preferences provided that the marginal utility
from impact is sufficiently low, see Lemma C.1 in Appendix C.32
We now analyze whether and how a regulatory taxonomy can
ensure a greenium, which is necessary to create real effects.

Intuitively, if ceteris paribus there is a greater supply of sustainable capital, this results in a greater share of sustainable investment.
Still the financing subsidy 𝛥𝑟∗ remains unchanged, as in equilibrium
this is pinned down by firms’ endogenous decision to become more
sustainable and the resulting indifference condition (17).
Moreover, we analyze the effects of the sustainability standard 𝜃𝑠 .

3.3. A taxonomy for ESG investments
We stipulate that the planner can set a lower standard 𝜃𝑠 > 𝜃𝑚 that
any sustainable investment must satisfy, thereby preventing the “race
to the bottom,” see Proposition 4. This restriction is consistent with
actual EU regulation: According to the July 2022 Article 9 guidance by
the European Commission, a ESG fund is prohibited from investing in
any firm that is not considered sustainable by the EU taxonomy.
We now analyze first when it is optimal to introduce a sustainability
classification for investments 𝜃𝑠 . Based on the extended equilibrium
characterization in Proposition 3, we can rewrite the planner’s objective
function (1) as follows:
𝑞∗
]
[ ( )
𝛺 =
(20)
𝑃 (𝑞)𝑑 𝑞 − 𝑞 ∗ 𝑐 𝜃𝑚 + 𝜌(𝜃 max − 𝜃𝑚 )
∫0
( )(
[ ( )
( )])
∗
+𝑞𝑠 𝜃𝑠 𝜌(𝜃𝑠 − 𝜃𝑚 ) − 𝑐 𝜃𝑠 − 𝑐 𝜃𝑚
,

Corollary 4. An increase in the sustainability standard 𝜃𝑠 decreases the
share of sustainable investment 𝜔∗ and increases the equilibrium financing
̄ no firm produces
subsidy 𝛥𝑟∗ . If 𝜃𝑠 is too stringent, so that 𝛥𝑟∗ > 𝑤,
sustainably.
While a higher sustainability standard does not have an effect on
aggregate output 𝑞 ∗ (see Lemma 1), it increases the cost differential
𝛥𝑐 for producing sustainably relative to the minimum standard. This
higher cost differential, in turn, requires the capital cost subsidy for
sustainable firms to go up, so as to keep sustainable production equally
attractive, see (17). The required increase in the subsidy needs to be
paid by households and, hence, reduces the attractiveness of the ESG
fund for all households. As a result, previously marginal households
no longer invest sustainably. This comparative statics highlights a key
trade-off that a regulator is facing in our upcoming normative analysis
in Section 3.3. While increasing the sustainability cutoff reduces the
negative externalities of sustainable firms, it reduces the fraction of
firms that choose to produce sustainably.
The laissez-faire standard for sustainable investments. Before analyzing
the planner’s optimization, we consider as a benchmark, a setting in
which competitive intermediaries indexed by 𝑗 sell funds with a sustainability label to retail investors.29 Given fund 𝑗’s cutoff for sustainability
𝜃𝑠𝑗 , all firms 𝑖 with 𝜃𝑖 ≥ 𝜃𝑠𝑗 are eligible for the sustainability label of
fund 𝑗 ∈ {1, 2, … , 𝑁}.30 We now determine the resulting laissez-faire
sustainability standard 𝜃𝑠𝑀 that all intermediaries choose.

where we make the dependence on 𝜃𝑠 explicit and exploit the fact that
firms optimally either choose 𝜃𝑚 or 𝜃𝑠 . The first line in (20) captures
the known baseline welfare if all investment were non-sustainable (cf.
expression (1)). The second line captures the incremental effect of
( )
sustainable output with quantity 𝑞𝑠∗ 𝜃𝑠 .
∗
As total output 𝑞 does not depend on 𝜃𝑠 , changes in 𝜃𝑠 only
affect the social planner’s objective through the second term. As a
result, the planner’s program reduces to that of maximizing the product
( )
( )
of 𝑞𝑠∗ 𝑣 𝜃𝑠 where 𝑣 𝜃𝑠 captures the incremental benefit per unit of
output, trading off the reduction of the externality with the increase in
cost,
( )
[ ( )
( )]
𝑣 𝜃𝑠 ∶= 𝜌(𝜃𝑠 − 𝜃𝑚 ) − 𝑐 𝜃𝑠 − 𝑐 𝜃𝑚 .
(21)

Proposition 4 (Greenwashing). In a laissez-faire equilibrium, all intermediaries choose the lowest possible threshold for the sustainability label, i.e., ∀𝑗,
𝜃𝑠𝑗 = 𝜃𝑠𝑀 = 𝜃𝑚 . The resulting greenium for sustainable firms is 𝛥𝑟 = 0.

( )
When is it optimal to introduce a taxonomy? Note that 𝑣 𝜃𝑠 is maximized for 𝜃𝑠 = 𝜃𝐹 𝐵 , see (2), which follows directly from the first-order
( )
condition 𝑣′ 𝜃𝑠 = 0. We then obtain

The argument for why the market cannot sustain a “real” sustainable fund is immediate, so that we cover it in the main text. If a
real sustainable fund 𝑗 required a standard 𝜃𝑠𝑗 > 𝜃𝑚 , it would have
to compensate firms for incremental costs 𝑐(𝜃𝑠 ) − 𝑐(𝜃𝑚 ) > 0. This,
in turn means that fund investors would need to accept a strictly
lower return on their investment, i.e., 𝛥𝑟 > 0. However, as long as
another fund 𝑘 offers an investment product with a sustainability label
at a lower return discount, warm-glow investors would flock to the
latter, undermining the viability of the “real” sustainable fund. This
race to the bottom ends when all funds choose the lowest possible
sustainability standard for firms, i.e., the regulatory minimum standard
(greenwashing).31 Thus, the lack of a greenium in equilibrium does

Proposition 5 (Optimality of a Taxonomy).The introduction of a sustainable investment taxonomy is strictly suboptimal if 𝜃𝑚 ≥ 𝜃𝐹 𝐵 and strictly
optimal if 𝜃𝑚 < 𝜃𝐹 𝐵 .
We note that Proposition 5 holds irrespective of whether the minimum standard is chosen optimally or results from an environmental
policy failure. As one would expect if environmental regulation is
sufficiently lax, as e.g., argued by Tirole (2012), a taxonomy increases
welfare by mitigating the effects of environmental policy failure. In
contrast, if the minimum standard 𝜃𝑚 is already very stringent, 𝜃𝑚 ≥
𝜃𝐹 𝐵 , the incremental benefit of introducing an even more stringent
( )
classification for sustainable investments is negative, 𝑣 𝜃𝑠 < 0, for
all 𝜃𝑠 > 𝜃𝑚 . Hence, the regulator should not introduce a category
for sustainable investments. While even in this case the availability
of sustainable investment opportunities (and the ensuing warm-glow)
would attract investors and thereby lead to subsidized capital costs for
sustainable firms, it would induce a fraction of firms to overinvest in
sustainability from a welfare perspective.33
The first part of Proposition 5 thus qualifies the notion of a general
social desirability of an ESG-classification of investment funds. Even

29
Our analysis, thus, abstracts from company-level ESG ratings, which
are theoretically analyzed by Azarmsa and Shapiro (2023). In their model,
greenwashing by firms may be detected by a ESG rater.
30
We note that the interpretation in terms of intermediaries is solely made
for expositional reasons. Formally, the results are identical if firms directly
seek funding with a self-designated ESG label, i.e., a fund solely consists of
one firm.
31
This logic is not impacted by the market structure for intermediaries. If
there were instead a monopolistic supplier of sustainable funds, there would
still be zero impact with 𝜃𝑠 = 𝜃𝑚 , but the fund would itself pocket a fee 𝜓 > 0.
In particular, the fund would choose its optimal management fee 𝜓 ∗ as to
maximize its revenues 𝜓[1−𝐹 (𝜓)] resulting in equilibrium “sustainable capital”
of size 𝐾[1 − 𝐹 (𝜓 ∗ )].

32
We thank an anonymous referee and Jean Tirole for suggesting this
extension.
33
Recall that the social planner’s objective only accounts for real effects,
but not investors’ warm-glow perception.

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Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

when such investment opportunities meet with positive demand, this
could represent “too much of a good thing.”
If 𝜃𝑚 is set optimally, we immediately obtain the following result as
a Corollary to Propositions 2 and 5.
Corollary 5. Under optimal environmental regulation, a taxonomy for
sustainable investments increases welfare if and only if 𝐴 < 𝐴𝐹 𝐵 .
That is, the introduction of a taxonomy for sustainable investments
can only increase welfare on top of optimal environmental regulation if
lack of financing is a source of a social inefficiency. Intuitively, if lack
of financing is not a concern, the regulator can simply choose stricter
environmental regulation for all firms (without having to worry about
financial constraints). This intuition for the primacy of environmental
regulation extends to the case of consequentialist investor preferences
(as long as the planner only cares about real effects), see Appendix C.
Moreover, we can interpret this result in the cross-section of
economies.
Corollary 6. In an economy where environmental policy (𝜃𝑚 ) is optimally
chosen, the additional introduction of a sustainable investment taxonomy is
more likely to be beneficial if, ceteris paribus, firms’ internal funds are more
limited (lower 𝐴) or the agency problem vis-à -vis external investors is more
severe (higher 𝐵∕𝛥𝑝).

(
)
(
)
Fig. 2. Jointly optimal policy 𝜃̂𝑚 , 𝜃̂𝑠 . The graph plots the optimal choice 𝜃̂𝑚 , 𝜃̂𝑠
if the planner can both flexibly a choose a minimum standard and a taxonomy for
sustainable investments 𝜃𝑠 > 𝜃𝑚 . For 𝐴 < 𝐴𝐹 𝐵 , 𝜃̂𝑚 < 𝜃̃𝑚 < 𝜃̂𝑠 . For 𝐴 ≥ 𝐴𝐹 𝐵 , we obtain
that 𝜃̂𝑚 = 𝜃̃𝑚 and no taxonomy for investments is introduced.

Hence, under optimal environmental policy the introduction of a
sustainable investment category is more likely to be socially beneficial
when (lack of) financial development or the (mal-)functioning of the
legal system sufficiently limit internal funding and raise the costs of
external financing. For a developed financial system, as prevailing in
the European Union, this would thus seem less likely.

In contrast, if 𝐴 < 𝐴𝐹 𝐵 , it is optimal to introduce the sustainable investments category by Corollary 5. Recall that, under optimal regulation with a minimum standard only, see Proposition 2,
the marginal consumer valuation exceeds the marginal social cost of
( )
(
)
production (including externalities), i.e., 𝑃 (𝑞 ∗ ) > 𝑐 𝜃̃𝑚 + 𝜌 𝜃 max − 𝜃̃𝑚 .
Therefore, ceteris paribus, an output expansion would be welfare enhancing. Equipped with the second tool of a taxonomy, it is possible to achieve this by setting the sustainability standard slightly
higher than in the benchmark economy, 𝜃𝑠 > 𝜃̃𝑚 , and then lower
the minimal standard 𝜃𝑚 < 𝜃̃𝑚 until the weighted average social
[ ( )
]
[ ( )
]
cost, (1 − 𝜔) 𝑐 𝜃𝑚 + 𝜌(𝜃 max − 𝜃𝑚 ) + 𝜔 𝑐 𝜃𝑠 + 𝜌(𝜃 max − 𝜃𝑠 ) matches
the one in the benchmark economy. This perturbation always improves welfare compared to the benchmark economy since it alleviates
underproduction in the economy by lowering the minimum standard.
The optimal calibration of the respective standards, i.e., 𝜃̂𝑠 and 𝜃̂𝑚 ,
see first-order conditions in Proof of Propositions 5 and 6, is illustrated
in Fig. 2 for an example specification: the optimal minimum standard is
below the one in the benchmark economy 𝜃̂𝑚 < 𝜃̃𝑚 (compare red line for
𝜃̂𝑚 to blue dotted line for 𝜃̃𝑚 for 𝐴 < 𝐴𝐹 𝐵 ) and the optimal sustainability
standard exceeds the minimum standard of the benchmark economy
(compare green line for 𝜃̂𝑠 to blue dotted line for 𝜃̃𝑚 ).
We finally note that the possibility of setting a carbon tax, as
discussed in Appendix B, does not affect the validity of Propositions 5
and 6. Intuitively, when 𝐴 > 𝐴𝐹 𝐵 , first-best welfare can already be
achieved, see Remark 1, so that sustainable finance is not needed. When
sustainable finance is needed, 𝐴 < 𝐴𝐹 𝐵 , the optimal carbon tax would
be zero so that only the minimum standard is used as an environmental
policy tool.

Optimal stringency of the taxonomy. We now characterize the optimal
stringency of the sustainability standard when the taxonomy improves
welfare as 𝜃𝑚 < 𝜃𝐹 𝐵 . This could either be because environmental policy
is inefficiently lax due to environmental policy failures or internal funds
are sufficiently limited.
Proposition 6 (Optimal Stringency of Taxonomy). Suppose that 𝜃𝑚 < 𝜃𝐹 𝐵 ,
so that it is strictly optimal to introduce a sustainable investment category.
Then the optimal threshold, 𝜃̂𝑠 , satisfies
( )
( )
| 𝜕 ln 𝑞 ∗ 𝜃𝑠 |
𝜕 ln 𝑣 𝜃𝑠
|
|
𝑠
=|
(22)
| > 0,
|
|
𝜕 𝜃𝑠
𝜕
𝜃
𝑠
|
|
so that 𝜃𝑚 < 𝜃̂𝑠 < 𝜃𝐹 𝐵 .
Similar to the pricing decision of a monopolist, the optimal calibration of 𝜃̂𝑠 can be expressed in terms of (semi)-elasticities: Ignoring the
( )
effect on the supply of sustainable capital 𝑞𝑠∗ 𝜃𝑠 , it would be optimal
𝜕 ln 𝑣(𝜃𝑠 )
to set
= 0 or equivalently 𝜃̂𝑠 = 𝜃𝐹 𝐵 . However, because the
𝜕 𝜃𝑠

planner additionally needs to account for the downward sloping supply
| 𝜕 ln 𝑞 ∗ (𝜃 ) |
of sustainable capital, i.e., || 𝜕𝜃𝑠 𝑠 || > 0, see Corollary 4, the optimal
𝑠
|
|
choice features 𝑣′ (𝜃̂𝑠 ) > 0, so that 𝜃̂𝑠 < 𝜃𝐹 𝐵 .
Intuitively, investor preferences are a key determinant of the supply
elasticity. As investor preferences become more sustainable, in the
sense of a monotone hazard rate shift in 𝐹 (𝑤), the feedback effect on
supply becomes dampened so that the regulator optimally increases 𝜃̂𝑠 .
We conclude this section with a brief discussion of the properties
of the optimal policy under the joint optimization of 𝜃𝑚 and 𝜃𝑠 . We
denote the respective optimizers as 𝜃̂𝑚 and 𝜃̂𝑠 . Since it is suboptimal
to use the second tool of a sustainable investment classification if
𝐴 ≥ 𝐴𝐹 𝐵 , by Corollary 5, the planner problem is akin to the one in
the benchmark economy (when the planner could only avail herself to
the one tool of the minimum standard). That is, the calibration of the
optimum minimum standard is characterized by Proposition 2 and the
minimum standard is, thus, given by 𝜃̂𝑚 = 𝜃̃𝑚 , (see Fig. 2 for 𝐴 ≥ 𝐴𝐹 𝐵 ).
Preferences for sustainable investing do not affect optimal policy.

4. Concluding remarks
Greenwashing is regularly mentioned as one of the key impediments
for impact of sustainable finance. In response, regulators around the
world are in the process of developing taxonomies for sustainable
(or ESG) investment products. We show that a regulatory standard in
the form of a taxonomy is necessary to prevent such a “race to the
bottom” and is, hence, instrumental to ensure a greenium and impact of sustainable finance in the presence of empirically documented
preferences for sustainability. However, is it beneficial to introduce a
classification for sustainable investments when a social planner can
optimally choose more direct policy instruments, such as a minimum
9

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

Declaration of competing interest

standard or Pigouvian taxes? The answer is non-trivial as the planner
in our model only cares about real effects, but not directly about the
warm glow that households experience when investing sustainably.
Our normative paper highlights two frictions that justify a public
intervention in the form of taxonomy. First and intuitively, if policy
failures render environmental regulation to be too lax, as e.g., argued
by Tirole (2012), a taxonomy can help to partially mitigate underinvestment in sustainability. Second, there is a role for harnessing
“sustainable capital” even if traditional environmental tools can be
optimally chosen, but this requires financial frictions to prevent the
economy from running at the socially efficient scale when the socially
desirable minimum standard or tax on externalities is set. In this
case, the sustainable investment classification adds a valuable second
instrument that mitigates the trade-off between achieving higher sustainability for production and generating an inefficient contraction of
economic activity.
Our analysis has normative implications for optimal policy across
countries. Economies with higher financial development, for which financial constraints are less relevant, should have stricter environmental
regulation. Then, there is no role for the introduction of a sustainable
investments category unless environmental policy is too lax. In contrast,
for economies with poorer financial development, binding financial
constraints imply a welfare-enhancing role for sustainable finance even
under optimal environmental policy as subsidies are required to finance
the transition.
Empirical researchers could calibrate a structural model to gauge
whether the two highlighted frictions, financial frictions and environmental policy failure, are sufficiently important in the data to warrant
an intervention via financial regulation. An important first step is to
determine the welfare-optimal environmental policy, which, e.g., incorporates measures of the social cost of carbon (Rennert et al., 2022).
Determining such optimal environmental policy (e.g., the size of the
carbon tax) is complex as it needs to account for international leakage,
i.e., shifting of production to other jurisdictions. One interesting aspect
is that while environmental regulation is limited to apply within a jurisdiction,34 the taxonomy for investments could be, in principle, extended
to firms outside of the jurisdiction (e.g., a European ESG fund could
subsidize a Chinese firm). Moreover, while our qualitative model abstracts, for ease of exposition, from firm or industry heterogeneity, such
a quantitative exercise should account for cross-sectional differences in
the relevance of financial constraints, as e.g., documented by FarreMensa et al. (2022). We believe that such a calibration exercise is
relevant, both from a research and a policy perspective.
More generally, our paper has analyzed the role of financial regulation for supporting a sustainable transition. We focused on one
particular tool, a taxonomy for sustainable investments. Other regulatory initiatives are ongoing, e.g., green monetary policy as studied
in Papoutsi et al. (2021), or green capital requirements as studied
in Oehmke and Opp (2022). The analysis of which (combination of)
tools is most impactful is an interesting question for future empirical
and theoretical research. The results of this paper suggest that financial
regulation is only part of the optimal policy mix if “finance” is the root
of the problem. Put differently, absent frictions in the financial sector,
environmental regulation should be at the top of the regulatory pecking
order.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Marcus Matthias Opp reports that financial support was provided by
the Marianne and Marcus Wallenberg Foundation (Project number:
2021.0122) and Jan Wallanders och Tom Hedelius stiftelse samt Tore
Browaldhs stiftelse (Project number: Fh23-0015). Roman Inderst reports that financial support was provided by the German Research
Foundation (DFG) and European Research Council (ERC).
Appendix A. Proofs
( )
Proof of Proposition 1. If 𝑐 𝜃𝑚 > 𝑃 (0), the production cost associated with the environmental minimum standard is so high that
profitable production is not even possible at the highest product price
𝑃 (0). Hence, no firm produces, so that aggregate output satisfies 𝑞 ∗ = 0.
( )
We now turn to the relevant case when 𝑃 (0) > 𝑐 𝜃𝑚 . We first want
to show that aggregate output satisfies 𝑞min < 𝑞 ∗ ≤ 𝑞̄ where 𝑞̄ denotes
the zero-profit output and 𝑞min is the output that can be produced as
internal funds 𝐴 approach zero, i.e.,
{
( )
𝐵
( 0 ( )) if 𝑃 (0) ≤ 𝛥𝑝 + 𝑐 (𝜃𝑚 ) .
(A.1)
𝑞min =
𝐵
𝐵
+ 𝑐 𝜃𝑚
𝑃 −1 𝛥𝑝
𝑃 (0) > 𝛥𝑝
+ 𝑐 𝜃𝑚
The lower bound follows from the fact that as long as 𝑃 (𝑞) >

( )
𝐵
+ 𝑐 𝜃𝑚 each individual firm’s borrowing constraint would not bind,
𝛥𝑝
see (IC) and (IR). The upper bound 𝑞̄ follows from the fact that for any
𝑞 > 𝑞̄ firms would earn a lower return than their outside option 𝑟0 = 0.
We now turn to the question whether output 𝑞̄ is feasible in the
presence of financial constraints. Suppose that aggregate output is at
.
𝑞,
̄ then the associated output capacity multiplier in (7) is 𝑘∗ = 𝛥𝑝
𝐵
Each individual firm takes this multiplier as given. We now distinguish
between two cases.
Case 1) If 𝐴 < 𝑞̄𝐵∕𝛥𝑝, then even if all firms were to lever up to the
), aggregate output
maximum (using the candidate multiplier 𝑘∗ = 𝛥𝑝
𝐵
of 𝑞̄ would not be feasible. Hence, 𝑞 ∗ is the unique solution to
𝑞 = 𝐴𝑘 (𝑞) .
Uniqueness follows from the fact that 𝑘 (𝑞) is strictly decreasing and
(
)
continuous in 𝑞 and 𝐴𝑘 𝑞min > 0.
Case 2) If 𝐴 ≥ 𝑞̄𝐵∕𝛥𝑝, it is feasible to produce aggregate output of
𝑞.
̄ In this case, at 𝑞 ∗ = 𝑞̄ firms are indifferent between investing and the
storage technology.
■

Lemma A.1 (No Shirking). A sufficient condition to rule out shirking in
equilibrium is:
(
)
( )
(
) 𝑃 𝑞min − 𝑐 𝜃𝑚
𝐵
< 𝑃 𝑞min −
,
(A.2)
𝛥𝑝
𝛥𝑝
where 𝑞min is given by (A.1).
Proof of Lemma A.1. Suppose the entrepreneur shirks in equilibrium,
then one only needs to consider the investors’ IR constraint:
( )
(IR∗ )
(1 − 𝛥𝑝) 𝐷𝑖 ≥ 𝑐 𝜃𝑚 𝑞𝑖 − 𝐴𝑖 .

CRediT authorship contribution statement

Binding (IR∗ ) now implies that the face value of debt is set to35 :
( )
𝑐 𝜃𝑚 𝑞𝑖 − 𝐴
𝐷𝑖 =
.
(A.3)
1 − 𝛥𝑝

Roman Inderst: Formal analysis, Writing. Marcus M. Opp: Formal
analysis, Writing.

35
Because the manager is protected by limited liability, i.e., 𝐷𝑖 ≤ 𝑃 (𝑞), there
may be an upper bound on the feasible quantity 𝑞𝑖 , but this is irrelevant for
our argument.

34

A Carbon-Border-Adjustment-Tax can mitigate such carbon leakage for
imported goods.
10

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

Then, the manager’s payoff, including the payoff from the storage
)
(
technology 𝐴 − 𝐴𝑖 , is:
]
[
( )
𝑐 𝜃𝑚 𝑞𝑖 − 𝐴𝑖
(
)
𝑈𝑖 = (1 − 𝛥𝑝) 𝑞𝑖 𝑃 (𝑞) −
+ 𝐵 𝑞𝑖 + 𝐴 − 𝐴𝑖
1 − 𝛥𝑝
[
]
( )
= 𝑞𝑖 (1 − 𝛥𝑝) 𝑃 (𝑞) − 𝑐 𝜃𝑚 + 𝐵 + 𝐴.
( )
If (A.2) holds, then (1 − 𝛥𝑝) 𝑃 (𝑞) − 𝑐 𝜃𝑚 + 𝐵 < 0 irrespective of
the product price 𝑃 (since 𝑃 is highest for 𝑞min ). As a result, the entrepreneur’s utility would be below the payoff received from investing
in the storage technology, 𝑈𝑖 < 𝐴, whenever 𝑞𝑖 > 0. Therefore, (A.2)
rules out shirking in equilibrium.
■
Proof of Corollary 1. We distinguish based on whether aggregate
output is constrained by financial frictions. If output is unconstrained,
( )
then 𝑃 (𝑞 ∗ ) = 𝑐 𝜃𝑚 , see (9). An increase in 𝐴 has no effect on 𝑞 ∗ . An
( )
increase in 𝜃𝑚 and concomitant increase in 𝑐 𝜃𝑚 decreases aggregate
∗
′
output 𝑞 because 𝑃 (𝑞) < 0.
Suppose next that aggregate output is constrained by financial frictions. Then, Proposition 1 implies that 𝑞 ∗ is determined from 𝐴𝑘 (𝑞) = 𝑞,
(
[
( )])−1
𝐵
where 𝑘 (𝑞) = 𝛥𝑝
− 𝑃 (𝑞) − 𝑐 𝜃𝑚
. Using the implicit function
theorem, we obtain that
𝑘 (𝑞)
𝜕𝑞∗
=
> 0,
(A.4)
𝜕𝐴
1 − 𝐴𝑘′ (𝑞)

(
)
Fig. A.3. Discontinuity of policy function. The black graph plots welfare 𝛺 𝜃𝑚 || 𝐴
̄
as a function of the minimum standard 𝜃𝑚 conditional on internal funds 𝐴 = 𝐴 for which
the planner is indifferent between causing financial constraints or not. The function has
two global maxima. The red dashed line plots the welfare function in the absence of
financial constraints, i.e., internal funds approaching infinity.

where the sign follows from 𝑘′ (𝑞) < 0 (so that the denominator is
positive) and 𝑘 (𝑞) > 0. Analogously, we obtain
𝐴 𝜕𝜕𝑘(𝑞)
𝜃𝑚
𝜕𝑞∗
=
< 0,
𝜕 𝜃𝑚
1 − 𝐴𝑘′ (𝑞)

characterized by the fixed point (10), from which 𝑞 ∗ is [a continuous,]
(
) 𝐵
strictly increasing function of 𝐴 over the domain 𝐴 ∈ 0, 𝑞̄ 𝜃𝐹 𝐵 𝛥𝑝
[
(
) (
)]
with range 𝑞min 𝜃𝐹 𝐵 , 𝑞̄ 𝜃𝐹 𝐵 . Note that we have made explicit the
dependency on 𝜃𝐹 𝐵 also for 𝑞min , as defined in (A.1). Given continuity
(
)
and strict monotonicity as well as 𝑞̄ 𝜃𝐹 𝐵 > 𝑞𝐹 𝐵 , it thus suffices that
(
)
(
)
𝑞min 𝜃𝐹 𝐵 < 𝑞𝐹 𝐵 = 𝑃 −1 𝑐(𝜃𝐹 𝐵 ) + 𝜌(𝜃 max − 𝜃𝐹 𝐵 ) . If 𝑞min = 0, the result
is immediate since first-best output 𝑞𝐹 𝐵 is by
(A1) positive.
( Assumption
(
) 𝐵)
If the minimum output satisfies 𝑞min = 𝑃 −1 𝑐 𝜃𝐹 𝐵 + 𝛥𝑝
, then 𝑞min <

(A.5)

< 0, follows from
where the negative sign of the numerator, 𝜕𝜕𝑘(𝑞)
𝜃𝑚
( )
𝑐 ′ 𝜃𝑚
𝜕 𝑘 (𝑞)
= −(
< 0.
[
( )])2
𝜕 𝜃𝑚
𝐵
− 𝑃 (𝑞) − 𝑐 𝜃𝑚
𝛥𝑝

𝐵
𝑞𝐹 𝐵 if and only if 𝛥𝑝
> 𝜌(𝜃 max − 𝜃𝐹 𝐵 ), which is condition (14).
Suppose now that, at the optimally chosen minimum standard,
aggregate output is constrained by financial frictions. Consider the
first-order condition (13) and notably the term
( )
( )
(
)
𝐺 = 𝑃 𝑞 ∗ − 𝑐 𝜃𝑚 − 𝜌 𝜃 max − 𝜃𝑚 ,
(A.6)

■
( )
𝐵
Proof of Corollary 2. If 𝑃 (0) ≤ 𝛥𝑝
+ 𝑐 𝜃𝑚 the result is immediate.
Otherwise, the proof of Proposition 1 implies that for any 𝐴 > 0,
(
]
(
)
aggregate output satisfies 𝑞 ∗ > 𝑞min so that 𝑞 ∗ ∈ 𝑞min , 𝑞̄ with 𝑃 𝑞min =
( )
( )
𝐵
+ 𝑐 𝜃𝑚 and 𝑃 (𝑞)
̄ = 𝑐 𝜃𝑚 . Hence, for any 𝐴 > 0, we obtain that
𝛥𝑝
(
)
( )
𝑃 (𝑞 ∗ ) < 𝑃 𝑞min = 𝐵∕𝛥𝑝 + 𝑐 𝜃𝑚 . Therefore, the capacity multiplier is
finite.
We now turn to the rents. If 𝐴 ≥ 𝑞̄𝐵∕𝛥𝑝, equilibrium output satisfies
( )
𝑞 ∗ = 𝑞̄ and 𝑃 (𝑞 ∗ ) = 𝑐 𝜃𝑚 . The firm is then indifferent between
investing its own funds productively or using the storage technology,
so that 𝑈𝑖∗ = 𝐴. This follows from inserting the equilibrium multiplier
𝑘∗ = 𝛥𝑝
into 𝑈𝑖∗ in (8).
𝐵
If 𝐴 < 𝑞̄𝐵∕𝛥𝑝, equilibrium output satisfies 𝑞 ∗ < 𝑞̄ so that a firm
would strictly prefer to expand output. Strictly positive firm rents,
𝑈𝑖∗ > 𝐴, follow from inserting the equilibrium multiplier 𝑘∗ > 𝛥𝑝
into
𝐵
𝑈𝑖∗ in (8).
■

which is zero at first-best and 𝐴 = 𝐴𝐹 𝐵 . We prove now by contradiction
that when 𝐴 > 𝐴𝐹 𝐵 , then 𝜃̃𝑚 > 𝜃𝐹 𝐵 . Assume thus that 𝐴 > 𝐴𝐹 𝐵 but
( )
𝜃̃𝑚 ≤ 𝜃𝐹 𝐵 . Then, from 𝜌 − 𝑐 ′ 𝜃̃𝑚 ≥ 0, the first-order condition requires
that 𝐺 ≥ 0. But compared to 𝐴 = 𝐴𝐹 𝐵 and 𝜃𝐹 𝐵 , now 𝑞 ∗ > 𝑞𝐹 𝐵 so that
( ) (
)
𝑃 (𝑞 ∗ ) is strictly lower, while 𝑐 𝜃𝑚 +𝜌 𝜃 max − 𝜃𝑚 is weakly higher (and
strictly so if 𝜃̃𝑚 < 𝜃𝐹 𝐵 ). This together implies 𝐺 < 0, a contradiction.
The case where 𝐴 < 𝐴𝐹 𝐵 and now 𝜃̃𝑚 < 𝜃𝐹 𝐵 is analogous.
If instead, at the optimal standard, aggregate output is not con( )
(
)
strained, 𝑞 ∗ = 𝑞̄ 𝜃𝑚 , 𝐺 = −𝜌 𝜃 max − 𝜃𝑚 is always negative, so that
at the optimum 𝜃̃𝑚 > 𝜃𝐹 𝐵 .
This concludes the proof. We additionally shed light on the discontinuity of the policy function in Fig. 1.
Let 𝐴̄ denote the value of 𝐴 for which the planner is indifferent
between setting a low value of the minimum standard lim𝐴→𝐴̄ − 𝜃̃𝑚 (so
that financial constraints constrain output 𝑞 ∗ < 𝑞)
̄ or setting a high
value of the minimum standard 𝜃̄𝑚 so that aggregate output is not
( )
constrained by financial constraints and given by 𝑞 ∗ = 𝑞̄ 𝜃̄𝑚 . (Recall
that 𝑞̄ is a strictly decreasing function of 𝜃𝑚 ). Formally, the objective
(
)
function 𝛺 𝜃𝑚 || 𝐴 has two global maxima for 𝐴 = 𝐴̄ (see Fig. A.3).

Proof of Proposition 2. Recall that first-best requires that all firms
choose the sustainability level 𝜃𝐹 𝐵 and aggregate output be at 𝑞𝐹 𝐵 .
The sustainability choice of 𝜃𝐹 𝐵 can only be ensured by setting the
minimum standard to 𝜃𝑚 = 𝜃𝐹 𝐵 . If output is unconstrained by financial
frictions and 𝜃𝑚 = 𝜃𝐹 𝐵 , it is immediate from the then prevailing zeroprofit condition, 𝑃 (𝑞 ∗ = 𝑞)
̄ = 𝑐(𝜃𝐹 𝐵 ), that output is socially excessive,
𝑞 ∗ > 𝑞𝐹 𝐵 . It is thus necessary that aggregate output be constrained by
financial frictions to achieve first-best. [
(
) 𝐵]
We now prove that for some 𝐴 ∈ 0, 𝑞̄ 𝜃𝐹 𝐵 𝛥𝑝
first-best can

Proof of Lemma 1. See main text.

𝐵
be achieved as long as 𝛥𝑝
≥ 𝜌(𝜃 max − 𝜃𝐹 𝐵 ), i.e., Condition (14)
holds. By Proposition 1, where we now set 𝜃𝑚 = 𝜃𝐹 𝐵 , output is

■

Proof of Proposition 3. To provide 𝑞𝑠∗ units of sustainable output,
( )
each firm demands 𝑐 𝜃𝑠 𝐴𝑘∗ − 𝐴 of capital from outside investors
11

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

while coinvesting 𝐴. Given 𝛥𝑟∗ , the total volume of supplied sustainable
capital is 𝐾 (1 − 𝐹 (𝛥𝑟∗ )). The equalization of demand and supply in
equilibrium thus implies that
( )
(
( ))
𝑐 𝜃𝑠 𝐴𝑘∗ − 𝐴 = 𝐾 1 − 𝐹 𝛥𝑟∗

If 𝜃𝑚 < 𝜃𝐹 𝐵 , the first-order condition for 𝜃𝑠 is given by
𝜕 𝑞𝑠∗ ( )
( ) ( )
𝑣 𝜃𝑠 + 𝑞𝑠∗ 𝜃𝑠 𝑣′ 𝜃𝑠 = 0,
𝜕 𝜃𝑠

𝜕𝑞∗

which can be transformed to obtain (22) in Proposition 6, where 𝜕 𝜃𝑠 <
𝑠
( )
0 follows from Corollary 4. As a result 𝑣′ 𝜃̂𝑠 > 0 at the optimum so
( )
that 𝜃̂𝑠 < 𝜃𝐹 𝐵 . Moreover, 𝜃̂𝑠 > 𝜃𝑚 so that 𝑣 𝜃̂𝑠 > 0.

Solving for 𝐴 yields the aggregate amount of internal funds provided
by all sustainable firms in equilibrium,
𝐾 (1 − 𝐹 (𝛥𝑟∗ ))
.
𝐴𝑠 =
( )
𝑐 𝜃𝑠 𝑘∗ − 1
Therefore, sustainable output, 𝑞𝑠∗ = 𝐴𝑠 𝑘∗ , is given by
(
( ))
𝑘∗
𝑞𝑠∗ = 𝐾 1 − 𝐹 𝛥𝑟∗
,
( )
𝑐 𝜃𝑠 𝑘∗ − 1

We now characterize the optimal choice of 𝜃𝑚 . Let 𝐶 ∶= (1 − 𝜔)
[ ( )
]
[ ( )
]
𝑐 𝜃𝑚 + 𝜌(𝜃 max − 𝜃𝑚 ) + 𝜔 𝑐 𝜃𝑠 + 𝜌(𝜃 max − 𝜃𝑠 ) denote the weighted
average social cost of production (including externalities). Then, the
first-order condition of (20) with respect to the minimum standard can
be stated as:

(A.7)

−

which restates (18). Since aggregate output is given by 𝑞 ∗ = min
{𝑞̄, 𝐴𝑘∗ } (by Proposition 1 , respectively Lemma 1) and total sustainable
output is given by (18), the ratio is given by (19).
The condition on the short supply of sustainable capital requires that
𝜔∗ < 1, i.e.,
{
}
(
( ))
𝑘∗
< min 𝑞̄, 𝐴𝑘∗ ,
𝐾 1 − 𝐹 𝛥𝑟∗
( )
𝑐 𝜃𝑠 𝑘∗ − 1

( )
𝑑 𝑞 ∗ 𝜃𝑚 [
𝑑 𝜃𝑚

( )
𝜕 𝜔∗ 𝜃𝑚 ( )
]
[
( )]
𝑃 (𝑞 ∗ ) − 𝐶 = 𝑞 ∗ (1 − 𝜔) 𝜌 − 𝑐 ′ 𝜃𝑚 + 𝑞 ∗
𝑣 𝜃𝑠 .
𝜕 𝜃𝑚

(A.11)

■
Proof of Corollary 5. As the social planner can now avail herself
of both instruments, her program is to choose 𝜃𝑚 and potentially a
sustainable investment category with threshold 𝜃𝑠 > 𝜃𝑚 so as to
maximize 𝛺 in (12). The optimal outcome is denoted by (𝜃̂𝑚 , 𝜃̂𝑠 ). We
note first that the derivative with respect to 𝜃𝑠 is identical to that in
the partial problem of Proposition 5, where we took 𝜃𝑚 as given. It
is thus strictly optimal to introduce a sustainable investment category
𝜃̂𝑠 > 𝜃̂𝑚 if 𝜃̂𝑚 > 𝜃𝐹 𝐵 and strictly suboptimal otherwise. It thus remains to
show that, also in the presence of both potential instruments, 𝜃̂𝑚 ≥ 𝜃𝐹 𝐵
(𝜃̂𝑚 < 𝜃𝐹 𝐵 ) if 𝐴 ≥ 𝐴𝐹 𝐵 (𝐴 < 𝐴𝐹 𝐵 ). We show this by contradiction.
Suppose that 𝐴 < 𝐴𝐹 𝐵 and suppose, instead that 𝜃̂𝑚 ≥ 𝜃𝐹 𝐵 . Then,
it would not be optimal to introduce a sustainable investment category
with 𝜃̂𝑠 > 𝜃̂𝑚 , in which case we know however from Proposition 2 that
𝜃̂𝑚 = 𝜃̃𝑚 < 𝜃𝐹 𝐵 , a contradiction.
For 𝐴 = 𝐴𝐹 𝐵 the argument is immediate as 𝜃̂𝑚 ≥ 𝜃𝐹 𝐵 achieves the
first best, while 𝛺 is strictly lower for any choice 𝜃̂𝑚 < 𝜃𝐹 𝐵 , irrespective
of the choice of 𝜃𝑠 .
Turning finally to 𝐴 > 𝐴𝐹 𝐵 , suppose that 𝜃̂𝑚 < 𝜃𝐹 𝐵 , in which case
it would be optimal to choose a threshold 𝜃̂𝑚 < 𝜃̂𝑠 < 𝜃𝐹 𝐵 . To show that
this is not optimal, it is sufficient to argue that welfare is strictly higher
by setting instead 𝜃𝑚 = 𝜃̂𝑠 , without a sustainable investment category.
̃
Denote the thereby realized value by 𝛺,

which is always satisfied if the amount of capital owned by investors
with sustainability preferences, 𝐾, is sufficiently small.
We now adapt Lemma A.1 to account for investors with sustainability preferences. A sufficient condition to rule out shirking in equilibrium is:
(
)
[{ ( )
( )}]
̄ 𝑐 𝜃𝑚
(
) 𝑃 𝑞min − min 𝑐 𝜃𝑠 (1 − 𝑤),
𝐵
< 𝑃 𝑞min −
.
(A.8)
𝛥𝑝
𝛥𝑝
This can be derived by the same steps as in the proof of Lemma A.1,
taking into account that a shirking firm can now also become sustainable. To take
( ) this into account, we generally
( )denote the firm’s interest
rate by 𝑟 𝜃𝑖 and its production cost by 𝑐 𝜃𝑖 , so that a shirking firm’s
payoff now reads as follows:
[
( )
( )
]
( )
𝑈𝑖 = 𝑞𝑖 (1 − 𝛥𝑝) 𝑃 (𝑞) − 𝑐 𝜃𝑖 (1 + 𝑟 𝜃𝑖 ) + 𝐵 + 𝐴𝑖 𝑟 𝜃𝑖 + 𝐴.
( )
( )
If (A.8) holds, then (1 − 𝛥𝑝) 𝑃 (𝑞) − 𝑐 𝜃𝑖 𝑞𝑖 (1 + 𝑟 𝜃𝑖 ) + 𝐵 < 0 holds
now
at cost
( )also regardless
( ) of whether the firm produces(unsustainably
)
𝑐 𝜃𝑚 with 𝑟 𝜃𝑚 = 0 or sustainably at cost 𝑐 𝜃𝑠 with the highest
̄
financing subsidy 𝑤.
■

̃=
𝛺

The invariance of 𝛥𝑟∗ follows from (17). Equi-

Proof of Corollary 3.
librium output 𝑞 ∗ and, hence, the multiplier 𝑘∗ are also unaffected by
𝐹 (𝑤) as a result of Proposition 1. A first-order stochastic dominance
shift of the distribution 𝐹 (𝑤) must now decrease 𝐹 (𝛥𝑟∗ ) and, hence
increases 𝑞𝑠∗ . The same holds for an increase in 𝐾. ■

𝑞 ∗ (𝜃̂𝑠 )

∫0

[ ( )
]
𝑃 (𝑞)𝑑 𝑞 − 𝜌𝑞 ∗ (𝜃̂𝑠 ) 𝑐 𝜃̂𝑠 + 𝜌(𝜃 max − 𝜃̂𝑠 ) ,

̃ − 𝛺,
where we have set 𝜃𝑚 = 𝜃̂𝑠 . Calculating now the difference 𝛺
this can be decomposed as follows: first, while quantity 𝑞𝑠∗ is produced
with standard 𝜃̂𝑠 , quantity 𝑞 ∗ (𝜃̂𝑠 ) − 𝑞𝑠∗ is now produced with standard
𝜃𝑚 = 𝜃̂𝑠 and no longer with the supposedly optimal minimum standard
𝜃̂𝑚 ; second, total output is reduced from 𝑞 ∗ (𝜃̂𝑚 ) to 𝑞 ∗ (𝜃̂𝑠 ). With this
̃ − 𝛺 = 𝛥1 + 𝛥2 , where
decomposition we have 𝛺
( )]]
( ∗
)
[
[ ( )
𝛥1 = 𝑞 (𝜃̂𝑠 ) − 𝑞𝑠∗ 𝜌(𝜃̂𝑠 − 𝜃̂𝑚 ) − 𝑐 𝜃̂𝑠 − 𝑐 𝜃̂𝑚 ,

Proof of Corollary 4. We first prove the effect on 𝛥𝑟∗ . An increase
∗
in 𝜃𝑠 increases 𝛥𝑐. Differentiating (17) implies that 𝜕𝜕𝛥𝑟
> 0, because
𝛥𝑐
𝐵
𝑃 (𝑞 ∗ ) − 𝛥𝑝
> 0, which follows from (IC). Thus, from (18) 𝑞𝑠∗ decreases
̄
with 𝛥𝑐 (and thus 𝜃𝑠 ), so that 𝜔∗ in (19) decreases as well. If 𝛥𝑟∗ > 𝑤,
even an investor with the highest warm glow 𝑤̄ would not invest in
sustainable firms, so that no firm would be able to get financing for
producing sustainably.
■
Proof of Proposition 4. See main text.

(A.10)

which is strictly positive from 𝜃̂𝑚 < 𝜃̂𝑠 < 𝜃𝐹 𝐵 , and
𝑞∗ [
[ ( )
]]
𝛥2 = −
𝑃 (𝑞) − 𝑐 𝜃̂𝑚 + 𝜌(𝜃 max − 𝜃̂𝑚 ) 𝑑 𝑞 ,
∫𝑞 ∗ (𝜃̂𝑠 )
which is strictly positive when, at the lower boundary,
[ ( )
]
𝑃 (𝑞 ∗ (𝜃̂𝑠 )) − 𝑐 𝜃̂𝑚 + 𝜌(𝜃 max − 𝜃̂𝑚 ) < 0.

■

This follows by construction, as with 𝐴 > 𝐴𝐹 𝐵 the marginal social
return is negative at least for all 𝜃𝑚 ≤ 𝜃𝐹 𝐵 , and thus also for 𝜃𝑚 =
𝜃̂𝑠 < 𝜃𝐹 𝐵 and the corresponding quantity 𝑞 ∗ (𝜃̂𝑠 ). ■

Proof of Propositions 5 and 6. We first consider the optimal choice
of 𝜃𝑠 . The social planner’s objective function in (20) reduces to that of
maximizing
( ) ( )
𝑞𝑠∗ 𝜃𝑠 𝑣 𝜃𝑠 ,
(A.9)
( )
where 𝑣 𝜃𝑠 is given by((21).
) Proposition 5 follows immediately from
the observation that 𝑣′ 𝜃𝑠 is strictly positive for all 𝜃𝑠 < 𝜃𝐹 𝐵 and
strictly negative for all 𝜃𝑠 > 𝜃𝐹 𝐵 .

Proof of Corollary 6. We prove that 𝐴𝐹 𝐵 is strictly increasing in
𝐵
the severity of the agency problem, 𝜉 = 𝛥𝑝
. For this recall the definition of 𝐴𝐹 𝐵 from the proof of Proposition 2, which requires that
(
)
𝐺 𝜃𝐹 𝐵 , 𝐴𝐹 𝐵 = 0, where we use the definition of the term 𝐺 in (A.6)
and make explicit the dependency on internal funds, while substituting
12

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

so that 𝑞 ∗ = 𝑞𝐹 𝐵 . Define next 𝐴𝐶 𝑇 = 𝑞𝐹 𝐵 𝐵∕𝛥𝑝, where 𝜏(𝐴𝐶 𝑇 ) = 𝜌.
Observe that there 𝑞 ∗ is also obtained from the now modified zeroprofit output condition for 𝑞,
̄ 𝑃 (𝑞𝐹 𝐵 ) = 𝑐̃(𝜃𝐹 𝐵 ). Consequently, as we
leave 𝜏 = 𝜌 unchanged for all 𝐴 ≥ 𝐴𝐶 𝑇 the first best is obtained so that
𝑞 ∗ = 𝑞̄ = 𝑞𝐹 𝐵 (and financial constraints do not bind).
Finally if (14) does not hold, the only difference is that the planner
needs to set a positive tax for all levels of 𝐴. This tax is still given by
(B.12). ■

first-best for the optimally chosen standard. From this we thus have
that
∗

𝑃 ′ (𝑞 ∗ ) 𝑑𝑑𝑞𝜉
𝑑 𝐴𝐹 𝐵
𝑑 𝑞 ∗ ∕𝑑 𝜉
=−
=− ∗
> 0,
𝑑 𝑞∗
′
∗
𝑑𝜉
𝑑
𝑞 ∕𝑑 𝐴
𝑃 (𝑞 )
𝑑𝐴

∗

which uses that 𝑑𝑑𝑞𝐴 > 0 and 𝑑 𝑞 ∗ ∕𝑑 𝜉 < 0 under constrained output
(using Eq. (10) in Proposition 1, 𝑞 ∗ = 𝐴𝑘(𝑞 ∗ )).
■
Appendix B. Pigouvian tax

Incidentally, our results would need to be slightly adjusted when
the planner could only use a carbon tax, but not a minimum standard.
Intuitively, as the tax reduces firms’ financial resources, a carbon tax
alone could achieve first best only if financial constraints are less
pronounced. Formally, a carbon tax achieves first best if and only if
𝐴 ≥ 𝐴𝐶 𝑇 .

In this section, we show robustness of our main results to a more
general environmental policy. In particular, we allow the regulator to
also impose a tax 𝜏 ≥ 0 per unit of externality (so that the standard
Pigouvian tax level would be 𝜏 = 𝜌). For the purpose of this extension
only, denote the thus adjusted marginal costs of production, now
including taxes on externalities, by 𝑐̃(𝜃𝑖 ) = 𝑐(𝜃𝑖 ) + 𝜏(𝜃 max − 𝜃𝑖 ). Hence,
( )
the firm now needs to raise now the amount 𝑐̃ 𝜃𝑖 𝑞𝑖 − 𝐴, and with
this modification the incentive and participation constraints, (IC) and
(IR) respectively, remain unchanged, as does the characterization of the
firm’s payoff 𝑈𝑖 .
Ignoring the minimum standard, to maximize 𝑈𝑖 the firm would
choose 𝜃𝑖 so as to minimize 𝑐̃(𝜃𝑖 ), 𝑐 ′ (𝜃𝑖 ) = 𝜏. If the respective solution
were above the minimum standard, the latter would be superfluous. On
the other hand, any standard that is implemented by a specific choice
of the tax 𝜏 can be implemented as well by directly imposing this as the
minimum standard. By levying (additionally) a tax, the planner extracts
some of the firm’s funds.
If 𝐴 < 𝐴𝐹 𝐵 , extracting funds from firms is strictly suboptimal, as
this leads to additional reduction in output. Therefore, the planner only
uses the minimum standard as characterized by Proposition 2.36
In contrast, if 𝐴 > 𝐴𝐹 𝐵 , the tax allows the planner to limit overproduction. By calibrating the tax accordingly, this allows to achieve
first-best output, 𝑞 ∗ = 𝑞𝐹 𝐵 , while at the same time setting the minimum
standard to 𝜃𝐹 𝐵 .

Appendix C. Consequentialist preferences and Greenwashing

We now discuss robustness of our results when investor preferences
also care about impact 𝜃𝑠 − 𝜃𝑚 . In particular, we consider preferences
(
)
of the following form: 𝑤 + 𝜂 𝜃𝑠 − 𝜃𝑚 for some bounded
concave)and
(
twice differentiable function 𝜂 with 𝜂 (0) = 0, e.g., 𝜅 1 − 𝑒−(𝜃𝑠 −𝜃𝑚 ) for
some constant 𝜅 > 0. We then obtain the following result:
Lemma C.1 (Robustness of Greenwashing). If the marginal utility from
𝐵
𝑃 (𝑞 ∗ )− 𝛥𝑝
(
)
( )
′
impact is sufficiently small, 𝜂 ′ 𝜃𝑠 − 𝜃𝑚 < (
)2 𝑐 𝜃𝑠 for all 𝜃𝑠 ,
𝐵
𝑃 (𝑞 ∗ )− 𝛥𝑝
+𝛥𝑐

the market equilibrium features greenwashing.

Proof of Lemma C.1. A “greenwashing” fund with 𝜃𝑠 = 𝜃𝑚 will
generate utility 𝑤 to the investor. Suppose another fund offered an
“impact” fund requiring all firms to meet the threshold 𝜃𝑠 > 𝜃𝑚 . Then,
firm indifference would require a financing subsidy of
( )
𝛥𝑐
𝛥𝑟∗ 𝜃𝑠 =
.
𝐵
∗
𝑃 (𝑞 ) − 𝛥𝑝
+ 𝛥𝑐

Proposition 7 (Minimum Standard and Carbon Tax). Suppose now the
planner can use both a minimum standard and a carbon tax. If condition
holds (14) and 𝐴 < 𝐴𝐹 𝐵 , first-best welfare cannot be attained. The optimal
carbon tax is zero and the optimal minimum standard and output are
characterized by Propositions 1 and 2. Otherwise, first best can be achieved.
If 𝐴 > 𝐴𝐹 𝐵 holds strictly, achieving first-best requires a positive tax 𝜏 > 0
next to the first-best standard 𝜃𝑚 = 𝜃𝐹 𝐵 .

Hence, investors in this impact fund would get a net utility of 𝑤 −
( )
𝛥𝑟∗ 𝜃𝑠 + 𝜂(𝛥𝜃). By optimality of investor choices, such a fund is viable
(
)
( )
in the market if and only if 𝜂 𝜃𝑠 − 𝜃𝑚 − 𝛥𝑟∗ 𝜃𝑠 > 0 for some 𝜃𝑠 > 𝜃𝑚 .
𝐵
∗
𝑃 (𝑞 )− 𝛥𝑝
(
)
( )
(
)
′
However, if 𝜂 ′ 𝜃𝑠 − 𝜃𝑚 < (
)2 𝑐 𝜃𝑠 , the term 𝜂 𝜃𝑠 − 𝜃𝑚 −
𝑃 (𝑞 ∗ )− 𝐵 +𝛥𝑐

𝛥𝑝
( )
𝛥𝑟∗ 𝜃𝑠 is strictly negative for all 𝜃𝑠 > 𝜃𝑚 . Hence, greenwashing is the
only possible market equilibrium.
■

Proof of Proposition 7. If (14) holds and 𝐴 ≤ 𝐴𝐹 𝐵 , the characterization follows immediately from the argument in the main text and from
Proposition 2.
We now consider the case 𝐴 > 𝐴𝐹 𝐵 . We now characterize the
optimal tax 𝜏 > 0 which, together with 𝜃𝑚 = 𝜃𝐹 𝐵 , ensures the socially
optimal output 𝑞 ∗ = 𝑞𝐹 𝐵 .
For this suppose first that (14) holds. We write out explicitly the
(implicit) characterization of 𝑞 ∗ when financial constraints bind, but
using now costs 𝑐̃(𝜃𝑖 ) = 𝑐(𝜃𝑖 ) + 𝜏(𝜃 max − 𝜃𝑖 ). When 𝜃𝑚 = 𝜃𝐹 𝐵 and 𝑞 ∗ = 𝑞𝐹 𝐵
is achieved, it thus must hold that
1
𝑞𝐹 𝐵 = 𝐴 𝐵 [ (
(B.12)
)
(
)
].
max − 𝜃
−
𝑃
𝑞
−
𝑐
𝜃
𝐹𝐵
𝐹 𝐵 − 𝜏(𝜃
𝐹𝐵)
𝛥𝑝

When Greenwashing arises in equilibrium, see sufficient Condition
in Lemma C.1, a taxonomy is needed to ensure impact. Given some
taxonomy standard 𝜃𝑠 , the critical threshold investor now obtains a
non-pecuniary dividend of
𝑤∗ = 𝛥𝑟∗ − 𝜂(𝜃𝑠 − 𝜃𝑚 ).
Apart from this different cut-off, all of our analysis holds true: First, the
supply of sustainable funds is still given by 𝐾[1 − 𝐹 (𝑤∗ )]; second, 𝑞𝑠∗
is still obtained by applying the derived equity multiplier, so that we
now obtain
(
)
𝑘∗
𝑞𝑠∗ = 𝐾[1 − 𝐹 𝛥𝑟∗ − 𝜂(𝜃𝑠 − 𝜃𝑚 ) ] ( )
.
𝑐 𝜃𝑠 𝑘∗ − 1

Recall that at 𝐴 = 𝐴𝐹 𝐵 this is satisfied when 𝜏 = 0. As the righthand side of (B.12) is continuous and strictly increasing in 𝐴 as well as
strictly decreasing in 𝜏, there exists a strictly increasing function 𝜏(𝐴)

Third, and most importantly, all of our subsequent analysis applies, as
this does not depend on the specific characterization of the cutoff 𝑤∗ .
That is, it is still true that introducing a taxonomy is only valuable if
either environmental policy is sufficiently lax or financial constraints
bind under optimal environmental policy.

36
The minimum standard is equivalent to a tax when tax receipts are
rebated back to firms in lump-sum fashion. Hence, tax rebates do not change
the main result that first-best cannot be achieved for 𝐴 < 𝐴𝐹 𝐵 .

13

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp

Appendix D. Sustainable finance disclosure regulation (SFDR)

Bartram, Söhnke M., Hou, Kewei, Kim, Sehoon, 2022. Real effects of climate policy:
Financial constraints and spillovers. J. Financ. Econ. 143 (2), 668–696.
Berg, Florian, Kölbel, Julian F., Rigobon, Roberto, 2022. Aggregate Confusion: The
Divergence of ESG Ratings. Rev. Finance 26 (6), 1315–1344.
Berk, Jonathan, van Binsbergen, Jules H., 2021. The impact of impact investing. J.
Financ. Econ. (forthcoming).
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of environmental and financial regulation. Working Paper, Erasmus University
Rotterdam and Tilburg University.
Edmans, Alex, Levit, Doron, Schneemeier, Jan, 2022. Socially responsible divestment.
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Finance (forthcoming).
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The European Union’s Sustainable Finance Disclosure Regulation
(SFDR) aims at enhancing sustainability-related disclosure. The regulation is part of the European Commissions’ Action Plan on Sustainable
Finance. It applies to all financial products domiciled in the EU or sold
to EU investors. The SFDR came into force in two steps (December 2019
and, with some delay, January 2023).37
The SFDR sets out three categories of investment products. Products
that meet certain ESG criteria are referred to as Article 8 or Article
9 products. All other products are now referred to as Article 6 products, and it is compulsive to label them as “non-sustainable.” Article
8 products are often referred to as “light green,” as they promote
environmental or social characteristics in the pursuit of other financial
objectives. Article 9 products are often referred to as “dark green,” as
they seek to make a positive impact on society or the environment
through sustainable investment. Hence, a non-financial objective is at
the core of the latter products.
At the heart of the distinction, as well as of the disclosure requirements, is the concept of taxonomy-aligned investments. A financed
economic activity is either taxonomy-aligned or not. Article 9 funds
must ensure that all the companies they invest in are EU taxonomyaligned. Article 8 products must report the fraction of investments
that are taxonomy-aligned. For this, funds need to divide the market
value of taxonomy-aligned investments by the total market value of all
investments. This calculation can rely either on the taxonomy report of
invested companies, or on data gathered directly by the fund. The key
concept of taxonomy-alignment is explained next:
The undertaken, taxonomy-aligned economic activity must have a
substantial positive environmental impact or it must reduce (otherwise
incurred) negative impacts. An eligible economic activity is an economic activity that is described in the regulation and satisfies technical
screening criteria set out in the taxonomy. The taxonomy has technical
screening criteria for over 170 activities (as set out in the Climate Delegated Act and the Environmental Delegated Act) and is evolving. These
activities make a substantial contribution to one or more of the acts’
climate and environmental objectives (climate protection, adaptation to
climate change, sustainable use of water or marine resources, transition
to a circular economy, prevention or control of pollution and protection
and restoration of biodiversity and ecosystems).
For example, electricity generation from wind power is an eligible
activity, while electricity generation from coal is not eligible. Also,
manufacturing of batteries can contribute to climate change mitigation,
and it must be shown that their production and use results in substantial
greenhouse gas emissions reductions.
Eligible economic activities must also not do significant harm to
the other climate and environmental objectives and the respective
undertakings must demonstrate compliance with minimum standards
on human rights, social responsibility, labor rights, and anti-corruption
procedures (as set out in the OECD Guidelines for Multinational Enterprises, the UN Guiding Principles on Business and Human Rights,
the International Labour Organization’s declaration on Fundamental
Rights and Principles at Work and its core conventions, as well as the
International Bill of Human Rights).
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Oxford University.

37
Phase 1 focuses on broad entity-level disclosures around topics such as
the entity’s policies regarding principal adverse sustainability impacts (PASIs)
and related actions. Level 2 focuses on more detailed entity- and product-level
disclosures.

14

Journal of Financial Economics 163 (2025) 103954

R. Inderst and M.M. Opp
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investments. Available at SSRN 4183855.
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Riedl, Arno, Smeets, Paul, 2017. Why do investors hold socially responsible mutual
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pollution. Rev. Financ. Stud. 35 (2), 576–635.

15


==> JFE11 - Biodiversity finance.txt <==
Journal of Financial Economics 164 (2025) 103987

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Biodiversity finance
Caroline Flammer a,b,c,d,* , Thomas Giroux e , Geoffrey M. Heal a,b
a

Columbia University, New York, NY 10027, USA
National Bureau of Economic Research (NBER), Cambridge, MA 02138, USA
c
Centre for Economic Policy Research (CEPR), London EC1V 0DG, UK
d
European Corporate Governance Institute (ECGI), Brussels 1180, Belgium
e
CREST, ENSAE Paris, Institut Polytechnique de Paris, Palaiseau 91764 CEDEX, France
b

A R T I C L E I N F O
Dataset link: Replication package for
"Biodiversity Finance" (Reference data)
Keywords:
Biodiversity finance
Natural capital
Blended finance
Impact investing
Sustainable finance
Public good

A B S T R A C T

We study biodiversity finance—the use of private capital to finance biodiversity conservation and restor­
ation—which is a new practice in sustainable finance. First, we provide a conceptual framework that lays out
how biodiversity can be financed by pure private capital and blended financing structures. In the latter, private
capital is blended with public or philanthropic capital, whose aim is to de-risk private capital investments. The
main element underlying both types of financing is the “monetization” of biodiversity, that is, using investments
in biodiversity to generate a financial return for private investors. Second, we provide empirical evidence using
deal-level data from a leading biodiversity finance institution. Our findings are consistent with a threedimensional efficient frontier (return, risk, and biodiversity impact)—deals with a favorable risk-return profile
tend to be financed by pure private capital, whereas for other deals the biodiversity impact needs to be suffi­
ciently large for blended finance to be used. Overall, our results suggest that blended finance is an important tool
for improving the risk-return profile of these projects, thereby increasing their appeal to private investors and
crowding in private capital. Finally, our results suggest that private capital is unlikely to substitute for effective
public policies in addressing the biodiversity crisis.

1. Introduction
Biodiversity loss is one of the grand challenges our society is facing.
A recent study by the WWF (2022) reports an average 69 % decline in
global populations of mammals, fish, birds, reptiles, and amphibians
since 1970, referring to the current situation as a “code red” alert for
humanity (p. 6). The loss of biodiversity represents an existential threat
to the global economy, as more than half of the world’s GDP is depen­
dent on nature and the services it provides (United Nations, 2022).

Moreover, the climate and biodiversity crises are deeply intertwined.
Meeting the goals of the Paris Climate Agreement depends on the suc­
cessful conservation, restoration, and management of biodiversity
(United Nations, 2022).1 In short, protecting biodiversity is critically
important and urgent—it is important for the planet, our health and
well-being, as well as the world’s economy.
Biodiversity provides many services to humans.2 These include sta­
bilizing the climate, enhancing food supplies, contributing to the
development of medicines, providing recreational value, and

Toni Whited was the editor for this article. We are grateful to the editor, an anonymous reviewer, Andrew Karolyi, Steve Lydenberg, and John Tobin, as well as
seminar participants at Columbia, Cornell, Wharton, Yale, the Federal Reserve Board, Deutsche Bundesbank, ESSEC, Norwegian School of Economics (NHH),
University of Amsterdam, University of Mannheim, University of Zurich, University of Georgia (Terry), University of Pittsburgh (Katz), Dalhousie University, Alliance
Bernstein, Osmosis Investment Management, the Alliance for Research on Corporate Sustainability (ARCS), the ESG and the Future of Business Conference at
Fordham University, the HKU-TLV Summer Finance Forum, and the PRI Academic Seminar Series for helpful comments and suggestions. We thank Yangyang Wang
for excellent research assistance.
* Corresponding author at: Columbia University, New York, NY 10027, USA.
E-mail address: caroline.flammer@columbia.edu (C. Flammer).
1
The importance and urgency of biodiversity conservation is stressed, e.g., by the United Nations’ Biodiversity Finance Initiative (BIOFIN), the Taskforce on
Nature-related Financial Disclosures (TNFD), as well as numerous other organizations and forums such as the Conference of the Parties to the UN Convention on
Biological Diversity (COP 15).
2
Biodiversity is a measure of the variability that exists in “living” natural capital, and hence represents a feature of natural capital. Natural capital can be defined
as “the world’s stocks of natural assets, which include geology, soil, air, water and all living things” (World Forum on Natural Capital, 2021).
https://doi.org/10.1016/j.jfineco.2024.103987
Received 23 November 2023; Received in revised form 8 December 2024; Accepted 11 December 2024
Available online 19 December 2024
0304-405X/© 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

strengthening a person’s spiritual life, among many others. Most of these
services are provided as public goods. That is, their consumption is nonrival, as they are available to everyone in a particular region and those
unwilling to pay cannot be excluded from consuming the public good. A
long-standing literature in public economics shows that the efficient
provision of public goods is challenging, as the free-rider problem, along
with the preference revelation problem, have proven hard to overcome
(e.g., Dasgupta, 2021; Heal, 2000). In a nutshell, the key challenge is
that self-interested individuals prefer to consume the public good
without paying for it, and it is difficult to persuade them to reveal how
much they are willing to pay, as they realize that what they respond will
influence how much they will be required to pay. This free-rider prob­
lem also implies that biodiversity as a public good is likely undervalued
and underprovided. Despite these obstacles, there are frameworks
within which we can hope to mitigate these challenges and enhance
biodiversity protection.
Potential solutions to preserve and restore biodiversity include i)
intergovernmental measures such as the Convention on Biological Di­
versity (CBD) and other global treaties, ii) government measures that aim
to regulate the quantity of natural capital (e.g., by establishing protected
areas, introducing technology standards, or adopting cap-and-trade
programs) and the price of natural capital (e.g., through tax incentives
and subsidies that encourage more sustainable production or con­
sumption patterns), and iii) biodiversity finance, that is, the use of private
capital to finance biodiversity conservation and restoration. While
intergovernmental and governmental mechanisms play an important
role in the public provision of biodiversity (e.g., Barrett, 2022), the
implementation of these mechanisms is not without challenges (e.g.,
Dasgupta, 2021), which calls for other ways to help protect biodiversity.
In this regard, biodiversity finance is gaining momentum in practice
and public policy. Yet, many investors feel underinformed about the
risks and opportunities related to biodiversity (World Economic Forum,
2023). Similarly, academic research on biodiversity finance remains
nearly nonexistent, as highlighted by Karolyi and Tobin-de la Puente’s
(2023) recent call for research in biodiversity finance. As they note,
“there are no studies in the top tier journals in Finance that have framed
the risks related to biodiversity loss, how those risks might be priced, or
how the private financing flows need to be intermediated” (p. 1). This
research gap was further echoed in Laura Starks’ Presidential Address at
the 2023 American Finance Association Meetings (Starks, 2023). It is
likely due to both i) a lack of awareness on how private capital can
contribute to biodiversity conservation and restoration, and ii) a lack of
data on biodiversity finance.
Our study aims to fill this gap by i) introducing a conceptual
framework that lays out how private capital can contribute to biodi­
versity conservation, and ii) providing first evidence on biodiversity
finance. In doing so, we aim to lay the ground and stimulate future
research on biodiversity finance.
First, our conceptual framework lays out how biodiversity conser­
vation can be financed by (i) pure private capital and (ii) blended
finance. In the latter, private capital is “blended” with public or phil­
anthropic capital, whose aim is to subsidize and de-risk private capital
investments. The main element underlying both types of financing is the
“monetization” of biodiversity, that is, using investments in biodiversity
to generate a financial return for private investors. This monetization
comes in different flavors—for example, the preservation of pollinators
(such as bees, beetles, and butterflies) can enhance the farmland’s
productivity and hence improve the farmers’ profits; the preservation of
forest ecosystems generates carbon credits that can be sold for a profit;
their preservation may also attract ecotourists and hence increase the
income of local hotels and tour guide services; the protection of coastal
ecosystems (e.g., mangroves) improves the habitat for fishes and other
species, which can benefit local fisheries; their protection may also serve
as a natural defense against flooding, thereby increasing real estate
values around the protected area—and provides a direct mechanism
through which biodiversity conservation projects can attract private

capital.
A challenge with these monetization mechanisms is that the financial
returns may not be high enough and/or they might be considered too
risky to attract private investors. Their risk-return profile can be
enhanced by using blended finance structures, in which philanthropic or
public funding is used to subsidize and de-risk private capital. To
characterize the underlying economics, we develop a simple portfolio
selection model with mean-variance investors and a set of projects that
differ based on their biodiversity impact. We assume that private capital
can be blended with concessionary capital, such that an increase in the
degree of blending raises the expected return and lowers the variance of
the returns of the project, without affecting the level of biodiversity
impact. In this setup, we show that the blending helps expand the effi­
cient frontier to allow projects with a higher biodiversity impact to be
part of the efficient set. Intuitively, blended finance is attractive for
projects that have high biodiversity impact and whose risk-return profile
can be “pushed” to a level that appeals to private investors. In an
extension, we further formalize the possibility that biodiversity in­
vestments face higher ambiguity (Knightian uncertainty) due to the lack
of familiarity with the monetization mechanisms of biodiversity con­
servation and/or the lack of track record of biodiversity investments. In
this setup, the higher ambiguity of biodiversity investment induces a
need for “fact-finding” (e.g., running pilot programs or establishing
proof of concept) that can be financed by concessionary capital in
blended financing structures. In this setup, the higher the ambiguity the
higher the attractiveness of blended finance.
Second, we empirically examine this new asset class. To do so, we
obtained access to the proprietary database of a recognized leader in
biodiversity finance, which we refer to as “Biodiversity Investment
Manager” (BIM) for confidentiality reasons. This database covers the 33
biodiversity finance deals that were closed by BIM between 2020 and
2022. For each deal, the database provides detailed information about
the underlying biodiversity project, the expected biodiversity impact,
the deal structure, the expected financial return (IRR), and the financial
risk of the project.
Our analysis of these biodiversity deals provides several insights.
First, we observe that about 60 % of the deals are financed by pure
private capital, while the remaining 40 % are blended finance deals. This
underscores the importance of both forms of financing. Second, the deals
that have a higher expected financial return tend to be financed by pure
private capital (on average, their expected IRR is 15 %, compared to 12
% for blended finance deals). Their scale is smaller, however, and so is
their expected biodiversity impact. For larger-scale projects with a more
ambitious biodiversity impact, blended finance is the more prevalent
form of financing. While these projects have lower expected returns than
those funded by pure private capital, they are also less risky (as
measured by the potential deviation from the expected IRR). This sug­
gests that the blending—and the corresponding de-risking of private
capital—is an important tool for improving the risk-return tradeoff of
these projects, thereby increasing their appeal to private investors.
Overall, our findings point toward a tradeoff between financial returns
and biodiversity impact, with implications for the type of financing.
Profitable projects can be viably financed by pure private capital but
tend to have lower biodiversity impact. Projects with higher biodiversity
impact tend to be less profitable but can nevertheless appeal to private
investors through blending. As such, our results suggest the existence of
a three-dimensional “risk-financial return-biodiversity return frontier,”
which is in line with our conceptual framework. Moreover, we show that
a significant fraction of the blended finance deals uses concessionary
funding to finance fact-finding, which underscores the appeal of using
blended finance structures for biodiversity projects with higher
ambiguity.
Finally, BIM also granted us access to information on biodiversity
projects that were under consideration for inclusion into their portfolios
but were ultimately discarded. Compared to the projects that made it to
the portfolio stage, these projects tend to be less profitable and have
2

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Journal of Financial Economics 164 (2025) 103987

lower biodiversity impact to begin with. This suggests that (i) a certain
risk-return threshold needs to be met for the deal to appeal to private
investors, and (ii) the biodiversity impact needs to be sufficiently
favorable for blended finance to be applicable. These findings offer
additional insights into the three-dimensional frontier. They indicate
that, while blended finance can help finance projects with higher
biodiversity impact, such financing structures are unlikely to be
considered if the investment’s initial risk-return profile is too unfavor­
able. In other words, for a given biodiversity impact, the (pre-blending)
risk-return tradeoff needs to meet a certain threshold for blended
finance to be effective in “pushing” it to a level that would be attractive
to private investors. Moreover, these findings indicate that private
capital (either as standalone or in blended form) is unlikely to provide a
silver bullet against the biodiversity crisis, but can nevertheless be a
useful addition to the toolbox. Arguably, while private investing can
help close the financing gap and contribute to the conservation and
restoration of biodiversity, it is unlikely to substitute for the imple­
mentation of effective public policies.
Naturally, we caution that our results are obtained from a small
sample of biodiversity deals. Given the lack of data on biodiversity deals
(Karolyi and Tobin-de la Puente, 2023), we see this evidence as a first
step in understanding biodiversity finance. Our hope is that, as biodi­
versity finance grows, new datasets will become available that will allow
researchers to shed additional light on this new asset class.
This study makes several contributions to the academic literature.
First, by exploring how private investing can contribute to the protec­
tion of biodiversity, it adds to the sustainable finance literature whose
focus has been primarily on climate finance (e.g., Bolton and Kacpercyk,
2021, 2023; Flammer, 2021; Hong et al., 2020; Ilhan et al., 2023;
Krueger et al., 2020; Pastor et al., 2022; Sautner et al., 2023). Second,
our work contributes to the environmental economics literature that
studies the economics of biodiversity conservation (Dasgupta, 2021;
Heal, 2003, 2004, 2020), and the public provision of this public good
through intergovernmental and governmental mechanisms (e.g., Bar­
rett, 2022). Third, our study aims to spur follow-up work on the
financing of biodiversity, in keeping with the initial effort of Karolyi and
Tobin-de la Puente (2023), as well as the Review of Finance’s recent call
for research proposals for an upcoming special issue on biodiversity and
natural resource finance. Fourth, our study relates to the work by
Coqueret et al. (2025), Garel et al. (2024), Giglio et al. (2023), and Xiong
(2023), who examine how biodiversity risks affect equity prices.
The remainder of this paper is organized as follows. Section 2 pro­
vides a conceptual framework that lays out how private capital can
contribute to biodiversity protection taken into account the public good
nature of biodiversity. Section 3 describes the data and presents the
results. Section 4 compares biodiversity finance versus impact finance.
Finally, Section 5 concludes and discusses avenues for future research.

From the private capital market’s perspective, it is critical to un­
derstand how the conservation and restoration of biodiversity can yield
financial returns for investors. Typically, monetization mechanisms
would include the transformation of natural capital (e.g., logging and
mining). Yet, in the case of biodiversity finance, revenues need to be
generated from protecting as opposed to transforming natural capital.
While this question may seem puzzling at first, generating financial
returns from biodiversity conservation is feasible—it requires the
bundling of biodiversity with private goods whose value it enhances
(Heal, 2003, 2004).
To name a few examples, the protection of natural parks, wildlife,
and coral reefs can increase income from ecotourism and the value of
real estate around the protected area. Sustainable agriculture and fish­
eries can enhance the local communities’ revenues by both increasing
productivity (e.g., through improved soil fertility, increase in pollina­
tors, prevention of overfishing) and the prices that can be charged for
biodiversity-friendly products. The protection of coastal ecosystems and
green infrastructures in urban areas helps prevent flooding and damages
to private (and public) property from climate events. Also, given that
biodiversity helps nature absorb emissions—providing so-called naturebased solutions to climate change—its protection allows the relevant
actors (such as investors and corporations) to earn carbon credits.
Table 1 provides a more systematic overview of the different types of
natural capital assets, along with the corresponding monetization
mechanisms.
Private investments in biodiversity span all types of natural capital
assets. As an illustration, Table A1 of the Online Appendix provides
examples of biodiversity funds by natural capital asset types.

2. Private investing in natural capital—a conceptual framework

2.2. Types of financing

Historically, the conservation and restoration of biodiversity has
been primarily financed through public funding and private philan­
thropic giving. Various public funding instruments are used to finance
biodiversity conservation, including debt-for-nature swaps, official
development assistance (ODA), sovereign biodiversity bonds (e.g., sov­
ereign ocean bonds, rhino bonds, and others), payments for ecosystem
services (PES), and biodiversity offsets, among others. Private philan­
thropic donors include environmental nonprofit organizations such as
the Environmental Defense Fund (EDF), The Nature Conservancy (TNC),
and the World Wildlife Fund (WWF), among others.3
Despite the use of public funding and private philanthropic giving, a
large financing gap for the protection of biodiversity remains. TNC

2.2.1. Pure private capital and blended finance
Private investments in biodiversity can be grouped into two broad
categories: pure private capital and blended finance. The former is akin
to investing private capital in traditional asset classes. In the latter,
private capital is blended with public or philanthropic capital, whose
aim is to subsidize and de-risk private capital investments.
In both cases, private investors can gain (i) direct financial returns
from their investments in natural capital, (ii) indirect financial returns
from gaining biodiversity or carbon credits from their investments in
natural capital, and (iii) non-financial biodiversity returns (from their
investments’ biodiversity impact).
The direct financial returns are the monetary gains that are directly
generated by their investments in natural capital and ecosystem ser­
vices. Given the bundling of biodiversity with private goods, these direct
financial returns are obtained through the monetization mechanisms
described in Section 2.1.

estimates a $722–967 billion per year of additional financing that is
needed to close the financing gap and effectively address the biodiver­
sity crisis (TNC, 2020). With the aim of closing this financing gap, a new
practice has emerged in recent years: private investments in natural
capital. While still in its infancy, private investing in natural capital is a
rapidly growing, yet not well-understood financing mechanism.
Importantly, it raises puzzling questions: a) how can the conservation and
restoration of biodiversity yield financial returns to investors? and b) to the
extent that this financial return is not competitive enough to attract capital
from private investors, how can one design financial products that would
nevertheless be of appeal to them? In what follows, we provide conceptual
arguments that guide the answer to these questions. In doing so, we
describe how biodiversity protection can be “monetized” through the
bundling of public and private goods, and characterize the financing
structures that can be used to leverage these monetization mechanisms
and ultimately appeal to private investors.
2.1. Monetization mechanisms

3
For more information about public funding instruments, see Deutz et al.
(2020), OECD (2020), and Tobin-de la Puente and Mitchell (2021).

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Journal of Financial Economics 164 (2025) 103987

2.2.2. De-risking mechanisms of blended finance
In practice, there are several de-risking mechanisms through which
blending can improve the risk-return profile of private investments. In
the following, we distinguish between de-risking mechanisms at the (i)
fund level and (ii) project level.
De-risking mechanisms at the fund level. Biodiversity funds are typi­
cally structured as partnerships with one general partner (GP) making
the investment and multiple limited partners (LP) investing capital. Each
LP commits a specific amount to the fund by the closing date. Once the
closing date is reached, the investment process begins. Payments are
made by the LPs during the life cycle of the fund through drawdown
notices that apply to all LPs at a pro rata of their capital contributions. If
an LP defaults on one of the payments, the GP can request additional
drawdowns from the other LPs. In such cases, the required capital
contribution of each LP is increased on a pro-rata basis to cover the
amount that remains to be funded.
At the fund level, there are three different mechanisms through
which blended financing can de-risk private capital investments: (i)
seniority, (ii) preferred rate of return, and (iii) financial guarantees.

Table 1
Natural capital asset types and monetization mechanisms of ecosystem services.
Natural capital asset types
A. Land
Agriculture: soil and pollinators

Monetization mechanisms of ecosystem
services
​

Forests

Agricultural productivity; price of farmland;
certification as “biodiversity-friendly”
agricultural products (higher prices); carbon
credits; fire suppression; water quality
Ecotourism (hotel nights, tour guide services);
carbon credits (carbon capture and storage);
biodiversity credits; health; recreational value;
bioprospecting for medicine; certification as
“biodiversity-friendly” wood (higher prices);
hydropower (pay for success)
Value of real estate (proximity to park, green
roofs provide heat isolation); prevention of
flooding; carbon credits (carbon capture and
storage); recreational value (e.g.,
birdwatching tours, sports activities, etc.)
Ecotourism (hotel nights, tour guide services);
value of real estate around the park;
biodiversity credits
Protection against diseases (humans, plants,
food, animals); bioprospecting for medicine;
biodiversity credits

Urban parks and other green
infrastructures in urban areas

Natural parks & wildlife
protection
Genetic resources
B. Sea
Watersheds
Coastal ecosystems

Fisheries
Oceans (incl. coral reef)

• Seniority. Private investors can be granted a higher seniority
compared to other LPs who provide capital for the blending. For
example, development finance institutions—such as MIGA (the
World Bank’s Multilateral Investment Guarantee Agency), USAID
(the U.S. Agency for International Development), and SIGA (the
Swedish International Development Agency)—can commit the initial
tranche of capital as junior LPs. Private investors would then commit
capital as senior LPs. Due to their seniority, private investors are paid
first, which reduces the risk of their investment.
• Preferred rate of return. The fund can allow for a different preferred
rate of return (that is, the minimum return LPs must receive before
the profits can be shared with the GP), such that the preferred rate is
higher for private investors relative to other LPs who provide capital
for the blending.
• Financial guarantees. Relatedly, development finance institutions
(such as MIGA, USAID, and SIDA) or other entities may provide
financial guarantees that compensate private investors in case the
preferred rate of return is not achieved by the fund.

​

Green infrastructure services; water
purification
Ecotourism (hotel nights, tour guide services);
value of real estate (prevention of coastal
flooding); carbon credit (carbon capture and
storage); biodiversity credits; food production
Food production; certification as “biodiversityfriendly” seafood products (higher prices)
Ecotourism (hotel nights, tour guide services);
carbon credits; biodiversity credits; value of
real estate (prevention of hurricanes and
coastal flooding)

Notes. This table provides examples of monetization mechanisms of ecosystem
services by natural capital asset types.

In addition to the direct financial returns, investors may also benefit
from indirect financial returns in the form of biodiversity credits from
their investments in natural capital. Moreover, as biodiversity plays an
important role in reducing carbon emissions, the protection of biodi­
versity can generate carbon credits, which further improves the attrac­
tiveness of such investment for investors who aim to fulfill their carbon
pledges. Both biodiversity and carbon credits are commonly used in
biodiversity finance.4
While traditional investors may only value their investments’ (direct
and indirect) financial returns, other investors—so-called “impact
investors”—also value the non-financial returns gained from their in­
vestments.5 In this regard, investments in the conservation and resto­
ration of biodiversity yields non-financial “biodiversity returns” that can
also appeal to private investors.
In the case of blended financing structures, the blending of private
capital with public or philanthropic funding aims to improve the riskreturn tradeoff faced by private investors, and hence increase the ap­
peal of these investments to private investors. In what follows, we
discuss the de-risking mechanisms used in blended finance.

In addition to these de-risking mechanisms at the fund level, blended
financing structures can also feature de-risking mechanisms at the
project level, which we describe next.
De-risking mechanisms at the project level. At the project level, derisking mechanisms fall into three broad categories: (i) concessional
finance, (ii) ex-ante risk mitigation, and (iii) ex-post risk mitigation.6
• Concessional finance. In the case of concessional finance, public or
philanthropic funders (including philanthropic foundations, donors,
multi-donor funds, and development finance institutions) provide
grants or funding at below-market rates to the investee to help
“crowd in” private capital investments.7
• Ex-ante risk mitigation. In addition to concessional finance, the pro­
vision of (i) design and preparation grants and (ii) technical assis­
tance grants can help de-risk the project ex ante. These grants are
typically provided by philanthropic foundations, donors, and multidonor funds. Design and preparation grants aim to improve the
viability of the project before securing the necessary financing. These
grants are used to support the proof of concept, establish a baseline,

4
Carbon and biodiversity credits are not without challenges, however.
Concerns have been raised about the measurement and valuation of these
credits, and their potential for greenwashing practices, among others (e.g.,
Bloomberg, 2022; S&P Global, 2021; The Guardian, 2023; West et al., 2023).
5
Conceptually, traditional investors can be viewed as a special case of impact
investors who allocate zero value to non-financial returns. Considerable het­
erogeneity exists across impact investors in the extent to which they value
financial versus non-financial returns (see, e.g., Gibson-Brandon et al., 2022;
Heeb et al., 2023).

6
See Earth Security (2021) for a more detailed discussion of these de-risking
mechanisms at the project level, along with several practical examples.
7
Concessional capital can also be granted conditional on the achievement of
specific key performance metrics (so-called “impact-linked loans” or “resultsbased financing”), which provides additional assurance of the project’s ability
to meet the intended environmental and social impact.

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Journal of Financial Economics 164 (2025) 103987

establish a monitoring and verification system, develop a pipeline,
resolve some ambiguity and uncertainty about the project’s
outcome, and provide the pre-commercial funding needed prior to
the investment stage. Technical assistance grants are used to build the
technical capacity of investees and their key stakeholders such as
local communities that may be crucial to the successful imple­
mentation and ultimately the commercial viability of the project.
They can also be used to build capacity in other areas such as
financial management, contracting, business model development, or
impact monitoring and evaluation. These grants are often provided
by donors through a dedicated fund that runs in parallel to the actual
investment (Earth Security, 2021).
• Ex-post risk mitigation. Financial guarantees and risk insurance pro­
vide additional ways to de-risk biodiversity projects. These mecha­
nisms operate ex post, as they protect private investors against
realized losses from the project. The guarantor—often a develop­
ment finance institution such as MIGA, USAID, SIDA—commits to
cover the losses (in full or in part) that may arise from the project,
which reduces the risk of private investments and provides a signal of
the viability of the investment to private investors.8

An increase in the degree of blending raises the mean return and
lowers the variance of the returns of any project, ∂∂br > 0, ∂∂bv < 0. This
mirrors the way the blending is done in practice. For example, if the
concessionary capital is in the form of a loan with a below-market in­
terest, the blending increases the expected return r from the private
investors’ perspective. Similarly, if the concessionary capital is in the
form of financial guarantees, the blending reduces the variance v of the
returns.
Fig. 2 illustrates how an increase in b affects the efficient frontier B =
f(r, v) along the B − r and B − v planes. In the figure, the solid (dashed)
line denotes the new (old) efficient set following an increase in b, while
the gray lines represent the investor’s indifference curves. As can be
seen, increased blending implies more r and less v for a given B. Fig. 3
further combines the two planes into a 3-dimensional graph and shows
how the efficient frontier is shifted through higher blending. For a given
biodiversity impact B, increased blending implies a more favorable riskreturn profile for private investors.
Formally, we write B = f(r, v | b) to explicitly denote that the degree
of blending is a parameter of the function f so that the relationship
between B, r and v depends on the value of b. The assumptions made
about the function B = f(r, v | b) imply that if b1 < b2 then

As the above considerations illustrate, the de-risking of private in­
vestments through blended finance comes in different flavors. While a
variety of de-risking mechanisms exist, their objective is always the
same: act as a catalyst in attracting private capital by improving the riskreturn tradeoff of biodiversity projects. Importantly, these de-risking
mechanisms can foster “additionality” if they lead to the financing of
new biodiversity projects that would not have been undertaken
otherwise.9
A summary of the above discussion is provided in Table 2, which
compiles the different returns and de-risking mechanisms of biodiversity
investments, and in Fig. 1, which illustrates the structure of biodiversity
finance deals.

{B, r, v : B ≤ f(r, v | b1 )}⊂{B, r, v : B ≤ f(r, v | b2 )}.
In words, the feasible set for b1 is a subset of the feasible set for
b2 . Accordingly, it follows that
Max U(r, v, B) subject to B = f(r, v | b1 )
< Max U(r, v, B) subject to B = f(r, v | b2 ).
If the income elasticity of demand for B is strictly positive, then this
implies that a higher B is chosen at b2 than at b1 . That is, blending is
positively linked to the choice of projects with a greater biodiversity
impact. Accordingly, a testable prediction is that, among the set of
biodiversity investments, blended finance deals (as opposed to pure
private capital deals) are likely to be more prevalent among projects that
have higher biodiversity impact. In Section 3, we bring this prediction to
the data and characterize the 3-dimensional efficient frontier that arises
in this setup.

2.3. Portfolio choice with biodiversity benefits and blended finance
As discussed above, the use of blended finance helps subsidize and
de-risk private capital, thereby improving the risk-return trade-off of
projects that have high biodiversity impact but too low of an expected
return, or too high of a risk, to attract private capital. In what follows, we
introduce a simple model of portfolio choice that formalizes this
intuition.
Specifically, we adapt the mean-variance approach to portfolio
choice and assume that a private investor in a biodiversity conservation
project has a utility function that depends on the expected return r, the
variance of returns v, and the level of biodiversity conservation B (for
example, the number of species that are preserved at the project’s
location). That is, their utility is given by U(r, v, B) such that ∂∂Ur > 0, ∂∂Uv

2.4. Fact-finding and the reduction of ambiguity
In biodiversity projects, the concessionary capital is often used to
finance basic fact-finding (e.g., running pilot programs or establishing
proof of concept) in order to clarify the nature and potential of the
project. Such fact-finding is valuable given the lack of experience and
familiarity with the monetization mechanisms listed in Table 1. In this
regard, fact-finding helps reduce the ambiguity of the project. Concep­
tually, ambiguity (Knightian uncertainty) differs from risk—ambiguity
refers to situations where probabilities are unknown, while risk refers to
uncertainties described by known probability distributions.
Fact-finding in biodiversity projects can be seen as a means of
reducing ambiguity in the above sense. In Online Appendix A, we
develop a simple model that characterizes the value of reducing ambi­
guity through fact-finding. In the model, we assume that initially there
are multiple probability distributions over the outcomes of a project that
are consistent with what is known about it. If there are multiple distri­
butions, then there are many possible expected outcomes, one per dis­
tribution. We then think of concessionary capital as funding
investigations that convert ambiguity to risk by establishing which of
these distributions over project outcomes is the real distribution, moving
from a multiplicity of possible distributions to a unique one.
A direct prediction from this model is that blended financing (and
hence the reliance on concessionary capital) is likely to be more prev­
alent among biodiversity projects that have higher ambiguity. While this
prediction is not testable per se—ambiguity is difficult to measure
empirically—we show in Section 3 that a significant share of the blended

< 0, and ∂∂UB > 0.
The return r and the variance v depend on the level of blending in the
project b, r(b) and v(b). The private investor seeks to maximize their
utility subject to the available investment opportunities, which are

described by an efficient set B = f(r,v). This function f satisfies ∂∂fr < 0, ∂∂vf
> 0, meaning that more biodiversity conservation can be obtained at the
cost of lower returns and higher risk. The investor’s optimal portfolio
selection problem is then given by:
Maximize U(r(b), v(b), B) subject to B = f(r, v).

8

Another potential benefit of guarantees is that private investors may remain
committed to the investment even after the guarantees expire, which fosters the
financial sustainability of such investments.
9
Additionality is an important challenge in sustainable finance. For a dis­
cussion of this challenge in the context of green financing, see Flammer (2020).
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Journal of Financial Economics 164 (2025) 103987

Table 2
Returns and de-risking mechanisms of biodiversity investments.
A. Returns
Direct financial returns
Indirect financial returns
• Biodiversity credits
• Carbon credits
Non-financial biodiversity returns
B. De-risking mechanisms
Fund-level de-risking mechanisms
• Seniority
• Preferred rate of return
• Financial guarantees
Project-level de-risking mechanisms
• Concessional finance
• Ex-ante risk mitigation
- Design and preparation grants
- Technical assistance grants
• Ex-post risk mitigation
- Financial guarantees
- Risk insurance

Notes. This table summarizes the returns and de-risking mechanisms of biodiversity investments discussed in Section 2.2.

Fig. 1. Structure of biodiversity finance deals.

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Journal of Financial Economics 164 (2025) 103987

Fig. 3. Three-dimensional efficient frontier.
This figure combines the two planes of Fig. 2 into a three-dimensional graph
and shows how an increase in blending (represented by the shift from the
dashed to the solid curves) affects the three-dimensional efficient frontier in the
model of Section 2.3.

sustainable investing. BIM and its affiliates have about $30 billion in
assets under management. It is active throughout the world, and its
clientele comprises both individual and institutional investors. BIM of­
fers equity and fixed income investment strategies to its clients and helps
finance projects and companies at any stage of their life cycle.
Since all our data are obtained from BIM, a potential caveat is that
our sample may not be representative of other providers of biodiversity
finance investments. Unfortunately, it is difficult to provide a compar­
ative analysis of BIM vs. other biodiversity finance funds due to the lack
of quantitative information (e.g., on financial returns, deal structure,
and biodiversity impact) for other biodiversity finance funds. Indeed,
the only reason we were able to access BIM’s data is through a restrictive
non-disclosure agreement (NDA). That being said, this caveat is allevi­
ated by the fact that BIM is one of the leading asset managers in biodi­
versity conservation and natural capital more broadly, and hence at the
forefront of the market practices. Hence, at the very least, our analysis
captures the practices of a key player in biodiversity finance.
While BIM is active in several areas of sustainable investing, we focus
on their biodiversity finance deals. BIM invests in biodiversity projects
throughout the world and across nearly all natural capital asset types.
These projects are financed using blended finance as well as pure private
capital investments.
The database covers all 33 biodiversity finance deals that were closed
by BIM between 2020 and 2022.11 Note that these deals are still ongoing
(their average maturity is 8 years) and hence we do not have informa­
tion about their realized performance. The data are very detailed. For
each deal, we were granted access to BIM’s internal documentation that
contains a wealth of information about the underlying biodiversity
project, the expected biodiversity impact, the deal structure, the ex­
pected financial return, and BIM’s risk assessment, among others.
Out of the 33 biodiversity finance deals, 19 deals (58 %) were
financed by pure private capital, while the remaining 14 deals (42 %)
were financed through blended finance. In what follows, we

Fig. 2. Blending and efficient frontier.
This figure illustrates how an increase in blending (represented by the shift
from the dashed to the solid curve) affects the efficient frontier in the model of
Section 2.3. Panel A refers to the biodiversity-financial return (B – r) plane
(holding the variance v constant), while Panel B refers to the biodiversityvariance (B – v) plane (holding the return r constant). The gray lines repre­
sent the investors’ indifference curves.

finance deals uses concessionary funding to finance fact-finding, which
is in line with the above prediction.10
3. Private investing in natural capital—first empirical evidence
on biodiversity finance
3.1. Data
To study private investments in biodiversity, we obtained access to
the proprietary database of a recognized leader in biodiversity finance,
and sustainable finance more broadly. As mentioned above, we refer to
this entity as “Biodiversity Investment Manager” (BIM) for confidenti­
ality reasons. BIM is a private equity firm that is fully dedicated to

10
Note that ambiguity differs from information asymmetry—information
asymmetry refers to a situation in which an economic agent has more infor­
mation than another (and incentives to act strategically based on this infor­
mational advantage), while ambiguity refers to a situation in which economic
agents do not know the true probability distribution. Ambiguity is likely to be
first order in the context of biodiversity projects because of the lack of famil­
iarity with the monetization mechanisms of biodiversity conservation as well as
the lack of track record of biodiversity investments. This is consistent with the
fact-finding result, in that fact-finding is about understanding the feasibility/
viability of biodiversity projects, as opposed to extracting information from
other (better informed) agents.

11
In addition, we were granted access to a set of deals that were under
consideration but ended up being discarded by BIM’s management. We study
these deals in Section 3.5.

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Journal of Financial Economics 164 (2025) 103987

characterize these deals across many dimensions.12

Table 4
Biodiversity finance deals by countries.
All

3.2. Descriptive statistics

(N = 33)

Deals by natural capital asset types. Table 3 provides a breakdown of
the 33 biodiversity finance deals by natural capital asset types. Note that
the BIM deals span the full set of natural capital asset types listed in
Table 1, except for ‘urban parks and other green infrastructures in urban
areas.’ The deals are almost equally distributed across the two broad
categories land (48.5 % of the deals) and sea (51.5 %). Within the land
category, the main natural asset types are ‘agriculture: soil and polli­
nators’ (24.2 %) and ‘forests’ (18.2 %). Within the sea category, the
main ones are ‘fisheries’ (30.3 %), ‘coastal ecosystems’ (9.1 %) and
‘oceans, incl. coral reef’ (9.1 %).
In the last four columns of Table 3, we distinguish between blended
finance deals and deals that are financed by pure private capital. As is
shown, the distribution across the different natural capital asset types is
similar in both groups. At the margin, the land category tends to be more
prevalent among blended finance deals (57.1 %), while it is less prev­
alent among deals financed by pure private capital (42.1 %).
Deals by countries. Table 4 provides a breakdown of the deals based
on the countries of the biodiversity projects. As can be seen, most of the
projects are undertaken in Latin America and the Caribbean (30.3 %),
Asia (24.2 %), and Africa (18.2 %). The distribution is again comparable
across blended finance deals and deals that are financed by pure private
capital.
Fig. 4 provides a visualization of the biodiversity projects’ location
on the world map. Darker-shaded areas indicate a greater number of
projects. Fig. 5 provides separate maps for blended finance deals (panel
A) and deals that are financed by pure private capital (panel B).
Deals by financing structure. In Table 5, we provide a breakdown of the

Africa
Ghana
Ivory Coast
Kenya
Madagascar
Morocco
Asia
Bhutan
India
Indonesia
Laos
Philippines
Vietnam
Multiple
countries
Europe
France
Norway
United Kingdom
Latin America and
Caribbean
Bahamas
Brazil
Colombia
Costa Rica
Mexico
Nicaragua
Peru
Oceania
Australia
Multiple
continents
Total

Table 3
Biodiversity finance deals by natural capital asset types.

Land
Agriculture: soil
and pollinators
Forests
Natural parks &
wildlife
protection
Genetic resources
Sea
Watersheds
Coastal
ecosystems
Fisheries
Oceans (incl.
coral reef)
Total

All

Blended finance

(N = 33)

(N = 14)

Pure private
capital
(N = 19)

#
Deals

Percent

#
Deals

Percent

#
Deals

Percent

16
8

48.5 %
24.2 %

8
3

57.1 %
21.4 %

8
5

42.1 %
26.3 %

6
1

18.2 %
3.0 %

3
1

21.4 %
7.1 %

3
0

15.8 %
0.0 %

1
17
1
3

3.0 %
51.5 %
3.0 %
9.1 %

1
6
0
0

7.1 %
42.9 %
0.0 %
0.0 %

0
11
1
3

0.0 %
57.9 %
5.3 %
15.8 %

10
3

30.3 %
9.1 %

4
2

28.6 %
14.3 %

6
1

31.6 %
5.3 %

33

100.0
%

14

100.0
%

19

100.0
%

Blended finance
(N = 14)

Pure private
capital
(N = 19)

#
Deals

Percent

#
Deals

Percent

#
Deals

Percent

6
1
1
2
1
1
8
1
1
2
1
1
1
1

18.2 %
3.0 %
3.0 %
6.1 %
3.0 %
3.0 %
24.2 %
3.0 %
3.0 %
6.1 %
3.0 %
3.0 %
3.0 %
3.0 %

3
0
0
1
1
1
3
1
0
0
0
1
1
0

21.4 %
0.0 %
0.0 %
7.1 %
7.1 %
7.1 %
21.4 %
7.1 %
0.0 %
0.0 %
0.0 %
7.1 %
7.1 %
0.0 %

3
1
1
1
0
0
5
0
1
2
1
0
0
1

15.8 %
5.3 %
5.3 %
5.3 %
0.0 %
0.0 %
26.3 %
0.0 %
5.3 %
10.5 %
5.3 %
0.0 %
0.0 %
5.3 %

5
2
1
2
10

15.2 %
6.1 %
3.0 %
6.1 %
30.3 %

3
1
0
2
3

21.4 %
7.1 %
0.0 %
14.3 %
21.4 %

2
1
1
0
7

10.5 %
5.3 %
5.3 %
0.0 %
36.8 %

1
2
1
1
3
1
1
1
1
3

3.0 %
6.1 %
3.0 %
3.0 %
9.1 %
3.0 %
3.0 %
3.0 %
3.0 %
9.1 %

0
1
1
0
0
0
1
1
1
1

0.0 %
7.1 %
7.1 %
0.0 %
0.0 %
0.0 %
7.1 %
7.1 %
7.1 %
7.1 %

1
1
0
1
3
1
0
0
0
2

5.3 %
5.3 %
0.0 %
5.3 %
15.8 %
5.3 %
0.0 %
0.0 %
0.0 %
10.5 %

33

100.0
%

14

100.0
%

19

100.0
%

Notes. This table reports the number and percentage of biodiversity finance
deals by countries. The statistics are reported for all BIM deals (first two col­
umns), and separately for blended finance deals (middle two columns) and deals
financed by pure private capital (last two columns).

deals based on their financing structure. Equity is the more prevalent
form of financing (33.3 % of the deals), followed by a mix of equity and
debt (24.2 %) and debt with profit sharing (18.2 %). In the latter case,
the interest paid on the debt is performance-based. It is typically spec­
ified as a floor interest rate plus a percentage of the project’s EBITDA
(sometimes subject to a cap). Other deals are financed through VERPA
(voluntary emission reduction purchase agreement), either as stand­
alone (12.1 %), or combined with equity (6.1 %). In VERPA-based
financing, the investors purchase ownership of the carbon credits that
are generated by the project.
In the last four columns of Table 5, we distinguish between blended
deals and pure private capital deals. As is shown, equity (28.6 % of the
blended deals and 36.8 % of the pure private capital deals) and a mix of
equity and debt (28.6 % and 28.1 %, respectively) remain the more
prevalent forms of financing for both types of deals. VERPA-based
financing is found among both types as well (14.3 % and 21.1 %,
respectively). One nuance is that VERPA-based financing is more likely
to be combined with equity for blended deals, while it is more likely to
be used as standalone for pure private capital deals.

Notes. This table reports the number and percentage of biodiversity finance
deals by natural capital asset types. The statistics are reported for all BIM deals
(first two columns), and separately for blended finance deals (middle two col­
umns) and deals financed by pure private capital (last two columns).

3.3. Deal characteristics
12

Due to confidentiality restrictions, we cannot disclose the identity of BIM’s
investors. However, we note that their private investors include large asset
owners (insurance companies, banks, and foundations) as well as a few cor­
porates that have made biodiversity commitments.

Table 6 provides the means and standard deviations for various deal
characteristics across all BIM deals, and separately for blended finance
deals and deals financed by pure private capital. The last column reports
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Journal of Financial Economics 164 (2025) 103987

Fig. 4. Biodiversity finance deals by countries.
This figure plots the number of biodiversity finance deals of BIM by countries. Darker-shaded areas indicate a greater number of deals.

Fig. 5. Types of biodiversity finance deals by countries.
This figure plots the number of biodiversity finance deals of BIM by type of deals and countries. Panel A refers to bended finance deals. Panel B refers to deals
financed by pure private capital. Darker-shaded areas indicate a greater number of deals.

the p-value of the difference-in-means test comparing blended finance
deals vs. pure private capital deals.
As can be seen from panel A, the average biodiversity deal has a
maturity of 7.9 years, a deal size of $22.8 M, and a ticket size (that is, the
amount invested by each investor) of $6.6 M, out of which $3.2 M (52
%) is in the form of equity, $2.8 M (35 %) in the form of debt, and $0.6 M
(13 %) in the form of VERPA-based financing. When comparing blended
deals vs. pure private capital deals, the main difference is that blended

deals tend to be larger—the average deal size is $29.2 M compared to
$18.2 M (p-value = 0.074). This indicates that the blending helps scale
up biodiversity investments. We also observe that blended deals tend to
rely on a larger share of debt financing and a smaller share of VERPAbased financing, although these differences are not significant at con­
ventional levels.
For each deal, the database provides the expected IRR. For about
two-thirds of the deals, the BIM documentation also includes a
9

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

IRR and the (pseudo) standard deviation in panel B. As can be seen, deals
that have a higher expected IRR tend to be financed by pure private
capital. On average, their expected IRR is 14.7 %, compared to 11.9 %
for blended finance deals. The difference is significant in statistical terms
(p-value = 0.026). While blended finance deals have lower expected
returns, they tend to have lower risk as well. On average, their (pseudo)
standard deviation from the target IRR is 6.3 % compared to 6.7 % for
deals that are financed by pure private capital. When computing the
ratio of the target IRR to the (pseudo) standard deviation from the ex­
pected IRR—similar in spirit to a Sharpe ratio—we find no significant
difference between the two types of deals (p-value = 0.834). Overall,
this suggests that the de-risking from the blending helps improve the
risk-return tradeoff of these projects, thereby increasing their appeal to
private investors.14
Panel C provides metrics that capture the environmental and social
impact of the biodiversity deals. A clear pattern emerges, in that the
blended deals are significantly more impactful along multiple di­
mensions. First, the total impact area (e.g., in terms of reforestation and
habitat conservation) is expected to be larger. On average, it is expected
to be 114,798 hectares for blended deals compared to 26,844 hectares
for pure private capital deals. The difference (based on the logarithm) is
significant at the 10 % level (p-value = 0.098). Similarly, blended

Table 5
Biodiversity finance deals by type of financing.
All

Blended finance

(N = 33)

Equity
Equity + Debt
Equity + Debt
with profit
sharing
Equity + VERPA
Debt
Debt with profit
sharing
VERPA
Total

(N = 14)

Pure private
capital
(N = 19)

#
deals

Percent

#
deals

Percent

#
deals

Percent

11
8
1

33.3 %
24.2 %
3.0 %

4
4
0

28.6 %
28.6 %
0.0 %

7
4
1

36.8 %
21.1 %
5.3 %

2
1
6

6.1 %
3.0 %
18.2 %

2
1
3

14.3 %
7.1 %
21.4 %

0
0
3

0.0 %
0.0 %
15.8 %

4
33

12.1 %
100.0
%

0
14

0.0 %
100.0
%

4
19

21.1 %
100.0
%

Notes. This table reports the number and percentage of biodiversity finance
deals by type of financing. The statistics are reported for all BIM deals (first two
columns), and separately for blended finance deals (middle two columns) and
deals financed by pure private capital (last two columns). VERPA refers to
voluntary emission reduction purchase agreements.
Table 6
Biodiversity deal characteristics.
All

Blended finance

N
A. Deal size and financing
​
Maturity (years)
33
Deal size ($ million)
33
Ticket size ($ million)
33
Equity ($ million)
33
Debt ($ million)
33
VERPA ($ million)
33
% Equity
33
% Debt
33
% VERPA
33
B. Financial performance and risk
​
Project return (target IRR)
33
Project risk (pseudo standard deviation)
20
Sharpe ratio (project return / project risk)
20
C. Environmental and social impact
​
Total impact area (ha, expected)
17
GHG emissions reduction (1000 tCO2e, expected)
18
# Beneficiaries (expected)
13
# New jobs created (expected)
15
Certification (1/0 dummy)
33
D. Environmental and social impact relative to deal size
Total impact area / deal size
17
GHG emissions reduction / deal size
18
# Beneficiaries / deal size
13
# New jobs created / deal size
15
E. Fact-finding
​
Fact-finding provisions (1/0 dummy)
33

Pure private capital

Difference in means

Mean

Std. dev.

N

Mean

Std. dev.

N

Mean

Std. dev.

p-value

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

​

7.94
22.84
6.62
3.21
2.79
0.62
0.52
0.35
0.13
13.52 %
6.55 %
2.71

3.03
17.47
3.86
4.00
4.20
1.62
0.44
0.42
0.33
3.68 %
3.81 %
1.34

73,408
5665
11,623
1846
0.79

2.70
18.39
3.99
4.45
4.34
0.53
0.44
0.46
0.11

11.88 %
6.32 %
2.63

9
8
6
6
14

5669
306.75
977.48
392.79
0.29

7.93
29.15
7.24
3.44
3.65
0.14
0.50
0.47
0.03

14
8
8

167,115
8649
11,779
4273
0.42

2793
233.59
724.56
130.03
0.09

14
14
14
14
14
14
14
14
14

9
8
6
6

114,798
9469
19,133
3358
0.79

2.86 %
3.81 %
1.43

0.21

0.026**
0.832
0.834

27,805
2824
3710
1050
0.42

1606
175.62
517.14
35.69
0.00

0.986
0.074*
0.443
0.781
0.320
0.147
0.881
0.172
0.124

3.81 %
3.97 %
1.34

26,844
2622
5185
838
0.79

8
10
7
9
19

3.32
15.63
3.79
3.74
4.08
2.03
0.46
0.39
0.42

14.72 %
6.71 %
2.77

8
10
7
9
19

7565
392.40
1333.84
624.17
0.43

7.95
18.19
6.17
3.04
2.16
0.97
0.53
0.26
0.21

19
12
12

226,016
11,900
13,812
6693
0.43

3849
306.06
966.54
271.56

14

19
19
19
19
19
19
19
19
19

2235
222.64
565.30
38.22

0.098*
0.096*
0.025**
0.279
0.980

0.00

0.433
0.386
0.432
0.270
0.035**

Notes. This table reports the mean and standard deviation of several deal characteristics across all BIM deals and separately for blended finance deals and deals
financed by pure private capital. VERPA refers to voluntary emission reduction purchase agreements. Total impact area is measured in hectares (ha). Greenhouse gas
(GHG) emissions are measured in 1000 t of CO2 equivalent (tCO2e). The calculation of the expected IRR, the pseudo standard deviation, and the Sharpe Ratio is
described in Online Appendix B. The last column reports the p-value of the difference-in-means test comparing blended finance deals vs. deals financed by pure private
capital. *, **, and *** denotes significance at the 10 %, 5 %, and 1 % level, respectively.

finance deals are expected to reduce greenhouse gas (GHG) emissions by
9.5 million tons of CO2 equivalent (tCO2e), compared to only 2.6
million tCO2e for pure private capital deals (p-value = 0.096). What is

sensitivity analysis that we use to compute a measure of the project’s
risk. Specifically, we compute the average deviation from the expected
IRR in the pessimistic and optimistic scenarios, which we refer to as the
“pseudo” standard deviation of the IRR.13 We report both the expected

14
In Table A2 of the Online Appendix, we report how the expected IRR differs
across the characteristics we considered in Tables 3–5. As can be seen, we find
that the expected IRR tends to be higher for projects that rely on equity (vs.
debt) financing, which is not surprising given the higher cost of equity.

13

Online Appendix B describes how BIM computes the expected IRR, con­
ducts the sensitivity analysis, and how we use the latter to compute the pseudostandard deviation of the IRR.
10

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

more, the number of beneficiaries (that is, individuals who benefit from
the project) is expected to be 19,133 people for blended deals, compared
to 5185 for pure private capital deals (p-value = 0.025). The number of
new jobs created is also expected to be higher for blended finance deals
(3358) compared to pure private capital deals (838), although the dif­
ference is not significant at conventional levels (p-value = 0.279).
Finally, the share of deals that are expected to be certified by third-party
organizations—such as EcoVadis, the Forest Stewardship Council (FSC),
and the Climate, Community, and Biodiversity (CCB) Standards, among
others—is about the same across both types of deals.
Panel D further shows that the differences in Panel C are not merely
reflective of the larger size of the blended finance deals. When scaling
the above metrics by the size of the deal, we find that blended finance
deals have a larger impact per dollar invested. In particular, on a per
dollar basis, the total impact area, the reduction in GHG emissions, and
the number of beneficiaries are 4.3 to 4.9 times larger for blended
finance deals.15
Overall, the evidence from Panels B-D indicates that, while deals that
have a higher expected financial return are more likely to be financed by
pure private capital, they tend to be smaller in scale and have lower
biodiversity impact. For larger-scale projects with a more ambitious
biodiversity impact, blended finance is the more prevalent mode of
financing. While these projects have lower expected returns, they are
also less risky. This suggests that the blending—and the corresponding
de-risking of private capital—is an important tool for improving the riskreturn tradeoff of projects with higher biodiversity impact, thereby
increasing their appeal to private investors. This is consistent with the 3dimensional frontier (return, risk, and biodiversity impact) that we
formalized in Section 2.3, and the prediction that blended finance
structures are more prevalent for projects with higher biodiversity
impact.
In Panel E, we use information from the project description to code a
dummy variable that is equal to one if part of the financing is used to
fund fact-finding (e.g., pilot programs). We find that 21 % of the blended
finance deals entail fact-finding provisions, while none of the pure pri­
vate capital deals does (the difference is significant at conventional
levels with p-value = 0.035). This is not surprising, given that factfinding is typically financed by concessionary capital that is only
available in blended finance structures. Importantly, this finding lends
support to our argument from Section 2.4 (and the underlying model in
Online Appendix A) that projects with more ambiguity (Knightian un­
certainty) are more likely to be funded by blended finance structures.
Naturally, we caution that, since our sample includes 14 blended
finance deals, the 21 % of deals with fact-finding provisions correspond
to only 3 deals. Hence, we see this finding as suggestive given the smallsample nature of the analysis.
In addition to the quantitative information provided in Table 6, the
BIM database also includes qualitative assessments of the biodiversity
deals along several ESG dimensions. For each ESG dimension, the
assessment is specified on a scale from 1 to 3 (1 referring to “Low,” 2
referring to “Medium,” and 3 referring to “High”). The means and
standard deviations of these assessments are provided in Table A3 of the
Online Appendix. In panel A (ESG assessment), a higher score represents
a more positive assessment. In panel B (ESG risk), a higher score rep­
resents higher risk. In panel C (ESG risk management), a higher score
represents a more positive assessment of the risk management process.
As can be seen from panel A, the ESG assessments are especially
favorable with regard to environmental dimensions, including ‘natural
ecosystems,’ ‘sustainable product lands & seascapes,’ and ‘climate
change mitigation.’ Relatedly, the ESG risks in panel B tend to be
assessed between low and medium. In particular, the categories ‘pollu­
tion control, energy and water use risk’ and ‘biodiversity conservation

risk’ are rated favorably, in keeping with the nature of biodiversity
projects. This is further reflected in the quality of the ESG risk man­
agement processes in panel C, which tend to be rated between medium
and high.16
3.4. Ex-post performance
The 33 biodiversity finance deals considered in this paper were
closed by BIM between 2020 and 2022, and have an average maturity of
about 8 years (Table 6). Accordingly, all deals are still ongoing, and
hence we cannot assess their realized performance. To nevertheless gain
perspective on their ex-post performance, we asked BIM for information
about the year-to-year performance of these deals. They agreed to share
information on the environmental and social impact of the deals (cor­
responding to the metrics listed in Panel C of Table 6). We report this
information in Fig. 6.
For each metric—e.g., the total impact area (in terms of reforestation
and habitat conservation)—we compute the ratio of the realized benefit
relative to the target in any given year, where the years are recorded in
event time relative to the closing year (year 0). For example, if a deal is
closed in 2021, has a target impact area of 50,000 ha, and an actual
impact area of 5000 ha in 2021, 6000 ha in 2022, and 10,000 in 2023,
the ratio is computed as 10 % in year 0, 12 % in year 1, and 20 % in year
2. We then take the average across all deals and event years for which
data are available, and plot these averages in Fig. 6.
As can be seen, the social impacts of the deals (in terms of job cre­
ation and the number of beneficiaries) are faster to generate compared
to their environmental impacts (in terms of impacted area and GHG
sequestration). After three years, about 54–76 % of the targeted social
gains are already achieved. This suggests that a large share of the ex­
pected social benefits is already achieved by setting up the project
infrastructure and creating jobs at the project’s location. In contrast, the
environmental benefits take longer to materialize, with only 17 % of the
targeted impact area and 13 % of the targeted GHG sequestration being
achieved after three years. In our conversations with the BIM team, we
learned that the environmental impacts typically follow a J-curve in
which the bulk of the gains accrue in the last years of the project. This is
consistent with the pattern we uncover in Fig. 6, but of course incom­
plete since the ex-post impact metrics are not yet available for the later
years of the projects.17
Interestingly, while BIM did not share data on the ex-post financial
performance of the deals, they noted in our conversations that the
financial performance of the biodiversity deals is also expected to follow
a J-curve with the highest gains being realized relatively late in the
project’s life. This suggests that the biodiversity gains and financial
gains tend to be somewhat in-sync during the projects’ life.
Finally, BIM also shared with us the set of Key Performance In­
dicators (KPIs) that they use internally to monitor the environmental
and social performance of the projects. The list of KPIs is provided in
Table 7.
While BIM did not provide quantitative data on those KPIs, the list in
16
Due to the coarse, three-category answers underlying the ratings, these
qualitative data are not well suited to detect differences across groups of deals.
And indeed, in the last six of columns of the table, we see little variation in
these ratings across the blended finance and pure private capital deals.
17
In Table A4 of the Online Appendix, we examine whether the projects’ expost environmental and social impact varies across deals that are financed by
pure private capital vs. blended financing. Specifically, for each impact metric
and each deal for which we have ex-post data available, we compute the
realized impact (relative to the targeted impact) until the last year for which we
have data (that is, up to three years post-closing). We then compute the mean
among deals that are financed by pure private capital and blended financing. As
can be seen, we find no significant difference between the two groups, which
suggests that both types of projects contribute to their intended impact at a
similar pace.

15
While these differences are large in economic terms, we caution that they
are not significant at conventional levels.

11

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

Fig. 6. Ex-post performance.
This figure plots the average realized environmental and social impact of the biodiversity projects in our sample in event time relative to the closing year (year 0). All
impact metrics are expressed as a percentage of the project’s targeted impact.
Table 7
Key performance indicators (KPI).
A. Environmental
Certification
• Internationally recognized certifications achieved
Sustainable productive lands and seascapes
• Area of reforestation/afforestation (including agroforestry) [ha]
• Hectares of land under sustainable management (production or conservation/restoration) [ha]
• Hectares of land under sustainable productive management [ha]
• Carbon sequestration practices
Climate change mitigation
• Total GHG emissions avoided/reduced or sequestered [tCO2e]
• Avoided/reduced greenhouse gas emissions [tCO2e]
• Tons of GHG sequestered [tCO2e]
• Tons of GHG sequestered that led to the generation of verified tradable carbon units [tCO2e]
• Tons of GHG avoided/reduced that led to the generation of verified tradable carbon units [tCO2e]
Natural ecosystems
• Hectares of land under conservation or restoration [ha]
• Volume of waste treated or valued [metric tons]
B. Social
Community engagement
• Community engagement events held [#]
• Number of people attending community engagement events [#]
Livelihoods and decent work
• Number of employees [#]
• Employees expressed in full-time equivalent [#]
• People with their main source of income provided by the project (excluding direct employees), [#]
• People expected to benefit directly from the project (excluding employees) [#]
• Households benefitting directly from livelihoods generated by the project (excluding employees and individual beneficiaries) [#]
Inclusion
• Gender ratio for management roles [%]
• Gender ratio for senior executive roles [%]
• Gender ratio at board level [%]
• Ratio of female employees [%]

Notes. This table provides the list of key performance indicators (KPI) used by BIM to track the biodiversity, environmental, and social performance of their biodi­
versity deals on an annual basis.

itself is insightful. Indeed, a key challenge in biodiversity finance is how
to come up with metrics that are relevant and informative as to the
biodiversity impact of the underlying projects (Karolyi and Tobin-de la
Puente, 2023). BIM relies on a series of metrics pertaining to i) the
achievement of internationally recognized certifications, ii) sustainable

productive lands and seascapes (e.g., hectares of reforestation and
afforestation), iii) climate change mitigation (e.g., volume of GHG
emissions that are avoided, reduced, or sequestered), and iv) natural
ecosystems (e.g., hectares of land under conservation or restoration). In
addition to these environmental and biodiversity metrics, BIM also
12

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

tracks a set of KPIs pertaining to the social performance of the biodi­
versity projects, including metrics of i) community engagement, ii)
livelihood and decent work, and iii) diversity and inclusion.

addressed through blended financing structures, in which concessionary
capital is used to subsidize and de-risk private capital investments.
Third, the lack of experience and familiarity with the monetization
mechanisms of biodiversity projects, as well as the limited track record
of biodiversity investments, increase the ambiguity of the projects. This
in turn increases the value of fact-finding (e.g., pilot projects) that is
often financed through concessionary capital in blended financing
structures. In our conceptual framework (Section 2), we discuss these
three dimensions in detail.
More broadly, it is informative to compare the returns of biodiversity
finance with those of impact finance. In their 2024 report, Preqin (2024)
reports an average IRR of impact funds of 13.5 %, compared to 15 % for
non-impact private capital funds (based on a sample of 215 impact funds
and 10,812 non-impact funds). The former is close to the average ex­
pected IRR in our sample which is 13.52 % for private investors.
Therefore, according to the IRR metrics, our sample offers limited
financial trade-off compared to more traditional impact funds.
Finally, it is worth noting that blended finance is gaining traction in
impact investing as well. However, little is known about the structure
and economics of these deals.19 As such, the insights from this study
could help inform the practice of blended finance for non-biodiversity
projects as well, especially among the set of projects whose monetiza­
tion is based on the bundling of public and private goods (e.g., infra­
structure projects).

3.5. Deals that were discarded by BIM
In addition to the 33 in-portfolio deals described above, BIM also
granted us access to a set of deals that were under consideration for
portfolio inclusion but were ultimately discarded by BIM’s management.
While the information available for these deals is sparser, it nevertheless
includes a set of relevant variables that can be used to characterize the
selection process.
In total, we have relevant information for 32 of the discarded deals.
In Table 8, we contrast these 32 deals (“discarded deals”) vis-à-vis the 33
deals that made it to the portfolio stage (“portfolio deals”) on the basis of
several characteristics. The last column provides the p-value of the
difference-in-means test for each characteristic.
As is shown, the discarded deals tend to be both less profitable and
less impactful. Specifically, their average target IRR is 11.3 % (compared
to 13.5 % for in-portfolio deals, p-value = 0.035), their average total
impact area is 19,684 hectares (compared to 73,408 hectares, p-value =
0.006), their average GHG emissions reduction is 1.3 million tCO2e
(compared to 5.7 million tCO2e, p-value = 0.096), their average number
of beneficiaries is 3727 people (compared to 11,623 people, p-value =
0.045), and their average number of new jobs created is 1192 (compared
to 1846, p-value = 0.652). This suggests that, in order to be financed by
private capital—either as standalone or in blended structures—deals
need to cross a certain threshold in terms of both their financial return
and biodiversity impact. As such, these findings shed additional light
into the three-dimensional frontier that we formalized in Section 2.3.
Specifically, they indicate that, while blended finance can help improve
the risk-return profile of projects with high biodiversity impact, such
blended financing structures are unlikely to be considered if the in­
vestment’s initial risk-return profile is not favorable enough. Intuitively,
the initial (that is, pre-blending) risk-return tradeoff needs to cross a
certain threshold for blended finance to be effective in enhancing the
project’s risk-return profile to a level that would be attractive to private
investors. Accordingly—and this is the other side of the coin—this im­
plies that private capital (even in blended financing structures) is un­
likely to be a realistic option for a potentially large set of biodiversity
projects.

5. Conclusion
As massive amounts of financing are required to effectively address
the biodiversity crisis (TNC, 2020), biodiversity finance could play an
important role by helping mobilize private funding for the protection
and restoration of biodiversity.
While biodiversity finance is getting traction among investors, little
is known about this new practice. The objective of this study was to shed
light on it. In a nutshell, our contribution is twofold. First, we introduce
a conceptual framework that lays out how biodiversity can be financed
by pure private capital and blended financing structures. The main
element underlying both types of financing is the monetization of
biodiversity, that is, the extent to which investments in biodiversity can
generate a financial return for private investors. Second, we provide first
evidence on biodiversity finance. Using deal-level data from BIM, we
show that projects with higher expected returns tend to be financed by
pure private capital. Their scale is smaller, however, and so is their
expected biodiversity impact. For larger-scale projects with more
ambitious biodiversity impact, blended finance is the more prevalent
form of financing. While these projects have lower expected financial
returns, their risk is also lower. This suggests that the blending—and the
corresponding de-risking of private capital—is an important tool for
improving the risk-return tradeoff of these projects, thereby increasing
their appeal to private investors. Finally, we examine a set of projects
that were under consideration by BIM, but did not make it to the port­
folio stage. These projects tend to have lower financial and biodiversity
returns. This suggests that, in order to be financed by private capital­
—either as standalone or in blended structures—biodiversity projects
need to exceed a certain threshold in terms of both their financial return
and biodiversity impact. Accordingly, while private capital can help
close the financing gap and contribute to the conservation and restora­
tion of biodiversity, it is unlikely to provide a panacea against the
biodiversity crisis.
More broadly, an important question is how to scale up private in­
vestments in biodiversity. While blended financing can help enhance the

4. Biodiversity finance vs. impact finance
While biodiversity finance is a relatively new asset class, it shares
some similarities with impact finance. Like biodiversity funds, impact
funds pursue both financial and societal objectives. In their character­
ization of impact investing, Barber et al. (2021) show that impact funds
tend to achieve lower returns relative to traditional funds. By comparing
the IRR of impact vs. traditional funds and estimating a
willingness-to-pay (WTP) model with random utility, they estimate that
investors are willing to accept IRRs that are lower by 2.5–3.7 percentage
points for impact funds. In this regard, impact finance relies primarily on
“impact investors,” that is, investors who are willing to accept
below-market returns for the nonpecuniary benefit of societal impact.
Biodiversity finance differs in a number of ways. First, the moneti­
zation mechanisms are quite distinct, in that they require the bundling
of biodiversity (a public good) with private goods whose value it en­
hances. This is in contrast to traditional impact investments, in which
the monetization mechanisms are usually directly tied to private goods
(e.g., solar panels, wind turbines, business ventures in disadvantaged
urban areas).18 Second, the risk-return profile of biodiversity projects
need not be competitive enough to attract private capital. This can be
18

19
An exception is the companion paper by Flammer et al. (2024) that studies
the set of blended finance deals made by the World Bank’s IFC (International
Finance Corporation) and formalizes the decision-making of DFIs (development
finance institutions) in providing blended financing.

For example, see Boulongne et al. (2024) and Geczy et al. (2021).
13

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Journal of Financial Economics 164 (2025) 103987

Table 8
Deals that were discarded by BIM.
In-portfolio deals
A. Financial performance
Project return (target IRR)
B. Environmental and social impact
Total impact area (ha, expected)
GHG emissions reduction (1000 tCO2e, expected)
# Beneficiaries (expected)
# New jobs created (expected)

Discarded deals

Difference in means

N

Mean

Std. dev.

N

Mean

Std. dev.

p-value

​

​

​

​

​

​

​

​

​

​

​

​

​

​

33
17
18
13
15

13.52 %

3.68 %

73,408
5665
11,623
1846

167,115
8649
11,779
4273

32
28
12
11
12

11.29 %
19,684
1253
3727
1192

4.60 %
43,148
2094
3899
2813

0.035**
0.006***
0.096*
0.045**
0.652

Notes. This table reports the mean and standard deviation of several deal characteristics across all BIM deals that made it to the portfolio stage (“in-portfolio deals”) and
BIM deals that were discarded (“discarded deals”). Total impact area is measured in hectares (ha). Greenhouse gas (GHG) emissions are measured in 1000 t of CO2
equivalent (tCO2e). The last column reports the p-value of the difference-in-means tests comparing in-portfolio deals vs. discarded deals. *, **, and *** denotes
significance at the 10 %, 5 %, and 1 % level, respectively.

risk-return tradeoff of such investments, other hurdles are likely to
hamper the growth of this market. First, coordination among the rele­
vant actors is likely to be challenging. On one hand, project-holders
(“sellers”) and their local NGO partners have limited knowledge about
international investors’ preferences and requirements in terms of eligi­
bility criteria and reporting KPIs. On the other hand, international in­
vestors (“buyers”) know little about local markets and the challenges of
biodiversity projects. Second, these challenges are compounded by the
lack of common frameworks that could be used to assess biodiversity
projects and provide a basis for third-party certification. Such frame­
works are difficult to design due to the inherent challenges in measuring
biodiversity benefits, as well as the projects’ other societal benefits (e.g.,
community economic development). Arguably, making progress on
these dimensions is likely to help foster the growth of this market.
Lastly, our study is subject to two main limitations. First, our
empirical analysis is based on a sample of 33 biodiversity finance deals.
While these deals provide helpful insights, we caution that they need not
be representative of the broader population of biodiversity deals. In this
regard, our hope is that, as biodiversity finance continues to grow and
more comprehensive datasets become available, future work will be able
to provide larger-scale evidence on this new phenomenon. Second, since
the deals we examined are still ongoing, we only have limited infor­
mation on their ex-post performance, and hence our analysis is based
primarily on ex-ante projections at the time the deals were closed. We
again hope that, as time passes and post-completion data become
available, future work will shed additional light on the financial per­
formance and biodiversity impact of such investments. More broadly, a
key objective of this study was to lay the ground and stimulate future
research on biodiversity finance. In particular, more research is needed
to understand investors’ and companies’ attitudes toward biodiversity,
their perception of the economic value of biodiversity conservation, and
their perception of biodiversity risks; develop informative metrics of
firm- and project-specific biodiversity footprint and exposure to biodi­
versity risks; understand the interaction between biodiversity and
climate risks; understand the equilibrium implications of incorporating
biodiversity and natural capital in portfolio construction; and under­
stand how the increasing risks and costs associated with biodiversity loss
are likely to affect portfolios’ performance in the long run in the absence
of mitigation. These are exciting avenues for future work to pursue.

Declaration of competing interest
Caroline Flammer and Geoffrey M. Heal have no conflicts of interest
to disclose. Thomas Giroux reports a working relationship with BIM.
There are no other conflicts of interest to disclose.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.jfineco.2024.103987.
Data availability
Replication package for "Biodiversity Finance" (Reference data)
(Mendeley Data)
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CRediT authorship contribution statement
Caroline Flammer: Writing – review & editing, Writing – original
draft, Conceptualization, Data curation, Formal analysis, Investigation,
Methodology, Project administration, Resources, Supervision, Valida­
tion, Visualization. Thomas Giroux: Writing – review & editing,
Writing – original draft, Data curation, Formal analysis, Investigation,
Methodology, Resources, Validation, Visualization. Geoffrey M. Heal:
Writing – review & editing, Writing – original draft, Conceptualization,
Formal analysis, Resources, Visualization.
14

C. Flammer et al.

Journal of Financial Economics 164 (2025) 103987

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University.

15


==> JFE12 - ESG A panacea for market power.txt <==
Journal of Financial Economics 165 (2025) 103991

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/finec

ESG: A panacea for market power?✩
Philip Bond, Doron Levit ∗
University of Washington, United States of America

ARTICLE

INFO

Dataset link: Code used in "ESG: A Panacea for
Market Power?" (Original data)
JEL classification:
D74
D82
D83
G34
K22

ABSTRACT
We study the equilibrium effects of the “S” dimension of ESG under imperfect competition. ESG policies are
pledges made by firms that constrain managers to treat their stakeholders better than market conditions alone
dictate. Moderate policies limit market power and prompt managers to be more competitive; aggressive polices
backfire, both for adopting firms and intended beneficiaries. In contrast to the “shareholder primacy” paradigm,
competition in ESG policies under the “stakeholder capitalism” paradigm is a panacea for market power,
delivering the first-best outcome in equilibrium. We discuss drivers behind the recent rise in ESG, ESG-linked
compensation, and disclosure practices.

Keywords:
ESG
Shareholder primacy
Stakeholder capitalism
Corporate social responsibility
Corporate governance
Market power

1. Introduction

There is a long-running debate in academic and policy circles over
whether the purpose of the corporation is or, should be, to maximize
value for shareholders or, instead, to operate in the interest of all
of its various stakeholders. These questions have far-reaching implications, including whether and how companies and boards take into
account Environmental, Social and Governance (ESG) considerations
when developing and delivering products and services, making business
decisions, managing risk, developing long-term strategies, recruiting
and retaining talent and investing in the workforce, implementing
compliance programs, and crafting public disclosures. A growing number of empirical studies have examined whether firms indeed pursue

ESG policies, whether these policies achieve their putative aims, and
whether equity markets reward such policies. Theoretical studies have
also examined whether and how shareholder actions incentivize firms
to behave in socially responsible ways. However, largely absent from
the literature is an examination of how firms’ ESG policies affect
equilibrium outcomes in the real input and output markets that they
operate in. Our paper aims to fill this gap, and to study the “basic
economics” of ESG policies.
Specifically: We focus on the “S” component of ESG in labor and
product markets. We interpret a typical firm’s policy in this realm as a
pledge to treat its workers or customers better than market conditions
alone dictate. Leading real-world examples of such practices are pledges

✩ Philipp Schnabl was the editor for this article. We thank the editor for helpful comments. We are grateful to Daniel Green, Deeksha Gupta, Andrey Malenko,
Robert Marquez, Martin Oehmke, Johann Reindl, Karin Thorburn, conference participants at the UNC-Duke Corporate Finance Conference 2023, Finance Theory
Webinar 2023, Adam Smith Workshop in Corporate Finance 2023, Financial Intermediation Research Society 2023, BI Conference on Corporate Governance
2023, NBER SI Corporate Finance 2023, ECGI 2024, and seminar participants at the University of British Columbia, the University of Bonn, the Federal Reserve
Board, Frankfurt School of Finance and Management, the University of Geneva, INSEAD, CEU, the University of Vienna, Reichman University, HKUST, Rice
University, the University of Utah, Boston University, Copenhagen Business School, Iowa State University, Yeshiva University, and Wharton, for helpful comments
and discussions.
∗ Corresponding author.
E-mail addresses: apbond@uw.edu (P. Bond), dlevit@uw.edu (D. Levit).

https://doi.org/10.1016/j.jfineco.2024.103991
Received 4 April 2024; Received in revised form 20 December 2024; Accepted 23 December 2024
Available online 24 January 2025
0304-405X/© 2024 Published by Elsevier B.V.

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

to pay employees above market wages,1 to provide generous benefits,
to invest in worker training, and to create a friendly work environment;
and, in the context of product markets, to offer products with low environmental impact, high safety standards, strong protection of customer
privacy/cybersecurity, low prices and/or high quality-to-price, etc.
We study how individual firm pledges to depart from market clearing prices affect equilibrium outcomes. We first characterize outcomes;
and then analyze how firms pick policies in anticipation of the outcomes they generate. We are especially interested in the effect of such
pledges in markets where firms wield market power and standard welfare theorems do not apply. Indeed, one of our main results shows that
competition in ESG policies between socially minded firms eliminates
market power distortions.
Our analysis revolves around two robust consequences of ESG policies that pledge to treat workers/customers better than market conditions dictate. On the one hand, such policies make workers more
expensive to hire/customers less profitable to serve, in turn leading to
a smaller firm that provides softer competition for its competitors. On
the other hand, such policies ameliorate monopsony/oligopoly temptations to moderate hiring/production; this in turns leads to a larger
firm that provides stronger competition for its competitors. We label
these conflicting effects as the anti- and pro-competitive effects of ESG
policies.
We first characterize the effects of just one firm adopting an ESG
policy. For example, a firm may be a “thought leader” or “early
adopter” in ESG, or may be better able to credibly pledge to treat
stakeholders well than its competitors. For mild ESG policies – meaning
pledges to treat workers/customers only moderately better than market
conditions require – the pro-competitive effect dominates. In this case,
the ESG firm gains market share at the expense of competitors; and
the ESG policy generates positive spillovers for workers/customers of
other firms. In contrast, for aggressive ESG policies the anti-competitive
effect dominates: the ESG firm loses market share, and while the ESG
firm’s own workers/customers benefit, the reduced competitiveness
engendered by the ESG policy produces negative spillovers for other
firms’ workers/customers.
When multiple firms adopt ESG policies, the gain in market share
associated with incremental increases in ESG is even more pronounced.
Specifically: if firms adopt the same ESG policy then this shared-ESG
policy determines the overall size of the market, but not its division
among competing firms. Marginally outdoing the ESG policies of competing firms breaks the indeterminacy, and discretely increases the
market share of the ESG-winner.
We turn next to firms’ choices of ESG policies, assuming that firms
anticipate the consequences of these policies for market outcomes. We
consider two corporate governance paradigms: “shareholder primacy”
and “stakeholder capitalism.” In the first case, a firm chooses ESG
policies to maximize profits; while in the second case, a ‘‘purposeful’’
firm chooses ESG policies to maximize the combination of profits and
employee/customer surplus.
While we consider both corporate governance paradigms, i.e., alternative objectives of boards/controlling shareholders, we focus throughout on the case in which firms’ operational decisions are made by
managers who seek to maximize profits. Consequently, and in contrast
to the case of profit-maximizing firms, for purposeful firms there is

a meaningful distinction between the economic agents who set ESG
policies and those who make operational decisions constrained by these
policies.
An individual profit-maximizing firm benefits from adopting a mild
ESG policy. At first sight it may seem surprising that a pledge to
pay higher wages/charge lower prices increases profits. The underlying economic force is that mild pledges are pro-competitive, because
they commit a firm to ignoring monopsony/oligopoly distortions; and
commitment is generally valuable in competitive settings. Interestingly, ESG policies of the type we consider – again, pledges to treat
workers/customers better than market conditions alone dictate – are
enough to give a profit-maximizing firm all the commitment that it
desires. Even though such a firm selects an ESG policy with only
its own profits in mind, and the policy directly affects only its own
wages/prices, the equilibrium outcome is to increase welfare for both
its own workers/customer and those at other firms. However, a firm’s
ESG policy distorts production by driving a wedge between its marginal
product and that of its competitors; and under some circumstances, this
distortion is sufficiently large that overall social surplus declines.
An individual purposeful firm adopts a stronger ESG policy than a
profit-maximizing firm, as one would expect. More interesting is that a
purposeful firm always adopts an ESG policy that is excessive from the
perspective of overall social surplus; on the margin, the aforementioned
production distortion dominates other effects. At the same time, and
differently from its profit-maximizing counterpart, a purposeful firm
wishes it had additional tools at its disposal beyond the ESG policies
that we focus on (e.g., ESG-linked executive pay)—though access to
such tools would be socially costly, and further reduce social surplus.
The advantages that a firm gains from pledging to treat its stakeholders well naturally give rise to competition on a new front: ESG
policies. We first consider competition in ESG policies under the shareholder primacy paradigm. As noted above, a firm gains significant
market share by marginally outdoing its competitor’s ESG policy. Because of this, ESG policies are strategic complements at moderate levels.
However, if a competitor has adopted an aggressive ESG policy then
abandoning ESG is a better response than further escalation; the cost
of treating stakeholders even more generously exceeds the benefit of
additional market share. Hence, ESG policies are strategic substitutes
at aggressive levels. These observations naturally result in competing
firms adopting different ESG policies, even when ex ante identical.
Relative to a no-ESG benchmark, competition in ESG policies between
profit-maximizing firms reduces industry profits while benefiting workers/customers. Nevertheless, ESG-competition leaves an industry that is
too small from a social perspective, because it ameliorates but does not
eliminate market power distortions. Furthermore, competition in ESG
policies has the potential to reduce overall social surplus, because of
the production distortions mentioned earlier.
ESG-competition between purposeful firms plays out differently.
The main reason is that ESG policies are stronger strategic complements for purposeful firms than for shareholder-value maximizing
ones. Similar to a profit-maximizing firm, a purposeful firm benefits
from marginally outdoing its competitor’s ESG policy. Unlike a profitmaximizing firm, however, a purposeful firm is not tempted to undercut
its competitor by abandoning ESG policies, since it internalizes the
direct gains to its stakeholders. In this case, we obtain a striking welfare
theorem: Competing purposeful firms pick equilibrium ESG policies
that lead to the first-best outcome for the industry. In this respect, ESG
is a panacea to market power. We emphasize that this result holds even
though each individual firm aims only to maximize its own surplus,
which as discussed above has adverse welfare effects when only a
subset of firms are purposeful.
Our welfare theorem is driven by two opposing forces. On the
one hand, a purposeful firm seeks to be large. Similar to our earlier
discussion, an unconstrained purposeful firm would operate above
its first-best size. On the other hand, a profit-maximizing manager
operates at a scale at which marginal profits are positive; this causes

1
As a representative example of such policies: In recent years, Bank of
America has adopted a nationwide minimum hourly wage for its employees,
which has risen from $15 in 2017 to $23 in 2023. According to Bank of
America’s CHRO Sheri Bronstein, “Providing a competitive minimum rate
of pay is foundational to being a great place to work.” Moreover, “By
investing in a variety of benefits to attract and develop talented teammates,
we are investing in the long-term success of our employees, customers and
communities. Our commitment to $25 by 2025 is how we share success with
you and lead the way for other companies.” (www.shrm.org, “Bank of America
Bumps Up Minimum Wage”).

2

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

aggressive ESG policies to backfire and reduce a firm’s size. Combining
these two observations: the misalignment between the objectives of a
purposeful board and its profit-maximizing managers drives firms to
be large—but not too large; and competition between purposeful firms
delivers the first best outcome. Moreover, the ESG policy that balances
the misaligned objectives of purposeful boards and profit-maximizing
manager is robust to perturbations to the board’s objectives, and consequently our welfare theorem holds as long as the weight placed on
worker/consumer welfare is sufficiently large.
Our analysis has important implications that go beyond the specific
context of our model. First, our analysis suggests two possible drivers
for the recent rise in ESG: the rise of concentration and market power
in key industries across the US economy and a shift in the strength of
investors’ pro-social preferences.
Second, relative to non-ESG firms, the output of firms that adopt
moderate ESG policies is less sensitive to own productivity shocks, but
more sensitive to productivity shocks hitting competitors.
Third, our analysis suggests that ESG-linked executive pay offers
no discernible social value, and stakeholder capitalism is best served
when managers maintain a focus on profit-maximization, with boards
strategically setting ESG policies to mitigate any adverse impacts that
profit-maximization may have on other stakeholders of the firm.
Last, while regulations that facilitate transparency and disclosure of
ESG policies contribute to the efficacy and adoption of these policies
under the shareholder primacy paradigm, they matter much less for the
adoption of ESG policies under the stakeholder capitalism paradigm.
Overall, our analysis relates the adoption of ESG policies to the
nature of competition between firms and the prevailing corporate
governance paradigm. We conclude with a large set of novel empirical
predictions for how ESG policies affect profits, market shares, margins,
responsiveness to productivity shocks, wages/prices, welfare of stakeholders; and also for how competition, transparency, peer-firms’ ESG
policies, and corporate governance affect ESG.

executes them generates novel implications with respect to the desirability of additional ESG tools such as ESG-linked executive pay and the
effectiveness of regulations that facilitate transparency and disclosure
of ESG policies.
Xiong and Yang (2024) explore a different motive for ESG policies
by shareholder-value maximizing firms that specifically operates for
network goods. Albuquerque et al. (2019) model ESG as a characteristic
that directly impacts consumer demand. Besley and Ghatak (2007)
argue that public-good provision by competing profit-maximizing firms
neither ameliorates nor amplifies the free-rider problem associated with
direct contributions to public goods. Dewatripont and Tirole (2024)
study a model of imperfect competition with socially responsible consumers. Unlike in our framework, in their model firms adopt ESG
policies that affect consumers’ welfare above and beyond the price they
charge. They show that the degree of competitive pressure is irrelevant
for the adoption of ESG policies if prices are flexible. In contrast, we
examine policies aimed at treating firms’ stakeholders well in situations
where excessive market power disadvantages them, and establish that
in these cases firms typically adopt more aggressive ESG policies as
markets become less competitive.
At an abstract level, the idea of firms’ ESG choices affecting subsequent equilibrium outcomes under imperfect competition is related to
literature studying the effects of other types of firm decisions, including, for example, Brander and Lewis (1986)’s analysis of debt choices
and Fershtman and Judd (1987)’s, as well as Sklivas (1987)’s analysis
of managerial contracts. A central theme in much of this literature is
that firms can effectively commit to compete more aggressively via
decisions made prior to product market interactions, and that doing
so is a potential source of advantage. Perhaps surprisingly, this same
effect operates in our setting also—after all, it is not obvious whether
constraining managers to pay workers more leads firms to compete
more or less aggressively.2 More generally, the application of the idea
that commitment helps in imperfect competition settings to the specific
context of ESG yields numerous insights, including the extent to which
competition in ESG firms pushes the equilibrium outcome toward the
socially optimal one.
A sizeable literature has addressed the topic of a firm’s objectives.
See, for example, Tirole (2001); or for a recent survey, Gorton et al.
(2022). Magill et al. (2015) note that just including the surpluses of the
firm’s own consumers and workers in the firm’s objective does not lead
to efficiency, and that underweighting these stakeholders in the firm’s
objective function could improve efficiency. Allen et al. (2015) study
the strategic behavior between stakeholder-oriented firms, defined as
firms that overweight their survival relative to what their own shareholders would internalize; they do not study firms’ choices to adopt ESG
polices. Geelen et al. (2023) study how differences in social preferences
between the firm’s manager and owner affect the sustainability of the
organization. Allcott et al. (2023) quantitatively estimate the relative
importance of firm’s profits, consumer and worker surplus, and a subset
of externalities including carbon emissions.
While the theoretical literature on the effects of ESG policies on
product and labor market is small, a larger theoretical literature considers the effects of responsible investment on corporate policies: Heinkel
et al. (2001), Davies and Van Wesep (2018), Oehmke and Opp (2024),
Edmans et al. (2022), Landier and Lovo (2020), Green and Roth (2024),
and Chowdhry et al. (2019), Huang and Kopytov (2022), Gupta et al.
(2022), and Piccolo et al. (2022).
Finally, in the labor-market application of our model, a firm can increase its profits by paying above market-clearing wages to its workers.
In this respect, our paper adds a new channel to the extensive literature

Related literature
The literature on the consequences of ESG policies for the equilibria
of the real markets in which firms operate, and in turn for the ESG
choices of competing firms, is relatively sparse.
The closest relevant study is Stoughton et al. (2020), which analyzes
imperfect competition between firms that commit to maximize an
objective that weights both profits and worker/customer surplus. Our
analysis shares with Stoughton et al. the observation that shareholder
value is potentially raised by a firm’s commitment to deviate from
profit-maximizing behavior. However, in contrast to Stoughton et al.
we model an ESG policy as a firm’s explicit promise to treat its stakeholders well, which operates as a constraint on the minimum level of
utility to stakeholders. This difference in how we conceptualize ESG
policies has important implications. First, while in Stoughton et al. ESG
policies are always pro-competitive, many of our results stem from
the interplay of the pro- and anti-competitive effects of ESG, which
in turn stems from the separation between high-level firm objectives
(e.g., of the board) and profit-maximization at the operations stage
(e.g., by the manager). In particular, the presence of anti-competitive
effects means that aggressive ESG policies can backfire both for the
firm and their intended beneficiaries. Second, in Stoughton et al. ESG
policies are always strategic substitutes, while in our analysis ESG
polices are strategic complements at moderate levels and strategic
substitutes at extreme levels, thereby capturing in a natural way both
a firm’s incentives to outdo a competitor’s modest ESG policies, and
a firm’s willingness to severely undercut a competitor’s “generous”
policy. Third, the combination of the first two points plays a crucial role
in our central welfare theorem that competition between purposeful
firm delivers efficiency. Last, our distinction between the objective of
the board/shareholder who sets ESG policies and the manager who

2
In a non-ESG setting, Rey and Tirole (2019) study the use of price caps by
firms selling complementary goods, and show that such price caps can alleviate
double-marginalization problems for firms. In their analysis, firms collectively
agree to price-cap arrangements.

3

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

on efficiency wages that has explored a variety of ways in which
firms may benefit from above market-clearing wages (see Katz (1986)
for a literature review). The distinguishing feature of our channel is
that it operates via inter-firm strategic interactions; a firm’s promise
of higher pay can induce competitors to compete less aggressively.
In contrast to the existing efficiency wage literature, paying higher
wages ends up lowering (rather than raising) the productivity of a firm’s
marginal worker. Related, unlike the literature on minimum wages, in
our model minimum wages are self-imposed, allowing for variations
across firms and richer welfare implications. Nonetheless, our model
is consistent with recent empirical evidence by Azar et al. (2023), who
show that minimum wage increases lead to positive employment effects
in concentrated labor markets.3

by executives who have incentives to maximize profit.
We emphasize that, in practice, ESG promises to treat workers well
often cover multiple dimensions of the employment relation, including
non-pecuniary benefits of various kinds (e.g., health care coverage,
paid family leave, and workplace flexibility), and that 𝜔𝑖 should be
understood as the monetary-equivalent of these various promises.
We consider two corporate governance paradigms throughout the
analysis. Under the shareholder primacy paradigm, a firm’s board
adopts an ESG policy 𝜔𝑖 with the objective of maximizing firm profits,
i.e., shareholder value. We label such firms as shareholder firms. Under
the stakeholder capitalism paradigm, a firm’s board instead adopts an
ESG policy 𝜔𝑖 with the objective of maximizing a broader measure of
a firm’s impact, namely total surplus created by the firm—which here
equals the sum of firm-profits and worker-surplus. We label such firms
as purposeful firms. Leading cases in which purposeful firms potentially
emerge are if shareholders are socially conscious, if workers gain board
representation, or if the firm is incorporated as a Benefit Corporation
(“B Corp”) with a legal obligation to consider the impact of its policies
not only on shareholders but also on other stakeholders such as its
employees. Note that purposeful firms are “narrow” consequentialists
in the sense that they internalize the impact of their policies on all
stakeholders of their firm, i.e., their own shareholders and workers, but
not the stakeholders of their competitors. The same assumption is made
in prior literature, including, for example, Magill et al. (2015).6
For both corporate governance paradigms we assume that managers
maximize profits, subject to the constraints imposed by ESG policies.
In Section 4.2, we show that shareholder firms do not gain from
also incentivizing managers to directly internalize the welfare of the
firm’s employees, e.g., via ESG-linked executive pay. In contrast, our
analysis in Section 4.3 demonstrates that purposeful firms could gain
from providing such incentives, but that doing so would reduce social
welfare. See Section 6.4 for a discussion of alternative ESG tools.

2. Set-up
For transparency, we present our analysis in terms of ESG policies
for workers. Parallel implications hold for ESG policies for suppliers
and for customers; see Section 6.1. Consider an imperfectly competitive
labor market with two firms.4 Each firm 𝑖 ∈ {1, 2} deploys labor
( )
𝑙𝑖 ∈ [0, 1] to produce 𝑓𝑖 𝑙𝑖 , where 𝑓𝑖 (⋅) is strictly increasing and
concave. Throughout, we assume firms hire a strictly positive number
of workers by imposing the standard Inada condition 𝑓𝑖′ (0) = ∞.
The productivity of the two firms is unambiguously ordered, i.e., the
comparison between 𝑓1′ (𝑙) and 𝑓2′ (𝑙) is independent of 𝑙. Without loss,
firm 1 is weakly more productive, 𝑓1′ (⋅) ≥ 𝑓2′ (⋅). We write 𝐿 ≡ 𝑙1 + 𝑙2
for total labor employed at all firms. There is a continuum of workers,
with a measure normalized to 1, and ordered on [0, 1] by outside option
𝑊 (𝑙) for worker 𝑙 ∈ [0, 1], where 𝑊 ′ (⋅) > 0. Hence the inverse labor
supply curve is 𝑊 (𝐿).
Firms compete in Cournot fashion. That is, firms’ managers simultaneously announce hiring 𝑙1 , 𝑙2 , and the market wage is determined
by 𝑊 (𝐿). There is significant evidence that employers enjoy market
power in labor markets; see, for example, Lamadon et al. (2022).
The objective of the manager of each firm is to maximize its profits.
We assume
𝑊 ′′ (𝐿) 𝐿 + 𝑊 ′ (𝐿) > 0,

Remark on the framework of competition
Our analysis builds on a standard Cournot model of imperfect
competition. This makes transparent the role of the novel aspects of
our analysis, namely, firms’ ESG policies to treat their stakeholders
well. The Cournot model has the specific advantages of allowing for
a clear separation between ESG policies (expressed in terms of price)
and subsequent actions in the imperfect-competition game (in Cournot,
quantities).7 It also naturally generates the pro- and anti-competitive
effects of ESG policies that are central to our analysis.
Related, the assumption of downwards sloping quantity-reaction
functions is intuitive and widely-imposed in the literature. It is an important ingredient in our analysis of shareholder firms, but matters less
for the case of purposeful firms (see discussion at end of Section 4.3.)8

(1)

which ensures both that managers’ reaction functions to other managers’ hiring decisions slope down (see Lemma 1 below) and that the
employment cost 𝑊 (𝐿) 𝐿 faced by a monopsonistic firm is convex
(i.e., 𝑊 ′′ (𝐿) 𝐿 + 2𝑊 ′ (𝐿) > 0).
The key innovation of our analysis is that firms can adopt ESG
policies. Specifically, before managers make hiring decisions, the board
of each firm 𝑖 may adopt an ESG policy that constrains the firm
to pay its workers at least 𝜔𝑖 ≥ 0. Hence an ESG policy is fully
characterized by 𝜔𝑖 . If firm 𝑖 adopts policy 𝜔𝑖 , it pays its workers
{
}
max 𝜔𝑖 , 𝑊 (𝐿) .5 Firms’ ESG policies are public, and in particular
observed by competitors. The firm’s manager maximizes firm-profits
subject to this constraint. That is: The board of directors of the firm
adopts an ESG policy that can be monitored and enforced (wages and
benefits are observable and verifiable), but the hiring decision is made

6
Even among proponents of stakeholder capitalism, there exists considerable skepticism whether firms should internalize the welfare of stakeholders
affiliated with their competitors; see, e.g., Bebchuk and Tallarita (2020) and
Mayer (2022).
7
Kreps and Scheinkman (1983) show that, under some circumstances, the
Cournot outcome arises if firms first choose maximum capacities, and then
subsequently engage in price competition. Similarly, we conjecture that equilibria in our setting coincide with the outcomes of a game in which (i) boards
of directors set ESG policies; (ii) profit-maximizing managers make capacity
decisions; (iii) profit-maximizing managers engage in price competition.
8
Note that although the distinction between actions as strategic substitutes
and complements is sometimes related to quantity versus price competition,
the two notions are separate; quantity competition can generate strategic complementarity, while price competition can generate strategic substitutability.
Indeed, in models of price competition based on firm “location,” this last
point is often overlooked because many analyses focus for simplicity on the
case in which all consumers buy from at least one firm; see, for example, the
discussion in Mas-Colell et al. (1995), and especially exercise 12.c.14.

3
For more evidence on the effects of minimum wages see, e.g., Card and
Krueger (1995), Neumark and Wascher (2008) and references in Azar et al.
(2023).
4
In Appendix I of the Online Appendix, we analyze competition between
one ESG firm and 𝑁 ≥ 2 non-ESG firms, and show that the results are similar
to those reported in Section 4. Moreover, the analysis of one ESG firm and
a competitive fringe is also similar to the analysis in Section 4 since the
competitive fringe will never adopt an ESG policy. Analyzing competition
between 𝑁 > 2 ESG firms is substantially more complicated and left for future
research.
5
ESG policy 𝜔𝑖 has no effect on firm 𝑖’s production or revenue. A positive
and direct effect on the firm’s production function would be analogous to the
effect of efficiency wages.

4

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

Thus, the first-best allocation is 𝑙𝑖∗∗ such that for 𝑖 ∈ {1, 2}
( )
(
)
𝑓𝑖′ 𝑙𝑖∗∗ = 𝑊 ∗∗ ≡ 𝑊 𝑙1∗∗ + 𝑙2∗∗ .

Remark on commitment
An ESG policy in our model is a firm’s pledge to treat its stakeholders well. This formulation implicitly assumes that shareholder firms,
whose objective is profit maximization, refrain from subsequently
breaking these ESG pledges.9
A firm that breaks its pledges risks damaging public perception of
its ethical standards. By itself, this incentivizes a firm to honor its
pledges so as to maintain the trust of its stakeholders. Transparency and
disclosure of ESG policies, along with information intermediaries such
as Glassdoor and Great Place To Work for labor markets, and organizations such as the American National Standards Institute and Consumer
Reports for product markets, reinforce these incentives. Moreover, in
practice, many pledges to stakeholders involve up-front investments or
third-party contracts; subsequent divestment or reneging on contracts
is then costly. For example, employee retirement and healthcare plans
often involve contracts with major financial institutions. Such commitments are complex and infrequently revised (e.g., Yang (2024)).
Likewise, generous warranty programs for durable goods are not easily
reversible. Moreover, firms that neglect pledges to product safety,
privacy, or cybersecurity measures expose themselves to legal action
and regulatory scrutiny. In all scenarios, non-trivial commitment can
be achieved at least for the short to medium run, which is the minimal
assumption our model requires.
We model a firm’s pledge to treat its stakeholders well as a commitment to provide a minimum level of utility. Theoretically, ESG
policies could also be stated in quantities, e.g., a commitment to hire
a specific number of workers. However, commitments to such quotas
are less likely to entail significant upfront investments or third-party
contracts, and instead rely more heavily on alternative commitment
mechanisms such as reputation , and thus are less inherently credible.
Moreover, verifying and enforcing quota-based policies can be challenging; a profit-maximizing manager might justify under-hiring due
to a purported lack of qualified applicants or undermine it by reducing
advertising, lowering benefits, or raising hiring standards. This might
explain why such policies are uncommon.
ESG policies constrain the range of feasible outcomes, relative to
direct commitment to quantities. However, as we observe in Section 4.2, for shareholder firms, the limited commitment generated by
these policies suffices.10 In contrast, Section 4.3 highlights that for
purposeful firms, the distinction between commitment in quantities
versus commitments in wages/utilities matters. This contrast is further
explored in Section 5.3, particularly concerning the role of the wedge
between the purposeful board and the profit-maximizing managers
in our key findings, as well as in Section 6.4 concerning ESG-linked
executive compensation implications.

(3)

Note that 𝑙𝑖∗∗

would be the equilibrium outcome if both firms were
controlled by a single owner whose objective is to maximize surplus
rather than profit. It is also immediate that the first-best allocation
would arise if the labor market was fully competitive, so that each firm
acts as a price-taker. Indeed, let
( )
(4)
𝜆𝑖 𝑊0 ≡ ar g max 𝑓𝑖 (𝑙) − 𝑙𝑊0
𝑙

be firm 𝑖’s profit-maximizing hiring decision if facing a constant wage
𝑊0 . Then, 𝑙𝑖∗∗ = 𝜆𝑖 (𝑊 ∗∗ ). Notice that 𝜆𝑖 (⋅) is a decreasing function. We
use this notation throughout. Since firm 1 is weakly more productive
it hires more workers under the first-best allocation, 𝑙1∗∗ ≥ 𝑙2∗∗ . (Never)
′ ∗∗
theless,
( ∗∗ ) the marginal productivity of both firms is identical, 𝑓1 𝑙1 =
′
𝑓2 𝑙2 .
3.2. No-ESG benchmark
Consider a benchmark in which firms do not adopt ESG policies
(i.e., 𝜔1 = 𝜔2 = 0). Firm 𝑖 takes firm −𝑖’s hiring 𝑙−𝑖 (as given
) and
maximizes profits, generating firm 𝑖’s reaction function 𝑟𝑖 𝑙−𝑖 ; 0 . Here,
0 denotes No-ESG policy (𝜔𝑖 = 0). Formally,
(
)
(
)
𝑟𝑖 𝑙−𝑖 ; 0 ≡ ar g max 𝑓𝑖 (𝑙) − 𝑙𝑊 𝑙 + 𝑙−𝑖 .
(5)
𝑙

(
)
Lemma
(
)1. The reaction function 𝑟𝑖 𝑙−𝑖 ; 0 is strictly decreasing in 𝑙−𝑖 and
𝑟𝑖 𝑙−𝑖 ; 0 + 𝑙−𝑖 is strictly increasing in 𝑙−𝑖 .
All omitted proofs are in Appendix A. Lemma 1 establishes that if
firm −𝑖 hires more then firm 𝑖 hires less, because firm −𝑖’s increased
hiring raises wages. However, firm 𝑖 reduces its hiring by less than
the increase in firm −𝑖’s hiring, so that overall hiring increases. To
see the latter point, note that if firm 𝑖 instead reduces its hiring by
the same amount that firm −𝑖 increases its, then wages would remain
unchanged, while firm 𝑖’s marginal productivity is higher (since 𝑓 is
concave), implying that firm 𝑖 is not optimizing.
Next, we characterize the equilibrium of the No-ESG benchmark.
Lemma 2. In the unique
of the No-ESG benchmark, each firm
( 𝐵 equilibrium
)
; 0 , i.e.,
𝑖 = 1, 2 hires 𝑙𝑖𝐵 = 𝑟𝑖 𝑙−𝑖
( )
(
)
(
)
𝑓𝑖′ 𝑙𝑖𝐵 = 𝑊 ′ 𝑙1𝐵 + 𝑙2𝐵 𝑙𝑖𝐵 + 𝑊 𝑙1𝐵 + 𝑙2𝐵 .
(6)
Moreover, 𝑙1𝐵 ≥ 𝑙2𝐵 ,

3. Preliminaries
We start by stating several basic results and definitions that we use
throughout.

𝑙1𝐵 + 𝑙2𝐵 < 𝑙1∗∗ + 𝑙2∗∗ ,

(7)

and both firms pay their workers
(
)
𝑊 𝐵 ≡ 𝑊 𝑙1𝐵 + 𝑙2𝐵 < 𝑊 ∗∗ .

(8)

As in the first-best benchmark, the more productive firm hires more
workers, 𝑙1𝐵 ≥ 𝑙2𝐵 . However, unlike the first-best
( )benchmark,
( ) the larger
firm has a higher marginal productivity, 𝑓1′ 𝑙1𝐵 ≥ 𝑓2′ 𝑙2𝐵 . Intuitively,
monopsony power stops firms from fully internalizing the social benefit
of increasing employment, and the larger firm fails to internalize it to
a larger extent.
Lemma 2 confirms that the usual monopsony distortion arises, so
that total employment and wages are below first-best levels. Forcing both firms to hire more and pay higher wages would move the
economy closer to efficiency. Regulators who aim to maximize social
welfare would be tempted to impose a minimum wage on the industry.
However, such an intervention would need to be tailored to industryspecific conditions that are likely to be hard for a regulator to observe.
In contrast, firms have a better knowledge of the industry in which
they operate, motivating our interest in studying their incentives to
self-impose ESG policies.

3.1. First-best benchmark
The first-best allocation maximizes industry surplus, which equals
total output net of the outside options of workers employed:
𝑙1 +𝑙2
(
)
( )
( )
𝑊 (𝑙) 𝑑 𝑙.
(2)
𝑆 𝑙1 , 𝑙2 ≡ 𝑓1 𝑙1 + 𝑓2 𝑙2 −
∫0
9
The same arguments apply to purposeful firms, although for these firms,
commitment is less needed. See Lemma D-12 in the Online Appendix and the
discussion that follows Corollary 1 in Section 4.3.
10
Specifically, the equilibrium allocations characterized by Proposition 2
would not change if instead the shareholder firm adopts an ESG policy that is
stated in quantities rather than wages/utilities.

5

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

)
(
3.3. An ESG firm’s reaction function 𝑟𝑖 ⋅; 𝜔𝑖
Suppose that, before hiring, firm 𝑖’s board adopts the ESG policy 𝜔𝑖 ,
{
}
thereby constraining the firm to pay its workers max 𝜔𝑖 , 𝑊 (𝐿) . Given
this constraint, firm 𝑖’s manager chooses 𝑙𝑖 to maximize its profits. Here,
we characterize firm 𝑖’s hiring response 𝑙𝑖 to firm −𝑖’s hiring 𝑙−𝑖 , given
firm 𝑖’s ESG policy 𝜔𝑖 —that is, firm 𝑖’s reaction function.
Firm 𝑖’s profits given employment decisions 𝑙𝑖 and 𝑙−𝑖 and firm 𝑖’s
ESG policy 𝜔𝑖 is
(
)
( )
{ (
)
}
𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 𝜔𝑖 ≡ 𝑓𝑖 𝑙𝑖 − max 𝑊 𝑙𝑖 + 𝑙−𝑖 , 𝜔𝑖 𝑙𝑖 .
(9)
Note that firm 𝑖’s profits are affected by firm −𝑖’s ESG policy only
via firm −𝑖’s hiring decision 𝑙−𝑖 . As such, firm 𝑖’s reaction function is
independent of firm −𝑖’s ESG policy:
(
)
(
)
(10)
𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 ≡ ar g max 𝜋𝑖 𝑙, 𝑙−𝑖 ; 𝜔𝑖 .

Fig. 1. An ESG firm’s labor reaction function.

𝑙

(
)
To characterize 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 , we first define 𝛬𝑖 (𝜔) as the solution to
𝛬 + 𝑟−𝑖 (𝛬; 0) = 𝑊 −1 (𝜔) .

of the firm is to choose the residual level of demand such that the
resulting market wage exactly equals its self-imposed minimum wage.
Put differently, the manager of firm 𝑖 ignores the monopsony distortion
as long as there are enough workers who are willing to accept a wage
of 𝜔𝑖 . Notice that while firm 𝑖 is not paying above the market wage, its
ESG policy increases the market wage above the level that would have
emerged if it were to set 𝜔𝑖 = 0. We label this region as the residual
region.
( )
In the third region, where 𝑙−𝑖 > 𝛬−𝑖 𝜔𝑖 , firm 𝑖’s ESG policy is not
(
)
(
)
( )
binding, i.e., 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 = 𝑟𝑖 𝑙−𝑖 ; 0 . To see this, note that 𝑙−𝑖 > 𝛬−𝑖 𝜔𝑖
(
(
))
is equivalent to 𝑊 𝑙−𝑖 + 𝑟𝑖 𝑙−𝑖 ; 0 > 𝜔𝑖 , which says that firm 𝑖’s profit
maximizing response to 𝑙−𝑖 pushes the market wage above 𝜔𝑖 even
absent any ESG-imposed constraint. We label this as the non-binding
region.
Fig. 1 also shows how firm 𝑖’s reaction function shifts as its ESG
policy grows more aggressive; this is the shift from the solid blue line
to the dashed green line. The price-taking, residual, and non-binding
regions all shift to the right. For intermediate hiring by firm −𝑖, roughly
the residual region, a more aggressive ESG policy 𝜔𝑖 leads firm 𝑖 to hire
more, and the reaction function shifts up. This is the pro-competitive
effect of ESG; a more aggressive ESG policy extends the perfectly elastic
portion of the supply curve that firm 𝑖’s manager faces. But for low
hiring by firm −𝑖, roughly the price-taking region, a more aggressive
ESG policy 𝜔𝑖 leads firm 𝑖 to hire less, and the reaction function shifts
down. This is the anti-competitive effect of ESG; a more ESG policy
makes workers more expensive, and the manager hires less.

(11)

In words, 𝛬𝑖 (𝜔) is the level of hiring by firm 𝑖 such if firm −𝑖 is a nonESG firm and responds optimally then the resulting wage is 𝜔. Define
(
)
(
)
𝛬𝑖 (𝜔) = 0 if 𝑊 𝑟𝑖 (0; 0) > 𝜔 and 𝛬𝑖 (𝜔) = ∞ if 𝑊 𝛬 + 𝑟𝑖 (𝛬; 0) < 𝜔
for all 𝛬. Note that 𝛬𝑖 (𝜔) is well-defined because, by Lemma 1, the left
hand side of (11) is strictly increasing in 𝛬, so at most one solution
exists. For use below, note that Lemma 1 also implies that 𝛬𝑖 (⋅) is
strictly increasing.
The next result, formally characterizing the firm’s reaction function,
uncovers two contrasting effects of the firm’s ESG policy on the manager’s hiring decisions: The pro-competitive effect prompts the manager
to adopt a more aggressive stance in the labor market, while the
anti-competitive effect leads to a more cautious approach in hiring.
(
)
Lemma 3. Firm 𝑖’s reaction function is given by 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 , which equals
( )
(
)
(
)
(
)
𝜆𝑖 𝜔𝑖 if 𝑙−𝑖 ≤ 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ; equals 𝑊 −1 𝜔𝑖 − 𝑙−𝑖 if 𝑙−𝑖 ∈
( )
( )
( )
(
)
( )
(𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 , 𝛬−𝑖 𝜔𝑖 ); and equals 𝑟𝑖 𝑙−𝑖 ; 0 if 𝑙−𝑖 ≥ 𝛬−𝑖 𝜔𝑖 .
Equivalently,
(
)
{ ( )
{
( )
(
)}}
𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 = min 𝜆𝑖 𝜔𝑖 , max 𝑊 −1 𝜔𝑖 − 𝑙−𝑖 , 𝑟𝑖 𝑙−𝑖 ; 0
.
(12)
The solid line in Fig. 1 graphically illustrates Lemma 3, and in
particular shows the three regions of firm 𝑖’s ESG reaction function.
As one would expect, the reaction function is weakly decreasing in 𝑙−𝑖 .
( )
( )
(
)
In the first region, where 𝑙−𝑖 ≤ 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 , we have 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 =
( )
( (
)
)
𝜆𝑖 𝜔𝑖 and 𝑊 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖 . Since demand by firm −𝑖 is
relatively low, the market wage is below firm 𝑖′ 𝑠 self-imposed minimum
wage 𝜔𝑖 . Hence, firm 𝑖 pays its employees above the market wage and
hires as if it faces a perfectly elastic supply at 𝜔𝑖 .11 In other words, the
ESG policy mutes the monopsony distortion of the manager, who acts
as a price taker. We label this as the price-taking region.
( )
( )
( )
In the second region, where 𝑙−𝑖 ∈ (𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 , 𝛬−𝑖 𝜔𝑖 ), we
(
)
( )
( (
)
)
−1
have 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 = 𝑊
𝜔𝑖 − 𝑙−𝑖 , which implies 𝑊 𝑟𝑖 𝑙−𝑖 ; 𝜔𝑖 + 𝑙−𝑖 =
𝜔𝑖 . That is, the market wage is equal to firm 𝑖’s self-imposed minimum
wage. In this region, demand by firm −𝑖 is higher, and if firm 𝑖 were to
hire as if it faces a perfectly elastic supply at 𝜔𝑖 , the resulting market
wage would be higher than its self-imposed minimum wage, which in
turn would incentivize firm 𝑖 to hire less, as if it faces no minimum
wage constraint. However, since firm −𝑖’s demand is not so high, if firm
(
)
𝑖 were to hire as if it has no constraints, that is 𝑙𝑖 = 𝑟𝑖 𝑙−𝑖 ; 0 , then the
resulting market wage would be lower than its self-imposed minimum
wage, which in turn, would incentivize it to hire more aggressively, as
if it faces perfectly elastic supply at 𝜔𝑖 . Therefore, the best response

4. Competition between ESG and non-ESG firms
To develop our first set of results, we start by considering the
case in which only firm 𝑖 adopts an ESG policy. For example, only
firm 𝑖 is able to credibly constrain its manager to treat workers well;
or alternatively, firm 𝑖 is a “thought leader” or a “first mover” and
considers a policy that has not occurred to firm −𝑖. This analysis will
also develop key intuitions that will be instrumental in Section 5, where
we study competition in ESG policies between firms.
4.1. Labor market equilibrium with one ESG firm
As a first step, we characterize the labor market equilibrium that
arises when only firm 𝑖 adopts an (exogenous) ESG policy 𝜔𝑖 .
Proposition 1.
equilibrium is:

Suppose 𝜔−𝑖 = 0. Then, the for any 𝜔𝑖 the unique

(i) If 𝜔𝑖 ≤ 𝑊 𝐵 then the No-ESG benchmark is obtained.
{ ( )
( )} ∗
(
)
(ii) If 𝜔𝑖 > 𝑊 𝐵 then 𝑙𝑖∗ = min 𝛬𝑖 𝜔𝑖 , 𝜆𝑖 𝜔𝑖 , 𝑙−𝑖
= 𝑟−𝑖 𝑙𝑖∗ ; 0 ,
(
(
))
∗ = 𝑊 𝑙∗ + 𝑟
∗
𝑊𝑖∗ = 𝜔𝑖 , and 𝑊−𝑖
−𝑖 𝑙𝑖 ; 0 .
𝑖

11

If 𝜔𝑖 > 𝑊 (𝐿) then firm 𝑖 may face excess supply. In this case, the
employment in firm 𝑖 is rationed and workers are randomly allocated to firm
𝑖 until 𝑙𝑖 of them are hired.
6

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

(
)
Fig. 2. Firm 2 adopts a moderate ESG policy 𝜔2 ∈ 𝑊 𝐵 , 𝑊̂ 2 .

Fig. 4. Firm 2 adopts the size-maximizing ESG policy 𝜔2 = 𝑊̂ 2 .

In words, 𝑊̂ 𝑖 is the ESG level at which pro-competitive effects end and
anti-competitive effects begin. Fig. 4 graphically depicts this point: the
ESG firm’s reaction function intersects with the non-ESG firm’s reaction
function exactly at the kink, where the price-taking and the residual
regions of the reaction function meet. Below, we consider the optimal
choice of ESG policies by firms’ boards of directors. We first study
the choice of a shareholder firm, and then, in turn, the choice of a
purposeful firm.
4.2. Shareholder-value maximizing ESG policies
To analyze a shareholder firm’s choice of ESG, we start with the
observation that modest ESG policies increase profits for the adopting
firm. Intuitively, a modest ESG policy effectively commits firm 𝑖 to
compete more aggressively in the labor market, which in turn induces
the competitor firm −𝑖 to retreat. Importantly, different from a standard Cournot setting, the commitment attainable with ESG policies is
limited; as discussed above, any policy more aggressive than 𝑊̂ 𝑖 will
backfire and have the opposite effect. The maximal employment that
firm 𝑖 can achieve is 𝜆𝑖 (𝑊̂ 𝑖 ).
If, however, firm 𝑖 is adopting ESG policies purely in order to
maximize profits, then the limited commitment power they generate
is more than enough. Specifically, a shareholder firm 𝑖 would adopt an
ESG policy strictly below 𝑊̂ 𝑖 , the size-maximizing ESG policy. This is
readily seen from the following expression for firm 𝑖’s marginal profits
from committing to increase hiring 𝑙𝑖 :
( )
(
(
))
𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
(
))
(
(
))
− 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑙𝑖 𝑊 ′ 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .
(14)

(
)
Fig. 3. Firm 2 adopts an aggressive ESG policy 𝜔2 ∈ 𝑊̂ 2 , 𝑊 ∗∗ .

{ ( )
Proposition 1, the ESG firm’s hiring is 𝑙𝑖∗ = min 𝛬𝑖 𝜔𝑖 , 𝜆𝑖
( From
)}
𝜔𝑖 . The two terms in the minimand correspond, respectively, to the
equilibrium falling in the residual and price-taking regions of firm 𝑖’s
reaction function.
( As
) firm 𝑖’s ESG policy 𝜔𝑖 becomes more
( )aggressive,
the first term 𝛬𝑖 𝜔𝑖 increases, while the second term 𝜆𝑖 𝜔𝑖 decreases,
corresponding to the pro- and anti-competitive effects
( of ESG
) discussed
above. At the No-ESG benchmark 𝑊 𝐵 we know 𝛬𝑖 𝑊 𝐵 = 𝑙𝑖𝐵 ; while
the( monopsony
distortion in the No-ESG benchmark implies 𝑙𝑖𝐵 <
)
𝜆𝑖 𝑊 𝐵 . Consequently, if
( firm
) 𝑖 adopts an ESG policy moderately above
𝑊 𝐵 then it hires 𝑙𝑖∗ = 𝛬𝑖 𝜔𝑖 > 𝑙𝑖𝐵 , which is increasing in the ESG policy
𝜔𝑖 . Fig. 2 illustrates this pro-competitive effect: Comparing the black
dot, which shows the No-ESG benchmark, with the blue square, which
is the equilibrium when firm 2 adopts a moderate ESG policy, shows
that a moderate ESG policy increases firm 2’s hiring at the expense of
firm 1, and in equilibrium, firm 2 operates in the residual region of its
reaction function. As firm 𝑖 continues to increase its ESG
( )policy the anticompetitive effect eventually dominates, and 𝑙𝑖∗ = 𝜆𝑖 𝜔𝑖 . In particular,
we know the anti-competitive effect dominates as 𝜔𝑖 approaches the
first-best wage level 𝑊 ∗∗ , because the monopsony distortion and the
definition of 𝑊 ∗∗ imply

This expression is negative at 𝑙𝑖 = 𝜆𝑖 (𝑊̂ 𝑖 ). The third term is the
monopsony distortion, and is negative. Evaluated at 𝑙𝑖 = 𝜆𝑖 (𝑊̂ 𝑖 ),
the combination of the first two terms is 0, because by definition
𝑓𝑖′ (𝜆𝑖 (𝑊̂ 𝑖 )) = 𝑊̂ 𝑖 .
The next result characterizes the ESG policy that maximizes shareholder value, which we denote by 𝜑∗𝑖 ,12 and compares the properties of
the equilibrium that unfolds to the No-ESG benchmark.

𝜆𝑖 (𝑊 ∗∗ ) + 𝑟−𝑖 (𝜆𝑖 (𝑊 ∗∗ ); 0)
(
)
(
)
< 𝜆𝑖 (𝑊 ∗∗ ) + 𝜆−𝑖 𝑊 ∗∗ = 𝑊 −1 𝑊 ∗∗ ,
( )
( )
in turn implying (Lemma 1) 𝜆𝑖 𝜔𝑖 < 𝛬𝑖 𝜔𝑖 . Fig. 3 illustrates this anticompetitive effect: Comparing the blue square with the green triangle,
which is the equilibrium when firm 2 adopts an extreme ESG policy,
shows that an extreme ESG policy decreases the employment of firm 2
(while increasing the employment of firm 1), and in equilibrium, firm
2 produces in the price-taking region of its reaction function.
It follows
that
(
) the ESG policy that maximizes firm 𝑖’s employment is
𝑊̂ 𝑖 ∈ 𝑊 𝐵 , 𝑊 ∗∗ , defined as the (unique) intersection of the functions
𝛬𝑖 (⋅) and 𝜆𝑖 (⋅):
𝛬𝑖 (𝑊̂ 𝑖 ) = 𝜆𝑖 (𝑊̂ 𝑖 ).

Proposition 2. Suppose firm 𝑖’s opponent adopts the No-ESG policy
(i.e., 𝜔−𝑖 = 0). Then, the shareholder-value maximizing ESG policy of
( )
firm 𝑖 satisfies 𝜑∗𝑖 ∈ (𝑊 𝐵 , 𝑊̂ 𝑖 ). Under ESG policy 𝜑∗𝑖 , 𝑙𝑖∗ = 𝛬𝑖 𝜑∗𝑖 ,
(
(
)
)
∗ = 𝑟
∗
∗
∗
∗
𝑙−𝑖
−𝑖 𝛬𝑖 𝜑𝑖 ; 0 , and 𝑊𝑖 = 𝑊−𝑖 = 𝜑𝑖 . Relative to the No-ESG
benchmark, worker welfare, industry employment, and firm 𝑖’s employment
and profit are higher. In contrast, firm −𝑖’s employment and profit are lower.
Both firms pay the same wage, which is higher than the No-ESG benchmark.

12
For the non-generic cases in which the maximizer is not unique, we focus
on the smallest maximizer.

(13)
7

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

4.3. A purposeful firm’s preferred ESG policy
We next characterize and study the implications of a purposeful
firm’s choice of ESG policy. A purposeful firm’s board adopts an ESG
policy with the objective of maximizing the surplus created by the
firm, which here equals the sum of profits and worker surplus. Worker
surplus depends on workers’ outside options, which in turn depends
on how workers are allocated across different firms. The minimum and
maximum values of the combined outside options of firm 𝑖’s workers
𝑙
𝑙 +𝑙
are, respectively, ∫0 𝑖 𝑊 (𝑙) 𝑑 𝑙 and ∫𝑙 𝑖 −𝑖 𝑊 (𝑙) 𝑑 𝑙. We define firm 𝑖’s
−𝑖

surplus using a weighted average of these possibilities, with weight
𝜇 ∈ (0, 1).17
𝑙𝑖
𝑙𝑖 +𝑙−𝑖
(
)
( )
𝑆𝑖 𝑙𝑖 , 𝑙−𝑖 ≡ 𝑓𝑖 𝑙𝑖 − 𝜇
𝑊 (𝑙) 𝑑 𝑙 − (1 − 𝜇)
𝑊 (𝑙) 𝑑 𝑙.
(15)
∫0
∫𝑙−𝑖
(
)
Note that, by maximizing 𝑆𝑖 𝑙𝑖 , 𝑙−𝑖 , a purposeful firm’s board cares
about the direct actions of the firm but not about equilibrium consequences for competitor-firms and their workers.
The next result characterizes a purposeful firm’s most-preferred ESG
policy, which we denote as the optimal purposeful ESG policy.

Fig. 5. Firm 𝑖’s employment as a function of its own ESG policy.

Fig. 5 below plots the firm’s employment as a function of its own
ESG policy, and in particular, illustrates that the shareholder-value
maximizing ESG policy 𝜑∗𝑖 is pro-competitive.
While firm 𝑖’s shareholders benefit from its ESG policy at the expense of firm −𝑖’s shareholders, the employees of both firms gain from
firm 𝑖’s ESG policy. Indeed, in equilibrium, both firms pay their workers
𝜑∗𝑖 > 𝑊 𝐵 .13 Moreover, while employment at firm 𝑖 increases at the
∗ < 𝑙𝐵 ), total
expense of employment at firm −𝑖 (i.e., 𝑙𝑖∗ > 𝑙𝑖𝐵 and 𝑙−𝑖
−𝑖
∗ > 𝑙𝐵 + 𝑙𝐵 ). That is, firm 𝑖 increases
employment increases (i.e., 𝑙𝑖∗ + 𝑙−𝑖
𝑖
−𝑖
its employment by more than firm −𝑖 reduces it. Therefore, worker
welfare always increases relative to the No-ESG benchmark. In this
respect, the unintended consequences of a profit-motivated ESG policy
are beneficial to workers. Interestingly, since ESG and non-ESG firms’
wages coincide in equilibrium, it is empirically challenging to identify
which firm is the ESG-firm based purely on employment conditions
(and in particular, without information on productivity).14 The effect
of firm 𝑖’s ESG policy on industry profits and surplus is more nuanced.
In the proof of Proposition 2 in the Appendix A, we show that if firm
𝑖 is the (weakly) less-productive firm (i.e., 𝑖 = 2), then total industry
profits decrease relative to the No-ESG benchmark. That is, the increase
in firm 𝑖’s profits is lower than the decline firm −𝑖’s profits. Intuitively,
as firm 𝑖 increases employment at the expense of its more productive
opponent, production is shifted the “wrong” way, toward the firm with
the lower marginal productivity and a smaller monopsony distortion
in the first place. This force also explains why industry surplus could
decline due to firm 𝑖’s ESG policy, which we illustrate by example in
Appendix E of the Online Appendix. In this respect, when unproductive
firms use ESG policies to gain a competitive advantage in real markets,
they create distortions that are beneficial to the firm’s shareholders
but can be costly from a social perspective. In contrast, if firm 𝑖 is
the more productive firm (i.e., 𝑖 = 1), then it is possible that total
industry profits increase relative to the No-ESG benchmark. In this case,
the adoption of the ESG policy is a Pareto improvement and industry
surplus increases.15 In fact, industry surplus can increase in those cases
in which industry profitability declines. Intuitively, when the more
productive firm uses ESG to enhance its competitive advantage, production is shifted the “right” way and toward the firm whose monopsony
distortion creates a larger social cost (and hence, increasing production
is marginally more valuable).16

13

(

(

)

(

(

)

Proposition 3. Suppose firm 𝑖’s opponent adopts the No-ESG policy
(i.e., 𝜔−𝑖 = 0). Then, the optimal purposeful ESG policy of firm 𝑖 is 𝑊̂ 𝑖 .
∗ = 𝑟 (𝛬 (𝑊
̂ 𝑖 ); 0),
Under optimal ESG policy 𝑊̂ 𝑖 , 𝑙𝑖∗ = 𝛬𝑖 (𝑊̂ 𝑖 ) = 𝜆𝑖 (𝑊̂ 𝑖 ), 𝑙−𝑖
−𝑖 𝑖
∗
∗
̂
and 𝑊𝑖 = 𝑊−𝑖 = 𝑊𝑖 . Relative to the No-ESG benchmark, worker
welfare, industry employment, and firm 𝑖’s employment are higher. Firm −𝑖
’s employment and profit are lower. Both firms pay the same wage, which
is higher than the No-ESG benchmark.
Proposition 3 resembles Proposition 2, with the exception that purposeful firms adopt more aggressive ESG policies than their
shareholder-value maximizing counterparts, i.e., 𝑊̂ 𝑖 > 𝜑∗𝑖 . In particular, a purposeful firm adopts the size-maximizing ESG policy, 𝑊̂ 𝑖 .
Intuitively, in order to maximize surplus, a purposeful firm wants to
be large, even at the expense of profits.
The next result shows that the purposeful board of firm 𝑖 would like
it to be even larger than the size 𝜆𝑖 (𝑊̂ 𝑖 ) that it attains under ESG policy
𝑊̂ 𝑖 .
Corollary 1. The marginal total surplus of firm (𝑖 is strictly
positive under
)
𝜕 𝑆 𝑙 ,𝑙∗
the optimal purposeful ESG policy 𝑊̂ 𝑖 , that is, 𝑖 𝜕𝑙𝑖 −𝑖 |𝑙 =𝜆 (𝑊̂ ) > 0.18
𝑖

𝑖

𝑖

𝑖

To see the intuition, recall that the total surplus created by a firm
is the sum of profits and worker-surplus. Since 𝑊̂ 𝑖 satisfies 𝑓𝑖′ (𝜆𝑖 (𝑊̂ 𝑖 )) =
𝑊̂ 𝑖 , the marginal worker hired produces zero profits. At the same time,
the marginal worker hired produces strictly positive worker surplus,
( )
since firm 𝑖 evaluates the marginal worker’s outside option as 𝜇 𝑊 𝑙𝑖 +
(1 − 𝜇) 𝑊̂ 𝑖 < 𝑊̂ 𝑖 .
Corollary 1 has three significant implications. First, it shows that the
result that a purposeful firm adopts policy 𝑊̂ 𝑖 is robust to perturbing
the weights placed on shareholder profits and worker welfare. Second,
and in contrast to a shareholder firm, the board of a purposeful firm
wishes it had additional tools at its disposal beyond an ESG promise
to treat workers well. But under the assumption that this is the only
tool available, increases in ESG policy 𝜔𝑖 beyond 𝑊̂ 𝑖 backfire, because

))

16
Formally, we show in the proof of Proposition 2 in the Appendix A that
industry surplus is always increasing if the more productive firm chooses an
ESG policy in the neighborhood of 𝑊 𝐵 .
(
)
(
)
17
Our results hold for any 𝜇 ∈ [0, 1]. If 𝜇 = 12 then 𝑆𝑖 𝑙𝑖 , 𝑙𝑗 + 𝑆𝑗 𝑙𝑗 , 𝑙𝑖 =
(
)
𝑆 𝑙𝑖 , 𝑙𝑗 , that is, the sum of individual firms’ surplus equals the industry
surplus.
18
Corollary 1 says that firm 𝑖’s marginal surplus is positive even holding
the hiring of its competitor −𝑖 fixed. This conclusion is only strengthened if
𝜕 𝑆 (𝑙 ,𝑟 (𝑙 ;0))
𝜕 𝑆 (𝑙 ,𝑙∗ )
firm −𝑖 responds: 𝑖 𝑖 𝜕𝑙−𝑖 𝑖 |𝑙𝑖 =𝑙𝑖∗ > 𝑖 𝜕𝑙𝑖 −𝑖 |𝑙𝑖 =𝑙𝑖∗ > 0.

Since 𝑊−𝑖∗ = 𝑊 𝛬𝑖 𝜑∗𝑖 + 𝑟−𝑖 𝛬𝑖 𝜑∗𝑖 ; 0 , by the definition of 𝛬𝑖 (⋅),
𝑊−𝑖∗ = 𝜑∗𝑖 .
14
Notice that if firms were symmetric then the ESG firm would be larger
than the non-ESG firm since it employs more workers. However, in general,
when firms are asymmetric, it is hard to identify which one is the ESG firm
since less productive firms can adopt ESG policy and still hire less.
15
Recall the shareholder value of the competing firm always declines. Hence
a Pareto improvement only arises if shareholders are diversified across the two
firms, e.g., common ownership.

𝑖

8

𝑖

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

then adopting an ESG policy that is slightly more aggressive than 𝑊 𝐵
reduces the ESG firm’s profits, as can be seen directly from (14).
In contrast, the assumption of downward-sloping reaction functions
is not crucial for our results on a purposeful firm’s choice of ESG. In
particular, Proposition 3’s prediction for firm surplus is independent
of the slope of reaction functions: A moderate ESG policy increases a
firm’s hiring, in turn increasing the surplus generated by the firm.

they reduce firm 𝑖’s hiring. Third, Lemma D-12 in the Online Appendix
shows that a purposeful firm adopts policy 𝑊̂ 𝑖 even if its choice is
unobserved by its competitor. The reason is that a purposeful firm
adopts ESG policies in order to more-closely align its manager’s actions
with the wishes of the board and/or shareholders. This stands in stark
contrast to a shareholder firm which adopts ESG policies solely because
of their strategic impact on competitors. Indeed, a firm’s ESG policy
increases its profits only if its competitors are aware of the policy.
Thus, while regulations that facilitate transparency and disclosure of
ESG policies would contribute to the effectiveness and adoption of ESG
policies by shareholder firms, they would matter much less for the
adoption of ESG policies by purposeful firms.
Returning to Proposition 3, it follows that firm 𝑖 ’s hiring and total
industry employment are both maximized under the optimal purposeful
ESG policy, whereas firm −𝑖’s hiring is minimized. Since total employment is higher than under a shareholder firm’s preferred ESG policy 𝜑∗𝑖
and the wages paid by both firms also higher, employees of both firms
benefit more from the optimal purposeful ESG policy than from 𝜑∗𝑖 .
As in the case of a shareholder firm adopting ESG, the competitor’s
(firm −𝑖) profits are lower under the optimal purposeful ESG policy
than in the No-ESG benchmark. However, it is not guaranteed that firm
𝑖’s profits are higher than in this benchmark. After all, a purposeful
firm’s ESG policy is not chosen to maximize profits; and indeed, since
the optimal purposeful ESG policy leads the adopting firm to equate
marginal productivity with wages, the firm would increase profits by
moderating its ESG policy.
Interestingly, the optimal purposeful ESG policy does not maximize
industry surplus.

5. Competition in ESG policies
In the analysis above, only firm 𝑖 has the capacity to adopt ESG
policies. In this section, we consider what ESG policies firm −𝑖 would
optimally adopt in response to firm 𝑖’s ESG choice, and given the
expected reaction of firm −𝑖, we analyze firm 𝑖’s optimal ESG policy.
Similar to the structure of Section 4, we consider both corporate
governance paradigms, starting with the shareholder primacy paradigm
and then turning to the stakeholder capitalism paradigm.
As a preliminary observation: We will show that for many ESG
policies 𝜔𝑖 adopted by firm 𝑖, its competitor firm −𝑖 would ideally
respond by adopting a policy that is infinitesimally more aggressive.
Consequently, the characterization of firm −𝑖’s response to 𝜔𝑖 faces an
open-set problem. Accordingly, we restrict firm −𝑖’s policy 𝜔−𝑖 to lie
in a finite grid of possible choices, with grid size 𝜖 > 0. We state all
results below for the case in which this grid is sufficiently fine, i.e., 𝜖
sufficiently close to 0.
5.1. Labor market equilibrium
As a preliminary step, we characterize the labor market equilibrium
arising from an arbitrary pair of ESG( policies,
thereby generalizing
)
∗ = 𝑟 𝑙∗ ; 𝜔
for
𝑖 ∈ {1, 2}, and firm
Proposition 1. In equilibrium,
𝑙
𝑖
𝑖
−𝑖
{ 𝑖(
)
}
𝑖 pays its workers 𝑊𝑖∗ = max 𝑊 𝑙1∗ + 𝑙2∗ , 𝜔𝑖 .

Corollary 2. The optimal purposeful ESG policy of firm 𝑖 does not
maximize industry surplus. The industry-surplus maximizing ESG policy of
firm 𝑖 leads to less employment at firm 𝑖 and more employment at firm −𝑖,
relative to the optimal purposeful ESG policy 𝑊̂ 𝑖 .

(
)
Proposition 4. For a given pair of ESG policies 𝜔1 , 𝜔2 , a labor market
equilibrium exists:

Purposeful firms do not internalize how their ESG policies affect
competitor-surplus. In particular, under firm 𝑖’s optimal purposeful ESG
( )
( )
′ 𝑙∗ 19 : marginal productivity is lower at
policy 𝑓𝑖′ 𝑙𝑖∗ = 𝑊̂ 𝑖 < 𝑓−𝑖
−𝑖
purposeful ESG firm 𝑖 than at its non-ESG competitor. Industry surplus
would increase if firm 𝑖 hired less and firm −𝑖 hired more; but firm 𝑖
adopts an ESG policy with only its own surplus in mind and neglects
this potential welfare gain. In this respect, a purposeful firm adopts
an ESG policy that is too aggressive from a social perspective. Recall
that a shareholder firm adopts a less aggressive ESG policy (𝜑∗𝑖 < 𝑊̂ 𝑖 ).
Thus, to maximize industry surplus, a purposeful firm must overweight
shareholders relative to its other stakeholders, for example, by giving
shareholders greater board-representation. By doing so, the firm adopts
a more moderate ESG policy, thereby reducing its hiring—which as
shown above is socially beneficial. (In contrast: A “broad” consequentialist purposeful firm would, by definition, internalize competitor
welfare and adopt the socially optimal ESG policy.)

(i) If max𝑖 𝜔𝑖 ≤ 𝑊 𝐵 then the unique equilibrium coincides with the
No-ESG Benchmark.
( )
(ii) If min𝑖 𝜔𝑖 ≥ 𝑊 ∗∗ then the unique equilibrium is 𝑙𝑖∗ = 𝜆𝑖 𝜔𝑖 and
𝑊𝑖∗ = 𝜔𝑖 for 𝑖 = 1, 2.
(iii) If 𝜔𝑖 = 𝜔−𝑖 = 𝜔 ∈ (𝑊 𝐵 , 𝑊 ∗∗ ) then for any 𝑖 = 1, 2 and 𝑙∗ in the
interval
[ −1
{
}
{
}]
(16)
𝑊 (𝜔) − min 𝛬−𝑖 (𝜔) , 𝜆−𝑖 (𝜔) , min 𝛬𝑖 (𝜔) , 𝜆𝑖 (𝜔)
(∗ ∗)
(∗
)
−1
∗
there is an equilibrium in which 𝑙𝑖 , 𝑙−𝑖 = 𝑙 , 𝑊 (𝜔) − 𝑙 and
∗ = 𝜔. No other equilibrium exists.
𝑊𝑖∗ = 𝑊−𝑖
∗∗
(iv) If 𝜔𝑖 > 𝜔−𝑖 , {𝜔𝑖 >( 𝑊)𝐵 and
equilibrium
( 𝜔
)}−𝑖 <∗ 𝑊 then
( the unique
)
is 𝑙𝑖∗ = min {𝛬𝑖 𝜔𝑖 (, 𝜆𝑖 𝜔𝑖 (, 𝑙−𝑖
=))}
𝑟−𝑖 𝑙𝑖∗ ; 𝜔−𝑖 , 𝑊𝑖∗ = 𝜔𝑖 and
∗ = max 𝜔 , 𝑊 𝑙∗ + 𝑟
∗
𝑊−𝑖
. If firm 𝑖 is weakly more
−𝑖
−𝑖 𝑙𝑖 ; 𝜔−𝑖
𝑖
∗ .
productive and 𝜔𝑖 < 𝑊 ∗∗ then 𝑙𝑖∗ > 𝑙−𝑖

Remark on downward-sloping reaction functions
Proposition 2’s implication that a moderate ESG policy increases
a firm’s profits depends on the assumption that reaction functions
slope down (see (1)). To see this, we briefly consider the opposite
case in which reaction functions slope up, at least locally at the NoESG benchmark. In this case, adopting a moderate ESG policy 𝜔𝑖
that is slightly more aggressive than the non-ESG wage 𝑊 𝐵 shifts
firm 𝑖’s reaction function upwards, and effectively commits it to hire
more. Thus, the effect of the firm’s ESG policy on its manager’s hiring
decisions (and hence, on workers’ welfare) is qualitatively similar to
the case of downward-sloping reaction functions. However, different
(
)
from the baseline model, if reaction functions slope up (𝑟′−𝑖 𝑙𝑖 ; 0 > 0)

Proposition 4 has several important takeaways. First, by part (i), if
both firms adopt ESG-policies milder than 𝑊 𝐵 , then the labor market
equilibrium coincides with the No-ESG benchmark. Intuitively, these
mild ESG policies are non-binding and have no effect. Second, by part
(ii), if both firms adopt ESG-policies that are more aggressive than the
first-best wage 𝑊 ∗∗ , then each firm pays its self-imposed minimum
wage and hires as if facing a perfectly elastic supply at that level. If at
least one firm adopts 𝜔𝑖 > 𝑊 ∗∗ then both firms pay wages strictly above
the market clearing level.20 If both firms adopt an ESG policy of 𝑊 ∗∗
then the first-best obtains. Figs. 6 and 7 depict the reaction functions
and labor market equilibrium for symmetric firms when 𝜔1 = 𝜔2 = 𝑊 𝐵
and 𝜔1 = 𝜔2 = 𝑊 ∗∗ , respectively.

19
Firm −𝑖’s hiring reflects the monopsony distortion and hence marginal
productivity exceeds the wage.

( )
( ( )
( ))
20
If 𝜔𝑖 > 𝑊 ∗∗ then 𝜆𝑖 𝜔𝑖 < 𝜆𝑖 (𝑊 ∗∗ ), and hence, 𝑊 𝜆1 𝜔1 + 𝜆2 𝜔2 <
(
)
𝑊 𝜆1 (𝑊 ∗∗ ) + 𝜆2 (𝑊 ∗∗ ) = 𝑊 ∗∗ < 𝜔𝑖 .
9

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

(
)
Fig. 8. Moderate ESG reaction functions: 𝜔2 = 𝜔1 ∈ 𝑊 𝐵 , 𝑊̂ .

Fig. 6. Reaction functions under ESG policies 𝜔2 = 𝜔1 = 𝑊 𝐵 .

(
)
Fig. 9. Moderate ESG reaction functions: 𝜔′2 > 𝜔1 ∈ 𝑊 𝐵 , 𝑊̂ .

Fig. 7. Reaction functions under ESG policies 𝜔2 = 𝜔1 = 𝑊 ∗∗ .

Third, by part (iii), if both firms adopt the same ESG policy 𝜔 then
multiple equilibria exist. In all of these equilibria, both firms pay the
market wage, which equals their identical self-imposed minimum wage
𝜔, and total employment is 𝑊 −1 (𝜔). Although firms pay the market
wage, both this wage and total employment exceed their counterparts
in the No-ESG benchmark. Multiple equilibria arise from different splits
of the constant employment level across the two firms. The multiplicity
stems from the fact that the reaction functions always intersect in the
residual-demand region, which has a slope of −1. There, both firms
have incentives to hire just enough workers such that the market
wage equals the self-imposed minimum wage. Indeed, neither firm has
incentives to hire more, since doing so would derive the wage up (the
monopsony effect). At the same time, neither firm has an incentives
to hire less, since doing so would push the market wage below its
self-imposed minimum wage.21
Finally, by part (iv), if the competing firms are similar, the firm that
adopts a more aggressive ESG-policy hires more workers in equilibrium.
Intuitively, an aggressive ESG-policy commits a firm to hire more and
consequently pushes its competitor to hire less. If the more productive
firm also adopts a more aggressive ESG policy, then it will be more aggressive in the labor market both due to its ESG policy and its inherent
higher productivity. If the less productive firm adopts a more aggressive
ESG policy, then the two forces operate in opposite directions, and the
ranking with respect to the ESG policies is ambiguous.
Fig. 8 depicts the reaction functions of the symmetric firms when
they adopt the same moderate ESG policy. The overlapping 45-degree

(
)
Fig. 10. Aggressive ESG reaction functions: 𝜔2 = 𝜔1 ∈ 𝑊̂ , 𝑊 ∗∗ .

lines are the graphical representation of equilibrium multiplicity. Fig. 9
shows how the equilibrium set collapses to the green triangle if firm 2
increases its ESG policy above its opponent’s (𝜔′2 > 𝜔2 = 𝜔1 ). Here, the
equilibrium is unique, with firm 2 hiring more but firm 1 hiring less.
Fig. 10 is similar to Fig. 8 with the exception that the two firms
adopt a relatively extreme ESG policy (i.e., 𝜔1 , 𝜔2 ∈ (𝑊̂ , 𝑊 ∗∗ )). Fig. 11
shows how the equilibrium set collapses to the green triangle when firm
2 decreases its ESG policy below its opponent’s. Here, the equilibrium
is unique, with firm 2 hiring less but firm 1 hiring (weakly) more.
5.2. ESG competition between shareholder firms

21

It is worth stressing that equilibrium multiplicity arises in the general
case of asymmetric firms, and is not in any way special to the symmetric case;
indeed, in the residual-demand region a firm’s hiring decision is independent
of its production function.

With Proposition 4’s characterization of labor-market outcomes in
hand, we turn to the analysis of competition in ESG policies between
shareholder firms. We present our results in this section for cases in
10

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P. Bond and D. Levit

Proposition 5. Suppose firms choose ESG policies to maximize their
shareholder values:
(𝑖) Either: Firm 𝑖 chooses an ESG policy 𝜔𝑖 < 𝜑∗−𝑖 and firm −𝑖 chooses
𝜔−𝑖 = 𝜑∗−𝑖 . The equilibrium is payoff equivalent to the equilibrium that
emerges when firm 𝑖 adopts the No-ESG policy (𝜔∗𝑖 = 0) and firm −𝑖
adopts the policy 𝜑∗−𝑖 defined in Proposition 2.
Or: Firm 𝑖 chooses the ESG policy 𝑊̌ −𝑖 and firm −𝑖 chooses a
non-binding ESG policy.
(𝑖𝑖) Worker welfare is higher and industry profits are lower than in the
No-ESG benchmark.
Proposition 5(i) establishes that either firm 𝑖 adopts an ESG policy
that is too moderate to deter firm −𝑖, which in turn outdoes firm 𝑖’s ESG
policy and obtains an advantage in the labor market, or firm 𝑖 adopts
an ESG policy that is aggressive enough to deter firm −𝑖 from matching
it, and firm 𝑖 consequently retains its advantage in the labor market. In
choosing between the two scenarios firm 𝑖 faces the following trade-off:
in the first scenario firm 𝑖 faces an aggressive competitor in the labor
market, but is itself essentially unconstrained. In the second scenario,
firm 𝑖 instead faces a weak competitor in the labor market, but is
constrained by its own aggressive ESG policy to pay high wages.
Regardless of which of these two scenarios prevails in equilibrium,24
Proposition 5(ii) establishes that competition in ESG policies between
shareholder firms benefits workers; but it reduces profits, and for some
parameterizations reduces industry surplus also. As discussed earlier,
the misallocation of labor that arises after ESG adoption is socially
detrimental. Thus, competition in ESG policies that are motivated by
profit-maximization can cause more harm than good. In contrast, in
the next section we show that competition in ESG policies between
purposeful firms always raises industry surplus.
Because competition in ESG policies reduces industry profits, if
there is ex-ante uncertainty about which firm is the first-mover in the
ESG-game then firms find it mutually beneficial to coordinate on lowimpact ESG policies. Ideally, from the shareholders’ perspective, firms
would agree to abstain from ESG altogether. But in practice this may
not be possible, since the gain to deviation would be highest in this
case, and firms may instead have to settle on coordinating on mild ESG
policies in order to reduce deviation-incentives. This conclusion raises
anti-trust concerns for the seemingly benevolent adoption of industrywide ESG standards, and for moves by large asset managers (“common
owners”) to promote ESG.
Proposition 5 uses the best-ESG-response result of Lemma 4 to
characterize a leader–follower game. One can also ask: What happens
if firms choose ESG policies independently, without observing each
others’ choices? In this case, Lemma 4 implies that no pure strategy
equilibrium exists25 since firms have incentives to “top” their competitors’ moderate ESG policies and “abandon” their own ESG policies
altogether when competitors’ policies are aggressive. Specifically: If
both firms adopt relatively moderate ESG policies, the firm with the
(weakly) milder policy would deviate and adopt a more aggressive
policy; but if firm 𝑖 adopts an aggressive policy, its competitor −𝑖 adopts
a policy so mild that it is non-binding—but then firm 𝑖 would deviate
to a less aggressive policy.

(
)
Fig. 11. Aggressive ESG reaction functions: 𝜔′2 < 𝜔1 ∈ 𝑊̂ , 𝑊 ∗∗ .

which firms are sufficiently similar in the sense that the differences
between the firms’ production functions are relatively small.
Lemma 4. There exists 𝑊̌ −𝑖 ∈ (𝑊̂ 𝑖 , 𝑊 ∗∗ ) such that the ESG policy that
maximizes firm −𝑖’s shareholder value in response to firm 𝑖 adopting ESG
policy 𝜔𝑖 has the following properties:
(𝑖) If 𝜔𝑖 < 𝑊̌ −𝑖 then firm −𝑖 adopts a more aggressive ESG policy than
firm 𝑖, i.e., 𝜔−𝑖 > 𝜔𝑖 . Moreover, firm −𝑖’s policy weakly increases in
𝜔𝑖 in this region.
(𝑖𝑖) If 𝜔𝑖 ≥ 𝑊̌ −𝑖 then firm −𝑖 either adopts the No-ESG policy (𝜔−𝑖 = 0),
or else an ESG policy that is sufficiently moderate to generate the
same outcomes.
Lemma 4 shows that ESG policies are strategic complements when
the policies are moderate and strategic substitutes when they are
extreme.22 If firm 𝑖’s ESG policy is very moderate (𝜔𝑖 < 𝜑∗−𝑖 ),23 then
firm −𝑖 simply responds by picking 𝜔−𝑖 = 𝜑∗−𝑖 , viz., the ESG policy
that it would adopt if firm 𝑖 had not adopted any ESG policy at all. In
this case, the “leader” firm 𝑖’s ESG policy does not affect the “follower”
firm’s choice.
If firm 𝑖’s ESG policy is intermediate (𝜑∗−𝑖 < 𝜔𝑖 < 𝑊̌ −𝑖 ), then by
Proposition 4’s characterization of the labor-market equilibrium, firm
−𝑖 gains nothing from adopting an ESG policy more moderate than its
competitor’s. So instead, firm −𝑖 responds by outdoing firm 𝑖’s ESG
policy. In this case, as firm 𝑖’s ESG choice becomes more aggressive,
firm −𝑖 responds by adopting progressively more and more aggressive
ESG policies. In all numerical simulations that we have examined firm
−𝑖 adopts an ESG policy infinitesimally more aggressive than 𝜔𝑖 .
Finally, if firm 𝑖’s ESG policy is sufficiently aggressive (𝜔𝑖 > 𝑊̌ −𝑖 )
then the benefit to firm −𝑖 of outdoing 𝜔𝑖 is too small to justify the
cost of paying higher wages. This is immediate once 𝜔𝑖 crosses the firstbest level 𝑊 ∗∗ , since in this case firm −𝑖’s hiring shrinks if it outdoes
firm 𝑖’s ESG policy, while its labor costs increase (Proposition 4). By
continuity, this conclusion extends to an interval of firm 𝑖’s ESG policies
below 𝑊 ∗∗ . Conditional on not outdoing firm 𝑖’s ESG choice, firm −𝑖 is
best-off abandoning ESG (or, strictly speaking, picking an ESG policy
so moderate that it has no effect on its behavior).
The next result characterizes the equilibrium when shareholder
firms compete in ESG policies. Specifically, firm 𝑖 chooses( 𝜔𝑖 and) then
firm −𝑖 responds by choosing 𝜔−𝑖 . Given ESG policies 𝜔𝑖 , 𝜔−𝑖 , the
firms compete in the labor market.

5.3. ESG competition between purposeful firms
Next, we analyze competition in ESG policies between purposeful
firms. We start by characterizing the best-response ESG policy of a
purposeful firm:

22

Lemma 4 does not require firms to be sufficiently similar.
Both in the main text and in the Appendix A, for the non-generic case
in which there are multiple ESG policies that maximize firm −𝑖’s profits when
played against the No-ESG policy 𝜔𝑖 , for expositional transparency we let 𝜑∗−𝑖
be the least aggressive such policy. We emphasize, moreover, that nothing is
at stake with this choice.
23

24
Appendix G of the Online Appendix gives examples to illustrate that both
scenarios can arise in equilibrium.
25
See formal proof in Appendix C of the Online Appendix.

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P. Bond and D. Levit

Lemma 5. The ESG policy that maximizes the surplus created by purposeful
firm −𝑖 in response to firm 𝑖 adopting ESG policy 𝜔𝑖 has the following
properties:

by its ESG policy. This force pushes each firm to adopt the firstbest wage as its equilibrium ESG policy. Put differently, the strategic
complementarity in ESG policies between competing purposeful firms
achieves the first-best outcome. In this respect, ESG is a panacea to
market power.
Proposition 6’s conclusion that purposeful competition in ESG delivers the first-best outcome is robust to perturbing the weights that a
purposeful firm puts on shareholder and worker surplus. Specifically,
as long as a purposeful firm puts sufficiently large weight on worker
welfare, even if it does not fully internalize it as we currently assume,
then the firm has incentives to marginally outdo any ESG choice by
its competitor that is less than 𝑊 ∗∗ . Moreover, as long as a purposeful firm’s hiring decision is made by a profit-maximizing manager,
a purposeful firm’s board never sets an ESG policy more aggressive
than 𝑊 ∗∗ . This observation highlights that if the purposeful board
were to incentivize the manager to fully internalize worker surplus, the
first best would not be obtained in equilibrium. In fact, under these
circumstances, competition between purposeful firms “overshoots” relative to the first best, resulting in higher worker surplus but lower
social welfare. Indeed, the misalignment between the objectives of
a purposeful board and a profit-maximizing manager is a key force
behind Proposition 6; the attempt of the latter to mitigate the ESG
policy of the former imposes a robust balance on how the firm conducts
itself in the marketplace. See Section 6.4 for additional discussion.
We have established Proposition 6 in the same leader–follower
framework that we used to analyze ESG competition between shareholder firms. But exactly the same outcome arises if two purposeful firms select ESG firms independently, as in a simultaneous-move
game.26

(i) If 𝜔𝑖 < 𝑊 ∗∗ then firm −𝑖 adopts a more aggressive ESG policy than
firm 𝑖, i.e., 𝜔−𝑖 > 𝜔𝑖 .
(ii) If 𝜔𝑖 > 𝑊 ∗∗ then firm −𝑖 adopts 𝜔−𝑖 < 𝑊 ∗∗ .
(iii) If 𝜔𝑖 = 𝑊 ∗∗ then firm −𝑖 adopts 𝜔−𝑖 = 𝑊 ∗∗ .
Part (i) of Lemma 5 parallels part (i) of Lemma 4’s analysis of
a shareholder firm’s choice of ESG. Specifically, if the leader firm 𝑖
adopts a moderate ESG policy then firm −𝑖 responds by outdoing it. The
difference between the cases of purposeful and shareholder ‘‘follower’’
firms is that a purposeful follower outdoes the ‘‘leader’’ firm for a
wider range of leader-policies. Specifically, there is a range of ESG
policies milder than the first-best level 𝑊 ∗∗ that induce a shareholdervalue maximizing follower to respond by giving up on its own ESG
efforts. In contrast, a purposeful follower outdoes any ESG that its
competitor adopts, provided only that it is less than the first-best
𝑊 ∗∗ . The difference between the two cases reflects the lower cost of
ESG policies for purposeful firms. Specifically, the increase in wages
engendered by ESG is not a cost for a purposeful firm; instead, it is
simply a transfer from shareholders to workers.
Similarly, part (ii) of Lemma 5 parallels part (ii) of Lemma 4: once
the leader adopts a sufficiently aggressive ESG policy, the follower
responds by undercutting rather than outdoing the follower’s policy. In
the purposeful-firm case, the advantage of undercutting the ESG policy
is that it leads to more hiring, which the purposeful firm values.
Part (iii) of Lemma 5 is new to the purposeful-firm case: There
is a leader-ESG policy that the follower simply matches. Moreover,
this policy is precisely the first-best wage 𝑊 ∗∗ . The economics behind
part (iii) is that if the follower responds to 𝑊 ∗∗ by adopting a more
moderate policy then it hires less, because it is the “losing” ESG firm
(see Proposition 4), reducing surplus; but if instead it responds with a
more aggressive policy it again hires less, in this case because of the
anti-competitive effect of aggressive ESG, and again reducing surplus.
Paralleling Corollary 1, this is another case in which firm −𝑖’s board
wishes it had more tools at its disposal, since the marginal worker hired
produces strictly positive surplus for firm −𝑖, and so the firm would
ideally like to be larger. However, no choice of ESG policy exists that
leads firm −𝑖’s manager to actually hire more.
We use Lemma 5 to analyze the result of ESG competition between
purposeful firms:

6. Discussion and implications
6.1. Other stakeholders: suppliers and consumers
For concreteness, we have described our analysis in terms of firms
adopting policies that constrain their managers to treat workers well.
But as emphasized in the introduction, our analysis has parallel implications for similar commitments to suppliers and to customers.
Especially for inputs obtained from lower-income countries, firms
face pressures to treat the suppliers of these inputs well, and sometimes
respond to such pressures by offering public commitments to do so.
Prominent examples include coffee, chocolate, diamonds, and, more
recently, rare-earth elements. The outcomes of such policies are exactly
the same as those for analogous promises to treat workers well. Moderate promises improve welfare both of an ESG firm’s own suppliers,
and also of suppliers to competing non-ESG firms. Moreover, moderate
policies raise the ESG firm’s profits, at the expense of competitors. In
contrast, aggressive ESG policies hurt the suppliers to non-ESG firms,
and reduce an ESG firm’s profits.
Similarly, firms face pressures to treat their customers better than
market conditions alone dictate. A prominent example is public pressure on pharmaceutical firms to moderate their prices. In other instances, the public’s “demand” is that firms offer higher quality (including higher environmental standards and greater privacy protections)
without higher prices. These cases be can analyzed in a dual version
of our model in which firms acquire inputs from a competitive market,
but compete oligopolistically in the product market. Formally, let 𝑃 be
the inverse demand curve in a given industry, and 𝑐𝑖 be firm 𝑖 ’s cost
function; then firm 𝑖 chooses output 𝑞𝑖 to maximize profits
(
)
( )
𝑃 𝑞𝑖 + 𝑞−𝑖 𝑞𝑖 − 𝑐𝑖 𝑞𝑖 .
(17)

Proposition 6. In the unique equilibrium, both purposeful firms adopt ESG
policy 𝑊 ∗∗ , leading to the first-best outcome.
Proposition 6 is striking: competition in ESG policies between purposeful firms entirely eliminates the monopsony distortion and delivers
the first-best industry surplus. This is true even though each individual firm’s objective is to maximize only its own surplus, which as
Corollary 2 shows can have adverse welfare effects because firms do
not internalize the externalities that they inflict on competitors’ surplus
.
In Proposition 6 firm 𝑖 anticipates firm −𝑖 ’s best response. Firm 𝑖
would like to adopt an ESG policy that induces its manager to be more
aggressive in the labor market than firm −𝑖, but it cannot achieve this
because firm −𝑖 always responds with a more aggressive policy, 𝜔−𝑖 >
𝜔𝑖 . Thus, the best firm 𝑖 can do is to adopt an ESG policy that maximizes
its employment; it has incentives to grow larger. In principle, since
purposeful firms do not internalize the externalities they inflict on their
competitors, they have incentives to grow beyond even above the firstbest employment level. However, since the hiring decision is made
by a profit-maximizing manager and the firm cannot commit to an
employment level, the second-best is to choose the highest employment
such that marginal productivity is equal to the minimum wage imposed

26
The proof of Lemma 5(i) also shows that if 𝜔𝑖 < 𝑊 ∗∗ then firm −𝑖′ 𝑠 best
(
)
response is 𝜔−𝑖 ∈ 𝜔𝑖 , 𝑊 ∗∗ , which establishes that the first best is the unique
equilibrium outcome of the simultaneous-move game.

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P. Bond and D. Levit

In this context, an ESG policy is a promise to not charge customers
“excessive” prices relative to quality, i.e., to set prices no greater than
some level 𝜌𝑖 . Our analysis implies that moderate promises reduce
prices and improve welfare for an ESG firm’s own customers, and
also of customers of competing non-ESG firms. Moreover, moderate
policies raise the ESG firm’s profits, at the expense of competitors,
by effectively committing the ESG to compete more aggressively. In
contrast, aggressive ESG policies lead an ESG firm to produce limited
quantities, softening product-market competition and leading to higher
prices for its competitors’ output.
Finally, the influence of ESG policies extends beyond their immediate application, creating spillover effects in interconnected input and
product markets. For example, within the labor market, the adoption
of a pro-competitive ESG policy, exemplified by an aggressive hiring
strategy leading to increased employment, also leads to an expansion
in output. Thus, a pro-competitive hiring policy not only deters rivals in
the labor market but also generates a competitive edge in the product
market, as competitors anticipate larger production capacities resulting
from increased workforce. Conversely, anti-competitive ESG policies
have the potential to adversely impact both stakeholders. In essence,
ESG policies targeting different stakeholder groups and markets at least
partly substitute for one another.

Second, to the extent to which the rise of ESG reflects a real shift in
the strength of shareholders’ pro-social preferences, our comparison of
shareholder and purposeful firms predicts that purposeful firms adopt
more aggressive ESG policies (Propositions 2 and 3). One further implication is worth highlighting here. If firms’ shareholder bases (or boards)
are heterogeneous in the strength of their pro-social preferences, so
that only a subset of firms are purposeful in our terminology, Lemma 4
nonetheless implies that shareholder firms also adopt more aggressive
ESG policies to keep up with their purposeful rivals.
6.3. How do ESG firms react to productivity shocks?
Our analysis abstracts from uncertainty, but it nevertheless has some
interesting implications for how ESG adopters react to productivity
shocks. Specifically, suppose firm 𝑖 experiences a shock to its productivity before deciding how many workers to hire. Absent ESG policies,
the firm naturally hires more (less) workers in response to positive
(negative) productivity shocks. Next, consider a firm that has adopted a
(
)
moderate ESG policy 𝜔𝑖 ∈ 𝑊 𝐵 , 𝑊̂ 𝑖 (while firm −𝑖 is a non-ESG firm).
From Proposition 1, firm 𝑖 hires 𝛬𝑖 (𝜔); this is (locally) independent
of firm 𝑖’s productivity, because the reaction functions intersect in
the “residual” region of firm 𝑖’s reaction function (see Fig. 2). Hence
a moderate ESG policy reduces firm 𝑖’s sensitivity to shocks to its
productivity.
In contrast, a moderate ESG policy increases firm 𝑖’s sensitivity
to shocks to firm −𝑖’s productivity, relative to the case of no-ESG.
This again follows from the fact the reaction functions intersect in the
residual region of the ESG firm’s reaction function.
From Proposition 2, a firm that seeks to maximize shareholder value
adopts a moderate ESG policy in the range (𝑊 𝐵 , 𝑊̂ 𝑖 ) for which the
above analysis applies. Moreover, this implication extends to the case
the firm anticipates the possibility of productivity shocks.
If a firm adopts an aggressive ESG policy 𝜔𝑖 > 𝑊̂ 𝑖 then its responsiveness to own- and competitor productivity shocks is reversed.
Now, the ESG policy renders the firm more responsive to shocks to
its own productivity, but unresponsive to shocks to its competitor’s
productivity. This case is most likely to arise for the case of a purposeful
firm; Proposition 3 predicts that such a firm will adopt an ESG policy of
𝑊̂ 𝑖 , i.e., exactly on the boundary between the moderate and aggressive
cases (see Fig. 4). Consequently, a further implication is that purposeful
ESG firms respond asymmetrically to shocks, viz., are unresponsive
to positive shocks to their own productivity but highly responsive to
negative shocks; and are highly responsive to positive shocks to a
competitor’s productivity, but unresponsive to negative shocks.

6.2. The evolution of ESG policies
Proposition 2 in particular highlights that even a shareholder firm
benefits from adopting ESG policies. This observation in turn begs the
question of why ESG policies have achieved such salience in recent
years.
One possibility is simply that “ESG” is a new label for an older
phenomenon. That is: Firms’ promises to treat workers, customers,
and suppliers well have a long history, and predate the rise of both
ESG and the related concept of “Corporate Social Responsibility.” A
second possibility is that the increased prominence of ESG in the public
consciousness has led some firms to experiment with policies that they
had previously and wrongly believed to be unprofitable, only to then
discover that moderate ESG in fact increases profits. We believe both
possibilities have at least some explanatory power.
More interestingly, our model suggests two further possible drivers
for the recent rise in ESG. First, our analysis links the incentives for
both shareholder and purposeful firms to adopt ESG policies to the
competitiveness of the market. Specifically, equilibrium ESG policies
grow more aggressive as the supply curve becomes more elastic, and
in the limit in which markets are perfectly competitive, no ESG policy
is adopted. Similarly, a firm’s ESG policy is generally less aggressive
in markets with more competitors.27 Considerable evidence suggests
concentration has increased in many areas of the US economy (e.g.,
Autor et al. (2020) and De Loecker et al. (2020)), with the increase
occurring roughly contemporaneously to the rise of ESG.

6.4. Alternative ESG tools
Our analysis shows that a purposeful firm – in contrast to a shareholder firm – would gain from access to instruments that go beyond
promises to ensure the well-being of stakeholders. One such instrument
is ESG-linked executive pay structures, which redirect managerial objectives away from pure profit-maximization and toward internalizing
stakeholder welfare. As such, our analysis implies that purposeful
firms are more inclined to incorporate ESG metrics into compensation
contracts compared to shareholder firms. This prediction aligns with
empirical findings from Cohen et al. (2023), which show a higher
prevalence of ESG-linked executive pay in countries with more stringent ESG regulations and greater societal sensitivity toward sustainability. Moreover, given that purposeful firms embrace more aggressive
ESG policies than shareholder firms, our analysis further predicts a
higher likelihood of ESG-linked executive pay adoption among firms
making more aggressive ESG commitments.
Nevertheless, given that purposeful firms already adopt ESG policies that are excessively aggressive from a societal standpoint (see
Corollary 2), our analysis suggests that ESG-linked executive pay offers no discernible social value. Specifically, our analysis implies that

27
It is immediate that the ESG policy adopted by a firm facing a single
competitor is more aggressive than the ESG policy adopted by a firm facing
𝑁 − 1 competitors for 𝑁 sufficiently large, relative to the benchmark wage
that arises absent ESG policies. In Appendix H of the Online Appendix, we
analytically establish that the elasticity comparative static holds monotonically
for the case of symmetric firms, Cobb–Douglas production, a constant-elasticity
of supply, and one-ESG firm—and regardless of whether the ESG firm is a
shareholder or purposeful firm. Using the same parameterization of our model,
in Appendix J of the Online Appendix we establish the comparative static with
respect to the number of competing firms—though here, the comparative static
for shareholder firms is established by exhaustive numerical simulation, while
the comparative static for purposeful firms is established analytically. These
comparative statics with respect to the number of firms hold starting from the
case of 𝑁 = 2 firms; in contrast, a shift from 𝑁 = 1 firms to 𝑁 = 2 firms is
fundamentally different, and is associated with a shift from no ESG policy an
ESG policy that binds.

13

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

7. Empirical predictions

total social surplus is lowered if firms compensate managers based
on ESG-metrics. More broadly, Proposition 6 says that stakeholder
capitalism is most effectively implemented by managers focusing on
profit-maximization, with boards strategically setting ESG policies to
mitigate any adverse impacts this objective may have on the firm’s
other stakeholders.

Our analysis provides a framework to think through how the “S”
dimension of ESG policies affects the markets in which firms operate.
As such, it produces a large number of empirical predictions. Several
predictions arise from our analysis when the firm’s ESG policy is
exogenous (corresponding to cases in which external factors affect the
firm’s ESG polices), some when only one firm adopts an ESG policy
(i.e., becoming an industry leader in ESG practices), and others for cases
where firms compete and optimally select their ESG policies. Here, we
outline some of the key predictions.

6.5. Alternative approaches to modeling ESG
Throughout, and motivated by our reading of firms’ real-world
behavior, we have modeled a firm’s ESG policy in the S-dimension as
a commitment to treat its customers/employees/suppliers better than
market conditions alone dictate. At the same time, we acknowledge
that other ESG policies are feasible. Here, we briefly discuss three such
alternatives.
First, one might think of a firm as simply increasing the weight
it places on stakeholder welfare; indeed, this is the class of policies
considered by Stoughton et al. (2020), discussed in detail above in
the literature review. The contrast between a shareholder firm and
a purposeful firm in our analysis highlights the importance of distinguishing between the firm’s objective and the type of ESG policies it
implements. Second, a subcategory of employee-targeted ESG policies
is a pledge to develop employee human capital. If credible, such pledges
can help firms solve the much-studied “hold-up” problem associated
with relationship-specific investments. More generally, our modeling
approach abstracts from any direct effects of firms’ ESG policies on
productivity. However, as the discussion that follows Proposition 2
highlights, ESG policies in our model have interesting indirect effects
on the firm’s productivity in equilibrium. Third, if stakeholders have
heterogeneous preferences over ESG policies, firms’ adoption of ESG
policies enhances their ability to price discriminate. The ultimate effect
on firm profits and stakeholder welfare is nuanced, and is likely to
depend on the substitutability of different firms from stakeholders’
perspective; see, for example, Rhodes and Zhou’s (2024) analysis of
personalized pricing in oligopolistic competition.

1. The profits and market share of an ESG firm, as well as total
industry employment, are increasing and then decreasing in the
aggressiveness of its ESG policy.
2. The margins of an ESG firm are decreasing in the aggressiveness
of its ESG policy.
3. The profits and market share of a non-ESG firm competing
with an ESG firm are decreasing and then increasing in the
aggressiveness of the ESG firm’s policy.
4. Welfare and wages of workers at the non-ESG firm are increasing
and then decreasing in the aggressiveness of the ESG firm’s
policy.29 Similarly, in the product market application of our
model, consumer welfare at the non-ESG firm is increasing and
then decreasing in the aggressiveness of the ESG firm’s policy,
and product prices of the non-ESG firm are decreasing and then
increasing in the aggressiveness of the ESG firm’s policy.
5. There is no wage difference between ESG and the non-ESG firms
at moderate ESG policies. For extreme ESG policies, the ESG firm
offers higher wages than the non-ESG firm, and the difference
increases with the aggressiveness of the ESG firm’s policy. Similarly, in the product market application of our model, there is
no price difference between the ESG and the non-ESG firms at
moderate ESG policies. For extreme ESG policies, the ESG firm
offers lower prices than the non-ESG firm, and the difference
increases with the aggressiveness of the ESG firm’s policy.
6. ESG policy and firm size are positively correlated, with causality
running in both directions: moderate ESG policies increase a
firm’s size; while more productive firms are both larger and have
greater incentives to adopt ESG.30
7. ESG policy’s aggressiveness is negatively correlated with the
elasticity of supply (for labor and supplier applications) and
demand (for customer applications).
8. Relative to a no-ESG firm, a moderate-ESG firm is more responsive to shocks to competitor productivity and less responsive to
shocks to own-productivity.
9. Relative to shareholder firms, regulations that facilitate transparency and disclosure of ESG policies have less effect on the
adoption of these policies by purposeful firms.
10. When multiple firms adopt ESG, these choices are generally
strategic complements .
11. Periods in which competing firms adopt moderate ESG policies
are followed by periods of aggressive ESG policies, which are
then followed again by periods of moderate ESG policies, and so
on.

6.6. Supply effects of ESG policies
We have assumed that a firm’s wages depend only on the combination of its own ESG policy and total labor demand; specifically,
each firm pays its workers at least 𝑊 (𝐿). This represents a minimal
departure from the standard Cournot model and it ensures that ESG
policies affect other firms entirely through labor demand.28
In particular, this assumption rules out the possibility that firm 𝑖’s
ESG policy disproportionately draws workers with the highest outside
options, thereby expanding the supply of labor available to firm −𝑖. In
principle, if “supply effects” of this sort existed, then firm −𝑖’s demand
would depend on the firm 𝑖’s ESG policy above and beyond its hiring
decision. For example, in this case, if firm −𝑖 reduces its hiring to
a point at which its competitor 𝑖’s ESG policy binds, then firm −𝑖’s
wages would further fall because of the endogenous matching of the
lowest-outside-option workers with firm −𝑖.
Clearly, if firms benefit from hiring workers with low outside options (e.g., such workers are easier to retain and motivate), then they
will compete for these workers regardless of ESG, and thereby bid
the wage up to at least 𝑊 (𝐿), exactly as our analysis assumes. The
equilibrium outcome and the relevance of these intricate supply effects
are left for future research.

28
Recall that absent ESG policies, each firm pays workers 𝑊 (𝐿), and the 𝐿
workers with lowest outside options are employed. One possible microfoundation is that firms cannot observe workers’ outside options, but they have
an infinitesimal preference to hire workers with the lowest outside option.
Consequently, a situation in which firm 𝑖 hires the 𝑙𝑖 workers with lowest
outside options, and pays 𝑊 (𝑙𝑖 ) < 𝑊 (𝐿), cannot arise, since in this case firm
−𝑖 would try to poach firm 𝑖’s workers away.

29
Notice that total employment at the non-ESG firm is decreasing at
moderate levels of aggressiveness of the ESG firm’s policy. However, since
industry employment is increasing, all displaced workers can find a job at the
ESG firm.
30
Appendix F of the Online Appendix formally shows that more productive
firms has stronger incentives to adopt ESG policies.

14

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

)
(
We first note that 𝑊 (𝐿) 𝐿 − 𝑙−𝑖 is strictly convex. If 𝑊 ′′ (𝐿) ≥ 0 then
this is immediate. Otherwise, consider any 𝐿 such that 𝑊 ′′ (𝐿) < 0, and
note that
)
(
𝜕 2 𝑊 (𝐿) 𝐿 − 𝑙−𝑖

8. Concluding remarks
In this paper we study the “S” dimension of ESG, focusing on
firm policies that effectively pledge to treat stakeholders better than
market conditions alone dictate. As our analysis demonstrates, it is
far from obvious how such pledges affect equilibrium outcomes. We
elucidate the economic forces at play, both in the determination of
market outcomes, and in how firms select their ESG policies. A striking
result is that competition in ESG policies between socially conscious
firms eliminates market power distortions. Our analysis generates novel
empirical predictions and a rich set of implications regarding the
drivers behind the recent rise in ESG, the desirability of ESG-linked
compensation, and the necessity/effectiveness of regulations promoting
transparency and disclosure of ESG policies.
We have deliberately structured our analysis to illuminate the “basic
economics” of ESG policies. As such, it inevitably bypasses various
avenues of potential interest, and we hope that subsequent research
explores some of these. First, it would be interesting to explore how ESG
policies interact with heterogeneous stakeholders; for example, perhaps
some employees or costumers care more about pro-social policies than
others. Indeed, ongoing advances in “big data” raise the prospect
of price discrimination based on social preferences playing a larger
role in the future. Second, while our analysis is equally applicable
to labor, input, and product markets, it treats each of these three
markets in isolation; it would be interesting to explore interactions
between these markets, such as the possibility that a promise to treat
workers and suppliers better directly raises consumers’ valuations in
the product market, or alternatively, that promises to produce safe
and environmentally friendly products increase a firm’s attractiveness
as an employer. Third, market power creates a dead weight loss in
our framework due to the usual monopsony/monopolistic distortion.
However, in some cases market power results from investments in
innovation; in these cases, reducing the fruits of market power, as we
have argued that ESG policies have the capacity to do, may carry the
cost of reducing incentives for innovation. Fourth, our analysis deals
with firms engaged in horizontal competition, and leaves open the
question of how ESG policies affects firms in vertical relationships,
and/or those selling complementary products. Last, since ESG policies
are strategic complements at moderate levels and strategic substitutes
at extreme levels, a dynamic version of our model could give rise
to “ESG-cycles:” phases where moderate ESG policies alternate with
aggressive ones, and vice versa.

𝜕(𝐿2
)
= 𝑊 ′′ (𝐿) 𝐿 − 𝑙−𝑖 + 2𝑊 ′ (𝐿)
> 𝑊 ′′ (𝐿) 𝐿 + 2𝑊 ′ (𝐿) > 0,
where the final inequality follows from (1). It follows that the firm’s
objective is strictly concave, and hence has a unique maximizer.
(
)
Next, we establish that 𝑟𝑖 𝑙−𝑖 , 0 is decreasing. This follows from the
FOC
( )
(
)
(
)
𝑓𝑖′ 𝑙𝑖 = 𝑊 ′ 𝑙𝑖 + 𝑙−𝑖 𝑙𝑖 + 𝑊 𝑙𝑖 + 𝑙−𝑖 .
The derivative of the RHS with respect to 𝑙−𝑖 is
(
)
(
)
(
)
𝑊 ′′ 𝑙𝑖 + 𝑙−𝑖 𝑙𝑖 + 𝑊 ′ 𝑙𝑖 + 𝑙−𝑖 = 𝑊 ′′ (𝐿) 𝐿 − 𝑙−𝑖 + 𝑊 ′ (𝐿) ,
which is strictly positive: this is immediate if 𝑊 ′′ (𝐿) ≥ 0, and follows
from (1) if 𝑊 ′′ (𝐿) < 0. The result follows.
(
)
Finally, we establish that 𝑟𝑖 𝑙−𝑖 , 0 + 𝑙−𝑖 is strictly increasing in 𝑙−𝑖 .
This follows from the single-crossing property applied to firm 𝑖 profits
(
)
(
)
𝑓𝑖 𝐿 − 𝑙−𝑖 − 𝑊 (𝐿) 𝐿 − 𝑙−𝑖 . Specifically, consider 𝐿 and 𝐿̃ > 𝐿 such
that
(
)
(
)
̃ 𝐿̃ − 𝑙−𝑖 ) ≥ 𝑓𝑖 𝐿 − 𝑙−𝑖 − 𝑊 (𝐿) 𝐿 − 𝑙−𝑖 .
𝑓𝑖 (𝐿̃ − 𝑙−𝑖 ) − 𝑊 (𝐿)(
Then for any ̃
𝑙−𝑖 > 𝑙−𝑖 , we claim
̃ 𝐿̃ − ̃
𝑓𝑖 (𝐿̃ − ̃
𝑙−𝑖 ) − 𝑊 (𝐿)(
𝑙−𝑖 ) > 𝑓𝑖 (𝐿 − ̃
𝑙−𝑖 ) − 𝑊 (𝐿) (𝐿 − ̃
𝑙−𝑖 ).
This holds because
𝑓𝑖 (𝐿̃ − ̃
𝑙−𝑖 ) − 𝑓𝑖 (𝐿 − ̃
𝑙−𝑖 )
(
)
> 𝑓𝑖 (𝐿̃ − 𝑙−𝑖 ) − 𝑓𝑖 𝐿 − 𝑙−𝑖
(
)
̃ 𝐿̃ − 𝑙−𝑖 ) − 𝑊 (𝐿) 𝐿 − 𝑙−𝑖
≥ 𝑊 (𝐿)(
̃ 𝐿̃ − ̃
> 𝑊 (𝐿)(
𝑙−𝑖 ) − 𝑊 (𝐿) (𝐿 − ̃
𝑙−𝑖 ),
where the first inequality follows from the concavity of 𝑓𝑖 , and the third
inequality follows from 𝑊 being strictly increasing.
■
(
)
Proof of Lemma 2. In equilibrium, 𝑙𝑖𝐵 solves 𝑙 = 𝑟𝑖 𝑟−𝑖 (𝑙, 0) , 0 . Since
the slopes of 𝑟𝑖 (⋅, 0) and 𝑟−𝑖 (⋅, 0) are strictly below one (Lemma 1), the
(
)
slope of 𝑟𝑖 𝑟−𝑖 (⋅, 0) , 0 is strictly below one as well, and hence 𝑙𝑖𝐵 is
unique. Inada conditions ensure existence.
To establish (7), suppose to the contrary that 𝑙1𝐵 +𝑙2𝐵 ≥ 𝑙1∗∗ +𝑙2∗∗ . Then
(
)
(
)
(
)
𝑓𝑖′ 𝑙𝑖𝐵 = 𝑊 ′ 𝑙1𝐵 + 𝑙2𝐵 𝑙𝑖𝐵 + 𝑊 𝑙1𝐵 + 𝑙2𝐵
( ∗∗
)
(
)
> 𝑊 𝑙1 + 𝑙2∗∗ = 𝑓𝑖′ 𝑙𝑖∗∗ ,

CRediT authorship contribution statement
Philip Bond: Writing – review & editing, Writing – original draft,
Visualization, Validation, Resources, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. Doron Levit:
Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Project administration, Methodology, Investigation,
Formal analysis, Conceptualization.

which implies 𝑙𝑖𝐵 < 𝑙𝑖∗∗ , contradicting 𝑙1𝐵 + 𝑙2𝐵 ≥ 𝑙1∗∗ + 𝑙2∗∗ .
To establish 𝑙1𝐵 ≥ 𝑙2𝐵 , note that 𝑓1′ ≥ 𝑓2′ implies 𝑟1 (𝑙; 0) ≥ 𝑟2 (𝑙; 0).
Since 𝑟𝑖 (𝑙; 0) is a decreasing function,
( (
) )
( (
) )
𝑙1𝐵 = 𝑟1 𝑟2 𝑙1𝐵 ; 0 ; 0 ≥ 𝑟1 𝑟1 𝑙1𝐵 ; 0 ; 0
( (
) )
≥ 𝑟2 𝑟1 𝑙1𝐵 ; 0 ; 0 = 𝑙2𝐵 . ■

Declaration of competing interest
No conflict to disclose.
Proof of Lemma 3. Let
(
)
( )
𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 ≡ 𝑓𝑖 𝑙𝑖 − 𝜔𝑖 𝑙𝑖 .

Appendix A

We can write the profit of firm 𝑖 given ESG policy 𝜔𝑖 as
(
)
𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 𝜔𝑖
(
)}
{ (
)
= min 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 , 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖
{ ( )
(
)
( )
}
= min 𝑓𝑖 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑙−𝑖 𝑙𝑖 , 𝑓𝑖 𝑙𝑖 − 𝜔𝑖 𝑙𝑖 .
(
)
Notice that 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 𝜔𝑖 is concave in 𝑙𝑖 since it is the lower envelope
of two concave functions. We make two useful observations:

A.1. Proofs for Section 3
Proof of Lemma 1. It is convenient to rewrite firm 𝑖’s maximization
problem as
(
)
(
)
max 𝑓𝑖 𝐿 − 𝑙−𝑖 − 𝑊 (𝐿) 𝐿 − 𝑙−𝑖 .
𝐿

15

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

( )
( )
Fig. A.12. Case 1: 𝑙−𝑖 ≤ 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 .

( )
(
)
Fig. A.14. Case 3: 𝑊 −1 𝜔𝑖 − 𝑟𝑖 𝑙−𝑖 ; 0 ≤ 𝑙−𝑖 .

)
( ( )
)
)
( (
conthe above implies 𝜋𝑖 𝑟𝑖 𝑙−𝑖 ; 0 (, 𝑙−𝑖 ; 0) < 𝜋𝑖 𝜆𝑖 𝜔𝑖 , 𝑙−𝑖 ; 0 , which
(
)
tradicts the observation that 𝑟𝑖 𝑙−𝑖 ; 0 is the maximizer of 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 .
Finally, we rewrite the condition on 𝑙−𝑖 from Case 2. Note that
( ( )
( )
( ) )
𝜋𝑖 𝜆𝑖 𝜔𝑖 , 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ; 0
(
)
(
(
)
)
= 𝜋𝑖𝑐 𝜆𝑖 𝜔𝑖 ; 𝜔𝑖 = max 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 ,
𝑙𝑖

Fig. A.13. Case 2: 𝑊

−1

(
( )
( ) )
( )
implying 𝑟𝑖 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ; 0 < 𝜆𝑖 𝜔𝑖 . Hence
( )
( )
(
( )
( ) )
( )
𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 + 𝑟𝑖 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ; 0 < 𝑊 −1 𝜔𝑖 ,
( )
( )
i.e., at 𝑙−𝑖 = 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ,
(
)
(
)
𝑙−𝑖 + 𝑟𝑖 𝑙−𝑖 ; 0 < 𝑊 −1 𝜔𝑖 .

( )
( )
( )
(
)
𝜔𝑖 − 𝜆𝑖 𝜔𝑖 ≤ 𝑙−𝑖 ≤ 𝑊 −1 𝜔𝑖 − 𝑟𝑖 𝑙−𝑖 ; 0 .

( )
(
)
(
)
1. Recall 𝜆𝑖 𝜔𝑖 = ar g max𝑙𝑖 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 and 𝑟𝑖 𝑙−𝑖 ; 0 = ar g max𝑙𝑖 𝜋𝑖
(
)
𝑙𝑖 , 𝑙−𝑖 ; 0 .
(
)
(
)
(
)
2. Note that 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 > 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 ⇔ 𝑊 𝑙𝑖 + 𝑙−𝑖 > 𝜔𝑖 . If
(
)
(
)
(
)
𝑊 𝑙𝑖 + 𝑙−𝑖 = 𝜔𝑖 then 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 = 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 and at this point,
(
)
𝜕 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0

Hence
( )
( )
( )
𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 < 𝛬−𝑖 𝜔𝑖 .

𝜕𝑙
( ) 𝑖
(
)
(
)
= 𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑙−𝑖 − 𝑊 ′ 𝑙𝑖 + 𝑙−𝑖 𝑙𝑖
(
)
( )
(
) 𝜕 𝜋 𝑐 𝑙𝑖 ; 𝜔𝑖
.
< 𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑙−𝑖 = 𝑖
𝜕 𝑙𝑖
(
)
(
)
Hence 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 crosses 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 from above.

Hence the condition on 𝑙−𝑖 is equivalent to
[
( )
( )
( )]
𝑙−𝑖 ∈ 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 , 𝛬−𝑖 𝜔𝑖 .
This completes the proof of the first equality in the statement of the
result.
The
(
) second equality follows from the property (Lemma 1) that
𝑟𝑖 𝑙−𝑖 , 0 + 𝑙−𝑖 is strictly increasing.
■

There are three cases to consider.
( ( )
)
Case 1: Suppose 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖 , which holds if and only if
(
)
(
)
( )
(
)
𝑙−𝑖 ≤ 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 . At 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 , 𝑊 𝑙𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖 and so
(
)
(
)
(
)
(
)
𝑐
𝑐
𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 ≤ 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 . So 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 crosses 𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 from above
( )
(
)
𝑐
to the right of 𝜆𝑖 𝜔𝑖 , which is the maximizer of 𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 . Hence the
(
)
( )
maximum of 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 𝜔𝑖 is 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 (see Fig. A.12).
( (
)
)
( ( )
)
Case 2: Suppose 𝑊 𝑟𝑖 𝑙−𝑖 ; 0 + 𝑙−𝑖 ≤ 𝜔𝑖 ≤ 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 , which
( )
( )
( )
(
)
−1
−1
holds if and only if 𝑊
𝜔 −𝜆𝑖 𝜔𝑖 ≤ 𝑙−𝑖 ≤ 𝑊
𝜔𝑖 −𝑟𝑖 𝑙−𝑖 ; 0 . Note
(
)𝑖
( )
(
)
(
)
that, in this case, 𝑟 𝑙−𝑖 ; 0 ≤ 𝜆𝑖 𝜔𝑖 . At 𝑙𝑖 = 𝑟𝑖 𝑙−𝑖 ; 0 , 𝑊 𝑙𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖
(
)
(
)
( )
( ( )
)
𝑐
and so 𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 ≤ 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 . At 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 , 𝜔𝑖 ≤ 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 ,
(
)
(
)
and so 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 ≤ 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 . Hence the crossing point of the
(
)
(
)
[ (
)
functions 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 and 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 occurs in the interval 𝑟𝑖 𝑙−𝑖 ; 0 , 𝜆
(
)
(
)
( )]
𝑐
𝜔𝑖 , with 𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 ≤ (≥) 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 to the left (right) of the crossing
{ (
)
(
)}
point. Hence min 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 , 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 is strictly increasing up to
the crossing point, and strictly decreasing after the crossing point, and
so is maximized at the crossing point. The crossing point 𝑙𝑖 satisfies
(
)
( )
𝑊 𝑙𝑖 + 𝑙−𝑖 = 𝜔𝑖 , i.e., 𝑙𝑖 = 𝑊 −1 𝜔𝑖 − 𝑙−𝑖 (see Fig. A.13).
)
( (
)
Case 3: Suppose 𝜔𝑖 ≤ 𝑊 𝑟𝑖 𝑙−𝑖 ; 0 + 𝑙−𝑖 , which holds if and only
( )
(
)
(
)
(
)
−1
if 𝑙−𝑖 ≥ 𝑊
𝜔𝑖 − 𝑟𝑖 𝑙−𝑖 ; 0 . At 𝑙𝑖 = 𝑟𝑖 𝑙−𝑖 ; 0 , 𝜔𝑖 ≤ 𝑊 𝑙𝑖 + 𝑙−𝑖 ,
(
)
(
)
(
)
(
)
and so 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 ≤ 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 . If 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 ≤ 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 for all
{ (
)
(
)}
𝑙𝑖 , it is immediate that the maximizer of min 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 , 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0
(
)
(
)
(
)
is 𝑟𝑖 𝑙−𝑖 ; 0 . Otherwise, 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0 crosses 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 from above at a
(
)
(
)
point to the left of 𝑟𝑖 𝑙−𝑖 ; 0 . Hence 𝜋𝑖𝑐 𝑙𝑖 ; 𝜔𝑖 is increasing up to this
{ 𝑐(
)
(
)}
crossing point, and the maximizer of min 𝜋𝑖 𝑙𝑖 ; 𝜔𝑖 , 𝜋𝑖 𝑙𝑖 , 𝑙−𝑖 ; 0
is
(
)
again 𝑟𝑖 𝑙−𝑖 ; 0 (see Fig. A.14).
( ( )
)
( (
)
Observe that it cannot be 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖 ≤ 𝑊 𝑟𝑖 𝑙−𝑖 ; 0 +
)
( ( )
)
( (
)
)
𝑙−𝑖 . If it did, then 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 ≤ 𝑊 𝑟𝑖 𝑙−𝑖 ; 0 + 𝑙−𝑖 implies
( )
(
)
( ( )
)
(
(
)
)
𝜆𝑖 𝜔𝑖 < 𝑟𝑖 𝑙−𝑖 ; 0 , 𝑊 𝜆𝑖 𝜔𝑖 + 𝑙−𝑖 ≤ 𝜔𝑖 implies 𝜋𝑖𝑐 𝜆𝑖 𝜔𝑖 ; 𝜔𝑖 ≤
( ( )
)
( (
)
)
( (
)
𝑐
𝜋𝑖 𝜆𝑖 𝜔𝑖 , 𝑙−𝑖 ; 0 , and 𝜔𝑖 ≤ 𝑊 𝑟𝑖 𝑙−𝑖 ; 0 + 𝑙−𝑖 implies 𝜋𝑖 𝑟𝑖 𝑙−𝑖 ; 0 ;
)
( (
)
)
(
(
)
)
(
(
)
)
𝜔𝑖 > 𝜋𝑖 𝑟𝑖 𝑙−𝑖 ; 0 , 𝑙−𝑖 ; 0 . Since 𝜋𝑖𝑐 𝑟𝑖 𝑙−𝑖 ; 0 ; 𝜔𝑖 ≤ 𝜋𝑖𝑐 𝜆𝑖 𝜔𝑖 ; 𝜔𝑖 ,

A.2. Proofs for Section 4
Proof of Proposition 1. Proposition 1 is a special case of Proposition 4
when 𝜔−𝑖 = 0, which we prove below.
■
Proof of Proposition 2. Proposition 2 follows directly from the arguments that precede its statement in the main text. Here, we establish
the results about industry profits and industry surplus that we refer to
in the discussion that follows Proposition 2.
First, we prove that if firm 𝑖 is the (weakly) less-productive firm
(i.e., 𝑖 = 2), then total industry profits decrease relative to the No-ESG
benchmark. Industry profits are
( )
( (
)) (
(
)) (
(
))
𝑓𝑖 𝑙𝑖 + 𝑓−𝑖 𝑟−𝑖 𝑙𝑖 ; 0 − 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .
The derivative of industry profits with respect to 𝑙𝑖 is
( )
(
) ′ ( (
))
𝑓𝑖′ 𝑙𝑖 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑓−𝑖
𝑟−𝑖 𝑙𝑖 ; 0
(
(
))
(
(
))
− 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
(
))
(
(
))
(
(
))
− 1 + 𝑟′−𝑖 𝑙𝑖 ; 0
𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 𝑊 ′ 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .
From the FOC for firm −𝑖, this simplifies to
( )
(
) ′ ( (
))
𝑓𝑖′ 𝑙𝑖 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑓−𝑖
𝑟−𝑖 𝑙𝑖 ; 0
(
(
))
(
(
))
′
− 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑓−𝑖
𝑟−𝑖 𝑙𝑖 ; 0
(
(
))
(
(
))
′
− 1 + 𝑟−𝑖 𝑙𝑖 ; 0 𝑙𝑖 𝑊 ′ 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
and hence to
(
))
(
(
))
( )
( (
)) (
′
𝑓𝑖′ 𝑙𝑖 − 𝑓−𝑖
𝑟−𝑖 𝑙𝑖 ; 0 − 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑙𝑖 𝑊 ′ 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .

(A.1)

Suppose that firm 𝑖 is weakly less productive. The facts that 𝑙𝑖 ≥ 𝑙𝑖𝐵 and
𝐵 ≥ 𝑙𝐵 imply
𝑙−𝑖
𝑖
16

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

))
( )
(𝐵)
( (
( )
′
′
𝑙−𝑖 ≤ 𝑓−𝑖
𝑟−𝑖 𝑙𝑖 ; 0 .
𝑓𝑖′ 𝑙𝑖 ≤ 𝑓𝑖′ 𝑙𝑖𝐵 ≤ 𝑓−𝑖

To establish the claim in footnote 1, recall the derivative of (A.3)
with respect to 𝑙𝑖 is
( )
( )
(
(
))
𝑓𝑖′ 𝑙𝑖 − 𝜇 𝑊 𝑙𝑖 − (1 − 𝜇) 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
)
[
(
(
))
( (
))]
− (1 − 𝜇) 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 − 𝑊 𝑟−𝑖 𝑙𝑖 ; 0 .
( ( ))
Recalling 𝑓𝑖′ 𝜆𝑖 𝑊̂ 𝑖 = 𝑊̂ 𝑖 , this expression at 𝑙𝑖 = 𝜆𝑖 (𝑊̂ 𝑖 ) evaluates to
[
(
)]
𝜇 𝑊̂ 𝑖 − 𝑊 𝜆𝑖 (𝑊̂ 𝑖 )
(
)[
( (
))]
− (1 − 𝜇) 𝑟′−𝑖 𝜆𝑖 (𝑊̂ 𝑖 ); 0 𝑊̂ 𝑖 − 𝑊 𝑟−𝑖 𝜆𝑖 (𝑊̂ 𝑖 ); 0 .
(
)
Since 𝑟′−𝑖 𝑙𝑖 ; 0 < 0 the second term is positive, as required.
■

Hence expression (A.1) is strictly negative, i.e., total profits are decreasing in 𝑙𝑖 .
Next, we prove that industry surplus is always increasing if the more
productive firm chooses an ESG policy in the neighborhood of 𝑊 𝐵 .
Industry surplus is
𝑙𝑖 +𝑟−𝑖 (𝑙𝑖 ;0)
))
( (
( )
𝑊 (𝐿) 𝑑 𝐿.
𝑓𝑖 𝑙𝑖 + 𝑓−𝑖 𝑟−𝑖 𝑙𝑖 ; 0 −
∫0
The derivative of industry surplus with respect to 𝑙𝑖 is
))
(
) ′ ( (
( )
𝑟−𝑖 𝑙𝑖 ; 0
𝑓𝑖′ 𝑙𝑖 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑓−𝑖
(
))
(
(
))
(
− 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .
From the FOC for firm −𝑖, this simplifies to
( )
(
(
))
𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
)
(
)
(
(
))
+ 𝑟′−𝑖 𝑙𝑖 ; 0 𝑟−𝑖 𝑙𝑖 ; 0 𝑊 ′ 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .

Proof of Corollary 2. Industry surplus is
𝑙𝑖 +𝑟−𝑖 (𝑙𝑖 ;0)
( )
( (
))
𝑊 (𝑙) 𝑑 𝑙,
𝑓𝑖 𝑙𝑖 + 𝑓−𝑖 𝑟−𝑖 𝑙𝑖 ; 0 −
∫0
The derivative of (A.5) with respect to 𝑙𝑖 is
(
))
(
( )
𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
))
(
(
))]
(
)[ ′ ( (
𝑟−𝑖 𝑙𝑖 ; 0 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
+ 𝑟′−𝑖 𝑙𝑖 ; 0 𝑓−𝑖
(
)
(
(
))
< 𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 .

(A.2)

Evaluated at 𝑙𝑖𝐵 , expression (A.2) equals
(
))
(
))
(
(𝐵
(
)
𝑙𝑖 + 𝑟′−𝑖 𝑙𝑖𝐵 ; 0 𝑟−𝑖 𝑙𝑖𝐵 ; 0 𝑊 ′ 𝑙𝑖𝐵 + 𝑟−𝑖 𝑙𝑖𝐵 ; 0 .

(
)
Suppose that firm 𝑖 is weakly more productive. Then 𝑙𝑖𝐵 ≥ 𝑟−𝑖 𝑙𝑖𝐵 ; 0 ,
and so the above expression is (using Lemma 1) strictly positive,
i.e., total surplus is increasing in 𝑙𝑖 in the neighborhood of 𝑙𝑖 = 𝑙𝑖𝐵 . ■
Proof of Proposition 3. Firm 𝑖’s surplus is
𝑙𝑖
𝑙𝑖 +𝑟−𝑖 (𝑙𝑖 ;0)
( )
𝑓𝑖 𝑙𝑖 − 𝜇
𝑊 (𝑙) 𝑑 𝑙 − (1 − 𝜇)
𝑊 (𝑙) 𝑑 𝑙,
∫0
∫𝑟−𝑖 (𝑙𝑖 ;0)

(A.5)

where the inequality follows from the monopsony distortion in non-ESG
( (
))
(
(
))
′ 𝑟
firm’s hiring decisions, 𝑓−𝑖
> 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 , along with
−𝑖 𝑙𝑖 ; 0
(
)
′
the fact that 𝑟−𝑖 𝑙𝑖 ; 0 < 0.
From Proposition 3, the ESG policy that maximizes firm 𝑖’s surplus
( )
is 𝑊̂ 𝑖 , and the associated employment level is such that 𝑓𝑖′ 𝑙𝑖 =
(
(
))
𝑊̂ 𝑖 = 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 . Hence the derivative of (A.5) with respect to
𝑙𝑖 is strictly negative at this point, implying that the ESG policy that
maximizes industry surplus must induce strictly lower employment at
firm 𝑖. (No ESG policy can induce strictly more employment.)
■

(A.3)

The derivative of (A.3) with respect to 𝑙𝑖 is
( )
( )
𝑓𝑖′ 𝑙𝑖 − 𝜇 𝑊 𝑙𝑖
(
(
)) (
(
))
− (1 − 𝜇) 1 + 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
) ( (
))
+ (1 − 𝜇) 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑟−𝑖 𝑙𝑖 ; 0
(
)
(
)
(
(
))
= 𝑓𝑖′ 𝑙𝑖 − 𝜇 𝑊 𝑙𝑖 − (1 − 𝜇) 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0
(
)
[
(
(
))
( (
))]
− (1 − 𝜇) 𝑟′−𝑖 𝑙𝑖 ; 0 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 − 𝑊 𝑟−𝑖 𝑙𝑖 ; 0
( )
(
(
))
> 𝑓𝑖′ 𝑙𝑖 − 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 ,
(A.4)
(
)
(
′
where
follows because 𝑟−𝑖 𝑙𝑖 ; 0 < 0 and 𝑊 𝑙𝑖 + 𝑟−𝑖
(
)) the inequality
( )
𝑙𝑖 ; 0 > 𝑊 𝑙𝑖 .
̂
There are two cases to consider. First, suppose 𝜔𝑖 ∈ [𝑊 (𝐵 , 𝑊
) 𝑖 ).
Increasing
𝜔
corresponds
to
increasing
𝑙
.
In
this
case,
𝑙
=
𝛬
𝜔
𝑖
𝑖
( )
( )
(
(𝑖 ))𝑖 𝑖 <
𝜆𝑖 𝜔𝑖 , or equivalently, 𝑓𝑖′ 𝑙𝑖 > 𝜔𝑖 ; and 𝜔𝑖 = 𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 . Hence
(A.4) is strictly positive. It follows that 𝜔𝑖 = 𝑊̂ 𝑖 delivers higher firm
surplus than any choice in [𝑊 𝐵 , 𝑊̂ 𝑖 ).
̂
Second, consider 𝜔𝑖 >
to increasing
( 𝑊)𝑖 . Decreasing 𝜔𝑖 corresponds
( )
′
𝑙𝑖 . (In this case,
𝑙
=
𝜆
𝜔
𝑖 , or equivalently, 𝑓𝑖 𝑙𝑖 = 𝜔𝑖 ; and 𝜔𝑖 >
𝑖
(
))𝑖
𝑊 𝑙𝑖 + 𝑟−𝑖 𝑙𝑖 ; 0 . Hence (A.4) is strictly positive. It follows that 𝜔𝑖 =
𝑊̂ 𝑖 delivers higher firm surplus than any choice in 𝜔𝑖 > 𝑊̂ 𝑖 .
As in the proof of Proposition 2, firm 𝑖′ 𝑠 employment, total employment, wages, and workers’ surplus, are all higher in equilibrium
relative to the No-ESG benchmark. Moreover, firm’s −𝑖′ 𝑠 employment
and profitability are lower, and if 𝑖 = 1 then total profitability is also
lower.
■

A.3. Proofs for Section 5.1
The next sequence of auxiliary results will be used for the proof of
Proposition 4. The proofs of these results can be found in Appendix B
of the Online Appendix.
Lemma A.6. If 𝜔1 ≠ 𝜔2 then there is at most one labor market equilibrium.
Lemma A.7. If max𝑖 𝜔𝑖 ≤ 𝑊 𝐵 then in any equilibrium, 𝑙𝑖∗ = 𝑙𝑖𝐵 and
𝑊1∗ = 𝑊2∗ = 𝑊 𝐵 .
( )
Lemma A.8. If 𝜔𝑖 ≥ 𝑊 ∗∗ then 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 .
( )
Lemma A.9. If 𝜔𝑖 ∈ (𝑊 𝐵 , 𝑊̂ 𝑖 ] and 𝜔−𝑖 ≤ 𝜔𝑖 then 𝑙𝑖∗ = 𝛬𝑖 𝜔𝑖 ,
( )
( )
∗
∗
∗
−1
𝑙−𝑖 = 𝑊
𝜔𝑖 − 𝛬𝑖 𝜔𝑖 , and 𝑊1 = 𝑊2 = 𝜔𝑖 is an equilibrium; and
is the unique equilibrium if 𝜔−𝑖 < 𝜔𝑖 .
Lemma A.10. Suppose 𝜔𝑖 ∈ (𝑊̂ 𝑖 , 𝑊 ∗∗ ] and 𝜔−𝑖 ≤ 𝜔𝑖 . Then,
( ) ∗
( ( )
is an equilibrium in which, 𝑙𝑖∗ = 𝜆𝑖 𝜔𝑖 , 𝑙−𝑖
= 𝑟−𝑖 𝜆𝑖 𝜔𝑖 ;
(𝑖) There
)
( )
( )
∗
−1
𝜔−𝑖 ≤ 𝑊
𝜔𝑖 − 𝜆𝑖 𝜔𝑖 , and 𝑊𝑖 = 𝜔𝑖 .
in part (i) is the unique equilibrium
(𝑖𝑖) If 𝜔−𝑖 < 𝜔𝑖 then( the) equilibrium
( )
∗ < 𝑊 −1 𝜔 − 𝜆 𝜔 . Moreover:
and 𝑙−𝑖
𝑖
𝑖
𝑖

Proof of Corollary 1. Note that
(
)
𝜕 𝑆𝑖 𝑙𝑖 , 𝑙−𝑖
( )
( )
(
)
= 𝑓𝑖′ 𝑙𝑖 − 𝜇𝑊 𝑙𝑖 − (1 − 𝜇) 𝑊 𝑙𝑖 + 𝑙−𝑖 ,
𝜕 𝑙𝑖
(
)
and hence, if 𝑙𝑖 = 𝜆𝑖 (𝑊̂ 𝑖 ) and 𝑙−𝑖 = 𝑟−𝑖 𝜆𝑖 (𝑊̂ 𝑖 ); 0 , then
(
)
𝜕 𝑆𝑖 𝑙𝑖 , 𝑙−𝑖
(
)
= 𝑊̂ 𝑖 − 𝜇 𝑊 𝜆𝑖 (𝑊̂ 𝑖 ) − (1 − 𝜇) 𝑊̂ 𝑖
𝜕 𝑙𝑖
(
(
))
= 𝜇 𝑊̂ 𝑖 − 𝑊 𝜆𝑖 (𝑊̂ 𝑖 ) > 0,

( )
( )
( ( ) )
∗ = 𝑊 −1
𝑊 −1 𝜔−𝑖 − 𝜆𝑖 𝜔𝑖 ≥ 𝑟−𝑖 𝜆𝑖 𝜔𝑖 ; 0 then 𝑙−𝑖
(𝑎) If
( )
( )
∗
𝜔−𝑖 − 𝜆𝑖 𝜔𝑖 and 𝑊−𝑖 = 𝜔−𝑖 .
( )
( )
( ( ) )
(
∗ = 𝑟
𝑙−𝑖
(𝑏) If( 𝑊) −1 ) 𝜔−𝑖 − 𝜆𝑖 𝜔𝑖 (< 𝑟(−𝑖 )𝜆𝑖 𝜔𝑖 (; 0 ( then
−𝑖 𝜆𝑖
)
))
∗ =𝑊 𝜆 𝜔 +𝑟
𝜔𝑖 ; 0 and 𝑊−𝑖
𝑖
𝑖
−𝑖 𝜆𝑖 𝜔𝑖 ; 0 .
( ( )
)
( )
( )
∗ = 𝑟
−1 𝜔 − 𝜆 𝜔 and
(𝑖𝑖𝑖) If 𝜔−𝑖 = 𝜔𝑖 then 𝑙−𝑖
−𝑖 𝜆𝑖 𝜔𝑖 ; 𝜔−𝑖 = 𝑊
𝑖
𝑖
𝑖
∗
𝑊−𝑖 = 𝜔𝑖 .

as required.
17

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

Proof of Proposition 4. Part (i) follows from Lemma A.7. Part (ii)
follows from Lemma A.8. Consider part (iii). Suppose 𝜔2 = 𝜔1 = 𝜔 ∈
(𝑊 𝐵 , 𝑊 ∗∗ ). As we show in the proof of Lemma A.9, inequality (B-5)
holds, that is
)
(
(A.6)
𝑟−𝑖 𝛬𝑖 (𝜔) ; 0 < 𝜆−𝑖 (𝜔) .
(
)
Since 𝛬𝑖 (𝜔) + 𝑟−𝑖 𝛬𝑖 (𝜔) ; 0 = 𝑊 −1 (𝜔), then (B-5) implies

A.4. Proofs for Section 5.2
Proof of Lemma 4. We consider separately upwards and downwards
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛 𝜔
responses by firm −𝑖 to firm 𝑖’s policy 𝜔𝑖 . Let 𝜋−𝑖
𝑖 and 𝜋−𝑖 𝜔𝑖
respectively denote the maximal profits that firm −𝑖 can obtain if
restricted to policies 𝜔−𝑖 < 𝜔𝑖 and 𝜔−𝑖 ≥ 𝜔𝑖 . From Lemmas A.7–A.10,
both these functions are continuous in 𝜔𝑖 . Further, for 𝑗 = 𝑖, −𝑖 define
{
}
{
min 𝛬𝑗 (𝜔) , 𝜆𝑗 (𝜔)
if 𝜔 ≥ 𝑊 𝐵
𝐿𝑗 (𝜔) =
𝑙𝑗𝐵
if 𝜔 ≤ 𝑊 𝐵 .

𝑊 −1 (𝜔) < 𝛬𝑖 (𝜔) + 𝜆−𝑖 (𝜔) .
Since 𝜔 > 𝑊 𝐵 , repeating the arguments in the proof of Lemma A.9 that
shows (B-6), for 𝑖 = 1, 2 we have

Consider first downwards responses 𝜔−𝑖 < 𝜔𝑖 . From Lemmas A.7–A.10,
( )
𝑙𝑖∗ = 𝐿𝑖 𝜔𝑖 regardless of the specific value of 𝜔−𝑖 . So firm −𝑖’s profits
( )
are maximized by playing the unconstrained best response to 𝐿𝑖 𝜔𝑖 ,
which can be achieved by choosing 𝜔−𝑖 = 0. Hence
)
( ( )
( )
( )
𝑑 𝑜𝑤𝑛
𝜋−𝑖
𝜔𝑖 = max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝑊 𝐿𝑖 𝜔𝑖 + 𝑙−𝑖 .

𝑊 −1 (𝜔) < 𝛬𝑖 (𝜔) + 𝛬−𝑖 (𝜔) .
Since 𝜔 < 𝑊 ∗∗ , we have
(
)
𝑊 −1 (𝜔) < 𝑊 −1 𝑊 ∗∗ = 𝜆𝑖 (𝜔) + 𝜆−𝑖 (𝜔) .

𝑙−𝑖

( )
𝑑 𝑜𝑤𝑛 𝜔
𝐵
Consequently, 𝜋−𝑖
𝑖 is constant for 𝜔𝑖 ≤ 𝑊 ; strictly decreasing
𝐵
over 𝜔𝑖 ∈ [𝑊 , 𝑊̂ 𝑖 ]; and strictly increasing for 𝜔𝑖 ≥ 𝑊̂ 𝑖 . Moreover, note
(
)
(
)
′ 𝜆 (𝑊 ∗∗ ) , which implies
that 𝑊 𝜆𝑖 (𝑊 ∗∗ ) + 𝜆−𝑖 (𝑊 ∗∗ ) = 𝑊 ∗∗ = 𝑓−𝑖
𝑖
the monopsony distortion, namely:
( ∗∗ )
𝑑 𝑜𝑤𝑛
𝑊
𝜋−𝑖
(
(
))
> 𝑓−𝑖 𝜆−𝑖 𝑊 ∗∗
( ∗∗ ) ( ( ∗∗ )
(
))
− 𝜆−𝑖 𝑊
𝑊 𝜆𝑖 𝑊
+ 𝜆−𝑖 𝑊 ∗∗
( )
= max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝑊 ∗∗ .
(A.7)

Combined, these three inequalities establish the interval in (16) is not
empty.
Let 𝑙∗ be an element in interval (16). Then,
[
]
𝑙∗ ∈ 𝑊 −1 (𝜔) − 𝜆−𝑖 (𝜔) , 𝛬𝑖 (𝜔) .
Notice 𝑙∗ ≤ 𝛬𝑖 (𝜔) implies 𝑊 −1 (𝜔) − 𝑙∗ ≥ 𝑟−𝑖 (𝑙∗ ; 0) and 𝑊 −1 (𝜔) −
𝜆−𝑖 (𝜔) ≤ 𝑙∗ implies 𝜆−𝑖 (𝜔) ≤ 𝑊 −1 (𝜔) − 𝑙∗ . Thus, from Lemma 3,
𝑟−𝑖 (𝑙∗ ; 𝜔) = 𝑊 −1 (𝜔) − 𝑙∗ . Moreover
[
]
𝑙∗ ∈ 𝑊 −1 (𝜔) − 𝛬−𝑖 (𝜔) , 𝜆𝑖 (𝜔)

𝑙−𝑖

We next consider upwards responses 𝜔−𝑖 ≥ 𝜔𝑖 . For 𝜔𝑖 ≤ 𝑊 𝐵 is
immediate from Lemma A.7 and Proposition 2 that firm −𝑖 adopts 𝜑∗−𝑖 .
For 𝜔𝑖 ≥ 𝑊 𝐵 , Lemmas A.8–A.10 imply that firm −𝑖’s profits from any
(
( ))
( )
policy 𝜔̃ −𝑖 > 𝜔𝑖 are 𝑓−𝑖 𝐿−𝑖 𝜔̃ −𝑖 −𝐿−𝑖 𝜔̃ −𝑖 𝜔̃ −𝑖 , and in particular, are
independent of firm 𝑖’s policy 𝜔𝑖 . Hence an increase in 𝜔𝑖 affects firm
−𝑖 solely by shrinking the set of upwards responses available, implying
𝑢𝑝 ( )
both that the profit function 𝜋−𝑖
𝜔𝑖 is weakly decreasing in 𝜔𝑖 and
that firm −𝑖’s policy is weakly increasing in 𝜔𝑖 (conditional on firm −𝑖
adopting 𝜔−𝑖 ≥ 𝜔𝑖 ).
Moreover, from Lemma A.8, if 𝜔𝑖 = 𝑊 ∗∗ then any upwards response
𝜔−𝑖 yields profits
(
( ))
( )
( )
𝑓−𝑖 𝜆−𝑖 𝜔−𝑖 − 𝜆−𝑖 𝜔−𝑖 𝜔−𝑖 = max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝜔−𝑖 ,

and so
(
)
[
]
𝑟−𝑖 𝑙∗ ; 𝜔 = 𝑊 −1 (𝜔) − 𝑙∗ ∈ 𝑊 −1 (𝜔) − 𝜆𝑖 (𝜔) , 𝛬−𝑖 (𝜔) .
Thus, from Lemma 3
( (
) )
(
)
𝑟𝑖 𝑟−𝑖 𝑙∗ ; 𝜔 ; 𝜔 = 𝑊 −1 (𝜔) − 𝑟−𝑖 𝑙∗ ; 𝜔 = 𝑙∗ ,
(
)
establishing that 𝑙∗ , 𝑊 −1 (𝜔) − 𝑙∗ is an equilibrium. The fact that both
firms pay 𝜔 is immediate.
Finally, we show that there are no other equilibria. We have just
(
)
shown that the function 𝑟𝑖 𝑟−𝑖 (⋅; 𝜔) ; 𝜔 has an interval of fixed points,
and that over this interval the function has slope 1. From the proof
(
)
of Lemma A.6, it follows that the set of fixed points of 𝑟𝑖 𝑟−𝑖 (⋅; 𝜔) ; 𝜔
coincides with the interval over which the function has slope 1. From
the proof of Lemma A.6, and from Lemma 3, this interval is defined by
the pair of conditions
[
]
𝑙𝑖 ∈ 𝑊 −1 (𝜔) − 𝜆−𝑖 (𝜔) , 𝛬𝑖 (𝜔)
[
]
𝑊 −1 (𝜔) − 𝑙𝑖 ∈ 𝑊 −1 (𝜔) − 𝜆𝑖 (𝜔) , 𝛬−𝑖 (𝜔)

𝑙−𝑖

which combined with (A.7) implies that
( ∗∗ )
)
𝑢𝑝 (
𝑑 𝑜𝑤𝑛
𝜋−𝑖
𝑊
> lim 𝜋−𝑖
𝑊 ∗∗ .

(A.8)

(𝜖 → 0 means 𝜔−𝑖 ↘ 𝜔𝑖 = 𝑊 ∗∗ ).
Below, we establish that
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛
𝜔𝑖 if 𝜔𝑖 ≤ 𝑊̂ 𝑖 .
lim 𝜋−𝑖
𝜔𝑖 > 𝜋−𝑖

(A.9)

𝜖→0

𝜖→0

which together is exactly the interval in (16). This completes part (iii).
Consider part (iv). If 𝜔−𝑖 < 𝜔𝑖 then the equilibrium is unique based
( )
on Lemma A.6. Based on Lemma A.9, if 𝜔𝑖 ∈ (𝑊 𝐵 , 𝑊̂ 𝑖 ] then 𝑙𝑖 = 𝛬𝑖 𝜔𝑖
and 𝑊𝑖∗ = 𝜔𝑖 . Based on Lemma A.10 part (i), if 𝜔𝑖 ∈ (𝑊̂ 𝑖 , 𝑊 ∗∗ ] then
( )
( )
( )
𝑙𝑖∗ = 𝜆𝑖 𝜔𝑖 and 𝑊𝑖∗ = 𝜔𝑖 . Since 𝜔𝑖 ≤ 𝑊̂ 𝑖 ⇔ 𝛬𝑖 𝜔𝑖 ≤ 𝜆𝑖 𝜔𝑖 , this can be
( )}
{ ( )
∗
∗
written as 𝑙𝑖 = min 𝛬𝑖 𝜔𝑖 , 𝜆𝑖 𝜔𝑖 and 𝑊𝑖 = 𝜔𝑖 as required. Notice
∗ and 𝑊 ∗ follow from the definition of equilibrium, and their explicit
𝑙−𝑖
−𝑖
characterization is given in Lemmas A.9 and A.10.
Finally, we prove that if firms 𝑖 are symmetric (i.e., have the same
production functions) or 𝑖 = 1 (the larger firm adopts a more aggressive
∗ . If 𝜔 ∈ (𝑊 𝐵 , 𝑊
̂ 𝑖 ] then based on Lemma A.9,
ESG policy), then 𝑙𝑖∗ > 𝑙−𝑖
𝑖 ( )
( )
( )
∗
∗
𝑙𝑖 > 𝑙−𝑖 ⇔ 𝛬𝑖 𝜔𝑖 > 𝑊 −1 𝜔𝑖 − 𝛬𝑖 𝜔𝑖 . Inequality (B-6) from
the proof of Lemma A.9 implies 𝛬𝑖 (𝜔) + 𝛬−𝑖 (𝜔) > 𝑊 −1 (𝜔). Thus,
( )
( )
( )
𝛬𝑖 𝜔𝑖 > 𝑊 −1 𝜔𝑖 − 𝛬𝑖 𝜔𝑖 must hold. If 𝜔𝑖 ∈ (𝑊̂ 𝑖 , 𝑊 ∗∗ ] then based
( )
( )
( )
∗
∗ < 𝑊 −1 𝜔
on Lemma A.10 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 and 𝑙−𝑖
𝑖 − 𝜆𝑖 𝜔𝑖 . Recall
∗∗
∗∗
−1
∗∗
∗∗
𝜆𝑖 (𝑊 )+𝜆−𝑖 (𝑊 ) = 𝑊 (𝑊 ). If 𝜔𝑖 < 𝑊 and firms are symmetric
( )
( )
( )
or 𝜆𝑖 (⋅) > 𝜆−𝑖 (⋅) then 𝜆𝑖 𝜔𝑖 > 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 .
■

( )
( )
𝑑 𝑜𝑤𝑛 𝜔 and 𝜋 𝑢𝑝 𝜔 , combined with the observations
Continuity of 𝜋−𝑖
𝑖
𝑖
−𝑖
that the former functions is increasing for 𝜔𝑖 ≥ 𝑊̂ 𝑖 while the latter is
weakly decreasing, along with (A.8), implies that there exists a unique
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛 𝜔 if 𝜔 < 𝑊
̌ −𝑖 and
𝑊̌ −𝑖 ∈ (𝑊̂ 𝑖 , 𝑊 ∗∗ ) such that lim𝜖→0 𝜋−𝑖
𝜔𝑖 > 𝜋−𝑖
𝑖
𝑖
)
(
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛 𝜔 if 𝜔 > 𝑊
̌
lim𝜖→0 𝜋−𝑖 𝜔𝑖 < 𝜋−𝑖
.
𝑖
𝑖
−𝑖
Proof of (A.9). There are three subcases. First, if 𝜔𝑖 < 𝜑∗−𝑖 then if
firm −𝑖 adopts 𝜑∗−𝑖 it hires 𝛬−𝑖 (𝜑∗−𝑖 ) at wage 𝜑∗−𝑖 (see Lemma A.9).
By Proposition 2, firm −𝑖’s profits strictly exceed those in the No(
)
𝑑 𝑜𝑤𝑛 𝑊 𝐵 , and which in turn exceeds
ESG benchmark, which equal 𝜋−𝑖
( )
𝑑
𝑜𝑤𝑛
̂
𝜋−𝑖
𝜔𝑖 provided 𝜔𝑖 ≤ 𝑊𝑖 . Hence
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛
𝜋−𝑖
𝜔𝑖 > 𝜋−𝑖
𝜔𝑖 if 𝜔𝑖 < min{𝜑∗−𝑖 , 𝑊̂ 𝑖 }.
(A.10)
Second, if min{𝜑∗−𝑖 , 𝑊̂ 𝑖 } ≤ 𝜔𝑖 < min{𝑊̂ 𝑖 , 𝑊̂ −𝑖 } then if firm −𝑖 adopts
( )
𝜔−𝑖 = 𝜔𝑖 + 𝜖 it hires 𝛬−𝑖 𝜔−𝑖 at wage 𝜔−𝑖 (see Lemma A.9). Moreover,
∗
𝐵
because 𝑊 < min{𝜑−𝑖 , 𝑊̂ 𝑖 } ≤ 𝜔𝑖 ,
( )
(
)
𝐵
𝛬−𝑖 𝜔𝑖 > 𝛬−𝑖 𝑊 𝐵 = 𝑙−𝑖
18

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

( ( ) )
) )
( (
(
)
= 𝑟−𝑖 𝑙𝑖𝐵 ; 0 = 𝑟−𝑖 𝛬𝑖 𝑊 𝐵 ; 0 > 𝑟−𝑖 𝛬𝑖 𝜔𝑖 ; 0 .

(A.11)
( )
The function 𝑓−𝑖 (𝑙)−𝑙𝜔𝑖 is concave with a unique maximizer at 𝜆−𝑖 𝜔𝑖 .
( )
( )
( ( ) )
Note that 𝜔𝑖 < 𝑊̂ −𝑖 implies 𝛬−𝑖 𝜔𝑖 < 𝜆−𝑖 𝜔𝑖 ; and 𝑟−𝑖 𝛬𝑖 𝜔𝑖 ; 0 <
( )
(
( )
𝛬−𝑖 𝜔𝑖 from (A.11); and hiring levels 𝑙𝑖 = 𝛬𝑖 𝜔𝑖 and 𝑙−𝑖 = 𝑟−𝑖 𝛬𝑖
( ) )
𝜔𝑖 ; 0 result in wage 𝜔𝑖 . It follows that, for 𝜖 sufficiently small, firm
−𝑖’s profits from 𝜔−𝑖 strictly exceed
( )
( ( ) )
( ( ( ) ))
𝑑 𝑜𝑤𝑛
𝜔𝑖 .
𝑓−𝑖 𝑟−𝑖 𝛬𝑖 𝜔𝑖 ; 0 − 𝑟−𝑖 𝛬𝑖 𝜔𝑖 ; 0 𝜔𝑖 = 𝜋−𝑖

Note that these profits are weakly below what firm 𝑖 would
( get
) under
the No-ESG policy 𝜔𝑖 = 0 if firm −𝑖 continues to hire 𝜆−𝑖 𝜔−𝑖 ,
( (
( ) ))
𝑓𝑖 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 0
(
( ) ) (
( )
(
( ) ))
− 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 0 𝑊 𝜆−𝑖 𝜔−𝑖 + 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 0
( )
(
( )
)
= max 𝑓𝑖 𝑙𝑖 − 𝑙𝑖 𝑊 𝜆−𝑖 𝜔−𝑖 + 𝑙𝑖 .
(A.18)
𝑙𝑖

( )
Because 𝜔−𝑖 ≤ 𝑊̌ −𝑖 for 𝜖 sufficiently small, 𝜆−𝑖 (𝑊̌ −𝑖 ) ≤ 𝜆−𝑖 𝜔−𝑖 , and
profits (A.18) are in turn weakly below
( )
(A.19)
max 𝑓𝑖 𝑙𝑖 − 𝑙𝑖 𝑊 (𝜆−𝑖 (𝑊̌ −𝑖 ) + 𝑙𝑖 ).

Consequently (and regardless of whether 𝜔−𝑖 = 𝜔𝑖 + 𝜖 is the best
upwards response to 𝜔𝑖 for firm −𝑖),
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛
𝜔𝑖
𝜔𝑖 > 𝜋−𝑖
lim𝜖→0 𝜋−𝑖
if min{𝜑∗−𝑖 , 𝑊̂ 𝑖 } ≤ 𝜔𝑖 < min{𝑊̂ 𝑖 , 𝑊̂ −𝑖 }.

𝑙𝑖

Moreover, there exists some 𝛿 > 0 such that profits (A.19) exceed (A.17)
by at least 𝛿, regardless of 𝜔𝑖 ∈ [𝑊̂ −𝑖 , 𝑊̌ −𝑖 ), as follows.(For)𝜔𝑖 and hence
𝜔−𝑖 bounded
from 𝑊̂ −𝑖 , firm −𝑖’s hiring 𝜆−𝑖 𝜔
( away
)
( −𝑖 (is bounded
)
)
below 𝛬−𝑖 𝜔−𝑖 , which(by Lemma
implies that 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 𝜔𝑖 is
( ) A.10
)
bounded away from 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 0 and hence that (A.17) is bounded
away from (A.18). If instead 𝜔𝑖 and hence 𝜔−𝑖 is bounded away from
𝑊̌ −𝑖 then (A.18) is bounded away from (A.19).
By the definition of 𝑊̌ −𝑖 , and the fact that we are in the case with
𝑊̌ −𝑖 > 𝑊̂ −𝑖 , firm −𝑖’s profits from adopting a policy 𝑊̌ −𝑖 against 𝜔𝑖 just
below 𝑊̌ −𝑖 are the same as from adopting 𝜔−𝑖 = 0 against 𝜔𝑖 = 𝑊̌ −𝑖 ,
i.e.,

(A.12)

Third, if min{𝑊̂ 𝑖 , 𝑊̂ −𝑖 } ≤ 𝜔𝑖 < 𝑊̂ 𝑖 then 𝑊̂ −𝑖 ≤ 𝜔𝑖 < 𝑊̂ 𝑖 . Because 𝜔𝑖 < 𝑊̂ 𝑖 ,
( )
( )
( ( )
)
𝑑 𝑜𝑤𝑛
𝜔𝑖 = max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝑊 𝛬𝑖 𝜔𝑖 + 𝑙−𝑖 .
(A.13)
𝜋−𝑖
𝑙−𝑖

( ( )
)
Note that the wage 𝑊 𝛬𝑖 𝜔𝑖 + 𝑙−𝑖 at the profit-maximizing choice of
𝑙−𝑖 in (A.13) equals 𝜔𝑖 . Because 𝜔𝑖 ≥ 𝑊̂ −𝑖 , if firm −𝑖 adopts 𝜔−𝑖 = 𝜔𝑖 + 𝜖
( )
𝑢𝑝 ( )
𝜔𝑖 weakly exceeds the profits
it hires 𝜆−𝑖 𝜔−𝑖 at wage 𝜔−𝑖 , and so 𝜋−𝑖
from this policy. Hence
( )
( )
𝑢𝑝 ( )
𝑑 𝑜𝑤𝑛
lim𝜖→0 𝜋−𝑖
𝜔𝑖 ≥ max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝜔𝑖 > 𝜋−𝑖
𝜔𝑖
𝑙−𝑖

if min{𝑊̂ 𝑖 , 𝑊̂ −𝑖 } ≤ 𝜔𝑖 < 𝑊̂ 𝑖 .

𝑓−𝑖 (𝜆−𝑖 (𝑊̌ −𝑖 )) − 𝜆−𝑖 (𝑊̌ −𝑖 )𝑊̌ −𝑖
( )
= max 𝑓−𝑖 𝑙−𝑖 − 𝑙−𝑖 𝑊 (𝜆𝑖 (𝑊̌ −𝑖 ) + 𝑙−𝑖 ).

(A.14)

𝑙−𝑖

Combined, (A.10), (A.12), and (A.14) establish (A.9), completing the
proof.
■

(A.20)

If firm 𝑖 adopts 𝜔𝑖 = 𝑊̌ −𝑖 its profits equal 𝑓𝑖 (𝜆𝑖 (𝑊̌ −𝑖 )) − 𝜆𝑖 (𝑊̌ −𝑖 )𝑊̌ −𝑖 .
For the case of symmetric firms (𝑓𝑖 ≡ 𝑓−𝑖 ), equality (A.20) implies
that these profits equal (A.19), which strictly exceeds the profits from
𝜔𝑖 ∈ [𝑊̂ −𝑖 , 𝑊̌ −𝑖 ), given by (A.17). That is, any policy 𝜔𝑖 = [𝑊̂ −𝑖 , 𝑊̌ −𝑖 ) is
dominated by 𝜔𝑖 = 𝑊̌ −𝑖 .
Because of the bound 𝛿 between profits (A.17) and (A.19), the same
conclusion holds whenever the two firms’ production functions are
sufficiently similar. This completes the proof of part (i).
Consider part (ii). From Lemma 4 and the arguments above, the labor market equilibrium
that
equilibrium choice of (ESG poli(
) follows the
)
∗
∗
cies is either (A), 𝑙𝑖∗ , 𝑙−𝑖
= (𝑟𝑖 (𝛬−𝑖 (𝜑∗−𝑖 ), 0), 𝛬−𝑖 (𝜑∗−𝑖 )), or (B) 𝑙𝑖∗ , 𝑙−𝑖
=
̌
̌
(𝜆𝑖 ((𝑊−𝑖 ), 𝑟−𝑖)(𝜆𝑖 (𝑊−𝑖 ), 0)). In both cases, firms pay wages of at least
∗ . So the worker welfare conclusion follows provided that
𝑊 𝑙𝑖∗ + 𝑙−𝑖

Proof of Proposition 5. To avoid excessive mathematical complication
we assume that the grid determining firm −𝑖’s policy choices includes
𝑊̌ −𝑖 .
We show that, for the leader firm 𝑖: (A) any policy choice 𝜔𝑖 ∈
[𝜑∗−𝑖 , min{𝑊̂ −𝑖 , 𝑊̌ −𝑖 }) is dominated by 𝜔𝑖 < 𝜑∗−𝑖 ; (B) any policy choice
𝜔𝑖 ≥ min{𝑊̂ −𝑖 , 𝑊̌ −𝑖 } with 𝜔𝑖 ≠ 𝑊̌ −𝑖 is dominated by 𝜔𝑖 = 𝑊̌ −𝑖 .
Proof of (A): This case only arises if 𝜑∗−𝑖 < 𝑊̌ −𝑖 . On the one
hand, if firm 𝑖 adopts 𝜔𝑖 < 𝜑∗−𝑖 then, by Lemma 4, Lemma A.9, and
Proposition 2, firm −𝑖 responds by adopting policy 𝜑∗−𝑖 . By Lemma A.9,
the labor market outcome is that firm 𝑖 hires 𝑙𝑖 = 𝑊 −1 (𝜑∗−𝑖 ) −𝛬−𝑖 (𝜑∗−𝑖 ) =
𝑟𝑖 (𝛬−𝑖 (𝜑∗−𝑖 ); 0) at wage 𝜑∗−𝑖 , for firm 𝑖 profits of
( )
max 𝑓𝑖 𝑙𝑖 − 𝑙𝑖 𝑊 (𝛬−𝑖 (𝜑∗−𝑖 ) + 𝑙𝑖 ).
(A.15)

∗
𝑙𝑖∗ + 𝑙−𝑖
> 𝑙1𝐵 + 𝑙2𝐵 .

(A.21)

∗
In case
( 𝐵(A),
) this follows immediately from Lemma 1 and 𝛬−𝑖 (𝜑−𝑖 ) >
𝛬−𝑖 𝑊 . In case (B), it follows from Lemma 1 and
(
)
𝜆𝑖 (𝑊̌ −𝑖 ) > 𝜆𝑖 𝑊 ∗∗ = 𝑙𝑖∗∗ ≥ 𝑙𝑖𝐵 ,

𝑙𝑖

On the other hand, if firm 𝑖 adopts 𝜔𝑖 ∈ [𝜑∗−𝑖 , min{𝑊̂ −𝑖 , 𝑊̌ −𝑖 }) then by
Lemma 4, firm −𝑖 responds by adopting 𝜔−𝑖 > 𝜔𝑖 . From Lemma A.10,
it follows straightforwardly that any 𝜔−𝑖 ≥ 𝑊̂ −𝑖 is a strictly worse
response for firm −𝑖 than 𝜔−𝑖 = 𝑊̂ −𝑖 . Hence firm −𝑖’s response satisfies
𝜔−𝑖 ∈ (𝜔𝑖 , 𝑊̂ −𝑖 ], and by Lemma A.9 the labor market outcome is that
( )
(
( ) )
( )
firm 𝑖 hires 𝑙𝑖 = 𝑊 −1 𝜔−𝑖 − 𝛬−𝑖 𝜔−𝑖 = 𝑟𝑖 𝛬−𝑖 𝜔−𝑖 ; 0 at wage 𝜔−𝑖 ,
for firm 𝑖 profits of
( )
(
( )
)
max 𝑓𝑖 𝑙𝑖 − 𝑙𝑖 𝑊 𝛬−𝑖 𝜔−𝑖 + 𝑙𝑖 .
(A.16)

where the final inequality holds strictly for symmetric firms (𝑓𝑖 ≡ 𝑓−𝑖 )
and hence holds for sufficiently similar firms also.
Regardless of whether case (A) or (B) holds, the industry profit conclusion follows from the same argument as in the proof of Proposition 2,
combined with the observation that the conclusion straightforwardly
extends to sufficiently similar firms (regardless of which one is more
productive).
■

𝑙𝑖

( )
( )
Since 𝛬−𝑖 𝜔−𝑖 > 𝛬−𝑖 𝜔𝑖 ≥ 𝛬−𝑖 (𝜑∗−𝑖 ) it follows that profits (A.15)
exceed profits ((A.16)), completing the proof of (A).
Proof of (B): First note that, by Lemma 4, if firm 𝑖 adopts 𝜔𝑖 ≥ 𝑊̌ −𝑖
then firm −𝑖 adopts a non-binding policy. From Lemma A.10, firm 𝑖
( )
hires 𝜆𝑖 𝜔𝑖 at wage 𝜔𝑖 . The resulting profits for firm 𝑖 are strictly
decreasing in 𝜔𝑖 . Hence any policy 𝜔𝑖 > 𝑊̌ −𝑖 is dominated from firm
𝑖’s perspective by 𝜔𝑖 = 𝑊̌ −𝑖 .
Next, we consider the case in which firm 𝑖 adopts 𝜔𝑖 ∈ [𝑊̂ −𝑖 , 𝑊̌ −𝑖 ).
From Lemma 4 , firm −𝑖 responds by adopting 𝜔−𝑖 > 𝜔𝑖 . Moreover,
because 𝜔𝑖 ≥ 𝑊̂ −𝑖 , it follows from the same argument as directly above
that firm −𝑖’s unique best response 𝜔−𝑖 is the smallest value on the grid
that strictly exceeds 𝜔𝑖 . From Lemma A.10, firm 𝑖’s profits are
( (
( )
))
𝑓𝑖 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 𝜔𝑖
(
( )
) (
( )
(
( )
))
−𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 𝜔𝑖 𝑊 𝜆−𝑖 𝜔−𝑖 + 𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 𝜔𝑖 .
(A.17)

A.5. Proofs for Section 5.3
The next auxiliary lemma is used in the proof of Lemma 5. Its proof
is given in Appendix B of the Online Appendix.
(
)
Lemma A.11. If 𝜔𝑖 = 𝜔−𝑖 ∈ 𝑊 𝐵 , 𝑊 ∗∗ then at least one firm can
profitably deviate to some 𝜔 > 𝜔𝑖 = 𝜔−𝑖 .
Proof of Lemma 5. As an initial step we establish:
Claim. If 𝜔𝑖 < 𝑊̂ −𝑖 then firm −𝑖 hires 𝑙−𝑖 ≤ 𝜆−𝑖 (𝑊̂ −𝑖 ), with equality if and
only if 𝜔−𝑖 = 𝑊̂ −𝑖 .
19

Journal of Financial Economics 165 (2025) 103991

P. Bond and D. Levit

(
)
( ) )
(
𝑟𝑖 𝜆−𝑖 𝜔−𝑖 ; 0 < 𝑟𝑖 𝜆−𝑖 (𝑊 ∗∗ ) ; 0 < 𝜆𝑖 (𝑊 ∗∗ ). Hence firm 𝑖 hires 𝑙𝑖 <
( )
(
)
∗∗ and 𝑓 ′ 𝑙∗∗ = 𝑊 𝑙∗∗ + 𝑙∗∗ , it
𝜆𝑖 (𝑊 ∗∗ ) = 𝑙𝑖∗∗ . Combined with 𝑙−𝑖 > 𝑙−𝑖
𝑖
𝑖
𝑖
−𝑖
′
follows that firm 𝑖 𝑠 surplus is strictly higher from adopting 𝜔𝑖 = 𝑊 ∗∗
then any 𝜔𝑖 < 𝑊 ∗∗ .
Finally, if the leader adopts 𝜔𝑖 > 𝑊 ∗∗ then by Lemma A.8 it hires
( )
𝑙𝑖 = 𝜆𝑖 𝜔𝑖 < 𝜆𝑖 (𝑊 ∗∗ ) = 𝑙𝑖∗∗ . By Lemma 5, firm −𝑖 adopts 𝜔−𝑖 < 𝑊 ∗∗ ,
∗∗ .
and as noted in the proof of Lemma 5, hires 𝑙−𝑖 > 𝜆−𝑖 (𝑊 ∗∗ ) = 𝑙−𝑖
It again follows that firm 𝑖′ 𝑠 surplus is strictly higher from adopting
𝜔𝑖 = 𝑊 ∗∗ than any 𝜔𝑖 > 𝑊 ∗∗ .
■

Proof of claim. Immediate if 𝜔−𝑖 ≥ 𝜔𝑖 . Suppose instead that 𝜔−𝑖 < 𝜔𝑖 .
The result is immediate if 𝜔𝑖 ≤ 𝑊 𝐵 . If 𝜔𝑖 ∈ (𝑊 𝐵 , 𝑊̂ 𝑖 ] then 𝑙−𝑖 =
( )
( )
( )
𝑊 −1 𝜔𝑖 − 𝛬𝑖 𝜔𝑖 < 𝛬−𝑖 𝜔𝑖 ≤ 𝛬−𝑖 (𝑊̂ −𝑖 ). If 𝜔𝑖 > 𝑊̂ 𝑖 then 𝑙−𝑖 <
)
(
)
(
𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 < 𝑊 −1 (𝑊̂ −𝑖 ) − 𝜆𝑖 (𝑊̂ −𝑖 ) < 𝜆−𝑖 (𝑊̂ −𝑖 ).
We next consider, sequentially, the cases 𝜔𝑖 < 𝑊̂ −𝑖 , 𝜔𝑖 ∈ [𝑊̂ −𝑖 , 𝑊 ∗∗ ),
𝜔𝑖 ≥ 𝑊 ∗∗ .
Case 1 : 𝜔𝑖 < 𝑊̂ −𝑖 . If firm −𝑖 adopts 𝜔−𝑖 = 𝑊̂ −𝑖 then (Lemma A.9)
the firms hire 𝑙−𝑖 = 𝜆−𝑖 (𝑊̂ −𝑖 ) = 𝛬−𝑖 (𝑊̂ −𝑖 ) and 𝑙𝑖 = 𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 𝜔𝑖 ) =
𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 0). Note that
(
))
( )
(
′
𝑙−𝑖 .
𝑊 𝑙−𝑖 + 𝑟𝑖 𝑙−𝑖 ; 0 = 𝑊̂ −𝑖 = 𝑓−𝑖

Appendix B. Supplementary material

Hence for any 𝑙̃−𝑖 < 𝜆−𝑖 (𝑊̂ −𝑖 ),

Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.jfineco.2024.103991.

𝑆−𝑖 (𝑙̃−𝑖 , 𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 𝜔𝑖 )) < 𝑆−𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ), 𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 𝜔𝑖 )).

Data availability

Since 𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 𝜔𝑖 ) ≤ 𝑟𝑖 (𝑙̃−𝑖 ; 𝜔𝑖 ) and firm −𝑖’s surplus 𝑆−𝑖 is strictly
decreasing in firm 𝑖’s hiring,

Code used in "ESG: A Panacea for Market Power?" (Original data)
(Mendeley Data)

𝑆−𝑖 (𝑙̃−𝑖 , 𝑟𝑖 (𝑙̃−𝑖 ; 𝜔𝑖 )) ≤ 𝑆−𝑖 (𝑙̃−𝑖 , 𝑟𝑖 (𝜆−𝑖 (𝑊̂ −𝑖 ); 𝜔𝑖 )).
So from the claim, firm −𝑖’s strict best response to 𝜔𝑖 < 𝑊̂ −𝑖 is to adopt
𝜔−𝑖 = 𝑊̂ −𝑖 .

References

Case 2: 𝜔𝑖 ∈ [𝑊̂ −𝑖 , 𝑊 ∗∗ ). Suppose that 𝜔−𝑖 < 𝜔𝑖 . If 𝜔𝑖 > 𝑊̂ 𝑖 then
( )
( )
( )
(Lemma A.10) the firms hire 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 and 𝑙−𝑖 < 𝑊 −1 𝜔𝑖 − 𝜆𝑖 𝜔𝑖 <
( )
( )
𝜆−𝑖 𝜔𝑖 . If instead 𝜔𝑖 ≤ 𝑊̂ 𝑖 then (Lemma A.9) the firms hire 𝑙𝑖 = 𝛬𝑖 𝜔𝑖
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Lemma A.11 it then follows that firm −𝑖’s surplus is maximized by some
(
)
𝜔−𝑖 ∈ 𝜔𝑖 , 𝑊 ∗∗ .
( )
Case 3: 𝜔𝑖 ≥ 𝑊 ∗∗ . By Lemma A.8, 𝑙𝑖 = 𝜆𝑖 𝜔𝑖 ≤ 𝜆−𝑖 (𝑊 ∗∗ ). If firm −𝑖
( )
∗∗
adopts 𝜔−𝑖 ≥ 𝑊 then (Lemma A.8 again) 𝑙−𝑖 = 𝜆−𝑖 𝜔−𝑖 ≤ 𝜆−𝑖 (𝑊 ∗∗ ).
Since
(
(
))
( (
)
(
))
′
𝑓−𝑖
𝜆−𝑖 𝑊 ∗∗ = 𝑊 ∗∗ = 𝑊 𝜆𝑖 𝑊 ∗∗ + 𝜆−𝑖 𝑊 ∗∗
( ( )
(
))
(A.22)
≥ 𝑊 𝜆𝑖 𝜔𝑖 + 𝜆−𝑖 𝑊 ∗∗ ,

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it follows that adopting 𝜔−𝑖 = 𝑊 ∗∗ gives firm −𝑖 strictly greater surplus
than any 𝜔−𝑖 > 𝑊 ∗∗ .
Subcase: 𝜔𝑖 = 𝑊 ∗∗ . If firm −𝑖 adopts 𝜔−𝑖 < 𝑊 ∗∗ then
{
( )
(
)
( (
) )}
𝑙−𝑖 ≤ max 𝑊 −1 𝜔−𝑖 − 𝜆𝑖 𝑊 ∗∗ , 𝑟−𝑖 𝜆𝑖 𝑊 ∗∗ ; 0 .
Note that
( )
(
)
(
)
(
)
(
)
𝑊 −1 𝜔−𝑖 − 𝜆𝑖 𝑊 ∗∗ < 𝑊 −1 𝑊 ∗∗ − 𝜆𝑖 𝑊 ∗∗ = 𝜆−𝑖 𝑊 ∗∗
(
)
while certainly 𝑟−𝑖 𝜆𝑖 (𝑊 ∗∗ ) ; 0 < 𝜆−𝑖 (𝑊 ∗∗ ), and so 𝑙−𝑖 < 𝜆−𝑖 (𝑊 ∗∗ ). By
(A.22), it follows that adopting 𝜔−𝑖 = 𝑊 ∗∗ gives firm −𝑖 strictly greater
surplus than any 𝜔−𝑖 < 𝑊 ∗∗ .
( )
Subcase: 𝜔𝑖 > 𝑊 ∗∗ . Note that 𝜆−𝑖 (𝑊 ∗∗ ) < 𝑊 −1 (𝑊 ∗∗ ) − 𝜆−𝑖 𝜔𝑖 .
( )
∗∗
Hence for all 𝜔−𝑖 in an open neighborhood around 𝑊 , 𝜆−𝑖 𝜔−𝑖 <
( )
( )
𝑊 −1 𝜔−𝑖 − 𝜆−𝑖 𝜔𝑖 , implying that if firm −𝑖 adopts 𝜔−𝑖 in a neigh( )
borhood below 𝑊 ∗∗ it hires 𝑙−𝑖 = 𝜆−𝑖 𝜔−𝑖 . So firm −𝑖’s hiring strictly
decreases in 𝜔−𝑖 in the neighborhood below 𝑊 ∗∗ . Since 𝜔𝑖 > 𝑊 ∗∗ , the
inequality in (A.22) holds strictly. Hence firm −𝑖’s surplus is strictly
raised by reducing 𝜔−𝑖 below 𝑊 ∗∗ . Moreover, note for use in the proof
of Proposition 6 that firm −𝑖’s surplus-maximizing choice of 𝜔−𝑖 must
lead to hiring 𝑙𝑖 > 𝜆−𝑖 (𝑊 ∗∗ ).
■
Proof of Proposition 6. If the leader adopts 𝜔𝑖 = 𝑊 ∗∗ then by
Lemma 5 the follower likewise adopts 𝜔−𝑖 = 𝑊 ∗∗ , and the firms hire
∗∗ = 𝜆 (𝑊 ∗∗ ).
𝑙𝑖∗∗ = 𝜆𝑖 (𝑊 ∗∗ ) and 𝑙−𝑖
−𝑖
If the leader adopts 𝜔𝑖 < 𝑊 ∗∗ then by Lemma 5 the follower
adopts 𝜔−𝑖 > 𝜔𝑖 , where from the proof of Lemma 5, 𝜔−𝑖 ∈ [𝑊̂ 𝑖 , 𝑊 ∗∗ ).
( )
By Lemma A.10, firm −𝑖 hires 𝑙−𝑖 = 𝜆−𝑖 𝜔−𝑖 > 𝜆−𝑖 (𝑊 ∗∗ ). Note
(
)
(
)
that 𝑊 −1 𝜔𝑖 − 𝜆−𝑖 𝜔−𝑖 < 𝑊 −1 (𝑊 ∗∗ ) − 𝜆−𝑖 (𝑊 ∗∗ ) = 𝜆𝑖 (𝑊 ∗∗ ) and
20

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21


==> JFE13 - Sustainability vs performance.txt <==
Journal of Financial Economics 155 (2024) 103831

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Sustainability or performance? Ratings and fund managers’ incentives
Nickolay Gantchev , Mariassunta Giannetti *, Rachel Li
Prof Mariassunta Giannetti, Stockholm School of Economics Department of Finance, Sweden

A R T I C L E I N F O

A B S T R A C T

JEL Classification:
G11
G12
G23
G2

We explore how mutual fund managers and investors react when the tradeoff between a fund’s sustainability and
performance becomes salient. Following the introduction of Morningstar’s sustainability ratings (the “globe”
ratings), mutual funds increased their holdings of sustainable stocks to attract flows. Such sustainability-driven
trades, however, underperformed, impairing the funds’ overall performance. Consequently, a tradeoff between
sustainability and performance emerged. In the new equilibrium, the globe ratings do not affect investor flows
and funds no longer trade to improve their globe ratings.

Keywords:
Sustainability
ESG
Mutual funds
Fund flows
Ratings

Demand for sustainable investments has increased dramatically over
the last two decades, and partially due to increased demand, sustainable
investments have been performing well (Pastor et al., 2022). Hence, it is
still a matter of contention whether investors select sustainable in­
vestments because of their nonpecuniary preferences for sustainability
(Riedl and Smeets, 2017) or because they consider sustainability as a
signal of future performance (Amel-Zadeh and Serafeim, 2017). As
Starks (2023) highlights in her presidential address, it is also unclear

how investors trade off sustainability and (financial) performance. Be­
sides being important for understanding investors’ preferences, evi­
dence on how mutual fund investors approach the tradeoff between
sustainability and performance would be useful for evaluating whether
transparency about mutual funds’ portfolios can increase the allocation
of capital to sustainable investments.1
Morningstar’s introduction of the globe ratings, which rank the
sustainability of mutual funds’ portfolios, offers a unique opportunity to

Nikolai Roussanov was the Editor for this article. Send correspondence to Mariassunta Giannetti (mariassunta.giannetti@hhs.se). Gantchev (nickolay.gantchev@
wbs.ac.uk) is with the Warwick Business School at the University of Warwick, CEPR, and ECGI; Giannetti is with the Stockholm School of Economics, CEPR, and
ECGI; Rachel Li (rachelli.research@gmail.com) is with the U.S. Securities and Exchange Commission (SEC). We thank the Editor, an anonymous referee, Darwin Choi,
Diane Del Guercio, Chotibhak (Pab) Jotikasthira, Marcin Kacperczyk, Loriana Pelizzon, Anjana Rajamani, José Scheinkman, Patrick Verwijmeren, and Qifei Zhu for
helpful discussions, and seminar participants at the MIT Financial Policy and Environment Conference, the 11th MSUFCU Conference on Financial Institutions and
Investments, the FMA Consortium on Asset Management at the University of Cambridge, the Center for Economic Policy Research (CEPR) Endless Summer Con­
ference, the Hanken School of Economics/Journal of Corporate Finance Conference on Ownership and Corporate Social and Sustainable Policies, the 2022 Hedge
Fund Research Conference, the China International Conference in Finance, the Asian Bureau of Finance and Economic Research (ABFER) 8th Annual Conference, the
2023 HKU-TLV Finance Forum, American University, Baylor University, City University of Hong Kong, Durham University, ESSEC Business School, Hebrew Uni­
versity, Louisiana State University, Queen Mary University of London, the Securities and Exchange Commission, Stockholm School of Economics, University of
Bristol, University of Cambridge, University of Exeter, University of Kansas, University of Liverpool, University of Oregon, University of Porto, University of Vienna,
and University of Warwick. Giannetti acknowledges financial support from the Swedish House of Finance, the Karl-Adam Bonnier Foundation, the Nasdaq Nordic
Foundation, and the Jan Wallander and Tom Hedelius Foundation. The Securities and Exchange Commission disclaims responsibility for any private publication or
statement of any SEC employee or Commissioner. This article expresses the author’s views and does not necessarily reflect those of the Commission, the Com­
missioners, or members of the staff. This paper was initially released prior to the author joining the Commission.
* Corresponding author.
E-mail address: mariassunta.giannetti@hhs.se (M. Giannetti).
1
With this objective, in 2021, the European Union introduced the Sustainable Finance Disclosure Regulation (SFDR), which pertains to all asset managers,
regardless of whether they have an ESG or sustainability focus. The Securities and Exchange Commission is also ruling about disclosures to be made by investment
funds that market themselves as sustainable (see https://www.ft.com/content/6fefdb2c-f72e-4e52-b95b-c0727aeb1a94).
https://doi.org/10.1016/j.jfineco.2024.103831
Received 21 June 2023; Received in revised form 5 March 2024; Accepted 12 March 2024
Available online 27 March 2024
0304-405X/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

explore these critical issues. Morningstar rates mutual funds along a
variety of dimensions and its ratings have been shown to affect flows
(see, e.g., Del Guercio and Tkac, 2009; Ben-David et al., 2022; Heath
et al., 2023). The sustainability ratings are no exception. In the after­
math of their introduction in March 2016, these easy-to-process and
attention-grabbing signals significantly increased flows to the funds that
received the highest sustainability ratings; in contrast, the funds with
the lowest sustainability ratings experienced outflows (Hartzmark and
Sussman, 2019).2 Yet, these results cannot distinguish whether fund
investors interpreted the globe ratings as a signal of future performance
or whether they followed the ratings because of their preferences for
sustainability.
We show that the aftermath of the globe ratings’ introduction pro­
vides a laboratory to explore this important question. We document that
a tradeoff between a fund’s aspirations to achieve (maintain) a better
globe rating and the fund’s performance emerged because fund man­
agers do not appear to be very skilled at trading the stocks that can
improve their funds’ globe ratings. As a result, sustainability (in terms of
a better globe rating) became associated with bad performance, and the
top globe ratings became unlikely to be perceived as a signal of superior
future returns. In this context, we study whether investors continue to
pursue funds with higher globe ratings and whether fund managers
continue to tilt their portfolios towards high ESG stocks.
Fig. 1 illustrates the main result of our paper. Panel A shows that
globe ratings’ changes stopped affecting flows shortly after their intro­
duction. When we distinguish between upgraded funds with bad and
good performance in Panel B, it becomes evident that outflows from
funds experiencing poor performance drive this finding.
In what follows, we document how the globe ratings affected fund
managers’ incentives and performance, and how this in turn led to
outflows from the funds that succeeded in achieving (maintaining) a
better globe rating. We show that ultimately the globe ratings became
irrelevant, suggesting that investors initially cared about the globe rat­
ings because they erroneously interpreted them as a signal of future
performance.
We start by exploring how the globe ratings affected mutual funds’
trading. Fund managers, whose compensation depends on assets under
management (Geczy et al., 2021; Ibert et al., 2018; Ma et al., 2019),
compete for flows. Their incentives to pursue different objectives
depend on the relative weights that mutual fund investors in the
aggregate put on performance versus sustainability. Naturally,
observing that the globe ratings affected flows upon their introduction,
managers with higher chances to achieve a better globe rating (or to be
downgraded) should have changed their investment strategies to
improve the sustainability rankings of their portfolios. Accordingly, we
show that after the introduction of the globe ratings, mutual funds,
whose current holdings placed them close to the cutoffs for the top and
bottom ratings, increased (decreased) their investments in stocks with
high (low) sustainability scores more than other funds.
However, we show that mutual funds that were striving to achieve
better sustainability ratings experienced poor performance in the high
sustainability stocks they purchased, but not in the remaining portions
of their portfolios. In addition, these funds sold stocks with poor sus­
tainability ratings that ended up performing well, creating profitable
trading opportunities for other market participants. The poor perfor­
mance experienced by funds that traded to a larger extent to increase
their portfolios’ sustainability is not explained by stock characteristics,
such as value, size, or ESG rating, which may have been associated with
negative shocks. Hence, these patterns are unlikely to be related to shifts
in sustainability concerns, stemming from changes in the US adminis­
tration, but rather are due to the fact that fund managers did not follow

their strategies, skills, and information in their attempts to obtain better
globe ratings. In particular, our findings are consistent with the idea that
ESG information is complex and only few funds, even among those
specialized in ESG, are able to incorporate it successfully in their in­
vestment process and generate alpha (Cremers et al., 2023).
Furthermore, we show that the funds that traded most to enhance
their sustainability ratings experienced poor overall performance. As a
result, the globe ratings stopped affecting flows, suggesting that in­
vestors favored performance over sustainability, and funds that were
attempting to achieve better sustainability ratings ended up suffering
net outflows. Unsurprisingly, experiencing costs in terms of performance
and no benefits in terms of sustainability-driven flows, asset managers
stopped tilting their portfolios to achieve better globe ratings.
Taken together, our results suggest that in the long term the globe
ratings became ineffective because of the tradeoff between sustainabil­
ity and performance and are in line with survey evidence that sustain­
ability is viewed by some investors as positively predicting future
performance (Amel-Zadeh and Serafeim, 2017) but are inconsistent with
the idea that investors’ nonpecuniary motives had a significant impact
on flows (Hartzmark and Sussman, 2019). Our findings also indicate that
fund managers, like the econometrician, were initially unable to discern
why the globe ratings were associated with flows. When the globe rat­
ings became irrelevant for flows, fund managers chose to pursue per­
formance, which consistently leads to higher flows. Thus, our empirical
investigation implies that given the preferences of US investors, trans­
parency about asset managers’ portfolios should not be presumed to
increase flows to sustainable investments.
Different metrics to evaluate environmental and social performance
are widely debated, and the globe ratings are no exception. However,
our analysis shows that right after their introduction, the globe ratings
affected fund flows and asset managers’ portfolios, suggesting that
market participants perceived the ratings as a valid sustainability indi­
cator. Nevertheless, within less than a year after the ratings’ introduc­
tion, fund flows stopped responding to globe rating upgrades and
downgrades, despite the continued high interest in the ratings, as evi­
denced by Google Trends searches, and the high frequency of globe
ratings’ upgrades and downgrades. Morningstar’s subsequent changes in
the criteria for assigning the ratings, which should have attracted
considerable investor attention, did not make the ratings more relevant
for flows. Even for funds with an explicit sustainability focus as indi­
cated in their prospectuses, the globe ratings do not affect flows after the
initial period, suggesting that the average investor in these ESG-focused
funds is unlikely to have genuine pro-social preferences.
This paper contributes to a growing literature that explores how
sustainability affects investors’ strategies and performance. Socially
responsible investors are generally believed to put sustainability before
performance (Riedl and Smeets, 2017; Barber et al., 2021; Bauer et al.,
2021). Arguably for this reason, socially responsible mutual funds have
been shown to have a lower flow-performance sensitivity (Bollen, 2007;
Pastor and Vorsatz, 2020). However, there is no consensus on whether
ESG investment is positively or negatively associated with performance,
with a number of studies highlighting that sustainability improves per­
formance and limits downside risk (see, e.g., Edmans, 2011; Lins et al.,
2017; and Albuquerque et al., 2019), and others showing that these
effects are only driven by temporary increases in demand (Pastor et al.,
2022).3 For these reasons, even ESG funds are believed to have con­
flicting objectives (Li et al., 2023). It is, therefore, important to examine
a context in which the tradeoff between sustainability and performance
becomes salient, as we do in this paper. We show that too few US mutual
fund investors value sustainability over performance to generate any

3
Confusion about the effects of ESG factors on financial performance is also
frequently discussed in the press. See “ESG outperformance narrative ‘is
flawed’, new research shows”, Financial Times, May 3, 2021, available at http
s://www.ft.com/content/be140b1b-2249-4dd9-859c-3f8f12ce6036.

2

Ammann, Bauer, Fischer, and Müller (2018) and Ceccarelli, Ramelli, and
Wagner (2024) also show that flows to funds with high sustainability ratings
increase in the aftermath of the ratings’ introduction.
2

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Fig. 1. Globe rating changes, fund flows, and performance
This figure compares the cumulative flows for funds that experienced a globe upgrade or downgrade (Panel A) and funds that were upgraded to globe 2 or globe 5 and
had experienced good (bad) performance over the prior month (Panel B). We classify a fund as having good (bad) performance if the fund’s performance between
t=− 1 and t = 0 belongs to the top (bottom) quartile, compared to other funds during the same month. Fund flows are adjusted by the average fund flows within each
Morningstar category during each month. The 90 % confidence intervals are also reported.

long-term effects of the globe ratings on the allocation of capital.
Another strand of the mutual fund literature studies how investor
flows respond to attention-grabbing and easy-to-process signals, such as
external rankings of the funds’ performance (see, e.g., Del Guercio and
Tkac, 2009; Evans and Sun, 2021; Ben-David et al., 2022; Kim, 2022;

Reuter and Zitzewitz, 2021) or of the sustainability of the funds’ port­
folios (Hartzmark and Sussman, 2019; Ammann et al., 2018). Specif­
ically, we build on the work of Hartzmark and Sussman (2019), who
investigate the effects of the globe ratings on fund flows in a narrow time
frame after the ratings’ introduction, abstracting from general

3

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

equilibrium implications. We explore how asset managers respond to the
ratings and how their response is driven by flows. In addition, while
Hartzmark and Sussman (2019) conclude that both investors’ expecta­
tions about the performance of funds with high sustainability ratings
and nonpecuniary motives could explain the effects of the globe ratings
on flows, our results imply that nonpecuniary motives did not play any
role.
Prior work has shown that fund managers’ pursuit of better star
ratings affects stock demand and prices (Han et al., 2022; Kim, 2022).
We are silent on whether the poor performance that fund managers
experience when attempting to increase the sustainability of their
portfolios arises because their behavior causes demand pressure or
because they do not follow their strategies, skills, and information and
execute poor trades. Regardless of the reasons driving poor perfor­
mance, we highlight the tensions arising when funds are rated along two
different dimensions that may create opposing incentives for fund
managers. We show that in the long run, only ratings on the dimension
that is followed by a larger proportion of investors matter.

The globe ratings exhibit a small positive correlation of 6.8 % with
the star performance ratings, but as Table IA.1 in the Internet Appendix
(IA) shows, star and globe ratings capture different fund characteristics
with most globe five funds having star ratings below five.
Since the ESG scores of the securities typically change annually, the
main determinant of the monthly changes in globe ratings is the fund’s
trading. Table 1 compares the frequency of globe rating upgrades and
downgrades to that of the star ratings. Given that the star ratings depend
on historical performance, it is unsurprising that the frequency of globe
rating upgrades and downgrades is higher than that of the star ratings. A
total of 277 (334) funds were upgraded (downgraded) to the top (bot­
tom) rating in the first 18 months after the introduction of the globe
ratings.
Based on the evidence presented in Table 1, changes in the globe
ratings should have an effect on flows, just as star rating upgrades and
downgrades do (see, e.g., Del Guercio and Tkac, 2009; Evans and Sun,
2021; Ben-David et al., 2022; Kim, 2022; Reuter and Zitzewitz, 2021).
As we show, this does not seem to be the case in the data, even as the
globe ratings continue to be frequently changed and prominently pub­
licized. Our paper provides an explanation for why the globe ratings do
not appear to affect flows in the long term.

1. Morningstar’s sustainability ratings
The objective of Morningstar’s globe ratings is to rank the sustain­
ability of mutual funds’ portfolios and to provide a way for investors to
evaluate how a fund’s investments meet environmental, social, and
governance standards. The globe ratings and their methodology were
publicly announced to mutual fund investors on March 1, 2016, when
the sustainability ratings were first revealed. Since then, funds’ globe
ratings have been prominently displayed on Morningstar’s website,
along with the star ratings, which rank funds within a Morningstar
category based on their performance over the previous three-, five-, and
ten-year periods (if available). The globe ratings were and continue to be
the subject of numerous press releases by Morningstar and are therefore
widely covered by the media.4 The sustained interest attracted by the
globe ratings is evident from the time series of Google Trends searches
for the term “globe rating”, which as shown in Fig. 2, if anything, have
increased in frequency since the ratings were first introduced.
A fund’s globe rating is based on the fund’s portfolio sustainability
score, which is also available to Morningstar users, albeit less promi­
nently displayed than the globe rating. A fund’s portfolio sustainability
score is computed as a weighted average of the ESG scores of the secu­
rities in the fund’s portfolio, with the fund’s portfolio shares as weights.
The ESG scores of the securities are the ESG ratings of the issuers, ob­
tained from Sustainalytics. Morningstar rates only funds that hold at
least 50 % of their portfolios in securities with sustainability ratings.
A fund’s globe rating is the percentile rank of its portfolio sustain­
ability score relative to other mutual funds in the same Morningstar style
category; thus, systematic differences in the ESG scores of the invest­
ment opportunities of funds with different specializations (e.g., growth
vs. value) do not affect the initial version of the globe ratings we analyze
in our main tests.5 Only funds belonging to categories with at least ten
funds are ranked.
Morningstar gives five globes and rates a fund as “High” sustain­
ability if the fund is in the top 10 % of funds in its category. A fund is
given four globes and rated as “Above Average” if it is ranked between
10 % and 32.5 %; it is given three globes and rated “Average” if it is
ranked between 32.5 % and 67.5 %; and it is given two globes and rated
“Below Average” if it is ranked between 67.5 % and 90 %. Finally, a fund
is given one globe and rated “Low” sustainability if it is ranked in the
bottom 10 % of its category.

2. Data and descriptive statistics
We obtain data on mutual funds’ equity holdings from Morningstar
and mutual funds’ characteristics from Morningstar Direct. Our sample
includes all US-domiciled funds, which invest in US equity and end up
having globe ratings. This restriction ensures that we can explore
changes in mutual funds’ portfolios and performance in a relatively
homogeneous sample. Since we focus on funds that invest in US equity,
our sample is somewhat smaller than that in Hartzmark and Sussman
(2019), who include all US-domiciled funds. Importantly, we confirm
that flows increase (decrease) for funds with the top (bottom) globe
rating in the aftermath of the ratings’ introduction (Hartzmark and
Sussman, 2019), indicating that before the tradeoff between sustain­
ability and performance becomes apparent, mutual fund investors care
about sustainability, and the globe ratings in particular.
As is common in the literature (Chevalier and Ellison, 1997), we
include funds that have at least $10 million in assets under management.
We also require funds to have information about their returns, age,
expense ratio, TNA, and Morningstar category. Since in our tests we
compare the effects of the sustainability and performance ratings on
fund flows, we also require that funds have star ratings, which are
assigned only to funds that are at least three years old.
Our main sample period ranges between July 2015 and September
2017 and includes 1959 unique funds. Among these, 1761 are active.
Since most of our tests aim to capture the effects of funds’ strategic
behavior, we focus on active funds, unless noted otherwise.
We are unable to extend the sample before July 2015 because the
availability of funds’ portfolio sustainability scores is limited, prevent­
ing our analysis. However, we perform robustness tests on more recent
periods (up to September 2020), which we introduce later in the paper.
The sample funds belong to the following Morningstar categories: US
Fund Large Blend; US Fund Large Growth; US Fund Large Value; US
Fund Mid-Cap Blend; US Fund Mid-Cap Growth; US Fund Mid-Cap
Value; US Fund Small Blend; US Fund Small Growth; and US Fund
Small Value.
Similar to Albuquerque et al. (2023), we also use fund prospectuses
to identify funds with an explicit sustainability objective. We find 118
funds that mention words associated with social and environmental

4

See, e.g., https://www.morningstar.co.uk/uk/news/227541/morningstarglobes-top-rated-sustainable-funds-in-2022.aspx.
5
This feature of the globe ratings changed in a subsequent revision of the
methodology. We show in Table 11 that this change does not affect our
findings.
4

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Journal of Financial Economics 155 (2024) 103831

Fig. 2. Google Trends searches for “Globe rating”
This figure presents the search volume of the term “Globe rating” from Google Trends between March 2016 and February 2018. The monthly search volume is the
four-week moving average of the weekly measure.

characteristics indicate that the sample is very similar to that of Hartz­
mark and Sussman (2019). Other fund characteristics, such as expenses,
equal to 1.1 % of TNA, are comparable to those in other studies of US
mutual funds specialized in US equity (see, e.g., Han, Roussanov, and
Ruan, 2022). The sample funds are around 18 years old, which is
somewhat older than the average US-domiciled mutual fund investing in
US equity because we restrict the sample to funds that have at least three
years of historical performance by requiring the availability of star
ratings.
Consistent with the globe rating definition, the median fund has a
rating of 3, while the top (bottom) decile is 5 (1). As noted earlier, the
globe ratings change more often than the widely studied star ratings,
which rank funds based on their historical performance.
Panel C of Table 2 also summarizes stock characteristics, which we
obtain from Compustat and CRSP, and the stocks’ effective ESG scores,
which are provided by Sustainalytics. We use this information to eval­
uate the performance of different portions of the mutual funds’ portfo­
lios and to explore how funds trade in stocks with different
characteristics. In most empirical tests, we use monthly fund informa­
tion because all funds report flows and performance at the monthly
frequency, except in the tests exploring funds’ trading in different types
of stocks, where we use quarterly information because approximately 30
% of the funds report their positions only at the quarterly frequency.

Table 1
Morningstar’s star and globe rating upgrades and downgrades
This table shows the frequency of globe and star rating upgrades and down­
grades in the first half of the sample period (from March to December 2016) and
the second half of the sample period (from January to September 2017). Panel A
includes all globe/star rating upgrades and downgrades, whereas Panel B fo­
cuses on upgrades from globe/star 1 to 2 and 4 to 5 and downgrades from globe/
star 5 to 4 and 2 to 1 (i.e., changes from/to the bottom/top ratings).
Globes
Upgrade

Downgrade

Stars
Upgrade

Downgrade

7.19 %
9.42 %

6.29 %
5.88 %

6.56 %
6.25 %

Panel B: change to/from top/bottom rating
2016.3 - 2016.12
2.46 %
2.21 %
2017.1 - 2017.9
3.00 %
2.99 %

1.85 %
1.82 %

2.05 %
1.85 %

Panel A: all rating changes
2016.3 - 2016.12
8.07 %
2017.1 - 2017.9
9.55 %

objectives in their prospectuses and we define these funds as having an
explicit sustainability focus.6 Thus, the vast majority of our sample
consists of managers without a definite ESG focus. Interestingly, as
shown in Fig. 3, most ESG funds have above average globe ratings,
confirming that the globe ratings are informative.
Table 2 summarizes the main variables, distinguishing between the
period before and the period after the introduction of the globe ratings.
Detailed variable definitions are in the Appendix. For each fund, we
aggregate fund size (TNA) and flows across share classes and calculate
the fund’s mean expense ratio and returns. On average, the sample funds
have around $2500 million in assets under management and experience
outflows equivalent to 0.4 % (0.6 %) of their TNA in the quarters pre­
ceding (following) the introduction of the globe ratings. Both

3. The introduction of the sustainability ratings and funds’
demand for high ESG stocks
We explore how the introduction of the sustainability ratings affects
funds’ trading behavior. Fund managers should have incentives to
improve their funds’ globe ratings if they expect better globe ratings to
increase assets under management.
As shown for corporations that attempt to manipulate their credit
ratings by changing their capital structure (Kisgen, 2006), these in­
centives should be particularly strong for funds close to the rating cutoffs
because they are more likely than other funds to achieve a better rating,
or equivalently, to avoid a downgrade. Thus, we expect such mutual
funds, on average, to rebalance their portfolios towards stocks with high
ESG ratings more than other funds.
To evaluate how the globe ratings affect fund managers’ incentives,
we construct a quarterly fund-stock-level panel and investigate the
change in the position of fund f in stock i in quarter t, defined as:

6
We define funds to have an explicit sustainability focus if their prospectuses
include the following words/phrases: ESG, carbon, carbon neutral, clean en­
ergy, clean fuel, climate, climate impact, climate initiative, climate pledge,
climate risk, CO2, conserve environment, CSR, data security, DEI, efficient
energy, electric vehicle, emission, energy efficiency, energy reform, environ­
mental, equality, fossil fuel, GHG, global warm, green, green business, green
economy, green energy, greenhouse gas, less fossil, low carbon, mitigate car­
bon, new energy, Paris Accord, pollution, reduce carbon, reduce fossil,
renewable, social impact, social issue, solar, SRI, stakeholder, sustainability
impact, sustainability need, sustainability outcome, sustainability reference,
sustainability report, wind energy, wind power, woman/women.

5

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Fig. 3. Globe rating distribution for ESG-focused funds and other funds
This figure presents the distribution of globe ratings in the sample of ESG-focused funds and other funds. ESG funds are identified by searching for words associated
with social and environmental objectives in the funds’ prospectuses. Morningstar gives five globes and rates a fund as “High” sustainability if the fund is in the top 10
% of funds in its category. Similarly, Morningstar assigns four globes (“Above Average”) if a fund is ranked between 10 % and 32.5 %; three globes (“Average”) if a
fund is ranked between 32.5 % and 67.5 %; and two globes (“Below Average”) if a fund is ranked between 67.5 % and 90 %. A fund is given one globe and rated
“Low” sustainability if it is ranked in the bottom 10 % of its category.

6

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 2
Summary statistics
This table reports summary statistics of monthly mutual fund characteristics from July 2015 to February 2016 in Panel A (Pre-globes) and from March 2016 (when the
globe ratings were first published) to September 2017 in Panel B (Post-globes) as well as quarterly stock characteristics from July 2015 to September 2017 in Panel C.
The sample includes US-domiciled funds that invest in US equities and have at least $10 million in assets under management. All variables are defined in the Appendix.
Num obs

Mean

Std dev

10th pctl

Median

90th pctl

Panel A: Fund (Monthly) – Pre-globes
Flow (% TNA)
TNA ($ million)
Fund Age (Years)
Expense Ratio (%)
Star Rating
Fund Turnover (% TNA)
Position Change (Fund-Stock-Qtr)

14,636
14,636
14,636
14,636
14,636
14,636
426,240

− 0.004
2219.14
18.155
1.102
3.231
0.644
− 0.004

0.035
5502.92
12.038
0.417
1.016
0.446
0.337

− 0.031
36.484
5.75
0.56
2
0.141
− 0.189

− 0.004
541.924
16.25
1.13
3
0.561
0

0.023
4956.70
29.917
1.567
5
1.243
0.171

Panel B: Fund (Monthly) – Post-globes
Flow (% TNA)
TNA ($ million)
Fund Age (Years)
Expense Ratio (%)
Star Rating
Globe Rating
Fund Turnover (% TNA)
Abnormal ESG Trading
Abnormal ESG Turnover
Position Change (Fund-Stock-Qtr)
Fund return
FF4-Adj return
DGTW-adj return
Buy high ESG return
Sell low ESG return
Buy other return
Sell other return
No-trade high ESG return
No-trade low ESG return

29,556
29,556
29,556
29,556
29,556
29,556
29,267
29,151
29,151
1,427,023
29,556
29,499
27,652
27,652
27,652
27,652
27,652
27,652
27,652

− 0.006
2386.54
18.789
1.077
3.214
2.983
0.648
0.129
0.029
0.001
1.535
− 0.159
0.014
0.007
0.022
0.051
0.003
− 0.043
0.051

0.032
5799.00
12.294
0.416
1.014
1.118
0.445
0.132
0.078
0.274
2.643
1.211
1.068
3.056
2.313
3.061
2.095
1.959
2.144

− 0.03
38.467
5.75
0.543
2
1
0.156
− 0.02
− 0.038
− 0.106
− 1.367
− 1.507
− 1.204
− 3.217
− 2.54
− 3.164
− 2.176
− 2.118
− 2.366

− 0.006
579.495
17
1.106
3
3
0.56
0.119
0.013
0
1.242
− 0.143
− 0.024
0
0
0
0
− 0.041
− 0.018

0.016
5406.51
31
1.52
4
4
1.244
0.303
0.114
0.101
4.938
1.187
1.313
3.265
2.644
3.394
2.286
2.042
2.583

Panel C: Stock (Qtrly) – Pre-/Post-globes
Effective ESG Score
Ln Market Cap
Book to Market
ROA
Ret
Leverage
Sales Growth Rate

16,907
36,349
36,317
35,434
36,198
34,949
35,399

44.647
6.867
0.531
0.012
0.023
0.228
0.035

7.088
1.797
0.423
0.047
0.195
0.219
0.223

37.233
4.314
0.093
− 0.051
− 0.213
0
− 0.161

43.592
6.78
0.449
0.019
0.017
0.177
0.019

54.166
9.294
1.095
0.054
0.265
0.541
0.224

Position Change(f , i, t) =

Price(i, t − 1)*[(NumShares(f , i, t) − NumShares(f , i, t − 1)]
.
TNA(f , t − 1)

We normalize fund f’s change in the holdings of stock i by the fund’s
TNA at the beginning of the quarter and value the position using the
beginning-of-quarter price of stock i (Price(i, t − 1)).7
We consider funds whose portfolio sustainability scores in quarter t-1
are within +/- 2.5 % from the top and bottom globe ratings as those with
the strongest incentives to purchase (sell) stocks with high (low) sus­
tainability scores. We label them Border Funds. This definition of border
funds is not only consistent with theory (Bordalo et al., 2013) and evi­
dence (Hartzmark, 2015) that ranking effects matter most for the best
and the worst performers, but also takes into account that presumably
managers of funds without an explicit sustainability focus care mostly
about (not) being singled out for their very high (very poor) portfolio
sustainability with a top (bottom) rating. In what follows, we test the
plausibility of this assumption.
Mutual fund managers may have become aware of the globe ratings’
planned introduction and methodology after August 2015, when Mor­
ningstar purchased (a large stake in) Sustainalytics, the company whose

firm-level sustainability ratings are used to compute the fund portfolios’
sustainability scores. Therefore, the investment policies of asset man­
agers could have started to change during the second half of 2015, that
is, before the official publication of the ratings.
In Table 3, we explore how funds’ trading of stocks with high sus­
tainability scores changes starting from the third quarter of 2015.8 To
investigate whether funds trade preemptively to improve their portfolio
sustainability scores, we define a pre-globes period from the third
quarter of 2015, when asset managers may have learned about the
impending introduction of the globe ratings, to the first quarter of 2016.
We also subdivide the post-globes period, following the official intro­
duction of the globe ratings, into a first half – from the second quarter to
the fourth quarter of 2016 – and a second half – from the first quarter to
the third quarter of 2017.
Since the globe ratings were not yet available at the end of 2015 and
during the first quarter of 2016, we use funds’ portfolio sustainability

8
Our sample starts in the third quarter of 2015 because the availability of
funds’ sustainability scores is limited before that time, which prevents the
analysis.

7

As we show in Table IA.2, results are invariant if we use the end-of-quarter
stock price to evaluate the change in position.
7

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Journal of Financial Economics 155 (2024) 103831

Table 3
Mutual fund trading and stocks’ ESG scores
Panel A of this table estimates the relation between funds’ position changes ( × 100) and stocks’ Sustainalytics ESG scores. We consider active funds in columns 1–3
and index funds in columns 4–6. We define an indicator Border Funds, which equals one for funds with portfolio sustainability scores within +/− 2.5 % of the globe
rating cutoffs for globe 1 and globe 5, and zero otherwise. The sample period is from the third quarter (Q3) of 2015 to the third quarter (Q3) of 2017, divided into a preglobes period (Q3 2015 – Q1 2016, columns 1 and 4) and a post-globes main period of two equal subperiods – first half (Q2 2016 – Q4 2016, columns 2 and 5) and
second half (Q1 2017 – Q3 2017, columns 3 and 6). Panel B includes only active funds and reports estimates using indicators for High ESG (Low ESG) stocks, defined as
those with ESG scores in the top (bottom) tercile of the Sustainalytics ESG scores. All specifications include lagged firm-level controls, including firm size, book-tomarket ratio, leverage, ROA, sales growth rate, and quarterly stock return, and interactions of fund and year-quarter fixed effects. Standard errors are clustered at
the fund level. Statistical significance at the 10 %, 5 %, and 1 % level is denoted by *, **, and ***, respectively.
Panel A. Border funds’ trading and stocks’ ESG scores
(1)
Active Funds
Pre-globes

(2)

(3)
Position Change (f,i,t)

Post-globes

(4)

(5)

Index Funds
Pre-globes

Post-globes

(6)

Border Fund definition: Within 2.5 %, Globes 1/5

2015Q3–2016Q1

2016Q2–2016Q4

2017Q1–2017Q3

2015Q3–2016Q1

2016Q2–2016Q4

2017Q1–2017Q3

ESG Score

− 0.014*
(− 1.946)
− 0.004
(− 0.123)
299,967
0.147
Yes
Fund*YQ

− 0.005
(− 0.791)
0.049**
(2.003)
441,014
0.183
Yes
Fund*YQ

0.014**
(2.507)
0.016
(0.846)
515,780
0.224
Yes
Fund*YQ

− 0.011
(− 1.245)
0.026
(0.560)
126,246
0.408
Yes
Fund*YQ

− 0.009*
(− 1.735)
0.046
(1.277)
200,791
0.554
Yes
Fund*YQ

− 0.001
(− 0.198)
0.050
(0.965)
269,389
0.610
Yes
Fund*YQ

(4)

(5)

(6)

Pre-globes

Post-globes

2015Q3–2016Q1

2016Q2–2016Q4

2017Q1–2017Q3

− 0.232*
(− 1.665)
− 0.511
(− 0.783)
391,253
0.152
Yes
Fund*YQ

0.102
(0.958)
− 0.936**
(− 2.056)
488,192
0.182
Yes
Fund*YQ

− 0.230**
(− 2.351)
− 0.147
(− 0.459)
570,563
0.223
Yes
Fund*YQ

ESG Score × Border Funds
Observations
Adjusted R-squared
Controls
Fixed effects

Panel B. Indicators for high and low sustainability stocks
(1)
Pre-globes

(3)
Position Change (f,i,t)
Active Funds
Post-globes

Border Fund definition: Within 2.5 %, Globes 1/5

2015Q3–2016Q1

2016Q2–2016Q4

2017Q1–2017Q3

High ESG

− 0.020
(− 0.149)
− 0.938
(− 1.264)

− 0.001
(− 0.012)
1.051**
(2.572)

− 0.026
(− 0.235)
0.513
(1.424)

391,253
0.152
Yes
Fund*YQ

488,192
0.182
Yes
Fund*YQ

570,563
0.223
Yes
Fund*YQ

High ESG × Border Funds
Low ESG

(2)

Low ESG × Border Funds
Observations
Adjusted R-squared
Controls
Fixed effects

scores to compute the cutoffs for the globe ratings that would eventually
be introduced. Throughout the analysis, we control for various stock
characteristics, including market capitalization, stock returns, book-tomarket ratio, etc., which could be correlated with a stock’s ESG score.
We also include interactions of fund and quarter fixed effects, which
capture the propensity of different funds to trade in a given quarter,
including changes in the funds’ assets under management.9
Panel A investigates funds’ purchases of stocks with different Sus­
tainalytics effective ESG scores. Column 1 shows that on average, active
funds are not inclined to purchase stocks with high ESG scores, as
captured by the negative and statistically significant coefficient on ESG
Score. The funds that would eventually become Border Funds because of
their portfolio sustainability scores are no different. Thus, there is no
evidence that border funds tried to preemptively improve the sustain­
ability of their portfolios. This is not entirely surprising: Engaging in a
preemptive attempt to tilt the sustainability of fund portfolios in
expectation of a higher globe rating (or to avoid being downgraded)
requires considerable effort. Since the globes are based on a relative

ranking, fund managers would need up-to-date information for all funds
within the same category (a variable that is itself changing).
While on average fund managers avoided high ESG-rated stocks
before the introduction of the globe ratings, possibly because they
believed that their valuations were too high (Pastor et al., 2022), man­
agers’ incentives changed after March 2016, when they started
observing that the globe ratings actually mattered for flows and they
could use reported percentile rankings and information about their
closest rivals within their category as a predictor of future rankings.
In the aftermath of the globe ratings’ introduction, border funds
engaged in trading to improve their portfolios’ sustainability scores. The
positive coefficient on the interaction term ESG Score × Border Funds in
column 2 indicates that Border Funds rebalanced their portfolios towards
stocks with high ESG scores. In terms of economic magnitudes, a onestandard-deviation increase in a stock’s ESG score is associated with
an increase in border active funds’ positions in the stock of 24.4 % of the
interquartile variation in our sample (calculated as 7.92×0.049/(0.52 (- 1.07)). Notably, this behavior of Border Funds is observed only until
the fourth quarter of 2016. As seen in column 3, the interaction term is
not statistically significant in the second half of the post-globes period,
indicating that these funds had on average the same trading behavior as
other funds.

9

Following the introduction of the globe ratings, border funds experienced
net flows similar to those of other funds. As seen in Table IA.3, there are also no
statistically significant differences in fund size and turnover in the first half of
the post-globes period, but border funds appear to have marginally higher
expense ratios and marginally lower performance ratings.
8

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Journal of Financial Economics 155 (2024) 103831

Since the globe ratings continue to be updated throughout the
sample period, as shown in Table 1, it is unlikely that the lack of port­
folio reallocation in the later part of the sample is due to the fact that
funds had already achieved their desired sustainability ratings. Funds
continue to be upgraded and downgraded, but the aspiration to achieve
a better globe rating does not seem to affect their trading any longer.
This evidence casts doubt on the presence of long-term effects of the
globe ratings on fund managers’ incentives. In the rest of the table, we
scrutinize whether this finding is robust.
In the remaining columns of Panel A, we consider index funds, which
we identify using the Morningstar flag. While active funds can strate­
gically increase their holdings of stocks with high ESG scores, index
funds must passively follow their benchmark indexes. Therefore, we
should not observe that index funds whose portfolio ESG score is in a
neighborhood of the cutoffs for the top and bottom globe ratings attempt
to increase their holdings of stocks with high ESG scores. Consistent with
this conjecture, in columns 4–6, we do not find any evidence that border
index funds increase their holdings of stocks with high ESG scores. On
average, index funds sell stocks with higher ESG ratings during the first
three quarters after the introduction of the globe ratings (column 5).
These findings support our interpretation that in the aftermath of the
globe rating introduction, the trading behavior of active border funds is
driven by strategic considerations.
Panel A considers as Border Funds only the funds within a narrow
+/− 2.5 % neighborhood of the cutoffs for the top and bottom ratings.
These funds should have particularly strong incentives to trade to
improve or maintain their globe ratings because being categorized as
low (high) sustainability is expected to be particularly consequential for
flows. Unable to stand out in terms of their funds’ sustainability, fund
managers whose portfolio sustainability scores are close to the cutoffs
for the intermediate globe ratings are less likely to care about obtaining
a higher or lower globe rating, especially because most sample funds do
not have an explicit sustainability mandate.
To investigate this conjecture, in Table IA.4, we broaden the defi­
nition of border funds. As mentioned above, we continue to focus only
on active funds. In columns 1–3, we define Border Funds as funds within
+/− 2.5 % from the cutoffs of all globe ratings. We expect this broader
definition of border funds to include fund managers with weaker in­
centives to purchase stocks with high ESG scores. As expected, we do not
find evidence that such funds trade to improve their globe ratings.
In columns 4–6 of Table IA.4, we extend the definition of Border
Funds by considering a +/− 5 % neighborhood around the cutoffs for the
bottom and top ratings. As they are not as close to being upgraded/
downgraded, these funds are less likely to be able to improve their
portfolio sustainability scores relative to their peers. Therefore, we
expect this broader definition of border funds to include fund managers
with weaker incentives to purchase stocks with high ESG scores. The
parameter estimates in column 5 are indeed smaller in magnitude,
compared to column 2 of Panel A. Importantly, as in Panel A, it still
appears that the aspiration to improve the fund’s globe rating or to avoid
a downgrade affects border fund behavior only up to three quarters after
the ratings’ introduction. Even though as shown in Table 1, the turnover
in all globe ratings, and the bottom and top globe ratings in particular,
continues to be high, we find no evidence of a differential effect in the
trading of border funds in the last three quarters of the sample.
Since the managers of funds with sustainability scores close to the
bottom and top ratings appear to have stronger incentives to improve
the sustainability of their portfolios, in what follows, we consider as
border funds only the funds whose portfolio sustainability scores are
in a +/− 2.5 % neighborhood of the cutoffs for the bottom and top
ratings.
So far, we have explored how the trading of border funds varies
depending on the stock’s continuous sustainability score. Funds that
attempt to achieve better globe ratings should not only purchase stocks
with high sustainability scores but also sell stocks with low sustain­
ability scores. To distinguish between stock purchases and sales, in Panel

B of Table 3, we replace the continuous Sustainalytics ESG Score with
indicators for High/Low ESG stocks, defined as those with ESG scores in
the top/ bottom tercile of the Sustainalytics ESG scores. As seen in col­
umns 2 and 5, managers of Border Funds purchase relatively more stocks
with high ESG scores and sell more stocks with low ESG scores only in
the first three quarters after the introduction of the globe ratings (up to
the end of 2016). The effect is not only statistically, but also economi­
cally significant. For example, border funds reduce their positions in Low
ESG stocks by 58.9 % of the interquartile variation during the first half of
our sample period (− 0.936/(0.52 - (− 1.07)).
Interestingly, we observe that all active funds exhibit a tendency to
purchase stocks with high ESG scores in the last part of the sample
period (column 3 of Panel A and columns 3 and 6 of Panel B), when
differences between border funds and other funds are no longer statis­
tically significant. This tendency appears to be driven by the propensity
to sell low ESG stocks (column 6 of Panel B). One possibility is that the
sales of border funds may have driven down the returns of these stocks,
and the funds that had purchased low ESG stocks on the cheap subse­
quently sell them after having realized the profits from their positions.
We also explore whether funds with an explicit ESG objective as
disclosed in their prospectuses may have continued to trade to improve
their ESG scores. Urging caution in interpretation due to the fact that we
have a small sample of ESG funds, we show in Table IA.5 that ESG funds
in general, and border ESG funds in particular, trade in a way that is not
statistically different from other funds. In particular, we find no evi­
dence that border ESG funds continued to trade to improve their ESG
scores after the initial period.
Overall, the evidence described in this section shows that the intro­
duction of the globe ratings initially influenced funds’ portfolio alloca­
tions, but also raises the question why funds stopped pursuing better
globe ratings only nine months after the ratings’ publication. Since globe
rating upgrades and downgrades continued to occur during the sample
period, the lack of portfolio reallocation cannot be explained by the fact
that funds had achieved their target rating. For this reason, to under­
stand the tradeoffs managers face, in the next section, we explore the
effects of ESG trading on fund performance.

Fig. 4. Differences in ESG trading across funds
This figure compares the Abnormal ESG Trading (as defined in the Appendix) of
border funds and other funds after the official publication of the globe ratings.
We consider only active mutual funds and separately present the average ESG
trading during March to December 2016, when border funds appear to have
incentives to improve their globe ratings, and from January to September 2017,
when border funds do not appear to trade in a way to improve their globe
ratings. Border funds are funds with portfolio sustainability scores within
+/− 2.5 % of the rating cutoffs for globe 1 and globe 5.
9

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Journal of Financial Economics 155 (2024) 103831

4. Tradeoff between sustainability and performance

0.156, compared to 0.127 for other funds. This difference is statistically
significant, with a t-statistic of 7.30. In the second half, we do not see
statistically different trading between the two groups; moreover, the
abnormal ESG trading of all funds decreases.
We validate our ESG trading proxy using actual globe rating changes.
Table 4 shows that funds that tilt their portfolios towards stocks with
high sustainability ratings are more likely to experience a globe rating
upgrade and less likely to experience a downgrade. All specifications in
Table 4 and the following tables, in which we explore the effects of
Abnormal ESG Trading, control for the funds’ portfolio turnover as well
as the turnover in ESG stocks, alleviating the concern that funds with
abnormally high ESG trading simply trade more stocks with high ESG
scores. Specifically, the variable Abnormal ESG Turnover controls for any
trading in high and low ESG stocks, including sales of high ESG stocks
and purchases of low ESG stocks that would result in a decrease of the
funds’ portfolio ESG scores.
The estimates confirm that our proxy captures the extent to which
funds trade to improve their sustainability ratings. The effect is not only
statistically, but also economically significant: An interquartile change
in Abnormal ESG Trading (0.208 – 0.033 = 0.175) is associated with a

4.1. Abnormal ESG trading
In this subsection, we consider the consequences of the funds’
trading strategies on their portfolios’ composition and ratings. Our ul­
timate goal is to test whether funds that tilted more their portfolios to
improve their ESG scores and achieve a better globe rating (or avoid
being downgraded) experienced worse performance.
We conjecture that funds’ performance suffers if managers deviate
from the funds’ usual trading strategies and do not rely on their infor­
mation and skills to select high ESG stocks to purchase and low ESG
stocks to sell. To evaluate this conjecture, we define a fund to have
Abnormal ESG Trading if it purchased a large amount of stocks with high
sustainability scores and/or sold a large amount of stocks with low
sustainability scores, relative to its overall turnover and in comparison
to the fund’s trading in the period prior to the introduction of the globe
ratings.
Specifically, we construct Abnormal ESG Trading as a fund-month
variable that we relate to the fund’s monthly performance:10

Abnormal ESG Trading(f , t) = ESG Trading(f , t) −
∑gabs

March2016−
∑ 12
1
×
ESG Trading(f , τ)
24 τ=March2016− 36

j=1 (NumShares(f , j, t) −

where ESG Trading(f , t) = ∑nabs

NumShares(f , j, t − 1)) × Price(j, t − 1)

i=1 (NumShares(f , i, t) − NumShares(f , i, t − 1)) × Price(i, t − 1)

,

1.79 % (=0.102×0.175) higher probability of a globe rating upgrade,
which is equivalent to a 20 % increase, compared to the average prob­
ability of a globe rating upgrade of 8.97 %. While this effect may appear
small, it is important to consider that all funds have incentives to trade to
improve their portfolio sustainability scores to be upgraded or avoid
being downgraded. The actual outcome depends on factors that are not
entirely under managerial control, such as stock prices affecting the
portfolio shares and peer funds’ actions. The mechanism resembles that
of career concern models in which managers exert suboptimally high
effort (Holmstrom, 1982), even though this has small effects on their
reputation and compensation because all managers that they are
competing with are also exerting suboptimally high effort.
Overall, these findings validate our interpretation that some funds
tilt their portfolios towards stocks with high ESG scores to improve their
globe ratings in the aftermath of the globe rating introduction. We can
thus explore how pursuing a strategy that aims to improve a fund’s
sustainability rating affects the fund’s performance.

i is any stock held by fund f and
j ∈ {High ESG stocks|NumShares(f , j, t) − NumShares(f , j, t − 1) > 0}
U {Low ESG stocks|NumShares(f , j, t) − NumShares(f , j, t − 1)< 0}
That is, the numerator of ESG Trading(f, t) captures fund f’s pur­
chases of high ESG stocks, valued using the stock price at t-1, plus the
fund’s sales of low ESG stocks, also valued using the stock price at t-1.
High (Low) ESG stocks are defined as stocks in the top (bottom) tercile of
the Sustainalytics effective ESG score. The denominator is the absolute
value of the total trading of the fund (i.e., the change in the number of
shares in any traded stock i, multiplied by the price of stock i at t-1). To
capture deviations from the fund’s usual trading strategy, we subtract
the average ESG trading in the two years prior to the introduction of the
globe ratings, excluding the 12 months closest to the introduction when
the fund’s behavior may have started to change.11
Consistent with the evidence in Table 3, mutual funds’ ESG trading is
larger in the first nine months after the introduction of the globe ratings
(0.139 vs. 0.116, respectively). Importantly, Fig. 4 shows that in the first
three quarters after the introduction of the globe ratings, the average
abnormal ESG trading of border funds (as defined in Table 3, Panel A) is

4.2. ESG trading and fund performance
We test how a fund’s performance depends on its abnormal ESG
trading. We relate the abnormal ESG trading of all (active) funds in our
sample to various measures of performance because any fund may have
incentives to improve or maintain its portfolio sustainability score and
globe rating, even though these incentives are particularly strong for
border funds that are closest to the cutoffs and have a higher probability
of succeeding in being upgraded or not being downgraded. In addition,
not all border funds would have the same incentives, and hence, the
dichotomous variable Border Funds is too noisy to demonstrate the

10
Whenever possible, we use funds’ monthly portfolio holdings, which are
available for roughly two thirds of the funds in our sample. For the remaining
funds, we use quarterly holdings to construct a quarterly ESG trading. In the
regressions that rely on samples with monthly frequency, we input the (quar­
terly) Abnormal ESG Trading for all the months in a quarter. We proceed in the
same way with the construction of Abnormal ESG Turnover. Our results are
qualitatively invariant if we restrict the sample to funds that report monthly
holdings (see Table IA.6 and Table IA.7).
11
In this way, we make sure that we compare a fund’s trading after the
introduction of the globe ratings to that in a period before the globe ratings
were published.

10

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

ratings, that is, when some funds actively tried to achieve better globe
ratings.14 Interestingly, in columns 1 and 2, Abnormal ESG Turnover is
also negatively related to fund performance, indicating that the higher
ESG turnover of mutual funds during the period immediately following
the introduction of the globe ratings was largely driven by the funds’
purchases of high ESG stocks and sales of low ESG stocks. Thus, while
Abnormal ESG Turnover has a larger coefficient (its average and standard
deviation are lower than those of Abnormal ESG Trading) and higher
statistical significance than Abnormal ESG Trading, its sign indicates that
in the first half of the sample it largely captures the same effect as
Abnormal ESG Trading. However, the sign of Abnormal ESG Turnover
changes in the second half of the sample, when funds stopped trading to
improve their globe ratings and funds with ESG expertise could trade
high and low ESG stocks without worrying about their portfolios’ ESG
scores. This suggests that funds that traded stocks with ESG ratings
without specifically attempting to improve the funds’ ESG scores expe­
rienced better performance in the second half of the sample.
Panel B provides more direct evidence on our conjecture that
Abnormal ESG Trading is negatively associated with fund performance
after the introduction of the globe ratings because fund managers had
incentives to improve their portfolio sustainability scores without
following their skills and information when picking stocks. As discussed
before, these incentives should be disproportionately stronger for border
funds that are closer to the cutoffs, and ceteris paribus, have a higher
likelihood of being upgraded or not downgraded. We define the indi­
cator Border Funds as equal to one for the funds with portfolio sustain­
ability scores within +/− 2.5 % from the cutoffs for the top and bottom
ratings.
Consistent with our conjecture, funds with stronger incentives to tilt
their portfolios towards stocks with high ESG scores and to deviate from
their usual trading strategy appear to drive the negative effect of
abnormal ESG trading on performance, as the direct effect of Abnormal
ESG Trading is not statistically significant. However, for border funds, a
one-standard-deviation increase in Abnormal ESG Trading results in a
− 2.37 % annualized return (=0.129×(− 0.35–1.184)×12). Since for
border funds Abnormal ESG Trading better captures the incentives to
deviate from the normal strategy in order to pursue a higher portfolio
sustainability score, this evidence indicates that not following a fund’s
information and skills is indeed costly for its performance.
While the results in Panels A and B are obtained including fund fixed
effects, in Panel C, we explore the robustness of our findings to different
measures of fund performance, which capture the funds’ different ex­
posures to systematic risk factors, include time fixed effects, and test for
statistical differences in the effect of ESG trading in the first and the
second part of the sample after the introduction of the globe ratings.
In column 1, we continue to use a fund’s excess returns as a measure
of performance. In column 2, we compute the fund’s monthly abnormal
return as the weighted average of the monthly abnormal returns of the
fund’s stockholdings at the beginning of the month. To control for the
risk of different stocks, we use the risk-adjustment method proposed by
Daniel et al. (1997), denoted as “DGTW”. Specifically, we subtract the
return of the characteristic-based benchmarks obtained by sorting stocks
according to size quintiles, book-to-market quintiles, and prior return
quintiles from the return of each individual stock. In column 3, we
measure the fund’s abnormal performance by its alpha, estimated from a
Fama and French (1993) three-factor model, augmented by Carhart’s
(1997) momentum factor. In all specifications, we find that funds that
engage in more ESG trading underperform other funds in the first part of

Table 4
Funds’ ESG trading and globe rating upgrades and downgrades
This table studies the relation between the likelihood of an active fund experi­
encing a globe rating upgrade or downgrade and the fund’s Abnormal ESG
Trading (as defined in the Appendix). The sample period is from March 2016 to
September 2017. In column 1 (column 2), the dependent variable is an indicator
equal to one if the fund experiences an upgrade (downgrade) in its globe rating
in month t + 1, and zero otherwise. All specifications include Abnormal ESG
Turnover and lagged fund-level controls as well as interactions of Morningstar
category and year-month fixed effects. Standard errors are clustered at the fund
level. Statistical significance at the 10 %, 5 %, and 1 % level is denoted by *, **,
and ***, respectively.

Abnormal ESG Trading
Abnormal ESG Turnover
Fund Turnover (% TNA)
One Star
Two Stars
Four Stars
Five Stars
One Globe
Two Globes
Four Globes
Five Globes
Ln TNA
Age
Flow
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

(1)
Globe Upgrade

(2)
Globe Downgrade

0.102***
(6.464)
0.090***
(3.178)
− 0.003
(− 0.690)
− 0.004
(− 0.387)
0.004
(0.767)
− 0.004
(− 0.763)
0.010
(1.387)
0.067***
(6.008)
0.052***
(6.547)
− 0.051***
(− 8.450)
− 0.113***
(− 25.314)
− 0.003**
(− 2.007)
0.000
(0.115)
0.062
(0.851)
− 0.000
(− 0.034)
0.155***
(5.044)
24,696
0.062
Cat*YM

− 0.132***
(− 8.642)
0.157***
(5.987)
0.016***
(3.136)
0.008
(0.809)
0.006
(1.053)
− 0.004
(− 0.856)
− 0.003
(− 0.449)
− 0.102***
(− 22.722)
− 0.023***
(− 3.458)
0.051***
(6.799)
0.044***
(4.163)
− 0.003**
(− 2.249)
− 0.004
(− 1.164)
0.101
(1.537)
0.003
(0.369)
0.173***
(5.734)
24,696
0.041
Cat*YM

mechanism we aim to study.12 Thus, we recognize that Abnormal ESG
Trading is more likely to capture that funds, and to a larger extent border
funds, are not following their information and skills when trading to
improve their portfolio ESG scores and provide evidence on how ESG
trading affects fund performance.
Table 5 shows that the funds that attempt to improve their sustain­
ability ratings suffer worse performance. In Panel A, we measure per­
formance using the fund’s portfolio monthly return in excess of the riskfree rate at t + 1 and control for fund characteristics, including the
fund’s past flows and TNA, both computed over the previous month,
which capture any effects of changes in size on performance.13 It appears
that ESG trading, that is, abnormal purchases of high ESG stocks and
sales of low ESG stocks relative to the fund’s usual trading strategy, are
negatively related to the fund’s performance and that this negative effect
emerges only in the first nine months after the introduction of the globe

14
We also do not find that ESG funds with high ESG trading perform better
(Table IA.8). This is consistent with growing evidence that US mutual funds,
even those that declare an ESG objective, engage in greenwashing (see, e.g.,
Kim and Yoon, 2023), and on average, are unable to successfully incorporate
complex ESG information in their investment process to generate alpha
(Cremers, Riley, and Zambrana, 2023).

12

Econometrically, the variable Border Funds is too weak as an instrument for
ESG trading.
13
As shown in Fig. 5, funds with high ESG trading shrink, indicating that these
funds do not underperform because of negative scale effects (Berk and Green,
2004).
11

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 5
Funds’ ESG trading and performance
This table explores the relation between an active fund’s Abnormal ESG Trading and its performance. In Panel A, the dependent variable is the fund’s monthly return in
excess of the risk-free rate at t + 1. In Panel B, we interact the fund’s Abnormal ESG Trading with an indicator variable for Border Funds, which equals one for funds with
portfolio sustainability scores within +/− 2.5 % of the globe rating cutoffs for globe 1 and globe 5, and zero otherwise. In Panels A and B, column 1 reports estimates for
the full sample period (from March 2016 to September 2017), column 2 studies the first half of the sample period (from March to December 2016), and column 3
focuses on the second half (from January to September 2017). In Panel C, the dependent variable is the fund’s monthly return in excess of the risk-free rate at t + 1 in
column 1, the fund’s DGTW risk-adjusted portfolio return (Daniel et al., 1997) at t + 1 in column 2, and the fund’s monthly alpha from a Fama-French-Carhart
four-factor model estimated on a rolling window between month t-60 to t-1 in column 3. The indicator variable First half equals one if the sample period is be­
tween March and December 2016. All specifications include Abnormal ESG Turnover and lagged fund-level controls. Panels A and B include fund fixed effects, whereas
Panel C includes fund and year-month fixed effects. Standard errors are clustered at the fund level. Statistical significance at the 10 %, 5 %, and 1 % level is denoted by
*, **, and ***, respectively.
Panel A. Funds’ ESG trading and excess returns

(1)
Full Sample
2016.3–2017.9

Abnormal ESG Trading
Abnormal ESG Turnover
Globe One
Globe Five
Fund Turnover (% TNA)
Flow
Ln TNA
Age
Constant
Observations
R-squared
Fixed effects
Panel B. ESG trading of Border Funds

Fund Excess Return

− 0.186
(− 1.398)
− 0.649***
(− 2.739)
0.084
(1.066)
− 0.050
(− 0.603)
0.252**
(2.105)
− 0.287
(− 0.412)
− 2.543***
(− 10.504)
− 4.446***
(− 11.672)
64.414***
(13.893)
26,273
0.043
Fund
(1)

Fund Excess Return
Full Sample
2016.3–2017.9
Abnormal ESG Trading
Border funds
Abnormal ESG Trading × Border Funds
Abnormal ESG Turnover
Abnormal ESG Turnover × Border Funds
Globe One
Globe Five
Fund Turnover (% TNA)
Flow
Ln TNA
Age
Constant
Observations
R-squared
Fixed effects
Panel C. Alternative performance measures

Abnormal ESG Trading

− 0.099
(− 0.702)
0.145*
(1.779)
− 0.761**
(− 2.042)
− 0.689***
(− 2.752)
0.370
(0.564)
0.083
(1.063)
− 0.051
(− 0.613)
0.253**
(2.119)
− 0.279
(− 0.400)
− 2.545***
(− 10.526)
− 4.443***
(− 11.682)
64.423***
(13.913)
26,273
0.043
Fund

(2)

(3)

First half
2016.3–2016.12

Second half
2017.1–2017.9

− 0.479*
(− 1.936)
− 2.744***
(− 5.379)
0.104
(0.637)
− 0.116
(− 0.674)
− 0.084
(− 0.224)
5.078***
(3.504)
− 7.926***
(− 8.848)
− 15.973***
(− 12.378)
204.700***
(12.138)
12,628
0.103
Fund

0.151
(0.946)
2.740***
(8.175)
0.168
(1.611)
− 0.077
(− 0.782)
0.473***
(3.234)
− 2.261***
(− 3.119)
− 2.759***
(− 7.304)
0.674
(0.791)
54.149***
(7.565)
13,625
0.162
Fund

(2)

(3)

First half
2016.3–2016.12

Second half
2017.1–2017.9

− 0.351
(− 1.343)
0.413***
(2.600)
− 1.184*
(− 1.756)
− 2.711***
(− 5.090)
− 0.333
(− 0.303)
0.106
(0.652)
− 0.129
(− 0.756)
− 0.071
(− 0.189)
5.092***
(3.516)
− 7.931***
(− 8.840)
− 16.012***
(− 12.376)
204.852***
(12.128)
12,628
0.103
Fund

0.194
(1.149)
− 0.014
(− 0.170)
− 0.356
(− 0.869)
2.645***
(7.748)
0.948
(1.101)
0.172*
(1.653)
− 0.080
(− 0.810)
0.478***
(3.268)
− 2.266***
(− 3.123)
− 2.757***
(− 7.288)
0.684
(0.803)
54.088***
(7.542)
13,625
0.162
Fund

(1)
Fund Excess Return

(2)
DGTW-Adj Return

1.415***

0.170**

(3)
FF4-Alpha
0.268***
(continued on next page)

12

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 5 (continued )
Panel C. Alternative performance measures

Abnormal ESG Trading × First half
Abnormal ESG Turnover
Abnormal ESG Turnover × First half
Globe One
Globe Five
Fund Turnover (% TNA)
Flow
Ln TNA
Age
Expense Ratio
Constant
Observations
R-squared
Fixed effects

(1)
Fund Excess Return

(2)
DGTW-Adj Return

(3)
FF4-Alpha

(10.290)
− 2.015***
(− 10.060)
− 0.640**
(− 2.404)
− 0.999***
(− 2.757)
0.048
(0.955)
− 0.008
(− 0.145)
0.157**
(1.970)
− 1.409***
(− 3.298)
− 1.184***
(− 10.283)
0.708*
(1.816)
− 0.528*
(− 1.879)
23.688***
(9.827)
26,273
0.650
Fund, YM

(2.013)
− 0.373***
(− 3.145)
0.065
(0.386)
0.211
(0.863)
0.051
(1.514)
− 0.039
(− 1.110)
0.003
(0.075)
− 0.255
(− 0.918)
− 0.572***
(− 8.702)
0.550**
(2.169)
− 0.009
(− 0.057)
9.944***
(6.899)
24,924
0.136
Fund, YM

(3.084)
− 0.331**
(− 2.498)
− 0.168
(− 0.930)
0.559**
(2.301)
0.039
(0.997)
− 0.065
(− 1.582)
0.010
(0.182)
− 0.812**
(− 2.553)
− 0.512***
(− 7.737)
0.424
(1.344)
0.095
(0.587)
8.766***
(5.905)
26,216
0.112
Fund, YM

the sample. Specifically, an interquartile change in ESG trading is
associated with a 1.26 % (=(− 2.015 + 1.415)*0.175×12)) lower
annualized excess return, a 0.43 % lower DGTW-adjusted return, and a
0.13 % lower Fama-French four-factor-adjusted return.15
These findings assuage concerns that the negative association be­
tween ESG trading and performance is due to the fact that the stocks
with high (low) ESG ratings differ along other characteristics driving
their performance. The results are also consistent with evidence in
Hartzmark and Sussman (2019) that if anything, globe 5 funds under­
performed globe 1 funds. However, we show that the differences in
performance are associated with the funds’ ESG trading, even if we
control for their bottom and top globe ratings. Thus, our results provide
an explanation for why the underperformance of top-rated funds may
have emerged. Funds that strived to be upgraded (or not to be down­
graded) experienced poor performance in trading stocks with high and
low ESG scores. Put differently, the association between ESG trading and
poor performance during the period in which fund managers appear to
have attempted to achieve a better globe rating suggests that managers
may not have performed much analysis for their ESG-driven trades or
lacked expertise and information to select which high (low) ESG stocks
to trade; instead, they may have just focused on the objective of
obtaining a better globe rating.
It is possible, however, that managers with higher ESG trading have
lower skills and underperform in all trades. Being unable to achieve
superior performance, these managers could instead focus on sustain­
ability. To identify the drivers of the performance of funds with high ESG
trading, we investigate which subsets of stocks in a fund’s portfolio drive
the poor performance we observe in the first half of the sample after the
introduction of the globe ratings. Specifically, if the underperformance
is driven by the manager’s trades aiming to improve the fund’s portfolio
sustainability score, we would expect the underperformance to arise
primarily from trades of stocks with high and low ESG scores, rather

than from stocks without ESG scores.
We thus partition each manager’s portfolio into several subportfolios of stocks; that is, high ESG stocks purchased, low ESG stocks
sold, other stocks purchased, other stocks sold, high ESG stocks with
unchanged positions, and low ESG stocks with unchanged positions. We
decompose a fund’s performance by considering the average abnormal
performance of the stocks in each of these sub-portfolios. To estimate a
stock’s abnormal performance and control for its risk exposure, we
continue to use the risk-adjustment method proposed by Daniel et al.
(1997).
Table 6 indicates that funds that do more ESG trading underperform
because of the stocks with high ESG scores they buy and the stocks with
low ESG scores they sell. In column 1, the dependent variable is the
average abnormal return at t + 1 of the high ESG stocks that fund f
purchased in month t. The negative and statistically significant coeffi­
cient on the interaction between Abnormal ESG Trading and First Half
clearly shows that these high ESG stocks experience lower returns
relative to their benchmarks. Specifically, an interquartile increase in
ESG trading is associated with a 1.00 % lower annualized return from
the high ESG stocks that funds purchase.
Similarly, in column 2, the dependent variable is the average per­
formance of the stocks with low ESG scores that a fund sells. These low
ESG stocks appear to subsequently outperform their benchmarks, as
seen from the positive and statistically significant coefficient on the
interaction between Abnormal ESG Trading and First Half. The effect is
not only statistically significant, but also economically large: An average
level of ESG trading is associated with an annualized loss from the sales
of low ESG stocks of 0.19 %.
Thus, the performance of funds that intentionally attempt to improve
their globe ratings suffers because they sell low ESG stocks that end up
performing well and purchase high ESG stocks that subsequently
perform poorly. As seen in columns 3 and 4, we do not observe similar
patterns for the stocks with average sustainability ratings or without
sustainability ratings that these funds trade. These trades are more likely
to have been driven by the funds’ information and usual trading stra­
tegies because these stocks have limited or no impact on the funds’
portfolio sustainability scores, and consequently, on changes in the
globe ratings. These findings suggest that the funds’ underperformance

15

We do not find any clear patterns for Abnormal ESG Turnover, which is
negative and significant on average as well as during the first half of the sample
in column 1, insignificant in column 2, and positive and significant in column 3.
Table IA.9 shows that our results are invariant if we do not include Abnormal
ESG Turnover as a control.
13

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 6
Funds’ ESG trading and performance in different sub-portfolios of stocks
This table explores the relation between an active fund’s Abnormal ESG Trading and the performance of sub-portfolios of stocks based on the stocks’ ESG ratings. The
dependent variables are the fund’s average DGTW risk-adjusted returns of different sub-portfolios of stocks. The indicator variable First half equals one if the sample
period is between March and December 2016. High ESG (Low ESG) stocks are those with Sustainalytics ESG scores in the top (bottom) tercile; Other stocks are those
with no ESG scores or stocks with ESG scores not in the top or bottom tercile. All specifications include Abnormal ESG Turnover and lagged fund-level controls as well as
fund and year-month fixed effects. Standard errors are clustered at the fund level. Statistical significance at the 10 %, 5 %, and 1 % level is denoted by *, **, and ***,
respectively.

Abnormal ESG Trading
Abnormal ESG Trading × First half
Abnormal ESG Turnover
Abnormal ESG Turnover × First half
Fund Turnover (% TNA)
Flow
Ln TNA
Age
Expense Ratio
Constant
Observations
R-squared
Fixed effects

(1)
Buy High ESG

(2)
Sell Low ESG

(3)
Buy Other

(4)
Sell Other

(5)
No-Trade High ESG

(6)
No-Trade Low ESG

0.557**
(2.356)
− 1.032***
(− 3.215)
− 0.522
(− 1.348)
1.871***
(3.738)
0.207*
(1.674)
− 0.210
(− 0.259)
− 0.587***
(− 3.737)
0.065
(0.089)
1.283**
(2.006)
9.936***
(2.783)
24,924
0.096
Fund, YM

− 0.663***
(− 2.750)
0.753**
(2.476)
0.448
(1.005)
0.374
(0.703)
0.222
(1.585)
0.054
(0.065)
− 0.397***
(− 2.640)
1.954**
(2.340)
0.963*
(1.941)
1.393
(0.366)
24,924
0.077
Fund, YM

0.051
(0.233)
− 0.035
(− 0.132)
0.115
(0.308)
− 0.053
(− 0.109)
− 0.167*
(− 1.793)
− 1.115*
(− 1.906)
− 0.553***
(− 4.809)
0.710
(1.199)
− 0.028
(− 0.083)
9.262***
(3.578)
24,924
0.093
Fund, YM

0.297*
(1.663)
− 0.681***
(− 2.748)
0.308
(0.949)
0.198
(0.509)
− 0.187*
(− 1.846)
− 0.429
(− 0.739)
− 0.428***
(− 4.266)
0.102
(0.165)
0.332
(1.122)
8.021***
(3.094)
24,924
0.092
Fund, YM

0.294**
(2.201)
− 0.277
(− 1.378)
0.019
(0.086)
0.221
(0.793)
0.137
(1.604)
− 0.658
(− 1.234)
− 0.073
(− 0.747)
− 0.526
(− 1.076)
− 0.382*
(− 1.916)
3.196
(1.402)
24,924
0.188
Fund, YM

− 0.359**
(− 2.129)
0.713***
(3.289)
− 0.214
(− 0.656)
0.342
(0.904)
0.042
(0.455)
− 0.491
(− 0.877)
− 0.297***
(− 2.674)
0.947*
(1.713)
0.047
(0.200)
3.307
(1.277)
24,924
0.193
Fund, YM

is directly related to their ESG trades rather than driven by poor
managerial skills.
Another possible concern is that stocks with high and low ESG scores
are affected by unexpected shocks, such as the unanticipated outcome of
the US presidential election in the last quarter of 2016, which could have
driven the poor performance of the funds trading in these stocks. If this
were the case, we would expect to observe that these funds under­
performed also in the portfolio of stocks with high ESG scores that they
held and for which they did not vary their positions during the month. In
column 5, we do not find any evidence that a fund’s ESG trading is
associated with underperformance in the high ESG stocks in which the
fund did not change positions, suggesting that underperformance in the
portfolio of stocks with high ESG scores is due to bad trades.
In column 6, however, we find outperformance in the sub-portfolio
of low ESG stocks that funds with high ESG trading hold, suggesting
that the funds’ performance suffers from excluding low ESG stocks,
which are potentially subject to positive shocks during the sample
period. Importantly, the sub-portfolio of other stocks that high-ESGtrading funds sell underperforms (column 4), indicating that fund
managers exhibit skills in selecting which stocks to sell when they are
not encumbered by ESG considerations.
Overall, this evidence suggests that funds’ underperformance is
driven by their ESG-related trading, that is, by purchasing stocks with
high ESG scores at prices that are too high and selling stocks with low
ESG scores that end up performing well during the period in which we
observe particularly strong incentives for funds to improve their globe
ratings. This may be the case because stocks with high (low) ESG scores
become over- (under)-valued in the first few months after the intro­
duction of the globe ratings due to the demand pressure created by the
mutual funds pursuing better globe ratings. It is equally possible, how­
ever, that the managers of funds striving for better globe ratings did not
use their information and usual investment strategies in their ESGdriven trades and consequently underperformed. In either case, the
ESG-driven trades were bad trades.
In the next section, we show how the funds’ underperformance and

the relative importance of performance and sustainability ratings in
attracting flows can explain why fund managers appear to have stopped
trading to improve their globe ratings.
5. Consequences for fund flows
5.1. Dynamic effects of the globe ratings on flows
In this section, we consider fund flows and study how the apparent
tradeoff between sustainability and performance we describe in Section
4 affected investors’ and fund managers’ incentives. Managers’
compensation depends on the fees they earn, which in turn are driven by
the funds’ net assets under management (Chevalier and Ellison, 1997;
Ibert et al., 2018; Ma et al., 2019). Thus, funds aim to maximize net
flows. If some investors value sustainability over performance in their
fund selection, there might exist an equilibrium in which some funds
pursue better sustainability ratings, while other funds strive for better
performance, even if the funds that achieve the top globe rating
underperform. However, if investors do not trade off sustainability and
performance but consider sustainability as a signal of superior future
performance, sustainability signals that become associated with poor
performance should stop affecting flows.
Table 7 explores to what extent this is the case focusing on active
funds as in the earlier tests.16 As is evident from columns 2 and 5 of
Panels A and B in Table 7, during the first nine months after the globe
ratings’ introduction, funds with the top globe rating experienced higher
inflows, while those with the bottom globe rating suffered outflows.
Such a finding is revealed in Panel A, where we estimate specifications
similar to those in Hartzmark and Sussman (2019), controlling for the
funds’ prior-month categorical star ratings. We confirm these results in

16
In Table IA.10, we show that our results would be invariant if we considered
all funds (including passive funds), as fund investors may not necessarily apply
different selection criteria when they choose among passive funds.

14

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 7
Effects of the globe ratings on fund flows
Panel A reports the effects of the globe ratings on monthly active funds’ flows. Panel B performs a horse race between the star and globe ratings at t-1 to evaluate their
effects on fund flows. Columns 1 and 4 show results for the full sample period (from March 2016 to September 2017), columns 2 and 5 report results for the first half of
the sample (March to December 2016), and columns 3 and 6 report results for the second half (January to September 2017). Columns 1–3 use globe 3 as the baseline,
whereas columns 4–6 use the three middle globe ratings as the baseline. All specifications include lagged controls for the fund’s returns, size, age, and expense ratio as
well as interactions of the fund’s Morningstar category and year-month fixed effects. Standard errors are clustered at the fund level. Statistical significance at the 10 %,
5 %, and 1 % level is denoted by *, **, and ***, respectively.
Panel A. Globe ratings and fund flows
(1)
Flow (%TNA)
Full Sample
2016.3–2017.9
One Globe
Two Globes
Four Globes
Five Globes
Star Rating
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

− 0.000
(− 0.443)
− 0.000
(− 0.135)
0.001
(1.286)
0.003**
(2.430)
0.008***
(16.843)
0.004***
(7.790)
− 0.002***
(− 6.256)
− 0.003***
(− 4.278)
− 0.001
(− 0.503)
0.001
(0.253)
25,108
0.096
Cat*YM

Panel B. Star and globe ratings and fund flows
(1)
Flow (%TNA)
Full Sample
2016.3–2017.9
One Globe
Two Globes
Four Globes
Five Globes
One Star
Two Stars
Four Stars
Five Stars
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

− 0.001
(− 0.694)
− 0.000
(− 0.269)
0.001
(1.227)
0.002**
(1.963)
− 0.010***
(− 6.104)
− 0.006***
(− 6.929)
0.008***
(11.246)
0.022***
(12.186)
0.004***
(8.039)
− 0.002***
(− 6.563)
− 0.002***
(− 3.748)
− 0.001
(− 1.169)
0.025***
(4.732)
25,108
0.101
Cat*YM

(2)

(3)

(4)

(5)

(6)

First half
2016.3–2016.12

Second half
2017.1–2017.9

Full Sample
2016.3–2017.9

First half
2016.3–2016.12

Second half
2017.1–2017.9

− 0.003**
(− 2.119)
− 0.000
(− 0.425)
0.002*
(1.900)
0.004***
(2.649)
0.008***
(14.618)
0.005***
(8.609)
− 0.002***
(− 5.504)
− 0.002**
(− 2.152)
0.001
(0.595)
− 0.004
(− 0.681)
11,212
0.111
Cat*YM

0.002
(1.167)
0.000
(0.146)
0.000
(0.116)
0.002
(1.119)
0.008***
(14.514)
0.003***
(4.375)
− 0.001***
(− 4.950)
− 0.003***
(− 4.764)
− 0.001
(− 1.065)
0.004
(0.732)
13,896
0.085
Cat*YM

− 0.001
(− 0.748)

− 0.003***
(− 2.674)

0.001
(1.206)

0.003**
(2.429)
0.008***
(16.878)
0.003***
(7.752)
− 0.002***
(− 6.273)
− 0.003***
(− 4.222)
− 0.001
(− 0.475)
0.001
(0.285)
25,108
0.096
Cat*YM

0.004**
(2.559)
0.008***
(14.692)
0.005***
(8.555)
− 0.002***
(− 5.597)
− 0.002**
(− 2.019)
0.001
(0.653)
− 0.004
(− 0.627)
11,212
0.111
Cat*YM

0.001
(1.170)
0.008***
(14.513)
0.003***
(4.376)
− 0.001***
(− 4.953)
− 0.003***
(− 4.779)
− 0.001
(− 1.068)
0.004
(0.748)
13,896
0.085
Cat*YM

(2)

(3)

(4)

(5)

(6)

First half
2016.3–2016.12

Second half
2017.1–2017.9

Full Sample
2016.3–2017.9

First half
2016.3–2016.12

Second half
2017.1–2017.9

− 0.003**
(− 2.364)
− 0.000
(− 0.421)
0.002*
(1.711)
0.004**
(2.239)
− 0.009***
(− 4.943)
− 0.007***
(− 6.069)
0.009***
(8.694)
0.024***
(10.722)
0.005***
(8.580)
− 0.002***
(− 5.815)
− 0.001*
(− 1.676)
− 0.000
(− 0.092)
0.021***
(3.290)
11,212
0.118
Cat*YM

0.001
(1.024)
0.000
(0.003)
0.000
(0.172)
0.001
(0.808)
− 0.011***
(− 5.012)
− 0.006***
(− 5.392)
0.008***
(9.431)
0.020***
(10.484)
0.003***
(4.612)
− 0.001***
(− 5.174)
− 0.003***
(− 4.406)
− 0.002
(− 1.544)
0.027***
(4.444)
13,896
0.087
Cat*YM

− 0.001
(− 0.985)

− 0.004***
(− 2.903)

0.001
(1.068)

0.002*
(1.950)
− 0.010***
(− 6.126)
− 0.006***
(− 6.938)
0.008***
(11.262)
0.022***
(12.219)
0.004***
(7.999)
− 0.002***
(− 6.579)
− 0.002***
(− 3.690)
− 0.001
(− 1.141)
0.026***
(4.787)
25,108
0.101
Cat*YM

0.003**
(2.148)
− 0.009***
(− 4.926)
− 0.007***
(− 6.052)
0.009***
(8.728)
0.024***
(10.848)
0.005***
(8.532)
− 0.002***
(− 5.906)
− 0.001
(− 1.552)
− 0.000
(− 0.045)
0.022***
(3.400)
11,212
0.118
Cat*YM

0.001
(0.843)
− 0.011***
(− 5.029)
− 0.006***
(− 5.394)
0.008***
(9.428)
0.020***
(10.490)
0.003***
(4.609)
− 0.001***
(− 5.176)
− 0.003***
(− 4.409)
− 0.002
(− 1.544)
0.027***
(4.462)
13,896
0.088
Cat*YM

Panel B, where we instead include dichotomous variables for each of the
lagged star ratings, using the middle globe/star ratings as the omitted
variables. The estimates are economically significant: For instance, in
column 2 of Panel B, achieving a globe rating of 5 in the first half of the

sample period is associated with a 0.36 % increase in fund flows, which
is equivalent to about 22.4 % of the interquartile variation in flows.
Figure IA.1 further shows that in the aftermath of the ratings’ intro­
duction, the dynamics of flows to globe 1 and globe 5 funds are fully
15

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

consistent with Hartzmark and Sussman (2019).
However, performance is also important for fund flows, and as seen
in Table 5, ESG trading is associated with worse performance. For
example, lower performance attributable to an average amount of ESG
trading is associated with a decrease of about 0.09 % in flows, which
offsets around 25 % of the inflows from achieving a globe 5 status. Given
that many funds attempt to improve their portfolio sustainability scores,
high ESG trading only slightly increases the probability of achieving or
maintaining a top globe rating. Thus, even a small drop in performance
may translate into a net loss. In addition, Border Funds do more ESG
trading than the average fund. Based on Panel A of Table 3, about 10 %
of the funds that are closest to the cutoffs for the top and bottom ratings
have strong incentives to trade to achieve a better globe rating or avoid
being downgraded. According to our estimates in column 2 of Panel B, if
a fund’s ESG trading is in the top decile, the associated poor perfor­
mance could lead to a 0.22 % decrease in flows, offsetting more than
59.7 % of the inflows from achieving a top globe status, which is an
uncertain and very low-probability outcome.
Poor performance can lead to lower flows also through a fund’s star
rating. In this respect, a comparison of the coefficients on the globe and
star ratings is also informative: the star ratings have larger effects on
flows than the corresponding globe ratings even in the first half of the
sample. Thus, poor performance, increasing the likelihood of a star
rating downgrade in the future, can again lead to lower assets under
management because collectively investors appear to care more about
performance. Overall, it appears that even during the first half of the
sample, when the globe ratings affected flows, the tradeoff between
sustainability and performance may have been such that managers that
care about assets under management had incentives to disregard the
sustainability of their portfolios and the globe ratings.
Managerial incentives should have further weakened in the second
half of the sample period because the globe ratings stopped affecting
flows, as seen from the statistically insignificant coefficients on the globe
rating dummies in columns 3 and 6 of Panels A and B. It is unlikely that
the globe ratings lose power in attracting flows just because all investors
that wanted to hold sustainable mutual funds quickly reallocated their
portfolios in the immediate aftermath of the globe ratings’ introduction.
This could be the case if fund investors did not need to switch funds
because the globe ratings are rarely changed once they are assigned.
However, Table 1 shows that the globe ratings continued to exhibit high
turnover throughout our sample period.
The insignificant effect of the globe ratings on flows suggests that
investors put performance ahead of sustainability, and the globe ratings
may initially have affected flows because they were interpreted as a sign
of future performance. This conclusion is confirmed when we consider
different specifications. Table 8 estimates the reaction of flows to globe
rating upgrades and downgrades, controlling for the initial rating. We
find no evidence that investors respond to upgrades and downgrades
from/to the bottom/top globe rating. Only a fund’s performance and its
star rating changes appear to matter.
These findings indicate that flows stop responding to the globe rat­
ings after their initial disclosure, arguably because investors gradually
become aware of the tradeoff with performance, as Panel B of Fig. 1
suggests. In Fig. 5, we relate the globe rating changes and ESG trading to
fund flows. Upgraded funds with low ESG trading, which were less likely
to have underperformed, did not attract flows. Upgraded funds with
high ESG trading, that is, the funds that were more likely to experience
worse performance as a result of their trading of ESG stocks, experienced
outflows. Overall, investors may have started associating globe rating
upgrades with poor future performance (on average) and stopped
considering them as a predictor of superior performance.
Table 9 provides more direct evidence that the initially coveted
upgrade from the bottom rating or to the top rating failed to increase
flows because of the poor performance of the managers that achieved an
upgrade. To test this conjecture, we rank funds’ returns each month into
deciles, and define Poor Performance as an indicator variable that equals

Table 8
Effects of globe rating upgrades and downgrades on fund flows
This table reports the effects of star and globe rating upgrades and downgrades
on monthly active funds’ flows. Panel A considers upgrades/downgrades to/
from all globes, whereas Panel B includes only upgrades/downgrades to/from
the top/bottom globe ratings. Column 1 presents results for the full sample
period (March 2016 to September 2017), column 2 reports results for the first
half of the sample (March to December 2016), and column 3 reports results for
the second half (January to September 2017). All specifications include lagged
controls for the fund’s returns, size, age, and expense ratio as well as interactions
of the fund’s Morningstar category and year-month fixed effects. Standard errors
are clustered at the fund level. Statistical significance at the 10 %, 5 %, and 1 %
level is denoted by *, **, and ***, respectively.
Panel A. Upgrades/downgrades to/from all globes
(1)
(2)
Flow (%TNA)
Full Sample
First half
2016.3–2017.9
2016.3–2016.12
Globe Downgrade
Globe Upgrade
Star Downgrade
Star Upgrade
One Globe
Two Globes
Four Globes
Five Globes
One Star
Two Stars
Four Stars
Five Stars
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

Globe Upgrade to Globe
2/5
Star Downgrade
Star Upgrade
One Globe
Two Globes

Second half
2017.1–2017.9

− 0.001
(− 0.947)
− 0.001
(− 1.259)
− 0.004***
(− 4.622)
0.004***
(5.189)
− 0.001
(− 0.698)
− 0.000
(− 0.233)
0.001
(1.153)
0.002*
(1.886)
− 0.010***
(− 6.450)
− 0.006***
(− 7.245)
0.008***
(11.597)
0.023***
(12.365)
0.004***
(7.971)
− 0.002***
(− 6.789)
− 0.002***
(− 3.680)
− 0.001
(− 1.056)
0.027***
(4.927)

− 0.000
(− 0.311)
− 0.001
(− 0.760)
− 0.004***
(− 3.252)
0.006***
(5.040)
− 0.003**
(− 2.324)
− 0.000
(− 0.400)
0.002
(1.574)
0.004**
(2.209)
− 0.010***
(− 5.341)
− 0.007***
(− 6.413)
0.009***
(9.095)
0.025***
(10.952)
0.005***
(8.579)
− 0.002***
(− 6.053)
− 0.001
(− 1.607)
0.000
(0.043)
0.023***
(3.454)

− 0.001
(− 1.052)
− 0.001
(− 1.032)
− 0.004***
(− 3.540)
0.003**
(2.536)
0.001
(0.981)
0.000
(0.038)
0.000
(0.162)
0.001
(0.737)
− 0.011***
(− 5.202)
− 0.006***
(− 5.572)
0.008***
(9.635)
0.021***
(10.618)
0.003***
(4.561)
− 0.002***
(− 5.327)
− 0.003***
(− 4.372)
− 0.002
(− 1.470)
0.028***
(4.604)

25,108
0.103
Cat*YM

11,212
0.121
Cat*YM

13,896
0.089
Cat*YM

Panel B. Upgrades/downgrades to/from the top/bottom ratings
(1)
(2)
Flow (%TNA)
Full Sample
First half
2016.3–2017.9
2016.3–2016.12
Globe Downgrade to
Globe 1/4

(3)

(3)
Second half
2017.1–2017.9

− 0.001

− 0.000

− 0.002

(− 1.175)
− 0.001

(− 0.221)
− 0.001

(− 1.283)
− 0.001

(− 0.539)
− 0.004***
(− 4.605)
0.004***
(5.185)
− 0.001
(− 0.574)
− 0.000
(− 0.135)

(− 0.395)
− 0.004***
(− 3.254)
0.006***
(5.034)
− 0.003**
(− 2.195)
− 0.000
(− 0.400)

(− 0.438)
− 0.004***
(− 3.507)
0.003**
(2.541)
0.001
(1.061)
0.000
(0.187)
(continued on next page)

16

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

was remarkably poor in the nine months after the introduction of the
globe ratings (column 2). Interestingly, an upgrade from globe 1 to globe
2 does not magnify the negative effect of poor performance (columns
7–9), but we find that this negative effect on flows is larger for funds that
are upgraded to the top rating, as the coefficient on the interaction term
between Poor Performance and Upgrade to Globe 5 is negative and sta­
tistically significant (column 5). The effect is also economically signifi­
cant – an upgraded fund with a record of poor performance experiences
an additional 1.7 % outflows (equivalent to 38.9 % of the standard de­
viation of fund flows). This suggests that some investors in the upgraded
funds redeemed, possibly fearing that a change in strategy towards
sustainability would have resulted in persistently poor performance.
This evidence provides an explanation for why fund managers
stopped trading to improve their portfolio ESG scores. Realizing that
globe rating upgrades and downgrades did not matter for flows, and that
high ESG trading ‘backfired’ because of the negative effects on perfor­
mance, fund managers stopped tilting their portfolios towards stocks
with higher sustainability scores.
Overall, the findings we have presented so far suggest that in the long
term, the globe ratings are unlikely to lead to an increase in financial
flows to sustainable investments. Nevertheless, it could be that a top
globe rating insulates funds from redemptions following weak perfor­
mance (Bollen, 2007). In turn, this could give underperforming asset
managers incentives to invest in sustainable stocks. In Table IA.11 in the
Internet Appendix, we show that a top globe rating does not mitigate the
negative effects of weak performance. The interactions between bottom
and top globe ratings and fund performance are not statistically
significant.17
In sum, the globe ratings appear to leave flows unaffected in the
second half of the sample period. These findings are confirmed in Table
IA.13, where we distinguish between funds’ institutional and retail
share classes. While immediately after the introduction of the globe
ratings, institutional investors allocate capital to funds with the top
globe rating (column 2) and retail investors also redeem capital from
funds with the bottom globe rating (column 5), the sustainability ratings
lose power in explaining the flows for both categories of investors in the
second half of the sample.
The evidence that mutual fund investors pay close attention to per­
formance and the star rating upgrades and downgrades further suggests
that the poor performance of the funds that achieved the highest sus­
tainability rating may have led investors to subsequently ignore the
globe ratings. This effect is likely to have been stronger for institutional
share classes as more sophisticated institutional investors realized that a
top globe rating was not a costless marketing tool, but instead came at
the expense of performance.
It is also possible that some or all investors that value sustainability
over performance are inattentive and do not track changes in the globe
ratings. However, even if mutual fund investors were inattentive to the
globe rating changes, we would still conclude that increased trans­
parency about the sustainability of funds’ portfolios does not provide
long-term incentives for fund managers to tilt their portfolios towards
sustainable investments. Furthermore, the insignificant interaction term
between the globe ratings and fund performance in Table IA.11 does not
support such an interpretation.

Table 8 (continued )
Panel B. Upgrades/downgrades to/from the top/bottom ratings
(1)
(2)
Flow (%TNA)
Full Sample
First half
2016.3–2017.9
2016.3–2016.12
Four Globes
Five Globes
One Star
Two Stars
Four Stars
Five Stars
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

(3)
Second half
2017.1–2017.9

0.001
(1.241)
0.002**
(2.104)
− 0.010***
(− 6.443)
− 0.006***
(− 7.253)
0.008***
(11.603)
0.023***
(12.365)
0.004***
(7.986)
− 0.002***
(− 6.789)
− 0.002***
(− 3.671)
− 0.001
(− 1.055)
0.026***
(4.900)

0.002*
(1.660)
0.004**
(2.276)
− 0.010***
(− 5.337)
− 0.007***
(− 6.420)
0.009***
(9.089)
0.025***
(10.947)
0.005***
(8.597)
− 0.002***
(− 6.038)
− 0.001
(− 1.607)
0.000
(0.038)
0.022***
(3.431)

0.000
(0.214)
0.001
(1.001)
− 0.011***
(− 5.198)
− 0.006***
(− 5.568)
0.008***
(9.655)
0.021***
(10.627)
0.003***
(4.565)
− 0.002***
(− 5.328)
− 0.003***
(− 4.355)
− 0.002
(− 1.468)
0.028***
(4.572)

25,108
0.103
Cat*YM

11,212
0.121
Cat*YM

13,896
0.089
Cat*YM

Fig. 5. Fund flows, ESG trading, and globe upgrades
This figure compares the cumulative flows for active mutual funds that were
upgraded to globe 2 or globe 5 at t = 0. Specifically, we separate active funds
into two groups based on the extent to which they have engaged in Abnormal
ESG Trading (as defined in the Appendix) between t=− 1 and t = 0. We classify a
fund as High (Low) ESG trade if the fund’s Abnormal ESG Trading belongs to the
top (bottom) quartile, compared to other funds within the same Morningstar
category during the same month. Fund flows are adjusted by the average fund
flows within each Morningstar category during each month. The 90 % confi­
dence intervals are also reported.

5.2. Do globe ratings still matter for ESG-focused funds?
We also consider funds that we identity as having an explicit sus­
tainability focus based on their prospectuses as those that are more
likely to have investors that value sustainability. We then test whether
the top and bottom globe ratings continued to be relevant for these ESGfocused funds, which are upgraded and downgraded as frequently as

one if a fund’s monthly return belongs to the bottom decile. We also
introduce an interaction between the dummy for a fund’s poor perfor­
mance and its upgrade from globe 1 or to globe 5, respectively. The
estimates show that even funds that managed to be upgraded, which as
shown in Table 4 was an uncertain event due to competition with other
funds, did not attract flows. While the direct effect of an upgrade is
positive but not statistically significant in the first part of the sample,
upgraded funds lost assets under management when their performance

17
In addition, Table IA.12 shows that globe 5 funds do not attract flows even
if they have a top star rating.

17

N. Gantchev et al.

Table 9
Globe rating upgrades, fund performance, and flows
This table studies the effects of the interaction between negative performance and globe rating upgrades on active funds’ flows. Each month, we rank funds’ returns into deciles and define Poor Performance as an indicator
variable that equals one if a fund’s monthly return belongs to the bottom decile. The dependent variable is a fund’s monthly flow. Columns 1, 4, and 7 show results for the full sample period (March 2016 to September
2017), columns 2, 5, and 8 report results for the first half (March to December 2016), and columns 3, 6, and 9 report results for the second half (January to September 2017). All specifications include lagged controls for the
fund’s categorical star rating, returns, size, age, and expense ratio as well as interactions of the fund’s Morningstar category and year-month fixed effects. Standard errors are clustered at the fund level. Statistical
significance at the 10 %, 5 %, and 1% level is denoted by *, **, and ***, respectively.
(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

First half
2016.3–2016.12

Second half
2017.1–2017.9

Full Sample
2016.3–2017.9

First half
2016.3–2016.12

Second half
2017.1–2017.9

Full Sample
2016.3–2017.9

First half
2016.3–2016.12

Second half
2017.1–2017.9

− 0.004***
(− 5.218)
− 0.000
(− 0.088)
− 0.007**
(− 2.099)

− 0.005***
(− 5.106)
− 0.001
(− 0.737)
− 0.011**
(− 2.210)

− 0.003***
(− 2.684)
0.001
(0.330)
− 0.003
(− 0.714)

− 0.004***
(− 5.307)

− 0.005***
(− 5.208)

− 0.003***
(− 2.712)

− 0.004***
(− 5.463)

− 0.006***
(− 5.456)

− 0.003***
(− 2.787)

− 0.001
(− 0.584)
− 0.014**
(− 2.241)

− 0.003
(− 1.053)
− 0.017*
(− 1.938)

− 0.000
(− 0.087)
− 0.010
(− 1.144)

Upgrade to Globe 2

0.001
(0.419)

0.000
(0.047)

0.001
(0.518)

Poor Performance ×
Upgrade to Globe 2

− 0.002
(− 0.503)

− 0.005
(− 1.150)

0.001
(0.169)

25,108
0.096
Yes
Cat*YM

11,212
0.110
Yes
Cat*YM

13,896
0.084
Yes
Cat*YM

Poor Performance
Upgrade to Globe 2/5

18

Poor Performance ×
Upgrade to Globe 2/5
Upgrade to Globe 5
Poor Performance ×
Upgrade to Globe 5

Observations
Adjusted R-squared
Controls
Fixed effects

25,108
0.096
Yes
Cat*YM

11,212
0.111
Yes
Cat*YM

13,896
0.084
Yes
Cat*YM

25,108
0.096
Yes
Cat*YM

11,212
0.111
Yes
Cat*YM

13,896
0.085
Yes
Cat*YM

Journal of Financial Economics 155 (2024) 103831

(1)
Flow (%TNA)
Full Sample
2016.3–2017.9

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

together with other information about the fund, albeit less prominently
than the fund’s globe rating. It has the advantage to give an absolute
ranking of the sustainability of the fund’s portfolio rather than ranking
the fund relative to the other funds in the same category and may
therefore be preferred by investors with pro-social preferences. In this
case, the sustainability of a fund’s portfolio could attract flows, even if
the globe ratings stop being relevant.
To evaluate this possibility, in Table IA.14, we substitute the fund’s
globe rating with its sustainability score. Consistent with our earlier
findings, the sustainability score appears to be positively related to flows
only in the first half of the sample period, confirming that only the fund’s
performance matters for flows in the long term.

Table 10
Effects of the globe ratings on ESG funds’ flows
This table reports the effects of the globe ratings on monthly active ESG funds’
flows. ESG Funds are defined by searching words associated with social and
environmental objectives in the funds’ prospectuses. Column 1 shows results for
the full sample period (March 2016 to September 2017), column 2 reports re­
sults for the first half of the sample (March to December 2016), and column 3
reports results for the second half (January to September 2017). All columns use
the three middle globe ratings as the baseline. All specifications include lagged
controls for the fund’s returns, size, age, and expense ratio as well as interactions
of the fund’s Morningstar category and year-month fixed effects. Standard errors
are clustered at the fund level. Statistical significance at the 10 %, 5 %, and 1 %
level is denoted by *, **, and ***, respectively.

One Globe
Five Globes
ESG Funds
One Globe × ESG Funds
Five Globes × ESG Funds
One Star
Two Stars
Four Stars
Five Stars
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

(1)
Full Sample
2016.3–2017.9

(2)
First half
2016.3–2016.12

(3)
Second half
2017.1–2017.9

− 0.001
(− 1.018)
0.002*
(1.742)
0.001
(0.440)
0.002
(0.619)
0.001
(0.180)
− 0.010***
(− 6.139)
− 0.006***
(− 6.935)
0.008***
(11.238)
0.022***
(12.188)
0.004***
(7.990)
− 0.002***
(− 6.548)
− 0.002***
(− 3.651)
− 0.001
(− 1.178)
0.025***
(4.746)
25,108
0.101
Cat*YM

− 0.004***
(− 2.909)
0.003*
(1.743)
0.001
(0.409)
0.003
(0.852)
0.004
(0.644)
− 0.009***
(− 4.910)
− 0.007***
(− 6.056)
0.009***
(8.714)
0.024***
(10.870)
0.005***
(8.525)
− 0.002***
(− 5.869)
− 0.001
(− 1.485)
− 0.000
(− 0.079)
0.022***
(3.352)
11,212
0.118
Cat*YM

0.001
(1.022)
0.001
(0.917)
0.001
(0.408)
0.000
(0.020)
− 0.002
(− 0.430)
− 0.011***
(− 5.042)
− 0.006***
(− 5.396)
0.008***
(9.373)
0.020***
(10.463)
0.003***
(4.622)
− 0.001***
(− 5.168)
− 0.003***
(− 4.403)
− 0.002
(− 1.570)
0.027***
(4.449)
13,896
0.087
Cat*YM

5.3.2. New globe rating methodologies and other sustainability metrics
Since the globe ratings’ initial introduction, Morningstar has made
several changes to the methodology to compute them. These modifica­
tions occurred after the sample period on which we have focused so far.
Specifically, in October 2018, Morningstar announced some changes to
the criteria used to assign the globe ratings, which became effective in
November 2018. First, Morningstar started assigning the globe ratings
based on a fund’s historical sustainability score, which also considers the
sustainability of the fund’s portfolio in the past, even though more
recent scores are assigned higher weights. Second, instead of ranking
funds within the Morningstar category, Morningstar started considering
the Morningstar Global category, a coarser classification. In this way,
funds have a larger number of peers.
The methodology was once again changed in November 2019, when
Morningstar started also considering the absolute Historical Portfolio
Sustainability Score of a fund. Funds in categories like energy could score
well within their categories even if their portfolios have poor sustain­
ability. The new methodology does not allow these funds to have a globe
rating above 3. Morningstar also introduced a 1 % buffer around the
rating cutoffs so that a fund must move by at least 1 % above (below) the
threshold to be upgraded (downgraded).
These changes in the methodology for the globe rating computation
may indicate that Morningstar wanted to address some of the problems
arising from funds’ attempts to improve their globe status. Making a
fund’s globe rating less sensitive to the current portfolio holdings,
increasing the number of peers and allowing for a buffer should have
decreased funds’ incentives to manipulate their globe ratings.
However, in columns 1 to 3 of Table 11, we find no evidence that the
arguably improved methodology may have increased the relevance of
the sustainability ratings for fund flows. We also consider whether a
higher historical sustainability score attracts flows. In column 4, we find
that a fund’s Historical Portfolio Sustainability Score is not statistically
significant. These findings mirror our results for the latter part of our
main sample period and confirm that the globe ratings and portfolio
sustainability scores do not contribute much to the allocation of capital
across different funds because investors seem to focus mostly on per­
formance, as captured by the funds’ past returns and star ratings.
Finally, we consider an alternative measure to evaluate whether our
results can be generalized to other sustainability metrics. This is
particularly important because several recent papers have raised con­
cerns about the informativeness of ESG ratings (see, e.g., Freiberg et al.,
2020; Cohen et al., 2023). Thus, investors with pro-social preferences
may have started using other measures of sustainability. Specifically, we
exploit that in April 2018, Morningstar introduced the Low Carbon
Designation, identifying mutual funds that have portfolios aligned with
the transition to a low carbon economy. In column 5, we find no evi­
dence that this new measure affects fund flows, supporting our inter­
pretation that when evaluating the tradeoff between sustainability and
performance, mutual fund managers and their investors over­
whelmingly choose performance.

other funds during the sample period.
Table 10 estimates the specifications in columns 4 to 6 in Panel A of
Table 7 adding an interaction between the top (bottom) globe rating and
an indicator variable for ESG funds. The interaction terms are never
statistically significant, while the top (bottom) globe rating appears to
be associated with positive (negative) flows only during the first part of
the sample.
Interpreting these results with caution due to the fact that our sample
includes only 118 funds with an explicit sustainability focus, we
conclude that investors in ESG funds are similar to investors in other
funds and value performance over sustainability. More specifically, they
may have invested in ESG funds in expectation of superior performance,
that is, for the same reason as investors who initially invested in funds
with the top globe ratings and spurned funds with the bottom globe
ratings.
5.3. Robustness
5.3.1. Sustainability scores vs. globe ratings
The globe ratings may no longer affect flows because investors rely
on other portfolio sustainability metrics. For instance, investors could
consider the funds’ portfolio sustainability scores as opposed to their
globe ratings. The sustainability score is displayed by Morningstar
19

N. Gantchev et al.

Journal of Financial Economics 155 (2024) 103831

Table 11
Morningstar’s modified methodologies and fund flows
This table reports the effects of an active fund’s globe rating and Historical Portfolio Sustainability Score on monthly fund flows after November 2018 (columns 1, 3 and
4) and November 2019 (column 2), when Morningstar implemented two modifications of its globe rating methodology. In columns 1–3, we use globe 3 as the baseline.
In column 4, we replace a fund’s globe rating with its Historical Portfolio Sustainability Score. In column 5, we consider instead the effect of Morningstar’s Low Carbon
Designation after its introduction in April 2018. All specifications include lagged controls for the fund’s returns, size, age, and expense ratio as well as interactions of the
fund’s Morningstar category and year-month fixed effects. Standard errors are clustered at the fund level. Statistical significance at the 10 %, 5 %, and 1 % level is
denoted by *, **, and ***, respectively.

One Globe
Two Globes
Four Globes
Five Globes
Historical Portfolio Sustainability Score
Low Carbon Designation
One Star
Two Star
Four Star
Five Star
Fund return
Ln TNA
Age
Expense Ratio
Constant
Observations
Adjusted R-squared
Fixed effects

(1)
Flow (%TNA)
2018.11–2019.9

(2)

(3)

(4)

(5)

2019.11–2020.9

2018.11–2020.9

2018.11–2020.9

2018.4–2020.9

− 0.002
(− 1.097)
0.001
(0.730)
− 0.001
(− 0.749)
− 0.000
(− 0.144)

0.001
(0.870)
− 0.000
(− 0.080)
− 0.000
(− 0.133)
− 0.001
(− 0.597)

− 0.000
(− 0.332)
0.000
(0.516)
− 0.000
(− 0.520)
− 0.000
(− 0.217)

− 0.003**
(− 2.322)
− 0.004***
(− 3.737)
0.010***
(10.374)
0.021***
(11.456)
0.004***
(6.683)
− 0.001***
(− 3.650)
0.002
(1.626)
− 0.000**
(− 2.363)
− 0.002
(− 0.306)
12,742
0.104
Cat*YM

− 0.004**
(− 2.324)
− 0.001
(− 1.269)
0.009***
(9.643)
0.024***
(12.497)
0.003***
(6.892)
− 0.001***
(− 2.794)
0.001
(1.022)
0.000
(1.024)
− 0.008
(− 1.057)
12,316
0.090
Cat*YM

− 0.004***
(− 2.848)
− 0.003***
(− 3.365)
0.010***
(13.014)
0.023***
(14.561)
0.003***
(8.526)
− 0.001***
(− 3.792)
0.002*
(1.687)
− 0.000
(− 0.720)
− 0.006
(− 0.991)
26,207
0.096
Cat*YM

− 0.000 (− 0.011)
− 0.004***
(− 2.901)
− 0.003***
(− 3.362)
0.010***
(12.828)
0.023***
(14.380)
0.003***
(8.739)
− 0.001***
(− 3.499)
0.002*
(1.718)
− 0.000
(− 0.759)
− 0.007
(− 0.877)
26,371
0.096
Cat*YM

− 0.001 (− 1.317)
− 0.005***
(− 4.170)
− 0.003***
(− 4.011)
0.009***
(13.778)
0.022***
(15.743)
0.003***
(9.968)
− 0.001***
(− 4.313)
0.001
(1.301)
− 0.000
(− 1.441)
− 0.001
(− 0.211)
33,939
0.101
Cat*YM

6. Conclusion

Data availability

Rating financial intermediaries on the basis of the sustainability of
their portfolios may appear to be an effective mechanism that allows
investors to allocate funds in accordance with their environmental and
social preferences. We show that if most investors care to a larger extent
about performance, a tradeoff between portfolio sustainability and
performance arises, which reduces the subsequent effectiveness of the
sustainability ratings.
The behavior of mutual funds and their investors is consistent with
evidence showing that a majority of ESG proposals is not supported by
shareholders, and in particular by mutual funds He et al., (2023), sug­
gesting that ultimately these investors care predominantly about per­
formance. Our findings indicate that increased transparency may be
insufficient, and regulation may be necessary to direct capital to more
sustainable investments.
Finally, our results can inform on the drivers of socially responsible
investing (SRI) growth. The returns of sustainable stocks have been
benefitting from flows into sustainable investments (Pastor et al., 2022).
Hence, flows into SRI funds may not necessarily have been driven by
investor preferences for sustainable investments because investors may
have interpreted sustainability as a signal of superior future perfor­
mance. Our findings suggest that a stop in flows may translate to a large
setback for sustainable funds because sustainable stocks would stop
outperforming in the absence of inflows.

Dataset link: Replication code and pseudo data for "Sustainability or
Performance" available at https://data.mendeley.com/datasets/7pb
jvjsbvb/2.
CRediT authorship contribution statement
Nickolay Gantchev: Writing – review & editing, Writing – original
draft, Visualization, Validation, Supervision, Software, Resources,
Project administration, Methodology, Investigation, Funding acquisi­
tion, Formal analysis, Data curation, Conceptualization. Mariassunta
Giannetti: Writing – review & editing, Writing – original draft, Visu­
alization, Validation, Supervision, Software, Resources, Project admin­
istration, Methodology, Investigation, Funding acquisition, Formal
analysis, Data curation, Conceptualization. Rachel Li: Writing – review
& editing, Writing – original draft, Visualization, Validation, Supervi­
sion, Software, Resources, Project administration, Methodology, Inves­
tigation, Funding acquisition, Formal analysis, Data curation,
Conceptualization.
Declaration of competing interest
Nickolay Gantchev declares that he has no relevant conflicts or
material financial interests that relate to the research described in this
paper.
Mariassunta Giannetti declares that she has no relevant conflicts or
material financial interests that relate to the research described in this
20

Journal of Financial Economics 155 (2024) 103831

N. Gantchev et al.

paper.
Rachel Li declares that she has no relevant conflicts or material

financial interests that relate to the research described in this paper.

Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jfineco.2024.103831.
Appendix: Variable Definition
Variable Name
Panel A: Fund Trading
Effective ESG Score
Abnormal ESG
Trading

Position Change
Fund turnover (%
TNA)
Abnormal ESG
turnover

Definition
The normalized company-level ESG score minus a Sustainalytics controversy deduction. The company-level ESG score is normalized using a z-score
transformation within each company’s peer group. Morningstar’s Portfolio Sustainability Score is based on the weighted average of the stocks’ effective
scores, with the funds’ portfolio shares as weights.
The abnormal ESG trading of fund f in month t is defined as:
∑
1
12
Abnormal ESG Trading(f, t) = ESG Trading(f, t) −
× March16−
τ=March16− 36 ESG Trading(f, τ)
24
∑g
j=1 abs(NumShares(f, j, t) − NumShares(f, j, t − 1)) × Price(j, t − 1)
where ESG Trading(f, t) = ∑n
,
i=1 abs(NumShares(f, i, t) − NumShares(f, i, t − 1)) × Price(i, t − 1)
i is any stock held by fund f and j is
j ∈ {High ESG stocks|NumShares(f, j, t) − NumShares(f, j, t − 1) > 0} U {Low ESG stocks|NumShares(f, j, t) − NumShares(f, j, t − 1) < 0}
The position change in stock i of fund f in quarter t, defined as:
Price(i, t − 1)*[(NumShares(f, i, t) − NumShares(f, i, t − 1)]
Position Change(f, i, t) =
TNA(f, t − 1)
Fund f’s quarterly portfolio turnover, computed as the aggregate absolute value of the position change between quarters t-1 and t across all stock holdings,
computed using the stock price at time t-1, divided by the fund’s TNA at the end of quarter t-1, multiplied by two.
Fund f’s quarterly ESG turnover, computed as the absolute value of the aggregate fund position change between quarters t-1 and t across the fund’s holdings
of High ESG stocks and Low ESG stocks, valued using the stocks’ prices at time t-1, divided by the fund’s TNA at the end of quarter t-1.
∑
1
12
Abnormal ESG Turnover (f, t) = ESG Turnover(f, t) −
× March2016−
τ=March2016− 36 ESG Turnover(f, τ)
24

Panel B: Fund Performance
Fund excess return
Fund f’s monthly net return in excess of the risk-free rate.
DGTW-Adj return
Fund f’s monthly portfolio return, risk-adjusted following the methodology of Daniel et al. (1997). Portfolio weights are based on the value of the fund’s
portfolio holdings at t-1.
FF4-Alpha
Fund f’s monthly alpha, estimated using Fama-French-Carhart four-factor model on a rolling-window between month t-60 to t-1.
Buy High ESG
The average abnormal return of the high ESG stocks (defined as those with Sustainalytics ESG scores in the top tercile) that fund f has purchased in month t,
risk-adjusted following the methodology of Daniel et al. (1997).
Sell Low ESG
The average abnormal return of the low ESG stocks (defined as those with Sustainalytics ESG scores in the bottom tercile) that fund f has sold in month t, riskadjusted following the methodology of Daniel et al. (1997).
Buy Other
The average abnormal return of other stocks (i.e., stocks with no Sustainalytics ESG scores or stocks with Sustainalytics ESG scores not in the top tercile) that
fund f has purchased in month t, risk-adjusted following the methodology of Daniel et al. (1997).
Sell Other
The average abnormal return of other stocks (i.e., stocks with no Sustainalytics ESG scores or stocks with Sustainalytics ESG scores not in the bottom tercile)
that fund f has sold in month t, risk-adjusted following the methodology of Daniel et al. (1997).
No-Trade High ESG
The average abnormal return of the high-ESG stocks (defined as those with Sustainalytics ESG scores in the top tercile) that fund f held in month t and did not
trade in month t, risk-adjusted following the methodology of Daniel et al. (1997).
No-Trade Low ESG
The average abnormal return of the low-ESG stocks (defined as those with Sustainalytics ESG scores in the bottom tercile) that fund f held in month t and did
not trade in month t, risk-adjusted following the methodology of Daniel et al. (1997).
Panel C: Fund Characteristics
TNAj,q − TNAj,q− 1 × (1 + Rj,q )
Flow (% TNA)
A fund’s quarterly flows, defined as Flowsj,q =
.
TNAj,q− 1
Expense Ratio
Ratio of total fees (as a percentage) that shareholders pay for a fund’s operating expenses, including 12b-1 fees.
Ln TNA
Natural logarithm of the fund’s month-end total net assets.
Fund Age
Natural logarithm of the fund’s age, calculated as the number of years since the oldest share class was made available to investors.
Fund Return
Monthly net return of a fund.
Star Rating
Rating based on a fund’s Morningstar Risk-Adjusted Return% Rank for all funds in a given category. Morningstar calculates ratings based on the fund’s
historical performance in the previous three-, five-, and ten-year periods. The fund must have at least 36 continuous months of historical performance in
order to receive a rating. More stars mean better performance. A fund’s peer group for the three-, five-, and ten-year ratings is based on the fund’s current
category without adjusting for category changes. The overall star rating is based on a weighted average (rounded to the nearest integer) of the number of stars
received for the past three-, five-, and 10-year performance.
Globe Rating
A fund’s sustainability rating, based on its portfolio sustainability scores. Funds are ranked within their Morningstar categories. A fund rating is based on its
percentile rank within the fund’s Morningstar category. To receive a globe rating, the fund’s Morningstar category must have at least 10 funds with portfolio
sustainability scores.
Low Carbon
A fund is assigned a Low Carbon Designation by Morningstar if its portfolio holdings have low carbon risk scores and low levels of fossil fuel exposure. The
Designation
designation is an indicator that the companies held in a portfolio are in general alignment with the transition to a low carbon economy.
Panel D: Stock Characteristics
Monthly Abnormal
A firm’s monthly abnormal return calculated using the Fama-French four-factor model, with betas estimated over the previous 36-months, computed using
Return
the quarter-end stock price.
Ln Market Cap
Natural logarithm of a firm’s market capitalization.
Book to Market
Book-to-market ratio, calculated as book value of equity scaled by market value of equity, computed using the quarter-end stock price.
Leverage
Calculated as the sum of long-term debt and debt in current liabilities scaled by total assets.
ROA
Return on assets, calculated as operating income, divided by lagged total assets.
Sales Growth
Net sales at t minus net sales at t-1, divided by net sales at t-1.
Stock Ret
Quarterly stock return.

21

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Journal of Financial Economics 155 (2024) 103831

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==> JFE14 - Dissecting green returns.txt <==
Journal of Financial Economics 146 (2022) 403–424

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Dissecting green returnsR
Ľuboš Pástor a,c,d,e, Robert F. Stambaugh b,c, Lucian A. Taylor b,∗
a

University of Chicago, 5807 S. Woodlawn Ave., Chicago, IL 60637, USA
University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104, USA
NBER, USA
d
CEPR, United Kingdom
e
National Bank of Slovakia, Slovakia
b
c

a r t i c l e

i n f o

Article history:
Received 1 February 2022
Revised 24 July 2022
Accepted 24 July 2022
Available online 12 August 2022
JEL classiﬁcation:
G12
G14

a b s t r a c t
Green assets delivered high returns in recent years. This performance reﬂects unexpectedly strong increases in environmental concerns, not high expected returns. German green
bonds outperformed their higher-yielding non-green twins as the “greenium” widened,
and U.S. green stocks outperformed brown as climate concerns strengthened. Despite that
outperformance, we estimate lower expected returns for green stocks than for brown, consistent with theory. We estimate expected returns in two ways: ex ante, using implied
costs of capital, and ex post, using realized returns purged of shocks from climate concerns and earnings. A theoretically motivated green factor explains much of value stocks’
recent underperformance.

Keywords:
Sustainable investing
ESG
Environment
Climate change
Green bonds

© 2022 Elsevier B.V. All rights reserved.

1. Introduction
R
Dimitris Papanikolaou was the editor for this article. The views in
this paper are the responsibility of the authors, not the institutions they
are aﬃliated with. We are grateful for comments from Alex Edmans,
Stefano Giglio, Mark Hulbert, Ralph Koijen, Stefan Nagel, Dimitris Papanikolaou, Zacharias Sautner, Lee Seltzer, Kent Smetters, David Zerbib,
Lu Zhang; conference participants at the 2022 AFA meetings, 2022 Frankfurt 1st Sustainability Standards Watchers Conference, 2022 Jackson Hole
Finance Conference, 2022 Luxembourg Sustainable Finance Conference,
2022 Mayo Center/ICI Virtual Asset Management Symposium, 2022 NBER
Asset Pricing meeting, 2021 NBER Conference on Measuring and Reporting Corporate Carbon Footprints and Climate Risk Exposure, 2021 Australasian Banking and Finance Conference, 2021 Brazilian Finance Society
Meeting, 2021 KPMG Annual M&A and Economic Forum, 2021 Q Group
Fall Seminar, 2021 QES Global Quant and Macro Investing Conference;
and seminar participants at the Bank of Italy, Erste Bank Asset Management, Jacobs Levy Center webinar, RCEA webinar, U.S. Department of the
Treasury, and the following universities: Chicago, Colorado, CUHK, Drexel,
Georgetown, LBS, Massachusetts at Amherst, McGill, Peking, Pennsylvania,
South Carolina, Southern California, Southern Methodist, Texas at Austin,
Texas at Dallas, Utah, Warwick, Washington, and Zurich. We thank Livia

https://doi.org/10.1016/j.jﬁneco.2022.07.007
0304-405X/© 2022 Elsevier B.V. All rights reserved.

The growth of sustainable investing is a leading trend
in the investment industry over the past decade. Sustainable investing applies environmental, social, and governance (ESG) criteria, with environmental concerns playing the leading role. For example, 88% of the clients of
BlackRock, the world’s largest asset manager, rank environment as “the priority most in focus” among ESG criteria
(BlackRock, 2020). Investments considered environmentally
friendly are often referred to as “green,” with “brown” denoting the opposite.

Amato and Anna-Theresa Helmke for excellent research assistance. This
research was funded in part by the Fama-Miller Center for Research in
Finance at the University of Chicago Booth School of Business.
∗
Corresponding author.

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Investors often cite improved returns as a top motivation for applying ESG criteria.1 Moreover, asset managers
often market sustainable investment products as offering
superior risk-adjusted returns.2 Past performance is a popular marketing tool, and indeed a number of studies report
superior historical returns to sustainable strategies (e.g.,
Edmans, 2011; Nagy et al., 2016; In et al., 2019). Of course,
as the SEC generally requires of all marketed funds, managers must warn that past performance does not necessarily predict future performance. In this study we show why
investors would be especially well advised to heed that
warning when investing in green assets.
What does the past performance of green assets imply about their future performance? We address this
question empirically, guided by the equilibrium model of
Pástor et al. (2021, henceforth PST). The PST model predicts
that green assets have lower expected returns than brown,
for two reasons: investors have green tastes, and greener
assets are a better hedge against climate risk. Greener assets’ lower expected returns thus reﬂect both a taste premium and a risk premium. PST also explain, however, that
green assets can have higher realized returns while agents’
demands shift unexpectedly in the green direction. This
wedge between expected and realized returns is central
to our paper. PST identify two ways green demands can
shift. First, investors’ demand for green assets can increase,
directly driving up green asset prices. Second, consumers’
demand for green products can strengthen—for example,
due to environmental regulations—driving up green ﬁrms’
proﬁts and thus their stock prices. Similarly, investors’ demand for brown assets or consumers’ demand for brown
products can decrease, again making green stocks outperform.
Our analysis focuses primarily on the U.S. stock market.
Using environmental ratings from MSCI, a leading provider
of ESG ratings, we assign greenness measures to individual
stocks. Our sample begins in November 2012, when MSCI’s
data coverage increased sharply, and ends in December
2020. Over this period, the value-weighted portfolio of
stocks in the top third of greenness outperformed the bottom third by a cumulative return difference of 174%. This
return spread, which we denote as GMB (green-minusbrown), has a monthly Sharpe ratio of 0.33, larger than the
stock market’s Sharpe ratio during this bull-market period.
In short, green stocks strongly outperformed brown in recent years.
Should green stocks’ recent outperformance lead one
to expect high green returns going forward? No, we argue. That outperformance likely reﬂects an unanticipated
increase in environmental concerns. We reach this conclusion after computing a measure of concerns about

climate change, using the media index constructed by
Ardia et al. (2021). We observe a strong increase in climate
concerns during the last decade, with the level of our measure nearly doubling. We ﬁnd that shocks to climate concerns exhibit a signiﬁcant positive relation to GMB. Green
stocks thus tend to outperform brown when there is bad
news about climate change, consistent with green stocks
being better hedges against climate shocks.
We compute an ex post estimate of GMB’s expected return by purging unanticipated shocks from its average realized return. If we set the climate shocks to zero, GMB’s
counterfactual performance becomes essentially ﬂat. That
is, green stocks would not have outperformed brown without strengthened climate concerns. In fact, they would
have underperformed had there been no surprises to either
climate concerns or earnings of green versus brown ﬁrms.
If we zero out both climate and earnings shocks, GMB’s
counterfactual performance becomes slightly negative, indicating a negative expected return for GMB.
Our empirical explanation of green stocks’ outperformance accords with the PST model. During a period
when climate concerns strengthen suﬃciently and unexpectedly, GMB delivers a positive return, as investors demand greener stocks or customers demand greener products. Outperformance caused by the strengthening of investor concerns is followed by lower expected performance
of GMB going forward. That is, a shift in GMB’s expected
future performance relates inversely to its realized performance.
An inverse relation between realized returns and shifts
in expected returns is not new in the stock return literature.3 With stocks, a challenge to documenting this relation is that expected stock returns are generally hard to estimate. With bonds, however, we can see the relation more
clearly. The inverse relation between a bond’s realized return and the change in its yield to maturity is well understood, and the yield provides direct information about
expected return, especially for buy-and-hold investors.
The case of German “twin” bonds illustrates this inverse
relation in the context of climate concerns. Since 2020, the
German government has issued green bonds, along with
virtually identical non-green twins. The green bonds trade
at lower yields, indicating lower expected returns compared to non-green bonds. The yield spread between the
green and non-green twins, known as the “greenium,” reﬂects investors’ willingness to accept a lower return in exchange for holding assets more aligned with their environmental values. Since issuance, the 10-year greenium experienced almost a four-fold widening, possibly due to growing climate concerns. As a result, the green bond outperformed its non-green twin by a signiﬁcant margin over the
same period. However, this outperformance does not imply
green outperformance going forward. Rather the opposite
is clearly true, given the now wider greenium.
We deﬁne an equity analogue to the greenium, the “equity greenium,” as the difference between the expected returns of green and brown stocks, i.e., GMB’s expected re-

1
Improved returns is the ﬁrst- or second-ranked motivation for ESG investing in surveys of investors by BlackRock (2020), BNP Paribas (2019),
and Schroders (2020). In addition, in the BNP Paribas survey, 60% of respondents expect their ESG portfolios to outperform over the next ﬁve
years.
2
For example, BlackRock believes that “integrating sustainability can
help investors build more resilient portfolios and achieve better longterm, risk-adjusted returns” (Fink, 2021). According to State Street, “ESG is
a source of alpha that leads to positive portfolio performance” (Lester and
He, 2018).

3
For example, this inverse relation ﬁgures prominently in empirical
analyses of the equity premium by Fama and French (2002) and Pástor
and Stambaugh (2001, 2009).

404

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

turn. Given the diﬃculty in estimating expected stock returns, the equity greenium cannot be measured as precisely as the greenium for bonds. Complementing our ex
post approach, we estimate the equity greenium ex ante
by the difference between the implied costs of capital
of green and brown stocks. We ﬁnd a consistently negative equity greenium throughout our sample. This evidence
lends further support to our argument that the outperformance of green stocks in our sample period was unexpected. The equity greenium widens in the second half
of our sample, consistent with strengthening investor demands for green assets.
Our main results relating climate shocks to stock returns rely on the time series of GMB. We also conduct a
parallel analysis by running panel regressions on individual
stocks, leading to several ﬁndings. First, there is a positive
cross-sectional relation between a stock’s greenness and
its return. Second, that relation disappears when we interact greenness with climate-concern shocks, revealing that
these shocks fully account for the superior performance
of green stocks during the sample period. In fact, the relation becomes slightly negative when we add earnings
shocks as controls. These results echo our time-series evidence: despite having lower expected returns, green stocks
outperform brown due to positive surprises over the sample period. Finally, industry-level greenness, as opposed to
within-industry differences in greenness, largely accounts
for the superior performance of green stocks as well as
the importance of climate shocks in explaining that performance.
We ﬁnd that small stocks react to climate news with a
delay. In panel regressions of individual stock returns on
greenness interacted with climate shocks, previous-month
shocks enter more strongly than current-month shocks,
indicating a delayed reaction for some stocks. There is
no signiﬁcant delay in the response of GMB, whose long
and short legs are value-weighted, to climate shocks. But
when we replicate GMB’s construction separately within
the large- and small-cap segments, we ﬁnd that small-cap
GMB responds mostly to previous-month climate shocks,
whereas large-cap GMB responds mostly to same-month
shocks. At a weekly frequency, large-cap GMB reacts more
strongly than small-cap GMB to climate shocks in the
current and previous week, whereas small-cap GMB reacts more strongly to shocks at longer lags, especially the
three-week lag. This evidence suggests that smaller stocks
react more slowly to climate news, consistent with prior
evidence that small stocks react more slowly to news in
general (Lo and MacKinlay, 1990). Our evidence of a delay complements that of Hong et al. (2019). They also ﬁnd
that stock prices are slow to react to climate-change risks,
but they look at different assets (stocks in food industries
across countries) and different climate shocks (trends in
the risks of drought).
Green stocks’ recent outperformance helps us understand the poor performance of value stocks in the 2010s,
the worst decade on record for the HML factor of Fama and
French (1993). We leverage PST’s theoretical result that assets are priced by a two-factor model, where the factors
are the market portfolio and the ESG factor. Focusing on
the “E” part of ESG, we construct a “green factor” by fol-

lowing PST’s procedure. The green factor is the return on
a portfolio that goes long green and short brown stocks,
where the stocks are weighted by their greenness. We ﬁnd
that the two-factor model explains much of HML’s recent
underperformance. From November 2012 through December 2020, HML’s monthly CAPM alpha is a marginally signiﬁcant −71 bps, whereas HML’s two-factor alpha is an insigniﬁcant −15 bps. In contrast, the green factor’s alpha
with respect to the Fama-French three-factor model is a
signiﬁcant 38 bps. The green factor and HML are negatively
correlated, as value stocks are more often brown than
green. Insofar as recent average performance, however, the
two-factor model explains HML’s underperformance better than the three-factor model explains the green factor’s
outperformance. The two-factor model can also explain
the momentum strategy’s positive performance over the
same period: momentum’s monthly CAPM alpha is 66 bps,
whereas its two-factor alpha is −6 bps.
Our study relates to a large empirical literature
investigating returns on green versus brown assets.
One set of studies examine returns on an ex ante
basis, using proxies for expected future returns. In
the bond market, for example, Baker et al. (2018),
Zerbib (2019), and Larcker and Watts (2020) analyze
yields on green bonds versus brown. In the stock market, Chava (2014) and El Ghoul et al. (2011) compare
implied costs of capital estimated for green ﬁrms versus brown. Most of these studies ﬁnd lower ex ante returns on green assets, consistent with theory. A second,
larger set of studies examine returns on an ex post basis, measuring realized green-versus-brown returns, generally for stocks. Examples include Garvey et al. (2018),
In et al. (2019), Bolton and Kacperczyk (2021), Bolton and
Kacperczyk (2022), Görgen et al. (2020), Hsu et al. (2022),
and Aswani et al. (2021). We examine returns both ex ante
and ex post, focusing on the distinction between expected
and realized returns, in the spirit of Elton (1999). We show
why high green returns realized in recent years are likely
to be misleading predictors of the future.
Our evidence on how climate shocks affect realized
returns also relates to studies investigating the pricing of climate risk. Recent work examines that pricing
in equities (e.g., Bolton and Kacperczyk, 2021; Bolton
and Kacperczyk, 2022; Hsu et al., 2022; Faccini et al.,
2021), corporate bonds (Huynh and Xia, 2021; Seltzer
et al., 2021), municipal bonds (Painter, 2020; Pinkham
et al., 2021), options (Ilhan et al., 2021), and real estate (Bernstein et al., 2019; Baldauf et al., 2020; Giglio
et al., 2021b). Engle et al. (2020) develop a procedure to
dynamically hedge climate risk with the help of mimicking portfolios and textual analysis of news sources.
Krueger et al. (2020) document the importance of climate
risk in a survey of institutional investors. For a survey of
the climate ﬁnance literature, see Giglio et al. (2021a).
Our empirical analysis is guided by the theoretical model of PST, in which investors’ tastes for
green assets play a key role. Other models featuring tastes for green assets can be found in Fama and
French (2007), Baker et al. (2018), Pedersen et al. (2021),
Avramov et al. (2022), and Zerbib (2022). PST’s model
assumes that markets are eﬃcient, so that if green ﬁrms
405

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424
Table 1
German government bond yields and returns.
Panel A reports the yields to maturity of the 10-year German
government green bond (column 1), 10-year German government
conventional bond (column 2), and their difference (column 3),
all in basis points per year. Average yields are computed over the
full sample period of September 8, 2020 to November 17, 2021.
The yields on the ﬁrst and last days of this period are also reported. Panel B reports the realized returns on the same green
bond (column 1), same conventional bond (column 2), and their
difference (column 3). Average returns are in basis points per day.
Cumulative returns are in percent over the full sample period.
The t-statistics, which are shown in parentheses, are adjusted for
any statistically signiﬁcant autocorrelation in the underlying series.

are expected to be more proﬁtable than brown in the future, this difference is reﬂected in current prices. Pedersen
et al. show that if some investors anticipate this greater
proﬁtability before market prices respond, those investors
expect higher returns on green assets. While our analysis
is motivated primarily by PST’s eﬃcient-market perspective, we do ﬁnd some evidence of slow price response, as
noted earlier.
Our results have important implications for research
and practice. They underline the danger in using recent average returns to estimate expected returns. In particular,
the recent outperformance of green assets does not imply
high green returns going forward. In fact, if the outperformance resulted from increased demands by ESG investors,
then green assets’ expected returns are lower today than a
decade ago. In the same spirit, value stocks’ recent underperformance is less likely to continue, because value stocks
tend to be brown and growth stocks green. From the corporate ﬁnance perspective, our ﬁndings imply that greener
ﬁrms have lower costs of capital than their recent stock
performance might suggest. This is good news for ESG investors, because one way they exert social impact is by
decreasing green ﬁrms’ cost of capital (e.g., Heinkel et al.,
2001; PST).
This paper is organized as follows. Section 2 highlights
the gap between expected and realized returns in the
context of German twin bonds. Section 3 describes how
we measure greenness for U.S. stocks. Section 4 compares
the realized performance of green versus brown stocks.
Section 5 implements two approaches to estimating the
expected return on the green-minus-brown stock portfolio.
Section 6 documents the delayed reaction of stock prices
to climate news. Section 7 discusses how we construct the
green factor and explore its role in pricing value and momentum. Section 8 concludes.

Green bond

Non-green bond

Difference

Panel A. Yields to maturity (basis points per year)
Average
-46.72
-42.09
-4.63
(-13.53)
(-10.90)
(-6.19)
First day
-51.20
-49.60
-1.60
Last day
-40.60
-34.40
-6.20
Panel B. Realized returns
Average
-0.47
-0.59
0.12
(-0.35)
(-0.44)
(2.19)
Cumulative
-1.53
-1.90
0.37

and the same coupon payment dates. This pairing creates “twin” bonds, which offer identical streams of cash
ﬂows with identical credit risk but different greenness.
This clean twin pairing makes German government bonds
uniquely well suited for our purposes. By comparing the
prices of twin bonds, we can gain some insight into the
value assigned to greenness by bond market investors.
Even though the twin bonds are paired very carefully,
some differences between them remain. First, the issuance
date of the green bond always comes after the initial issuance date of the conventional bond. For example, the
green bond issued in September 2020 has a conventional
twin issued in June 2020. Second, conventional bonds tend
to be issued at larger volumes than their green twins. For
example, in 2020, the issuance of conventional bonds was
almost ﬁve times larger than that of the corresponding
green bonds. Conventional bonds could thus in principle be
more liquid than their green twins. However, the German
Finance Agency has committed to play an active role in the
secondary market for green bonds to make their liquidity
comparable to that of conventional bonds.
We obtain daily data on the ﬁrst pair of twin bonds,
downloading the end-of-day bond prices and mid-yields to
maturity for the 10-year green bond (ISIN DE0 0 01030708)
and the 10-year non-green bond (DE0 0 01102507) from
Bloomberg. We download data since the ﬁrst date of trading for the green bond, which is September 8, 2020,
through November 17, 2021. Over this time period, the two
bonds’ annual yields ﬂuctuate between −67 and −15 bps.
We plot these yields in Panel A of Fig. 1 and show their
means in Panel A of Table 1.5

2. German twin bonds
This paper emphasizes the difference between expected
and realized returns on green assets. In this section, we
illustrate this difference for bonds. Bonds’ expected returns
are tightly linked to yields to maturity, which are easily
observable.
Since 2020, the government of Germany, the largest
European economy, has been issuing green securities to
ﬁnance its transition towards a low-carbon, sustainable
economy.4 The ﬁrst green security, a 10-year bond, was issued in September 2020 in the amount of 6.5 billion euros. The second green security, a 5-year note, followed two
months later in the amount of 5 billion euros. Both securities have zero coupon rates. Germany plans to issue at
least one green security per year. We refer to these securities as “green bonds.”
Each green bond is issued with the same characteristics as an existing conventional bond issued by the German government. Besides having the same issuer, the two
bonds have the same maturity date, the same coupon rate,

5
In the Appendix, we plot the counterpart of Fig. 1 for the second
pair of twin bonds (ﬁve-year bonds), which was ﬁrst issued in November 2020. The results are similar to those presented in Fig. 1. We prioritize the ﬁrst twin pair due to its longer history. The Appendix is on the
authors’ websites.

4
For more details, see https://www.deutsche-ﬁnanzagentur.de/en/
institutional-investors/federal- securities/green- federal- securities/.

406

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Fig. 1. German twin bonds. Panel A plots the daily time series of annual yields on the German government’s 10-year green bond and its non-green twin.
Panel B plots the “greenium,” the yield difference between the green bond and its non-green twin. Panel C plots the performance of a portfolio that goes
long the 10-year green bond and short its non-green twin. The solid line plots this long-short portfolio’s daily cumulative realized return. The dashed line
plots the expected cumulative return as of the ﬁrst day of trading of the green bond (September 8, 2020), absent a subsequent change in the greenium,
which was −1.6 bps on that day.

Panel B of Fig. 1 plots the difference between the yields
of green and non-green bonds, also known as the greenium (e.g., Larcker and Watts, 2020). The greenium is always negative, averaging −4.6 bps and ranging mostly between −7 and −2 bps per year.6 Therefore, for investors
holding the bonds to maturity, the green bond always has
a lower expected return than the non-green bond. This evidence is in line with theories predicting that green assets
offer lower expected returns than non-green assets (e.g.,
PST).7

Given the lower yield of the green bond, one would
expect it to deliver a lower return than its conventional
twin. Instead, the green bond delivered a higher return in
our sample. We calculate bond returns as daily percentage changes in bond prices and report them in Panel B of
Table 1. The full-sample cumulative returns are negative,
−1.53% for the green bond and −1.90% for the non-green
bond, due to a rise in yields between September 2020 and
November 2021. More interesting, the green bond outperforms its non-green twin over this time period, as shown
by Panel C of Fig. 1. The ﬁgure plots cumulative returns on
a long-short portfolio, which goes long the green bond and
short the non-green bond. The portfolio’s average daily return of 0.12 bps is statistically signiﬁcant (t = 2.19), and its
cumulative return of 37 bps is substantial relative to German government bond yields.

6
These greenium values are close to those estimated by prior studies
in different settings. For example, Baker et al. (2018) estimate a greenium
of about −6 bps in a sample of over 2,0 0 0 U.S. municipal and corporate green bonds, whereas Zerbib (2019) estimates −2 bps in a sample of
over 10 0 0 supranational, sub-sovereign and agency, municipal, corporate,
ﬁnancial, and covered green bonds.
7
This conclusion is reinforced by liquidity considerations. As noted earlier, the non-green bond has been issued at larger volume than its green
twin. If this volume difference makes the conventional bond more liquid despite the aforementioned efforts of the German Finance Agency,

then the resulting liquidity premium pushes the greenium up, and the
expected return penalty associated with greenness is even larger.
407

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Importantly, the positive average return of the longshort portfolio does not imply that the portfolio’s expected
return is positive. On the contrary, we know with certainty
that the portfolio’s expected return is negative if the bonds
are held to maturity. For example, on September 8, 2020,
the green bond’s yield was −51.2 bps per year, whereas
the non-green bond’s yield was −49.6 bps. Therefore, if
both bonds are held to maturity, the green bond delivers
a return 1.6 bps lower than the non-green bond. The green
bond’s expected return is lower also if the bonds are not
held to maturity under a variety of plausible conditions,
such as changes in the greenium being unpredictable. That
condition is likely to hold, especially in eﬃcient, or neareﬃcient, markets. Under that condition, the green bond’s
expected return is lower at the beginning of the sample,
and the expected return of the long-short portfolio is negative. The cumulative value of this expected return is plotted by the dashed line in Panel C of Fig. 1, which is gently
downward-sloping.
How can we reconcile the higher realized return of the
green bond with its lower expected return? The answer is
that that the greenium in Panel B grows increasingly negative between September 2020 and November 2021, deepening from −1.6 to −6.2 bps. This deepening is responsible for the outperformance of the long-short portfolio in
Panel C. In the language of PST, if investors’ tastes shift
toward green assets, they push up the price of the green
bond relative to the non-green bond. However, the green
bond’s outperformance is temporary, as it comes entirely
at the expense of the bond’s future return. Investors buying
the bonds on September 8, 2020 and holding them to maturity expected to earn 1.6 bps less from the green bond,
but those buying on November 17, 2021 expected to earn
6.2 bps less.
Investors’ tastes for green assets could plausibly have
shifted unexpectedly due to heightened concerns about climate change. Those concerns are likely to have risen in
July 2021 when Germany, along with several other European countries, experienced catastrophic ﬂoods caused
by heavy rainfall that followed unprecedented heat waves.
Germany experienced around 200 fatalities in those ﬂoods,
which were the deadliest natural disaster in the country
in almost six decades. Consistent with a shift in investors’
tastes toward green German bonds, the greenium widened
from −5.5 bps on June 29, to −7.3 bps on August 4, before
easing back to −6 bps by mid-September. These changes
suggest a possible link between investors’ tastes and climate concerns.8 We further explore this link later in the
paper.
The case study of German twin bonds illustrates how
shifts in expected return drive a wedge between returns
expected ex ante and those realized ex post. Even though
the green bond’s realized return is higher than that of the
non-green bond, the green bond’s expected long-term re-

turn is demonstrably lower. In other words, the expected
return of the long-short portfolio is negative even though
the portfolio’s average realized return is positive and signiﬁcant. Unexpected events often happen, and one of them
was likely the outperformance of the German green bond
in the ﬁrst 14 months of its existence.
3. Measuring stocks’ greenness
While the German bond example is clean, it is essentially a case study. In this section, we begin our main analysis, which examines U.S. stocks. Focusing on stocks allows
us to examine the role of greenness in a larger asset universe over a longer time period.
We compute stock-level environmental scores based
on MSCI ESG Ratings data, a successor to the MSCI
KLD data used in many academic studies. Our data
have a number of advantages. According to Eccles and
Stroehle (2018), MSCI is the world’s largest provider of
ESG ratings. The MSCI ESG Ratings data are used by more
than 1700 clients, including pension funds, asset managers,
consultants, advisers, banks, and insurers.9 MSCI covers
more ﬁrms than other ESG raters, such as Asset4, KLD,
RobescoSAM, Sustainalytics, and Vigeo Eiris (Berg et al.,
2019). Berg et al. (2021) ﬁnd that MSCI’s ESG scores are
the least noisy among the eight ESG data vendors they
consider. MSCI generates its ratings based on a variety of
sources and updates those ratings at least annually. MSCI’s
ESG research unit employs more than 200 analysts and
incorporates artiﬁcial intelligence, machine learning, and
natural language processing into its methodology.
The availability of industry-unadjusted granular data is
another advantage of the MSCI data. With industry adjustment, a heavily polluting ﬁrm is classiﬁed as green
if it pollutes less than other ﬁrms in its heavily polluting industry. Without industry adjustment, such a ﬁrm
is classiﬁed as very brown. In principle, either classiﬁcation could be more relevant for green-versus-brown effects on investor and consumer demands. The MSCI data
allow us to explore that issue. MSCI’s composite ESG rating is industry-adjusted, as are ratings from other leading
providers, whereas MSCI’s granular data allow us to compute a greenness measure that is not industry adjusted. We
conduct our primary analyses using the latter all-in measure. This approach seems reasonable, as we later show
that the effects we identify are strongly associated with
industry-level greenness.
We use the MSCI variables “Environmental pillar score”
(E_score) and “Environmental pillar weight” (E_weight).
E_score is a number between 0 and 10 measuring the
ﬁrm’s weighted-average score across 13 environmental issues related to climate change, natural resources, pollution
and waste, and environmental opportunities. These scores
are designed to measure a company’s resilience to longterm environmental risks. E_weight, which is typically con-

8
According to the September 2021 ARD-DeutschlandTREND survey,
33% of Germans view climate as the ﬁrst or second most important problem facing Germany, ahead of immigration (22%), the coronavirus (18%),
and social injustice (16%). In the pre-ﬂood June 2021 survey, the proportion favoring climate was lower, 28%, indicating a substantial shift in Germans’ climate concerns in the summer of 2021.

9
See https://www.msci.com/our- solutions/esg- investing, as of May
2021. In addition, MSCI has been voted ‘Best ﬁrm for SRI research’ in
the Extel & SRI Connect Independent Research in Responsible Investment
Survey in each year from 2015 through 2019 (https://www.msci.com/zh/
esg-ratings).

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Journal of Financial Economics 146 (2022) 403–424

stant across ﬁrms in the same industry, is a number between 0 and 100 measuring the importance of environmental issues relative to social and governance issues.10
We compute the unadjusted greenness score of ﬁrm i
at the beginning of month t as

Gi,t−1 = −(10 − E _scorei,t−1 ) × E _weighti,t−1 /100,

(1)

where E _scorei,t−1 and E _weighti,t−1 are from company
i’s most recent MSCI ratings date before month t, looking back no more than 12 months. The quantity 10 −
E _scorei,t−1 measures how far the company is from a
perfect environment score of 10. The product (10 −
E _scorei,t−1 ) × E _weighti,t−1 measures how brown the ﬁrm
is, speciﬁcally, the interaction of how badly the ﬁrm
scores on environmental issues and how large the environmental impacts are for the industry’s typical ﬁrm (i.e.,
E _weighti,t−1 ). The initial minus sign converts the measure
from brownness to greenness.
Including E_weight in Eq. (1) is important for capturing
a company’s greenness. For example, in 2019, Exxon Mobil
and Best Buy had similar E_score values: 4.2 and 4.1, respectively. If we used only E_score, we would judge these
companies to be similarly green. But E_weight is 48 for
Exxon and only 11 for Best Buy, reﬂecting that oil and gas
companies have larger environmental impacts than consumer retail companies. Exxon and Best Buy end up with
Gi,t = −2.78 and −0.65, respectively, indicating that Best
Buy is much greener than Exxon. Similar to us, MSCI uses
the interaction of E _score and E _weight when computing
ﬁrms’ composite ESG ratings.11
The environmental score we use in our analysis is

gi,t = Gi,t − Gt ,

Fig. 2. MSCI coverage. The ﬁgure plots the number of stocks in our sample with non-missing MSCI environmental scores at the beginning of the
month. The dashed red line is at November 2012, where our sample begins. MSCI expanded its coverage in October 2012. We begin our sample
in November 2012, as we require lagged environmental scores.

U.S. stocks.12 Figure 2 plots the number of U.S. stocks with
non-missing lagged MSCI ratings. This number increases
sharply in November 2012, from roughly 500 to over 2,0 0 0.
Our purchased MSCI data end in March 2020, but we extend our sample through December 2020 by looking back
up to 12 months when computing Gi,t−1 .
Table 2 shows industries ranked by their equalweighted average gi,t scores at the end of 2019. The
lowest-ranked industries include chemicals, oil and gas exploration and production, steel, mining (including coal),
paper and forest products, and marine transport. It is reassuring that these industries, which are generally viewed
as having negative environmental impacts, appear at the
bottom of our ranking.
Among the 64 industries considered in Table 2, only 20
have positive values of average gi,t at the end of 2019. This
fact may appear at odds with our assumption that the average value of gi,t across all stocks is zero. However, our
assumption pertains to the market-value-weighted average
(see Eq. (3)). While the equal-weighted average of gi,t at
the end of 2019 is −0.33, the value-weighted average is indeed zero, by construction. The value-weighted average exceeds the equal-weighted one because greener ﬁrms tend
to be larger.

(2)

where Gt is the value-weighted average of Gi,t across all
ﬁrms i. Since we subtract Gt , gi,t measures the company’s
greenness relative to the market portfolio, as in PST. If
wt and gt denote the vectors containing stocks’ market
weights and gi,t values in month t, then

wt’ gt = 0,

(3)

a condition imposed by PST.
We compute gi,t in the sample of stocks with nonmissing MSCI data and CRSP share codes of 10 or 11.
We merge CRSP and MSCI by using a combination of
CUSIP, ticker, and company name. Our sample extends
from November 2012 to December 2020. We begin in
November 2012 because MSCI’s coverage increases dramatically in October 2012, when MSCI began covering small

4. Realized green stock returns
Green stocks strongly outperformed brown in recent
years. Figure 3 displays the performance of green and
brown stocks from November 2012 to December 2020. The
solid line, representing green stocks, plots the cumulative value-weighted return on the portfolio of stocks with
greenness scores in the top third. The dashed line, representing brown stocks, plots the corresponding return for
stocks with scores in the bottom third. We see that green
stocks strongly outperformed brown in the 2010s, with
a cumulative return difference of 174% over our 8.2-year

10
MSCI’s E, S, and G weights sum to 100. According to MSCI, “The
weightings take into account both the contribution of the industry, relative to all other industries, to the negative or positive impact on the environment or society; and the timeline within which we expect that risk
or opportunity for companies in the industry to materialize....” We follow
MSCI in using the GICS sub-industry classiﬁcation.
11
MSCI’s composite ESG rating is based on their “Weighted Average
Key Issue” score, which equals [E _score × E _weight + S_score × S_weight +
G_score × G_weight ]/100, where S and G refer to social and governance. So
if MSCI used a formula like Eq. (1) to compute greenness not just on environmental but also on social and governance dimensions, then we could
express MSCI’s composite ESG score as 10 plus the sum of E, S, and G
greenness.

12
Before October 2012, MSCI covered only the largest 1500 companies
in the MSCI World Index, plus large companies in the UK and Australia
MSCI indexes. In October 2012 MSCI added many smaller U.S. ﬁrms when
it began covering also the MSCI U.S. Investible Market Index.

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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Table 2
Industries ranked by environmental scores.
Average g is the environmental score averaged across ﬁrms within each MSCI industry at the end of 2019. MSCI uses the
GICS sub-industry classiﬁcation.
Rank

MSCI Industry

Avg. g

Rank

MSCI Industry

Avg. g

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

Asset Management & Custody Banks
Professional Services
Telecommunication Services
Consumer Finance
Health Care Equipment & Supplies
Health Care Providers & Services
Life & Health Insurance
Interactive Media & Services
Diversiﬁed Financials
Media & Entertainment
Diversiﬁed Consumer Services
Biotechnology
Pharmaceuticals
Multi-Line Insurance & Brokerage
Investment Banking & Brokerage
Banks
Restaurants
Construction & Engineering
Aerospace & Defense
Commercial Services & Supplies
Air Freight & Logistics
Household Durables
Software & Services
Electronic Equipment, Instruments
Leisure Products
Automobiles
Retail - Food & Staples
Retail - Consumer Discretionary
Road & Rail Transport
Household & Personal Products
Industrial Conglomerates
Technology Hardware, Storage

0.87
0.85
0.84
0.84
0.84
0.83
0.76
0.74
0.73
0.70
0.61
0.57
0.49
0.40
0.39
0.35
0.31
0.13
0.10
0.07
-0.06
-0.12
-0.13
-0.17
-0.17
-0.22
-0.25
-0.27
-0.30
-0.30
-0.36
-0.39

33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64

Textiles, Apparel & Luxury Goods
Auto Components
Property & Casualty Insurance
Casinos & Gaming
Real Estate Development
Semiconductors
Electrical Equipment
Construction & Farm Machinery
Tobacco
Trading Companies & Distributors
Industrial Machinery
Containers & Packaging
Energy Equipment & Services
Real Estate Management & Services
Airlines
Hotels & Travel
Building Products
Utilities
Integrated Oil & Gas
Food Products
Beverages
Metals and Mining, Precious
Oil & Gas Reﬁning, Marketing
Construction Materials
Specialty Chemicals
Marine Transport
Paper & Forest Products
Metals and Mining, Non-Precious
Steel
Oil & Gas Exploration & Production
Diversiﬁed Chemicals
Commodity Chemicals

-0.50
-0.51
-0.51
-0.54
-0.55
-0.66
-0.75
-0.76
-0.89
-0.99
-1.04
-1.09
-1.16
-1.20
-1.21
-1.57
-1.62
-1.90
-2.01
-2.02
-2.04
-2.19
-2.52
-2.56
-2.82
-2.83
-2.93
-2.95
-2.96
-3.01
-3.21
-3.78

than even the market portfolio’s Sharpe ratio of 0.30 over
the same period.
This strong performance of GMB cannot be explained
by exposures to return factors prominent in the asset pricing literature. The remaining columns of Table 3 report results of regressing GMB on various factors, including those
in the three- and ﬁve-factor models of Fama and French
(1993, 2015), the momentum factor (UMD) as constructed
by those authors, the traded liquidity factor of Pástor and
Stambaugh (2003), and the factors of Hou et al. (2015) and
Hou et al. (2021). In all cases, GMB’s alpha (regression constant) is economically and statistically signiﬁcant, ranging
from 47 to 71 bps per month, with t-statistics between
1.99 and 2.91.
GMB’s lowest alpha in Table 3 occurs in column 4,
where we adjust for the three Fama-French factors and
momentum. Its exposures to SMB, HML, and UMD indicate
that GMB tilts toward large stocks, growth stocks, and recent winners. Net of those exposures, the alpha of GMB is
47 bps per month (t = 2.14).
At ﬁrst sight, these results appear at odds with those
of Bolton and Kacperczyk (2021), who ﬁnd that stocks
of ﬁrms with higher carbon emissions earn higher riskadjusted returns. However, Bolton and Kacperczyk’s sample period, 2005 to 2017, is substantially different from
ours. Moreover, the sign of the carbon premium depends

Fig. 3. Returns on value-weighted green and brown portfolios. This ﬁgure plots the green and brown portfolios’ cumulative returns. The values
of the green and brown lines at the end of 2020 are 264.9 and 91.3, implying green stocks outperformed brown by 264.9 − 91.3 = 174 percentage points over this period.

sample period. The monthly return difference, which we
denote GMB (green-minus-brown), averaged 65 bps per
month (t-statistic: 3.23), as reported in the ﬁrst column of
Table 3. The monthly Sharpe ratio of GMB is 0.33, larger
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Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Table 3
GMB performance.
We estimate monthly time-series regressions using data from November 2012 to December 2020.
The dependent variable is the difference between the returns on the green and brown portfolios
(GMB). Mkt-Rf is the excess market return. SMB and HML are the size and value factors of Fama and
French (1993). UMD is the momentum factor of Carhart (1997). LIQ is the traded liquidity factor of
Pástor and Stambaugh (2003). RMW and CMA are the proﬁtability and investment factors of Fama and
French (2015). ME, I/A, and Roe are the size, investment, and proﬁtability factors of Hou et al. (2015). Eg
is the expected-growth factor of Hou et al. (2021). Returns are in percent per month. Robust t-statistics
are in parentheses.

Constant

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

0.65
(3.23)

0.71
(2.91)
-0.05
(-0.78)

0.50
(2.23)
0.02
(0.32)
-0.14
(-1.49)
-0.26
(-3.36)

0.47
(2.14)
0.05
(0.87)
-0.11
(-1.23)
-0.18
(-1.99)
0.13
(2.00)

0.50
(2.25)
0.01
(0.21)
-0.16
(-1.56)
-0.26
(-3.26)

0.50
(2.38)
0.04
(0.77)
-0.26
(-2.59)
-0.21
(-2.60)

0.55
(2.28)
-0.00
(-0.05)

0.49
(1.99)
0.01
(0.23)

-0.15
(-1.48)
-0.30
(-2.21)
0.09
(0.99)

-0.13
(-1.28)
-0.25
(-1.59)
0.02
(0.20)
0.12
(0.67)
98
0.14

Mkt-RF
SMB
HML
UMD
LIQ

0.04
(0.60)

RMW

-0.39
(-2.90)
-0.10
(-0.60)

CMA
ME
I/A
Roe
Eg
Observations
R2

98
0.00

98
0.01

98
0.19

98
0.22

on how exactly carbon emissions are measured. Bolton
and Kacperczyk ﬁnd a positive carbon premium associated with total emissions, but not with emission intensity
(i.e., emissions per unit of sales). Görgen et al. (2020) ﬁnd
an insigniﬁcantly negative carbon premium when they
combine multiple carbon-emission-related measures and
use a sample period closer to ours, 2010 to 2017. Finally, carbon emissions are only one of 13 ﬁrm characteristics that enter MSCI’s environmental scores, which
we use to determine ﬁrm greenness. For example, MSCI
also considers the ﬁrm’s handling of land use, water
stress, raw material sourcing, toxic waste, and opportunities in clean tech, green building, and renewable
energy.

98
0.19

98
0.26

98
0.13

pected return as its implied cost of capital (ICC), which is
the discount rate that equates the stock’s current price to
the present value of expected future cash ﬂows, with the
latter estimated using data available when the price is observed. With this ex ante approach, we construct the expected GMB return from the underlying stocks’ ICCs. The
second approach estimates the expected GMB return as the
average ex post return purged of unanticipated shocks to
quantities affecting the return. To identify those shocks,
we follow PST in noting that GMB’s realized performance
can be positive in periods of unanticipated increases in demands for green ﬁrms’ products and stocks (or decreases
in demands for brown ﬁrms’ products and stocks). These
demands can change for various reasons, but a likely leading source is increased concerns about climate change.
We use climate-concern shocks and earnings-news shocks
when pursuing the second approach.
As we detail below, the ex ante and ex post approaches
deliver similar negative estimates of the expected GMB return. These estimates contrast sharply with GMB’s strongly
positive realized performance. Later in the section we
show that our main conclusions about expected versus realized returns are robust along various dimensions, such
as including additional shocks and examining returns at
the individual stock level. We also show that our results
are driven more by industry-level greenness than withinindustry greenness.

5. The equity greenium
We next explore the equity analog to the bond greenium analyzed in Section 2. The equity greenium captures
the difference in expected returns on green versus brown
stocks. For concreteness, we deﬁne the equity greenium as
the expected return on the GMB spread. Expected stock returns are not directly observable, so the equity greenium
must be estimated. This section presents two approaches
to the estimation.
One approach uses ex ante data while the other uses
ex post data. The ﬁrst approach estimates each stock’s ex411

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

portfolio’s ICC, ranges from −0.4% to −2.4%, with an average of −1.4% per year. To the extent that the ICC is a
good proxy for expected stock return, this evidence of a
consistently negative equity greenium supports our argument that GMB’s strong performance in our sample period
was unexpected.
Additional insight into the equity greenium comes from
a panel regression of a stock’s ICC on the stock’s greenness,
with month ﬁxed effects. This regression produces a highly
signiﬁcant negative slope estimate (t = −11.90), again consistent with a negative equity greenium. When we add the
interaction of greenness with a time trend to the righthand side of the regression, both greenness and this interaction command highly signiﬁcant slope estimates, with
t-statistics of about −5.5. (We tabulate the results in the
Appendix.) These estimates imply not only that the equity greenium is negative but also that it widened over
our sample period. Consistent with the latter, in Panel B
of Fig. 4 the ICC of GMB declines from −1.2% to −1.9%
per year during our sample period, albeit far from monotonically. The greenium’s decline is especially steep from
2017 to 2020. This evidence of a widening equity greenium is consistent with investors’ demand for green assets
strengthening during our sample period.

5.1. ICC estimates of the equity greenium
Our ﬁrst approach to estimating the equity greenium,
using ex ante data, computes the ICC for each stockmonth. The ICC combines data on market prices and forecasted cash ﬂows to infer a discount rate using the standard discounted-cash-ﬂow formula. We follow the approach of Hou et al. (2012), which builds on the classic framework of Gebhardt et al. (2001) but replaces analysts’ earnings forecasts with regression-based forecasts.
Lee et al. (2021) compare ICC methods used in a number
of ﬁnance studies. We choose the method they ﬁnd produces the most precise expected return estimates in the
cross section. The Appendix provides further details.
Panel A of Fig. 4 plots the time series of the ICCs of
the green and brown portfolios, the long and short legs of
GMB. Each portfolio’s ICC is the value-weighted average of
its stocks’ ICCs. During our sample period, the green portfolio’s ICC declines from 7.6% to 4.9% per year, whereas the
brown portfolio’s ICC falls from 8.8% to 6.8% per year. Importantly, at each point in time, the green portfolio’s ICC
is below that of the brown portfolio, indicating a consistently negative equity greenium, i.e., lower expected return
on green stocks versus brown. Panel B plots the difference
between the two ICCs. This difference, which is the GMB

5.2. Inferring expected return from past realizations
Our second approach to estimating the equity greenium
addresses the general problem of inferring an asset’s unconditional expected return, μ = E {rt }, using ex post data.
One option is to use the asset’s sample average return, r̄, as
the estimate of μ. Another approach, which we follow, is
to exploit the additional information in the contemporaneous history of another variable, xt , that is correlated with
the return and for which E {xt } = 0. For example, as in our
setting, xt can be an unanticipated change in climate concerns. In the regression,

rt = a + bxt + t ,

(4)

a = μ because xt has zero mean ex ante. Therefore, we can
estimate μ by the sample estimate of a. This estimate is
given by the OLS intercept aˆ = r̄ − bˆ x̄, where bˆ is the OLS
slope and x̄ is the sample average of xt . We thus have two
alternative estimators of μ:

Estimator 1: r̄

(5)

Estimator 2: aˆ = r̄ − bˆ x̄ .

(6)

To obtain more insight into the second estimator, let xt
be signed such that b > 0. Suppose the realizations of xt
exceed their expectation on average, so that x̄ > 0. As a result, r̄ overstates μ by bx̄ on average. This overstatement is
essentially removed by the second estimator, aˆ, which reduces r̄ by bˆ x̄. Similarly, when instead x̄ < 0, one expects
r̄ to understate μ, and aˆ essentially adds back the understatement. In general, with x̄ = 0, the regression intercept
removes the associated ex post distortion in r̄. The same
argument applies if xt is a vector of variables whose sample means differ from their zero ex ante means.

Fig. 4. Implied costs of capital. Panel A plots the ICCs of green and brown
portfolios, computed as value-weighted averages of annual ICCs of stocks
within each portfolio. Panel B plots the green-minus-brown difference between the ICCs from Panel A.
412

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Journal of Financial Economics 146 (2022) 403–424

the wrong sign is about 0.33. For tx̄ = 0, that value is also
the probability of getting the wrong sign when estimating
μ by r̄, but the probability in this latter case rises quickly
as tx̄ increases, to the extent that getting the wrong sign
becomes very likely when x̄ is strongly signiﬁcant. Panel B
shows the probability that each estimate of μ not only gets
the wrong sign but is also statistically signiﬁcant at the
two-tailed 5% level. If μ is estimated by aˆ, this probability
is consistently less than 1%. If μ is instead estimated by r̄,
the probability grows quickly as tx̄ increases. For example,
if tx̄ = 4, there is a 25% probability of having r̄ be statistically signiﬁcant with the wrong sign. Overall, for samples
in which x̄ departs signiﬁcantly from its zero mean, the advantage of using aˆ rather than r̄ to estimate μ seems clear.
5.3. Measuring shocks to climate concerns and earnings
To implement the above approach that uses aˆ, we must
specify xt . We generalize the latter to be a vector of shocks
having two sources. First, climate concerns are likely to
play a key role in boosting demands by consumers for
green ﬁrms’ products as well as demands by investors
for green ﬁrms’ stocks (and reducing demands for brown
ﬁrms’ products and stocks). Therefore, news regarding climate concerns serves as one source of return shocks in
xt .14 Second, while the product-demand channel for climate news impacts returns via expectations of ﬁrms’ earnings, non-climate information also impacts earnings expectations and thus returns. We therefore include earnings
news directly as another source of return shocks in xt .
Next, we describe how we measure both sources of shocks.
Fig. 5. Comparing estimators of expected return. The ﬁgure displays the
indicated probabilities when the number of observations equals 68, the
regression R-squared is 20%, and the monthly return has a true mean (μ)
of −10 basis points and a standard deviation of 2%. In Panel B, statistical
signiﬁcance is at the two-tailed 5% level.

5.3.1. Climate concerns
We measure concerns about climate change with
the Media Climate Change Concerns index (MCCC) of
Ardia et al. (2021). This index, which is available from January 2003 through June 2018, is constructed by using data
from eight major U.S. newspapers. It captures the number
of climate news stories each day as well as their negativity and focus on risk. For each news article discussing
climate change, Ardia et al. compute a “concern” measure
that interacts two quantities: the fraction of total words related to risk and the scaled difference between negative
and positive words. They aggregate this measure to the
newspaper-day level by adding the concern values across
stories. Next, they aggregate to the day level by averaging
across newspapers, after adjusting for heterogeneity across
newspapers. Finally, they take the square root of this daily
measure because, as they put it, “One concerning article
about climate change may increase concerns, but 20 concerning articles are unlikely to increase concerns 20 times
more.”
Following Ardia et al. (2021), we measure shocks to climate concerns as prediction errors from AR(1) models applied to the underlying MCCC index. To compute the prediction error in month t, we estimate an AR(1) model using the 36 months of MCCC data ending in month t − 1

To illustrate quantitatively how r̄ and aˆ can provide different inferences, we analyze a setting that corresponds
roughly to our regressions presented later, just simpliﬁed
to the above case of one explanatory variable, xt . Specifically, we set T equal to 68 months, the sample length
in our regressions, and we assume that the regression in
Eq. (4) has an R-squared of 20%, which is broadly representative of our estimated regressions. We also assume that
the t ’s are normally distributed, independently and identically across months, and that the monthly return, rt , has
a standard deviation of 2%, matching that of GMB. Finally,
we set that spread’s expected return, μ, equal to −10 bps
per month, which is representative of both the −11.6 bps
implied by the earlier ICC estimate (−1.4% per year on average) as well as the estimates we obtain later using aˆ.
Figure 5 displays comparisons of r̄ and aˆ as estimators
of μ. Panel A shows the probability that an estimate of μ
is positive, i.e., has the wrong sign. The probability is conditioned on the magnitude of x̄, which we express on the
horizontal axis in terms of tx̄ , the t-statistic for x̄.13 Regardless of tx̄ , if μ is estimated by aˆ, the probability of getting

13

14
We do not take a stand on whether customers’ and investors’ responses to climate news reﬂect genuine concerns about climate or just
virtue signaling. Either way, asset prices can be affected.

The probabilities in Fig. 5 are derived in the Appendix.
413

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Journal of Financial Economics 146 (2022) 403–424

and voluntary forward guidance regarding future earnings. We compute stock returns in excess of the market
during the three-trading-day windows centered on these
announcement dates. We add the excess returns across
unique events within a given stock-quarter. For about
70% of observations, no summation is required because
the forward-guidance date coincides with the earningsannouncement date. We ﬁnd that our announcementreturn measure explains about 20% of the variance of quarterly stock-level returns (see the Appendix).
Our second measure captures news about long-term
earnings. Such news can arrive gradually over time, in between the quarterly announcements. This second measure
uses data on analysts’ forecasts of each ﬁrm’s long-run
earnings growth rate. For ﬁrm i and quarter t, the measure equals the earliest mean analyst forecast in quarter
t + 1 minus the latest mean forecast in quarter t − 1. Using forecasts from quarters t − 1 and t + 1 helps to capture
all news arriving in quarter t. The measure may also include a small amount of information that arrives in quarters t − 1 or t + 1, but those inclusions are innocuous since
they should not help explain returns in quarter t. We winsorize this measure at the 1% level. We ﬁnd that this measure is signiﬁcantly related to quarterly stock-level returns
but explains less than 1% of their variance (see the Appendix).
Since GMB is a spread between portfolio returns, we
need to convert our ﬁrm-level earnings measures into the
appropriate portfolio-level quantities to be included in xt .
We do so following GMB’s construction, each month computing value-weighted averages of the ﬁrm-level measures
within GMB’s green and brown legs and then taking the
difference.
Measuring the part of returns coming from earnings
news is known to be diﬃcult, and our measures surely
miss important earnings news. Our ﬁrst measure misses
short-term news that arrives outside the three-day announcement windows. One limitation of our second measure is that analysts’ forecasts can differ from investors’
forecasts. In addition, analysts’ long-term forecasts are only
three- to ﬁve-year forecasts, so the second measure also
misses changes in expectations of earnings that lie more
than ﬁve years in the future.
Changes in expectations of distant future earnings seem
especially likely to arise from shocks to climate concerns.
For example, the meteoric rise of Tesla’s stock price in
2020 may have been caused in part by climate-driven revisions to forecasts of electric vehicle sales at horizons
longer than ﬁve years. Such climate-driven shocks to earnings, and thus to returns, can nevertheless be captured by
our climate news measure, Ct , which is included in xt .
In general, the return shocks captured by our speciﬁcation
of xt can reﬂect changes in earnings expectations, either
climate-driven, and thus captured by Ct , or non-climatedriven, and thus captured by the earnings news measures.

Fig. 6. Climate concerns and GMB. Climate-concern shocks are prediction errors from rolling AR(1) models ﬁtted to the monthly MCCC index.
The dashed vertical line is at November 2012, where our sample begins.
Before November 2012, the GMB return, shown as a dotted line, is constructed using a much smaller number of stocks (recall Fig. 2). (For interpretation of the references to color in this ﬁgure legend, the reader is
referred to the web version of this article.)

(including data before November 2012), and we set the
prediction error to month t’s realization of MCCC minus
the AR(1) model’s prediction.
Figure 6 plots the cumulative shocks to climate concerns over the ten-year period between July 2009 and June
2018. We begin the plot immediately after the ﬁnancialcrisis-induced recession, which ended in June 2009. The
cumulative shocks trend down initially but then trend up
sharply from 2013 through 2017, before dipping slightly in
2018.15 GMB’s performance, also plotted in Fig. 6, looks
strikingly similar. It performs strongly in 2013 through
2018, cumulatively returning over 40%, whereas its pre2013 performance is negative. Of course, GMB’s performance before November 2012 is only approximate because
it is computed based on a sample of ﬁrms that is much
smaller and biased toward large-capitalization ﬁrms (recall
Fig. 2). We plot GMB’s imprecise earlier performance for
comparison purposes, but we do not use it in any of our
analysis.
We include month t’s climate-concern shock, which we
denote as Ct , in xt . We also include in xt the previous
month’s shock, Ct−1 , given our evidence of delayed stock
price reactions to climate news. (That evidence is analyzed
later in Section 6.)
5.3.2. Earnings news
Next, we include in xt two measures of earnings news
constructed using data from CRSP and I/B/E/S. The ﬁrst
measure is based on the idea that a large portion of earnings news occurs on days when ﬁrms make earningsrelated announcements (Beyer et al., 2010). We consider
two types of announcements: those of quarterly earnings

5.4. Estimates of the equity greenium using past realizations

15

Sautner et al. (2021) provide independent evidence that climate concerns strengthen after 2012. They measure ﬁrms’ climate change exposures by the extent to which climate change topics are discussed in ﬁrms’
earnings calls, ﬁnding a sharp increase in climate change exposure between 2013 and 2018.

The ﬁrst two columns of Table 4 report results from
regressions of GMB returns on xt , both with and without
the earnings variables included in xt . Including those vari414

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Table 4
Sources of GMB performance.
We estimate monthly time-series regressions using data from November 2012
through June 2018. The dependent variable is the GMB return in columns 1–2
and GMB’s Fama-French three-factor alpha in columns 3–4. We estimate alphas in
a time-series regression of GMB on the Fama-French factors. We set each month’s
alpha equal to the regression’s intercept plus residual. Both returns are in percent per month. “ Climate concerns” is the prediction error from rolling AR(1)
models applied to the MCCC index. The two earnings news measures, “Earnings
announcement returns” and “ Earnings forecasts,” are described in Section 5.5.
They correspond to the quarter that contains the given month. Robust t-statistics
are in parentheses.
Dependent variable
Independent variable

 Climate concerns (same month)
 Climate concerns (prev. month)

GMB return
4.08
(2.70)
2.98
(1.86)

Earnings announcement returns

 Earnings forecasts
Constant
Observations
R2

0.05
(0.20)
68
0.14

ables raises the R-squared from 0.14 to 0.25. The samemonth climate shock, Ct , and the earnings announcement
return both enter signiﬁcantly with their expected positive signs (t-statistics: 2.69 and 2.64). The positive Ct coeﬃcient supports the prediction that an increase in climate concerns is worse news for brown stocks than green
stocks. This conclusion, based on monthly returns, echoes
the conclusion reached by Ardia et al. (2021) at the daily
frequency. The previous month’s climate shock, Ct−1 also
enters positively and is marginally signiﬁcant (t-statistic:
1.77). This result, which suggests delayed stock price response to climate news, emerges more strongly among
smaller stocks, as we show in Section 6. The only variable
falling well short of statistical signiﬁcance is the change in
analysts’ long-term forecasts, although its coeﬃcient does
have the expected positive sign.
The key quantity of interest, the equity greenium, is estimated by the regression intercept aˆ. With the earnings
variables included in xt , the estimated equity greenium is
−4 bps per month. Recall that the ICC estimate is about
−12 bps per month. Both the ex ante and ex post approaches thus suggest a negative equity greenium whose
magnitude is modest, at least in comparison to the 65 bps
for GMB’s realized average return.
As noted earlier, GMB tilts toward large growth stocks.
Size and growth effects are not driving our results, however. The remaining columns of Table 4, labeled “GMB
alpha,” repeat the above regressions with the dependent
variable redeﬁned as the GMB return adjusted by the three
factors of Fama and French (1993). To construct that return,
we take the intercept plus the residual from the timeseries regression of GMB on the factors. The resulting slope
coeﬃcients are all quite similar to their counterparts in the
ﬁrst two columns. The intercept when the earnings variables are included shifts downward somewhat, from −4
bps to −15 bps.

3.75
(2.69)
2.86
(1.77)
0.77
(2.64)
6.93
(0.44)
-0.04
(-0.15)
68
0.25

GMB alpha
3.95
(2.79)
2.64
(1.97)

-0.10
(-0.41)
68
0.14

3.44
(2.70)
2.33
(1.82)
0.63
(2.31)
14.16
(0.96)
-0.15
(-0.66)
68
0.26

What if there had been no climate-concern shocks or
other shocks to green-versus-brown earnings? Panel A of
Fig. 7 compares GMB’s realized performance to its counterfactual performance in the absence of climate and earnings shocks. Using the regression estimated in column 2
of Table 4, we compute the counterfactual monthly GMB
return as the regression intercept, aˆ, plus the estimated
residual. (Equivalently, the counterfactual equals the realized value minus the regressors times their respective
coeﬃcients.) The dashed line plots the cumulative counterfactual return, and the solid line shows the cumulative realized return. We also plot a 95% conﬁdence interval around the counterfactual, recognizing that the regression coeﬃcients are estimated with error. To compute
this interval, we repeatedly draw regression coeﬃcients
from their estimated sampling distribution, use those coeﬃcients to compute simulated counterfactual returns, and
plot the simulated returns’ 95% conﬁdence intervals. Panel
B of Fig. 7 repeats the same analysis using the GMB alpha
and the regression estimated in column 4 of Table 4.
Both panels of Fig. 7 deliver the striking message that,
absent shocks to climate concerns and earnings, GMB’s
performance is slightly downward-trending, reﬂecting the
negative intercepts in the second and fourth columns of
Table 4. Moreover, GMB’s counterfactual performance is reliably below its realized performance, as the latter lies well
outside the 95% conﬁdence interval in both panels.
The sharp contrast between the realized and counterfactual performance in Fig. 7 reﬂects the difference between r̄ and aˆ, the two estimators in Eqs. (5) and (6). The
main source of this difference is that the climate-concern
shock, Ct , had average realizations that were unexpectedly high during the sample period. Note in column 1
of Table 4 that when controlling for just climate-concern
shocks, aˆ is merely 5 bps, compared to 65 bps for GMB’s
average return, r̄. The t-statistic for the average of Ct is
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Journal of Financial Economics 146 (2022) 403–424

story, ﬁrst recall that we use a moving 36-month estimation window when computing Ct as the prediction error
from an AR(1) model. The AR(1) model’s intercept absorbs
the recent level and trend in the climate index. Second, an
equal split of the sample period gives results contrary to
the above anticipation story. When we estimate the regressions in Table 4 separately in both subperiods, the climateconcern shocks actually enter somewhat more strongly in
the second half (results are in the Appendix). If Ct had
become anticipated later in the sample period, then returns should have reacted to Ct less strongly in the second subperiod, not more strongly.
5.5. ESG ﬂows and assets
Increased climate concerns can impact green-versusbrown stock returns not only through expected earnings
(via product demands) but also by impacting investors’
desires to hold green stocks rather than brown. As perhaps the most prominent recent trend in the investment
management industry, sustainable investing has experienced rapid growth. At the same time, however, the dollar amounts reallocated by sustainable investing thus far,
especially in the U.S., appear to be fairly small relative to
aggregates. Consider the universe of U.S. mutual funds and
ETFs, for example. In 2020 its assets totaled about $29 trillion, but sustainable funds’ assets accounted for only $230
billion, less than 1% of the total.16
When sustainable investing’s asset share is small, so
too is the likely effect of that investment on expected
stock returns. In PST’s calibrated version of their model,
a small value for the fraction of the market’s total assets
owned by ESG-conscious investors (λ in their setting) implies a small effect on expected return. Berk and Binsbergen (2021) show that the effects of ESG divestment on expected return are quite small in both theoretical and empirical settings where the fraction of assets being divested
is small.
Important to remember, though, is that the magnitude
of the equity greenium does not depend only on such
taste-related investment effects. Green stocks’ expected returns can also reﬂect those stocks’ greater ability to hedge
against adverse climate news. Evidence of such ability appears in our Table 4 in the form of a signiﬁcantly positive
relation between GMB and Ct , as well as in prior studies mentioned earlier. All investors can be willing to pay
for that climate-hedging property of green stocks, whether
or not some investors reallocate due to the warm glow
(anguish) they get from holding green (brown) stocks. If
climate-hedging demand increased during our sample period, this is yet another source of increased investor demand, and hence unexpected returns, for green assets.
Given that the asset footprint of ESG investing is still
fairly small, one might reasonably surmise that ESG investing did not exert signiﬁcant effects on GMB’s realized returns. Nevertheless, some exploration of such potential effects seems warranted, especially given evidence that stock

Fig. 7. Counterfactual GMB performance. The solid line shows realized
cumulative, compounded returns on GMB (Panel A) and GMB’s FamaFrench three-factor alpha (Panel B). Alphas are computed as in Table 4.
The dashed line shows the returns’ counterfactual counterparts computed from columns 2 and 4, respectively, of Table 4. The counterfactual monthly return equals the realized return minus the regressors times
their respective regression slopes. Dotted lines indicate the counterfactual’s 95% conﬁdence interval. We compute conﬁdence intervals using the
following steps: (1) Estimate the regression from column 2 of Table 4 and
store the estimated coeﬃcients and their covariance matrix. (2) Repeat
the following steps (2a)–(2c) 500 times: (2a) draw a new coeﬃcient vector from a normal distribution with mean and variance saved in step (1);
(2b) use the new coeﬃcient to compute each period’s counterfactual return; (2c) compute and store cumulative counterfactual returns. (3) Each
month, compute the 2.5th and 97.5th percentiles of the counterfactual cumulative returns stored in step (2c).

4.01. Recall from Fig. 5 that with such an outcome in the
single-variable version of xt , getting a misleading estimate
of the equity greenium is much more likely when using
the average realized performance, r̄, than when using the
average counterfactual performance, aˆ. In essence, given
that a substantial portion of the increase in climate concerns was unanticipated, so too was GMB’s signiﬁcant positive performance. Accordingly, that performance should
not lead one to infer that the expected return on green
stocks is higher than brown.
Given the high realized average of Ct , one might question whether its non-zero values were truly unanticipated.
An alternative story could be that positive shocks early in
the sample period led investors to anticipate subsequent
increases in the climate-concern index. In considering that

16
Sources: Morningstar’s 2021 Sustainable Funds U.S. Landscape Report
and the Investment Company Institute’s 2021 Investment Company Fact
Book.

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Journal of Financial Economics 146 (2022) 403–424

prices can respond signiﬁcantly to seemingly small demand shifts (e.g., Koijen and Yogo, 2019; Gabaix and Koijen, 2021). In looking for ESG investing effects, we also examine green and brown returns separately, because such
effects are more likely to be evident in brown stocks. For
example, Nofsinger et al. (2019) ﬁnd that institutions are
more likely to underweight stocks with negative environmental and social indicators than they are to overweight
stocks scoring positively on those dimensions. The experimental evidence of Humphrey et al. (2020) shows the
strengths of green versus brown preferences exhibit a similar asymmetry.
We construct two variables to investigate effects of ESG
investing. The ﬁrst uses ﬂows into sustainable funds as
a proxy for shifts in investor demand for green assets.
From Morningstar’s 2021 Sustainable Funds U.S. Landscape
Report, we obtain data on quarterly total ﬂows into U.S.
sustainable funds.17 We scale these ﬂows, which we refer to as “ESG ﬂows,” by the average total market capitalization of CRSP stocks during the quarter. ESG ﬂows increased dramatically in 2013–2020, especially beginning in
2019.
The second investing variable uses sustainable funds’
lagged total assets (AUM) as a proxy for the level of investors’ ESG tastes. This variable is motivated by PST’s theoretical result that expected green-minus-brown returns
depend negatively on the average strength of ESG tastes
(see Eq. (33) in PST), and the size of the ESG industry depends positively on those tastes (see Fig. 5 in PST). We
compute sustainable fund AUM from the previously mentioned Morningstar report, as detailed in the Appendix. We
scale ESG AUM by the total market capitalization of CRSP
stocks.
Columns 1 and 2 of Table 5 report results from regressions of GMB returns on the two investing variables and
the previous climate and earnings variables. In columns
3 and 4, the dependent variable is the return on the
green leg, and in columns 5 and 6, the brown leg of the
GMB spread. Reverse causation is a potential concern when
regressing returns on contemporaneous ﬂows. Instead of
ﬂows (or shifts in investors’ ESG demands) causing returns, ﬂows could be chasing recent returns within the
same period. We address this potential endogeneity by instrumenting for same-quarter ESG ﬂow using its previousquarter value and estimating the regression by two-stage
least squares. The exclusion restriction plausibly holds, because ﬂows cannot chase future realized returns. We ﬁnd
large ﬁrst-stage t-statistics, indicating that the relevance
condition holds and there is no problem with weak instruments.
The coeﬃcients on ESG ﬂows and assets in Table 5 all
have their predicted signs, whether or not climate concerns are included in the regression. That is, ESG ﬂows enter positively for the GMB spread and its green leg but

negatively for the brown leg, whereas ESG assets enter
negatively for the GMB spread and its green leg but positively for the brown leg. For the GMB spread and its green
leg, none of the above coeﬃcients are statistically signiﬁcant. This insigniﬁcance could be related to the fact, noted
above, that ESG investment during this period is still relatively small. For the brown leg, however, when climate
concerns are excluded from the regression, ESG ﬂows enter
with a t-statistic of −2.55, and ESG assets get a marginally
signiﬁcant t-statistic of 1.78. These stronger effects of ESG
investing on the brown leg are consistent with the asymmetry noted earlier. When climate concerns are included
in the regression, though, the brown leg’s coeﬃcients on
ESG ﬂows and assets also become insigniﬁcant.18 A reasonable interpretation is that the effects of ESG investing
on brown stocks’ returns are driven largely by climate concerns. Overall, the results in Table 5 justify having excluded
ESG ﬂows and assets from our primary regression analyses
in Table 4.
5.6. Adding other shocks
As explained earlier, our measure of climate concerns
builds on that of Ardia et al. (2021). Those authors in turn
acknowledge the prior work of Engle et al. (2020), who
construct two media-based measures of climate concerns.
Ardia et al. discuss those alternative measures and explain
that their measure adds risk as another component of climate concerns. We rely on that more recent measure, but
we also examine the robustness of our results to including the Engle et al. measures. We ﬁnd that doing so does
not change our conclusions. We augment the independent
variables in column 2 of Table 4 by including climateconcern shocks based on both Engle et al. measures. One
of their measures enters signiﬁcantly, whereas the Ardia
et al. measure always enters positively and signiﬁcantly,
either for the current or previous month. When we add
the one signiﬁcant measure from Engle et al. to the righthand side of the regression in column 2 of Table 4, we obtain the same conclusions: the counterfactual GMB return
slopes down slightly. The plot is in the Appendix.
Besides their MCCC index, Ardia et al. (2021) also construct sub-indices capturing eight themes related to climate change: agreement and summit, agricultural impact,
disaster, environmental impact, ﬁnancial and regulation,
research, societal impact, and “other.” To see which themes
correlate most closely with GMB returns, we ﬁrst compute
the Ct series for each of the eight sub-indices and then
regress GMB on both Ct and its lag, analogous to our
analysis for the MCCC index. For each of the eight themes,
we ﬁnd positive slope estimates on both Ct and its lag. At
least one of those measures is statistically signiﬁcant for
ﬁve of the eight themes. (We tabulate the results in the
Appendix.) Therefore, the results in Table 4 are not driven
by any single type of climate concerns.
The three themes that deliver the largest R-squareds
in the above regressions are agreement and summit (R2 =

17
The data combine active and passive funds, equity and bond funds,
open-end funds, and ETFs. Morningstar deﬁnes a sustainable fund as follows: “For a fund to be included in the sustainable funds universe, it
must hold itself out to be a sustainable investment. In other words, ESG
concerns must be central to its investment process and the fund’s intent
should be apparent from a simple reading of its prospectus....”

18
When we adjust the GMB spread for the three Fama-French factors,
all the coeﬃcients on ESG ﬂows and assets retain the same signs, but
none of them are statistically signiﬁcant. See the Appendix for details.

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Journal of Financial Economics 146 (2022) 403–424

Table 5
The roles of ESG ﬂows and assets.
This table builds on Table 4 by adding controls for ESG ﬂows and assets. “ESG ﬂows” equals the quarter’s
dollar ﬂow into ESG funds scaled by the average total CRSP market capitalization during the quarter that
contains the given month, times 10 0 0. In the speciﬁcations that drop  Climate concerns, the sample
extends through September 2020. We instrument for contemporaneous ESG ﬂow by using its previousquarter value. The ﬁrst-stage t-statistic for lagged ﬂows is 3.50 in the shorter samples and 5.68 in the
longer samples. We do not tabulate R2 because it is diﬃcult to interpret in an IV setting. “ESG assets”
equals total AUM in ESG funds scaled by the total CRSP market capitalization and measured at the beginning of the quarter containing the given month, times 10 0 0. The dependent variable is the GMB return
in columns 1–2 and the market-hedged return on GMB’s green (brown) leg in columns 3–4 (5–6), all
in percent per month. We compute the market-hedged portfolio returns by replacing individual stock
returns with r˜te , the market-adjusted return deﬁned in Section 7.1. Remaining details are the same as in
Table 4.
Dependent variable
Independent variable

 Climate concerns (same month)
 Climate concerns (prev. month)
Earnings announcement returns

 Earnings forecasts
ESG ﬂows
ESG assets
Constant
Observations

GMB return
4.02
(2.74)
3.30
(2.13)
0.84
(3.06)
9.97
(0.70)
32.96
(1.51)
-0.56
(-0.82)
-0.34
(-0.28)
68

0.88
(2.69)
2.00
(0.15)
9.00
(1.42)
-0.74
(-1.13)
1.80
(1.37)
95

0.15), societal impact (R2 = 0.12), and ﬁnancial and regulation (R2 = 0.12). Ardia et al. (2021) ﬁnd these three
themes are also closely related to the returns on their
green-minus-brown portfolio, which is constructed differently from ours. Moreover, these are the three most discussed themes in the media, according to Ardia et al. The
theme that delivers the lowest R-squared is disaster (R2 =
0.02). GMB returns are thus more closely associated with
climate-related policy news than with news about disasters.
We also examine the robustness of our results to the inclusion of oil price shocks, which have clear environmental
relevance, and long-term bond returns, which could be related to differences in duration between green and brown
stocks. We measure oil price shocks as the monthly change
in the expected “front month” value of oil, derived from oil
futures contracts.19 We take the long-term bond return to
be the return on the 30-year U.S. Treasury bond. When we
add both variables to the right-hand side of the regression
in column 2 of Table 4, the counterfactual performance of
GMB is again essentially ﬂat. See the Appendix.

1.93
(2.78)
0.42
(0.67)
0.20
(1.61)
4.56
(0.82)
7.30
(0.95)
-0.27
(-0.89)
0.18
(0.28)
68

0.22
(1.54)
5.20
(1.06)
1.91
(0.54)
-0.27
(-0.81)
0.64
(1.02)
95

Brown leg
-1.90
(-1.69)
-3.04
(-2.62)
-0.63
(-2.88)
-6.70
(-0.59)
-29.69
(-1.60)
0.61
(1.08)
0.03
(0.03)
68

-0.60
(-2.51)
3.23
(0.31)
-11.99
(-2.55)
0.84
(1.78)
-1.75
(-1.80)
95

Table 6 reports regressions of individual stock returns in
month t on various regressors. All regressions include time
ﬁxed effects and therefore capture cross-sectional variation
in returns. We begin in column 1 with a single regressor, the stock’s greenness, gi,t−1 . The remaining columns
add regressors that capture shocks to climate concerns and
earnings. The climate-concern shocks are interacted with
the stock’s greenness, and the earnings variables are the
ﬁrm-level constituents of the earlier portfolio-level versions used in Table 4. The last column includes additional stock-speciﬁc variables as controls: log of market equity, log of book-to-market, and return from months t − 12
through t − 2.
When greenness is the only regressor, it has a significantly positive relation to return (column 1), consistent
with the outperformance of green stocks reﬂected in GMB.
The coeﬃcient on greenness becomes negative when the
regressors include the climate-concern and earnings variables (columns 3 and 4), consistent with GMB’s negative
expected return estimate given by the intercept in column
2 of Table 4. Thus, consistent with the GMB results, the
relation between greenness and return ﬂips from strongly
positive to modestly negative when controlling for shocks
to returns from climate concerns and earnings.
The coeﬃcients on the climate-concern variables indicate that green stocks outperform when climate concerns
increase, consistent with that same conclusion delivered by
the regressions for GMB in Table 4. The timing is somewhat different, however, in that the lagged climate-concern
shock now enters more strongly than the contemporaneous shock. In Table 6 the coeﬃcient on gi,t−1 interacted
with Ct is positive but insigniﬁcant, while the coeﬃcient

5.7. Greenness and individual stock returns
All of our empirical analysis thus far is based on the
time series of green-versus-brown portfolio returns. To
show that our conclusions do not hinge solely on portfolio returns, we next run panel regressions using individual
stocks.
19

Green leg

We thank Erik Gilje for providing these data.
418

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Journal of Financial Economics 146 (2022) 403–424

Table 6
Greenness and individual stock returns.
This table shows results from panel regressions in which the dependent variable
is stock i’s percent return in month t. gi,t−1 is the stock’s lagged greenness. Ct is
month t’s change in aggregate climate concerns, computed as the prediction error
from a rolling AR(1) model applied to the MCCC index. “[Earnings announcement
ret.]i,t ” is the stock’s sum of the three-trading-day excess percent returns (stock minus market) around earnings announcements and management earnings forecasts
(if available) during the quarter containing month t. “[ Earnings forecast]i,t ” is the
change in analysts’ mean long-term earnings growth rate forecast for stock i during
the quarter containing month t. The last column adds controls (untabulated) for the
log of lagged market equity, log of lagged book-to-market ratio, and the stock’s return from months t − 12 through t − 2, following Lewellen (2015). The sample begins
in November 2012. All regressions include month ﬁxed effects, cluster by month, and
use robust standard errors.
(1)

(2)

(3)

(4)

0.21
(2.24)

0.00
(0.02)
0.83
(1.42)
1.70
(2.66)

218,208
0.18
No

153,884
0.11
No

-0.02
(-0.23)
0.81
(1.59)
1.54
(2.78)
0.32
(13.28)
5.89
(5.02)
133,290
0.18
No

-0.04
(-0.41)
0.72
(1.28)
1.65
(2.68)
0.32
(12.38)
5.91
(4.58)
114,355
0.19
Yes

gi,t−1
gi,t−1 × Ct
gi,t−1 × Ct−1
[Earnings announcement ret.]i,t
[ Earnings forecast]i,t
Observations
R2
Additional controls

on the interaction with Ct−1 is larger and signiﬁcant. In
Section 6 we further analyze the delayed reaction of stock
prices to climate news.
5.8. Industry greenness
Our analysis thus far is based on gi,t , a measure of the
ﬁrm’s total greenness that reﬂects two components: the
greenness of the ﬁrm’s industry and the relative greenness
of the ﬁrm within its industry. How do each of those components contribute to our results? To investigate this question, we decompose gi,t as

gi,t = gAcrossi,t + gW ithini,t ,

(7)

with gAcrossi,t equal to the average gi,t of all ﬁrms within
the same industry as stock i in month t, and gW ithini,t =
gi,t − gAcrossi,t .
Figure 8 displays the original GMB analyzed earlier as
well as an alternative GMB series constructed the same
way but with gW ithini,t replacing gi,t−1 . We see that
the cumulative performance of this alternative, industryadjusted GMB is much weaker than the original. While the
original GMB’s average return is positive and highly significant (t = 3.23; see column 1 of Table 3), the average return of the industry-adjusted GMB is four times smaller
and insigniﬁcant (t = 0.99; see the Appendix). Therefore,
the original GMB’s performance owes much to industrylevel greenness.
The technology industry, especially “big tech,” has delivered high stock returns in recent years. However, our results are not driven by big tech. To show this, we compute monthly returns on the value-weighted portfolio of
“FAANG” stocks, which include Meta (formerly Facebook),
Amazon, Apple, Netﬂix, and Alphabet (formerly Google).

Fig. 8. Effect of industry adjustment. The dashed line plots the cumulative return on the original GMB (green-minus-brown) portfolio constructed with ﬁrms’ total greenness (i.e., not industry-adjusted). The solid
line plots the cumulative return on an industry-adjusted GMB portfolio,
which is constructed using g scores demeaned at the industry × month
level.

The FAANG portfolio’s return is not signiﬁcantly related to
either the original GMB or changes in climate concerns.
The Appendix shows the details.
The importance of industry greenness is also evident
in individual stock returns. Table 7 reports the same regressions as Table 6, except that each independent variable containing gi,t is replaced by two variables, one for
each component in Eq. (7). We ﬁrst see that, as with GMB,
the superior performance of green stocks relative to brown
is largely attributable to industry greenness. In column 1
of Table 7, the coeﬃcient on gAcrossi,t , industry greenness,
is 3.6 times the coeﬃcient on gW ithini,t , within-industry
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Journal of Financial Economics 146 (2022) 403–424

Table 7
Greenness and individual stock returns: Effects within and across industries.
This table repeats the regressions in Table 6, except that we decompose g into
gAcross and gW ithin, representing across- and within-industry variation. We deﬁne
gAcross as the average of g within the industry×month, and gW ithin = g − gAcross,
so that g = gAcross + gW ithin.
(1)

(2)

(3)

(4)

0.25
(2.14)
0.07
(1.11)

-0.00
(-0.01)
0.02
(0.28)
1.08
(1.49)
-0.13
(-0.28)
2.01
(2.58)
0.49
(1.05)

218,208
0.18
No

153,884
0.11
No

-0.02
(-0.18)
-0.02
(-0.27)
1.05
(1.66)
-0.08
(-0.17)
1.86
(2.74)
0.34
(0.70)
0.32
(13.28)
5.85
(5.01)
133,290
0.18
No

-0.05
(-0.39)
-0.01
(-0.11)
0.94
(1.33)
-0.09
(-0.16)
1.94
(2.57)
0.56
(1.00)
0.32
(12.38)
5.88
(4.57)
114,355
0.19
Yes

gAcrossi,t−1
gW ithini,t−1
gAcrossi,t−1 × Ct
gW ithini,t−1 × Ct
gAcrossi,t−1 × Ct−1
gW ithini,t−1 × Ct−1
[Earnings announcement ret.]i,t
[ Earnings forecast]i,t
Observations
R2
Additional contrls

greenness; the former coeﬃcient is statistically signiﬁcant
(t = 2.14), whereas the latter is not (t = 1.11).
Industry greenness continues to play the dominant role
in Table 7’s remaining columns, which analyze the sources
of green stocks’ outperformance. Recall that a key result in
Table 6 is the signiﬁcantly positive coeﬃcient on gi,t−1 interacted with month t − 1’s climate-concern shock. When
the latter shock is instead interacted with industry greenness (gAcrossi,t ), the coeﬃcient on that variable is signiﬁcantly positive in each of columns 2 through 4. In contrast,
when the same climate shock is interacted with withinindustry greenness (gW ithini,t ), the coeﬃcient is insignificant throughout. Therefore, we conclude that industry
greenness is the key component of a ﬁrm’s greenness, capturing both the superior past performance of green stocks
as well as the climate-shock source of that performance.

brown legs. We then regress these GMB returns on the
current and lagged month’s C. The ﬁrst row of Table 8
reports the results. For large-cap GMB, same-month C is
signiﬁcant (t = 2.46), whereas previous-month C is not
(t = 1.74). In contrast, for small-cap GMB, same-month C
is insigniﬁcant (t = 1.23), whereas previous-month C is
strongly signiﬁcant (t = 2.99), and its coeﬃcient signiﬁcantly exceeds its large-cap counterpart (t = 2.35). In sum,
while both large-cap and small-cap GMB exhibit strong
positive reactions to C, the reaction is signiﬁcantly more
delayed in the small-cap segment.
We bring sharper focus to the timing of this sizerelated difference in reactions by looking at a weekly frequency. We construct the weekly C as the prediction
error from an AR(1) model estimated using the previous
three years of observations of the weekly MCCC , computed as the within-week average of the daily MCCC values. We also compute the weekly difference in returns
between large-cap and small-cap GMB. Then we regress
that return difference on C lagged each of τ weeks,
for τ = 0, . . . , 7. Fig. 9 displays the estimated coeﬃcients
along with their 95% conﬁdence intervals. The plot reveals that large-cap GMB reacts more strongly than smallcap GMB to C in the current and most recent week,
with the difference being statistically signiﬁcant for the
current week. In contrast, small-cap GMB reacts more
strongly at longer lags, signiﬁcantly so at the three-week
lag.
The apparent slower reaction of small stocks to climate
news is consistent with prior evidence that small stocks
react more slowly in general. For example, Lo and MacKinlay (1990) show that returns on small stocks generally lag
those of large stocks. Also, it is well known that small
stocks are less liquid and less covered by analysts and
media, potentially making them more susceptible to underreaction. A large literature attributes numerous return
anomalies to underreaction, and Chen et al. (2021) ﬁnd

6. Delayed stock price reaction to climate news
In this section, we take a closer look at the timing of
the strong positive relation between green-versus-brown
returns and the shock to climate concerns, C. As shown
in the previous section, the GMB return is strongly related
to C in the current month, whereas C in the previous
month enters more strongly in the panel regression using
individual stocks. We conjecture this difference relates to
stocks’ market capitalization. The long- and short-leg portfolios of GMB are value-weighted, making GMB most representative of the largest stocks. The panel regression is instead representative of a typical stock, which is substantially smaller than the largest stocks.
To investigate the role of size, we replicate GMB’s
construction separately within the large- and small-cap
segments. Small (large) stocks are those in the bottom
(top) quartile of market capitalization based on NYSE
breakpoints. As in the original GMB, we continue valueweighting stocks within each GMB spread’s green and
420

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

Table 8
Stock size and the response to climate news.
This table shows results from six time-series regressions of monthly portfolio percent
returns on C, the change in climate concerns, from the same and previous months.
The ﬁrst row shows results for two value-weighted GMB portfolios, the second shows
results for two green portfolios, and the third shows results for two brown portfolios. The green and brown portfolios form the two legs of GMB. For each portfolio,
we form one version using small-cap stocks and a second version using large-cap
stocks. Small (large) stocks are those in the bottom (top) quartile of market capitalization, using monthly unconditional NYSE breakpoints. The column “Lg. - Sm.”
shows the difference between the large- and small-cap portfolios’ coeﬃcients. The
green and brown portfolios’ returns are market-adjusted, meaning we subtract from
each stock’s excess return the stock’s estimated market beta times the excess market return. Each regression has 68 observations and uses data from November 2012
through June 2018. Robust t-statistics are in parentheses.

C (same month)

C (prev. month)

Portfolio

Small

Large

Lg. - Sm.

Small

Large

Lg. - Sm.

GMB

2.83
(1.23)
0.03
(0.01)
-1.81
(-0.61)

3.91
(2.46)
2.27
(3.19)
-1.39
(-1.26)

1.08
(0.56)
2.24
(0.75)
0.42
(0.15)

7.49
(2.99)
-0.14
(-0.06)
-8.49
(-2.71)

2.79
(1.74)
0.62
(0.83)
-2.35
(-2.10)

-4.70
(-2.35)
0.75
(0.28)
6.14
(2.29)

Green
Brown

Separating the green and brown legs also reveals that
the effect of climate news on small stocks is limited to
brown stocks. The green leg’s coeﬃcients on both the
same-month and previous-month C are virtually zero
(t = 0.01 and −0.06, respectively), whereas the brown
leg exhibits negative reactions to both C’s. Only the
previous-month C is statistically signiﬁcant, not surprisingly, given the similar result for the small-cap GMB
spread.
7. The green factor
PST introduce an ESG factor and show that, along with
the market factor, the ESG factor prices assets in equilibrium. Motivated by that insight, we use stocks’ greenness
scores to construct a green factor, thereby continuing our
focus on the prominent role of “E” in ESG investing. In
this section, we explain the green factor’s construction and
show that it helps explain the recent underperformance of
value stocks. We also ﬁnd that the green factor, appropriately scaled, is empirically similar to GMB analyzed above.

Fig. 9. Weekly response of GMB to climate news: Large versus small
stocks. This ﬁgure plots the coeﬃcients βτ from a regression of largeminus-small GMB weekly percent returns on weekly shocks to climate
concerns lagged by τ weeks, for τ = 0, . . . , 7 weeks. The large-minussmall GMB portfolio is deﬁned in Table 8. Weekly shocks to climate concerns are prediction errors from rolling AR(1) models ﬁtted to the weekly
MCCC index. Dashed lines indicate 95% conﬁdence intervals.

7.1. Constructing the green factor
those anomalies are stronger among ﬁrms with lower media coverage.
Underreaction of stock prices to climate news may not
be limited to small stocks. Recall from the ﬁrst row of
Table 8 that large-cap GMB’s coeﬃcient on the previous
month’s C borders on signiﬁcance (t = 1.74). Stronger evidence of large-cap underreaction emerges when we examine GMB’s green and brown legs separately in the remaining rows of Table 8. For large stocks, both the green and
brown legs exhibit signiﬁcant reactions to C in the expected directions, i.e., positive for green and negative for
brown. However, the green leg’s signiﬁcant reaction occurs for the same month (t = 3.19), whereas the brown
leg’s signiﬁcant reaction occurs for the previous month
(t = −2.10). The other t-statistics for the large-cap legs are
insigniﬁcant.

We apply the PST methodology to construct the green
factor. PST show that the factor’s realizations can be estimated month by month by running cross-sectional regressions of market-adjusted excess stock returns on the
stocks’ greenness, with no intercept. The slope from one
such regression, which represents the green factor’s realization in month t, is given in Eq. (34) of PST as

fˆgt =

g’t−1 r˜te
g’t−1 gt−1

(8)

where r˜te ≡ r˜t − βm,t−1 r˜mt is the vector of stocks’ marketadjusted excess returns. Speciﬁcally, r˜t is the vector of
stocks’ returns in excess of the risk-free rate, r˜mt is the
market return in excess of the risk-free rate, and βm,t−1 is
the vector of stocks’ market betas, which we estimate from
421

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

rolling monthly regressions of individual stocks’ excess returns on excess market returns using up to 60 months (and
no less than 36 months) of data ending in month t.
Equation (8) implies that fˆgt , a linear combination of
the elements of r˜te , is the market-hedged excess return on
a portfolio containing long positions in green stocks (with
positive gi,t−1 ’s) and short positions in brown stocks (with
negative gi,t−1 ’s). In common terminology, the green factor is therefore the return on a “zero-cost” long-short factor. The green factor, however, differs in both motivation
and construction from typical zero-cost factors in the ﬁnance literature. Motivation for the latter factors is often
empirical, whereas PST derive the green factor theoretically, showing that assets are priced in equilibrium by two
factors, the market portfolio and the green factor. The construction of many zero-cost factors can be somewhat arbitrary, with stocks in the long and short legs often weighted
by market cap (e.g., Fama and French, 1993; Fama and
French, 2015). In contrast, the analytically derived green
factor weights each stock by its greenness, with green
stocks receiving positive weights and brown stocks negative weights. Also, the typical factor’s long and short returns are not market-hedged, whereas the green factor is
constructed with market-hedged excess returns.
In addition to market hedging and weighting stocks by
greenness, the green factor’s construction differs from that
of the typical zero-cost factor in another technical respect.
The typical factor is a difference between two unlevered
rates of return: the return on the long leg minus the return
on the short leg. The green factor is generally not a return
difference with the same simple form, at least not quite.
Speciﬁcally, we can rewrite Eq. (8) as fˆgt = fˆgreen,t − fˆbrown,t ,
with the contribution from green stocks being fˆgreen,t =

Fig. 10. Green factor. This ﬁgure compares the cumulative returns of the
green factor (solid line) and GMB (dashed line).
Table 9
Explaining value and momentum with the green factor. We estimate monthly time-series regressions of either HML (in columns
1 and 2) or UMD (in columns 3 and 4) on the excess market return and the green factor by using data from November 2012
to December 2020. Returns are in percent per month. Robust tstatistics are in parentheses.
Value
Constant
Mkt-RF

-0.71
(-1.93)
0.14
(1.18)

Green factor
Observations
R2

+ e+
gt−1
r˜t /(gt−1 gt−1 ), where g+
contains positive values of
t−1
gt−1 and r˜te+ contains those stocks’ excess returns. Similarly, the contribution to fˆgt from brown stocks is fˆ
=

98
0.04

-0.15
(-0.50)
0.07
(0.70)
-0.80
(-4.55)
98
0.35

Momentum
0.66
(1.92)
-0.37
(-3.75)

98
0.17

-0.06
(-0.22)
-0.27
(-3.14)
1.05
(6.18)
98
0.49

Recall that GMB is the green-versus-brown return
spread analyzed earlier. We scale the green factor to have
its monthly volatility match that of GMB over the sample
period, 1.99%. Fig. 10 plots the green factor’s cumulative return (solid line) along with that of the cumulative GMB return (dashed line). The plotted lines exhibit strong similarities in both cumulative performance and ﬂuctuations. The
monthly Sharpe ratios over the period are similar, 0.29 for
the green factor versus 0.33 for GMB, and the monthly correlation between the green factor and GMB is 0.72. Therefore, despite the various differences in construction between GMB, a typical zero-cost return, and our green factor, the latter is well viewed empirically as a green-versusbrown return difference over the sample period.21

brown,t

− e−
−gt−1
r˜t /(gt−1 gt−1 ), where g−
contains negative values
t−1
of gt−1 and r˜te− contains those stocks’ excess returns. Both
fˆgreen,t and fˆ
are market-hedged excess returns on
brown,t

portfolios, but generally those portfolios have differing degrees of implied leverage, because the sum of the elements
+
of gt−1
does not necessarily equal minus the sum of the el−
ements of gt−1
. In our data, for example, the latter sum’s
magnitude is about 1.9 times the former sum, on average.
Moreover, neither of those sums generally equals gt−1 gt−1
in magnitude, meaning that neither fˆgreen,t nor fˆ
is
brown,t

the unlevered excess return on the market-hedged portfolio of its underlying stocks. Note ﬁnally that gt−1 is meaningfully deﬁned only up to multiplication by a positive
scalar, whose value is irrelevant to satisfying the condition
in Eq. (3). The right-hand side of Eq. (8) can be multiplied
by any positive scalar without affecting the green factor’s
pricing ability. We choose the scalar to achieve a desired
volatility of the green factor, as explained next.20

7.2. Value and momentum
During our sample period, the market-adjusted monthly
alphas of HML and UMD are −71 bps and 66 bps, respectively, with t-statistics of −1.93 and 1.92, as shown in
columns 1 and 3 of Table 9. GMB’s signiﬁcant exposures
to value and momentum, noted earlier, prompt us to ask
a performance question in the reverse direction: To what

20
Note that the green factor’s greenness always equals one. Following
 r˜e has greenness
PST, a portfolio with market-adjusted excess return xt−1
t
 g

equal to xt−1
t−1 . The green factor in Eq. (8) has xt−1 = (1/gt−1 gt−1 )gt−1 ,


so the factor’s greenness equals (1/gt−1 gt−1 )gt−1 gt−1 = 1.

21
This result seems somewhat similar to an observation made independently by Lioui and Tarelli (2021).

422

Ľ. Pástor, R.F. Stambaugh and L.A. Taylor

Journal of Financial Economics 146 (2022) 403–424

extent can the strong performance of green stocks relative
to brown account for the last decade’s historic underperformance of value, or for the positive performance of momentum?
To address this question, we turn to PST’s two-factor
model, in which the factors are the market portfolio and
the green factor. HML’s and UMD’s alphas with respect
to the two-factor model, which are shown in columns 2
and 4 of Table 9, are much smaller in magnitude than
with just market adjustment. HML’s alpha becomes −15
bps instead of −71 bps; UMD’s alpha becomes −6 bps instead of 66 bps. The t-statistics shrink to −0.50 and −0.22.
These results show that nearly 80% of HML’s negative alpha, and all of UMD’s positive alpha, disappear after controlling for the green factor’s strong performance. Recognizing the brown nature of value stocks, and the green nature of growth stocks, thus helps us understand why the
value strategy experienced its worst decade ever in the
2010s.
The green factor also explains about two thirds of
the underperformance of an industry-neutral HML factor.22
This factor’s monthly CAPM alpha in our sample period
is −66 bps (t = −2.69), but the alpha drops to −23 bps
(t = −1.37) when we add the green factor to the regression. As with the original HML, the industry-neutral HML
has a signiﬁcantly negative loading on the green factor. See
the Appendix for details.
Recall that PST’s two-factor model includes the green
factor, not GMB, as the second factor alongside the market.
When we depart from the model and replace the green
factor with GMB, the two-factor alphas of both HML and
UMD move farther away from zero: HML’s alpha becomes
−32 bps instead of −15 bps, and UMD’s alpha becomes 21
bps instead of −6 bps. A full table is in the Appendix. The
green factor thus performs better than GMB in explaining
value and momentum over the past decade.
While exposure to the green factor explains most or all
of HML and UMD, the reverse is not true. The green factor’s strong performance over the last decade survives controlling for HML and UMD exposures. When we rerun the
regression reported in column 4 of Table 3, replacing GMB
with the green factor, fˆgt , we ﬁnd a positive and signiﬁcant alpha of 34 bps per month (t = 2.46). Details are in
the Appendix.

in climate concerns. Another proxy for the portfolio’s expected return, its implied cost of capital, is also consistently negative. A two-factor asset pricing model featuring
a theoretically motivated green factor absorbs much of the
historic underperformance of value stocks in the 2010s. Finally, our evidence suggests that small stocks underreact
to climate news.
Our results contain a warning for investigations of the
pricing of climate risk. We ﬁnd that green stocks typically outperform brown when climate concerns increase.
This result echoes similar ﬁndings by Choi et al. (2020),
Engle et al. (2020), and Ardia et al. (2021). Equilibrium expected returns of stocks that are better hedges against adverse climate shocks include a negative hedging premium
if the representative investor is averse to such shocks (e.g.,
PST). Empirically conﬁrming a climate risk premium, however, must confront the large unanticipated positive component of green stock returns during the last decade. Without accounting for those unexpectedly high returns on
stocks that appear to be good climate hedges, one could
be led astray. That is, one could infer that stocks providing
better climate hedging have higher expected returns, not
lower as theory predicts.
We use two approaches to estimate the green-minusbrown portfolio’s expected return, which we label the equity greenium. The ﬁrst approach, the implied cost of capital, has been applied by prior studies to different data.
The second approach, which removes unanticipated shocks
from the realized average return, seems novel. Future research can apply this latter approach to estimate expected
returns in other settings.

8. Conclusion

References

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data, we show that the portfolio’s recent outperformance
vanishes after removing the effects of unexpected increases

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22

Data Availability
We have uploaded our code and a portion of our data
to Mendeley Data. The remaining data are proprietary.

Supplementary material
Supplementary material associated with this article can
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2022.07.007.

We thank Peter Hecht of AQR for providing this factor’s returns.
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==> JFE15 - Real effects of climate policy: Financial constraints and spillovers.txt <==
Journal of Financial Economics 143 (2022) 668–696

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Real effects of climate policy: Financial constraints and
spillovers ✩
Söhnke M. Bartram a,b, Kewei Hou c, Sehoon Kim d,∗
a

University of Warwick, Warwick Business School, Finance Group, Coventry CV4 7AL, United Kingdom
Centre for Economic Policy Research (CEPR), London, United Kingdom
c
The Ohio State University, 820 Fisher Hall, 2100 Neil Avenue, Columbus, OH 43210, United States
d
University of Florida, Warrington College of Business, PO Box 117168, Gainesville, FL 32611–7168, United States
b

a r t i c l e

i n f o

Article history:
Received 23 October 2019
Revised 1 March 2021
Accepted 28 March 2021
Available online 23 June 2021
JEL classiﬁcation:
G18
G31
G32
Q52
Q54
Q58

a b s t r a c t
We document that localized policies aimed at mitigating climate risk can have unintended
consequences due to regulatory arbitrage by ﬁrms. Using a difference-in-differences framework to study the impact of the California cap-and-trade program with U.S. plant-level
data, we show that ﬁnancially constrained ﬁrms shift emissions and output from California
to other states where they have similar plants that are underutilized. By contrast, unconstrained ﬁrms do not make such adjustments. Overall, unconstrained ﬁrms do not reduce
their total emissions, whereas constrained ﬁrms increase their total emissions after the
cap-and-trade rule, undermining the effectiveness of the policy.
© 2021 Elsevier B.V. All rights reserved.

Keywords:
Climate policy
California cap-and-trade
Financial constraints
Internal resource allocation
Regulatory arbitrage
Spillover effects

✩
We thank William Schwert (the editor) and an anonymous referee as well as Ian Appel (discussant), Tony Cookson (discussant), Sudipto Dasgupta,
Mark Flannery, Zhenyu Gao (discussant), Stefano Giglio, Xavier Giroud (discussant), Christopher James, Andrew Karolyi, Michelle Lowry, Shema Mitali,
William Mullins (discussant), Peter Nagle (discussant), Micah Oﬃcer (discussant), Steven Ongena (discussant), Paige Ouimet (discussant), Nora Pankratz
(discussant), Jay Ritter, Sophie Shive, Laura Starks, René Stulz, Yuehua Tang, Sheridan Titman, Baolian Wang, Jeffrey Wurgler, Deniz Yavuz (discussant),
conference/seminar participants at the 2020 American Finance Association Annual Meeting, the 2019 Western Finance Association Annual Meeting, the
2019 European Finance Association Annual Meeting, the 2019 European Economic Association/Econometric Society European Meetings Annual Meeting, the
2019 Royal Economic Society Annual Meeting, the 2019 Commodity and Energy Markets Association Annual Meeting, the University of Oklahoma Energy
and Commodities Finance Conference, the Chinese University of Hong Kong-Shenzhen Sustainable Finance Forum, the University of Connecticut Finance
Conference, the Asian Bureau of Finance and Economic Research/Center for Economic Policy Research/Chinese University of Hong Kong Symposium, the
European Bank for Reconstruction and Development/European Central Bank/Center for Economic Policy Research Symposium, the Florida State University SunTrust Conference, the Global Research Alliance for Sustainable Finance and Investment Conference, the International Symposium on Environment
and Energy Finance Issues Conference, the Ecole des Hautes Etudes Commerciales du Nord Finance of Climate Change Conference, the 2019 German Economic Association Conference, Banque de France, Collegio Carlo Alberto, Neoma Business School, The Ohio State University, University of Florida, University
Paris-Dauphine, and University of Warwick for valuable comments and suggestions. We are grateful for funding from the Risk Institute at The Ohio State
University Fisher College of Business and the Society of Risk Management and Regulation. Bartram also acknowledges ﬁnancial support from the British
Academy/Leverhulme Trust and Collegio Carlo Alberto, the Klaus Liebscher Award by the Oesterreichische Nationalbank, and the Humboldt Research Award
by the Alexander von Humboldt Foundation. We also thank Shu Zhang for excellent research assistance.
∗
Corresponding author.
E-mail address: sehoon.kim@warrington.uﬂ.edu (S. Kim).

https://doi.org/10.1016/j.jﬁneco.2021.06.015
0304-405X/© 2021 Elsevier B.V. All rights reserved.

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

1. Introduction

that unconstrained ﬁrms adjust emissions in response to
the new regulation, either in California or in other states.
The differences in responses between constrained and
unconstrained ﬁrms are statistically signiﬁcant across a
host of ﬁnancial constraint measures.
Our economic hypothesis is that ﬁnancially constrained
ﬁrms reallocate their emissions away from California to
other states in the face of heightened regulatory costs that
alter the relative net expected returns across plants. The
cost of external capital for constrained ﬁrms renders profitable emission projects mutually exclusive, and they reallocate as net returns from emitting at alternative locations become relatively more attractive than the returns
from continuing to emit in California after the regulatory
change.4 Based on back-of-the-envelope calculations, the
additional costs of emissions to constrained ﬁrms under
the California cap-and-trade rule is equivalent to a 9% increase in tax expenses or a 4% increase in interest expenses. For the subset of ﬁrms that reallocate their emissions the most in response to the policy, the impact of
the policy on costs is more severe, equivalent to a 15%
(11%) increase in taxes (interest expenses). We posit that
this increase in the regulatory cost distorts the ranking
of net returns on capital across plants, incentivizing constrained ﬁrms to reallocate even though emitting in California might remain proﬁtable.
Our conjecture and ﬁndings are consistent with criticisms by the media and small business owners that
the regulatory costs from the cap-and-trade rule are not
large enough to constitute signiﬁcant deterrents to emissions for ﬁrms with deep pockets, but raise the burden
for less ﬁnancially capable players causing emission leakages.5 Anecdotal evidence also supports the economic importance of the spillover effects we uncover. For example, a major petroleum products company recovering from
large operating losses after the ﬁnancial crisis in the early
2010s strongly objected to the implementation of the capand-trade rule. It rallied other ﬁrms and warned citizens
against the legislation with placards at their California gas
pumps that it would cost jobs and consumer welfare. After the rule went into effect at the beginning of 2013, the
company reduced emissions by one of its largest Califor-

Climate change is among the most intensely debated
socioeconomic issues of current times.1 As a response to
potential catastrophe risks from climate change, governments around the world are pushing for various forms
of regulations to curb greenhouse gas emissions.2 However, no consensus has been reached on optimal policy
approaches; thus, climate policies are highly fragmented
across the jurisdictions in which they are designed and implemented. More importantly, whether such localized yet
uncoordinated policies are able to internalize potential externalities that may impede addressing climate change as
a global phenomenon or simply distort allocations in the
economy is unknown. An example is the U.S., where at
the beginning of 2013, California became the ﬁrst and only
state to put a comprehensive mandatory carbon regulation
in place in the form of a cap-and-trade system that applies
universally to all industrial greenhouse gas emissions.3
Exploiting the introduction of the California cap-andtrade rule, we investigate the internal resource allocation
responses by ﬁrms and the real but unintended spillover
effects of localized climate policies that arise from the importance of ﬁnancial constraints. Our study helps us understand the interplay between climate policy and ﬁrm behavior, and informs policymakers regarding the effectiveness
of climate regulation.
Using detailed data on plant-level greenhouse gas
emissions from mandatory reporting to the United States
Environmental Protection Agency (EPA) hand-matched to
Compustat covering 2,806 industrial plants of 511 publicly
listed ﬁrms over the period 2010 to 2015, we show that the
2013 California cap-and-trade rule has real spillover effects
across the United States due to ﬁrm ﬁnancial constraints.
Speciﬁcally, we employ a difference-in-differences (DID)
framework and ﬁnd that while ﬁnancially constrained
ﬁrms reduce greenhouse gas emissions from plants located in California by 33% relative to plants in other states,
they signiﬁcantly increase emissions of plants in other
states by 29% more than those owned by ﬁrms without
a presence in California. By contrast, we ﬁnd no evidence

1
The economic consequences of climate change have recently garnered much interest among ﬁnancial economists. See, among others, Addoum, Ng, and Ortiz-Bobea (2020), Akey and Appel (2021),
Bernstein, Gustafson, and Lewis (2019), Engle, Giglio, Kelly, Lee, and
Stroebel (2020), Forster and Shive (2020), Krueger, Sautner, and
Starks (2020), and Painter (2020).
2
See Fig. A.1 in the Internet Appendix for recent trends in global temperatures and carbon emissions from the use of fossil fuels, and Fig. A.2
for a map of implemented or planned carbon pricing regulations around
the world, as of 2016.
3
Most climate regulations in the U.S. thus far have left states with
much discretion in implementing federal standards (e.g., Clean Air Act)
or have largely been conﬁned to the electricity production industry.
Since 2009, nine states (Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, New York, Rhode Island, and Vermont) have
been part of the Regional Greenhouse Gas Initiative, a cap-and-trade program that applies only to fossil fuel power plants generating 25MW or
more. States have also been adopting varying versions of Renewable Portfolio Standards requiring increased production of energy from renewable
energy sources. From 2003 to 2010, the Chicago Climate Exchange was
available for voluntary emissions trading, but ceased trading due to inactivity.

4
This conjecture is rooted in studies of the relationship between ﬁnancial frictions and the value of internal capital allocation, which argue that
the contribution of internal capital markets to ﬁrm value, and hence, the
value of corporate diversiﬁcation is greater when external ﬁnancial constraints are higher (see Billett and Mauer, 2003; Matvos and Seru, 2014;
Matvos, Seru, and Silva, 2018). Research documents that the propagation
of economic shocks through ﬁrm internal networks are stronger with
tighter ﬁnancial constraints, consistent with optimal resource reallocations (see Giroud and Mueller, 2019).
5
In July 2017, as the cap-and-trade rule was about to be extended, the
California state executive director of the National Federation of Independent Business stated on behalf of 22,0 0 0 small business members that as
“California has been experimenting with cap-and-trade policies… jobs are
moving to neighboring states with much more relaxed laws… Some believe cap-and-trade only impacts big businesses that buy and sell carbon
credits, but the truth is that small businesses and consumers all pay the
ultimate price.” An October 2017 Wall Street Journal opinion piece, “The
fatal ﬂaw in California’s cap-and-trade program” by Richard Sexton and
Steven Sexton, criticizes the cap-and-trade rule for its inability to effectively curtail carbon leakage and its failure to levy large enough burdens
to large ﬁrms.

669

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

nian reﬁneries by 8% over the next three years but sharply
increased emissions by some of its largest reﬁneries in
other states, for example, Louisiana and Texas, by more
than 10%.
We explore the economic mechanisms for our results
and ﬁnd that constrained ﬁrms reallocate their emissions
from their plants in California primarily to plants with
similar functions in other states, rather than to plants
that play different roles within their organizational structure. We also show that constrained ﬁrms are more likely
to carry excess capacity at their plants, consistent with
the hangover of surplus capacity built up during favorable
times (see Von Kalckreuth, 2006; Dasgupta et al., 2019). In
response to the cap-and-trade rule, they tend to reallocate
their emissions toward plants outside of California with
greater excess capacity, avoiding large ﬁxed costs associated with capacity adjustments. We ﬁnd that such emission reallocations across plants are the result of changes in
production activity rather than production eﬃciency.
Constrained ﬁrms also reallocate their emissions more
toward states that are nearby or less regulated, and more
likely to do so when they had invested little in abatement
technologies prior to the regulation. Finally, we provide evidence that ﬁrms affected by the regulation do not reduce
their ﬁrm-wide emissions. In fact, constrained ﬁrms increase their total emissions by as much as 21%. Overall, our
main results suggest corporate internal reallocation of pollutive activities and resources to avoid regulatory costs in
the face of limited access to external ﬁnancing, highlighting the hidden costs of environmental policies through ﬁnancial channels.
We interpret our ﬁndings as optimal responses by ﬁrms
to increased regulatory costs as a function of their ﬁnancial constraints. Hence, we are comfortable with the
fact that ﬁrms are not randomly assigned their constraint
characteristics, insofar as the assignment is not related to
whether ﬁrms own plants covered by the California capand-trade rule. Nevertheless, we exclude a number of alternative channels that may confound the interpretation of
our results. To eliminate the possibility of reverse causality
whereby ﬁnancial constraints are affected by the introduction of the cap-and-trade rule or ﬁrm responses to it, or
omitted variables simultaneously affecting constraints and
ﬁrm responses, we measure ﬁnancial constraints at least
three years before the effective start date of the cap-andtrade rule.
We also rule out explanations concerning observed or
unobserved plant characteristics such as their industry
purpose, maximum capacity, or technological obsoleteness,
by controlling for plant ﬁxed effects, and preclude the effects of common time trends within plant industries by
controlling for industry-by-year ﬁxed effects. Finally, we
also control for ﬁrm characteristics that may be related to
how much greenhouse gas ﬁrms are prone to release, such
as ﬁrms’ asset size, investment opportunities, proﬁtability,
leverage, or accumulated research and development (R&D)
stock. In short, we set a high bar to refute our conclusion
that the cap-and-trade rule entails spillover effects due to
the internal reallocation by ﬁnancially constrained ﬁrms.
Our study contributes to a recent and growing body
of research on climate risk and ﬁrm behavior by focusing

on the internal allocation of plant-level emissions within
ﬁrms driven by their ﬁnancial constraints, thus providing
a unique channel for the real effects of climate regulation. In particular, our ﬁndings highlight the importance
of climate-related regulatory risks for ﬁrms, consistent
with concerns by institutional investors (see Krueger et al.,
2020). Also closely related to our work are recent papers
linking ﬁnancial incentives and corporate environmental
policies. For example, Forster and Shive (2020) ﬁnd that
short-termist pressure for ﬁnancial performance from outside investors force public ﬁrms to emit more greenhouse
gases than private ﬁrms. Kim and Xu (2020) show that
ﬁnancial constraints exacerbate toxic pollution by ﬁrms
due to the costs of waste management, and this effect is
stronger when regulatory monitoring is weak. In a similar vein, Akey and Appel (2021) ﬁnd that ﬁrm subsidiaries
are more likely to increase toxic emissions when parent
companies have better liability protection for their subsidiaries’ environmental clean-up costs, consistent with the
binding effects of higher ﬁnancial burdens associated with
abatement. Complementing these studies, our paper highlights the reallocative effects of ﬁnancial constraints that
induce ﬁrms to internally shift their pollutive resources
across plants under heightened regulatory costs, which in
turn distort the outcome of regional environmental policies. Interestingly, while Akey and Appel (2021) ﬁnd the effects of limited liability are driven by lower “green” investments rather than by reallocation across plants, we show
that the reallocations of greenhouse gas emissions across
plants are prominent responses by ﬁrms to climate policy.
More broadly, our study makes important contributions
to the debate on policy remedies to climate change and
the effects they have on economic activity and welfare
(see Nordhaus, 1977a; 1977b; Fabra and Reguant, 2014;
Marin et al., 2018). Part of this debate focuses on coordination problems of locally implemented climate policies
and the impact of their externalities on global emission
levels (see Nordhaus and Yang, 1996; Martin et al., 2014;
Nordhaus, 2015; Fowlie et al., 2016; Bushnell et al., 2017).
The severity of such externalities depends on the costs
imposed by regulations, which are challenging to identify (see Jorgenson and Wilcoxen, 1990; Jaffe et al., 1995).
Recent studies ﬁnd that environmental regulations can
have costly effects on industrial economic activity, employment, and productivity (see Becker and Henderson, 20 0 0;
Greenstone, 2002, Greenstone et al., 2012, Ryan, 2012;
Walker, 2011; 2013).6 These costs imply that local climate
policies can result in unintended and signiﬁcant spillover
effects in the form of emission leakages, undermining
their objectives to prevent global warming.7 Building on
this literature, we utilize mandatorily reported data on
plant-level carbon dioxide equivalent (CO2 e) greenhouse
gas emissions in a DID analysis to explore both within-

6
See also Currie and Walker (2019), Schmalensee and Stavins (2019),
and Keiser and Shapiro (2019) for synopses of the impacts of the Clean
Air and Water Acts.
7
See Ederington, Levinson, and Minier (2005), Levinson and Taylor (2008), Wagner and Timmins (2009), and Ben-David, Jang, Kleimeier,
and Viehs (2020) for aggregate-level or survey-based analysis of such
spillover effects.

670

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

and between-plant variation in emissions induced by a
local policy whose clear mandate is to curb greenhouse
gas emissions. Our analysis identiﬁes ﬁrm ﬁnancial constraints as an important economic channel that generates unequally distributed incentives to reallocate emissions and productive activities.
Policy remedies to climate change are heatedly debated.
Such policies have important implications for the behavior of industrial ﬁrms and how they respond to regulatory
frictions, which are of key interest to ﬁnancial economists.
Understanding these effects is important to guide policymakers to internalize externalities that may otherwise result in unintended consequences and to more effectively
coordinate solutions to climate change. Given the importance of a sound evaluation of the eﬃcacy and real effects
of climate policy, this paper aims to take the debate on climate change, climate policy, and corporate environmental
responsibility one step closer in this direction.

free allowances to emit 350,0 0 0 t of greenhouse gas, which
is less than what constrained ﬁrms emitted from their
plants in California. The aggregate magnitudes of market
transactions are comparable to those of the free allocations
or auctions, in which the transaction prices not only exceed the contemporaneous auction settlement prices but
also steadily increase over time. Increasing allowance futures prices also corroborate these trends.10
Plants that emit more than the free allowance must acquire the rights to emit the difference either by bidding in
auctions or buying them from other market participants.
For our sample of constrained ﬁrms with such high emission plants, the cost of doing so amounts to $20 million,
based on a back-of-the-envelope calculation assuming an
average price on carbon of $12 per metric ton. This cost
is non-trivial, and is in the order of 9% of the tax expense
or 4% of the interest expense of the average ﬁrm. For the
top 10 ﬁrms that reallocate their emissions the most in response to the policy, the incremental cost is equivalent to
a 15% increase in their tax expenses or an 11% increase in
their interest expenses.
Together, the increase in costs of emitting greenhouse
gases due to the introduction of the California cap-andtrade rule is substantial and suﬃciently high for ﬁnancial constraints to matter. Given the magnitude of the estimated costs, we conjecture that although it may be large
for ﬁrms with high incremental ﬁnancing costs, it may not
be important for ﬁrms with deep pockets. This possibility
motivates our hypotheses for how the California cap-andtrade rule will affect ﬁrms’ greenhouse gas emissions, and
the role of ﬁnancial constraints as the economic channel.
We elaborate on the hypotheses in the following section.

2. Background and hypotheses development
2.1. California’s cap-and-trade program
At the beginning of 2013, the state of California’s Air
Resources Board started enforcing a state-wide carbon capand-trade rule to reduce greenhouse gas emissions. Covering all electric power plants and industrial plants that emit
25,0 0 0 t or more of CO2 e per year, the California cap-andtrade rule was the ﬁrst multi-sector cap-and-trade program in North America.8 The cap-and-trade rule is based
on an allocation of capped allowances with speciﬁc year
vintages and the market trading of those allowances. At
the allocation stage, allowances are distributed to plants
through a combination of quarterly held auctions and free
allowances. Firms are then required to pay off their plants’
emissions using these and additional allowances they may
buy via market transactions, according to a vintage-speciﬁc
schedule laid out by the program.9 Given this institutional
structure, the question is whether the cap-and-trade rule
constitutes a signiﬁcant regulatory cost for affected ﬁrms.
We demonstrate in a number of ways that it likely does
for ﬁrms that are ﬁnancially constrained.
According to statistics published by the California Air
Resources Board, current vintage allowances are completely sold out in every quarterly allowance auction starting in November 2012, bids outnumber available current
vintages, and the settlement prices for current vintages are
always higher than the initial reserve price despite the reserve price being increased every year. Furthermore, the
free allowance allocations leave substantial room for further incentives to bid in auctions or purchase at market
prices. For example, in 2014, the average plant received

2.2. Hypotheses development
Economic theory posits that proﬁt maximizing ﬁrms
allocate resources to where net returns are positive as
long as they are ﬁnancially unconstrained. If ﬁrms are ﬁnancially constrained, however, they can only allocate resources to a limited set of proﬁtable options among several mutually exclusive investment opportunities. For these
ﬁrms, the distribution and ranking of the net returns of
projects are important, even when they are all economically viable. Regional regulation, such as the statewide
cap-and-trade rule in California, introduces perturbations
to the distribution of net returns across regions and thus
motivates resource reallocation by ﬁnancially constrained
ﬁrms. Our hypotheses concern the direction and magnitude of this reallocation.
In our context, ﬁrms that have a plant presence both in
California and in other states are geographically diversiﬁed,
and thus can use their internal networks to reallocate resources when the proﬁle of net expected returns change
across their geographic segments due to the increase in
regulatory costs from the new cap-and-trade rule. How-

8
In 2014, the California cap-and-trade program was linked with the
cap-and-trade program in Quebec, Canada. As of 2015, total aggregate
emissions covered by the rule in California (Quebec) was approximately
400 (60) million metric tons. In 2015, the program was extended to fuel
distributors emitting more than 25,0 0 0 metric tons.
9
Emissions in any year are required to be paid off in full within the
following calendar year. Firms can purchase future vintage allowances in
advance but are not allowed to use future vintage allowances to pay for
current emissions.

10
See the Internet Appendix for publicly available aggregate data on
quarterly allowance auctions, free allocations, and market transactions
made available by the California Air Resources Board (Table A.2), as well
as the time series of emission allowance futures prices for each vintage
(Fig. A.3).

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Journal of Financial Economics 143 (2022) 668–696

ever, if ﬁrms have access to frictionless borrowing, they
would accommodate the change without shifting resources
across plants, since their costs of external capital would
be low enough to afford all emission projects as long as
their net expected returns remain positive. By contrast, ﬁnancially constrained ﬁrms that are geographically diversiﬁed would reallocate resources away from plants that are
subject to higher regulatory costs to plants they own elsewhere, as their costs of external capital would be too high
to ﬁnance costly emissions when the net returns from internally reallocating their resources would be greater.
To further clarify why ﬁnancially unconstrained ﬁrms
would not reallocate emissions whereas constrained ﬁrms
would, note a natural corollary to their capital budgeting
decisions: unconstrained ﬁrms are likely to be operating
at capacity wherever producing is proﬁtable, whereas constrained ﬁrms are likely to have excess capacity at relatively less proﬁtable locations. Several studies provide empirical support for this notion. Von Kalckreuth (2006), for
example, uses U.K. survey data to show that ﬁnancially
constrained ﬁrms have more persistent capacity gaps.
Dasgupta et al. (2019) demonstrate that constrained ﬁrms
are more likely to carry an inventory surplus over to unfavorable times. As such, to the extent that the reallocation
of emissions is achieved by shifting production resources,
unconstrained ﬁrms have neither the need nor means to
reallocate emissions across plants they have in place as
long as emitting in California remains proﬁtable. By contrast, constrained ﬁrms ﬁnd it necessary and possible to
internally shift emissions by closing capacity gaps without incurring large and ﬁxed capacity adjustment costs. Indeed, we document that plants owned by ﬁnancially constrained ﬁrms have greater excess capacity than plants
owned by unconstrained ﬁrms, and that they close capacity gaps at non-California plants as they reallocate their
emissions.
Fig. 1 illustrates our intuition by plotting the revenues
and costs from varying quantities of emissions. Suppose
an imperfectly competitive market with downward sloping
marginal (average) revenues mr (ar) and costs that depend
on the locale of production. Firms that operate a plant in
California face marginal (average) costs mcca (acca ) and an
optimum point I with average costs a and emission quantity d. The net return from the California plant is equal to
the size of the blue area bordered by a and d, denoted A.
Once the California cap-and-trade rule is implemented, the
cost functions move upward to mc’ca and ac’ca for quantities above the amount of the free allocations, shifting the
optimum to I’, where average costs are higher at b and
quantity is lower at e. The net return remains positive, but
it is smaller than before and equal to the size of the lighter
blue area bordered by b and e, denoted A’. Because the net
return is still positive, ﬁrms with unlimited access to capital will continue to emit despite the higher costs, as they
will continue to allocate capital to all proﬁtable projects.11

However, I’ is an undesirable equilibrium for ﬁnancially
constrained ﬁrms because the net returns are smaller than
before (i.e., A’ < A), so they reallocate their resources from
California to other states where there are investment opportunities with larger net returns that previously did not
seem as attractive. For example, if the costs from emitting
in other states follow cost functions mcoth and acoth , constrained ﬁrms will reallocate from I to I’’ because the size
of its net return, denoted B, is greater than A’ (i.e., A’ < B
< A). On the other hand, I and I’’ are not mutually exclusive options for unconstrained ﬁrms to begin with, so they
would have invested in both projects ex ante because they
are both proﬁtable. Therefore, unconstrained ﬁrms would
not reallocate, because the relative ranking of I’ and I’’ is irrelevant for them. Empirically, these predictions imply that
the cap-and-trade rule will push constrained ﬁrms to not
only reduce emissions from plants in California by more
than unconstrained ﬁrms (d for constrained ﬁrms vs. d–e
for unconstrained ﬁrms), but also increase emissions from
plants in other states by more (f for constrained ﬁrms vs.
no increase for unconstrained ﬁrms), under the hypothetical cost functions for California and other states.12
In other words, the value of internal reallocation would
be greater for ﬁnancially constrained ﬁrms when the costs
of emissions are increased due to policy changes. The
motivation of this hypothesis is grounded in the literature in ﬁnance on the value of internal capital markets in the presence of ﬁnancial frictions (for early studies, see Gertner et al., 1994; Lamont, 1997; Stein, 1997;
Shin and Stulz, 1998). Research in this literature shows
that the contribution of internal capital markets to ﬁrm
value and hence the value of corporate diversiﬁcation is
greater when external ﬁnancial constraints are higher, for
example, when large dislocations occur in ﬁnancial markets (see Billett and Mauer, 2003; Matvos and Seru, 2014;
Matvos et al., 2018). Our hypothesis is also consistent with
Giroud and Mueller (2019), who ﬁnd that the propagation of economic shocks through ﬁrm internal networks is
stronger with tighter ﬁnancial constraints, consistent with
a model of optimal within-ﬁrm resource allocation.
This economic rationale leads to three key research
questions regarding the effect of climate policy on ﬁrms:
(1) Does local climate policy (e.g., the California cap-andtrade rule) affect ﬁrms’ allocations of internal resources
and greenhouse gas emissions across plants? (2) Are ﬁrms’
reallocation responses to policy affected by their ﬁnancial constraints? (3) Do such policies achieve their goal of
reducing aggregate emissions? In the following sections,
we describe the data and construction of our sample, and

that the acceleration in GDP growth compared with the previous period
is greater in California than in other states.
12
In Fig. 1, the cost curve in other states lie below that of California.
If they did not, and if mcoth were identical to mcca , the ﬁgure would still
suggest a sharper decrease in California emissions by constrained ﬁrms
than by unconstrained ﬁrms, and a corresponding sharp increase in emissions from other states by constrained ﬁrms by the amount of d instead of
f. The central prediction that motivates our main hypothesis remains unchanged, and unconstrained ﬁrms would still not reallocate. Fig. 1, however, raises the possibility that the overall level of ﬁrm emissions could
increase as a result of the regulation, due to the reallocation by constrained ﬁrms. We formally test this hypothesis in Section 5.3.

11
The assumption that the net return from emitting in California after the implementation of the cap-and-trade rule remains positive is supported by state-level GDP growth data. In Table 8, we document that California not only exhibits higher growth than other states by a large margin during the years when the cap-and-trade rule is in effect, but also

672

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Journal of Financial Economics 143 (2022) 668–696

Fig. 1. Economic framework. The ﬁgure illustrates the economic channel of the main hypotheses. Revenues and costs (p) are plotted on the vertical axis,
and emissions and production quantities (q) are plotted on the horizontal axis. Marginal and average revenue curves (solid black), denoted mr and ar, are
downward sloping, consistent with an imperfectly competitive market. Marginal and average cost curves are plotted for three scenarios. In particular, mcca
and acca represent the pre-cap-and-trade costs of producing and emitting in California. mc’ca and ac’ca denote the post-cap-and-trade costs of emitting in
California, which are tilted upward from the pre-policy curves for emission quantities above the free allocation amount. mcoth and acoth are the cost curves
should ﬁrms reallocate their emissions exceeding the free allocation amount to other states. I, I’, and I’’ denote the equilibrium with the optimal amount
of emissions in California before the cap-and-trade rule, in California after the cap-and-trade rule, and in other states, respectively. The rectangular shaded
areas A and A’ show the proﬁts for producing in California before and after the cap-and-trade rule, respectively, whereas the shaded area B shows the
proﬁt of producing in other states.

formulate the empirical methodology that we use to test
these hypotheses.

tion on GHGs Tool (FLIGHT), providing plant-level information on the identity, geographic location, parent company
ownership, North American Industry Classiﬁcation System
(NAICS) industry code, and the quantity of greenhouse gas
emissions of the plant on an annual basis starting in 2010.
Our sample period extends from 2010 to 2015 — three
years before and after the beginning of the California capand-trade program — and the initial sample covers approximately 9,200 unique plants.14
To analyze the impact of ﬁnancial constraints, we handmatch the EPA plant-level dataset with annual ﬁnancial
accounting data from Compustat based on the names of
parent companies. To be included in our sample, we require that ﬁrms have positive total assets and sales greater
than $10 million. Although utilities and governmental ﬁrms

3. Data and sample
3.1. Data
In October 2009, the EPA published the Greenhouse Gas
Reporting Program (GHGRP) mandating that sources that
emit 25,0 0 0 t or more of CO2 e greenhouse gases per year
must report their emissions, compliant with the estimation methodologies prescribed by the EPA.13 Once the submitted information is veriﬁed by the EPA, the data are
made publicly available through the Facility Level Informa13
Although GHGRP reporters have some discretion over which of the
EPA-approved methods to use when reporting emission quantities, this
selection is unlikely to affect our conclusion, as the reporting responsibility falls to the plant rather than the parent company. Moreover, it is
diﬃcult to explain why plants would change reporting methods resulting
in not only a decline in reported emissions from California, but also an
increase in reported emissions from other states.

14
We do not include the years 2016 and 2017, which include potentially
confounding events such as the signing of the Paris Agreement and the
subsequent withdrawal by the U.S., as well as additional legislative packages signed by the state of California seeking to reduce greenhouse gas
emissions and other air pollutants.

673

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

may be signiﬁcant greenhouse gas emitters, common measures of ﬁnancial constraints are not likely to elicit strategic responses to climate policies from such ﬁrms in the
same way as they do for typical industrial ﬁrms, because
they are regulated locally by local public service commissions and also federally regarding interstate service transmissions. For this reason, we exclude not only ﬁnancial
ﬁrms (Standard Industrial Classiﬁcation codes (SIC) 60 0 0–
6999), but also utilities (SIC 4900–4999) and governmental
ﬁrms (SIC 90 0 0–9999).15 The ﬁnal sample is an unbalanced
panel of 2,806 plants of 511 ﬁrms over the sample period
2010 to 2015.
We use Compustat data to construct various variables
to be used as controls or to measure ﬁnancial constraints
such as total assets, Tobin’s q, proﬁtability, short-term debt,
long-term debt, cash, cash ﬂow, dividends, repurchases,
long-term (i.e., bond) and short-term (i.e., commercial paper) credit ratings, property, plant, and equipment (PP&E),
and capital expenditures. We take the difference between
the observation year and founding year as ﬁrm age as
in Jovanovic and Rousseau (2001). We also compute R&D
stock using the perpetual inventory method, where we initialize R&D capital stock at zero and accumulate R&D expenses with a depreciation rate of 15% (see Hall et al.,
2005). All continuous ﬁnancial variables are winsorized at
the top and bottom 1%.
In addition, we obtain plant-level sales and employment data from the National Establishment Time Series
(NETS) database produced by Walls & Associates. This survivorship bias-free data provide historical information on
publicly listed ﬁrms’ sales and employment at each of its
establishments on an annual basis from 1990 to 2015. We
take plant-level sales as a proxy for the value of its annual
production output. We also compute excess capacity as the
end-of-current-year number of employees at the plant per
million dollars of sales generated by the plant in the current year. A plant that has a higher employment-to-output
ratio than the median plant is classiﬁed as having high excess capacity in a given year.
We manually link the three datasets by matching on
parent company names. To ensure a high-quality match,
we corroborate the matching process with Capital IQ and
extensive google searches, to take into account parentsubsidiary linkages in case parent company names are
recorded differently in the three datasets. Plant-level data
are then matched on the address, latitude, longitude, and
industry of the plant, as well as the identity of the parent
company each year. To complement plant-level sales and
employment data, we further use the Compustat Segment
database to apportion residual segment sales and employment to plants if they are the only remaining plant in
an industry segment that cannot be matched to the NETS
data. Finally, we equally apportion residual ﬁrm sales and
employment to plants that still do not have valid sales or
employment data.
Lastly, we map vertical (i.e., upstream and downstream)
and horizontal linkages across plants within ﬁrms using

plant-level NAICS codes and the Bureau of Economic Analysis (BEA) input-output accounts. We start by computing
the share of NAICS goods produced or consumed by NAICS
industries using the 2007 make and use tables. When a
plant’s NAICS industry consumes or produces more than
10% of another plant’s NAICS industry goods, where the
two NAICS industries are distinct at the two-digit NAICS
level, these two plants are classiﬁed as vertically linked to
each other. If two plants have the same NAICS code, they
are classiﬁed as horizontally linked. If two plants belong to
distinct two-digit NAICS industries that do not consume or
produce more than 10% of the other industry’s goods, they
are classiﬁed as unrelated.
3.2. Measuring ﬁnancial constraints
To establish an economic channel through which ﬁnancial constraints determine how ﬁrms respond to climate
policy, measuring ﬁnancial constraints is a critical step in
our study. Based on ﬁnancial accounting information from
Compustat, we construct six alternative measures of ﬁnancial constraints commonly used in the literature. They are
the Kaplan-Zingales index (see Kaplan and Zingales, 1997;
Lamont et al., 2001), the Hadlock and Pierce (2010) index, the Whited and Wu (2006) index, ﬁrm size, payout,
and credit (i.e., bond or commercial paper) ratings (see
Almeida et al., 2004). In addition, we combine the six
proxies into a composite indicator as our primary measure
of ﬁnancial constraints.
For the Kaplan-Zingales, Hadlock-Pierce, and WhitedWu indices, as well as ﬁrm size and payout, ﬁrms are
assigned percentile rankings based on each measure every year. We then use the six years strictly before our
sample period (i.e., ﬁscal years 20 03–20 08) to compute
time series average percentile rankings for each ﬁrm and
each measure. Based on these average rankings, ﬁrms are
categorized as ﬁnancially constrained if they are above
the median for the Kaplan-Zingales, Hadlock-Pierce, and
Whited-Wu indices, and if they are below the median
for ﬁrm size and payout. For credit ratings, we ﬁrst examine long-term bond ratings and short-term commercial
paper ratings separately. If a ﬁrm did not have a bond
(commercial paper) rating as of the most recent year of
the 20 03–20 08 pre-sample period but had, on average,
positive long-term (short-term) debt during this period,
the ﬁrm is categorized as “long-term (short-term)” ﬁnancially constrained. If the ﬁrm did have a bond (commercial paper) rating as of the most recent year of the sixyear pre-sample period or had, on average, zero long-term
(short-term) debt during this period, the ﬁrm is “longterm (short-term)” unconstrained. If a ﬁrm is either longterm or short-term credit constrained, the ﬁrm is classiﬁed as constrained based on ratings and unconstrained
otherwise.
For the composite indicator of ﬁnancial constraints, a
ﬁrm is categorized as constrained if the majority of the six
proxies classify the ﬁrm as being constrained; otherwise,
the ﬁrm is unconstrained. Since ﬁrms are classiﬁed strictly
before they enter the sample period, we rule out reverse
causality concerns or omitted variables simultaneously affecting the evolution of constraints and ﬁrm responses to

15
We conduct a robustness test by including utilities in our sample and
ﬁnd similar results as in our baseline analysis (see Table 3).

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Journal of Financial Economics 143 (2022) 668–696

policy. A detailed list of all variable names and deﬁnitions
is included in the Internet Appendix (Table A.1).

and 74%, respectively), although unconstrained ﬁrms are
more likely to be diversiﬁed given the larger number of
plants they operate both in California and in other states.
Notwithstanding, the median ﬁrms with California plants
are geographically dispersed for both groups of ﬁrms. For
almost all plants, ownership is concentrated in one ﬁrm;
that is, rarely do multiple ﬁrms share and operate the
same plant.
Panel B of Table 1 shows the distribution of plantlevel emissions, excess capacity, sales, and employment for
the entire sample as well as separately for California and
non-California plants owned by geographically diversiﬁed
ﬁrms. Similar to ﬁrm-level emissions, plant emissions are
also positively skewed. Interestingly, constrained ﬁrms are
more emission intensive at the plant level, despite having
lower sales and fewer employees at each plant, and despite emitting less at the ﬁrm level due to owning fewer
plants. Importantly, plants owned by constrained ﬁrms also
tend to have higher excess capacity, consistent with constrained ﬁrms being less able to maximally exploit profitable production and emission opportunities than unconstrained ﬁrms, leading them to rank-order projects and
allocate resources accordingly. The increase in regulatory
costs due to the California cap-and-trade rule shifts the
ranking of projects, motivating constrained ﬁrms to reallocate toward low-cost production locations where they have
excess capacity without incurring high capacity adjustment
costs.

3.3. Sample statistics
Our sample of plants and ﬁrms owning these plants
covers virtually all states.16 Over the sample period, the average annual emissions per plant is approximately 289,0 0 0
t, implying an aggregate average annual amount of 810
million metric tons. According to the EPA, the average
amount of greenhouse gas emissions from the U.S. industrial sector over this period was 1430 million metric tons.
Hence, approximately 57% of all industrial greenhouse gas
emissions can be attributed to plants in our sample.
The focal state of our study, California, ranks third
among all states in terms of the number of sample ﬁrms
(i.e., 85 ﬁrms, or 17% of all ﬁrms), fourth in terms of
the number of greenhouse gas emitting plants (i.e., 161
plants), and seventh in terms of average annual emissions
per plant (i.e., 398,0 0 0 t). In short, California is a significant source of greenhouse gas emissions and takes up
a sizable portion of the plants and ﬁrms in our sample,
despite its dominance in the high-tech industry. The two
largest states in the sample are Texas and Louisiana. Approximately 14% of our sample ﬁrms (i.e., 70 out of 511)
and 82% of ﬁrms with a plant in California (i.e., 70 out
of 85) are geographically diversiﬁed in the sense that they
have a presence both in California and in other states. This
ﬁnal observation motivates our hypothesis that a policy
curbing emissions in California alone could very well have
spillover effects to other states that do not have such a
comprehensive program in place.
Table 1 describes the characteristics of the sample ﬁrms
and plants, separately for the set of ﬁnancially constrained
and unconstrained ﬁrms based on the composite measure
of ﬁnancial constraints. As shown in Panel A, the size of
ﬁrms and amount of greenhouse gas they emit are positively skewed, consistent with the fact that a smaller number of large ﬁrms own more emission generating plants.
Our sample is well balanced in terms of the composition
of ﬁnancially constrained and unconstrained ﬁrms. Financially constrained ﬁrms account for approximately 63% of
all ﬁrm-years in our sample and about 48% of the ﬁrmyears of geographically diversiﬁed ﬁrms. As one would expect, constrained ﬁrms tend to be smaller, younger, more
levered, equipped with less cash reserves, less proﬁtable in
terms of cash ﬂows and return on assets (ROA), less valuable relative to book value, less R&D intensive, and more
encumbered with physical assets. Due to their smaller size,
constrained ﬁrms tend to emit less greenhouse gasses than
unconstrained ﬁrms at the ﬁrm level. Notably, constrained
ﬁrms are substantially less likely to have credit ratings
on their long-term and short-term debt, consistent with
Almeida et al. (2004).
Both constrained and unconstrained ﬁrms are highly
likely to have a plant presence across different states conditional on also having a presence in California (i.e., 66%

4. Empirical methodology: difference-in-differences
Our empirical strategy tests the hypothesis that the
California cap-and-trade rule incentivizes ﬁnancially constrained ﬁrms to reallocate emissions. It exploits variation
in treatment of the California cap-and-trade rule in the
cross section (i.e., plants in California vs. other states; or
ﬁrms that own plants in California vs. ﬁrms that do not)
and time series (i.e., before and after 2013) to implement
DID regressions at the ﬁrm-plant-year level. If the trends
in emissions for treated plants and non-treated plants are
parallel prior to the implementation of the California capand-trade rule, the DID estimates will plausibly isolate the
effects of the rule itself, insofar as no confounding events
occur coincidentally with the introduction of the cap-andtrade rule. During our sample period from 2010 to 2015,
the 2013 California cap-and-trade rule was indeed the only
notable climate policy introduced to curb industrial greenhouse gas emissions.17 Anticipation about the cap-andtrade rule prior to its implementation is also unlikely an
17
It was the ﬁrst major regulation enforced to achieve the emission reduction objectives initially outlined and required by the landmark California state law AB 32, which was signed in 2006. After 2015, AB 32
was further strengthened by several subsequent legislative bills (e.g., SB
32 and AB 197 in 2016; AB 398 and AB 617 in 2017). Aside from AB 32,
the governor of California signed SBX1 2 in 2011, requiring that one-third
of the state’s electricity come from renewable sources by 2020, and in
2014, the energy eﬃciency requirements for newly constructed buildings
were tightened pursuant to updated Green Building Standards. However,
these policies are distinct from the cap-and-trade rule in their enforcement targets, intensity, and timing. Hence, the emission shifting between
industrial plants that we identify around 2013 primarily correspond to the
impact of the introduction of the cap-and-trade rule.

16
See Table A.3 in the Internet Appendix for a detailed distribution of
plants and ﬁrms across states.

675

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 1
Firm and plant characteristics.
The table presents sample summary statistics of ﬁrm characteristics (Panel A) and plant characteristics (Panel B). In Panel A, emissions (in thousands of
metric tons) are summed across plants owned by a ﬁrm and reported at the ﬁrm level. Total assets are in $ billion. Firm age is the difference between
the observation year and founding year as in Jovanovic and Rousseau (2001). Short-term/long-term/total debt, cash, and cash ﬂow are shown as fractions
of total assets. Payout ratio is cash dividends plus repurchases divided by income before extraordinary items. Tobin’s q is the market value of assets
divided by the book value of assets. Proﬁtability is return on assets (ROA). R&D is scaled by sales. R&D stock is calculated using the perpetual inventory
method (Hall et al., 2005). PP&E and capital expenditures are shown as fractions of total assets. Rated is a dummy variable for whether the ﬁrm has a
credit rating on either its long-term or short-term debt. DivFirm|CA plant is an indicator for whether the ﬁrm is geographically diversiﬁed conditional on
having a plant in California. The number of plants owned by the ﬁrm is shown for all plants as well as separately for California and non-California plants
conditional on the parent ﬁrm being geographically diversiﬁed. The panel reports the number of ﬁrm-year observations, average, median, and standard
deviation (std. dev.) of these variables separately for the subsamples of ﬁnancially constrained and unconstrained ﬁrms, classiﬁed based on the composite
ﬁnancial constraint measure. Panel B presents similar summary statistics for plant-level characteristics such as carbon emissions (thousand metric tons),
excess capacity (measured as workers per $ million of sales), sales (in $ billion), and employment. These plant characteristics are summarized separately
for constrained and unconstrained parent-ﬁrm subsamples, and also separately for California and non-California plants conditional on the parent ﬁrm
being geographically diversiﬁed, that is, having plants both in California and in other states. All ﬁrm-level ﬁnancial accounting data are from Compustat. Plant emissions and ownership data are from the EPA. Plant-level sales and employment data are from the NETS database, complemented with
Compustat/Compustat segments. The sample period is 2010–2015.
Panel A: Summary statistics of ﬁrm characteristics
Constrained ﬁrms

Unconstrained ﬁrms

Firm-year obs.

Average

Median

Std. dev.

Firm-year obs.

Average

Median

Std. dev.

1,257
1,257
1,257
1,256
1,250
1,249
1,256
1,254
1,257
1,180
1,254
1,257
1,257
1,256
1,253
1,257
1,257
181
1,257
119
119

1,342.99
6.23
23.27
0.02
0.30
0.32
0.08
0.13
0.39
1.40
0.03
0.01
0.08
0.52
0.11
0.47
0.01
0.66
5.08
1.68
7.11

288.04
2.56
18.00
0.00
0.28
0.30
0.06
0.12
0.11
1.27
0.04
0.00
0.00
0.48
0.06
0.00
0.00
1.00
3.00
1.00
5.00

3,847.42
10.20
17.10
0.05
0.20
0.21
0.09
0.11
1.40
0.56
0.11
0.04
0.36
0.24
0.12
0.50
0.07
0.48
9.28
0.99
6.23

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727
727
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709
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195
728
145
145

1,822.30
41.90
43.09
0.04
0.23
0.27
0.10
0.15
0.72
1.54
0.07
0.04
0.13
0.35
0.06
0.91
0.71
0.74
7.75
2.98
13.30

306.21
29.01
50.00
0.02
0.21
0.25
0.08
0.14
0.60
1.44
0.06
0.01
0.04
0.28
0.04
1.00
1.00
1.00
3.00
1.00
8.00

3,754.36
36.77
18.89
0.05
0.12
0.13
0.10
0.08
1.03
0.51
0.06
0.06
0.19
0.22
0.06
0.29
0.45
0.44
11.95
4.72
16.55

Carbon emissions (thousands of metric tons)
Total assets ($ billions)
Firm age
Short-term debt
Long-term debt
Total debt
Cash
Cash ﬂow
Payout ratio
Tobin’s q
Proﬁtability (ROA)
R&D
R&D stock
PP&E
Capital expenditures
Rated (long-term, >1 yr)
Rated (short-term, <1 yr)
DivFirm | CA plant
Number of plants owned by a ﬁrm
California | DivFirm
Other states | DivFirm
Panel B: Summary statistics of plant characteristics

Constrained ﬁrms

Unconstrained ﬁrms

Plant-year obs.

Average

Median

Std. dev.

Plant-year obs.

Average

Median

Std. dev.

Carbon emissions (thousands of metric tons)
California | DivFirm
Other states | DivFirm

6,382
200
845

264.52
430.19
641.73

62.14
58.24
132.99

588.63
843.28
1,038.92

5,637
432
1,929

235.34
333.36
231.49

53.22
76.52
53.68

578.00
702.11
564.88

Excess Capacity (workers/$ millions of sales)
California | DivFirm
Other states | DivFirm

6,327
200
846

2.36
2.66
2.56

1.51
1.98
2.43

2.64
2.61
2.29

5,637
432
1,929

2.33
2.12
2.02

1.27
1.00
0.86

2.69
2.56
2.78

Sales ($ billions)
California | DivFirm
Other states | DivFirm

6,390
200
846

0.43
0.55
0.62

0.08
0.06
0.08

1.58
1.28
1.69

5,640
432
1,929

1.51
0.82
0.80

0.31
0.90
0.27

3.37
0.93
1.91

Employment
California | DivFirm
Other states | DivFirm

6,327
200
846

613
424
629

87
100
130

2,733
903
1,626

5,637
432
1,929

2,312
872
954

325
744
297

6,195
1,090
3,304

issue, as ﬁrms derive no economic beneﬁt from preemptively reallocating their emissions when proﬁts from emitting in California are still high before the onset of regulatory costs. The absence of such anticipatory adjustments is
empirically evident in the emission trends.

In particular, we ﬁrst compare the emissions of plants
in and outside of California (see Panel A of Fig. 2). As our
main hypotheses are aimed at examining the reallocation
of emissions within ﬁrm internal networks, we focus our
inspection on the sample of ﬁrms that are geographically
676

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Fig. 2. Unconditional average emission responses to cap-and-trade rule. The ﬁgure shows average plant emissions (in thousands of metric tons) during
the sample period 2010–2015, that is, before and after the enactment of the California cap-and-trade program at the beginning of 2013. Emissions of the
treatment and control group are plotted as solid and dotted lines, respectively. Panel A shows emissions of plants in California and in other states based
on geographically diversiﬁed ﬁrms. Panel B shows emissions of non-California plants for ﬁrms with and without plants in California.

Motivated by these trends, we formally test whether
California and non-California plants adjust their emissions
differentially in response to the cap-and-trade rule, using
the following regression speciﬁcation:

diversiﬁed. The time trends show that emissions from California and non-California plants are closely aligned and
parallel to each other prior to treatment. However, unconditionally, no visible divergence occurs after the rule is implemented.
This picture changes dramatically when we split the
sample of geographically diversiﬁed ﬁrms into ﬁnancially
constrained and unconstrained ﬁrms (see Panel A of Fig. 3).
For unconstrained ﬁrms, emissions from California and
non-California plants move in parallel before the implementation of the cap-and-trade rule and largely maintain
this pattern after 2013. In sharp contrast, for constrained
ﬁrms, the parallel trends before 2013 begin to diverge afterwards, when California plants owned by constrained
ﬁrms reverse their prior upward trend and start reducing
emissions, whereas non-California plants sharply increase
emissions. These trends illustrate how ﬁnancial constraints
condition the impact of the cap-and-trade rule on the allocation of emissions by ﬁrms across their plants in California and in other states.





Log 1 + Emissionsi, j,t = α + β Cal P l ant j × A f tert
+ γ  Xi,t + a j + bk,t + εi, j,t ,

(1)

where Log(1+Emissionsi,j,t ) is the logarithm of metric tons
of CO2 e emitted by ﬁrm i at plant j in industry k. CalPlantj
is an indicator variable equal to 1 if plant j is located in
California, and 0 otherwise. Aftert is an indicator equal to
1 if the year is 2013 or after, and 0 otherwise. Xi,t denotes a vector of ﬁrm-level control variables. Finally, aj
and bk,t each denote plant ﬁxed effects and industry-byyear ﬁxed effects, respectively. Industry is deﬁned at the
plant level using their NAICS industry codes. The variables
CalPlantj and Aftert are not included by themselves in the
regressions, as they are subsumed by the ﬁxed effects.
We adjust standard errors for clustering at the ﬁrm and
state levels. To study the impact of ﬁnancial constraints on
677

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Fig. 3. Average emission responses of constrained vs. unconstrained ﬁrms. The ﬁgure shows average plant emissions (in thousands of metric tons) separately for constrained and unconstrained ﬁrms during the sample period 2010–2015, that is, before and after the enactment of the California cap-and-trade
program at the beginning of 2013. Emissions of the treatment and control group are plotted as solid and dotted lines, respectively. Separately for constrained and unconstrained ﬁrms, the ﬁgure shows two sets of graphs: Panel A shows emissions of plants in California and in other states based on
geographically diversiﬁed ﬁrms. Panel B shows emissions of non-California plants for ﬁrms with and without plants in California.

how ﬁrms respond to the cap-and-trade rule, we estimate
Eq. (1) separately for constrained and unconstrained ﬁrms,
and evaluate whether the coeﬃcients on the interaction
term CalPlantj × Aftert are signiﬁcantly different in the two
models.
To study emission spillovers to plants in other states
that would not have occurred otherwise, it is useful to
compare the emissions from plants outside of California
owned by ﬁrms that also have plants in California with
a control group of non-California plants owned by ﬁrms
without any operations in California. A visual comparison
of the emissions of these groups of plants shows that the
parallel trend assumption holds, but unconditionally, no
visible changes exist in the post-trends either (see Panel B
of Fig. 2). However, constrained ﬁrms with California plants
substantially increase emissions from their non-California
plants during the post-2013 period, whereas no changes
occur for plants owned by constrained ﬁrms without exposure to California or unconstrained ﬁrms regardless of
their California exposure (see Panel B of Fig. 3), suggesting

a strong spillover effect from constrained ﬁrms exposed to
the California cap-and-trade rule shifting their emissions
to other states.18
To test these spillover effects formally, we replace the
plant-level treatment dummy CalPlantj in Eq. (1) with
a ﬁrm-level dummy DivFirmi,t , which is an indicator for
whether a ﬁrm owns plants both in California and in other
states during a given year:

Log(1 + Emissionsi, j,t ) = α + β1 DivF ir mi,t

+ β2 DivF ir mi,t × A f tert + γ  Xi,t + a j + bk,t + εi, j,t .
(2)

As DivFirmi,t is not subsumed by ﬁxed effects, it is also
included as a regressor by itself. This ﬁrm-plant-year-level
18
Moreover,
paired t-tests
as
suggested
by
Roberts
and
Whited (2013) reveal that the average emission growth rates during
the pre-cap-and-trade period of 2010–2012 are not statistically different
between treatment and control plants, but are signiﬁcantly different
during the post-period of 2013–2015.

678

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

regression is run on the subsample of non-California plants
to assess whether their changes in emissions after the capand-trade rule depend on whether the parent companies’
assets are affected. The model is estimated separately for
constrained and unconstrained ﬁrms. Standard errors are
clustered at the ﬁrm level.
As an alternative to comparing coeﬃcients from separate DID regressions on constrained and unconstrained
subsamples, we run pooled regressions by including
a Constrainedi dummy in an expanded triple-difference
framework. The triple-difference speciﬁcations can be written as follows:

the differential treatment effect of the introduction of the
cap-and-trade rule on emissions. The ﬁrst column controls
for plant and year ﬁxed effects but does not include any
ﬁrm-level controls, whereas the second column additionally controls for plant industry-by-year ﬁxed effects as well
as ﬁrm size, Tobin’s q, ROA, total debt, and R&D stock. The
sign on the interaction term’s coeﬃcient is consistently
negative across the ﬁrst two columns, and the magnitude
is also similar despite the addition of controls in the second column. In the second column, the coeﬃcient on the
interaction term is negative (–0.151) and signiﬁcant at the
1% level. In terms of economic magnitude, the result indicates that ﬁrms reduce emissions from California plants by
15% more than from non-California plants.
The next four columns in Panel A examine whether
this effect is different for plants owned by ﬁnancially constrained ﬁrms and those operated by unconstrained ﬁrms.
These subsample regressions show that constrained ﬁrms
reduce their emissions from California plants more than
from plants in other states, whereas unconstrained ﬁrms
do not. This result holds controlling for plant and year
ﬁxed effects (columns (3) and (4)), and is also robust to
additionally controlling for industry-by-year ﬁxed effects
(columns (5) and (6)). As reported in columns (5) and (6),
constrained ﬁrms reduce emissions from California plants
by 28% more (signiﬁcant at the 1% level) compared with
non-California plants, whereas this effect is economically
and statistically insigniﬁcant for unconstrained ﬁrms. The
difference between the responses by constrained and unconstrained ﬁrms is statistically signiﬁcant with a onesided p-value of 0.01.
In column (7) of Panel A, we pool the samples of
constrained and unconstrained ﬁrms and include a Constrained dummy in a triple-difference regression following
Eq. (3), instead of running separate regressions and comparing coeﬃcients across the two models. The main coeﬃcient of interest is the triple-interaction term CalPlant × After × Constrained, which captures how ﬁrms change their
emissions from plants in California relative to plants in
other states, depending on whether they are ﬁnancially
constrained. We expect the coeﬃcient on this term to be
negative, as constrained ﬁrms are expected to reduce emissions in California by more. Also relevant is the coeﬃcient
on CalPlant × After, which in this context measures how
unconstrained ﬁrms behave. Because we ﬁnd virtually no
responses by unconstrained ﬁrms based on the results reported in the previous columns, we do not expect this coeﬃcient to be signiﬁcantly different from zero. The results
conﬁrm that it is indeed insigniﬁcant. Column (7) shows
that for ﬁrms with plants both in and outside of California, the coeﬃcient on the triple-interaction term is economically large and negative and statistically signiﬁcant
at the 1% level. The magnitude of the coeﬃcient, –0.39,
is also consistent with the size of the difference between
the coeﬃcients of constrained and unconstrained ﬁrms in
columns (5) and (6) of –0.28 and 0.09, respectively. The
coeﬃcient on CalPlant × After, on the other hand, is small
and insigniﬁcant, consistent with our prior.
In Panel B of Table 2, we investigate whether the treatment effect identiﬁed in Panel A can be explained by reallocations or spillovers to plants outside of California, by

Log(1 + Emissionsi, j,t ) = α + β1Constrainedi
+ β2 Aftert × Constrainedi + β3Cal P l ant j × Constrainedi
+ β4Cal P l ant j × Aftert
+ β5Cal P l ant j × Aftert × Constrainedi
+ γ  Xi,t + a j + bk,t + εi, j,t

(3)

and

Log(1 + Emissionsi, j,t ) = α + β1Constrainedi + β2 DivF ir mi,t
+ β3 Aftert × Constrainedi + β4 DivF ir mi,t × Constrainedi
+ β5 DivF ir mi,t × Aftert
+ β6 DivF ir mi,t × Aftert × Constrainedi
+ γ  Xi,t + a j + bk,t + εi, j,t .

(4)

This method overcomes issues related to model ﬁt or
misspeciﬁcation that may be compounded by comparing
coeﬃcients across multiple models, and enables the econometrician to control for differences across other coeﬃcients in the model as well. We use both the subsample and pooled regressions for the analyses on emissions
and focus on the pooled regression method in subsequent
analysis.
5. Results
5.1. Impact of ﬁnancial constraints
5.1.1. Reallocation of emissions and spillover effects
In Table 2, we report results from regressing the logarithm of emissions (Log(1+Emissions)) on treatment indicators, plant and industry-by-year ﬁxed effects, as well
as ﬁrm controls. In Panel A, we examine how geographically diversiﬁed ﬁrms that operate plants both in and outside of California respond to the California cap-and-trade
rule by adjusting their emissions in California relative to
their emissions elsewhere. In Panel B, we further explore
spillover effects induced by emission reallocations following the cap-and-trade rule, by focusing on non-California
plants comparing plants owned by ﬁrms affected by the
new regulation with those of ﬁrms that are not. In each
panel, we ﬁrst discuss unconditional results without exploiting heterogeneity in ﬁnancial constraints across ﬁrms
to understand the overall effects of the California capand-trade rule, and then further explore the ﬁnancial constraints channel through which they manifest.
In Panel A, we start by estimating Eq. (1) on the sample of geographically diversiﬁed ﬁrms. The key coeﬃcient
is on the interaction term CalPlant × After, which captures
679

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

estimating Eq. (2) on the sample of non-California plants.
In the ﬁrst two columns, the results indicate unconditionally signiﬁcant spillover effects, where the coeﬃcients on
DivFirm × After are positive and signiﬁcant at the 10%
level. Controlling for plant and industry-by-year ﬁxed effects as well as ﬁrm-level variables, non-California plants
owned by ﬁrms exposed to the California cap-and-trade
rule increase emissions by 14% more than plants of nondiversiﬁed ﬁrms.
Next, we run this regression separately for the sample
of ﬁnancially constrained and unconstrained ﬁrms, and formally compare the coeﬃcients on DivFirm × After across
the two models. The results in columns (3)–(6) of Panel B
are consistent with a strong spillover effect whereby constrained ﬁrms signiﬁcantly increase their emissions from

plants outside California if they are exposed to the increased regulatory burden of the California cap-and-trade
rule. Speciﬁcally, these ﬁrms increase their non-California
plant emissions by 29% more (signiﬁcant at the 5% level)
than those without plants in California when we control
for plant and year ﬁxed effects. Controlling for industry-byyear ﬁxed effects, the relative increase is 18% (signiﬁcant at
the 10% level). For unconstrained ﬁrms, the relative change
in emissions is not statistically signiﬁcant. The difference
between the responses by constrained and unconstrained
ﬁrms is signiﬁcant at the 5% level or better.
In column (7) of Panel B, we examine the coeﬃcient
on DivFirm × After × Constrained and DivFirm × After by
estimating Eq. (4). Based on the results in the previous
columns, we expect the triple-interaction term to be positive and signiﬁcant because constrained ﬁrms are more

Table 2
Plant emission responses to California cap-and-trade rule.
The table presents results from plant-level DID regressions. Panel A compares California and non-California plants of geographically diversiﬁed ﬁrms.
Panel B studies spillovers to non-California plants comparing plants of geographically diversiﬁed and non-diversiﬁed ﬁrms. The dependent variable is
log (1+Emissions). The indicator variable CalPlant equals 1 if the plant is located in California, and 0 otherwise. The indicator variable After is equal
to 1 if the time period is 2013 or onward, and 0 otherwise. The ﬁrm-level dummy variable DivFirm is an indicator for whether a ﬁrm owns plants
both in California and in other states during a given year. The ﬁrm-level dummy variable Constrained is an indicator for whether a ﬁrm is ﬁnancially
constrained according to our composite measure. Columns (1)–(2) present unconditional results. Columns (3)–(6) present conditional results for subsample splits based on ﬁnancial constraints, also reporting p-values from testing the statistical difference of the CalPlant x After coeﬃcients between
the constrained and unconstrained subsamples. Column (7) presents conditional analysis by pooling the constrained and unconstrained samples and
including the Constrained dummy variable instead. Control variables include ﬁrm size (log of total assets), Tobin’s q, ROA, total debt, and R&D stock as
well as plant and year or industry-by-year ﬁxed effects. The table reports coeﬃcients and their respective standard errors adjusted for clustering at the
ﬁrm and state levels (Panel A) or ﬁrm level (Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is
2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Financial constraint subsamples

CalPlant × After

(1)

(2)

Const.
(3)

–0.161∗ ∗ ∗
(0.014)

–0.151∗ ∗ ∗
(0.019)

–0.334∗ ∗ ∗
(0.053)

p: Const.<Unconst.

Unconst.
(4)

Const.
(5)

Unconst.
(6)

Pooled
(7)

0.079
(0.080)

–0.282∗ ∗ ∗
(0.096)

0.094
(0.118)

0.075
(0.073)

–0.340∗ ∗
(0.143)
0.201
(0.318)
1.900∗ ∗ ∗
(0.588)
3.081
(2.135)
–4.449
(5.613)

–0.390∗ ∗ ∗
(0.094)
0.778
(0.934)
0.030
(0.098)
–2.459∗ ∗ ∗
(0.891)
–0.167
(0.137)
0.196
(0.227)
1.589∗ ∗
(0.630)
2.294∗
(1.224)
–3.165
(5.304)

[0.00]

[0.01]

CalPlant × After × Const.
CalPlant × Const.
After × Const.
Const.
Size
Tobin’s q
ROA
Total debt
R&D stock

Plant FE
Year FE
Industry-by-year FE
Observations
Adjusted R2

Yes
Yes
No
3,961
0.862

0.101
(0.110)
0.132
(0.206)
0.553∗ ∗
(0.269)
–0.021
(0.524)
–5.920
(6.320)

0.066
(0.201)
0.138
(0.120)
1.802∗ ∗
(0.688)
1.568∗
(0.826)
2.069
(2.819)

–0.349∗ ∗ ∗
(0.116)
0.159
(0.269)
1.194∗ ∗
(0.458)
2.729
(1.878)
–3.461
(4.893)

0.020
(0.110)
0.162
(0.175)
1.836∗ ∗
(0.747)
1.647∗ ∗
(0.725)
2.065
(2.889)

Yes
No
Yes
3,592
0.865

Yes
Yes
No
963
0.905

Yes
Yes
No
2,187
0.832

Yes
No
Yes
961
0.904

680

Yes
Yes
No
No
Yes
Yes
2,178
3,149
0.832
0.858
(continued on next page)

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 2
(continued)
Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Financial constraint subsamples

DivFirm × After

(1)

(2)

Const.
(3)

0.140∗
(0.072)

0.139∗
(0.078)

0.285∗ ∗
(0.124)

p: Const.>Unconst.

Unconst.
(4)

Const.
(5)

Unconst.
(6)

Pooled
(7)

–0.089
(0.066)

0.175∗
(0.093)

–0.094
(0.082)

–0.040
(0.089)

[0.00]

[0.02]

–0.155
(0.176)

–0.182
(0.175)
0.022
(0.052)
0.079
(0.106)
0.003
(0.265)
0.268
(0.341)
0.435
(0.381)

–0.365∗
(0.200)
0.048
(0.135)
0.438∗ ∗
(0.199)
0.302
(0.404)
0.524
(0.534)
0.702
(1.090)

0.006
(0.185)
0.025
(0.210)
0.019
(0.137)
0.333
(0.369)
1.444
(1.163)
–0.728
(1.627)

–0.445∗ ∗
(0.176)
0.115
(0.155)
0.361∗
(0.193)
0.057
(0.445)
0.421
(0.473)
1.126
(1.101)

–0.049
(0.134)
0.029
(0.222)
0.050
(0.167)
0.248
(0.437)
1.500
(1.183)
–0.865
(1.669)

0.304∗ ∗
(0.130)
–0.614∗ ∗
(0.272)
–0.344∗ ∗ ∗
(0.115)
0.147
(0.263)
0.011
(0.192)
0.053
(0.095)
0.229∗
(0.124)
–0.024
(0.326)
0.731
(0.450)
0.947
(0.755)

Yes
Yes
No
12,521
0.745

Yes
No
Yes
11,272
0.742

Yes
Yes
No
5,466
0.716

Yes
Yes
No
4,854
0.779

Yes
No
Yes
5,457
0.724

Yes
No
Yes
4,842
0.781

Yes
No
Yes
10,401
0.733

DivFirm × After × Const.
DivFirm × Const.
After × Const.
Const.
DivFirm
Size
Tobin’s q
ROA
Total debt
R&D stock

Plant FE
Year FE
Industry-by-year FE
Observations
Adjusted R2

likely to shift their emissions to other states if their assets are exposed to the California cap-and-trade rule. We
also expect the double-interaction term to not be significantly different from zero, because unconstrained ﬁrms
should not exhibit differential changes in their plants outside of California. Consistent with these predictions, the
coeﬃcient on DivFirm × After × Constrained is positive
and large in magnitude, and also statistically signiﬁcant
at the 5% level. The magnitude of the coeﬃcient, 0.30,
closely matches the difference in the coeﬃcients for the
constrained and unconstrained ﬁrm subsamples. The coefﬁcient on DivFirm × After is indistinguishable from zero,
also consistent with our prediction.
Overall, the results in Table 2 suggest unintended
consequences of the cap-and-trade rule in the form of
spillover effects due to reallocation motives of ﬁrms whose
assets are affected by the regulation. Importantly, our ﬁndings provide an economic channel for such reallocations
and spillover effects, highlighting that ﬁnancial constraints
constitute an important friction that motivates ﬁrms to
shift resources internally across their plants. Without such
frictions, ﬁrms would simply raise additional capital to absorb the increased costs of emissions as long as operating
in California yields positive net returns.

5.1.2. Alternative speciﬁcations, samples, and placebo tests
Table 3 provides results from a number of robustness
tests using alternative measures of ﬁnancial constraints,
using alternative speciﬁcations and samples, studying plant
sales and acquisitions, and conducting placebo tests. Similar to the previous table, the results comparing emissions from California and non-California plants owned by
geographically diversiﬁed ﬁrms are reported in Panel A,
and the tests for spillover effects comparing non-California
plant emissions by diversiﬁed and non-diversiﬁed ﬁrms are
reported in Panel B. To streamline presentation, we discuss
Panels A and B together.
In the ﬁrst column, we reiterate our results from column (7) of Table 2 as the baseline benchmark. In columns
(2)–(7), we classify constrained and unconstrained ﬁrms
based on six alternative proxies, instead of using our composite measure. These proxies, which are the basis for
our composite measure, are the Kaplan-Zingales index,
Hadlock-Pierce index, Whited-Wu index, ﬁrm size, payout,
and credit rating availability. Our main result is qualitatively robust across all of these measures yielding economically meaningful and consistent estimates, the majority of
which are also statistically signiﬁcant. Panel A shows that
for ﬁrms with plants both in and outside of California, the
coeﬃcient on the triple-interaction term, CalPlant × Af-

681

S.M. Bartram, K. Hou and S. Kim

Table 3
Firm ﬁnancial constraints and plant emission responses: alternative speciﬁcations.
The table reports results from pooled triple-difference regressions. Results in Panel A compare California and non-California plants of geographically diversiﬁed ﬁrms. Panel B studies spillovers to non-California
plants comparing plants of geographically diversiﬁed and non-diversiﬁed ﬁrms. The dependent variable is log (1+Emissions). The indicator variable CalPlant equals 1 if the plant is located in California, and
0 otherwise. The indicator variable After is equal to 1 if the time period is 2013 or onward, and 0 otherwise. The ﬁrm-level dummy variable DivFirm is an indicator for whether a ﬁrm owns plants both in
California and in other states during a given year. The ﬁrm-level dummy variable Constrained is an indicator for whether a ﬁrm is ﬁnancially constrained according to each ﬁnancial constraint measure, that is,
alternatively, our composite measure (column (1)), the Kaplan-Zingales (KZ) index (column (2)), Hadlock-Pierce (HP) index (column (3)), Whited-Wu (WW) index (column (4)), ﬁrm size (column (5)), payout
ratio (column (6)), and credit rating (column (7)). Control variables include ﬁrm size (log of total assets), Tobin’s q, ROA, total debt, and R&D stock, all possible interactions between CalPlant (Panel A), DivFirm
(Panel B), After, and Constrained, as well as plant and industry-by-year ﬁxed effects. In column (8), we further include ﬁrm-by-year ﬁxed effects (Panel A) or ﬁrm ﬁxed effects (Panel B). In column (9), the
sample is extended to include ﬁrms in the utilities industry (i.e., two-digit SIC code 49). In columns (10)–(11), the dependent variable is replaced by indicator variables for whether the ﬁrm reduces (i.e., Plant
sales) or increases (i.e., Plant acquisitions) its ownership in a plant. In columns (12)–(13), California plants are dropped from the sample, and the treatment variables, CalPlant and DivFirm, are each replaced
by a dummy variable indicating whether the plant is located in a placebo state and a dummy variable indicating whether a non-placebo state plant is owned by a ﬁrm that also has a placebo state operation,
respectively, where Texas and Louisiana are used as alternative placebo states. The table reports coeﬃcients and their respective standard errors adjusted for clustering at the ﬁrm and state levels (Panel A) or
ﬁrm level (Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Alternative constraint measures

CalPlant × After × Const.
CalPlant × After
682

Plant FE
Industry-by-year FE
Firm-by-year FE
Controls and interactions
Observations
Adjusted R2

Alt. speciﬁcations and samples

Plant sales and acquisitions

Placebo states

Composite
(1)

KZ
(2)

HP
(3)

WW
(4)

Size
(5)

Payout
(6)

Rating
(7)

Firm-year FE
(8)

Include utilities
(9)

Plant sales
(10)

Plant acq.
(11)

Texas
(12)

Louisiana
(13)

–0.390∗ ∗ ∗
(0.094)
0.075
(0.073)

–0.189∗ ∗
(0.080)
–0.026
(0.082)

–0.512∗ ∗ ∗
(0.170)
–0.001
(0.059)

–0.184
(0.145)
–0.083
(0.062)

–0.590∗ ∗
(0.237)
0.015
(0.071)

–0.303∗ ∗
(0.145)
–0.055
(0.120)

–0.133
(0.111)
–0.053
(0.072)

–0.270
(0.195)
0.001
(0.092)

–0.455∗ ∗ ∗
(0.084)
0.102
(0.078)

0.088∗ ∗ ∗
(0.017)
0.008
(0.018)

–0.028
(0.019)
0.027
(0.021)

–0.152
(0.091)
–0.100∗ ∗ ∗
(0.037)

–0.151
(0.115)
–0.031
(0.067)

Yes
Yes
No
Yes
3,149
0.858

Yes
Yes
No
Yes
3,059
0.861

Yes
Yes
No
Yes
3,149
0.854

Yes
Yes
No
Yes
3,078
0.856

Yes
Yes
No
Yes
3,134
0.860

Yes
Yes
No
Yes
3,149
0.856

Yes
Yes
No
Yes
3,149
0.856

Yes
Yes
Yes
Yes
3,159
0.891

Yes
Yes
No
Yes
3,564
0.863

No
Yes
No
Yes
2,692
0.431

No
Yes
No
Yes
2,923
0.185

Yes
Yes
No
Yes
6,105
0.731

Yes
Yes
No
Yes
4,425
0.749

Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)

DivFirm × After × Const.
DivFirm × After

Plant FE
Industry-by-year FE
Firm FE
Controls and interactions
Observations
Adjusted R2

Alt. speciﬁcations and samples

Plant sales and acquisitions

Composite
(1)

KZ
(2)

HP
(3)

WW
(4)

Size
(5)

Payout
(6)

Rating
(7)

Firm-year FE
(8)

Include utilities
(9)

Plant sales
(10)

Plant acq.
(11)

Texas
(12)

Placebo states
Louisiana
(13)

0.304∗ ∗
(0.130)
–0.040
(0.089)

0.446∗ ∗
(0.211)
–0.043
(0.110)

0.124
(0.166)
0.042
(0.086)

0.236
(0.169)
0.058
(0.070)

0.356∗
(0.202)
0.036
(0.080)

0.064
(0.160)
0.110
(0.084)

0.254∗
(0.150)
–0.037
(0.100)

0.156
(0.138)
0.056
(0.084)

0.234∗ ∗
(0.112)
–0.017
(0.085)

–0.029
(0.055)
0.034
(0.035)

–0.012
(0.060)
0.055
(0.045)

–0.133
(0.133)
0.211∗ ∗
(0.086)

0.006
(0.226)
0.082
(0.157)

Yes
Yes
No
Yes
10,401
0.733

Yes
Yes
No
Yes
10,074
0.734

Yes
Yes
No
Yes
10,395
0.732

Yes
Yes
No
Yes
9,968
0.728

Yes
Yes
No
Yes
10,346
0.733

Yes
Yes
No
Yes
10,183
0.730

Yes
Yes
No
Yes
10,401
0.733

Yes
Yes
Yes
Yes
10,397
0.754

Yes
Yes
No
Yes
15,582
0.779

No
Yes
No
Yes
8,231
0.289

No
Yes
No
Yes
9,318
0.219

Yes
Yes
No
Yes
8,317
0.752

Yes
Yes
No
Yes
9,373
0.730

Journal of Financial Economics 143 (2022) 668–696

Alternative constraint measures

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

ter × Constrained, is economically large and negative (at
least statistically signiﬁcant at the 5% level for four of the
six measures), whereas the coeﬃcient on CalPlant × After is small and insigniﬁcant for all of the alternative ﬁnancial constraint measures. Panel B shows for the sample
of non-California plants that the coeﬃcient on the tripleinteraction term, DivFirm × After × Constrained, is economically large and positive (at least statistically signiﬁcant
at the 10% level for three of the six measures), whereas
the coeﬃcient on DivFirm × After is indistinguishable from
zero across all measures.
In column (8), we report the result from a stringent
speciﬁcation with ﬁrm-by-year (Panel A) or ﬁrm (Panel
B) ﬁxed effects, which subsumes the impact of any observed and unobserved ﬁrm characteristic that may be
time-varying or persistent. Although this regression makes
heavy demands on the data, we ﬁnd economically consistent point estimates for the coeﬃcients on the interaction
terms. In Panel A, the key term CalPlant × After × Constrained loads negatively with a point estimate of –0.27,
whereas the coeﬃcient on the CalPlant × After term remains close to zero. In Panel B, the coeﬃcient on DivFirm × After × Constrained is 0.16, whereas that on DivFirm × After is less than 0.06. In column (9), we run a robustness check by including utility ﬁrms (i.e., ﬁrms with
two-digit SIC codes 49) in our sample. Although the strategic responses by utilities to a local climate policy are unlikely to resemble those of unregulated industrial ﬁrms,
due to the fact that utilities are regulated both locally by
local public service commissions and federally regarding
any interstate service transmissions, we nonetheless ﬁnd
our results are robust to including them in the sample.
In columns (10) and (11), we ask whether ﬁrms also
shift their emissions by reconﬁguring the geographical distribution of their plants in response to the cap-and-trade
rule. If future regulatory costs are expected to exceed the
adjustment costs of selling or acquiring plants, ﬁrms may
choose to reallocate emissions on the extensive margin. On
the other hand, changes in variable operating costs imposed by the cap-and-trade rule may not be suﬃcient to
induce large investments or divestments of ﬁxed assets. To
answer this question, we deﬁne two binary variables, each
indicating whether the ﬁrm reduces or increases ownership in a plant, respectively, and use them as dependent
variables in a linear probability model analogous to the
pooled regression models in Eqs. (3) and (4). All plant
ownership reductions in our sample are transfers of plant
ownership to other ﬁrms, and none of them are physical
closures. Hence, we denote the dummy variable indicating a plant ownership reduction as Plant Sales. Increases in
plant ownership are indicated by the dummy variable Plant
Acquisitions.19 The results show that although ﬁnancially
constrained ﬁrms are more likely to sell plants in California, we ﬁnd no effect on ﬁrms’ decisions to acquire plants
in California or to sell or acquire plants in other states.
Unconstrained ﬁrms are unaffected in their likelihood of
adjusting plant ownership. Overall, the only external mar-

gin on which constrained ﬁrms adjust plant ownership is
the sale of California plants, which is consistent with these
ﬁrms selling less proﬁtable assets to improve ﬁnancial ﬂexibility.
In columns (12) and (13), we conduct placebo tests to
rule out concerns of spurious effects that may affect California and other heavy greenhouse gas emitting states similarly. We drop California plants from the sample and use
two alternative states that are the most important greenhouse gas emitters aside from California, namely Texas and
Louisiana, as placebo states. We test whether geographically diversiﬁed ﬁrms (i.e., ﬁrms with a presence both in
the placebo state and in other states) reduce plant emissions in the placebo state relative to other states, whether
these ﬁrms create emission spillovers in other states, and
whether these effects are related to ﬁrm ﬁnancial constraints. For both placebo states, we run regressions following Eqs. (3) and (4) and do not ﬁnd results similar to
our main ﬁndings. We ﬁnd no indication that plants in
placebo states owned by constrained ﬁrms signiﬁcantly reduce emissions by more than plants in other states, nor
any evidence of spillover effects from placebo states to
other states that are driven by ﬁnancial constraints. Given
the large number of observations in the placebo tests, the
lack of signiﬁcance is unlikely a result of low statistical
power. In short, our main results are not driven by confounding factors coinciding with the introduction of the
California cap-and-trade rule that affect other major greenhouse gas emitting states in similar ways.
In summary, our results provide strong and consistent
evidence that (a) ﬁrms owning plant operations both in
California and in other states reduce emissions from their
plants in California relative to plants in other states, (b)
that these ﬁrms increase emissions from their plants in
other states relative to ﬁrms with no presence in California, and (c) that these effects are almost exclusively due to
their ﬁnancial constraints.
5.2. Economic mechanisms
In this section, we perform several additional tests to
corroborate and sharpen the interpretation of our main results, and discuss the potential of alternative confounding explanations. In particular, we focus on examining how
ﬁnancially constrained ﬁrms reallocate emissions in response to the California cap-and-trade rule.
5.2.1. Economic role of plants within the supply chain
In Table 4, we study whether the role of plants within
a ﬁrm’s organizational structure, or supply chain, matters
for the emission reallocations by ﬁnancially constrained
ﬁrms. If ﬁrms are responding to the cap-and-trade rule by
shifting economic activity, emissions should be reallocated
from plants in California to plants in other states that play
similar economic roles. To test this hypothesis, we identify
whether plants owned by the same ﬁrm are “horizontally
linked,” “vertically linked,” or “unrelated” with each other,
using the BEA input-output accounts. Horizontally linked
plants are presumed to have similar functions in the ﬁrm’s
production network, whereas vertically linked or unrelated
plants are assumed to have distinct functions.

19
Most ownership changes in our sample are discrete, either changing
from complete ownership to zero ownership, or from zero ownership to
complete ownership. Fractional ownership changes are rare.

683

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 4
Emission reallocations within the supply chain.
The table reports results from triple-difference regressions testing emission reallocations toward plants outside of California that play similar (i.e.,
horizontally linked) or dissimilar (i.e., vertically linked or unrelated) roles to those in California owned by the same ﬁrm, identiﬁed using plant-level
NAICS codes and the 2007 make and use tables from the BEA input-output accounts. Results in Panel A compare emissions from California plants with
non-California plants with which they are horizontally linked (column (1)) or vertically linked/unrelated (column (2)). Panel B studies non-California
plants owned by geographically diversiﬁed and non-diversiﬁed ﬁrms, comparing plants horizontally linked (column (1)) or vertically linked/unrelated
(column (2)) to California plants with other plants owned by ﬁrms unaffected by the cap-and-trade rule. p-values from comparing the triple-interaction
terms across the two samples (columns (1) and (2)) are also reported. Columns (3)–(8) perform similar analysis, further controlling for the emissions,
number, and fraction of vertically linked or unrelated (horizontally linked) plants when analyzing horizontal (vertical or unrelated) reallocations. The
dependent variable is log (1+Emissions). The indicator variable CalPlant equals 1 if the plant is located in California, and 0 otherwise. The indicator
variable After is equal to 1 if the time period is 2013 or onward, and 0 otherwise. DivFirm is an indicator variable for whether a ﬁrm owns plants
both in California and in other states during a given year. Constrained is an indicator variable for whether a ﬁrm is ﬁnancially constrained according to
our composite measure. Control variables include ﬁrm size, Tobin’s q, ROA, total debt, and R&D stock, all possible interactions between CalPlant (Panel
A), DivFirm (Panel B), After, and Constrained, as well as plant and industry-by-year ﬁxed effects. The table reports coeﬃcients and their respective
standard errors adjusted for clustering at the ﬁrm and state levels (Panel A) or ﬁrm level (Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%,
and 10% level, respectively. The sample period is 2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Supply chain linkage with California plant
Horizontal
(1)
CalPlant × After × Const.
p: Hor<Ver
CalPlant × After

Vertical or
unrelated
(2)

Horizontal
(3)

Vertical or
unrelated
(4)

Horizontal
(5)

Vertical or
unrelated
(6)

(7)

Vertical or
unrelated
(8)

–0.359∗ ∗ ∗
–0.154∗
(0.103)
(0.078)
[0.06]

–0.359∗ ∗ ∗
0.030
(0.105)
(0.142)
[0.01]

–0.351∗ ∗ ∗
0.011
(0.109)
(0.125)
[0.01]

–0.370∗ ∗ ∗
–0.005
(0.102)
(0.152)
[0.02]

0.048
(0.105)

0.049
(0.097)
–0.001
(0.014)

0.052
(0.106)

–0.075
(0.133)

0.044
(0.104)

–0.045
(0.151)

–0.087
(0.070)

–0.554∗ ∗
(0.239)
0.196
(0.246)

–1.114
(0.759)

Yes
Yes
Yes
2,307
0.869

Yes
Yes
Yes
1,711
0.857

Horizontal
(7)

Vertical or
unrelated
(8)

0.318∗ ∗
(0.149)

0.038
(0.130)

0.075
(0.093)

Other network plant emissions

–0.095
(0.122)
–0.109∗ ∗
(0.050)

Other network plant number
Other network plant fraction

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Horizontal

Yes
Yes
Yes
2,307
0.869

Yes
Yes
Yes
1,711
0.851

Yes
Yes
Yes
2,307
0.869

Yes
Yes
Yes
1,711
0.868

Yes
Yes
Yes
2,307
0.869

Yes
Yes
Yes
1,711
0.868

Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Supply chain linkage with California plant
Horizontal

DivFirm × After × Const.

Horizontal

(1)

Vertical or
unrelated
(2)

0.332∗ ∗
(0.154)

0.073
(0.141)

p: Hor>Ver
DivFirm × After

Horizontal

(3)

Vertical or
unrelated
(4)

(5)

Vertical or
unrelated
(6)

0.315∗ ∗
(0.148)

0.026
(0.133)

0.316∗ ∗
(0.149)

0.017
(0.131)

[0.11]
–0.005
(0.103)

[0.07]
–0.117
(0.115)

Other network plant emissions

0.018
(0.098)
0.017
(0.017)

[0.07]
–0.060
(0.103)
–0.066∗
(0.040)

Other network plant number

[0.08]

0.021
(0.098)

–0.050
(0.097)

0.135
(0.117)

–0.362
(0.244)

Other network plant fraction

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Yes
Yes
Yes
8,152
0.717

Yes
Yes
Yes
2,552
0.841

Yes
Yes
Yes
8,152
0.717

684

Yes
Yes
Yes
2,552
0.848

Yes
Yes
Yes
8,152
0.718

Yes
Yes
Yes
2,552
0.847

0.011
(0.098)

–0.079
(0.100)

0.311
(0.245)

–0.509
(1.024)

Yes
Yes
Yes
8,152
0.717

Yes
Yes
Yes
2,552
0.842

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Using this mapping of plant networks within ﬁrms, we
analyze whether constrained ﬁrms reallocate their emissions in response to California’s cap-and-trade rule more
toward plants in other states that play roles similar to
their California plants. In Panel A of Table 4, we estimate
the triple-difference regression of Eq. (3) for subsamples in
which we compare emissions from California plants with a
subset of non-California plants with which they are horizontally linked (column (1)) or vertically linked/unrelated
(column (2)). The results indicate that California plants
owned by ﬁnancially constrained ﬁrms reduce their emissions signiﬁcantly more than plants outside California that
are horizontally linked to plants in California, but not as
much when compared with vertically linked or unrelated
non-California plants.
In Panel B, we study non-California plants owned by
geographically diversiﬁed and non-diversiﬁed ﬁrms, comparing plants that are horizontally linked (column (1)) or
vertically linked/unrelated (column (2)) to California plants
with other plants of ﬁrms unaffected by the cap-and-trade
rule. These results show that among non-California plants
that share horizontal linkages with other plants of the
same ﬁrm, plants that are horizontally linked to California plants increase their emissions signiﬁcantly more than
plants that are linked this way to other plants of ﬁrms that
have no exposure to California. By contrast, we ﬁnd nonCalifornia plants that are vertically linked or unrelated to
California plants do not differentially increase their emissions compared with plants that are linked in this way to
other plants of ﬁrms that do not have operations in California.
Columns (3)–(8) of Table 4 perform similar analysis, further controlling for the emissions, number, and fraction of
vertically linked or unrelated (horizontally linked) plants
when analyzing horizontal (vertical or unrelated) reallocations to take into account the confounding effects of alternative production linkages between plants when assessing
emission reallocations through one type of linkage. The results are robust to controlling for such effects.
Notably, the differences between horizontal and nonhorizontal reallocations are economically and statistically
signiﬁcant. For example, the coeﬃcients on the tripleinteraction terms in columns (3) and (5) are more than 10
times as large as those in columns (4) and (6), respectively.
The p-value comparing these coeﬃcients is 0.01 in Panel
A and 0.07 in Panel B. Together, these results suggest that
constrained ﬁrms indeed reallocate emissions by shifting
production across plants that play similar operational roles,
rather than categorically shifting activity toward different
types of plants.

order projects to allocate capital. Consistent with this idea,
we ﬁnd that ﬁnancially constrained ﬁrms have more excess
capacity at their plants (see Table 1). This excess capacity
motivates and enables constrained ﬁrms to reallocate their
emissions when the rankings of high excess capacity production locations improve. Plants with high excess capacity
are also where increasing production and emissions is the
least costly.
In Table 5, we test whether constrained ﬁrms reallocate emissions more toward plants with greater production gaps or higher excess capacity. We sort non-California
plants owned by ﬁrms exposed to California’s cap-andtrade rule into high and low excess capacity groups with
respect to the cross sectional median based on their ratio of employment to sales. In Panel A, we compare the
change in emissions around the cap-and-trade rule from
California plants with those from horizontally linked nonCalifornia plants with either high or low excess capacity in
two separate regressions. Focusing on the interaction term
CalPlant × After × Constrained, the results show that constrained ﬁrms reduce their emissions at California plants
compared with non-California plants with high excess capacity (coeﬃcient of –0.46, signiﬁcant at the 1% level), but
not when compared with non-California plants with low
excess capacity (coeﬃcient of –0.02, insigniﬁcant). The difference between these coeﬃcients is statistically signiﬁcant
with a p-value of 0.03.
Analogously, in Panel B of Table 5, we show that among
non-California plants that have horizontal linkages with
other plants of the same ﬁrm, plants of ﬁrms exposed to
California’s cap-and-trade rule signiﬁcantly increase emissions compared with plants of unaffected ﬁrms, primarily when they have high excess capacity (i.e., coeﬃcient
on DivFirm × After × Constrained of 0.41, signiﬁcant at
the 5% level) but not when they have low excess capacity (i.e., coeﬃcient of 0.14, insigniﬁcant). Overall, these results suggest that the response by ﬁnancially constrained
ﬁrms to California’s cap-and-trade rule arises from a distortion in the variable costs of production altering the relative net present value rankings of emission projects across
different locations, and are also consistent with theoretical models of investment adjustment costs and ﬁnancial
constraints.
5.2.3. Carbon eﬃciency vs. production shifting
An important social welfare question is whether plants
change emissions by producing the same quantity of goods
in a more environmentally eﬃcient manner or by shifting the quantity of production across plants. We answer
this question using data on plant-level sales and employment to estimate regression models similar to Eqs. (3) and
(4), but use carbon eﬃciency (i.e., emissions to sales ratio),
production output (i.e., sales), employment, and excess capacity (i.e., employment to sales ratio) as dependent variables.
Panel A of Table 6 shows how these metrics evolve
at plants in California compared with plants located elsewhere, for plants that are owned by geographically diversiﬁed ﬁrms. Panel B reports the responses for non-California
plants owned by ﬁrms exposed to the cap-and-trade rule
compared with plants owned by ﬁrms without any Cal-

5.2.2. Financial constraints and excess capacity
Key to understanding how ﬁnancially constrained ﬁrms
shift emissions in response to the cap-and-trade, and why
unconstrained ﬁrms do not, is the idea that constrained
ﬁrms’ resources are limited, and as a result of rankordering and choosing maximally proﬁtable projects, they
are more likely to carry excess capacity built up during
good times (see Von Kalckreuth, 2006; Dasgupta et al.,
2019). Unconstrained ﬁrms are likely to be at capacity as
long as doing so is proﬁtable, as they do not need to rank685

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 5
Emission reallocations to plants with excess capacity.
The table reports results from triple-difference regressions testing emission reallocations toward plants outside of California that have high or low excess
capacity, where excess capacity is measured as end-of-current-year employment divided by current-year sales. Plant-level sales and employment data are
from the NETS database, complemented with Compustat/Compustat Segment data as described in Section 3. The analysis considers the sample of plants
that share horizontal linkages with other plants owned by the same ﬁrm, in particular with California plants if the ﬁrm has operations in California.
For geographically diversiﬁed ﬁrms, results in Panel A compare emissions from California plants with non-California plants with higher (column (1))
or lower (column (2)) than median excess capacity in the previous year. Panel B studies non-California plants owned by geographically diversiﬁed and
non-diversiﬁed ﬁrms, comparing high (column (1)) or low (column (2)) excess capacity plants owned by ﬁrms affected by the cap-and-trade rule with
plants owned by ﬁrms unaffected by the rule. p-values from comparing the triple-interaction terms across the two samples (columns (1) and (2)) are
also reported. The dependent variable is log (1+Emissions). The indicator variable CalPlant equals 1 if the plant is located in California, and 0 otherwise.
The indicator variable After is equal to 1 if the time period is 2013 or onward, and 0 otherwise. DivFirm is an indicator variable for whether a ﬁrm
owns plants both in California and in other states during a given year. Constrained is an indicator variable for whether a ﬁrm is ﬁnancially constrained
according to our composite measure. Control variables include ﬁrm size, Tobin’s q, ROA, total debt, and R&D stock, all possible interactions between
CalPlant (Panel A), DivFirm (Panel B), After, and Constrained, as well as plant and industry-by-year ﬁxed effects. The table reports coeﬃcients and their
respective standard errors adjusted for clustering at the ﬁrm and state levels (Panel A) or ﬁrm level (Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the
1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Excess capacity at
target non-California plant

CalPlant × After × Const.

High
(1)

Low
(2)

–0.457∗ ∗ ∗
(0.147)

–0.021
(0.189)

p: High<Low

[0.03]

CalPlant × After

0.069
(0.113)

0.003
(0.089)

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Yes
Yes
Yes
1,987
0.857

Yes
Yes
Yes
854
0.880

Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Excess capacity at
target non-California plant

DivFirm × After × Const.

High
(1)

Low
(2)

0.409∗ ∗
(0.185)

0.137
(0.272)

p: High>Low

[0.20]

DivFirm × After

–0.159
(0.140)

0.256
(0.221)

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Yes
Yes
Yes
7,405
0.713

Yes
Yes
Yes
7,020
0.697

ifornia operations. We discuss both panels together for
ease of presentation. For comparison, the ﬁrst column reports our original emission results in Table 2. In the second column for both panels, we ﬁnd no evidence that carbon eﬃciency of plants owned by constrained or unconstrained ﬁrms are differentially affected by California’s capand-trade. Therefore, we cannot interpret the reduction in
constrained ﬁrms’ emissions in California as a sign of increased carbon eﬃciency, nor can we attribute the increase

in emissions in other states as an indication of lower eﬃciency.
In the third column, we ﬁnd clear evidence that constrained ﬁrms signiﬁcantly reduce output in California
compared with their output elsewhere (i.e., coeﬃcient on
CalPlant × After × Constrained of –0.49, signiﬁcant at the
1% level), while increasing output in other states compared
with ﬁrms that are not affected by the cap-and-trade rule
(i.e., coeﬃcient on DivFirm × After × Constrained of 0.42,
686

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 6
Carbon eﬃciency vs. production shifting.
The table reports results from triple-difference regressions. Results in Panel A compare California and non-California plants of geographically diversiﬁed ﬁrms. Panel B studies spillovers to non-California plants comparing geographically diversiﬁed and non-diversiﬁed ﬁrms. In column (1),
the baseline dependent variable is log (1+Emissions). In column (2), the dependent variable is replaced by plant-level carbon eﬃciency measured
as log (1+Emissions/Sales). In column (3), the dependent variable is plant-level output measured as log (1+Sales). In column (4), the dependent
variable is plant-level labor input measured as log (1+Employment). In column (5), the dependent variable is plant-level log (1+Excess Capacity),
where excess capacity is measured as end-of-current-year employment divided by current-year sales. Plant-level sales and employment data are
from the NETS database, complemented with Compustat/Compustat Segment data as described in Section 3. The indicator variable CalPlant equals
1 if the plant is located in California, and 0 otherwise. The indicator variable After is equal to 1 if the time period is 2013 or onward, and 0 otherwise. DivFirm is an indicator variable for whether a ﬁrm owns plants both in California and in other states during a given year. Constrained is an
indicator variable for whether a ﬁrm is ﬁnancially constrained according to our composite measure. Control variables include ﬁrm size, Tobin’s q,
ROA, total debt, and R&D stock, all possible interactions between CalPlant (Panel A), DivFirm (Panel B), After, and Constrained, as well as plant and
industry-by-year ﬁxed effects. The table reports coeﬃcients and their respective standard errors adjusted for clustering at the ﬁrm and state levels
(Panel A) or ﬁrm level (Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variables

CalPlant × After × Const.
CalPlant × After

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Log(1+Emissions)
(1)

Log(1+Emissions/Sales)
(2)

Log(1+Sales)
(3)

Log(1+Employment)
(4)

Log(1+Excess capacity)
(5)

–0.390∗ ∗ ∗
(0.094)
0.075
(0.073)

0.118
(0.092)
0.051
(0.086)

–0.491∗ ∗ ∗
(0.080)
0.044
(0.071)

–0.165∗ ∗ ∗
(0.037)
0.079∗ ∗ ∗
(0.021)

–0.237
(0.154)
0.354∗ ∗ ∗
(0.085)

Yes
Yes
Yes
3,149
0.858

Yes
Yes
Yes
3,149
0.899

Yes
Yes
Yes
3,149
0.871

Yes
Yes
Yes
3,149
0.831

Yes
Yes
Yes
3,135
0.832

Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variables

DivFirm × After × Const.
DivFirm × After

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Log(1+Emissions)
(1)

Log(1+Emissions/Sales)
(2)

Log(1+Sales)
(3)

Log(1+Employment)
(4)

Log(1+Excess capacity)
(5)

0.304∗ ∗
(0.130)
–0.040
(0.089)

–0.178
(0.195)
–0.088
(0.133)

0.418∗ ∗
(0.169)
0.043
(0.110)

–0.017
(0.055)
0.047
(0.043)

–0.402∗ ∗
(0.167)
0.047
(0.074)

Yes
Yes
Yes
10,401
0.733

Yes
Yes
Yes
10,401
0.861

Yes
Yes
Yes
10,411
0.874

Yes
Yes
Yes
10,368
0.862

Yes
Yes
Yes
9,693
0.835

signiﬁcant at the 5% level). The magnitude of the reallocation of output is comparable to if not larger than that
of emissions. Therefore, the natural interpretation for the
emission reallocation is that ﬁrms are shifting their production activity to outside California, rather than making
their production more carbon eﬃcient.
Results in the fourth column of Table 6 document a reduction in employment at California plants owned by constrained ﬁrms (i.e., coeﬃcient on CalPlant × After × Constrained of –0.17, signiﬁcant at the 1% level), whereas
no changes occur in employment at their non-California
plants (i.e., coeﬃcient on DivFirm × After × Constrained
is insigniﬁcant). Finally, the ﬁfth column shows that excess capacity declines at plants located outside California owned by constrained ﬁrms (i.e., coeﬃcient on DivFirm × After × Constrained of –0.40, signiﬁcant at the 5%
level). Altogether, these results indicate that constrained

ﬁrms respond to the cap-and-trade rule primarily by shifting production away from California toward other states
where they have more surplus production capacity, thereby
reducing their cost exposure in California while closing
their capacity gaps elsewhere without incurring substantial adjustment costs due to reallocations. This production
shift partially results in a decline in employment in California but does not manifest itself in an improvement or
deterioration in carbon eﬃciency.
5.2.4. Impact of reallocation and compliance costs
If ﬁnancially constrained ﬁrms reallocate emissions
across states to avoid the increase in regulatory costs from
the cap-and-trade rule in California, the costs associated
with reallocating emissions (e.g., distance, regulation at
target state) could undo the beneﬁts of avoiding tighter
emission rules in California and dampen the spillover ef-

687

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

fects. On the other hand, additional costs associated with
efforts to comply with the California cap-and-trade rule,
such as the development or acquisition of abatement technology, would exacerbate leakage.
To explore these predictions within the limitations of
the data, we conduct indirect tests using proxies for reallocation and compliance costs. Speciﬁcally, we assume
that reallocation costs are lower when ﬁrms shift emissions toward plants located in states near California or
states where environmental or climate-related regulatory
standards are lower. We also conjecture that ﬁrms that had
previously not invested in R&D or capital expenditures beyond normal business needs should shift emissions more
sharply as they would otherwise likely incur additional
costs from R&D investments to generate new abatement
technology (see Aghion et al., 2016) or to adopt existing
technology for a second abatement-related use (or “face”)
(see Cohen and Levinthal, 1989; Griﬃth et al., 2004) to
comply with the new regulation in California.
In the ﬁrst six columns of Table 7, we estimate regressions according to Eqs. (3) and (4) on subsamples consisting of plants in California and different sets of control plants located elsewhere conditional on whether reallocating to those states is likely cheaper or costlier. In
the ﬁrst two columns, the subsamples are based on the
distance of plants from California. The control plants in
the “Close” sample are located in nearby states deﬁned
as being within three states adjacent from California. The
control plants in the “Far” sample are in distant, or nonnearby, states. In columns (3)–(4) and columns (5)–(6), the
control samples are based on the environmental regulation
stringency of states according to the 50 State Index of Energy Regulations published by the Paciﬁc Research Institute
for Public Policy (PRI), or, alternatively, the 2005 Census
Pollution Abatement Costs & Expenditures (PACE) survey
rankings, respectively. The control plants in the “Low” or
“High” samples are located in lower- or higher-ranked (i.e.
less or more regulated) states, respectively. We hypothesize
that ﬁrms reallocating emissions to plants in the “Close” or
“Low” sample shift emissions more intensely due to lower
reallocation costs than ﬁrms reallocating to plants in the
“Far” or “High” samples, respectively.20
The regression results provide empirical support for this
hypothesis. In particular, in regressions comparing emissions from California and non-California plants of geographically diversiﬁed ﬁrms (Panel A), California plants
reduce emissions more sharply when compared with
plants in nearby versus distant states (i.e., coeﬃcient
on CalPlant × After × Constrained of –0.57 for “Close” sample, as compared to –0.33 for “Far” sample). The same
is true when they are compared with plants in lowregulation than high-regulation states (e.g., coeﬃcient on
CalPlant × After × Constrained of –0.51 for “Low” sample,
versus –0.33 for “High” sample, based on PRI index).
Similar or even stronger contrasts are found in the
spillover analysis comparing emissions from non-California
plants owned by geographically diversiﬁed and non-

diversiﬁed ﬁrms (Panel B). The emission spillovers
are much more pronounced for plants located in
closer than in farther states (i.e., coeﬃcient on DivFirm × After × Constrained of 0.55 for “Close” sample, versus
0.16 for “Far” sample) and also much sharper to plants in
low-regulation than in high-regulation states (e.g., coefﬁcient on DivFirm × After × Constrained of 0.58 for “Low”
sample, versus 0.04 for “High” sample, based on Census
PACE survey). The differences between the spillover effects
in the low and high reallocation cost samples are mostly
signiﬁcant.
In the last four columns of Table 7, we similarly run
regressions on subsamples consisting of plants owned by
ﬁrms that made negative (“Low”) or positive (“High”) abnormal R&D and capital expenditure (Capex) investments
prior to entering the sample. In columns (7) and (8), abnormal ex-ante R&D and Capex investments are computed
for each ﬁrm by taking the time series average of the residuals from the following ﬁrm-year-level regression over the
pre-sample period from 2003 to 2008,

R&Di,t + Capexi,t
= α + β1Constrainedi,t−1
Asset si,t−1
+ β2 log(Asset si,t−1 ) + β3 ROAi,t−1 + ak,t + εi,t ,

(5)

where we control for whether ﬁrm i is constrained in a
given year t, the ﬁrm’s asset size and proﬁtability, and its
growth opportunities or peer benchmarks in its industry k
by including an industry-by-year ﬁxed effect. In columns
(9) and (10), we alternatively use industry-demeaned R&D
and Capex investment.
Consistent with our hypothesis, ﬁrms with low ex-ante
abnormal investments in R&D and Capex are more likely
to reallocate emissions, resulting in lower emissions from
their California plants (i.e., coeﬃcient on CalPlant × After × Constrained is –0.65 for the “Low” sample and –0.10
for the “High” sample) and stronger emission spillovers
to non-California plants (i.e., coeﬃcient on DivFirm × After × Constrained is 0.42 for the “Low” sample and 0.11 for
the “High” sample). Although we acknowledge the limitations of our proxies (e.g., no detailed information is available on the precise nature of abnormal R&D and Capex or
how much of it is tied to abatement), these results are
broadly consistent with the idea that reallocation and compliance costs play an important role in moderating how
constrained ﬁrms shift emissions to avoid the regulatory
cost arising from the California cap-and-trade rule.
5.2.5. Are ﬁrms reallocating to chase better growth
opportunities?
A potential concern is that our results might be driven
by differential growth prospects across plants that are unrelated to the California cap-and-trade rule. For example,
if the economies of other states grow faster than California, ﬁrms with limited access to external capital could shift
their productive resources to these more promising states.
To evaluate this “opportunity chasing” story as an alternative explanation, we construct measures of growth opportunities and evaluate the robustness of our results controlling for them.
The ﬁrst measure is state-level annual real gross domestic product (GDP) growth from industries in the state

20
As an alternative to the PRI index or PACE survey, we use the political
alignment of states based on presidential election outcomes (e.g. Democrat or Republican) as a proxy for environmental or climate regulation
stringency, and ﬁnd consistent results in untabulated analysis.

688

S.M. Bartram, K. Hou and S. Kim

Table 7
Impact of reallocation and compliance costs on spillovers.
The table presents results from subsample regressions of Eqs. (3) and (4) in the main text. In columns (1)–(2), the subsamples are based on the distance of plants from California. The “Close” sample
comprises plants located in California or nearby (i.e., within three adjacent states). The “Far” sample includes plants in California and in distant states. In columns (3)–(4) and columns (5)–(6), the
subsamples are based on the stringency of state environmental regulation according to the 50 State Index of Energy Regulations published by PRI and the 2005 Census PACE survey, respectively. The
“Low” sample comprises plants located in California and in less regulated states. The “High” sample includes plants in California and in heavily regulated states. In columns (7)–(8), the subsamples are
based on abnormal R&D and Capex investments of ﬁrms prior to the sample period, where abnormal R&D and Capex investment is computed as the within-ﬁrm average of the residuals from regression
Eq. (5) over the period 20 03–20 08. In columns (9)–(10), the subsamples are based on industry-adjusted R&D and Capex investments of ﬁrms during 20 03–20 08. The “Low” sample comprises plants
owned by ﬁrms with negative ex-ante abnormal or industry-adjusted investments. The “High” sample comprises plants owned by ﬁrms with positive ex-ante abnormal or industry-adjusted investments.
The dependent variable is log (1+Emissions). Panel A compares California and non-California plants of geographically diversiﬁed ﬁrms. Panel B studies spillovers to non-California plants comparing
geographically diversiﬁed and non-diversiﬁed ﬁrms. The indicator variable CalPlant equals 1 if the plant is located in California, and 0 otherwise. After is an indicator variable equal to 1 if the time period
is 2013 or onward, and 0 otherwise. Constrained is an indicator variable for whether a ﬁrm is ﬁnancially constrained according to our composite measure. DivFirm is a dummy variable equal to 1 if a
ﬁrm owns a plant in California as well as in other states in a given year, and 0 otherwise. Control variables include ﬁrm size, Tobin’s q, ROA, total debt, and R&D stock, all possible interactions between
CalPlant (Panel A), DivFirm (Panel B), After, and Constrained, as well as plant and industry-by-year ﬁxed effects. The table reports coeﬃcients and their respective standard errors adjusted for clustering
at the ﬁrm and state levels (Panel A) or ﬁrm level (Panel B). It also reports p-values from one-sided t-tests comparing the coeﬃcients on the triple interaction terms between subsamples. ∗ ∗ ∗ , ∗ ∗ , and ∗
indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: California vs. non-California plants (geographically diversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
689

Target states
Distance from California

CalPlant × After × Const.

Close
(1)

Far
(2)

–0.565∗ ∗ ∗
(0.172)

–0.329∗ ∗ ∗
(0.037)

p: Close(Low)<Far(High)

PRI environmental
regulation stringency
Low
High
(3)
(4)
–0.509∗ ∗ ∗
(0.170)

[0.09]

–0.330∗ ∗ ∗
(0.064)

Firms
Census PACE survey
regulation stringency
Low
High
(5)
(6)
–0.461∗ ∗
(0.173)

[0.16]

–0.343∗ ∗ ∗
(0.059)

Prior abnormal R&D and
Capex
Low
High
(7)
(8)

Prior industry-adjusted R&D
and Capex
Low
High
(9)
(10)

–0.648∗ ∗ ∗
(0.191)

–0.506∗ ∗ ∗
(0.119)

[0.26]

–0.099
(0.089)
[0.00]

–0.058
(0.209)
[0.03]

0.131
(0.088)

0.038
(0.057)

0.128
(0.128)

0.056
(0.061)

0.094
(0.112)

0.066
(0.067)

0.237
(0.157)

–0.049
(0.053)

0.182
(0.125)

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Yes
Yes
Yes
1,561
0.863

Yes
Yes
Yes
2,191
0.862

Yes
Yes
Yes
1,979
0.832

Yes
Yes
Yes
1,777
0.894

Yes
Yes
Yes
1,921
0.827

Yes
Yes
Yes
1,831
0.899

Yes
Yes
Yes
1,603
0.889

Yes
Yes
Yes
1,530
0.933

Yes
Yes
Yes
Yes
Yes
Yes
1,919
1,217
0.892
0.919
(continued on next page)

–0.056
(0.057)

Journal of Financial Economics 143 (2022) 668–696

CalPlant × After

S.M. Bartram, K. Hou and S. Kim

Table 7
(continued)
Panel B: Spillovers to non-California plants (diversiﬁed vs. undiversiﬁed ﬁrms)
Dependent variable: Log(1+Emissions)
Target states
Distance from California

690

DivFirm × After × Const.

Close
(1)

Far
(2)

0.551∗ ∗
(0.247)

0.163
(0.137)

p: Close(Low)>Far(High)

PRI environmental
regulation stringency
Low
High
(3)
(4)
0.467∗ ∗
(0.231)

[0.08]

0.147
(0.129)

Firms
Census PACE survey
regulation stringency
Low
High
(5)
(6)
0.577∗ ∗ ∗
(0.215)

[0.11]

0.039
(0.118)

Prior abnormal R&D and
Capex
Low
High
(7)
(8)

Prior industry-adjusted R&D
and Capex
Low
High
(9)
(10)

0.415∗ ∗ ∗
(0.148)

0.441∗ ∗ ∗
(0.139)

[0.01]

0.107
(0.234)
[0.13]

0.057
(0.259)
[0.10]

–0.116
(0.160)

0.024
(0.109)

–0.140
(0.179)

0.050
(0.084)

–0.207
(0.161)

0.116
(0.084)

–0.041
(0.084)

0.069
(0.108)

–0.075
(0.065)

0.116
(0.162)

Plant FE
Industry-by-year FE
Controls and interactions
Observations
Adjusted R2

Yes
Yes
Yes
3,693
0.695

Yes
Yes
Yes
6,704
0.757

Yes
Yes
Yes
5,039
0.680

Yes
Yes
Yes
5,359
0.787

Yes
Yes
Yes
5,048
0.681

Yes
Yes
Yes
5,343
0.789

Yes
Yes
Yes
5,365
0.744

Yes
Yes
Yes
5,481
0.762

Yes
Yes
Yes
6,121
0.759

Yes
Yes
Yes
4,731
0.743

Journal of Financial Economics 143 (2022) 668–696

DivFirm × After

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

interaction term CalPlant × After × Constrained is –0.36
and signiﬁcant at the 1% level, comparable to –0.39 in
Table 2. The last three speciﬁcations study spillovers to
non-California plants, comparing geographically diversiﬁed
and non-diversiﬁed ﬁrms. Controlling for both growth opportunity variables and their respective interaction terms,
the spillover effect remains both economically and statistically robust. The coeﬃcient on the triple-interaction term
DivFirm × After × Constrained is 0.31 and signiﬁcant at the
5% level, comparable to 0.30 in Table 2. In short, resource
shifting by ﬁrms is primarily driven by the spillover effects
from the California cap-and-trade rule, rather than by unrelated investment opportunities.

of a plant, using GDP data from the BEA. Although GDP
growth captures the overall economic activity and growth
within the plant’s local economy at the state level, it reﬂects realized values rather than expectations and is noisy
at state-industry levels. A plant’s local economy may also
not coincide with the ﬁrm’s product market. Therefore, we
construct a second forward-looking measure as the median
Tobin’s q of ﬁrms that own plants in the same state and
industry as the plant of interest, and also primarily operate in that industry. This market-based measure provides a
matched benchmark for growth opportunities reﬂected in
a parent ﬁrm’s peers in the same industry that also share
similar production opportunities at the state-industry level.
Panel A of Table 8 reports the population-weighted
cross-state averages of these two measures separately for
California and other states, each year over our sample period from 2010 to 2015. According to GDP growth, California outperformed other states by a large margin in terms
of economic growth during the post California cap-andtrade rule period of 2013 to 2015. The average annual
growth rate of California over this period was 4.1%, the
fourth highest of all U.S. states. In the period before the
cap-and-trade rule from 2010 to 2012, by contrast, California’s average growth rate was 2.1%, ranking below the
20th fastest growing state. In other words, California was
not only among the fastest growing states during the period after the introduction of its carbon-trading scheme,
but also among the states whose growth rates vastly improved relative to the period before the regulation (i.e., a
signiﬁcant increase of 2 percentage points, in contrast to
no signiﬁcant increase in other states).
According to median Tobin’s q, which better captures
market assessments of the growth prospects of a plant’s
parent ﬁrms and their peers, growth opportunities in California and other states were not very different before
(1.32 vs. 1.36) or after (1.38 vs. 1.40) the introduction of
the California cap-and-trade rule. Overall, we ﬁnd no evidence that investment opportunities were better in other
states than in California during the latter half of the sample period, inconsistent with the alternative explanation
that ﬁrms reallocated resources simply to capture better
growth opportunities in other states. In fact, the trends
are more consistent with constrained ﬁrms having reallocated despite higher growth in California due to their
lack of ﬁnancial ﬂexibility to exploit such opportunities
amid increased regulatory costs. The trends also imply that
the net returns from emitting in California remain large
enough that unconstrained ﬁrms would have little incentive to shift emissions.
In Panel B of Table 8, we employ regressions augmented from Eqs. (3) and (4) to formally examine whether
growth opportunities explain plant emissions, irrespective
of the cap-and-trade rule itself. The ﬁrst three regressions compare emissions for California and non-California
plants based on the sample of geographically diversiﬁed
ﬁrms. The regressions suggest that neither GDP growth
nor Tobin’s q signiﬁcantly affect emissions regardless of
whether ﬁrms are constrained, and that the effects of the
cap-and-trade rule on emissions are robust to controlling
for both growth measures as well as their interactions
with ﬁnancial constraints. The coeﬃcient on the triple-

5.3. Aggregate outcomes
5.3.1. Firm-level outcomes
A critical policy implication of the results thus far is
that the California cap-and-trade rule may not necessarily lead to the desired reduction in greenhouse gas emissions overall, but potentially result in an increase in emissions, undermining the goal of the policy. For example, if
the costs of emissions are lower in other states than in
California, as illustrated in Fig. 1, the predicted reallocation may result in an overall increase in emissions. We test
this possibility by aggregating plant emissions within ﬁrms
and comparing the changes in total emissions due to the
implementation of the cap-and-trade rule between ﬁnancially constrained and unconstrained ﬁrms. The results are
reported in Table 9, where we run ﬁrm-level regressions as
follows:

Log(1 + F irm T otal Emissionsi,t ) = α + β1 Aftert

+ β2 Aftert × Constrainedi + γ  Xi,t + ci + εi,t .

(6)

Log(1+Firm Total Emissionsi,t ) is the logarithm of metric tons of greenhouse gases emitted by ﬁrm i in year t.
To test whether ﬁnancially constrained and unconstrained
ﬁrms increase or reduce emissions differently, we include Constrainedi , Aftert , and their interaction. Xi,t denotes
the vector of ﬁrm-level control variables. ci denotes ﬁrm
ﬁxed effects. Although we are interested in the coeﬃcients for both Aftert and Aftert × Constrainedi to infer
overall increases or reductions in emissions, we also alter
the speciﬁcation to include industry-by-year ﬁxed effects
and drop Aftert to control for time-varying industry effects. We estimate this regression for geographically diversiﬁed ﬁrms that have plants both in California and in other
states.
Columns (1) and (2) of Table 9 show that unconstrained
ﬁrms with plants in and outside of California do not significantly reduce their total emissions, whereas constrained
ﬁrms actually increase their total emissions. The coeﬃcient on After × Constrained is as large as 0.29 and signiﬁcant at the 5% level, whereas the coeﬃcient on After is –0.08 and statistically insigniﬁcant. This ﬁnding implies that ﬁnancially constrained ﬁrms signiﬁcantly increase their ﬁrm-wide emissions by approximately 21% after the implementation of the cap-and-trade rule. Controlling for industry-by-year ﬁxed effects, we ﬁnd the coefﬁcient on After × Constrained becomes even more pronounced, with a point estimate of 0.30 that is signiﬁcant at
691

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 8
Do emissions chase growth opportunities?
The table examines whether changes in emissions after the implementation of the California cap-and-trade rule are explained by variations in growth
opportunities associated with plants. We employ two measures of growth opportunities: (1) Annual industry real GDP growth of the state the plant
is located in, and (2) median Tobin’s q of ﬁrms that own a plant in the same state and industry as the plant and primarily operate in that industry.
Panel A reports the population-weighted cross-state average real GDP growth and median Tobin’s q (ﬁrst averaged within states) over our sample
period from 2010 to 2015. The averages for the Before (2010–2012) and After (2013–2015) periods are shown, as well as the difference between the
two and its corresponding t-statistic. State-level GDP data are from the BEA. The ﬁrst three columns of Panel B compare emissions for California and
non-California plants owned by geographically diversiﬁed ﬁrms, controlling for GDP growth and Tobin’s q. The dependent variable is log (1+Emissions).
The ﬁrst two columns each include either GDP growth or Tobin’s q as its explanatory variable as well as its interaction with the ﬁrm-level Constrained
dummy variable based on our composite constraint measure. The third column includes all growth opportunity variables and adds the main variables:
CalPlant (equal to 1 if the plant is located in California, and 0 otherwise), After (equal to 1 if the time period is 2013 or onward, and 0 otherwise),
Constrained (indicator variable for whether a ﬁrm is ﬁnancially constrained according to our composite measure), and their interaction terms. The
last three columns of Panel B study spillovers to non-California plants comparing geographically diversiﬁed and non-diversiﬁed ﬁrms. The sample is
restricted to plants located outside of California, and the variable DivFirm indicates whether a ﬁrm owns plants both in California and in other states
during a given year. GDP growth and Tobin’s q are further interacted with DivFirm x Constrained and DivFirm. Control variables include ﬁrm size,
Tobin’s q, ROA, total debt, and R&D stock, all possible interactions between CalPlant (column (3)), DivFirm (column (6)), After, and Constrained, as well
as plant and industry-by-year ﬁxed effects. Standard errors are adjusted for clustering at the ﬁrm and state levels (columns (1)–(3) of Panel B) or ﬁrm
level (columns (4)–(6) of Panel B). ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: Growth opportunities in California and other states
State
State GDP growth (%)
California
Other states
Difference
Median Tobin’s q
California
Other states
Difference

2010

2011

2012

2013

2014

2015

Before (2010–2012)

After (2013–2015)

After–Before

t-stat.

1.60
2.70
–1.10

1.50
2.01
–0.51

3.10
2.43
0.67

2.90
1.99
0.91

4.40
2.68
1.72

4.90
2.79
2.11

2.07
2.38
–0.31

4.07
2.49
1.58

2.00
0.11
1.89

2.52
0.34
3.00

1.29
1.34
–0.05

1.36
1.41
–0.05

1.31
1.34
–0.03

1.34
1.35
0.00

1.42
1.43
0.00

1.38
1.43
–0.06

1.32
1.36
–0.04

1.38
1.40
–0.02

0.06
0.04
0.02

1.94
1.04
1.12

Panel B: Controlling for growth opportunities
Dependent variable: Log(1+Emissions)
California vs. non-California plants
(geographically diversiﬁed ﬁrms)
(1)

(2)

Spillovers to non-California plants
(diversiﬁed vs. undiversiﬁed ﬁrms)
(3)

(4)

(5)

CalPlant × After

0.305∗ ∗
(0.135)
–0.052
(0.097)

DivFirm × After × Const.
DivFirm × After

%GDP
%GDP × Const.

0.002
(0.009)
–0.021
(0.016)

–0.000
(0.013)
–0.014
(0.016)

%GDP × DivFirm
%GDP × DivFirm × Const.
Median q
Median q × Const.

–0.060
(0.101)
–0.095
(0.215)

–0.070
(0.098)
–0.043
(0.157)

Yes
Yes
Yes
No
3,149
0.858

Yes
Yes
Yes
Yes
3,143
0.858

0.006
(0.015)
–0.018
(0.019)
0.007
(0.020)
–0.008
(0.026)

Median q × DivFirm
Median q × DivFirm × Const.

Plant FE
Industry-by-year FE
Controls
Interactions
Observations
Adjusted R2

(6)

–0.364∗ ∗ ∗
(0.108)
0.075
(0.085)

CalPlant × After × Const.

Yes
Yes
Yes
No
3,143
0.858

692

Yes
Yes
Yes
No
10,382
0.730

–0.227∗ ∗
(0.107)
0.585∗ ∗ ∗
(0.177)
0.018
(0.152)
–0.338∗
(0.191)

0.000
(0.015)
–0.008
(0.019)
0.011
(0.026)
–0.008
(0.030)
–0.319∗ ∗
(0.135)
0.621∗ ∗ ∗
(0.210)
0.290
(0.238)
–0.569∗
(0.309)

Yes
Yes
Yes
No
10,401
0.732

Yes
Yes
Yes
Yes
10,382
0.733

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 9
Firm-level outcomes.
The table presents results from ﬁrm-level regressions testing whether ﬁrms affected by the California cap-and-trade rule increase their overall emissions, whether their operational eﬃciency is affected, and whether ﬁnancial constraints affect these responses. The responses of geographically diversiﬁed ﬁrms with plants both in California and in other states are tested. After is an indicator variable equal to 1 if the time period is 2013 or onward, and
0 otherwise. Constrained is an indicator variable for whether a ﬁrm is ﬁnancially constrained according to our composite measure. In columns (1)–(3),
the dependent variable is log(1+ﬁrm total emissions), where ﬁrm total emissions are computed by summing emissions across all plants owned by a
ﬁrm in a given year. In column (3), an alternative sample of undiversiﬁed ﬁrms that either do not have plants in California or do not have operations
in other states is used. In columns (4)–(5), the dependent variable measures operational eﬃciency at the ﬁrm level using ROA (column (4)) and Tobin’s
q (column (5)). Control variables include ﬁrm size, Tobin’s q, ROA, total debt, and R&D stock, as well as ﬁrm and industry-by-year ﬁxed effects. The
table reports coeﬃcients and standard errors adjusted for clustering at the ﬁrm level. ∗ ∗ ∗ , ∗ ∗ , and ∗ indicate signiﬁcance at the 1%, 5%, and 10% level,
respectively. The sample period is 2010–2015.
Dependent variables
Log(1+Firm total emissions)

After × Constrained
After

Firm FE
Industry-by-year FE
Controls
Observations
Adjusted R2

Operational eﬃciency

(1)

(2)

Placebo sample
(3)

0.293∗ ∗
(0.114)
–0.084
(0.078)

0.300∗ ∗ ∗
(0.108)

–0.053
(0.088)

0.015
(0.013)

–0.041
(0.057)

Yes
No
Yes
249
0.975

Yes
Yes
Yes
222
0.976

Yes
Yes
Yes
1532
0.886

Yes
Yes
Yes
217
0.715

Yes
Yes
Yes
217
0.932

the 1% level. These regressions fail to show an overall reduction in ﬁrm-level emissions in response to the cap-andtrade rule, but highlight an increase for constrained ﬁrms.
This observation contrasts with the insigniﬁcant changes
for a placebo group of undiversiﬁed ﬁrms (in column (3))
that either do not have plants in California, and are thus
unaffected by the cap-and-trade rule, or do not have operations in other states to reallocate emissions to (i.e., coeﬃcient on After × Constrained of –0.05, not statistically
signiﬁcant).21
We also examine whether constrained ﬁrms experience
improvements in ROA or Tobin’s q after implementation of
the cap-and-trade rule. We ﬁnd no such evidence for either measure of operational eﬃciency. In other words, constrained ﬁrms maintain their proﬁtability and valuations
when reallocating to locations where the net returns of
emissions are relatively higher after the cap-and-trade reduces net returns of emissions in California. This ﬁnding is
consistent with earlier evidence that the emission reallocations are not associated with changes in production eﬃciency.
In short, we ﬁnd no evidence that ﬁrms reduce their
overall greenhouse gas emissions as a result of the California cap-and-trade rule. To the contrary, the evidence suggests that ﬁnancially constrained ﬁrms with plants both in
California and in other states increase their total emissions,
consistent with spillover effects resulting in outcomes contradictory to climate policy objectives.

ROA
(4)

Tobin’s q
(5)

5.3.2. Impact on sectoral employment and GDP
We have thus far documented emission spillover effects from the California cap-and-trade rule driven by ﬁrm
ﬁnancial constraints, and we have shown its impact on
ﬁrm-wide total emissions. How are these results related to
broad economic outcomes such as economic activity and
employment? This question is important for economists
and policymakers who are interested in the macroeconomic impact of climate policies. To provide insight into
this issue, we conduct state-sector-level analyses using employment and real GDP data from the BEA. Speciﬁcally, we
draw on our emission reallocation results and hypothesize
that the California cap-and-trade rule may differentially
lower employment and economic activity in affected industries in California relative to other states. We also conjecture that growth from other industries may compensate
for this relative economic contraction from “polluting” industries.
We ﬁrst deﬁne a plant’s industry as the narrowest
NAICS code with at least 50 plants in the entire cross section each year, and map it to the narrowest available twoto four-digit NAICS industry classiﬁcation for which the
BEA reports state-level employment and GDP. We then collapse the data to state-sector-year level, where we broadly
categorize sectors as either an “emission sector” or “nonemission sector.” All BEA industries with greenhouse gas
emitting plants are pooled to constitute the emission sector, and all remaining industries are grouped as the nonemission sector. We then aggregate employment (total
number of full- and part-time wage-earning workers) and
GDP (inﬂation adjusted with respect to 2009 dollars) up to
each state-sector-year, and run the following regression:

Ys,t = α + β Cals × Aftert + as + bt + εs,t .

21
Without industry-by-year ﬁxed effects, the After coeﬃcient for the
placebo group is insigniﬁcant at 0.02, highlighting the lack of evidence
of a signiﬁcant overall reduction in emissions as a result of the California
cap-and-trade rule.

(7)

Eq. (7) is estimated at the state-year level for the emission sector and non-emission sector separately. Ys,t is ei693

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

Table 10
Impact on sectoral GDP and employment.
The table examines whether the California cap-and-trade rule differentially affects employment and GDP in affected industries in California compared
with other states, and whether growth from other industries countervails this effect. A plant’s industry is deﬁned as the narrowest NAICS code with at
least 50 plants in the entire cross section each year, and mapped to the narrowest available two- to four-digit NAICS industry classiﬁcation for which
the BEA reports state-level employment and GDP. The data are collapsed to state-sector-year level where sectors are categorized as either “emission
sector” or “non-emission sector.” All BEA industries with greenhouse gas emitting plants are pooled together to constitute the emission sector, and
all remaining industries are grouped as the non-emission sector. Employment (number of wage-earning workers) and GDP (inﬂation adjusted with
respect to 2009 dollars) are aggregated up to state-sector-year level. In Panel A, columns (1)–(2) report results with log(1+Wage employment) as
the dependent variable, and columns (3)–(4) use log(1+GDP) as the dependent variable. For each outcome variable, separate regressions are run for
the emission sector and non-emission sector, also reporting p-values from testing the statistical difference of the Cal x After coeﬃcients between the
emission and non-emission sector subsamples. Cal is a state-level dummy variable indicating whether the state is California, and After is an indicator
variable for whether the year is 2013 and later. In Panel B, we further split non-California control states into low- or high-regulation states based
on the 2005 Census PACE survey, where states are ranked according to the ratio of state-level total abatement operating costs to the total value of
manufacturing shipments and sorted into low or high with respect to the median state. The effects of the California cap-and-trade rule on emission
and non-emission sector employment and GDP are then compared between California and low-regulation control states, or between California and
high-regulation control states. State and year ﬁxed effects are controlled for. Standard errors are adjusted for clustering at the state level. ∗ ∗ ∗ , ∗ ∗ , and ∗
indicate signiﬁcance at the 1%, 5%, and 10% level, respectively. The sample period is 2010–2015.
Panel A: Substitution between emission and non-emission sectors
Dependent variables
log(1+Wage employment)

Cal × After

log(1+GDP)

Emission sector
(1)

Non-emission sector
(2)

Emission sector
(3)

Non-emission sector
(4)

–0.138∗ ∗
(0.068)

0.092∗ ∗ ∗
(0.007)

–0.046
(0.039)

0.075∗ ∗ ∗
(0.026)

p: Emission<Non-emission

[0.00]

State FE
Year FE
Observations
Adjusted R2

[0.00]

Yes
Yes
299
0.953

Yes
Yes
288
0.997

Yes
Yes
299
0.990

Yes
Yes
287
0.953

Panel B: Heterogeneity of substitution effect in regulatory stringency
Dependent variables
Log(1+Wage employment)
Emission sector

–0.308∗ ∗ ∗
(0.048)

p: Low<High
p: Low>High

State FE
Year FE
Observations
Adj R2

Non-emission sector

Emission sector

Control state regulatory stringency based on 2005 Census PACE survey
High
Low
High
Low
High
(2)
(3)
(4)
(5)
(6)

Low
(1)
Cal × After

Log(1+GDP)

–0.184∗ ∗ ∗
(0.052)

0.081∗ ∗ ∗
(0.011)

0.078∗ ∗ ∗
(0.013)

–0.053
(0.050)

[0.04]

0.053
(0.041)

Non-emission sector
Low
(7)

High
(8)

0.056∗ ∗
(0.020)

0.043
(0.027)

[0.05]
[0.43]

Yes
Yes
131
0.995

Yes
Yes
132
0.980

Yes
Yes
120
0.998

[0.35]

Yes
Yes
132
0.997

ther log(1+Employment) or log(1+GDP), Cals is a statelevel dummy indicating whether the state is California, and
Aftert is an indicator for whether the year is 2013 or later.
We control for state ﬁxed effects, as , and year ﬁxed effects,
bt .22
Table 10 reports the regression results. The ﬁrst two
columns of Panel A document a sizable impact of the California cap-and-trade rule on sectoral employment. The
negative coeﬃcient on Cal × After in column (1) implies a
14% greater reduction in employment (signiﬁcant at the 5%

Yes
Yes
131
0.996

Yes
Yes
132
0.985

Yes
Yes
120
0.989

Yes
Yes
129
0.988

level) in the emission sector in California than other states.
By sharp contrast, column (2) shows a relative increase in
employment by 9% more in the non-emission sector in California. The close-to-zero p-value conﬁrms the statistical
signiﬁcance of the difference between the Cal × After coefﬁcients in the emission and non-emission sectors.
The next two columns show evidence of differential
GDP growth across the two sectors. Column (3) shows a
marginal and statistically insigniﬁcant reduction of 5% in
the economic output from the sector of industries affected
by the California cap-and-trade rule. On the other hand,
column (4) shows that GDP in the non-emission sector increases signiﬁcantly by 8% (signiﬁcant at the 1% level). The

22
A visual inspection of the parallel trends in both employment and
GDP validates the DID design (see Fig. A.4 in the Internet Appendix).

694

S.M. Bartram, K. Hou and S. Kim

Journal of Financial Economics 143 (2022) 668–696

difference between the emission and non-emission sectors
is highly statistically signiﬁcant.
In Panel B of Table 10, we compare emission and
non-emission sector employment and GDP in California
against those in low- or highly regulated control states,
based on Census PACE surveys that provide rankings of
state regulatory stringency. The California emission sector suffers disproportionate losses in employment and GDP
when compared with low-regulation counterparts (i.e., 31%
lower employment growth, 5% lower GDP growth), but
not as much when compared with other highly regulated
states (i.e., 18% lower employment growth, 5% higher GDP
growth). A substitution in employment and GDP growth
is observed in California’s non-emission sector when it is
compared with less regulated control states. These results
are consistent with the results in Table 7 of greater plantlevel emission reallocations within constrained ﬁrms toward less regulated states.
Overall, the results suggest a macroeconomic tradeoff
from the California cap-and-trade rule. Industries affected
by the regulation in California exhibit decreases in employment and GDP relative to other states, consistent with
ﬁrms shifting production and employment outside of California. At the same time, we ﬁnd a countervailing relative growth in employment and GDP in the non-emission
sector comprising “clean” industries. However, we are agnostic about the eventual welfare implications of these results and caution the reader that these macroeconomic
outcomes should be interpreted as relative reallocations
not only across industries but also across regulatory jurisdictions.

sions. In fact, constrained ﬁrms strictly increase their emissions ﬁrm-wide. Our results are consistent with the internal reallocation of corporate pollutive activities and resources to avoid regulatory costs when ﬁrms face ﬁnancial
constraints, highlighting the hidden costs of environmental
policies.
Our study makes a signiﬁcant contribution to the understanding of the interplay between climate policy and
ﬁrm behavior, and provides a stepping stone toward more
effectively coordinated solutions to climate change by informing policymakers of the potential externalities from
regionally segmented climate policies. This contribution is
important because if localized climate policies prove ineffective even within one country, they are unlikely to have
the intended effect of reducing emissions on a global scale
across countries. Our ﬁndings point to two policy guidelines: (1) Given the geographically diversiﬁed nature of
ﬁrms’ operations, climate policies should be harmonized
across jurisdictions to minimize leakage. (2) Given that
ﬁnancially constrained ﬁrms have stronger incentives to
reallocate, policymakers should carefully devise appropriately differentiated subsidies to mitigate distortions from
implementing climate policies (e.g., tax incentives).
Finally, this paper also contributes to the growing literature on corporate environmental policies by focusing on
the internal plant-level emission activities and resource allocations within ﬁrms, thus providing a unique channel for
the real effects of climate policy through the importance of
ﬁrm ﬁnancial constraints.

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==> JFE16 - Four facts about ESG beliefs and investor portfolios.txt <==
Journal of Financial Economics 164 (2025) 103984

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/finec

Four facts about ESG beliefs and investor portfolios✩
Stefano Giglio a ,∗, Matteo Maggiori b , Johannes Stroebel c , Zhenhao Tan a , Stephen Utkus d,e ,
Xiao Xu f
a Yale School of Management, United States
b

Graduate School of Business, Stanford University, United States
Stern School of Business, New York University, United States
d
Georgetown University, United States
e
University of Pennsylvania, United States
f
Vanguard, United States
c

ARTICLE

INFO

Dataset link: Replication Package (Original dat
a)
JEL classification:
G4
G5
Q50
Q54
Keywords:
Surveys
Expectations
Climate finance
ESG
Sustainable finance

ABSTRACT
We analyze survey data on ESG beliefs and preferences in a large panel of retail investors linked to
administrative data on their investment portfolios. The survey elicits investors’ expectations of long-term ESG
equity returns and asks about their motivations, if any, to invest in ESG assets. We document four facts. First,
investors generally expected ESG investments to underperform the market. Between mid-2021 and late-2023,
the average expected 10-year annualized return of ESG investments relative to the overall stock market was
−2.1%. Second, there is substantial heterogeneity across investors in their ESG return expectations and their
motives for ESG investing: 48% of survey respondents do not see any reason to invest in ESG, 24% are primarily
motivated by ethical considerations, 22% are driven by climate hedging motives, and 6% are motivated by
return expectations. Third, there is a strong link between individuals’ reported ESG investment motives and
their actual investment behaviors, with the highest ESG portfolio holdings among individuals who report ethicsdriven investment motives. Fourth, financial considerations matter independently of other investment motives:
we find meaningful ESG holdings only for investors who expect these investments to outperform the market,
even among those investors who reported that their most important ESG investment motives were ethical or
hedging reasons.

The last decade has seen a substantial growth in investment approaches that consider assets’ environmental, social, and governance
(ESG) characteristics, and, by the end of 2022, sustainability-focused
funds had more than $2.5 trillion in global assets under management (Bioy et al., 2023). While some proponents of ESG investing extol
its societal benefits, critics argue that retail investors might not fully
appreciate the possible financial return implications of incorporating
ethical considerations into investment decisions. Despite the growing
focus on the costs and benefits of ESG investing among researchers and
policymakers (see, for example, recent work by Goldstein et al., 2022;
Pástor et al., 2021; Pedersen et al., 2021), the actual motives of retail

investors for investing in ESG assets—including the relative importance
of financial and non-financial considerations—are not well understood.
To inform this ongoing debate, we document four facts about ESG
investing by linking survey data on ESG beliefs and preferences with
administrative data on investor portfolios for a large panel of U.S. retail
investors. The survey includes three questions on ESG investing. The
first such question elicits investors’ long-run (10-year) return expectations from investing in a diversified ESG equity portfolio. We compare
these expectations to the same investors’ long-run expected returns

✩ Nikolai Roussanov was the editor for this article. We are grateful to him and to an anonymous referee for their insightful comments. Stephen Utkus was
formerly employed at Vanguard in a research capacity. Xiao Xu is employed at Vanguard in a research capacity. Giglio, Maggiori, Stroebel, and Tan are unpaid
consultants at Vanguard in order to access the anonymized data. Vanguard provided anonymized portfolio and survey data as well as survey research services
for this project. Maggiori’s spouse is employed by Wellington Management Company LLP as a Managing Director in the Investment Science Group. ESG is one of
the group’s areas of research. Wellington manages funds on behalf of Vanguard. We are grateful for financial support from the Tobin Center for Economic Policy
at Yale University. The authors would like to thank Sophia Bunyaraksh, Catherine Clinton, Fiona Greig, Andy Reed and Jean Young at Vanguard for their help
with the project.
∗ Corresponding author.
E-mail addresses: stefano.giglio@yale.edu (S. Giglio), maggiori@stanford.edu (M. Maggiori), johannes.stroebel@stern.nyu.edu (J. Stroebel),
zhenhao.tan@yale.edu (Z. Tan), steveutkus@comcast.net (S. Utkus), xiao_xu@vanguard.com (X. Xu).

https://doi.org/10.1016/j.jfineco.2024.103984
Received 13 November 2023; Received in revised form 1 December 2024; Accepted 5 December 2024
Available online 21 December 2024
0304-405X/© 2024 Published by Elsevier B.V.

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.

for the overall stock market, which are also elicited in the survey.
The second question asks investors which of the following possible
ESG investment motives is most important to them: (i) no reason,
(ii) excess financial returns, (iii) non-pecuniary ethical considerations,
or (iv) hedging reasons, whereby ESG assets have relatively higher
returns when climate risks materialize. These reasons are often cited
as rationales for ESG investing in the academic literature and financial
press.1 A third question elicits investors’ level of concern about climate
change.
The survey is administered by Vanguard, one of the world’s largest
asset management firms, to its U.S.-based clients. In addition to the
three ESG-related questions, the survey also elicits investors’ beliefs
about stock returns, bond returns, and GDP growth. The survey participants are a random sample of U.S.-based clients of Vanguard, 80%
of whom have retail accounts at Vanguard, and 20% of whom have
retirement accounts. The original survey has been running every two
months since February 2017, and the ESG-related questions were added
in June 2021. In this paper, we analyze the sixteen waves of the survey
containing the ESG-related questions between June 2021 and December
2023. Each survey wave receives around 2000 responses, and investors
often respond to several waves, thus providing a substantial panel
dimension to the data.
We collect the results in this paper in four facts. Fact 1 is that
investors on average expected returns on ESG equities to be significantly lower than returns on the overall stock market, by about 2.1%
per year over a 10-year horizon. This expectation is consistent with
several potential explanations. For example, investors may believe
that ESG stocks are overpriced and likely to experience low returns
going forward. Alternatively, investors may perceive lower expected
returns as an equilibrium outcome driven by ESG stocks’ attractive
hedging properties against future climate disasters or their attractive
non-pecuniary benefits to investors with ethical considerations. The gap
between expected market returns and (lower) expected ESG returns has
widened during our sample period, from −1% in June 2021 to −2.5%
in December 2023.
Fact 2 describes the substantial heterogeneity across investors in
ESG return expectations and ESG investment motives. The standard
deviation of expected excess ESG returns across all investors is an
economically meaningful 5%, which is of similar magnitude as the
standard deviations of expected overall market returns (4%). While
there are some differences in expectations across demographic groups
(e.g., male respondents and those who live in more politically conservative areas are relatively more pessimistic about excess ESG returns),
observable characteristics explain only a small part of the heterogeneity
in these expectations. Interestingly, beliefs about the relative returns of
ESG investments are unrelated to beliefs elicited about market returns,
GDP growth, the probability of disasters, or bond returns. This suggests
that the large heterogeneity in beliefs about ESG returns represents
a separate dimension of the investors’ beliefs relative to traditional
variables that enter the investment decision.
There is also sizeable heterogeneity across investors in terms of
motives to invest in ESG assets. About 48% of survey respondents do
not see any specific reason to invest in ESG stocks. The remaining
respondents are split between different perceived primary reasons to
invest in ESG assets: 6% of respondents are primarily motivated by
return expectations, 22% perceive ESG stocks as a hedge against climate risk, and 24% are most motivated by ethical arguments for ESG
investing. Over time, individuals’ assessments of the reasons to invest
in ESG can change: while most respondents who believe there are no
good reasons to invest in ESG hold this view throughout our sample

period, many who initially report return considerations as their most
important motivation for ESG investing no longer hold this view later
in the sample. Over our 30 months sample, the share of respondents
who report that there are no good reasons to invest in ESG increased
by 5 percentage points.
The ESG investment motives that an investor perceives as most important are related to that investor’s ESG return expectations. Investors
who report return considerations as their most important investment
motive on average expect ESG investments to outperform the market
by 1% per year over the next ten years. Investors reporting each of
the other three investment motives on average expect ESG investments
to underperform the market. Those investors who do not perceive any
reason to invest in ESG hold the most negative views, with average
annual long-run expected excess ESG returns of −3.6%.
Our next fact, Fact 3, highlights that ESG beliefs regarding returns,
ESG motivations, and concerns for climate change are all related to
the actual holdings of ESG investments. To study ESG investments, we
focus on investments in ESG-focused mutual funds and ETFs rather than
individual securities.2 While it is not necessarily clear to what extent
ESG-focused funds actually hold securities consistent with this stated
objective and whether available classifications of funds and stocks as
ESG are reliable, we take the practical view that the labeling of a fund
as ESG-related is salient to investors, who are not necessarily checking
whether the ESG label is meaningful (see Hartzmark and Sussman,
2019). Only about 3.4% of respondents in our sample own at least some
ESG-focused funds. This propensity is declining in age and is higher for
investors living in politically more liberal areas but does not otherwise
vary substantially with investors’ demographic characteristics.
We find a statistically strong association between ESG beliefs and
investments: investors who report higher expected returns from ESG
investments hold a higher share of ESG funds in their portfolios. The
relation between ESG holdings and beliefs is stronger in the positive
domain (i.e., among investors who expect ESG funds to outperform
the market) relative to the negative domain (i.e., among investors who
expect underperformance), suggesting that frictions related to shorting
might play a role in determining retail investors’ ESG investments.
We also find a strong association between ESG holdings and reported motives for such investments. Investors who report perceiving
no reason to invest in ESG effectively own no ESG investments. Investors who report return-driven motives to invest in ESG assets and
those motivated by ethical reasons are similarly likely to hold ESG
investments (with those motivated by ethical reasons holding the larger
portfolio share), followed by those motivated to buy ESG funds as
climate hedges. Overall, about half of the investors actually holding
ESG assets report to be primarily motivated by ethical considerations.
Similar patterns hold for the reported level of concern for climate risk:
investors who are highly concerned about climate risks hold a larger
fraction of their portfolio in ESG funds, and 81% of actual ESG investors
report a high level of concern about climate risk.
Finally, we investigate the trade-off between reported ESG investment motives and return expectations in determining actual ESG investment behavior. Fact 4 highlights that within each group of investors
with the same perceived primary ESG investment motive, actual ESG
holdings vary substantially with investors’ expected return. For example, even among investors who report ethical considerations as their
primary motive for investing in ESG, the share of individuals with
actual ESG investments is 4% among those who expect an excess
return of less than −0.5%, and 11% among those who expect an excess
return of more than 0.5%. This finding suggests that traditional investment motives remain an important driver of portfolio allocation even

1
For example, Pástor et al. (2021) and Goldstein et al. (2022) emphasize ethical considerations, Engle et al. (2020) and Alekseev et al. (2022)
discuss hedging properties, and Baron (2001), Bénabou and Tirole (2010)
and Albuquerque et al. (2019) analyze the ability to generate excess returns.

2
We use a classification by Morningstar to divide the universe of mutual
funds and ETFs available to Vanguard retail clients into those that have an ESG
focus and those that do not. These include funds managed by both Vanguard
and other entities.

2

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S. Giglio et al.

among respondents who believe that there are important non-pecuniary
reasons for investing in assets with good ESG properties.
Beyond these four main facts, we document several other patterns
that characterize the behavior of beliefs about ESG investments in
our sample. For example, a variance decomposition of beliefs shows
that the large cross-sectional heterogeneity of ESG beliefs is persistent
over the 30-month period of our survey, hinting that ESG optimism or
pessimism may be a relatively fixed individual characteristic.
Taken together, our results show that expected excess ESG returns,
perceived ESG investment motives, and actual ESG investments vary
substantially among investors. The fact that ESG beliefs and preferences
are actually associated with portfolio allocation—though in a nuanced
way—is a relevant step in the transmission of these attitudes into asset
prices and ultimately to firm behavior. The heterogeneity that we document (in beliefs, ESG holdings, and climate concerns) has interesting
consequences for both theory and policy. On the theory side, it can
be used to calibrate and discipline theoretical models that explicitly
consider investors who are driven by different motivations for ESG investing (Heinkel et al., 2001; Berk and van Binsbergen, 2021; Goldstein
et al., 2022; Pástor et al., 2021). On the policy side, tracking the evolution of investors’ ESG attitudes and investments can help policymakers
align their regulatory and legislative responses to climate change with
corresponding pressures from investors and other market participants.
For both policy and economic theory, the heterogeneity in expected
returns and perceived ESG investment motives is an important input
in deciding whether ESG-oriented investment products should target
a broad population (e.g., as a default option in employer-sponsored
pension funds) or should best be left to individual decision makers.
Our paper focuses on a sample of investors with accounts at Vanguard. The very substantial size of Vanguard—the universe from whom
our sample is drawn holds about $2.5tr of assets—makes this an
important group of investors to study. However, as discussed in Giglio
et al. (2021c), it is possible that our findings may not generalize to
the rest of the U.S. retail investor population. Indeed, while Giglio
et al. (2021c) documented that Vanguard investors were very similar
to other U.S. retail investors on a number of important dimensions,
such as their beliefs about stock returns, they also found that Vanguard
investors were older and wealthier than the average retail investor.
In this paper, we explore how Vanguard investors differ from other
retail investors in terms of their ESG holdings, a dimension that was not
considered in prior work and which is particularly relevant to assess the
generalizability of our findings. We document that Vanguard investors
hold a somewhat lower fraction of assets in ESG investments compared
to the average U.S. investor, and argue that this likely reflects the more
limited supply of ESG funds offered by Vanguard than a difference
in ESG beliefs with the broader population (investors at Vanguard
disproportionately hold Vanguard funds). For example, we provide
evidence suggesting that our findings are unlikely to be driven by
investors who chose Vanguard because of its particular ESG philosophy,
and who may thus differ substantially from other investors. Indeed, the
facts we document (on both ESG beliefs and holdings) are essentially
identical if we focus only on those investors that joined Vanguard
before 2016 and prior to any salient public debates around the merits
of ESG investments.

willing to pay an average of 20 basis points to invest in funds with
an ESG mandate. Our work suggests that the average ESG investor
perceives those investments to outperform the market (even if they
may actually be expected to underperform after fees). Our data also
allows us to explore more broadly the strength of non-pecuniary investment motives in driving the decisions of ESG investors. Our work
also complements recent research that has used a variety of surveys or
field and laboratory experiments to explore whether investors have a
positive willingness to pay for sustainable or impact investments (Heeb
et al., 2023; Humphrey et al., 2021; Bauer et al., 2021; Haber et al.,
2022; Engler et al., 2023), and work that has explored investors motivations for ESG investments by studying investment flows (Renneboog
et al., 2011; Döttling and Kim, 2024). Li et al. (2023) investigate the
aggregate trading patterns of retail investors around ESG news events
for U.S. firms and conclude that U.S. retail investor shows interest in
firms’ ESG activities, primarily when these activities have a significant
financial impact on company performance.
Closely related to these studies of investors’ ESG investment motives
is work that studies those investments’ financial performance. This
research finds conflicting evidence on the financial returns to ESG
investing, thus providing little consistent insight into the importance
of either hedging benefits or non-pecuniary payoffs from such investments (Hong and Kacperczyk, 2009; Bolton and Kacperczyk, 2021;
Barber et al., 2021; Friede et al., 2015; Khan et al., 2016; Atz et al.,
2023). A key challenge for this literature is that ex-post average realized
returns are both noisily estimated in short samples and influenced by
temporary shifts in investor demand, complicating their interpretation
as forward-looking measures of expected return. This contrasts with
survey data, which provides an ex-ante measure of expected returns.
We find that the average retail investor expects ESG investments to
have negative expected returns, but that there is substantial heterogeneity in those expected returns. Among those individuals actually
investing in ESG funds, the expected returns of those investments are
positive.
More broadly, we add to literature on ‘‘climate finance’’, that studies
the role of climate risk in affecting returns and investments in financial
markets (Heinkel et al., 2001; Andersson et al., 2016; Broccardo et al.,
2022; Hong et al., 2021; Oehmke and Opp, 2020; Pedersen et al., 2021;
Alekseev et al., 2022; Alok et al., 2020; Bolton and Kacperczyk, 2021,
2020; Engle et al., 2020; Flammer et al., 2021; Giglio et al., 2021b;
Hartzmark and Sussman, 2019; Krueger et al., 2020; Acharya et al.,
2023). For recent reviews of this growing field, see Giglio et al. (2021a),
Stroebel and Wurgler (2021) and Hong et al. (2020).
1. Survey description
This paper explores data from a panel survey of investor beliefs—
the GMSU-Vanguard survey—linked to administrative data on those
investors’ portfolio holdings. The survey is fielded among U.S.-based
retail and retirement clients of Vanguard, one of the world’s largest
asset management firms. It has been conducted every two months since
February 2017, and receives about 2,000 responses per wave. The
online survey asks a randomly selected sample of Vanguard retail and
retirement clients a short set of questions about short-term and longterm expected stock and bond returns and expected GDP growth. In
June 2021, two ESG-related questions were added to the survey; a
third such question was added in December 2021. In this section, we
describe the new questions in detail. We also provide additional details
on the survey sample. For other information on the survey, including
details on questions not related to ESG investments, we defer to the
descriptions in Giglio et al. (2021c, 2020).

Related literature. Our paper contributes to three strands of literature.
The first strand explores investors’ motivations for ESG investing. An
important paper by Riedl and Smeets (2017) matches portfolio holdings
of a sample of Dutch investors with a 2012 survey and studies whether
social preferences or return expectations determine socially responsible
investments. We confirm several of the patterns that they documented
among a large sample of wealthy U.S. investors in a recent period
of increased focus on ESG investing. We provide new evidence in
several important dimensions, for example by directly studying the
motivations driving ESG portfolio choices and the trade-offs between
those motivations and expected returns.
In related work studying investors’ ESG preferences, Baker et al.
(2022) explore the fees for ESG funds to conclude that investors are

1.1. ESG questions
The newly added ESG questions, which appear at the end of the
regular survey, are shown in Fig. 1. While ESG investing has received
much attention in recent years—and our relatively sophisticated sample
3

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S. Giglio et al.

Fig. 1. ESG questions in GMSU-Vanguard survey. Figure shows the three questions on ESG investing in the GMSU-Vanguard survey.

of investors is thus likely to be familiar with the term—we begin by
providing a broad definition.
The first question asks respondents about the expected return on
a diversified U.S. ESG equity portfolio. The question focuses on the
average annualized return over a 10-year horizon. The phrasing of this
question is directly comparable to an earlier question in the survey
that asks about 10-year expected annual returns of the aggregate stock
market. The difference in the answers between expected returns of
ESG investments and expected returns of the stock market allows us to

measure expected excess returns of ESG investments over the general
stock market. We focus on 10-year returns because this longer horizon
is more relevant to realizations of climate change, a key force driving
the investor focus on ESG issues. The response is entered by survey
respondents in a text box that accepts up to 1 decimal point.
The second question aims to characterize the primary motives to
invest in ESG portfolios as perceived by the investors, chosen among
the main ones discussed in the literature. This question thus exploits a
key benefit of surveys, namely that they can provide insight into the
4

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S. Giglio et al.

thought process of respondents (Bailey et al., 2019). The survey asks
respondents to choose the investment motive that is most important
to them among four options. First, investors may perceive ESG funds
to have a higher long-run return than the market; this would, for
example, capture the beliefs of investors that currently think the market
is underpricing ESG investments. Second, investors may believe that
ESG portfolios act like climate hedges and would do particularly well
when climate risks materialize. Third, investors might view ethical
motives for ESG investments as most important to them, stating that
such investments are ‘‘the right thing to do’’. Finally, investors may
perceive no specific reasons to invest in ESG. While more qualitative in
nature, this second survey question helps to contextualize the beliefs
about expected returns on ESG investing elicited in the first question,
and can help us distinguish between several different views that might
be consistent with a given perceived excess return of ESG investments.3
The third ESG-related question asks whether investors are concerned about climate change. We generally combine the ‘‘Extremely
concerned’’ and ‘‘Very concerned’’ into ‘‘High concern’’ and the ‘‘Not
very concerned’’ and ‘‘Not at all concerned’’ into ‘‘Low concern’’. This
question allows us to explore whether beliefs and attitudes towards ESG
investments are determined by concerns about climate change.

The ESG questions appear at the end of the pre-existing survey
and the survey is not branded as ESG-related. Essentially all survey
participants provide answers to the ESG questions (see Appendix Table
B.1). This minimizes concerns that respondents to the ESG questions
are selected based on particular views on this issue.5 We analyze
the sixteen (thirteen) waves of the survey containing the first two
(third) ESG-related questions between June 2021 (December 2021) and
December 2023. Investors in our sample are relatively wealthy, with
an average of total Vanguard portfolio value of about $684k. About
64% of the respondents are male, and the average age is 63 years
old. Full summary statistics on the demographics of the respondents,
as well as analyses that explore whether and how respondents differ
from non-respondents, are presented in Appendix Table B.2.
In Appendix A we explore the differences between the ESG holdings
of Vanguard clients and the ESG share among the universe of U.S.
funds. We document that the average ESG share of all Vanguard retail
investors is around 0.4%. While this is similar to the average ESG
portfolio share of our survey respondents, it is lower than the 1.2%
ESG share of assets under management of the universe of U.S. funds
reported by Morningstar. There are three potential reasons why the ESG
holdings of Vanguard investors might be lower than for the broader
fund universe.
The first possibility is that holdings in U.S. ESG funds might disproportionately come from non-U.S.-based investors, and that the holdings
of our Vanguard sample actually correspond more closely to the ESG
holdings of U.S.-based retail investors (we are not aware of any aggregate data on ESG holdings of the universe of retail investors by
location).
A second possibility is that Vanguard investors might, on average,
view ESG issues less positively than the average U.S. retail investor. In
particular, it is possible that following the recent debates about the merits of ESG investment, Vanguard might have attracted relatively more
ESG-skeptical investors. However, given that our results are identical
when focusing on the sample of investors that joined Vanguard before
2016—that is, long before the recent debate about the merits of ESG
investing might have allowed investors to infer the ESG philosophies
among the large asset managers—we find this interpretation unlikely.6
A third possibility is that the ESG share of Vanguard investors
might in part reflect the more limited choice of ESG funds offered by
Vanguard to their clients, compared to other asset managers such as
BlackRock. In Appendix A we provide evidence consistent with this
explanation. Vanguard investors overwhelmingly tend to buy Vanguard
funds (specifically, Vanguard retail clients allocate 80% of their investments to Vanguard funds even though they are not generally restricted
from purchasing funds of other asset managers); and Vanguard ESG
funds have about 0.4% of the AUM of all funds offered by Vanguard, a
number that is significantly lower than that of other issuers and close
to the average ESG share among Vanguard investors. This explanation

1.2. Survey sample
As described in Giglio et al. (2021c), the random sample for the survey is selected so that 80% of contacted individuals are retail investors
and 20% are investors in defined contribution plans, subject to additional requirements (most importantly: that they are 21 years or older,
and that they have Vanguard assets of at least $10,000). Overall, the
sample of individuals who are potentially contacted represents about
$2.5 trillion in assets at Vanguard. The survey has a substantial panel
dimension: if individuals respond to the survey in any wave, they are
recontacted in each subsequent wave. New potential respondents are
additionally contacted in each wave. Individuals who do not respond
to the first three waves in which they are contacted, or those who at
any point opt out of the survey, are not contacted again. The survey
receives around 2,000 responses per wave, a large number of them from
re-respondents (see also Appendix Figure B.1).4 A detailed description
of the sample and overall response rates, as well as an analysis of the
demographic differences in response rates can be found in Giglio et al.
(2021c).

3

Of course, as with any survey question, there is a risk that both the
phrasing of the question and the structure of the allowable answers might
somehow influence the responses. In this type of question, for example, respondents have sometimes been shown to be hesitant to select ‘‘no reason’’ (see,
e.g., the extensive discussion in Bergman et al., 2020). In this particular case,
for example, one may worry that investors that are less positive about ESG
may quickly exclude pecuniary and ethical reasons to invest in ESG, and
then, among the remaining choices, choose the hedging option as it is the
only remaining one that is described with some explanation of why it may
make sense (the other being ‘‘No reason’’). While, in our setting, about 50%
of respondents do select ‘‘no reason’’, there might have been some respondents
who were discouraged from doing so, and selected hedging motives instead.
We leave it to future research to understand the extent such a concern
influences our results.
4
All waves prior to the last final one in December 2023 were administered
using the Radius platform. In the last wave, we randomly divided the prior
respondents between the Radius and Qualtrics platforms in preparation for
transitioning our survey operations to the Qualtrics platform starting in 2024.
In the Qualtrics version of the survey, the ESG-related questions were not
included, so the entirety of the responses in this paper come from the same
(Radius) platform. To ensure we reached our target number of participants in
the last wave despite splitting the sample or prior respondents between Radius
and Qualtrics, we included a higher volume of initial invitations. As a result,
the last wave saw an increase in new respondents and a decrease—by about
a half—in the number of re-respondents.

5
For example, one could be concerned that a survey specifically branded
as ESG-related might attract more participation from those investors who
specifically care about ESG issues. In our sample, many of the respondents
had already responded to the survey at least once before the ESG questions
were introduced and their answers are not meaningfully different on average
than those provided by newly contacted respondents.
6
Of course, it could still be that the kind of investors that have Vanguard
accounts might on average view ESG issues less positively than other investors,
even if they did not select to invest with Vanguard based on their ESG
preferences. We cannot rule this possibility out directly, but it is useful to note
that the analysis in Giglio et al. (2021c) compares Vanguard investors and U.S.
retail investors along multiple non-ESG dimensions, and shows that the two
investor groups are generally very similar on important dimensions, such as
flow-performance sensitivity, and, importantly, on the level and time-series
variation of their (non-ESG) beliefs. There are therefore no strong a-priori
reasons to expect Vanguard investors to be particularly more pessimistic about
ESG considerations relative to other investors.

5

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.
Table 1
Expected ESG returns.
Panel A: Expected 10Y return of ESG investments & stock market (% p.a.)

Pooled ESG
Pooled market

Mean

SD

P5

P10

P25

P50

P75

P90

P95

N

5.20
7.13

4.88
3.96

0
3

1
3

3
5

5
7

7
8

10
10

12
12

30,425
30,667

Panel B: Expected excess 10Y return of ESG investments (% p.a.) by demographic characteristics
Mean

SD

P5

P10

P25

P50

P75

P90

P95

N

Pooled

−2.06

5.34

−10

−6.5

−3

−1

0

2

4

30,105

By age
≤40
41–50
51–60
61–70
>70

−2.11
−2.00
−2.07
−2.13
−1.96

6.02
5.45
5.47
5.37
5.10

−13
−10
−10.5
−11
−10

−7
−7
−7
−7
−6

−3
−3
−3
−3
−3

−1
−1
−1
−1
−1

0
0
0
0
0

3
2
2
2
2

5
4
4
3.45
4

1,544
2,103
5,047
11,640
9,655

By gender
Female
Male

−1.75
−2.19

5.53
5.25

−10
−10

−6.5
−6.5

−3
−3

−1
−1

0
0

3
1.6

5
3

9,434
20,586

By wealth
<$100k
$100k–$500k
$500k–$1 m
>$1 m

−2.03
−2.06
−2.10
−2.02

6.29
5.59
5.07
4.37

−12
−10
−10
−8

−8
−7
−6
−6

−4
−3
−3
−3

−1
−1
−1
−1

0
0
0
0

3
2
2
1

6
4
3
2

5,644
10,602
5,872
7,902

By flood risk exposure
Low
Medium
High

−2.09
−2.05
−1.96

5.33
5.40
4.93

−10
−10
−9.5

−7
−6
−6

−3
−3
−3.5

−1
−1
−1

0
0
0

2
2
2

4
4
4

13,037
14,080
2,257

By political view in location
Democratic
Republican

−1.86
−2.40

5.09
5.75

−10
−12

−6
−7

−3
−4

−1
−1.8

0
0

2
2

4
4

16,254
7,800

Panel C: Expected excess 10Y return of ESG investments (% p.a.) by other ESG questions
Mean

SD

P5

P10

P25

P50

P75

P90

P95

N

By reasons of ESG investment
ESG will outperform
ESG hedges climate risk
It is the right thing to do
No specific reason

1.00
−0.65
−0.98
−3.64

4.68
4.84
3.70
5.82

−5
−7
−6
−15

−2
−5
−4
−9

0
−2
−2
−5

1
0
−1
−2

2
1
0
−1

5
3
2
0

8
6
4
1

1,890
6,439
7,291
14,352

By climate change concerns
Low
Moderate
High

−4.82
−2.17
−1.04

7.06
4.84
4.47

−19
−9
−7

−13
−6
−5

−6
−3.1
−2

−3
−1.9
−0.5

−1
0
0

0
1
2

2
3
4

6,310
6,175
11,901

Panel D: Expected excess 10Y return of ESG investments (% p.a.) by ESG holdings

By ESG investments
Has no ESG investments
Has ESG investments

Mean

SD

P5

P10

P25

P50

P75

P90

P95

N

−2.12
−0.16

5.36
4.46

−10
−5

−7
−3

−3
−1

−1
0

0
1

2
3

4
5

29,076
1,029

Panel A of the table shows summary statistics of the 10-year annualized expected return of ESG investment and the 10-year annualized expected return on the market portfolio,
pooled all responses. Panel B shows summary statistics of the 10-year annualized expected excess return of ESG investment (i.e., the difference between the expected returns on
ESG investments and the market), pooled all responses and divided by characteristics. Panel C shows summary statistics of the expected excess ESG returns, divided by the other
two ESG questions, which are the stated motivations of ESG investments and the level of concern about climate change. Panel D shows summary statistics of the expected excess
ESG returns, divided by whether a respondent has any ESG investment. The flood risk exposures are based on the average risk scores of the zip code area where the respondents
live (low: <1.5, medium: ≥1.5 & <3, high: ≥3). The average risk scores are measured by the flood risk models of the First Street Foundation. The political views of living areas
are based on county-level vote shares (considering only Democrat and Republican) from the 2020 US election.

2. Beliefs about ESG investments

would then contribute to the lower level of ESG holdings among Vanguard investors, but would not necessarily imply that the ESG beliefs
of Vanguard investors, or their portfolio-belief sensitivity, are different
from that of the average investors. Of course, one would also expect
the offering of funds from Vanguard to be at least somewhat responsive
to the clients’ preferences, making it hard to separate the demand and
supply explanations for the equilibrium set of funds on offer.
In the end, while the empirical evidence is not suggestive of Vanguard investors having particularly different ESG beliefs than the average investor, it is important to keep in mind that given the absolute size
of the Vanguard population under investigation (as mentioned above,
the potential survey respondents hold around $2.5 trillion in wealth), it
is an independently interesting group to study, even if one ought to be
somewhat cautious to extrapolate all findings to a broader set of retail
investors.

In this section, we explore the reported beliefs about ESG returns,
motivations, and climate change concerns from our survey, and summarize the results in our first two facts.
2.1. ESG return expectations
Table 1 summarizes the beliefs about ESG returns across survey participants.7 Panel A shows summary statistics for the 10-year expected

7
A small number of extreme outlier responses from individuals reporting
stock market or ESG returns in excess of 100 percent would potentially have
extreme effects on the analysis. Following Giglio et al. (2021c), we therefore

6

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.

annualized returns on ESG investments and the overall market, pooling
together all survey responses. The average expectation of long-run
returns on the market is about 7.1% per year—broadly consistent with
historical average returns of the U.S. stock market—with a standard
deviation across responses of 4%. Average expected 10-year returns for
ESG investments are lower—about 5.2% per year—and there is more
dispersion in beliefs about ESG returns than about market returns, with
a standard deviation across responses of 4.9% (see also Appendix Figure
B.2).
Panel B of Table 1 focuses on the difference between the expected
returns on ESG investments and the market, the expected excess ESG
return. As discussed in Pástor et al. (2021) and Alekseev et al. (2022),
data limitations including short time spans and structural breaks complicate estimating the relative performance of ESG investments from
time series data. A survey such as ours can thus complement the
existing evidence by giving a direct insight into the ex-ante returns
expected by investors.
The first row of Panel B shows the results when pooling all responses. Consistent with Panel A, we find the expected excess return
to be negative for the average investors’ answer, at about −2.1% per
year over the next ten years. We collect this result on expected ESG
returns in our first fact.

2.2. ESG investment motives
An important advantage of our survey is that we can investigate
investors’ motives for making ESG investments. To do this, we next
explore the second and third ESG-related questions in the GMSUVanguard survey. Table 2 summarizes the responses to these questions,
first pooled across all investors, and then by investor characteristics.
The columns report the share of investors in each group that selected a
given ESG investment motive or level of concern about climate change.
Different investors perceive different ESG investment motives as
the most important. About 48% of investors do not see any specific
reason to invest in ESG stocks; about 22% of investors perceive the most
important investment motive to be that ESG investments hedge climate
risk; another 24% make an ethical argument for investing in ESG stocks;
and about 6% of investors perceive the most important motivation
for ESG investments to be that these investments will outperform the
market.
The perceived primary ESG investment motives differ across demographic groups. Richer, older, and male investors are more likely to see
no specific reason to invest in ESG portfolios. Ethical motivations are
more important for female and younger investors. The belief that ESG
portfolios are primarily attractive because they provide climate hedges
varies by wealth, with wealthier investors placing less importance
on the hedging aspect. There is no variation across wealth in the
perception that ESG investing is the right thing to do. Respondents in
more Republican-leaning areas are less likely to perceive ESG investing
as the right thing to do, and more likely to find no particular reason
for such investments. There are no large differences across investors’
perceived motivations for ESG investment based on the flood risk
exposure in their areas of residence. Appendix Tables B.5 and B.6 show
that these univariate patterns are similar in multivariate specifications
that jointly control for all characteristics. The low levels of 𝑅2 in
those regressions highlight that observable demographic characteristics
explain only a small share of the variation across investors in their
reported investment motives.
Survey respondents also differ in their level of concern about climate risk, with about a quarter indicating low concern, a quarter
moderate concern, and half indicating high concern. Concern for climate change increases markedly for younger investors, as well as for
female investors and those living in areas with a larger vote share for
the Democratic party. There are at most small differences in concerns
about climate change by wealth and flood risk exposure.
We collect the results on the heterogeneity in expected excess
ESG returns, perceived motives for ESG investing, and concerns about
climate risk in our Fact 2:

Fact 1. Between mid-2021 and late-2023, investors on average expected
the 10-year return on ESG investments to underperform the market by about
2.1% per year.
Several economic theories are consistent with a negative expected
return on ESG investments. First, investors could perceive ESG investments to be more of a hedge (i.e., providing some systematic insurance
against aggregate risk factors such as climate risk) than the market.
Alternatively, some investors may, for ethical reasons, be willing to pay
a premium for ESG funds, which could lower the equilibrium return of
those investments. In both of these mechanisms, lower expected returns
from ESG investments would be compensated by other pecuniary or
non-pecuniary benefits to the investors who hold the assets. Finally,
investors might expect low excess returns because they believe that the
market value of ESG funds is temporarily overpriced, a market state
sometimes referred to as a ‘‘green bubble’’.
Table 1 also documents substantial across-individual dispersion in
the beliefs about excess ESG returns. About 10% of responses expect
ESG investments to underperform the market by at least 6.5% per
year over the next 10 years, and 10% expect them to outperform by
2% or more. About 22% of responses expect the annualized 10-year
return on ESG investments to fall within 0.5 percentage points of the
corresponding market return. Overall, only 20% of the responses expect
positive excess ESG returns.
Panel B also explores the distribution of ESG excess return expectations by investor characteristics. Differences across groups are
relatively modest, though they do display some meaningful patterns:
female respondents and those living in areas with higher Democratic
vote shares tend to be more optimistic about relative ESG returns.8
Importantly, each of these groups on average still expects lower returns
on ESG funds than on the market. Expectations of excess ESG returns do
not vary systematically with age, wealth, and the flood risk exposure in
the area where respondents live based on zip code-level data provided
by the First Street Foundation. Appendix Table B.3 provides additional
sample splits, and Appendix Table B.4 shows that these univariate
patterns generally survive a multivariate analysis, though the low levels
of 𝑅2 in those regressions also show that observable demographic characteristics only explain a small share of the across-investor variation in
expected excess ESG returns.

Fact 2. There is substantial across-investor heterogeneity in (i) beliefs about
excess ESG returns, with a cross-sectional standard deviation of expectations
of 5%; in (ii) the perceived most important motive for ESG investing, with
at least some investors mentioning each of financial performance (6% of
investors), hedging of climate risk (22%), ethical reasons to invest (24%),
and no reason at all (48%); and in (iii) the level of concern about climate
risk, with about half of investors reporting high concern.
Panel B of Table 2 also explores the relationship between investors’
perceived primary reasons to invest in ESG assets and their concerns
about climate change. Increases in climate risk concerns are associated
with investors more likely reporting ethical or hedging reasons as
the primary motives for ESG investing. Nevertheless, about 25% of
investors who report high concerns about climate change do not see
a specific reason to invest in ESG. One possible explanation for such
views is that these investors might not view ESG investments as a
sufficiently useful tool to reduce or hedge the effects of climate change
due to the fear of ‘greenwashing’ or because ESG mandates may be too
broad to address climate change.
Panel C of Table 1 explores how expected excess ESG returns
differ across investors who report different ESG investment motives

set extreme outlier responses (below the bottom percentile, and above the top
percentile) for each unbounded expectation question to missing.
8
Political views are attributed using the respondent location, based on the
county-level vote shares from the 2020 election.
7

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.
Table 2
Motivations for ESG investments.
Panel A: Share of investors by demographic characteristics
Reasons of ESG investments

Level of concerns

ESG will outperform

ESG hedges climate risk

It is the right thing to do

No specific reason

Low

Moderate

High

Pooled

0.06

0.22

0.24

0.48

0.26

0.25

0.49

By age
≤40
41–50
51–60
61–70
>70

0.10
0.07
0.07
0.06
0.05

0.23
0.19
0.22
0.21
0.23

0.29
0.28
0.25
0.23
0.23

0.38
0.45
0.46
0.50
0.49

0.19
0.25
0.25
0.28
0.26

0.22
0.26
0.27
0.25
0.25

0.58
0.49
0.48
0.47
0.49

By gender
Female
Male

0.07
0.06

0.25
0.20

0.28
0.22

0.41
0.52

0.23
0.28

0.23
0.26

0.54
0.46

By wealth
<$100k
$100k–$500k
$500k–$1 m
>$1 m

0.08
0.07
0.05
0.06

0.25
0.23
0.21
0.17

0.25
0.24
0.25
0.23

0.42
0.46
0.49
0.54

0.27
0.27
0.27
0.24

0.25
0.24
0.25
0.26

0.48
0.49
0.48
0.50

By flood risk exposure
Low
Medium
High

0.06
0.06
0.07

0.21
0.21
0.24

0.24
0.24
0.22

0.48
0.48
0.47

0.26
0.26
0.25

0.26
0.25
0.25

0.48
0.49
0.50

By political view in location
Democratic
Republican

0.07
0.06

0.22
0.21

0.27
0.19

0.44
0.55

0.21
0.34

0.25
0.28

0.54
0.38

It is the right thing to do

No specific reason

Panel B: Share of investors by other ESG questions
Reasons of ESG investments
ESG will outperform

Level of concerns

ESG hedges climate risk

By reasons of ESG investment
ESG will outperform
ESG hedges climate risk
It is the right thing to do
No specific reason
By climate change concerns
Low
Moderate
High

0.02
0.04
0.09

0.07
0.24
0.27

0.04
0.16
0.39

0.87
0.56
0.25

Low

Moderate

High

0.08
0.09
0.04
0.46

0.19
0.29
0.17
0.29

0.73
0.62
0.79
0.25

Panel C: Share of investors by ESG holdings
Reasons of ESG investments

By ESG investments
Has no ESG investments
Has ESG investments

Level of concerns

ESG will outperform

ESG hedges climate risk

It is the right thing to do

No specific reason

Low

Moderate

High

0.06
0.15

0.21
0.25

0.23
0.48

0.49
0.13

0.27
0.06

0.26
0.13

0.48
0.81

Table summarizes the fraction of respondents that selected each answer to the second (i.e., motivations for ESG investments) and third (i.e., level of concern about climate change)
ESG questions. Note that the third question was added in Dec 2021. Panel A shows the share of investors, pooled all responses and divided by demographic characteristics of the
respondents. Panel B shows the share of investors divided by another ESG question, such as the share of each stated motivation of ESG investments in relation to the level of
concern about climate change, and vice versa. Panel C reports the share of investors by whether a respondent has any ESG investment. The flood risk exposures are based on the
average risk scores (measured by the First Street Foundation) of the zipcodes where respondents are located. The political views of living areas are based on county-level vote
shares (considering only Democrat and Republican votes) from the 2020 US election.

and different levels of concern about climate change. On average,
investors who believe the best reasons for ESG investing are that such
investments will outperform the market indeed expect positive excess
ESG returns of about 1% per year.9 Investors who believe the best
ESG investment motive is to view ESG assets as climate hedges expect
negative excess returns of about 0.7% per year. Similarly, investors
who highlight ethical reasons to invest in ESG assets expect negative
excess returns of 1% per year on average. Finally, investors who report

not seeing any reason to invest in ESG expect significant underperformance relative to the market (more than 3% per year). We also
find strong relationships between climate concerns and expected excess
ESG returns, with unconcerned investors expecting the largest ESG
underperformance at −4.8 percentage points per year.
Importantly, since the expected excess returns of each investor take
existing stock prices as given, they do not need to be aligned with the
investors’ own willingness to accept lower returns for non-pecuniary or
hedging benefits. Nevertheless, it is interesting that those investors with
hedging or moral motives—investors who would presumably be willing
to give up some returns to hold ESG assets—reported expected excess
returns that are consistent with perceiving the other investors (reflected
in the equilibrium prices of ESG investments) also being willing to
accept lower returns. Alternatively, investors might be confusing partial
and general equilibrium in their thinking, failing to infer what motives
and information might already be reflected in current prices.

9
A small number of respondents who report that market outperformance is
the ESG investment motive most important to them also report expected ESG
returns that imply negative excess expected return relative to the market. This
could either be the result of differences in the investment horizon considered
for these two questions, or it could be driven by measurement error in one or
both of the expected return series used to calculate excess expected return.

8

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.
Table 3
Expected excess ESG returns and other beliefs.

(1) Expected excess 10Y return of ESG investments (% p.a.)
(2) Expected 1Y stock return (%)
(3) Probability 1Y stock return <−30% (%)
(4) St.D. expected 1Y stock return (%)
(5) Expected 3Y GDP growth (% p.a.)
(6) Expected 10Y GDP growth (% p.a.)
(7) Probability p.a. 3Y GDP growth <−3% (%)
(8) St.D. expected 3Y GDP Growth (% p.a.)
(9) Expected 1Y return of 10Y zero coupon bond (%)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

1.00
0.06
−0.07
0.01
0.06
−0.05
−0.10
0.05
0.03

1.00
−0.25
−0.02
0.24
0.09
−0.32
0.04
0.17

1.00
0.36
−0.06
0.01
0.43
0.17
−0.04

1.00
0.08
0.07
0.25
0.59
0.03

1.00
0.64
−0.26
0.25
0.15

1.00
−0.08
0.23
0.16

1.00
0.25
−0.07

1.00
0.08

1.00

Table shows within-survey correlations across questions eliciting beliefs about different objects.

Table 3 shows the correlation of expectations about excess ESG
returns with expectations about stock market returns and GDP growth
that are also elicited in the survey. Excess ESG return expectations are
essentially uncorrelated with these other beliefs (Appendix Table B.7
confirms this fact within groups of investors split by characteristics
such as wealth). This suggests that the expectations of the relative performance of ESG investments are not capturing information related to
beliefs about the market return or economic growth, either at short or
long horizons. ESG return expectations are also not related to people’s
risk perceptions (as captured, for example, by the perceived probability
of crashes in the stock market or in GDP). The low correlation instead
suggests that ESG beliefs capture a different dimension of the investment process relative to the variables typically elicited in surveys of
investor beliefs.

invests in ESG funds, and even when they do, the portfolio share is
relatively low. For example, the 90th percentile of ESG investors holds
only about one third of their portfolio in ESG funds. This suggests that
even investors that actively choose ESG funds prefer to only slightly
tilt their portfolio in that direction rather than holding a concentrated
portfolio with only (or mostly) ESG funds. This is perhaps unsurprising,
since the prominence of ESG funds is a relatively new phenomenon and
sluggish portfolio adjustment means that some investors who might
eventually allocate money to these funds have not yet done so. Also,
given that ESG considerations are just one of many dimensions of
investments, it should not be a surprise that ESG funds would represent
only a fraction of the overall portfolio.
ESG portfolio holdings also vary across demographic groups. Participation in ESG investments is higher for younger investors relative
to older investors. Less wealthy investors are less likely to invest in
ESG funds, but when they do, they tend to invest a larger share of
their portfolio in them. There is also much higher ESG participation
by investors resident in predominately Democratic areas compared to
Republican ones. Despite the meaningful gender differences in ESG
motivations and expectations documented in prior sections, actual
ESG investment behavior is very similar across genders. Table 5 and
Appendix Table B.11 generally confirm the findings from Table 4 in a
multivariate analysis.
We next document how individual ESG portfolio shares are associated with perceived ESG investment motives, expected excess ESG returns, and concerns about climate change. Then, we examine the tradeoff between ESG motivations and financial performance in determining
ESG investments.

3. ESG beliefs and portfolio allocation
As explained in Giglio et al. (2020, 2021c), a key advantage of
the GMSU-Vanguard survey is that it can be (anonymously) linked
to administrative data that includes the portfolio composition of the
respondents in their Vanguard accounts. Our next analysis exploits this
aspect of the data to document a strong association between ESG beliefs
and the actual ESG portfolio allocations of each respondent.
We compute the ESG portfolio share as the share of risky assets that
is allocated to ESG funds. Risky assets exclude money-market funds
and Vanguard settlement accounts, but contain bond and balanced
funds.10 We use the ‘‘Sustainable Investment Overall’’ indicator from
Morningstar to identify ESG funds.11 We do not categorize individual
bonds or stocks as ESG investments, motivated by the substantial
disagreement across firm-level ESG ratings of different providers (Berg
et al., 2022) and the fact that survey respondents predominantly invest
through funds rather than direct stock or bond holdings (Appendix
Table B.2). Similarly, we do not take a stand on whether ESG funds are
truly holding ESG stocks or whether the criteria used by Morningstar to
assign fund ESG labels are appropriate. Instead, our approach is motivated by the observation that the designation of a fund as ESG related is
highly salient to investors seeking to follow ESG strategies (Hartzmark
and Sussman, 2019).
Table 4 reports summary statistics on ESG holdings, pooled and
by demographic characteristics in Panel A, and by ESG investment
motives and level of concern about climate change in Panel B (see
Appendix Table B.10 for further sample splits). The first column reports
the extensive margin (i.e., what proportion of investors hold any ESG
funds), and the remaining columns the mean and percentiles of the ESG
portfolio share among investors with ESG investments. Several interesting patterns emerge. First, only about 3.4% of respondents actually

ESG investments and investment motives. Panel B of Table 4 links ESG
portfolio holdings to investors’ preferred ESG investment motives and
their levels of concern about climate change, documenting that survey
respondents invest in a way consistent with the views expressed in the
survey.
The highest average portfolio share in ESG funds is observed among
investors who report primarily ethical motivations for such investments. About 6.8% of such investors hold some ESG funds, and on
average investors with ESG investments and those beliefs hold about
16.2% of their assets in ESG funds. Indeed, some investors who believe
that ESG investments are the right thing to do hold sizeable positions
in such funds, with ESG portfolio shares of more than 50% at the
95th percentile. A complementary way to describe the relationship
between ESG investments and investment motives is by considering
only the subset of investors that actually hold ESG investments. Panel
C of Table 2 shows that nearly 50% of investors who actually hold
ESG funds in their portfolios perceive moral considerations to be their
most compelling ESG investment motive, relative to 24% among all
investors.12

10
Appendix Table B.8 and Appendix Figure B.3 shows the results if we only
focus on equity portfolios.
11
Appendix Table B.9 shows the 100 largest of these funds by assets under
management. In Appendix A, we explore an alternative approach to identify
ESG funds (i.e., fund or strategy names containing ESG-related terms) and find
that Morningstar’s definition is relatively comprehensive.

12
Conditional on investing in ESG, the perceived primary reasons for doing
so generally often does not vary substantially across demographics, though
the estimates are somewhat noisy (Appendix Table B.12). An exception is
that younger ESG investors generally perceive moral reasons as the primary
motivation for such investments.

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Table 4
ESG holdings.
Panel A: ESG holdings (Pooled and by demographic characteristics)
% Has any ESG

ESG portfolio share (%) - Conditional on having ESG investments
Mean

P5

P10

P25

P50

P75

P90

P95

Pooled

3.4

13.8

0.5

0.9

2.3

7.0

17.5

38.7

54.8

By age
≤40
41–50
51–60
61–70
>70

5.9
4.5
3.4
3.3
2.9

14.6
15.0
13.9
16.0
10.3

0.6
0.2
0.8
0.6
0.4

0.9
0.3
1.2
0.9
0.7

3.1
1.2
2.7
2.7
2.0

7.7
6.0
7.2
8.4
4.6

19.6
19.4
16.4
23.6
11.7

32.2
54.0
44.1
47.0
24.5

60.4
72.2
51.0
62.2
39.8

By gender
Female
Male

3.4
3.4

14.8
13.4

0.4
0.6

0.8
0.9

2.1
2.3

6.8
7.1

19.8
16.6

44.3
35.1

55.5
53.2

By wealth
<$100k
$100k–$500k
$500k–$1m
>$1 m

1.9
3.7
3.5
4.1

25.7
14.0
14.5
9.2

0.2
0.9
0.4
0.4

1.1
1.6
0.7
0.8

4.8
3.5
2.0
1.2

12.6
7.8
7.1
3.2

40.4
18.8
14.0
9.7

62.6
32.1
48.8
26.3

85.7
47.2
64.6
35.1

By flood risk exposure
Low
Medium
High

3.2
3.6
3.4

13.7
15.2
6.9

0.5
0.5
0.6

0.9
0.9
0.7

1.9
2.9
1.2

6.9
7.5
2.8

20.1
18.2
8.8

34.3
44.3
10.1

48.8
63.0
33.7

By political view in location
Democratic
Republican

4.2
2.0

14.4
9.7

0.5
0.6

0.9
0.8

2.5
1.7

7.7
4.8

18.5
9.8

39.1
22.9

55.9
45.9

Panel B: ESG holdings by other ESG questions
% Has any ESG

By reasons of ESG investment
ESG will outperform
ESG hedges climate risk
It is the right thing to do
No specific reason
By climate change concerns
Low
Moderate
High

ESG portfolio share (%) - Conditional on having ESG investments
Mean

P5

P10

P25

P50

P75

P90

P95

8.0
3.9
6.8
0.9

12.1
12.2
16.2
8.4

0.9
0.4
0.5
0.4

1.8
0.8
0.9
0.7

3.2
1.9
2.6
1.4

7.2
5.4
8.3
4.0

16.4
11.4
23.8
10.6

26.8
39.5
45.2
20.6

32.1
63.0
55.9
35.3

0.8
1.7
5.6

10.1
10.3
14.9

0.5
0.3
0.6

0.8
0.5
1.0

1.8
1.3
2.6

7.5
3.6
7.4

11.1
12.4
20.0

23.7
30.3
44.9

35.3
44.1
61.3

Panel A shows the distribution of ESG holdings as a fraction of Vanguard investments, pooled and separately by groups according to their demographic characteristics. Panel B
splits groups according to their answers to ESG questions, which are the stated motivations of ESG investments and the level of concern about climate change. The first column
reports the extensive margin (whether the investor holds any ESG in the portfolio), and the remaining columns report summary statistics of the ESG portfolio share among investors
with ESG investments. We compute the ESG portfolio share as the share of risky assets that are allocated to ESG funds. Appendix Table B.8 shows a version where we compute
the ESG portfolio share based on investments in equities. The flood risk exposures are based on the average risk scores (measured by the First Street Foundation) of the zipcodes
where respondents are located. The political views of living areas are based on county-level vote shares (considering only Democrat and Republican votes) from the 2020 US
election.

Among investors who report outperformance of ESG portfolios as
their primary ESG investment motive, about 8% hold ESG funds; the
average investor with ESG investments and those beliefs holds about
12.1% of their wealth in ESG funds. Investors who highlight the hedging property of ESG investments as their preferred ESG investment
motive also invest at a relatively high rate in ESG funds: 3.9% of them
hold at least one ESG fund in the portfolio, and the average share of
ESG assets in their portfolios (conditional on having at least some ESG
investments) is about 12.2%. Finally, very few investors who report
‘‘no specific reason’’ to invest in ESG hold any ESG funds in their portfolios.
Concerns about climate risks also vary substantially with actual
ESG portfolio holdings. The proportion of investors holding any ESG
investments increases from 0.8% for individuals with low concerns to
about 5.6% for individuals with higher concerns (see Table 4). As a
result, about 80% of all investors with ESG funds in their portfolios
have high levels of concern about climate change (see Table 2).

interpreting our findings, it is worth noting that in the context of ESG
investments, we do not have a clear quantitative benchmark on the
relationship between expected excess ESG returns and optimal ESG
portfolio share. In particular, for the aggregate market, simple models
like that of Merton (1969) represent a good, if stylized, benchmark
of what relationship between beliefs and holdings we should expect.
In the case of ESG assets, which are plausibly just a fraction of any
investor’s optimal portfolio, it is harder to calibrate a quantitative
benchmark, as it involves making assumptions on elements such as the
rest of the investment opportunity set, the covariance of ESG returns
with other assets, liquidity, and the presence and magnitude of possible
non-pecuniary benefits.
Fig. 2 explores the relationship between expected excess ESG returns
and the extensive and intensive margins of ESG investment. Three clear
patterns emerge. First, there is a positive relationship between beliefs
about excess ESG returns and ESG holdings: investors who are more
optimistic about ESG returns invest more in ESG funds. Consistent with
this finding, Panel D of Table 1 shows that, among those investors who

ESG investments and return expectations. We next explore the relationship between ESG return expectations and ESG investments. Before
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S. Giglio et al.
Table 5
Holdings by demographics & beliefs.
Has any ESG

ESG portfolio share (%)

(1)

(2)

(3)

(4)

(5)

(6)

Log(Wealth)

0.007***
(0.002)

0.007***
(0.002)

0.008***
(0.002)

−0.016
(0.033)

−0.006
(0.033)

0.007
(0.034)

Age ∈ (40,50]

−0.021*
(0.013)

−0.025*
(0.013)

−0.023*
(0.013)

−0.128
(0.268)

−0.230
(0.269)

−0.197
(0.268)

Age ∈ (50,60]

−0.032***
(0.012)

−0.032***
(0.012)

−0.029**
(0.012)

−0.374*
(0.214)

−0.411*
(0.222)

−0.360
(0.221)

Age ∈ (60,70]

−0.038***
(0.011)

−0.040***
(0.011)

−0.036***
(0.011)

−0.280
(0.218)

−0.378*
(0.225)

−0.318
(0.226)

Age > 70

−0.039***
(0.011)

−0.040***
(0.011)

−0.036***
(0.011)

−0.519***
(0.200)

−0.585***
(0.207)

−0.525**
(0.206)

Male

−0.003
(0.005)

−0.002
(0.005)

0.002
(0.005)

−0.024
(0.106)

0.031
(0.107)

0.091
(0.111)

Flood risk exposure: Medium

0.008
(0.005)

0.008
(0.005)

0.007
(0.005)

0.230*
(0.122)

0.228*
(0.125)

0.214*
(0.124)

Flood risk exposure: High

0.009
(0.009)

0.008
(0.009)

0.007
(0.009)

−0.078
(0.089)

−0.060
(0.091)

−0.077
(0.091)

Political view in location: Republican

−0.023***
(0.004)

−0.021***
(0.004)

−0.016***
(0.004)

−0.449***
(0.096)

−0.416***
(0.096)

−0.332***
(0.089)

0.002***
(0.000)

0.001***
(0.000)

0.041***
(0.009)

0.023***
(0.009)

Expected excess 10Y ESG return (% p.a.)
Reason: Outperform

0.071***
(0.011)

0.902***
(0.211)

Reason: Hedge

0.028***
(0.005)

0.387**
(0.164)

Reason: Right thing

0.057***
(0.006)

0.909***
(0.162)

Wave FE

Yes

Yes

Yes

Yes

Yes

Yes

𝑅2
Observations

0.81
24,813

1.26
23,644

3.09
23,540

0.48
23,660

0.74
22,579

1.56
22,485

Regressions (1) and (3) show coefficients of regressing a dummy variable, which indicates any ESG investment, and the ESG portfolio share (%) on various demographic
characteristics, controlling for wave fixed effect. Regressions (2) and (4) show coefficients of regressing the two dependent variables on several demographic characteristics
and the expected excess 10Y ESG return (% p.a.), controlling for wave fixed effect. Regressions (3) and (6) further control for the stated motivations of ESG investment. We
compute the ESG portfolio share as the share of risky assets that are allocated to ESG funds. The flood risk exposures and political views are dummy variables based on the average
risk scores (measured by the First Street Foundation) of respondents’ living areas (zip code level) and the county-level vote shares (considering only Democrat and Republican
votes) from the 2020 US election respectively. Standard errors are clustered at the respondent level.
* Significance levels: (p < 0.10).
** Significance levels: (p < 0.05).
*** Significance levels: (p < 0.01).

Fig. 2. Holdings of ESG Funds Broken Down by Expected Excess Return. Panel A shows the fraction of respondents who hold at least one ESG-focused fund in their portfolio
(y-axis) broken down by the survey-elicited expected returns of an ESG portfolio over the market over a 10-year horizon (annualized). Panel B uses the same breakdown on the
𝑥-axis, but instead plots the average portfolio share invested in ESG-focused funds. This figure plots the unconditional relationship. We compute the ESG portfolio share as the
share of risky assets that are allocated to ESG funds. Numbers at the top of the bars report the number of observations and the error bars report the 95% confidence intervals.
Standard errors are clustered at the respondent level. Appendix Figure B.4 shows binscatter plots with controls for investor characteristics.

11

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S. Giglio et al.

Fig. 3. Portfolio Shares in ESG Funds by Expected Excess Return and Motivation for ESG Investing. Figure construction follows Panel (b) of Fig. 2, but additionally breaks down
the data by the stated motivation for investing in ESG funds separately in each panel. Note that we compute the ESG portfolio share as the share of risky assets that are allocated
to ESG funds. Appendix Figure B.3 shows a version where we compute the ESG portfolio share based on investments in equities. Numbers at the top of the bars report the number
of observations and the error bars report the 95% confidence intervals.

hold ESG assets, the average expected excess return is substantially
higher than those who have no ESG investments.13
Second, the relationship between ESG beliefs and portfolio holdings
is nonlinear, with a stronger effect in the domain of positive expected
excess ESG returns. The lower sensitivity in the domain of negative
expected excess ESG returns is possibly due to the fact that, for a variety
of reasons explored widely in the literature, shorting occurs relatively
rarely, in particular among retail investors.
Third, investments in ESG funds are nonzero on average even
when investors expect negative excess returns. For example, Panel D
of Table 1 shows that while the median ESG investor expects ESG
portfolios to perform similarly to the market, at the 25th percentile
of the belief distribution, ESG investors expect those investments to
underperform the market by about 1 percentage point annually over
the next 10 years. Such investments are consistent, for example, with
investors perceiving pecuniary (hedging) or non-pecuniary benefits
from such investments. We summarize these findings in Fact 3:

3.1. The trade-off between expected ESG returns and other ESG investment
motives
In this section, we further explore investors’ willingness to trade off
expected returns against other perceived benefits of ESG investments
such as moral considerations or their ability to provide hedges against
climate change. To do this, Fig. 3 plots the relationship between ESG
portfolio shares and expected excess ESG returns separately by the
stated motivation for investing in ESG.14 The plot also reports 95%
confidence intervals and, above each bar, the raw number of responses
in each subgroup. Fig. 4 shows a corresponding plot exploring the
extensive margin of ESG investments.
Panel A focuses on investors who report financial returns as their
primary motivation to hold ESG investments. Most of these investors
indeed expect positive excess returns: the number of responses within
that group that report negative expected excess returns is small, and
standard errors on portfolio holdings are large and include zero (see
also Panel C of Table 1). Within the range of positive expected returns,
where most respondents are, ESG holdings increase with investors’
expected ESG returns.
Panel B of Fig. 3 focuses on investors who report the hedging of
climate risk as their key ESG investment motive. The panel shows two
interesting patterns. First, a nontrivial (and significantly different from
zero) number of these investors hold ESG investments in their portfolios
despite expecting negative excess ESG returns. This is consistent with

Fact 3. ESG beliefs are important drivers of actual portfolio allocation to
ESG investments. ESG holdings are the largest for investors with ethical ESG
investment motives and high concerns about climate change. ESG portfolio
holdings are also increasing in expected excess ESG returns.

13
We expect the sensitivity of portfolios to beliefs to vary with measures of
investor involvement with the stock markets (Giglio et al., 2021c). Appendix
Figures B.5 and B.6 explore how the patterns in Fig. 2 vary if we group
investors by their monthly turnover and by the number of different funds held
in their portfolios. The figures show that investors with low turnover and only
a few individual positions tend to participate little in ESG investments. All
three patterns highlighted above continue to hold within each group.

14
Appendix Figures B.7, B.8 and B.9 explore how the patterns in Fig. 3 vary
among first-time survey respondents, first-time ESG questions respondents and
repeated ESG questions respondents. Additionally, a version focusing solely on
positions in retail accounts is shown in Appendix Figure B.10. The documented
patterns are generally consistent across these various subgroups.

12

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Fig. 4. Holdings of ESG Funds by Expected Excess Return and Motivation for ESG Investing. Figure construction follows that of the panel (a) of Fig. 2 but additionally breaks down
the data by the stated motivation for ESG investment separately in each panel. Numbers at the top of the bars report the number of observations, and the error bars demonstrate
the 95% confidence intervals.

the prediction that those investors might value those funds for their
covariance properties, viewing the negative excess expected returns
akin to an equilibrium insurance premium for assets that pay out disproportionately when climate disasters materialize (Weitzman, 2012;
Giglio et al., 2021b). Second, even among these investors, there is a
clear positive relation between expected excess ESG returns and the
share of ESG holdings, at least when investors expect ESG to perform
better than the market and limits to shorting are less important.
Panel C focuses on investors who select moral reasons as their
primary ESG investment motive. Among this group of investors, a large
number hold ESG investments despite expecting financial underperformance. This suggests that the ethical motivations might induce a
willingness to give up financial returns. However, even among these
investors, we find a positive relation between ESG holdings and expected excess ESG returns, with a much larger share held by investors
who expect ESG to outperform the market compared to those who
expect underperformance. Complementary evidence is presented in
Appendix Table B.13, which reports the expected excess returns for
different groups of investors conditioning on actually having ESG funds
in their portfolios. Among investors with hedging or ethical concerns
for ESG investments, those who actually invest in ESG on average
expect those investments to perform similarly to the market (whereas
those who do not invest in ESG, as noted in the previous section, expect
larger underperformance). These findings suggest that financial return
considerations play an important role in determining participation
in ESG investments above and beyond the ethical motivations, even
among investors who state these motivations as the most important
reason to invest in ESG. Table 5 also confirms this finding. Even after
accounting for ESG motivations, we observe a rise in ESG portfolio
holdings corresponding to expected excess ESG returns.

Lastly, Panel D of Fig. 3 focuses on investors who do not see any
specific reason to invest in ESG and shows that they hold essentially no
ESG investments, independent of their expectations for excess returns
of such investments. We summarize the above results in Fact 4:
Fact 4. Both pecuniary and non-pecuniary considerations jointly drive
portfolio allocation to ESG. Financial considerations (expectation of excess
ESG returns) are an important driver of ESG allocations for all groups of
investors, including those who mention hedging or ethical motivations as key
reasons for investing in ESG. At the same time, morally motivated investors
hold some ESG investments even when they expect negative excess returns,
showing that the non-pecuniary considerations also play a role alongside
financial performance.
4. Additional patterns in the panel of ESG beliefs
In this section we further explore two related dimensions of our
panel data. First, we study the time-series dynamics of beliefs at both
the aggregate and individual levels. Second, we explore the determinants of the overall panel variation in beliefs.
4.1. The time-series of ESG beliefs and motivations
While our data has a large cross-section and a relatively short timeseries of 30 months, our survey was collected during a period of rapid
change in the ESG investmenting environment. In this section, we thus
discuss some aggregate time-series developments that occurred during
our sample period and then zoom in to study the dynamics of ESG
beliefs at the individual level.
Panel A of Fig. 5 reports the average expected excess return of
ESG investments over the market in each survey period. The graph
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S. Giglio et al.

Fig. 5. Time Series - ESG & Market Beliefs. Figure reports the time series of the average beliefs from the GMSU-Vanguard survey. The left panel visualizes the 10-year annualized
expected excess return of ESG investment (i.e., the difference between the expected returns on ESG investments and the market). The right panel decomposes the expected excess
returns into ESG and stock beliefs. The shaded areas represent the 95% confidence interval.

Table 6
Dynamics of ESG beliefs.
Expected excess 10Y return
of ESG investment (% p.a.)

ESG portfolio share (%)

Answer proportion

Avg. Start

Avg. End

Diff

Avg. Start

Avg. End

Diff

Pooled

−0.95

−2.56

−1.60

0.44

0.56

0.12

Avg. Start

Avg. End

Diff

By reasons of ESG investments
ESG will outperform
ESG hedges climate risk
Right thing to do
No specific reason

1.48
0.05
−0.54
−2.12

0.11
−0.78
−0.94
−4.41

−1.37
−0.83
−0.40
−2.28

1.03
0.60
0.81
0.05

2.26
0.60
0.95
0.15

1.22
0.01
0.14
0.11

0.08
0.22
0.26
0.44

0.05
0.21
0.25
0.50

−0.03
−0.01
−0.02
0.05

By climate change concerns
Low
Moderate
High

−2.51
−1.42
−0.56

−5.54
−2.37
−1.12

−3.03
−0.95
−0.55

0.19
0.05
0.85

0.16
0.24
0.91

−0.03
0.19
0.05

0.23
0.25
0.51

0.25
0.25
0.49

0.02
0.00
−0.02

The table reports dynamics (from the first to the last wave of ESG-related questions) of the 10-year expected excess return of ESG investment (% p.a.), ESG portfolio share (%),
and the answer proportions of two ESG questions, which are the stated motivations for ESG investments and the level of concern about climate change respectively. We compute
the ESG portfolio share as the share of risky assets that are allocated to ESG funds.

shows a downward trend from mid-2021 to early-2023, which seems
to align with the general underperformance of ESG investments in
2022 (Quinson, 2022). Panel B shows that the reduction in expected
ESG returns over the market is entirely driven by investors becoming
more pessimistic about ESG returns (rather than an increase in market
expected returns).
This differential behavior of ESG and market expectations is interesting. During the sample period, financial markets tended to perform
poorly, with the S&P 500 down almost 20% over the year 2022. Yet,
10-year market return expectations barely moved, consistent with the
findings in Giglio et al. (2021c), who showed that while short-term
market expectations moved with realized market returns, long-term
expectations were more stable. In the case of ESG returns expectations, though, even long-horizon expectations moved substantially over
time, in this case together with the realized underperformance of
the investment. These patterns are consistent with the fact that ESG
considerations are relatively new to investors, and investors have a
much shorter history to learn from; it is less surprising then that they
update more strongly on new information.
We next study the dynamics of beliefs for different groups of investors. The left panel of Table 6 shows the average expected excess
return at the beginning of the sample and at the end of the sample,
as well as the difference between the two, for investors who report
different reasons to invest in ESG and different levels of concerns for
climate risk. Consistent with Fig. 5, investors’ expected excess ESG
returns fell by about 1.6 percentage point over the sample. The trends
are markedly different across investors. The drop in expected excess
ESG returns is most significant for those who do not see specific reasons
to invest in ESG, and those with low concern about climate change.

Investors who primarily perceive moral ESG investment motives and
investors with high concerns for climate change have the smallest
decline in expected excess ESG returns over the sample period.15
Throughout our sample, the share of investors who report financial
returns, climate hedges, or moral considerations as their primary ESG
investment motive fell somewhat, while the share of investors reporting
that they viewed no specific ESG investment motive increased by five
percentage points.
Overall ESG portfolio shares increased by a modest 0.12 percentage
points over the sample, but this average masks substantial acrossinvestor heterogeneity (some of these changes are driven by the same
investors reporting different investment motives over time, and some
by portfolio changes of a given investor). Among investors with moral
ESG investment motives, the ESG portfolio share increased by 0.14
percentage point to 0.95% by the end of 2023. Those motivated by the
financial returns of ESG investments saw the largest increase of 1.22
percentage points, while the segment focusing on hedging benefits had
an essentially flat ESG portfolio share throughout our sample.
Table 7 further explores how individuals change their ESG investment motives and excess ESG return expectations. Panel A presents a
transition matrix of the probability that an investor would switch their
reported motive between consecutive responses of the survey. Overall,
the reasons behind investing in ESG are quite persistent, but the degree

15
These results do not keep the set of investors fixed across time. We see
similar results if we fix investors to their primary ESG investment motive as
of the beginning of the sample, and track their expected excess ESG returns
over time. This alternative analysis is reported in Appendix Table B.14.

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S. Giglio et al.
Table 7
Transition matrix.
Panel A: Probability of switching

ESG will outperform
ESG hedges climate risk
Right thing to do
No specific reason

ESG will outperform

ESG hedges climate risk

Right thing to do

No specific reason

0.37
0.08
0.05
0.01

0.29
0.52
0.17
0.08

0.20
0.19
0.63
0.06

0.14
0.22
0.15
0.85

Panel B: Average changes in expected excess 10Y return of ESG investment (% p.a.)

ESG will outperform
ESG hedges climate risk
Right thing to do
No specific reason

ESG will outperform

ESG hedges climate risk

Right thing to do

No specific reason

−0.34
0.59
1.07
1.35

−1.04
−0.24
0.01
0.62

−1.47
−0.54
−0.02
−0.02

−2.71
−1.30
−0.48
−0.31

Panel A of the table reports the transitions of the motivation of ESG investment between two consecutive responses from the same respondent. Panel B reports the average changes
in expected excess returns of ESG investment associated with the transitions of ESG investment motivation in panel A, again between two consecutive responses from the same
respondent.

of persistence varies across groups of investors with different initial ESG
investment motives. Those investors who do not see a specific reason
to invest tend to persist in their views; on the other hand, those who
initially were motivated by the return properties of ESG investments
are most likely to have adjusted their views by the end of the sample
period (this may partly be due to the specific time period we examine,
in which ESG investment did not perform well).
Panel B of Table 7 has a similar structure to Panel A, but reports,
in each cell of the table, the average change in ESG expected excess
returns that occur concurrently with the corresponding transition in
ESG investment motives. When investors who are initially motivated
by the return properties of ESG investments abandon that view, this is
associated with a marked decline in their reported expected excess ESG
returns. Correspondingly, the small number of investors who change
their preferred ESG investment motive towards financial returns from
a different initial perspective all report increased expected excess ESG
returns. Those who change their position towards reporting primarily moral ESG investment motives also tend to lower their reported
expected excess ESG returns.
Overall, our analyses show that the dynamics of investors’ beliefs
about ESG are complex even within a relatively short sample. The
evolution of the motivations is closely tied to the evolution of the
expectations about future performance.

All columns yield a consistent message: observable individual characteristics do a poor job of explaining the cross-sectional dispersion
of ESG expectations across investors. These findings suggest that more
work is required to better understand the sources of belief formation
about the broader market in general and ESG investments in particular.

Retail investors’ recent demand for ESG investment options has
been an important force driving the financial sector to consider its role
in transitioning towards a lower-carbon economy. Understanding the
drivers of this investment demand is thus crucial to assessing the ability
of finance to facilitate a range of sustainability objectives. In this paper,
we explore these drivers by analyzing a new survey of investor beliefs
that asked about the expected returns of ESG portfolios and investor
motivations behind ESG investment, combined with administrative
data on respondents’ portfolio holdings. We document large heterogeneity in investors’ beliefs about ESG asset returns and motivations
for holding such assets. We also show a significant relationship between
ESG belief and motivations and ESG holdings. Finally, we highlight that
both pecuniary and non-pecuniary motives play an important role in
determining asset allocations to ESG assets.

4.2. Decomposing the panel variance of beliefs

CRediT authorship contribution statement

In the final section, we explore in greater depth the panel variation in expected excess ESG returns. We start by decomposing the
panel variation into its cross-sectional and time-series dimensions. We
estimate a regression of the responses of investor 𝑖 at time 𝑡, 𝐵𝑖,𝑡 , on
time fixed effects, investor fixed effects, and on both, and report the
corresponding 𝑅2 s in Table 8. To ensure that the individual fixed effects
are sufficiently well estimated, we only perform our analysis using
responses for individuals that have responded at least three times in
our panel (Appendix Table B.15 shows that the results are similar if we
vary this threshold). Time fixed effects explain only a small fraction
of the total panel variance, while individual fixed effects have large
explanatory power: investors seem to have persistent views about ESG
returns that are well captured by the individual fixed effects.
Despite some average differences in expected excess ESG returns
across demographic groups, most of the panel variation in beliefs occurs
within rather than across these groups. To formally show this, we take
the individual belief fixed effects estimated in Table 8, and regress those
on the various demographic characteristics we observe (age, wealth,
location, etc.). Table 9 shows the 𝑅2 s of regressions of the fixed effect
onto the various demographic characteristics (see Appendix Table B.16
for the coefficients on these demographics). The columns of Table 9
correspond to fixed effects estimated using at least one, two, and up to
five responses per individual.

Stefano Giglio: Writing – review & editing, Writing – original draft,
Investigation, Formal analysis, Conceptualization. Matteo Maggiori:
Writing – review & editing, Writing – original draft, Investigation,
Formal analysis, Conceptualization. Johannes Stroebel: Writing – review & editing, Writing – original draft, Investigation, Formal analysis,
Conceptualization. Zhenhao Tan: Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Conceptualization.
Stephen Utkus: Writing – review & editing, Writing – original draft,
Investigation, Formal analysis, Conceptualization. Xiao Xu: Writing
– review & editing, Writing – original draft, Investigation, Formal
analysis, Conceptualization.

5. Conclusion

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Appendix A. Supplementary data
Supplementary material related to this article can be found online
at https://doi.org/10.1016/j.jfineco.2024.103984.
15

Journal of Financial Economics 164 (2025) 103984

S. Giglio et al.
Table 8
Decomposing the variation in beliefs: Individual and time fixed effects.
𝑅2 (percent) of panel regression

Expected 10Y stock return (% p.a.)
Expected 10Y return of ESG investments (% p.a.)
Expected excess 10Y return of ESG investments (% p.a.)

Observations

Time FE

Individual FE

Time + Individual FE

0.27
1.94
2.05

53.09
60.59
50.79

53.27
61.60
51.76

3,001
2,974
2,941

Table reports the 𝑅2 values corresponding to the following three regressions, and the number of individual respondents’ observations. We only include respondents who have
responded to at least three waves.
𝐵𝑖,𝑡 = 𝜒𝑡 + 𝜖1,𝑖,𝑡 ,
𝐵𝑖,𝑡 = 𝜙𝑖 + 𝜖2,𝑖,𝑡 ,
𝐵𝑖,𝑡 = 𝜙3,𝑖 + 𝜒3,𝑡 + 𝜖3,𝑖,𝑡 .
We denote the belief expressed by individual 𝑖 at time 𝑡 as 𝐵𝑖,𝑡 and estimate a set of time (i.e., survey wave) fixed effects 𝜒𝑡 and individual fixed effects 𝜙𝑖 . We also jointly estimate
both individual and time fixed effects. Each row corresponds to a different survey question that is used as the dependent variable.

Table 9
Belief heterogeneity and demographics.
𝑅2

#Resp ≥ 1

#Resp ≥ 2

#Resp ≥ 3

#Resp ≥ 4

#Resp ≥ 5

Expected 10Y stock return (% p.a.)
Expected 10Y return of ESG investments (% p.a.)
Expected excess 10Y return of ESG investments (% p.a.)

0.78
2.14
0.61

1.27
2.02
0.83

0.94
1.82
1.05

1.72
2.79
1.29

2.18
3.18
0.74

Table reports the 𝑅2 statistics corresponding to the following regression,
𝜙3,𝑖 = 𝛼 + 𝛤 𝐗𝑖 + 𝜖𝑖 ,
where 𝜙3,𝑖 are the individual fixed effects estimated in regression 𝐵𝑖,𝑡 = 𝜙3,𝑖 + 𝜒3,𝑡 + 𝜖3,𝑖,𝑡 (i.e., the third regression in Table 8) and 𝐗𝑖 are the following individual characteristics: log
wealth and dummy variables for age group, gender, flood risk exposure and political view in location. The flood risk exposures are based on the average risk scores (measured by
the First Street Foundation) of the zipcodes where respondents are located. The political views of living areas are based on county-level vote shares (considering only Democrat
and Republican votes) from the 2020 US election. In each column, going from left to right, we increase the minimum number of responses for an individual to be included in the
sample from 1 to 5. Each row corresponds to a different question in the survey.

Data availability

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17


==> JFE17 - Silence is safest: Information disclosure when the audience’s preferences are uncertain.txt <==
Journal of Financial Economics 145 (2022) 178–193

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Silence is safest: Information disclosure when the audience’s
preferences are uncertainR
Philip Bond a,∗, Yao Zeng b
a
b

Foster School of Business, University of Washington, 4273 E Stevens Way NE, Seattle, WA 98195, USA
Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104, USA

a r t i c l e

i n f o

Article history:
Received 18 July 2019
Revised 4 May 2021
Accepted 8 June 2021
Available online 20 September 2021
JEL classiﬁcation:
D81
D82
D83
G14

a b s t r a c t
We examine voluntary disclosure decisions when ﬁrms are uncertain about audience preferences and are risk averse. In contrast to classic “unraveling” results, some ﬁrms remain
silent in equilibrium. Silence is safer than disclosure; silence reduces the sensitivity of a
ﬁrm’s payoff to audience preferences. Increases in ﬁrm (audience) risk-aversion reduce (increase) disclosure. Our model explains why some ﬁrms do not disclose earnings breakdowns, executive compensation, or Environmental, Social, and Governance (ESG) performance when they face diverse audiences, and why they disclose less under regulatory rules
mandating that disclosure be entirely public.

Keywords:
Information disclosure
Risk-aversion
Uncertainty
Preferences

© 2021 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

R
Foster School of Business, University of Washington, and Wharton
School, University of Pennsylvania. We thank Ron Kaniel (editor), an
anonymous referee, Bruce Carlin, Selman Erol, Will Gornall, Brett Green,
Robin Greenwood, Alexander Guembel, Rick Harbaugh, Andrey Malenko,
Nadya Malenko, Steven Malliaris, Uday Rajan, Anjan Thakor, Ansgar
Walther, Christina Zhu, Ben Zou, and seminar and conference audiences
at Arizona State University, Columbia University, Copenhagen Business
School, Harvard University, Johns Hopkins University, Peking University,
Stockholm School of Economics, the University of Colorado, the University of Georgia, the University of Indiana, the University of Oxford, the
University of Texas at Dallas, the University of Toronto, the University
of Warwick, the University of Washington, Yeshiva University, the Federal Reserve Bank of Cleveland, the FTG-LSE summer conference, the UBC
summer conference, and the WFA for useful comments. Any errors are
our own.
∗
Corresponding author.
E-mail addresses: apbond@uw.edu (P. Bond),
yaozeng@wharton.upenn.edu (Y. Zeng).

Firms possess large amounts of information that is relevant to investors, customers, and other stakeholders, and
that ﬁrms could voluntarily disclose if they wished (e.g.,
Graham et al., 2005). However, there are many cases in
which valuable information that is potentially disclosable
is not disclosed, and ﬁrms instead stay silent. As examples: ﬁrms frequently report only aggregate earnings, without geographic or business segment decompositions; provide little guidance about future earnings; minimize the
information they disclose about executive compensation;
and refrain from reporting carbon emissions and Environmental, Social, and Governance (ESG) performance.1 This
silence on the part of ﬁrms with respect to value-relevant

1
See, respectively, and for example: Hope et al. (2013),
Harris (1998), Botosan and Stanford (2005), Bova et al. (2015),
Murphy (2012), Bolton and Kacperczyk (2020); Ilhan et al. (2020), and

https://doi.org/10.1016/j.jﬁneco.2021.08.012
0304-405X/© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/)

P. Bond and Y. Zeng

Journal of Financial Economics 145 (2022) 178–193

information is puzzling in light of the well-known “unraveling” argument that predicts that, in equilibrium, ﬁrms
disclose all information that they are able to.2 In brief,
the unraveling argument is that the ﬁrm with the most
favorable information certainly discloses; the audience for
the disclosure then interprets silence as indicating that the
ﬁrm does not have the most favorable information; but
then the ﬁrm with the second most favorable piece of information also discloses, and so on.
In this paper, we argue that in many settings ﬁrms stay
silent because doing so is safer than disclosure; speciﬁcally,
ﬁrms are uncertain about what it would be most beneﬁcial
for their audiences to believe, and silence reduces this risk.
For example, a ﬁrm making large proﬁts in a speciﬁc market would like to convey this information to its investors,
but would often like an array of other economic agents,
including competitors, tax authorities, regulators, and employee unions, to believe that proﬁts in this market are
low. If the ﬁrm is uncertain about the relative importance
of these different parts of its audience, it is accordingly
uncertain about whether it is better to try to convince its
combined audience that proﬁts in this market are high, or
low. We show that, in many cases, ﬁrms respond to this
uncertainty by staying silent, because doing so reduces the
variance of ﬁrm payoffs. Relative to leading explanations,
our analysis is able to account for silence even when disclosure has no direct cost, and even when there is no uncertainty that the ﬁrm possesses information to disclose
(see Grossman and Hart, 1980; Jovanovic, 1982; Dye, 1985).
Our analysis further implies that silence is driven by a
ﬁrm’s uncertainty about what its audience wants to see.
A number of extant empirical studies are consistent with
this prediction (Section 7). For example, ﬁrm silence is empirically associated with employees with more bargaining
power; exposure to public disapproval of tax avoidance via
“income shifting”; and fears of competition. Our analysis
also provides a simple explanation for the increasing willingness of ﬁrms to disclose carbon emissions and ESG performance over time, namely, increasing homogeneity of audience preferences; and is consistent with the view that
mandatory disclosure of executive compensation is costly
to ﬁrms because it exposes them to disapproval from outside the ﬁrm.
Closely related, our analysis predicts that when targeted disclosure to speciﬁc subsets of economic agents
is possible, ﬁrms will regularly avail themselves of this
opportunity, because doing so reduces their uncertainty
about what an audience wants to see. For this reason,
regulations that make targeted disclosure more diﬃcult,
such as Regulation Fair Disclosure in the U.S., may end up
reducing disclosure. Similarly, and perhaps paradoxically,
technological change that reduces frictions in sharing information3 may result in less disclosure, because it makes

targeted disclosure harder. Indeed, anecdotal accounts
suggest that ﬁrms and CEOs have become more reluctant
to make public remarks and instead are increasingly “acting like a politician” due to the increasing use of digital
communication and recordings, which allows gaffes to go
viral and trigger backlash from unfavorable audiences.4
Our paper contributes to the large literature on information disclosure. In our reading, the explanations of silence with widest applicability are that disclosure may be
costly (Grossman and Hart, 1980; Jovanovic, 1982) and that
some ﬁrms may be exogenously unable to disclose, leading
to endogenous silence by some ﬁrms that are able to disclose (Dye, 1985).5 An attractive feature of our analysis is
its ability to explain silence in settings in which disclosure
is both cheap and known to be feasible.
Researchers have proposed many alternative explanations for silence, as surveyed by Dranove and Jin (2010).
Among them, some share our focus on audience heterogeneity, though rely on very different economic forces.
For example, Fishman and Hagerty (2003) show that silence arises if some audience members are unable to process the information content of disclosure. Harbaugh and
To (2020) consider a setting in which the sender’s type
is drawn from the interval [0, 1], but disclosures are restricted to specifying which element of a ﬁnite partition
of [0, 1] the type belongs to. Moreover, the audience is
endowed with a private signal about the sender’s type.
Consequently, the best senders in a partition element may
prefer to remain silent to avoid mixing with mediocre
senders in the same partition element, and thus the unraveling argument breaks down. Similarly, Quigley and
Walther (2020) show that when disclosing is costly while
the audience observes a separate noisy signal about the
sender, the best sender may remain silent, rely on the audience’s signal, and thus save the disclosure cost. This then
generates “reverse unraveling” in which other sender-types
also remain silent to pool with higher sender-types.
Dutta and Trueman (20 02), Suijs (20 07), and
Celik (2014) all analyze relatively special situations in
which the ﬁrm as the sender is unsure how the audience
will respond to a disclosure. In Dutta and Trueman (2002),
the ﬁrm has two pieces of information, one representing a
“fact” about the ﬁrm and another governing how the audience would interpret the fact; the ﬁrm can only disclose
the former. However, there is a strictly positive probability
that the ﬁrm has no “fact” to disclose, so that the eco-

improve the quality and relevance of accounting information, thereby enhancing transparency and stakeholder decision making.”
4
See “Hold Your Peace,” The Economist, Vol. 429, Issue 9115.
5
Unraveling results have been generalized to wider classes of
economies by papers such as Okuno-Fujiwara et al. (1990) and
Seidmann
and
Winter
(1997).
In
particular,
OkunoFujiwara et al. (1990) stress the importance of the monotonicity of
the sender’s expected utility in the receiver’s beliefs, and include examples in which a failure of this property leads to full silence. Our paper
can be viewed as identifying a set of natural economic conditions that
generate non-monotonicity of the sender’s expected utility in receiver
beliefs. In doing so, we characterize the extent of silence—typically,
partial rather than full—along with comparative statics with respect
to sender and receiver risk aversion. Hagenbach et al. (2014) further
consider pre-play information disclosure before general Bayesian games
and provide suﬃcient conditions for unraveling.

Amel-Zadeh and Serafeim (2018). We detail our analysis’s application to
these speciﬁc examples in Section 7.
2
See Viscusi (1978), Grossman and Hart (1980), Milgrom (1981),
Grossman (1981), and Milgrom and Roberts (1986). Dranove and
Jin (2010) survey the literature.
3
See, for example, Warren et al. (2015) for a discussion of “How Big
Data Will Change Accounting,” including the prediction that “Big Data will
179

P. Bond and Y. Zeng

Journal of Financial Economics 145 (2022) 178–193

nomic forces that generate silence in Dye (1985) operate
in their paper also.6 In Suijs’s (2007) environment (unlike
ours), there is a direct beneﬁt to silence.7 In Celik (2014),
the ﬁrm as a seller both chooses whether to disclose a
location on a Hotelling line and makes a take-it-or-leave-it
price offer to a buyer whose location on the Hotelling line
is assumed to follow a uniform distribution.8 The details
of price formation are important: if instead there were
several competing buyers, the only equilibrium would be
full disclosure.

Before proceeding, we brieﬂy note an alternative interpretion, in which x denotes a ﬁrm’s carbon emissions (or
alternatively, an ESG score). Higher carbon emissions are
positively correlated with short-term cash ﬂows, but investors dislike them for a mixture of environmental concerns and fears of future regulation. The ﬁrm is uncertain
about the balance of investors’ conﬂicting desires, and so
is uncertain whether its payoff will be v(E [x − 1|μ]) or
v(E [−x|μ]).
In Fig. 1, we plot v(x − 1 ) and v(−x ). “Extreme” ﬁrms
that have high or low values of x face the most uncertainty
related to the audience’s identity (speciﬁcally, whether the
antagonist is passive or aggressive). Firms with intermediate values face little uncertainty; and the ﬁrm x = 12 faces
no uncertainty.
We write J (μ ) for the ﬁrm’s expected value under audience beliefs μ:

2. Example
We start with an illustrative example. We emphasize
that the example’s functional form choices and distributional assumptions are not essential, as our subsequent results demonstrate.
A ﬁrm can disclose to an audience value-relevant information, e.g., proﬁts in a particular market, denoted by x.
The value of x lies in [0, 1], and the audience’s priors about
x are given by the density function

f ( x ) = 1 − a ( 1 − 2x )

J (μ ) ≡

1
1
v(E [x − 1|μ]) + v(E [−x|μ]).
2
2

If the ﬁrm discloses x, the audience’s beliefs are concentrated on x, and with slight abuse of notation, the ﬁrm’s
expected value is

(1)

where a ∈ [−1, 1] is a parameter. The case a = 0 is the uniform distribution, while a = −1, 1 respectively are lower
and upper triangular distributions.
The audience for the ﬁrm’s disclosure consists of investors, and another party who we label an antagonist,
and depending on the application may variously represent
a regulator, tax authority, employee group, or competitor.
Let μ denote the audience’s beliefs about x, which depend on whether the ﬁrm discloses or stays silent. The
ﬁrm is uncertain whether the antagonist is passive or aggressive and attaches probability 12 to each possibility. The
ﬁrm’s risk preferences are represented by a strictly concave function v. If the antagonist is passive, the ﬁrm’s value
is v(E [x − 1|μ]), while if the antagonist is aggressive, the
ﬁrm’s value is v(E [x − 2x|μ]). Concretely, one can interpret
these payoffs as being composed of E [x|μ] from investors,
and either -1 or E [−2x|μ] from passive and aggressive antagonists, respectively.
We highlight three features of the example that are
important. First, the ﬁrm beneﬁts from investors believing that x is high, but beneﬁts from the antagonist believing that x is low. Second, the ﬁrm is uncertain about how
much it will beneﬁt from the antagonist believing that x
is low. Third, the ﬁrm is effectively risk-averse (either because of intrinsic preferences or contracting frictions) over
outcomes.

J (x ) =

1
1
v(x − 1 ) + v(−x ).
2
2

In Fig. 1 we also plot J (x ), the ﬁrm’s value from disclosure.
It is a strictly concave function of x. Additionally, and special to this example, it is symmetric about x = 12 .
An equilibrium is characterized by the set of ﬁrms S ⊂
[0, 1] that stay silent. All silent ﬁrms face the same audiS
ence beliefs, which we denote
 by
 μ ; and hence all silent
ﬁrms have the same payoff J μS .
2.1. Silence is safest
An immediate implication is that if an equilibrium entails silence, the silence set consists of “extreme” ﬁrms
with high or low values of x. That is, there are x and x̄
such that the silence set is

S = [0, x ) ∪ (x̄, 1].
Moreover, ﬁrms x and x̄ are indifferent between silence
and disclosure:





J (x ) = J (x̄ ) = J μS .

(2)

We next rewrite (2) more explicitly, focusing on the case of
a ≥ 0, so that the audience’s prior has an upwards sloping
density. (The case of a ≤ 0 is directly analogous.) Two features speciﬁc to the example are very helpful in rewriting
(2). First, the symmetry of J (x ) immediately implies that

6
Speciﬁcally, Dutta and Trueman (2002) state that if the probability of
the ﬁrm knowing the “fact” is 1, unraveling always happens in equilibrium.
7
Speciﬁcally, in Suijs’s (2007) model, disclosure gives a payoff of either
U (0 ) or U (1 ), with probabilities 1 − p(φ ) and p(φ
 ) respectively, where
φ is the sender’s type. Silence gives payoffs of U 12 and something at
least U (0 ), with corresponding probabilities, and regardless of audience
inferences about what silence means. So if the type space is such that
1 − p(φ ) is suﬃciently high for all types, silence is an equilibrium.
8
These assumptions imply that disclosing sellers at the ends of the line
face a severe trade off between proposing a higher price and achieving a
reasonable sale probability.

x̄ = 1 − x.

(3)

Second, a ﬁrm’s value after silence equals the value from
disclosing

 an x equal to the expected value of silent ﬁrms,
E x | μS :





 

J μS = J E x | μ S



.

(4)

The symmetry property (3) and the focus on upwards sloping densities (a ≥ 0) together imply that the average type
180

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Journal of Financial Economics 145 (2022) 178–193

Fig. 1. Graphical illustration of example of Section 2.

of a silent ﬁrm is above 12 . From (4), it follows that the
equilibrium condition (2) can be written simply as

1 − x = E [x|x ≤ x or x ≥ 1 − x].

Moreover, substitution of the density function into
(5) delivers the explicit solution:

(5)

x=

That is, silence induces audience beliefs such that the expected value of x of a silent ﬁrm coincides with a ﬁrm
that is happy to disclose. Disclosing ﬁrms are intermediate ﬁrms, which face less uncertainty from the audience’s
identity. By staying silent, extreme ﬁrms achieve safer outcomes, which they prefer because of risk aversion—that is,
silence is safest.

−(1 − |a| ) +





(1 − |a| ) 1 + 13 |a|
| |

4
a
3



.



It is straightforward to show that x ∈ 0, 12 , with x → 0, 12
as |a| → 1, 0.
In particular, the beneﬁt of silence lies in extreme ﬁrms
pooling together so that the audience believes they are average. This beneﬁt is largest when the audience’s prior beliefs attach similar probabilities to both “low” and “high”
types, leading to greater equilibrium silence.
3. Model

2.2. Equilibrium silence

We now state our formal model, which generalizes the
example. A ﬁrm has a type x drawn from a compact set
X ⊂ , which we normalize to X = [0, 1]. The ﬁrm is privately informed about its type x, which the audience does
not know. The audience’s prior of x is given by a probability measure μ0 , which has full support over X, and admits
a density function f .
The ﬁrm can costlessly disclose x to an audience, or alternatively, stay silent. Subsequent to a ﬁrm’s disclosure or
silence, audience beliefs are given by a probability measure μ. Speciﬁcally, if a ﬁrm discloses x, audience beliefs
are concentrated on x. If instead a ﬁrm stays silent, audience beliefs are given by μS , which is obtained from the
initial beliefs μ0 after conditioning on x belonging to the

If a = 0, the audience’s prior is uniform, and x = 12
solves (5). In this case, there is an equilibrium in which all
ﬁrms other than x = 12 remain silent; and even ﬁrm x = 12
is indifferent between silence and disclosure.
For a ∈ (0, 1 ), the left-hand side (LHS) of (5) is less
than the right-hand side (RHS) at x = 12 . On the other
hand, as x → 0, the LHS approaches 1, while the RHS apf 1
proaches f (0 )(+ f)(1 ) , which is strictly less than 1, because silence pools ﬁrms with low and high values of x together.
So by continuity, there exists x ∈ (0, 1 ) that solves (5), corresponding to an equilibrium in which some ﬁrms stay
silent and some disclose.

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Journal of Financial Economics 145 (2022) 178–193

set of ﬁrms that stay silent in equilibrium, which we denote by S.
The ﬁrm is uncertain about its audience. The ﬁrm’s payoff depends on the realized identity of its audience, and
on the audience’s beliefs about its type. The set of possible audiences is N and a speciﬁc audience is denoted by
i, and has probability Pr (i ). Let pi (μ ) be the ﬁrm’s payoff
from an audience i with beliefs μ about the ﬁrm’s type.
We assume that pi (μ ) is continuous as a function of μ,
i.e., if μn converges weakly to μ, then pi (μn ) → pi (μ ). We
write pi (x ) for the case in which the ﬁrm discloses and so
μ is concentrated on x. Note that pi (x ) is continuous in
x. The payoff function pi summarizes how audience i’s actions given beliefs μ affect the ﬁrm.
We assume that audiences are (weakly) risk-averse in
the sense that they dislike uncertainty about the ﬁrm’s
type, and this in turn negatively impacts the ﬁrm:

optimal, i.e.,

pi (μ ) ≤ E [ pi (x )|μ].

4. Silence is safest

J (μ ) ≤ J (E [x|μ] ).

We write J (x ) for the ﬁrm’s expected value after disclosing
x, henceforth the ﬁrm’s disclosure value.
As much as possible, we express results in terms of the
expected value function J. Note that J (x ) inherits continuity from pi (x ). As noted, at this point we have made no
assumptions on the shape of pi (x ).
We impose mild regularity assumptions:

pi (μ ) ≤ pi (E [x|μ] )

audiences

i ∈ N,

the



(AB)

(7)

for each audience i. Inequality (7) immediately implies
(AB).
Property (AB) directly implies a key property of any silence equilibrium:

Assumption 1. J (x ) has only a ﬁnite number of extrema.
all



Property (AB) says that if the audience’s beliefs about the
ﬁrm are given by μ, the ﬁrm would (weakly) beneﬁt from
the audience instead treating the ﬁrm as the average of
these types, E[x|μ]. This property can be viewed as a
strengthening of audience risk aversion (6). That is: if the
payoff functions pi (x ) are weakly concave (see discussion
below), then audience risk-aversion (6) implies

Pr (i )v( pi (μ ) ).

∂v ( pi (x ) )
remains bounded as x → 0, 1.
∂x



We ﬁrst characterize an important feature of silence
equilibria, namely, a sense in which “silence is safest,”
thereby generalizing our previous observations about the
example. Our subsequent analysis gives necessary and sufﬁcient conditions for silence equilibria to exist.
Speciﬁcally, we explore the implications of the ﬁrm’s
expected value function satisfying the following simple
property, which we label as “average is better” (AB):

i∈N

Assumption 2. For



Note that if all ﬁrms disclose, S = ∅, and J μS is not deﬁned. Indeed, full disclosure can always be supported as
an equilibrium by assigning off-equilibrium-path beliefs
in which the audience interprets silence as meaning that
the ﬁrm’s type is arg minx∈X J (x ). Our analysis characterizes when equilibria with silence exist, and the form they
take. We refer to any equilibrium with μ0 (S ) > 0 as a silence equilibrium; and further distinguish between equilibria with full silence, i.e., μ0 (S ) = 1, and with partial silence,
i.e., 0 < μ0 (S ) < 1. Similarly, an equilibrium with μ0 (S ) =
0 has full disclosure.

Audience risk-neutrality corresponds to (6) holding with
equality. We emphasize that pi (x ) may be increasing, decreasing, or even non-monotonic in x. Note that audience
risk aversion makes silence costly for the ﬁrm, making it
harder for silence to arise in equilibrium.
Because the ﬁrm is uncertain about its audience, the
ﬁrm’s expected value depends on its risk preferences,
which are captured by a strictly increasing function v,
henceforth the ﬁrm’s value. For now, we allow v to be either concave or convex. The ﬁrm’s expected value if the
audience has beliefs μ is hence

J (μ ) ≡ E [v( pi (μ ) )] =



J (x ) ≥ J μS for all s ∈
/ S.

(6)





J (x ) ≤ J μS for all x ∈ S

derivative

Proposition 1. Let (AB) hold. In any silence equilibrium, a ﬁrm

with type equal to the average type of silent ﬁrms, E x|μS ,
weakly prefers disclosure to silence; and the set of ﬁrm types
that strictly prefer silence to disclosure is not an interval.

( )
Assumption 3. For any constant κ > 0, limx→0 f (1−
κ x ) exists
f x

 

The ﬁrst statement in Proposition 1 is J E x|μS ≥
 S
J μ , which is simply a special case of (AB). For the sec-

and is strictly positive.

Assumption 1 rules out economically uninteresting
cases in which J (x ) is ﬂat, or oscillates inﬁnitely often.
Assumptions 2 and 3 cover extreme ﬁrm types, and relate
to audience preferences and the audience priors, respectively. We emphasize that Assumptions 2 and 3 are used
only by Proposition 6, which gives a set of suﬃcient conditions for a silence equilibrium to exist, and play no role
in the rest of our analysis.
An equilibrium is characterized by a “silence” set S of
ﬁrm types that do not disclose, and stay silent. The remaining ﬁrms X \S disclose. The equilibrium condition is
that each ﬁrm’s decision between disclosure and silence is

ond statement, suppose to the contrary that the stated set
is an interval. By Assumption 1, only a ﬁnite number of
ﬁrm types can be indifferent

 between silence and disclosure, implying that E x|μS belongs to the interval, contradicting the ﬁrst statement.
Proposition 1 says that in any silence equilibrium there
are ﬁrms sandwiched between silent ﬁrms that are happy
to disclose. The advantage of silence is that the audience
interprets
 it as
 meaning that the average type of silent
ﬁrms, E x|μS , corresponds to a happy-to-disclose type.
This averaging effect is the “safety” that a ﬁrm gains from
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Journal of Financial Economics 145 (2022) 178–193

staying silent; in other words, “silence is safest.”9 We develop this point further in Section 6.
As noted, a suﬃcient condition for (AB) is that the payoff functions pi (x ) are weakly concave. To give economic
meaning to the concavity of pi (x ), consider the case of audiences consisting of a mixture of investors and antagonists (see Section 2). Suppose that there is an audience in
which the antagonist is passive, so that if the ﬁrm knew it
faced this audience, it would focus on pleasing investors.
This investor-dominated audience can be taken as a “numeraire” audience: without loss, denote this audience as
audience 1, and identify a ﬁrm’s type with the reaction of
investors, i.e., p1 (x ) = x. Then the concavity of pi (x ) corresponds to antagonists growing increasingly unhappy at
marginal improvements in investor payoffs, i.e., increasing
marginal disutility. For much of our analysis we focus on
the case of concave payoff functions pi (x ), both because
we believe it to be economically relevant, and because if
pi (x ) are instead strictly convex, silence can arise for more
mechanical reasons, a point we explore in Appendix A.1.
We highlight that our paper’s central implication,
namely that a ﬁrm may remain silent if it is both uncertain about audience preferences and risk averse, is independent of both the concavity of pi (x ) and of (AB). In particular, the necessary conditions in Propositions 2–4 hold
independently of these properties.

is high, low, or perhaps intermediate, and (II) ﬁrm riskaversion. Moreover, it is important that (III) audiences are
not so risk-averse that they respond extremely negatively
to the uncertainty that silence leaves them with. All the
three conditions are necessary, as we next establish.
5.1.1. Uncertainty about audience preferences
First, silence only arises if at least some audiences differ
in their preference orderings:
Proposition 2. If there is no uncertainty over audience preference orderings, i.e., pi is ordinally equivalent to p j in the
sense that pi (x ) < (≤ ) p j (x˜) if and only if pi (x ) < (≤ ) p j (x˜)
for any i, j ∈ N, then Condition 1 holds and the only equilibrium is full disclosure.
By Proposition 2, uncertainty over only the strength
of audience preferences for a higher value of x is insufﬁcient to generate silence, since in this case all the audiences have ordinally equivalent preferences, and a version of the standard unraveling proof applies. In contrast,
silence requires the ﬁrm to be unsure about whether an
audience values higher or lower values of x, at least over
some range. For instance, if the example of Section 2 is
perturbed
so that the ﬁrm’s payoff is either E [x − 1|μ]

or E x − 12 x|μ , depending on the audience, then the only
equilibrium is full disclosure.
Proposition 2 is true even if pi (x ) is non-monotone in x,
illustrating that non-monotone audience preferences alone
are insuﬃcient to generate silence in equilibrium. Roughly
speaking, if pi (x ) is non-monotone, but all audiences have
ordinally equivalent preferences, the unraveling argument
still applies after a change in variables from x to pi (x ).

5. When do equilibria with silence emerge?
5.1. Necessary conditions for silence
Proposition 1 characterizes silence equilibria, conditional on such equilibria existing. We next derive necessary
conditions for such equilibria to exist. To state our results,
it is useful to ﬁrst express the unraveling condition (i.e.,
when full disclosure must happen) in terms of the ﬁrm’s
expected value function J:

5.1.2. Firm risk aversion
We now turn to our second necessary condition, ﬁrm
risk aversion. Recall that ﬁrm risk aversion naturally arises
from concentrated ownership, or from managerial riskaversion coupled with internal agency ﬁctions, or from external ﬁnancing frictions. If the ﬁrm is either risk-neutral
or risk-loving, then unraveling occurs, and all ﬁrms disclose.

Condition
 1. For any non-null set S, there exists x ∈ S such
that J μS < J (x ).
Condition 1 says that for any mix of ﬁrm types μS staying silent, there is always a ﬁrm type x ∈ S that would beneﬁt from separating itself from the other ﬁrms and disclosing. If Condition 1 holds, it is immediate that the only
equilibrium has full disclosure.
Equilibrium silence can only exist if Condition 1 is violated, as in the example of Section 2. The key ingredients
in the example are that (I) the ﬁrm is unsure whether it
would beneﬁt from convincing the audience that its type

Proposition 3. If the ﬁrm is either risk-neutral or risk-loving
(i.e., v weakly convex), then Condition 1 holds and the only
equilibrium is full disclosure.
In particular, if the ﬁrm is risk neutral (v linear) and
the payoff functions pi are linear, then one can simply
switch variables from x to E[ pi (x )], and apply the standard
unraveling argument with respect to E[ pi (x )]. The proof
of Proposition 3 extends this argument to cover convex v
functions and arbitrary pi functions.

9
We also note that if (AB) holds strictly for any μ with non-null support, then Proposition 1 can be straightforwardly
to state:
 strengthened

“In any silence equilibrium, a ﬁrm with type E x|μS strictly prefers disclosure to silence; and the set of ﬁrm types that weakly prefer silence to
disclosure is not an interval.” Along the same lines, if one assumes that
a ﬁrm always breaks indifference in favor of disclosure (a heuristic argument outside our model is that the ﬁrm knows its disclosure payoff from
a given audience, while its silence payoff depends on audience beliefs),
then Assumption 1 can be dropped, and Proposition 1 can be written simply as “In any silence equilibrium, a ﬁrm with type E x|μS discloses; and
the silence set is not an interval.”

5.1.3. Audience risk aversion
A third necessary condition is that audiences cannot
be too risk-averse. Recall that the risk-aversion of audience i is embodied in the relation between E [ pi (x )|μ] and
pi (μ ); greater risk aversion corresponds to a larger value
of E [ pi (x )|μ] − pi (μ ),10 with risk neutrality corresponding
10

183

See also 6.3, and the associated Appendix A.2.

P. Bond and Y. Zeng

Journal of Financial Economics 145 (2022) 178–193

to this expression equalling zero. So as to avoid imposing
functional forms on pi , we focus on the extreme case of inﬁnite audience risk aversion, and show that in this case the
only equilibrium is full disclosure. Formally, inﬁnite riskaversion corresponds to11

pi ( μ ) =

inf

x˜∈supp(μ )

pi (x˜).

5.2. Suﬃcient conditions for silence
We next turn to suﬃcient conditions for the existence
of silence equilibria. To establish that such silence equilibria exist in general (i.e., beyond the example of Section 2),
Proposition 6 establishes that the following conditions are
suﬃcient for silence equilibria: (I) At least some pair of
audiences has differing preference orderings over extreme
ﬁrm-types; (II) Firm risk-aversion; (III) Audiences are not
too risk-averse; and (IV) The probability of different audiences is such that extreme ﬁrm-types dislike disclosure
close-to-equally. These four suﬃcient conditions are the
counterpoints of the necessary conditions stated in, respectively, Propositions 2, 3, 4, and 5. As such, our previous
results about necessity show that if these conditions are
suﬃciently far from holding, then no silence equilibrium
exists.
We also suppose that the payoff functions pi (x ) are
weakly concave. For the reasons discussed in Section 4,
this is the case that we generally focus on. But we also emphasize that this property plays a much more minor role in
Proposition 6 than the features (I)-(IV) that we emphasize,
and could be straightforwardly replaced with considerably
weaker conditions.14

(8)

Proposition 4. If audiences are inﬁnitely risk-averse in the
sense of (8), then Condition 1 holds and the only equilibrium
is full disclosure.
Intuitively, silence is unlikely to be attractive if audiences are very risk-averse, because in such cases it imposes
so much risk on audiences that it harms ﬁrms by more
than they gain by pooling and reducing their own risk
stemming from uncertainty about audience preferences.
5.1.4. Non-monotonicity of disclosure value J (x )
Our ﬁnal necessary condition, which the example in
Section 2 illustrates, is that the ﬁrm’s disclosure value J (x )
must be non-monotone. Note that this is a necessary condition only for the case that we focus on, namely that in
which (AB) holds, discussed in Section 4.12 Recall that under (AB), silence equilibria entail disclosure by intermediate types, and silence by more extreme types. The only
way this can occur is if the disclosure value J (x ) is nonmonotone:

Proposition 6. Suppose the payoff functions pi (x ) are weakly
concave, along with: (I) There are audiences i, j such that
pi (0 ) < pi (1 ) and p j (0 ) > p j (1 ); (II) The ﬁrm’s value function v is strictly concave; (III) All audiences are suﬃciently
close to risk-neutral; and (IV) The distribution of audiences
{Pr(i )} is such that |J (0 ) − J (1 )| is suﬃciently small. Then a
silence equilibrium exists.

Proposition 5. If (AB) holds and the disclosure value J (x ) is
monotone, then Condition 1 holds and the only equilibrium is
full disclosure.

The proof of Proposition 6 is a generalization of the
ﬁxed point argument described at the start of 2.2 in the
context of the example.
In general, further results on suﬃcient conditions require considerably more parametric structure on the economy. That said, a very simple suﬃcient condition arises for
the case in which the payoff functions pi (x ) are linear and
audiences are risk-neutral, so that (AB) holds with equality
(as in the example of Section 2).

Propositions 2 and 3 already establish that both uncertainty about audience preferences and ﬁrm risk-aversion
are necessary for silence. Proposition 5 shows that these
conditions are not suﬃcient. In particular, these conditions
generate silence only if they generate a non-monotone disclosure value J (x ).
Whether or not uncertainty about audience preferences
and ﬁrm risk-aversion indeed generate a non-monotone
disclosure value J (x ) depends on the probability distribution of different audiences. Lemma 1 shows that there
exist probability distributions under which J (x ) is nonmonotone, at least for the case of concave payoff functions
that is our main focus.13

Proposition 7. Suppose the ﬁrm’s value function v is strictly
concave, pi (x ) are linear, and audiences are risk neutral. If
J (1 ) > (< )J (0 ) and arg maxx J (x ) is interior and weakly less
than (greater than) E [x|μ0 ] then there exists a silence equilibrium.

Lemma 1. If the payoff functions pi (x ) are concave, the ﬁrm
is risk-averse, and there is uncertainty about audience preferences (i.e., there exist ﬁrm types x, x˜ and audiences i, j such
that pi (x ) < p j (x˜) and pi (x˜) < p j (x )), then there is a neighborhood of probability distributions over audiences such that
J (x ) is non-monotone.

By Proposition 5, we know that silence only arises if
uncertainty about audience preferences15 leads to a nonmonotone disclosure value J (x ). Proposition 7 gives a simple lower bound on an “amount” of non-monotonicity that
is enough to deliver silence. That is, if J (1 ) > J (0 ), so that
overall the disclosure value J (x ) slopes up from left to
right, then the departure from monotonicity must be large

11
Note that inﬁnite risk-aversion violates the continuity axiom, and so
does not admit an expected utility representation.
12
Appendix A.1 presents an example in which J (x ) is monotone, (AB) is
violated, and full silence arises.
13
We also note that non-monotonicity of J (x ) does not nest uncertainty
about audience preferences. In particular, non-monotonicity of J (x ) can
easily arise even if the sender knows the audience’s preferences; if, for
example, there is only one audience with non-monotone preferences.

14
Speciﬁcally, it is straightforward to replace the weak concavity of
pi (x ) in Proposition 6 with the much milder assumption that J (x ) has a
minimum at either x = 0 or 1.
15
Linearity of the payoff functions pi (x ) and the condition that
arg maxx J (x ) is interior imply that the ﬁrm is uncertain about audience
preferences.

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Journal of Financial Economics 145 (2022) 178–193

enough that the peak of the disclosure value function J (x )
lies to the left of the average type E [x|μ0 ].
Remark (Aside): Although our focus is on the case
in which ﬁrms cannot commit to disclosure policies, one
can also ask what disclosure policy a ﬁrm would commit to if commitment were feasible prior to learning its
type x. When (AB) holds with equality, and a ﬁrm is riskaverse, the answer is that a ﬁrm would commit to full
silence, since for any possible silence set S that the ﬁrm
commits to,16

and

J (μ0 ) > E[J (x )|μX \S ] Pr(X \S ) + E[J (μS )] Pr(S ).

Corollary 2. In any silence equilibrium S there is at least one
marginal discloser xm for which

6. Characterization of silence equilibria

E p i μS

We further characterize silence equilibria, focusing on
the relationship between risk-aversion and “silence is
safest.” Given the analysis in Sections 4 and 5, for the
remainder of the paper we impose the following pair
of assumptions. First, we focus on strictly concave ﬁrm
value functions v, since otherwise silence does not arise
(Proposition 3). Second, and as discussed in Section 4, we
focus on weakly concave payoff functions, pi (x ), to rule out
more mechanical beneﬁts of silence.

Moreover, the inequality is strict if silence is partial and Condition 2 holds.

 

≤E [ pi (xm )].

(11)

6.2. Comparative statics with respect to ﬁrm risk-aversion
To further reinforce the point that a key economic
force behind silence is the reduction in risk it engenders,
we next consider comparative statics in ﬁrm risk-aversion.
By Corollary 2, silence reduces risk for at least one of
the marginal disclosers x and x̄. We show that as ﬁrm
risk-aversion increases, ﬁrms close to this marginal discloser switch from disclosure to silence. Concretely, variations in ﬁrm risk-aversion correspond to variation in
ownership concentration, managerial risk-version, internal
agency frictions, or external ﬁnancing frictions.
For the case of two audiences (|N| = 2 ), we establish
this result using Pratt (1964)’s general ordering of risk
preferences.

6.1. Silence is safest revisited
This last pair of assumptions allows us to more tightly
characterize silence equilibria. We use the following mild
condition, which implies that for any μ with a non-null
support, (7) holds strictly for some audience i, and hence
that (AB) also holds strictly, and guarantees strictness of
some key inequalities:

Proposition 8. Suppose that |N| = 2, Condition 2 holds, and
that a partial silence equilibrium exists when the ﬁrm’s value
function is v. Suppose that the ﬁrm’s value function changes
to v˜ = φ ◦ v for some increasing and strictly concave φ , corresponding to greater risk-aversion. Then there is a marginal
discloser xm for which silence
 is safer
 than disclosure in the
original equilibrium, i.e., E pi μS < E [ pi (xm )], and a new
silence equilibrium under v˜ , such that silence strictly increases
in the neighborhood of xm .

Condition 2. There exists at least one audience i for which
pi (x ) is strictly concave.
First, note that, since J (x ) is single-peaked, the structure
of a silence equilibrium can immediately be strengthened
to:
Corollary 1. In a silence equilibrium S, there are x, x̄ such that
S = [0, x ) ∪ (x̄, 1];

16



That is, the silence lottery is safer than the disclosure
lottery of at least one of the marginal disclosers, in the
following sense: since the lotteries provide the same expected value to a marginal discloser, a lower expected payment implies that the lottery must be safer. In this sense,
Corollary 2 is a more explicit demonstration that silence is
safest.

Assumptions 4 and 5 imply that J (x ) is strictly concave, and in particular single-peaked. As noted earlier,
Assumption 5 implies both (7) and (AB).



(10)

In Corollary 1, ﬁrms x and x̄ are marginal disclosers, in
the sense of being indifferent between disclosure and silence, as in (10).
Corollary 1 further implies:

Assumption 5. The payoff functions pi (x ) are weakly concave.





Moreover, both inequalities in (9) are strict if silence is partial
and Condition 2 holds.

Assumption 4. The ﬁrm’s value function v is strictly concave.

x ≤ E x|μS ≤ x̄;



J (x ) = J (x̄ ) = J μS .

The restriction to two audiences in Proposition 8 is
needed because, as is widely appreciated, it is hard
to produce general comparative statics on choices between risky lotteries with respect to risk preferences
without imposing signiﬁcant structure on either preferences or on the distribution of payoffs. See, for example, Ross (1981). Speciﬁcally, with just two audiences,
we show that, for at least one of the marginal disclosers xm ∈ {x, x̄}, the payoffs associated with silence,
i.e., p1 μS , p2 μS , lie within the range of possible payoffs associated with disclosure, i.e., lie in the interval

(9)

The following inequality is a consequence of

J (μ0 ) = J (E[x|μ0 ] )
> E [J (E [x|μX \S )] )] Pr(X \S ) + E [J (E [x|μS ] )] Pr(S )
> E[J (x )|μX \S ] Pr(X \S ) + E[J (E[x|μS ] )] Pr(S )
= E[J (x )|μX \S ] Pr(X \S ) + E[J (μS )] Pr(S ),
where the two inequalities follow from Jensen’s inequality, and the two
equalities are (AB).
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[min { p1 (xm ), p2 (xm )}, max { p1 (xm ), p2 (xm )}]. This property allows us to apply Hammond’s (1974) results.
For more than two audiences, we are unable to guarantee this property. Since we then lack structure on the distribution of payoffs, we must instead impose more structure on the risk-aversion ordering.

disclosure is known to be feasible. As discussed in the introduction, silence in these circumstances is often viewed
as puzzling. As an example, a ﬁrm can certainly disclose
the full details of its CEO’s compensation package, and in
many cases the direct costs of doing so are extremely low;
but yet ﬁrms very frequently remain silent about many
compensation details.

Proposition 9. Suppose that Condition 2 holds, and that a
partial silence equilibrium exists when the ﬁrm’s value function is v. Suppose that the ﬁrm’s value function changes to v˜ ,
where α v˜ (z ) + z = v(z ) for some constant α > 0, corresponding to greater risk-aversion. Then there is a marginal discloser
xm for which silence
 is safer
 than disclosure in the original
equilibrium, i.e., E pi μS < E [ pi (xm )], and a new silence
equilibrium under v˜ , such that silence strictly increases in the
neighborhood of xm .

7.2. Disclosure and uncertainty about audience preferences
Beyond the existence of silence, our primary empirical prediction is that silence is related to ﬁrm uncertainty
about what it would be most beneﬁcial to communicate to
its audience (see, in particular, Proposition 2). This prediction is supported by a number of empirical studies, as we
review below, which mostly fall under the rubric of a ﬁrm
disclosing to a mix of investors and “antagonists.”
Bova et al. (2015) present evidence that ﬁrms facing
employees with greater bargaining power (union representation, or tight local labor markets) are less likely to disclose “management guidance” to investors. In terms of our
model, ﬁrms face an audience composed of a mixture of
investors and employees. If ﬁrms are suﬃciently uncertain
about the relative desirability of moving investor and employee beliefs about future cash ﬂows, our analysis implies that they choose silence over disclosure. In contrast,
ﬁrms for which wage rates are determined primarily by
employees’ outside options do not face this uncertainty,
and standard unraveling arguments predict that such ﬁrms
disclose. Additionally, the authors ﬁnd that greater employee stock ownership increases disclosure. In terms of
our model, greater stock ownership means that a ﬁrm is
more conﬁdent that it would beneﬁt from convincing audience members that future cash ﬂows are high, thereby
reducing its uncertainty about audience preferences.
Hope et al. (2013) present evidence that multinational
ﬁrms that are likely using geographic “income shifting”
to reduce taxes are less likely to disclose the geographic
breakdown of earnings. In terms of our model, such ﬁrms
face an audience of investors, who would like to know the
geographic breakdown of earnings, and a mixture of “policy makers,” “citizen groups,” and “foreign tax authorities.”
As the authors put it, disclosure of “abnormally high geographic earnings in low-tax jurisdictions” would “potentially garner negative publicity from policy makers and citizen groups, attract the attention of foreign tax authorities,
and possibly damage the manager’s and the ﬁrm’s reputation” (p. 174). If ﬁrms are suﬃciently uncertain about
the relative pros and cons of pleasing different parts of
their audiences, our analysis implies that that will choose
silence over disclosure. In contrast, ﬁrms that are not
income-shifting do not face this uncertainty, and standard
unraveling arguments predict that such ﬁrms disclose.17
Studying a period in which US ﬁrms had substantial
discretion over whether or not to decompose operating
performance across business segments, Harris (1998) and
Botosan and Stanford (2005) present evidence that ﬁrms

The comparison of risk preferences used in
Proposition 9 amounts to saying that preferences represented by v˜ are more risk-averse than preferences
represented by v if v corresponds to a mixture of v˜ and
risk-neutral preferences. This ordering is closely related
to Ross’s (1981) notion of preferences becoming “strongly
more risk averse.” Note that in the speciﬁc case of mean
variance preferences, this comparison corresponds to a
greater dislike of variance.
6.3. Comparative statics with respect to audience
risk-aversion
While silence has the potential beneﬁt of reducing risk
for ﬁrms, it has the cost of increasing risk for audiences. If
audiences are risk-averse, this reduces ﬁrms’ beneﬁt from
silence.
As noted above, greater audience risk aversion corresponds to larger values of E [ pi (x )|μ] − pi (μ ). Equivalently,
holding pi (x ) constant, strictly greater audience
 risk
 aversion corresponds to strictly lower values of pi μS for any
non-null S. In Appendix A.2. we show that this deﬁnition
is equivalent to Pratt’s risk-aversion ordering in a standard
willingness-to-pay model.
Proposition 10. Suppose that Condition 2 holds and a silence
equilibrium exists. Suppose that audience j’s risk aversion increases. Then all equilibria feature more disclosure than the
equilibrium with the least amount of disclosure under audience j’s original risk preferences; and the relation is strict if
the original equilibrium has partial silence.
Note that, in our setting, disclosure by a ﬁrm eliminates
all risk for the audiences. However, the economic force in
Proposition 10 continues to hold even in situations where
disclosure reduces the risk faced by the audiences, instead
of completely eliminating it.
7. Empirical evidence and applications
7.1. Silence when disclosure is costless and known to be
feasible
An immediate implication of our analysis is that silence
can arise even when disclosure is costless, and even when

17
Hope et al. (2013) are very clear in not attributing their ﬁndings to a
direct need of ﬁrms to hide income-shifting because it is in fact illegal.

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were less likely to report such a decomposition when some
segments were operating in relatively uncompetitive industries. In terms of our model, a ﬁrm that has a business
segment in an industry with little competitive pressure
would like to convince investors that proﬁts in this industry are high, but would like to convince potential entrants
that proﬁts in this industry are low. If such a ﬁrm is uncertain about the strength of latent competition from new entrants, our analysis predicts it is more likely to stay silent
about its operating performance in this industry. Related
also, many respondents in Graham et al.’s (2005) survey
of executives cite a “concern that some disclosures might
jeopardize the ﬁrm’ s competitive position in the product
market” as a reason for non-disclosure.18
Firms are frequently silent about the details of executive compensation. In response, the U.S. has introduced a
sequence of disclosure mandates, starting in the 1930s, as
reviewed by Murphy (2012). Our analysis is consistent with
Murphy’s observation that, once disclosed, “executive contracts in publicly held corporations are not a private matter between employers and employees but are rather inﬂuenced by the media, labor unions, and by political forces
operating inside and outside companies” (p. 18). If ﬁrms
are unsure what the aggregate audience reaction will be to
compensation disclosure, our analysis predicts that some
ﬁrms stay silent, unless regulation forces disclosure.
Separate from the investor-antagonist setting of the
above cases, a distinct source of ﬁrm uncertainty about
audience preferences arises if investors also care about
non-ﬁnancial outcomes. A potentially important application is to ﬁrms’ disclosure of carbon emissions, climate
risks, and ESG performance more generally. Bolton and
Kacperczyk (2020) and Ilhan et al. (2020) ﬁnd direct evidence of investors’ heterogenous preferences over lower
ﬁrm carbon emissions, which are likely to conﬂict with
better ﬁnancial performance.19 From our analysis, such uncertainty can lead ﬁrms to stay silent about carbon emissions and climate risks. Moreover, to the extent to which
investor concern about climate change and ESG performance more generally has increasingly become the norm,
thereby reducing uncertainty about investor preferences,
our analysis explains the increasing disclosure of carbon
emissions and ESG performance.20 Related, to the extent
to which ﬁrms have a clearer idea of insitutional investors’
preferences than of retail investors’ preferences, our anal-

ysis predicts that greater institutional ownership is associated with more disclosure, as Ilhan et al. (2020) ﬁnd.

7.3. Disclosure of imperfect signals of the underlying
attribute
The above applications of our model are ones in which
audiences directly care about the information the ﬁrm discloses. But in many cases, the information that a ﬁrm considers disclosing is instead valuable because it is correlated with what investors and other audience members ultimately care about. For example, investors may be interested in CEO compensation, carbon emissions, or ESG performance primarily because it represents a signal about,
among other things, the corporate governance of the ﬁrm,
which in turn affect future cash ﬂows. Importantly, in
these cases investors may disagree about the correlation
between the object being disclosed and future cash ﬂows.
For example, some investors may believe the correlation
between CEO pay and future cash ﬂows is positive, while
others may believe just the opposite. The same is true for
carbon emissions and for ESG performance.
In this section we extend our model to analyze the disclosure of imperfect signals of an underlying attribute. By
doing so, we offer another explanation for why some ﬁrms
refrain from disclosing items such CEO compensation packages, carbon emissions, or ESG performance (see preceding
subsection).
Formally, let y be the future cash ﬂow, or, more generally, some other underlying attribute that audiences care
about. The ﬁrm cannot disclose y, but can disclose some
other quantity x, such as CEO pay, carbon emissions, or
ESG performance, that is potentially correlated with y.
Audiences care about cash ﬂows y, but do not have direct preferences over x. For simplicity, audiences are riskneutral over y.
Although all audiences have the same preferences, they
differ in what they believe x reveals about y. Speciﬁcally,
all audiences have the same prior of the distribution of y,
with support [0, 1]. However, they differ in their assessment of the distribution of the signal x conditional on y.
For simplicity, we focus on a stark case to illustrate our results. Each audience believes that x is either perfectly correlated with y, and speciﬁcally equals y; or that x is perfectly negatively correlated with y, and speciﬁcally equals
1 − y. Audience i attaches probabilities λi and 1 − λi to
these two possibilities.
Consequently, audience i’s conditional expectation of y
after observing x is21

18
Returning to the discussion following Proposition 2: By itself, competitive pressure is not enough to generate silence, because if ﬁrms were
simply interested in deterring competitors, then they would try to convince outsiders that earnings are low, and the usual unraveling argument
would apply (though starting from ﬁrms with low rather high earnings).
19
Speciﬁcally, Bolton and Kacperczyk (2020) ﬁnd that the disclosure of carbon emissions leads to divestment by some investors, and
Ilhan et al. (2020) directly survey institutional investors about their preferences.
20
Bolton and Kacperczyk (2020) document that over 1700 publicly
traded companies around the world (more than 15% of all listed companies) are disclosing their carbon emissions as of 2020. More broadly,
Amel-Zadeh and Serafeim (2018) write that “In the past twenty-ﬁve years,
the world has seen an exponential growth in the number of companies
measuring and reporting ... ESG data. While fewer than 20 companies disclosed ESG data in the early 1990s, the number of companies issuing sustainability or integrated reports had increased to nearly 90 0 0 by 2016.”

E[y|x] = λi x + (1 − λi )(1 − x ).

(12)

21
In expression (12), an audience does not update its beliefs about
whether x and y are positively or negatively correlated based on the observation of x. One interpretation is simply that different audiences have
heterogenous prior beliefs about these possibilities. Alternatively, if y is
symmetrically distributed over [0, 1], then the observation of x does not
generate any updating. In this case, (12) is consistent with audiences
starting from a common prior, but different audiences subsequently observing different pieces of information that lead to different posteriors on
whether x and y are positively or negatively correlated.

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From (12), one can see that if an audience i believes
that the signal is suﬃciently likely to be positively (negatively) correlated with the underlying attribute, that is,
λi > (< )1/2, the conditional expectation is increasing (decreasing) in x. This setting is thus covered by our analysis,
with pi (x ) = E[y|x].
Importantly, in this setting differences between audiences arise even though all audiences have the same preferences over the underlying attribute (e.g., they all prefer
higher cash ﬂows to lower cash ﬂows), but differ in other
information, which leads them to form different beliefs after disclosure.22
As a potential application and empirical prediction: in
practice, investor beliefs that items such as CEO pay, carbon emissions, and ESG performance are correlated with
future cash ﬂows are likely to stem from concerns about
ﬁrm governance. As such, we predict that ﬁrms are more
likely to stay silent about such items when there is substantial uncertainty about governance quality.

A leading application is to U.S. Regulation Fair Disclosure (Reg FD), which mandates that any disclosure by a
public ﬁrm must be fully public, and eliminates a ﬁrm’s
ability to target its disclosures.23 In particular, we interpret
the impact of Reg FD to be that once a ﬁrm discloses to
all investors, it is also de facto disclosing to antagonists of
the various types discussed above. Koch et al. (2013) survey the signiﬁcant literature that studies the effects of Reg
FD. As these authors note, “Many analysts expressed concerns that FD would inhibit disclosures because companies
would withhold information that had been previously selectively disclosed” (p. 620), often referred to as a “chilling
effect.” Koch et al. summarize the evidence as “generally
support[ing] a chilling effect for small or high-technology
ﬁrms” (p. 642).
Similarly, technological change that reduces frictions in
sharing information may result in less ﬁrm disclosure, because it undercuts a ﬁrm’s ability to engage in targeted
disclosure. Indeed, anecdotal evidence suggests that ﬁrms
and CEOs are increasingly reluctant to make public remarks and are “acting like a politician” due to the increasing use of digital communication and recordings, which
implies that any gaffes may go viral and trigger backlash
from unfavorable audiences.

7.4. Targeted disclosure and regulation fair disclosure
As we noted, the main empirical prediction of our analysis is that silence is related to ﬁrm uncertainty about
what it would be most beneﬁcial to communicate to its
audience. An immediate implication is that if a ﬁrm can
cheaply target disclose to just a subset of audiences for
which this uncertainty does not arise, then it will do so.
As a leading example: in cases in which ﬁrms can talk privately to sophisticated institutional investors, without fear
of information leaking, then they are likely to do so; and
to be much more transparent in these conversations than
in announcements to the broader public.
More formally, suppose that there is a subset of economic agents such that ordinal equivalence of preferences
(Proposition 2) holds for all possible audiences drawn from
this subset; and that it is common knowledge both that
the ﬁrm is able to disclose solely to this subset, at zero
cost, and that it can prevent all leakage of information beyond this subset. Under these conditions, the standard unraveling conclusion holds (again, Proposition 2), and any
equilibrium entails full disclosure to this subset of agents.
A closely related implication is that laws and technological improvements that make targeted disclosure harder
will—somewhat paradoxically—decrease rather than increase ﬁrm disclosures. Speciﬁcally, as just noted, when
targeted disclosure is easy and feasible, equilibria feature
full disclosure to groups for which the ﬁrm is certain about
preference orderings. If instead targeted disclosure is impossible, then under the conditions that our analysis characterizes, there are equilibria in which some ﬁrms stay
silent and do not disclose to anyone.

7.5. Which ﬁrms remain silent?
In addition to predicting that ﬁrms are more likely
to remain silent when uncertainty about audience preferences is greater, and when targeted disclosure is infeasible, our analysis makes a speciﬁc prediction on which
ﬁrms remain silent—namely those with “extreme” information (Corollary 1). In many settings, this prediction is
challenging to assess, since an econometrician does not observe the information possessed by ﬁrms that stay silent.
But it could be potentially tested in settings in which a
new mandatory disclosure requirement is introduced, and
in which the information being disclosed is persistent over
time. In such cases, the econometrician is effectively able
to observe the information of ﬁrms who stayed silent in
the voluntary disclosure regime.
8. Conclusion
There are many settings in which voluntary disclosure
is possible, but in which disclosure occurs with probabilities below 1, despite classic unraveling arguments. In this
paper we explore a possible explanation, which is new to
the literature, namely that potential disclosers do not know
their audiences’ preference orderings, and because of risk
aversion they dislike the risk this imposes. We show how
these two features together naturally deliver equilibrium
silence.
In contrast to leading explanations of silence, our explanation does not require disclosure to be either costly,

22
Note that the heterogeneity in audience information is independent
of the information the ﬁrm is disclosing, in contrast to Harbaugh and
To (2020) and Quigley and Walther (2020). Related, the forces behind silence in our paper are very different from in these papers, as evidenced
by the fact that ﬁrm risk-aversion plays a critical role in our results
(see Proposition 3), while coarse disclosure and disclosure costs respectively play a critical role in Harbaugh and To (2020) and Quigley and
Walther (2020).

23
Related but different from us, Guembel and Rossetto (2009) also argue that Reg FD may lead to less disclosure. In their model, unsophisticated audiences may misunderstand complex messages, and thus the ﬁrm
prefer to disclose to sophisticated audiences only. Under Reg FD, therefore, the ﬁrm may prefer not to say anything rather than risk being misunderstood.

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or impossible for some (unobservable) subset of would-be
disclosers. As such, we can explain silence even in settings
where disclosure is costless, and there is no uncertainty
about whether disclosure is possible.
Our explanation captures the intuitive notion that a
ﬁrm may prefer to stay silent because anything that it
says will make some audiences very unhappy, while staying silent avoids this extreme outcome. That is, silence is
safest. Speciﬁcally, silence reduces the risk borne by potential disclosers with extreme information. Consequently,
disclosure decreases when potential disclosers grow more
risk-averse, in a sense we make precise. On the other hand,
silence reduces the information available to the audience
for disclosures, thereby increasing the risk borne by the
audience. Because of this, potential disclosers beneﬁt more
from disclosing when audiences grow more risk-averse,
leading to increased equilibrium disclosure.

The sense in which convexity of pi generates a direct beneﬁt to silence is then that, since pi is strictly convex, for
any audience,

E [ pi (x )|μ0 ] − pi (E [x|μ0 ] ) > 0.
Thus, the ﬁrst difference in (A.1) is the direct beneﬁt to
silence induced by the convexity of pi , which is bounded
away from 0. The second term in (A.1) approaches 0 as
the slope of J (x ) approaches 0. So provided probabilities
{Pr(i )} are chosen so that J (x ) has a slope suﬃciently close
to 0, there is indeed an equilibrium in which no one discloses. As discussed, this equilibrium outcome is driven by
the fact that silence generates a direct beneﬁt.
A2. Micro-foundation for audience risk-aversion
We give a micro-foundation for the ﬁrm’s payoff pi
from an audience i. Consider the case in which the audience is buying something from the ﬁrm; for example,
a product, service, or ﬁnancial security. Let pi (x ) be the
amount that an audience would pay the ﬁrm if it knew
the ﬁrm’s type is x. Then for any audience beliefs μ about
the ﬁrm type, let pi (μ ) be determined by

Appendix A.
A1. Direct beneﬁts to silence
A subset of our results are predicated on the weak concavity of the payoff functions pi . As discussed in Section 4,
this condition has a natural economic interpretation. Moreover, concavity is also satisﬁed in the imperfect signal disclosure application in Section 7.3 (see (12)).
Here, we brieﬂy explore the opposite case in which the
payoff functions are strictly convex. As noted in the main
text, convexity of pi introduces a direct gain to silence.
Here we illustrate this point in more detail. Although this
is not uninteresting, this force is separate from the effects
due to ﬁrm uncertainty about the audience’s type, and ﬁrm
risk-aversion, both of which are necessary for silence, and
so are central effects we wish to study.
We focus on the speciﬁc case in which all audiences are
risk-neutral, and for all audiences i, there is a constant αi
such that pi (x ) = v−1 (αi x ). Since v is strictly concave, this
implies that pi is strictly convex. In this analytically very
tractable case, we show how the convexity of pi generates
a direct gain to silence, and in turn leads to an equilibrium
with full silence.
In this case, the ﬁrm’s expected value after disclosure,
J (x ), is linear. Assuming that αi does not have the same
sign for all audiences (see Proposition 2), we can choose
probabilities {Pr(i )} such that J (x ) has a slope arbitrarily
close to 0. And whenever the slope is suﬃciently close to
0, there is an equilibrium in which no one discloses, as we
next show.
If all ﬁrms are silent, the ﬁrm’s expected value after silence is

E [u( pi (x ) − pi )|μ] = ui (0 ),

A3. Generalized disclosure
Thus far, we have considered the case in which the ﬁrm
either discloses that its type is in the singleton set {x}, or
else discloses nothing. Here we consider instead the case
in which the ﬁrm can disclose any member A of some family of sets X , provided that x ∈ A. We assume that, at a
minimum, X contains all singletons, all closed subintervals
of the interval X, and all binary unions of closed subintervals of X. To avoid economically uninteresting mathematical complications, we assume that all members of X are
closed. Note that silence simply corresponds to disclosing
X.
This enlarged set of disclosure possibilities is most
likely to be relevant if disclosure takes the form of a trustworthy auditor reporting a ﬁrm’s type x to audiences; or
alternatively, if severe ex-post penalties can be inﬂicted on
ﬁrms who are found to have lied (see Glode et al., 2018).
If instead disclosure takes the form of simply displaying
some attribute to audiences, then our benchmark analysis
so far covers the relevant case.24

E [v(E [ pi (x )|μ0 ] )],
because audiences are risk-neutral ((6) at equality). Hence
the expected gain from silence relative to disclosure for
ﬁrm xˆ is

 

E [v(E [ pi (x )|μ0 ] )] − J xˆ

= E [v(E [ pi (x )|μ0 ] )] − E [v( pi (E [x|μ0 ] ) )]

 

+ J (E [x|μ0 ] ) − J xˆ .

(A.2)

where ui is continuous, strictly increasing and weakly
concave, reﬂecting (weak) audience risk aversion. That is,
(A.2) maps the primitive of an audience’s willingness-topay given known type x to the audience’s willingness-topay given beliefs μ. Inequality (6) in the main text (weak
audience risk aversion) follows directly from (A.2).
Under the above micro-foundation for pi (μ ), it further
follows that an increase in audience i’s risk-aversion in the
sense of Pratt (i.e., a concave transformation of ui ) corresponds to a decrease in pi (μ ), and hence an increase
in E [ pi (x )|μ] − pi (μ ), as stated in the main text prior to
Proposition 10.

24
Speciﬁcally, Glode et al. (2018) analyze a setting in which the sender
can disclose any subset of the type space that includes its own type. Their

(A.1)
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Note that this expansion of the ﬁrm’s disclosure
possibilities does not affect standard unraveling results.
Indeed, it is straightforward to adapt the proofs of
Propositions 2 and 3 to show that, under the conditions
stated in these results, in any equilibrium a ﬁrm discloses
{x} with probability one.
Our main result in this section is that, given the expanded set of disclosure possibilities, an equilibrium with
less than full disclosure—“silence” in the sense that the
ﬁrm does not fully disclose its type—exists under a very
wide range of circumstances. This is true if the key conditions we identify are satisﬁed, namely, ﬁrm risk-aversion,
differences in audience preferences, and audiences who are
not too risk-averse. In particular, we are able to establish
equilibrium existence with less than full disclosure without
imposing the suﬃcient condition that J (0 ) is suﬃciently
close to J (1 ), which we used to establish Proposition 6.

equilibrium beliefs ensure that any deviation is at least
weakly worse than the deviation of disclosing {x}—which
has already been established to be an unproﬁtable deviation, by the ﬁrst step of the proof.

Proposition 11. If (A) there exist ξ , ξ¯ ∈ (0, 1 ) and a pair of
   
some audiences i, j such that ξ = ξ¯ , J ξ = J ξ¯ , and pi (x ) =

choice is possible, note that if pk xk−1 > E pk (x )|μS
then
one can simply


 set xk = xk−1 ; while if instead
E pk (x )|μS ≥ pk xk−1 , let xk ∈ S be such that pk (xk ) >

A4. Proofs of results stated in main text
Proof of Proposition 2: Let S be a non-null set. Write
N = {1, 2, . . . , |N|}. For use below, note that ordinal equivalence of the functions pi (x ) and Assumption 1 imply that,

for each i, there exists x ∈ S such that pi (x ) > E pi (x )|μS .
We recursively deﬁne x1 , . . . , x|N| ∈ S as follows. First,







p j (x ) for x = ξ , ξ¯ , and (B) all audiences are suﬃciently close
to risk-neutral, then there is an equilibrium with less than full
disclosure, i.e., there is a positive probability of a ﬁrm disclosing a signal other than {x}.



 

















E pk (x )|μS ≥ pk xk−1 . Since pk (xk ) ≥ pk xk−1 , by ordi-



nal equivalence pi (xk ) ≥ pi xk−1







for any audience i, and

hence pi (xk ) > E pi (x )|μS for all audiences i = 1, 2, . . . , k,
establishing the recursive
 step.
 
 

So in particular, v pi x|N| > v E pi (x )|μS
for all

It is worth stressing that condition (A) is satisﬁed
whenever audiences have different preferences, and these
different preferences generate non-monotonicity of the expected utility from disclosing {x}, as given by the function
J.
The proof of Proposition 11 is very close to the previous
analysis, and we give it here. We establish
 the
 existence
of an equilibrium characterized by x, x̄ ∈ ξ , ξ¯ , in which
 
ﬁrms with x ∈ (x, x̄ ) and x ∈ X \ ξ , ξ¯ disclose their exact
type {x}, while the remaining ﬁrms with x ∈ ξ , x ∪ x̄, ξ¯
   
disclose simply ξ , x ∪ x̄, ξ¯ .



deﬁne x1 ∈ S such that p1 (x1 ) > E p1 (x )|μS . Next, suppose that x1 , . . . , xk−1
with
 are
 deﬁned,

 the properties
that xk−1 ∈ S, and pi xk−1 > E pi (x )|μS for all audiences
i = 1, 2,. . . , k − 1. Then, deﬁne
xk ∈ S such that pk (xk ) ≥

pk xk−1 and pk (xk ) > E pk (x )|μS . To see that such a



 
By (6), E pi (x )|μS ≥ pi μS . Hence
  S 
v p i x |N | > v p i μ
for all audiences i ∈ N, implying
   
that there exists x|N| ∈ S such that J x|N| > J μS , estabaudiences i ∈ N.

 



lishing Condition 1 and completing the proof.
Proof of Proposition 3: We establish that
Condition 1 holds. Suppose to the contrary
  that there
exists a non-null set S such that J (x˜) ≤ J μS for all x˜ ∈ S.







Expanding J μS , and using (6), for all x˜ ∈ S,

  

J (x˜) ≤ E v pi μS

The proof of Proposition 11 builds on the proof of
Proposition 6. First,
 restricts ﬁrms to disclose ei  if one
ther {x} or ξ , x ∪ x̄, ξ¯ , the proof is the same as that of



  

≤ E v E pi (x )|μS

Since v is weakly convex,

  

E v E pi (x )|μS





Proposition 6.25
It then remains to ensure that ﬁrms do not deviate to other disclosures. The equilibrium is supported
by the following off-equilibrium
   beliefs: If the ﬁrm discloses A ∈ X , and A = ξ , x ∪ x̄, ξ¯ , off-equilibrium beliefs
place full mass on the ﬁrm’s type being in arg minx˜∈A J (x˜).
These off-equilibrium
   beliefs
 immediately imply that ﬁrms
with x ∈ X \ ξ , x ∪ x̄, ξ¯ do not have a proﬁtable devia   
tion. For ﬁrms with x ∈ ξ , x ∪ x̄, ξ¯ , note that these off-

 

≤ E E v( pi (x ) )|μS







.





= E E [v( pi (x ) )]|μS = E J (x )|μS .
It follows that, for any x˜ ∈ S,





J (x˜) ≤ E J (x )|μS .
If v is strictly convex, the above inequality is strict, giving a
contradiction. If instead v is linear, then the above
 inequality holds with equality, that is, J (x˜) = E J (x )|μS for almost
all x˜ ∈ S, which contradicts Assumption 1, completing the
proof.
Proof of Proposition 4: Let S be a non-null set, and
write S̄ for the closure of S. By Assumption 1, there must
exist an audience i and an x ∈ S such that infx˜∈S̄ pi (x˜) <
pi (x ). For all audiences j = i, infx˜∈S̄ p j (x˜) ≤ p j (x ). Hence

analysis also differs from ours in two other important respects. First, the
receiver has all the bargaining power, which implies that any sender obtains zero surplus if it fully discloses its type. Second, their paper is primarily concerned with the case in which the sender can commit to a disclosure rule before seeing its type. As an extension, they also consider
the non-commitment case, and show that partial disclosure survives as
an equilibrium, since given the bargaining power assumption the sender
prefers to preserve some uncertainty about its type to obtain at least
some informational rent.
25
Indeed, the fact that ξ , ξ¯ ∈ (0, 1 ) means that the proof avoids the
complications of what happens to utility and density functions as x →
0, 1, which allows us to dispense with the regularity conditions contained
in Assumptions 2 and 3.


 S
J μ =E v

in f

( )

x˜∈supp μS

pi (x˜)

< E [v(x )] = J (x ),

establishing Condition 1 and completing the proof.
Proof of Proposition 5: By Assumption 1, J (x ) is either
strictly increasing or strictly decreasing. We give the proof
for the former case; the proof of the latter case is parallel.
190

P. Bond and Y. Zeng

Journal of Financial Economics 145 (2022) 178–193

 
Let S be a non-null set of ﬁrms S. By property (AB), J μS ≤
 

 
J E x|μS . Hence J μS < J (x ) for any x ∈ S such that x >
 S
E x|μ . So Condition 1 holds, completing the proof.


Hence, and using J (0 ) = J (1 ),

  

lim E E v( pi (x ) )|μX \[x,η (x)]
x→ 0

Proof of Lemma 1: Note that

It follows by (A.4) that



 


qv( pi (x ) ) + (1 − q )v p j (x ) − qv( pi (x˜) ) + (1 − q )v p j (x˜)

  

J (x ) − E v E pi (x )|μX \[x,η (x)]

is strictly positive at q = 0 and strictly negative at q =
1. Hence there exists qˆ ∈ (0, 1 ) at which this expression
is 0. So if audience probabilities are given by Pr (i ) = qˆ,
Pr ( j ) = 1 − qˆ, with all other audiences having zero probability, then J (x ) = J (x˜). Moreover, J (x ) is strictly concave
by the concavity of pi (x ) and ﬁrm risk-aversion. Hence J
is non-monotone at this probability distribution, and by
continuity, is likewise non-monotone in the neighborhood
around this probability distribution.
Proof of Proposition 6: Under the stated conditions,
there exists some distribution of audiences {Pr(i )}i∈N such
that J (0 ) = J (1 ). We establish the existence of a silence
equilibrium for this distribution, and for the case in which
all audiences are risk-neutral. The general result then follows by continuity.
Because audiences
 are risk-neutral,

 silence payoffs are
simply given by pi μS = E pi (x )|μS .
Note that the strict concavity of v and weak concavity
of pi (x ) implies that J (x ) is strictly concave. Deﬁne xmax =
arg maxx˜ J (x˜).
If J (xmax ) ≤ E [v(E [ pi (x )|μ0 ] )], then there is an equilibrium in which no ﬁrm discloses, and the proof is complete.
So for the remainder of the proof, we consider the case in
which

J (xmax ) > E [v(E [ pi (x )|μ0 ] )].



On the other hand, consider x˜ = h(1 ) < xmax , and so



So by continuity, there exists x ∈ (x˜, xmax ] such that





−1
E x|μ[0,x]∪[h (x),1] = x.







 

.

Strict concavity of v and the condition that there are audiences i, j ∈ N such that pi (0 ) < pi (1 ) and p j (0 ) > p j (1 )
then implies that



 



−E E v( pi (x ) )|μX \[x,η (x)]

> 0.







= J (x ) = J h−1 (x ) .

Hence there is an equilibrium in which ﬁrms S stay silent,
completing the proof.
Proof of Corollary 1: If silence is partial, the result is
immediate from (AB) and the strict concavity of J (x ).
In the case of full silence, Proposition 1 implies that
type E [x|μ0 ] is indifferent between disclosure and silence,
i.e., J (μ0 ) = J (E [x|μ0 ] ). By the strict concavity of J (x ), it
then follows that J (x ) < J (μ0 ) for x = E [x|μ0 ]. Setting x =
x̄ = E [x|μ0 ] completes the proof.
Proof of Corollary
2: If silence is full, then from


Corollary 1, E x|μS = x = x̄. Inequality (11) then follows
immediately from (7).
The remainder of the proof deals with partial silence.
From Corollary 1, S = [0, x ) ∪ (x̄, 1], with x < x̄. There are
two cases. If E [ pi (x )] is (weakly) monotone over [x, x̄] then,
by Corollary 1,

away from both 0 and −∞ as x → 0. Assumption 3 and
l’Hôpital’s rule then imply that the following limit exists,
and is bounded away from 0:

  



Deﬁne S = [0, x] ∪ h−1 (x ), 1 . Since property (AB) holds
with equality, it follows that

Assumption 2 then implies that ∂∂x η (x ) remains bounded

x→0





−1
E x|μ[0,x˜]∪[h (x˜),1] − x˜ = E x|μ[0,x˜] − x˜ < 0.

x=η ( x )

lim E v E pi (x )|μX \[x,η (x)]





J μS = J E x | μ S

(η (x ) ) ∂∂x η (x )



= J μX \[x,η (x)] .

−1
E x|μ[0,xmax ]∪[h (xmax ),1] − xmax = E[x|μ0 ] − xmax ≥ 0.

(A.3)

f (x )



Hence there is an equilibrium in which ﬁrms [x, η (x )] disclose, while ﬁrms X \[x, η (x )] remain silent and do not disclose, completing the proof.
Proof of Proposition 7: We prove the result for J (1 ) >
J (0 ); the case J (1 ) < J (0 ) is parallel. Note that, because
v(x ) is strictly concave and property (AB) holds, J (x ) is
strictly concave as well.
Deﬁne xmax = arg maxx J (x ). By supposition 0 < xmax ≤
E [x|μ0 ] < 1. Deﬁne h(x ) : [xmax , 1] → [0, xmax ] by J (h(x )) =
J (x ). Since J (0 ) < J (1 ) and J (x ) is strictly concave, the
function h is well-deﬁned. Moreover, h is continuous and
strictly decreasing.
On the one hand, h(xmax ) = xmax , and so

Since J (0 ) = J (1 ), and J (x ) is strictly concave,
∂
∂ x J (x ) remains bounded away from 0 as x → 0, 1.

( )
( )

(A.5)

<0

  

∂

x→0



J (x ) = J (η (x ) ) = E v E pi (x )|μX \[x,η (x)]

∂ x J ( x ) x=x
∂
η (x ) = ∂
.
∂x
∂ x J (x )

x
0 f x dx
= − lim
1
x→ 0 f
η (x ) f x dx



− J ( x ) = 0.

for all x suﬃciently close to 0.
Combined with (A.3), continuity then implies that there
exists some x ∈ (0, xmax ) such that

For any x ∈ (0, xmax ), deﬁne η (x ) ∈ (xmax , 1 ) by
J (η (x ) ) = J (x ). Note that η (x ) exists and is unique,
since J (0 ) = J (1 ) and J (x ) is strictly concave. Moreover, η
is continuous, with η (x ) → 1 as x → 0, and

lim



  

(A.4)

E p i E x | μS

Also note that

 

E E v( pi (x ) )|μX \[x,η (x)]




= E E [v( pi (x ) )]|μX \[x,η (x)] = E J (x )|μX \[x,η (x)] .



≤ max E [ pi (xm )],
xm =x,x̄

and (11) is immediate from (7).
If instead E [ pi (x )] is strictly non-monotone over [x, x̄],
note ﬁrst that Assumption 5 implies that E [ pi (x )] is strictly
191

P. Bond and Y. Zeng

Journal of Financial Economics 145 (2022) 178–193

   
E v p i μS
> E [v( pi (xm ) )], contradicting the equilib-

single-peaked over X, with the peak lying in the interval
[x, x̄]. Moreover, weak audience risk-aversion (6) implies

  
 



E pi μS ≤ E E pi (x )|μS = E E [ pi (x )]|μS ,

rium condition.
Completing
the
proof:
From
above,
  for
 at
least one xm ∈ {x, x̄}, we know
pi μS , p j μS ∈

(A.6)



and so there exists xˆ in the interior of S such that

  
  
E pi μS < E pi xˆ .



 

E p i μS

(A.7)







min pi (xm ), p j (xm ) , max pi (xm ), p j (xm )



≤ E [ pi (xm )],

  



along

with

the

and
equilibrium

  
Hence either xˆ < x and E pi μS < E [ pi (x )] or xˆ > x̄ and
  S 
E pi μ
< E [ pi (x̄ )], completing the proof.

condition E v pi μS
= E [v( pi (xm ) )]. So for any increasing and strictly concave function φ , Theorem 3 of
Hammond (1974) implies that

Proof of Proposition 8: Consider any partial silence
equilibrium, with a silence set [0, x ) ∪ (x̄, 1].
 
Claim
A:
For
each
audience
i,
p i μS ≤
max{ pi (x ), pi (x̄ )}.
Proof of claim: If pi is monotone over [x, x̄], then

E φ v p i μS



   



where the ﬁrst inequality follows from (7), and the second
inequality follows from Corollary 2 and the monotonicity
of pi over [x, x̄].
If instead pi is non-monotone over [x, x̄], then by concavity, it is strictly increasing over [0, x ) and strictly decreasing over (x̄, 1]. Hence pi (x ) < max{ pi (x ), pi (x̄ )} for all
x ∈ [0, x ) ∪ (x̄, 1]. So by (6),



 

pi μS ≤ E[ pi (x )|μS ] < max{ pi (x ), pi (x̄ )}.



Claim



B:

For



some



x ∈ {x, x̄},



E p i μS

   
pi μS , p j μS ∈

  

of

Hammond

(1974)

implies

< E [ pi (xm )].

(A.9)



> E [v˜ ( pi (xm ) )],

(A.10)

since otherwise (A.9) and the deﬁnition that v(x ) =
α v˜ (x ) + x at all x ∈ X implies that

  

E v p i μS

 
 
 
 
plies pi μS ≥ pi (x ) and p j μS ≥ p j (x̄ ), and so pi μS ∈
 S 

[ pi (x ), pi (x̄ )] and p j μ ∈ p j (x̄ ), p j (x ) .


If the sets [ pi (x ), pi (x̄ )] and p j (x̄ ), p j (x ) are ranked
by the strong set order (Veinott, 1989
 ), then the
 result
is straightforward: If [ pi (x ), pi (x̄ )]  p j (x̄ ), p j (x ) under
    

this order, then pi μS , p j μS ∈ pi (x ), p j (x ) ; while if in

 S
 
stead p j (x̄ ), p j (x )  [ pi (x ), pi (x̄ )], then pi μ , p j μS ∈
i


p j (x̄ ), pi (x̄ ) .
Next, consider  the cases where the two sets
[ pi (x ), pi (x̄ )] and p j (x̄ ), p j (x ) are not ranked by the
strong set order. There
In the ﬁrst
 are two sub-cases.

 sub
case, [ pi (x ), pi (x̄ )] ⊂ p j (x̄ ), p j (x ) , and so either pi μS ∈


  

p j (x̄ ), pi (x̄ ) or p j μS ∈ pi (x ), p j (x ) (or both), while
 S 

 S 

both pi μ ∈ p j (x̄ ), pi (x̄ ) and p j μ ∈ pi (x ), p j (x ) . In


the second sub-case, p j (x̄ ), p j (x ) ⊂ [ pi (x ), pi (x̄ )], and so
  

  

either pi μS ∈ pi (x ), p j (x ) or pi μS ∈ p j (x̄ ), pi (x̄ )
 S 

(or both), while both p j μ ∈ pi (x ), p j (x )
and
  

p j μS ∈ p j (x̄ ), pi (x̄ ) .
   
Claim
C:
If
x ∈ {x, x̄}
and
pi μS , p j μS ∈


 m 

min pi (xm ), p j (xm ) , max pi (xm ), p j (xm )
then
  
E pi μS ≤ E [ pi (xm )].
  
Proof of Claim: If instead E pi μS > E [ pi (xm )]
3



E v˜ pi μS



< E [v( pi (xm ) )],

contradicting the equilibrium condition when the ﬁrm’s
preferences are given by v. Given (A.10), the result follows
as in the last step of the proof of Proposition 8.
Proof of Proposition 10: Consider the equilibrium with
the least amount of disclosure. For
discloser
 any
 marginal

xm , the equilibrium condition E v pi μS
= E [v( pi (xm ) )]
holds. Following the increase in audience j’s risk-aversion,

if the silence set stays unchanged, then p j μS strictly decreases (whereas pi (xm ) stays unchanged for any i ∈ N).
Hence,
   forboth marginal disclosers xm ∈ {x, x̄}, we have
E v p i μS
< E [v( pi (xm ) )]. The result follows as in the
last step of the proof of Proposition 8.

and p j μS ≤ p j (x ). The equilibrium condition then im-

Theorem

(A.8)

It follows that

min pi (x ), p j (x ) , max pi (x ), p j (x ) .
Proof of Claim: Now consider any silence equilibrium
in which the silence set is [0, x ) ∪ (x̄, 1]. The equilibrium condition implies that pi (x̄ ) − pi (x ) and p j (x̄ ) −
p j (x ) have opposite signs. Without loss, assume pi (x ) ≤
 
pi (x̄ ) and p j (x̄ ) ≤ p j (x ). So Claim A implies pi μS ≤ pi (x̄ )

then

≥ E [φ (v( pi (xm ) ) )].

Moreover, under Condition 2, Claim A holds strictly (by
Corollary 2), and hence Claims B and C hold strictly also,
and so (A.8) likewise holds strictly.
Given inequality (A.8), a straightforward modiﬁcation
of the argument in the proof of equilibrium existence in
Proposition 6 implies that, for preferences v˜ , there exists
an equilibrium in which ﬁrms [0, x ) ∪ (x˜, 1] do not disclose,
where if xm = x, then x > x, and if˜ xm = x̄, then x˜ < x̄. This
completes the proof. ˜
Proof of Proposition 9: Given Corollary 1, when the
ﬁrm’s preferences are given by v, consider an equilibrium in which ﬁrms in [0, x ) ∪ (x̄, 1] do not disclose. By
Corollary 2, for some xm ∈ {x, x̄},

pi μS ≤ pi (E[x|μS ] ) ≤ max{ pi (x ), pi (x̄ )} ,





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==> JFE18 - Air pollution, affect, and forecasting bias: Evidence from Chinese financial analysts.txt <==
Journal of Financial Economics 139 (2021) 971–984

Contents lists available at ScienceDirect

Journal of Financial Economics
journal homepage: www.elsevier.com/locate/jfec

Air pollution, affect, and forecasting bias: Evidence from
Chinese ﬁnancial analystsR
Rui Dong a, Raymond Fisman b,∗, Yongxiang Wang c,d, Nianhang Xu e
a

Department of Finance, School of Business, Renmin University of China, Beijing 100872, PR China
Economics Department, Boston University, Room 304A, Boston, MA 02215, United States
c
Finance and Business Economics Department, Marshall School of Business, University of Southern California, HOH 716, Los Angeles, CA
90089, United States
d
Shanghai Advanced Institute of Finance, Shanghai Jiaotong University, Shanghai, China, 200030
e
Department of Finance, School of Business, Renmin University of China, Beijing 100872, PR China
b

a r t i c l e

i n f o

Article history:
Received 9 May 2019
Revised 12 June 2019
Accepted 13 June 2019
Available online 17 December 2019
JEL classiﬁcation:
D91
G41
Q5
Keywords:
Pollution
Forecasting bias
Investment analysts
Adaptation

a b s t r a c t
We document a negative relation between air pollution during corporate site visits by investment analysts and subsequent earnings forecasts. After accounting for analyst, weather,
and ﬁrm characteristics, an extreme worsening of air quality from “good/excellent” to
“severely polluted” is associated with a more than 1 percentage point lower proﬁt forecast, relative to realized proﬁts. We explore heterogeneity in the pollution-forecast relation
to understand better the underlying mechanism. Pollution only affects forecasts that are
announced in the weeks immediately following a visit, indicating that mood likely plays a
role, and the effect of pollution is less pronounced when analysts from different brokerages
visit on the same date, suggesting a debiasing effect of multiple perspectives. Finally, there
is suggestive evidence of adaptability to environmental circumstances – forecasts from analysts based in high pollution cities are relatively unaffected by site visit pollution.

1. Introduction
We study the relation between air pollution during corporate site visits by investment analysts in China and earnings forecasts issued in the days that follow. This setting
R
We thank G.William Schwert (the Editor), David Hirshleifer (the referee), Dongmin Kong, Honghai Yu, Yexiao Xu, and seminar participants
at the 2018 China Financial Research Conference, the 2018 China International Conference in Finance, the 2018 China Young Finance Scholars Society conference, Liaoning University, Renmin University of China for helpful comments and discussion. Xu acknowledges the ﬁnancial support from
the National Natural Science Foundation of China (Grant Nos. 71622010,
71790601 and 71532012). we retain responsibility for any remaining
errors.
∗
Corresponding author.
E-mail addresses: dongrui@ruc.edu.cn (R. Dong), rﬁsman@bu.edu (R.
Fisman), yongxiaw@marshall.usc.edu (Y. Wang), nhxu@ruc.edu.cn (N. Xu).

https://doi.org/10.1016/j.jﬁneco.2019.12.004
0304-405X/© 2019 Elsevier B.V. All rights reserved.

© 2019 Elsevier B.V. All rights reserved.

allows us to examine the effect of plausibly extraneous
ambient circumstances on judgment for individuals who
should have both the expertise and incentive to screen
out such inﬂuences. Investment analysts are well-educated,
well-trained, and well-motivated to make accurate assessments of corporate earnings (Beyer, Cohen, Lys, Walther,
2010). Analysts themselves recognize site visits as a crucial
input into proﬁt projections (Brown, Call, Clement, Sharp,
2015), so it is a task for which they should be particularly
attentive to objective determinants of proﬁtability.1
At the same time, there exists a decades-old literature
on the impact of environmental conditions on mood and

1
For the impact of corporate site visits in the China setting, see Cheng
et al. (2016) and Han et al. (2018) for the effect on forecast accuracy, and
Cheng et al. (2018) for the effect on stock prices.

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R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

the resultant effect on decision-making (for seminal contributions see Schwarz and Clore, 1983 and Cunningham,
1979). Finance scholars have extended this line of research
to study the effect of weather on stock market prices and
trading behavior, as mediated by weather’s effect on mood,
with the weight of the evidence indicating that better
weather leads to more optimism and higher prices (see
Saunders, 1993 and Hirshleifer and Shumway, 2003 for the
original “sunshine effect” on stock prices, Kamstra et al.,
2003 for the link between daylight and stock prices, and
Goetzmann et al., 2015 for the effect of cloud cover on institutional investors’ pessimism).
A more recent – and more closely related – body of
work links pollution both to mood, and also trading behavior and stock prices, with mood posited as the mediating channel (see Vert et al., 2017 on the association
between pollution and mood, Levy and Yagil, 2011 and
Lepori, 2016 for the association between pollution and
stock prices, and Huang et al., 2019, Li et al., 2019 the association between pollution and investor biases), further
reinforcing the possibility that pollution during site visits
may impact analyst forecasts.
China is a natural setting in which to study this link.
First, since 2009, the Shenzhen Stock Exchange has required that all site visits be disclosed, so we may observe
the timing of analysts’ visits (in the U.S., for example, such
disclosures are not required). These data allow us to identify 3,824 earnings forecasts made by 726 investment analysts in the weeks following corporate site visits during
2009–2015. Second, pollution is very severe on average
in China and highly variable both across geographies and
across time, which provides variation in ambient circumstances that is of such magnitude as to plausibly have a
causal impact on analyst affect. More speciﬁcally, the visits
in our data set take place in 105 cities, spread across the
country,2 which, when combined with the random variation in pollution caused by differing meteorological conditions across analysts’ visit dates, provides plausibly exogenous variation in pollution during site visits that we
may exploit to explore the relation with subsequent forecasts. (The short-term randomness of local conditions also
presents a ready placebo test, which we return to below.)
A natural conjecture, given the weather-mood relation
documented in earlier work, is that higher air pollution
will be associated with lower earnings forecasts. Consistent with higher pollution leading to increased pessimism,
we ﬁnd that a city’s air quality index (AQI) on the date
of a site visit is negatively correlated with the visiting
analyst’s subsequent earnings forecast, relative to realized
earnings. Intriguingly, since analysts’ forecasts are positively biased overall, pollution-induced pessimism brings
forecasts closer to unbiasedness.3

2
More precisely, visits are spread across the eastern half of China. Visits in the western provinces of Tibet and Xinjiang are rare, comprising
only 1% of our main sample.
3
This fact does not necessarily imply that pollution leads to better
forecasts. See Lim (2001), for a discussion of why analysts who utilize
management information on proﬁtability may optimally provide forecasts
that are positively biased.

We present several robustness checks and placebo tests
which bolster our conﬁdence in the AQI-pessimism relation: the pattern is robust to different functional forms and
treatment of outliers, and survives the inclusion of analyst
and city ﬁxed effects.4 Finally, we show that the correlation between pollution and pessimism is stronger for ﬁrms
that do not themselves produce high emissions. This ﬁnding helps to rule out the possibility that a ﬁrm’s own pollution causes a negative inference about its environmental
risks or productivity (indeed, our results may suggest the
opposite).
We further enrich our understanding of the channel
through which pollution impacts forecasting bias by examining factors that accentuate (or attenuate) the relation between AQI and earnings forecasts. First, we show that the
link between pollution and forecast bias dissipates with
the time elapsed between visit and forecast, as would be
expected if the link between pollution and forecast pessimism were driven by analyst mood during a visit. We
also ﬁnd that the negative pollution-forecast relation is
driven by longer-term forecasts, which involve more guesswork and speculation by the analyst.
We then explore how the pollution-pessimism relation
is affected by characteristics of visiting analysts. Most notably, the pessimism associated with pollution disappears
for cases in which analysts from different brokerage ﬁrms
visit the same site on the same date (there is no direct
effect of multiple analysts on forecast bias), possibly suggesting a debiasing effect of multiple perspectives. However, there is no signiﬁcant difference in the relation between pollution and forecast bias across individual analyst
attributes that reﬂect ability or experience.
Finally, we provide suggestive evidence that analysts acclimate to severe pollution, by exploiting variation in pollution in cities where analysts are based. We ﬁnd that the
difference between site visit pollution and home pollution
is predictive of bias, and in particular our main results are
driven exclusively by analysts visiting sites in regions with
higher pollution than their own. While these results are
only suggestive, they represent a new ﬁnding and possible
insight on environmental inﬂuences and mood – we know
of no prior work that looks at whether acclimation to environmental conditions limits their affective inﬂuence.
This result on analyst acclimation also provides indirect
evidence that the relation between pollution and forecasts
is driven by the effect on analysts, rather than the effect of
pollution on others (for example, corporate CEOs and other
senior managers who address questions from analysts) that
might indirectly impact analyst forecast. Further bolstering
this interpretation, we conduct a textual analysis of transcripts of CEOs and other top executives’ comments during site visit Q&As, and do not ﬁnd that pollution leads to
more negative responses by CEOs and other top executives.
Our ﬁndings contribute most directly to the large literature in accounting and ﬁnance on the behavioral bi-

4
We also present placebo tests using AQI ﬁgures 5 to 10 days before
and after the site visit. These non-visit pollution readings are unrelated
to forecast optimism once we control for visit-date AQI, and the correlation between visit-date AQI and forecast optimism is unaffected by the
inclusion of these “placebo” pollution controls.

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

ases of investment analysts and their role in ﬁnancial markets (see, for example, Hirshleifer et al., 2018; Hong and
Kubik, 2003; Hong and Kacperczyk, 2010). Most directly
related to our work, Dehaan et al. (2017) look at the relation between weather and response to earnings announcements. They show that bad weather negatively affects the
speed with which U.S. analysts respond to earnings announcements in adjusting their recommendations and (in
contrast to ancillary ﬁndings we report in our results) that
bad weather also leads to more pessimistic EPS forecasts
and target prices. We view our work as complementary to
theirs, given our focus on different shifts in environmental
conditions (weather versus pollution), different outcomes
(forecast bias versus delay), and a distinct input into analyst decision-making, which is enabled by the disclosure
rules governing Chinese analyses. Furthermore, our heterogeneity analyses provide a new window into the conditions that can exacerbate, or mitigate, the bias induced by
ambient circumstances. Our results suggest important roles
both for acclimation/adaptation and also group decisionmaking; these are ﬁndings that, to our knowledge, are new
to the literature.
Our work also ﬁts into the literature on how environmental conditions impact decision-making, discussed at
the outset, and more broadly the literature on the extent
to which decision-making in natural settings is aﬄicted
by the biases and errors in judgment documented by behavioral economists and social psychologists, particularly
among expert agents (see, for example, Harrison and List,
2008 on expertise and the winner’s curse, and Haigh and
List, 2005 on loss aversion among traders).
2. Background and data
Our data set is based on details gleaned from site
visit disclosures for publicly traded Chinese ﬁrms, combined with analysts’ reports issued in the 30 days following each visit. In the subsections that follow, we describe
in greater detail the data sources and variable construction.
In Appendix A, we describe the speciﬁcs of the ﬁnal data
set’s construction.
2.1. Analyst site visits and forecasts
Since 2009, the Shenzhen Stock Exchange (SZSE) has
mandated that all ﬁrms listed on the exchange must publicly disclose details about site visits, typically paid by
stock analysts, mutual/hedge fund managers, reporters and
individual investors, within two trading days of the visit,
including all visitors’ names, visit date, employers, and
where the site visit took place.5 (Firms listed on Shanghai
Stock Exchange are not subject to this regulation.)
We limit our sample to cases in which the visitors’
names are recorded, and the visitors are sell-side analysts
from Chinese brokerage ﬁrms (87% of all visits).

5

When the site visit does not take place at the ﬁrm’ s headquarters,
the record will generally list the exact location of the visit, which we use
to match to our pollution and weather measures. For records that do not
list a speciﬁc location, the site visit took place at the ﬁrm’ s headquarters.

973

These data are matched to analyst forecasts obtained
from the Chinese Stock Market and Accounting Research
(CSMAR) database, a commonly employed database available, for example, to North American researchers via Wharton Research Data Services. We look primarily at earnings
forecasts issued in the 15 calendar days following a visit,
to focus on assessments made as a result of information
gathered on site. However, we will show patterns for samples of earnings reports with cutoffs as short as 5 calendar
days and as long as 30 calendar days following the visit,
to explore whether the effect of pollution dissipates with
time.
Each earnings report may include multiple forecasts, for
different time horizons. We control for time horizon in the
analyses that follow, and maintain each forecast as a distinct (but non-independent) observation, as we will explore whether the relation between pollution and bias is
affected by forecast horizon.
A natural concern with conditioning on the delay between site visits and earnings forecasts is that pollution
may itself affect forecast timing. This possibility could in
turn bias our estimates of the relation between pollution
and forecast optimism. The direction of this bias is unclear – it depends on whether delayed forecasts tend to be
more optimistic (which would induce a bias toward zero)
or less optimistic (which would induce a negative bias).
In Appendix B we show that the timing of earnings forecasts is in fact uncorrelated with site visit pollution, largely
mitigating this concern.6 A related concern is that analysts
might time their visits to avoid high pollution days. In unreported analysis, however, we do not ﬁnd that day-level
pollution is correlated with site visit probability. Furthermore, even if pollution affected the choice of visit date, it
implies no obvious relation between pollution and forecast
bias.
Following Jackson (2005) and the vast literature in accounting on earnings forecasts, we deﬁne analysts’ forecast
optimism as follows:

F orecast _Optimismi jt = 100 ∗ (F EP Si jt − AEP Si jt )/Pj ,

(1)

where FEPSijt is analyst i’ s forecasted earnings per share
(EPS) for ﬁrm j for year t, AEPSijt is the realized EPS of
ﬁrm j for year t, and Pj is ﬁrm j’ s stock price on the day
prior to the earnings forecast. Following Huyghebaert and
Xu (2016), we keep the EPS forecasts of all years in a report
to explore whether pollution differentially affects analysts’
forecast biases across various forecast horizons.
2.2. Air quality and weather variables
For each city in China, we obtain the daily air quality index (AQI) from the oﬃcial website of the Ministry
of Environmental Protection of China (MEPC). These data
are derived from daily air quality reports provided by
province- and city-level environmental protection bureaus.
6
While this ﬁnding may appear in tension with the ﬁndings of Dehaan
et al. (2017), their emphasis is on processing time rather than affect. Furthermore, our measure of forecast delay is based on time elapsed following the site visit, during which time the analyst would have been working
in their home city.

974

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

The AQI is constructed based on the levels of six atmospheric pollutants: sulfur dioxide (SO2), nitrogen dioxide
(NO2), suspended particulates smaller than 10 μm in aerodynamic diameter (PM10), suspended particulates smaller
than 2.5 μm in aerodynamic diameter (PM2.5), carbon
monoxide (CO), and ozone (O3). Prior to 2014, the Chinese government monitored only SO2, NO2, and PM10,
which was used to construct the air pollution index (API)
that served as a summary measure of air quality in earlier years. While the API and AQI are not directly comparable, they are highly correlated (Zheng et al., 2014). For
notational simplicity we refer to both as AQI in what follows. For a small fraction of city-day observations, the AQI
readings are unavailable via the MEPC. We were able to ﬁll
in some of the missing data from the Qingyue Open Environment Data Center website, which obtains pollution data
directly from local governments.7
The MEPC distinguishes among six categories of AQI:
I-excellent (AQI ≤ 50), II-good (50<AQI ≤ 100), IIIlightly polluted (100<AQI ≤ 150), IV-moderately polluted
(150 < AQI ≤ 200), V-heavily polluted (200 < AQI ≤ 300)
and VI-severely polluted (AQI > 300).8
Since an earlier literature suggests that weather can
affect investors’ moods and trading behavior, we collect weather data to match to analysts’ site visits. Daily
weather data are obtained from the 194 international meteorological stations in China, provided by the China Integrated Meteorological Information Service System. Variables include hours of sun, temperature, humidity, precipitation and wind speed. We match each city to the closest
meteorological station based on straight line distance.
2.3. Firm and analyst characteristics
We control for basic ﬁrm attributes, including size
(log(Assets)), market to book ratio, intangible asset ratio,
stock price volatility, stock turnover, stock return, analyst attention, and industry (based on the China Securities Regulatory Commission (CSRC)’s 19 top-level industry
categories). We also collected data on time-varying analyst characteristics, including the number of ﬁrms followed,
and the number of forecasts made (we will include analyst ﬁxed effects in our main speciﬁcations, which absorb
the effects of any time-invariant analyst attribute). The analyst data were obtained from CSMAR and the ﬁrm controls from RESSET, a provider of Chinese ﬁnancial research
data.
Our main analysis sample is comprised of 3824 earnings forecasts issued following 1642 site visits (i.e., an average of 2.35 forecasts per visit). Extending the window to
30 calendar days, our longer sample includes 5108 earnings forecasts, highlighting that the frequency of forecasts
is considerably higher just following a site visit (the rate
of drop-off is relatively rapid, with 2756 of forecasts issued
within 8 days).
7
The Qingyue Open Environment Data Center (https://data.epmap.org)
is an organization which compiles environmental data from government
sources and provides them freely to the public in standard data formats.
8
The same six classiﬁcations were used both pre- and post-2014,
though based on only three pollutants in the earlier period.

We present summary statistics at the forecast-level in
Panel A of Table 1, for the sample of visits for which
the analyst provided a forecast within 15 calendar days.
The sample mean and standard deviation of forecast optimism are 2.05 and 3.49, respectively, consistent with the
prior literature which ﬁnds that sell-side analysts’ earnings forecasts are generally higher than the realized values
(e.g., Francis and Philbrick, 1993; Lim, 2001; Sedor, 2002).
There is also considerable variation in analysts’ excess optimism – the highest value is 63% and the lowest is -18 –
though we will minimize the inﬂuence of these extreme
errors by winsorizing the top and bottom 1% of observations (we will present the results without winsorizing to
show that this step does not affect our conclusions). Panel
B of Table 1 shows summary statistics for the ﬁrm-year
variables.
3. Results
Our main analyses are based on speciﬁcations of the
following form:

F orecast _Optimismi jt = β × AQIi jt /10 0 0 + γ × Xi jt + i jt ,
(2)
where Xijt is a vector of control variables including ﬁrm attributes, as well as industry, quarter, and analyst ﬁxed effects.  ijt is the error term (clustered at the ﬁrm level). We
divide AQI by 10 0 0 for ease of interpretation of the regression coeﬃcients.
We present these results in Table 2, with all variables
winsorized to limit the inﬂuence of outliers (results using
non-winsorized data are provided in Appendix C, and show
very similar patterns). For conciseness, we do not report
the coeﬃcients on control variables, though we provide the
full regression output in Appendix D. Column (1) shows
the bivariate relation between forecast optimism and air
pollution. The negative coeﬃcient on AQI indicates that
higher pollution during a site visit is associated with lower
forecasts relative to realized earnings. Its value of -3.56 indicates that a 1 standard deviation increase in (winsorized)
air pollution of 48 is associated with a reduction in earnings forecast of approximately 0.17 percentage points, or a
little less than 10% of the average over-optimism of forecasts for the sample overall. The inclusion of day-of-week
and year × quarter ﬁxed effects in column (2) reduces the
coeﬃcient on AQI by about 40%, though when we add industry, analyst and city ﬁxed effects (column (3)) and ﬁrm,
analyst and weather controls (column (4)), the coeﬃcient
becomes more negative, taking on values of −4.21 and
−3.77, respectively. Across all speciﬁcations, the coeﬃcient
on AQI is signiﬁcant at least at the 10% level.9
9
Two other natural outcomes to consider are target price and recommendations. Unfortunately, we have relatively few target prices (475) in
our data set that we can link to site visits, and in the case of recommendations there is very little variation – no analyst issues a sell recommendation, and 98% of the 1659 recommendations in our data set are either
“strong buy” or “buy.” When we do employ target price optimism or recommendation optimism as outcome variables, we obtain a point estimate
on AQI that is of the same sign as in our analyses in Table 2, but in neither case does any coeﬃcient approach statistical signiﬁcance, which we
view as unsurprising given the lack of statistical power.

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984
Table 1
Summary statistics.
F orecast _Optimism denotes the difference between annual EPS forecast
issued within calendar days [1,15] of the site visit and realized EPS, scaled
by price as of the trading day prior to the forecast, multiplied by 100.
AQI denotes the Air Quality Index of the site visit city on the visit date,
scaled by 10 0 0. log (Horizon) denotes the natural logarithm of the days
between the forecast date and the corresponding date of the actual earnings announcement. Hours_o f _Sun denotes hours of sun of the site visit
city on the visit date (0.1h). Temperature denotes the average temperature
of the site visit city on the visit date (0.1◦ C). Humidity denotes the average humidity of the site visit city on the visit date (1%). Precipitation denotes the total precipitation of the site visit city on the visit date (0.1mm).
W ind_Speed denotes the average wind speed of the site visit city on the
visit date (0.1m/s). log (Assets) denotes the natural logarithm of total assets at the beginning of the year when the site visit took place (visit year).
Market _to_Book denotes the ratio of market value of equity to book value
of equity at the beginning of the visit year. Intangible_Asset denotes the
ratio of intangible assets to total assets at the beginning of the visit year.
Volatility denotes daily volatility of stock returns during the year prior to
the visit year. Turnover denotes the daily turnover rate of the visit year.
Return denotes annual stock returns of the year prior to the visit year.
Analyst _At tent ion denotes the natural logarithm of the number of analysts
following the ﬁrm during the visit year. F ol l ow_Co_Num denotes the natural logarithm of the number of companies the analyst followed during
the visit year. F orecast _Num denotes the natural logarithm of the number
of reports issued by the analyst during the visit year. Panel A provides
summary statistics based on the main sample of forecast × analyst visit
observations. Panel B provides summary statistics collapsed to the ﬁrmyear level.

975

Table 2
The relation between air pollution and analyst forecast optimism.
Numbers in parentheses are standard errors clustered by ﬁrm. The
sample covers the period from 2009 to 2015. The dependent variable in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15]
of the site visit and realized EPS, scaled by price as of the trading day prior to the forecast, multiplied by 100. AQI denotes the Air
Quality Index of the visit city on the visit day, scaled by 10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes to Table 1 for
detailed deﬁnitions of the control variables. Appendix D shows the results
including point estimates for all control variables. Signiﬁcance: ∗ signiﬁcant at 10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)
Dependent variable
AQI

−3.558∗∗∗
(1.072)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Observations
R-squared

3824
0.004

(2)
(3)
F orecast _Optimism

(4)

−2.129∗
(1.104)

−4.206∗∗∗
(1.322)

−3.769∗∗∗
(1.420)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

3824
0.065

3824
0.443

3824
0.608

Panel A: Sample for main analysis
Variable name

Mean

StdDev

Observations

F orecast _Optimism
AQI
log (Horizon)
Hours_o f _Sun
Temperature
Humidity
Precipitation
W ind _Speed

2.051
0.089
5.920
49.978
172.825
68.855
37.127
22.201

3.486
0.052
0.828
41.051
91.507
17.038
109.890
10.037

3824
3824
3824
3824
3824
3824
3824
3824

Panel B: ﬁrm-year aggregates
Variable name

Mean

StdDev

Observations

log (Assets)
Market _to_Book
Intangible_Asset
Volatility
Turnover
Return
Analyst _At tent ion
F ol l ow_Co_Num
F orecast _Num

21.740
3.124
0.045
0.028
2.787
0.253
2.428
2.328
2.867

1.054
1.743
0.050
0.006
2.163
0.615
0.755
0.802
1.049

1046
1046
1046
1046
1046
1046
1046
1046
1046

While our focus is on the link between pollution and
forecast bias, we show the coeﬃcients on weather-related
covariates in Appendix D, and observe that the coeﬃcient on hours of sunshine is very small and does not
approach statistical signiﬁcance (nor do the coeﬃcients
on any other weather-related variables). The lack of a
weather-bias relation warrants some discussion because
of its contrast to the positive relation between sunshine
and stock market optimism observed by Hirshleifer and
Shumway (2003), and also the positive relation between
good weather and stock analyst forecasts as reported by
Dehaan et al. (2017). While it is outside of the scope of
our paper to fully explore the possible reasons for our dis-

tinct weather-optimism result, one possibility is that, given
the severity of (and high variance in) pollution in our setting, its effect dominates other possible ambient inﬂuences
of analysts’ moods.
In Table 3 we allow for greater ﬂexibility in the relation between pollution and forecast optimism, replacing
the linear form on the right-hand side of Eq. (2) with a
dummy variable for each of the Chinese government’s six
categories of air pollution (category I, least polluted, is the
omitted category). The results suggest that the linear speciﬁcation ﬁts the data well. In particular, in the full speciﬁcation in column (4) the coeﬃcients are monotonically
decreasing in pollution severity, with roughly comparable
decreases in the coeﬃcients for each pollution level.
We next turn to probing the robustness of our results
using a placebo test based on pollution in days surrounding the site visit. These results highlight the distinct relation between pollution on the site visit date and subsequent earnings forecasts. While there is, naturally, correlation across days in a given city in the extent of pollution,
there is also residual variation as a result of changes in
temperature, winds, and other factors. This short-run variation allows us to look at the effect of air pollution several days apart from the site visit date. In Table 4, we repeat our favored (saturated) speciﬁcation from column (4)
of Table 2, including air quality measures for the 5, 7, and
10 days prior to the analyst’s visit, as well as the 5, 7, and
10 days following the visit. The coeﬃcient on visit date air
quality is stable across all six speciﬁcations while, after accounting for visit date pollution, air pollution on surrounding dates has no predictive power.
While we have emphasized the effect of pollution on
analyst affect as the likely mechanism for our main result,

976

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

Table 3
The effect of different AQI categories.
Numbers in parentheses are standard errors clustered by ﬁrm. The
sample covers the period from 2009 to 2015. The dependent variable in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15]
of the site visit and realized EPS, scaled by price as of the trading
day prior to the forecast, multiplied by 100. AQI50 − 10 0, AQI10 0 −
150, AQI150 − 20 0, AQI20 0 − 30 0, and AQI30 0+ are indicator variables
that correspond to each of the government’s air pollution categories
(AQI < 50 is the omitted category). See the text for details. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes to Table 1 for
detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at
10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)
Dependent variable
AQI50 − 100
AQI100 − 150
AQI150 − 200
AQI200 − 300
AQI300+

−0.006
(0.152)
−0.342∗
(0.181)
−0.443∗∗
(0.223)
−0.567∗
(0.293)
−1.522∗∗∗
(0.289)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Observations
R-squared

3824
0.006

(2)
(3)
F orecast _Optimism

(4)

0.099
(0.150)
−0.161
(0.191)
−0.255
(0.215)
−0.296
(0.287)
−0.988∗∗∗
(0.340)

−0.232
(0.221)
−0.567∗∗
(0.256)
−0.779∗∗∗
(0.269)
−1.228∗∗∗
(0.366)
−1.057∗
(0.578)

−0.376
(0.230)
−0.664∗∗
(0.262)
−0.856∗∗∗
(0.297)
−1.062∗∗∗
(0.371)
−1.190∗
(0.624)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

3824
0.067

3824
0.444

3824
0.609

it is also possible that analysts’ negative proﬁt outlooks
could result from CEO and/or top management mood during the visit. While this explanation would still involve a
relation between pollution and affect, it is an explanation
that is quite distinct from the one we have put forth to
this point. To assess the plausibility of this mechanism, in
Appendix E we use the fraction of negative words used by
ﬁrm CEOs during site visit Q&As as the outcome variable.
To generate this measure, we follow Loughran and McDonald (2011) to classify words during visit Q&A sessions
(transcripts obtained from WIND, a provider of Chinese ﬁnancial research data) as positive, negative, or neutral. We
ﬁnd that there is no signiﬁcant relation between pollution
and top management negativity during a visit, and indeed
the point estimates are generally of the “wrong” sign.
We conclude this section by examining whether a ﬁrm’s
own pollution might be responsible for the patterns we
document in our main results. To do so, we deﬁne the indicator variable HighPollution to denote ﬁrms in one of the
16 industries classiﬁed as high polluters by the Ministry
of Ecology and Environment. These include sectors such as
thermal power, pulp and paper industry, and fermentation;
collectively these industries comprise 24.5% of our site visit
observations. If we were to ﬁnd that the negative relation
between pollution and earnings forecasts were driven by
this high pollution subsample, one may be concerned that

pollution from the ﬁrm itself might lead visitors to infer
that the company could face environmental enforcement
actions in the future, for example. In Table 5, we present
our main speciﬁcation augmented by the interaction of AQI
and HighPollution. In column (1), in the absence of any industry ﬁxed effects, we may observe the direct effect of
HighPollution on forecast optimism.10 We observe no correlation. When we add AQI∗ HighPollution as a covariate in
column (2), we ﬁnd that the coeﬃcient is positive and
roughly the same magnitude as the direct effect of AQI.
This ﬁnding argues against the ﬁrm’s own pollution as the
source of the negative relation with earnings forecasts. Indeed, the positive coeﬃcient on the interaction term may
reﬂect a (relatively) positive attribution from pollution for
ﬁrms whose production is itself the source of emissions.
3.1. Factors inﬂuencing the relation between pollution and
forecasting bias
In this section we explore several dimensions of heterogeneity in the relation between pollution and forecasting bias. We do so with the aim of enriching our understanding the underlying mechanisms behind the effect of
pollution on earnings forecasts, and of the factors that exacerbate or mitigate this relation.
We begin by examining two time-based dimensions of
heterogeneity: the time elapsed between site visits and
earnings reports, and the time horizon of forecasts in a
given report. We then look at heterogeneity based on several characteristics of the visiting analysts. First, we explore whether pollution in an analyst’s city of employment
moderates the impact of site visit pollution on forecasting. We then examine heterogeneity based on the number
of analysts visiting on a particular date, and also whether
the analysts are from the same brokerage ﬁrm or different
ones. And ﬁnally we examine whether individual analyst
attributes that reﬂect ability or experience are associated
with a stronger or weaker effect of pollution on forecasts.
Each of these analyses is motivated by a distinct intuition and prior research on circumstances that might be
expected to amplify (or attenuate) the impact of pollution
on analyst pessimism. We ﬁrst look at the time elapsed
because, to the extent that the negative relation between
pollution and forecasts is driven by analyst affect, this effect might dissipate after departing from the (polluted)
visit site. (Alternatively, if forecasts are calculated on-site
and only reported later, we would expect no effect of delay on the pollution-forecast relation.) We are motivated
to look at heterogeneity by forecast horizon based on earlier research in accounting, which ﬁnds that analysts’ forecasts over longer horizons have less precision and are more
prone to bias (Kang et al., 1994). If longer-run forecasts are
based more on speculation (rather than hard data) we argue they are potentially more swayed by analysts’ moods.
10
We can identify this relation despite the inclusion of industry ﬁxed
effects because the high pollution ﬂag has some within-industry variation. For example, the CSRC industry classiﬁcation for power includes
both wind power and thermal power, whereas only the latter is classiﬁed
as high pollution. If we include the more detailed industry ﬁxed effects,
the coeﬃcient on the AQI∗ HighPollution interaction is largely unaffected.

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

977

Table 4
The effect of pollution persistence on forecast optimism.
Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from
2009 to 2015. The dependent variable in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15] of the site visit and realized EPS,
scaled by price as of the trading day prior to the forecast, multiplied by 100. AQI denotes the Air Quality
Index of the visit city on the visit day, scaled by 10 0 0. AQI_Past5, AQI_Past7, and AQI_Past10 denote AQI
of the site visit city 5, 7, and 10 days prior to the visit date respectively, scaled by 10 0 0. AQI_F orward5,
AQI_F orward7, and AQI_F orward10 denote AQI of the site visit city 5, 7, and 10 days following the visit
date, respectively, scaled by 10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return,
Analyst _At tent ion, F ollow_Co_Num and F orecast _Num, with output suppressed to conserve space. See
the notes to Table 1 for detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at 10%; ∗ ∗
signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)

(2)

−3.548∗∗
(1.481)
−1.501
(1.649)

−3.813∗∗∗
(1.443)

Dependent variable
AQI
AQI_Past5
AQI_Past7

(3)
(4)
F orecast _Optimism
−3.772∗∗∗
(1.420)

−3.782∗∗∗
(1.407)

(5)

(6)

−3.841∗∗∗
(1.421)

−3.540∗∗
(1.461)

0.378
(1.346)
−0.360
(1.474)

AQI_Past10
AQI_F orward5

0.181
(1.764)

AQI_F orward7

0.501
(1.374)
−1.410
(1.142)

AQI_F orward10
Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Observations
R-squared

3824
0.609

3822
0.608

3822
0.608

3824
0.608

3824
0.608

3824
0.609

Our analysis of whether pollution in an analyst’s work
city mitigates the impact of site visit pollution is motivated
by the literature on affective forecasting and adjustment
(e.g., Wilson and Gilbert, 2003), which ﬁnds that individuals adjust relatively quickly to adverse circumstances. We
are motivated to examine individual and group attributes
of analysts to explore whether experience and ability –
whether collective or individual – affect how ambient circumstances inﬂuence judgments.
3.1.1. Forecast delay
In Fig. 1, we illustrate how our estimates of the relation
between air pollution and forecast optimism are affected
by the inclusion of forecasts that are further removed in
time from the site visit. In the graph, we present a series
of point estimates of β from speciﬁcation (2), allowing for
a range of forecast windows (and using the fully saturated
speciﬁcation), ranging from 1 to 5 dates following the visit,
to a [1,30] calendar day window. Interestingly, while the
negative relation holds for all samples, it is sharpest for
relatively short windows, and becomes insigniﬁcant for the
longer windows in the ﬁgure. This ﬁnding provides suggestive evidence that the affective impact of air pollution
(which, recall, is uncorrelated with the delay in providing
subsequent forecasts) may dissipate with time. Naturally,

there are alternative interpretations. For example, it is possible that visits which uncover little relevant information
do not lead to earnings forecasts in the days that follow,
so that the visit is irrelevant to forecasts generated some
weeks later. It is for this reason that we treat our interpretation of these ﬁndings with caution.
3.1.2. Forecast horizon
We next explore whether pollution differentially affects
forecasts over longer time horizons. To do so, we add
the interaction term AQI∗ log(Horizon) to speciﬁcation (2),
where Horizon denotes the days elapsed between the forecast date and the corresponding date of the actual earnings announcement. To facilitate interpretation of the direct effects in this speciﬁcation, we demean both AQI and
log(Horizon). We present the ﬁndings in Table 6, in speciﬁcations that parallel the presentation of our main results in
Table 2. Focusing ﬁrst on the direct effect of pollution and
forecast horizon, we observe a modest negative association
between pollution and forecast bias at the mean forecast
horizon. Consistent with Kang et al. (1994), we see a much
greater (positive) bias in forecasts over long horizons. Our
main interest in this table is in the interaction of these two
variables, which is consistently negative and signiﬁcant at
least at the 1% level across all columns, indicating a much

978

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

Fig. 1. The attenuating effect of forecast delay. This ﬁgure shows how the coeﬃcient estimates of AQI vary as a function of the number of days between
analyst site visits and subsequent earnings forecasts. Each circle indicates the point estimate from Eq. (1), including the full set of controls, and includes
all forecasts issued up to and including d days after the site visit, where d ranges from 5 to 30. The whiskers show the 95 percent conﬁdence interval of
each coeﬃcient estimate.

Table 5
The effect of ﬁrm type.
Numbers in parentheses are standard errors clustered by ﬁrm. The
sample covers the period from 2009 to 2015. The dependent variable in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15]
of the site visit and realized EPS, scaled by price as of the trading
day prior to the forecast, multiplied by 100. AQI denotes the Air Quality Index of the visit city on the visit day, scaled by 10 0 0. HighPollution is a dummy variable indicating that the visited ﬁrm belongs
to one of the 16 high pollution industies deﬁned by Ministry of
Ecology and Environment of China (see text for details). Controls
include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes to Table 1 for
detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at
10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)
Dependent variable

(2)
F orecast _Optimism

0.344
(0.349)
−3.625∗∗
(1.461)

−0.279
(0.473)
−5.378∗∗∗
(1.604)
7.410∗∗
(2.992)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls

Yes
Yes

Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Observations
R-squared

3824
0.601

3824
0.602

HighPollution
AQI
AQI∗ HighPollution

stronger effect of pollution on longer-term forecasts. In the
ﬁnal column, we include an extra speciﬁcation which includes analyst visit ﬁxed effects. In this ﬁnal column, all
covariates are effectively absorbed by the 1642 visit ﬁxed
effects, but we can still identify the forecast horizon term
and its interaction with AQI, which vary within a site visit.
Even in this saturated speciﬁcation, the interaction term is
negative and signiﬁcant at the 1% level.
3.1.3. Analyst adaptation and the effects of pollution
We next turn to the adaptation hypothesis, which
we emphasize is, to our knowledge, new to the analyst
forecasting literature speciﬁcally, and a novel ﬁnding on
forecasting bias more generally. We do so by examining
whether the negative relation between pollution and earnings forecasts is driven by analysts based in less polluted
cities. (Implicit in our examination of this question is the
presumption that pollution’s effect is asymmetric – exposure to pollution that is worse than one’s usual experiences has a negative impact on affect, relative to the positive impact of experiencing relatively low pollution.)
In Table 7 we explore the “adaptability” hypothesis in
a regression framework, in which we replace site visit
AQI with a site visit spline with a kink at home-city
AQI (i.e., the slope change will vary across analyst visits, with an analyst-speciﬁc knot in the spline, speciﬁcally captured by the terms AQI(When AQI < 0) and
AQI(When AQI ≥ 0)), where AQI equals to AQI −
AQI_home and AQI_home is the median AQI in the analyst’ s home city during the month preceding the site visit.
We reprise the analyses of Table 2 with this substitution.
Across all columns, the negative relation between AQI and

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

979

Table 6
The relation between air pollution and forecast optimism for different forecast horizons.
Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from 2009
to 2015. The dependent variable in all columns is F orecast _Optimism, which denotes the difference between
annual EPS forecast issued within calendar days [1,15] of the site visit and realized EPS, scaled by price as
of the trading day prior to the forecast, multiplied by 100. AQI denotes the (demeaned) Air Quality Index
of the visit city on the visit date, scaled by 10 0 0. log (Horizon) denotes the (demeaned) natural logarithm of
the days elapsed between the forecast date and the corresponding date of the actual earnings announcement.
Controls include Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book,
Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num, with output
suppressed to conserve space. See the notes to Table 1 for detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at 10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)

(2)

(3)
F orecast _Optimism

(4)

(5)

−1.817∗
(1.049)
1.607∗∗∗
(0.075)
−3.711∗∗∗
(0.964)

−2.285∗∗
(1.135)
1.603∗∗∗
(0.075)
−3.676∗∗∗
(0.952)

−3.836∗∗∗
(1.345)
1.629∗∗∗
(0.093)
−4.407∗∗∗
(1.340)

−4.388∗∗∗
(1.468)
1.630∗∗∗
(0.094)
−4.337∗∗∗
(1.356)

1.634∗∗∗
(0.106)
−4.282∗∗∗
(1.563)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Dependent variable
AQI
log (Horizon)
log (Horizon)∗ AQI
Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Visit FEs

Yes

Observations
R-squared

3824
0.213

3824
0.236

Table 7
Air pollution adaption and forecast optimism.
Numbers in parentheses are standard errors clustered by ﬁrm. The
sample covers the period from 2009 to 2015. The dependent variable
in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15] of the site
visit and realized EPS, scaled by price as of the trading day prior to
the forecast, multiplied by 100. AQI equals to AQI – AQI_home. AQI
denotes the Air Quality Index of the site visit city on the visit date,
scaled by 10 0 0. AQI_home is the median AQI in the analyst’s home
city during the month preceding the site visit, scaled by 10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes to Table 1 for
detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at
10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)
Dependent variable

AQI(When AQI ≤ 0)
AQI(When AQI > 0)

5.612∗∗
(2.593)
−5.035∗∗∗
(1.446)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Observations
R-squared

3824
0.004

(2)
(3)
F orecast _Optimism

(4)

3.072
(2.472)
−3.679∗∗∗
(1.388)

0.381
(4.719)
−4.993∗∗∗
(1.648)

−0.395
(4.529)
−3.885∗∗
(1.711)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

3824
0.066

3824
0.443

3824
0.608

forecast optimism is driven by analyst visits to sites that
are more polluted than their home base. We note, however, that the negative portion of the spline is imprecisely
measured so that we cannot reject equality of the two

3824
0.609

3824
0.612

3824
0.693

spline coeﬃcients. As such, these results may be seen as
merely suggestive.11
3.1.4. Individual analyst ability, experience, and forecast bias
We next turn to examining individual analyst attributes
that could plausibly mitigate the effects of pollution on
forecasting (and possibly reduce forecasting bias in general). Speciﬁcally, we consider the role of experience, as
captured by (the log of) the number of quarters since the
analyst’s ﬁrst forecast appeared, and two proxies for ability. The ﬁrst is Star, an indicator variable denoting that the
analyst is ranked as a star analyst by the New Fortune
Magazine at the beginning of the visit year, and the second measures analyst forecast accuracy. To provide roughly
comparable measures of accuracy for analysts with different experience levels, we focus on annual earnings forecasts made in the year prior to the site visit. Accuracy is
then deﬁned as:

Si − EP Si |
1
|EP
Accuracy = − in=1
,
n
|EPSi |

(3)

where n is the number of forecasts in the prior year, EPSi
S is the analyst’
is the realized earnings per share, and EP
i
s EPS forecast.
In the ﬁrst four columns of Table 8, in which we
look at the direct effect of analyst characteristics. Neither
star status (column (1)) nor past accuracy (column (3)) is
11
It is also natural to ask whether our spline speciﬁcation is simply
picking up on a non-linear or non-monotonic relation between site visit
AQI and earnings forecasts. We observe, however, that a spline at the median of site visit AQI and a quadratic speciﬁcation provide a poor ﬁt for
the data.

980

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

Table 8
Pollution, analyst skills, and forecasting bias.
Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from 2009 to 2015. The dependent variable in all columns
is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15] of the site visit and realized EPS, scaled
by price as of the trading day prior to the forecast, multiplied by 100. AQI denotes the Air Quality Index of the visit city on the visit day, scaled by 10 0 0.
Star is a dummy variable denoting whether the visiting analyst is ranked as a star by New Fortune magazine in the visit year. Experience is measured as the
natural logarithm of the number of quarters since the analyst make his/her ﬁrst forecast up to the end of the visit year. Accuracy is the average accuracy
of the analyst’s forecast within the past 1 year, with accuracy deﬁned as the absolute difference between annual EPS forecast and realized EPS, scaled
by the absolute value of realized EPS, multiplied by −1. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed,
log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num, with output suppressed to
conserve space. See the notes to Table 1 for detailed deﬁnitions of the control variables. Signiﬁcance: ∗ signiﬁcant at 10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant
at 1%.
(1)

(2)

(3)

−3.770∗∗∗
(1.423)
0.073
(0.273)

−3.746∗∗∗
(1.423)

−4.005∗∗∗
(1.458)

Dependent variable
AQI
Star

−0.295∗∗
(0.125)

Experience
Accuracy

0.080
(0.066)

(4)
(5)
F orecast _Optimism
−4.020∗∗∗
(1.460)
0.140
(0.275)
−0.317∗∗
(0.129)
0.079
(0.065)

AQI∗ Star

−4.075∗∗∗
(1.480)
−0.230
(0.388)

(6)

(7)

(8)

−3.570
(2.870)

−3.063
(2.583)

0.364
(0.782)

−3.028
(3.534)
−0.259
(0.379)
−0.309
(0.205)
0.044
(0.108)
4.857
(3.070)
−0.149
(1.243)
0.430
(0.776)

−0.287
(0.201)
0.049
(0.109)
3.624
(3.123)

AQI∗ Experience

−0.089
(1.252)

∗

AQI Accuracy
Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Observations
R-squared

3824
0.608

3824
0.609

3757
0.608

3757
0.608

3824
0.609

3824
0.609

3757
0.608

3757
0.608

robustly associated with forecast optimism. However, experience is negatively associated with optimism, whether
included on its own (column (2)) or together with other
analyst attributes (column (4)). Given the optimism bias
present on average, this result implies a higher level of accuracy among more experienced analysts. Of more direct
relevance for our paper, we add the interaction of each
variable with AQI in columns (5)–(7), and include all interactions in column (8). For the case of Star the coeﬃcient
suggests that star status may mitigate pollution-induced
pessimism, though even in this instance the interaction is
not statistically signiﬁcant even at the 10% level. Overall,
while we observe no evidence that the effects of pollution are mitigated by experience or ability, we cannot draw
strong conclusions from these analyses given the imprecision of our estimates.
3.1.5. Group visits and forecast bias
In our ﬁnal analyses we consider whether forecast bias
is correlated with the presence of other analysts during the
visit. We deﬁne two “group visit” variables. The ﬁrst captures whether there is at least one other analyst from the
same brokerage ﬁrm present (GroupV isit _Same), while the
second measures whether there is at least one other analyst from another brokerage present (GroupV isit _Other). We
are agnostic ex ante on the role of multiple visitors. On the
one hand, “groupthink” can lead to magniﬁcation of individual biases (see, e.g., Janis, 1972 for a classic reference).

The “wisdom of crowds” argues for the opposite – the aggregation of beliefs may help to erase individual errors. We
distinguish between within-brokerage and cross-brokerage
groups because one might, ex ante, expect the strength of
these effects to differ between the two. In particular, we
conjecture that analysts from the same brokerage will be
more subject to the forces of social conformity, which is
more apt to occur in groups with greater homogeneity in
culture or attitudes (see Ishii and Xuan, 2014 for a discussion in a ﬁnance-focused setting).
We present results that show the direct effect of
group visits (columns (1)–(3)) as well as their interactions with AQI (columns (4)–(6)) in Table 9. Neither type
of group visit is a direct predictor of forecast optimism.
When we include the interaction terms, we ﬁnd a positive coeﬃcient on AQI ∗ GroupV isit _Other, with a magnitude that is roughly equal to that of the direct effect of
AQI (signiﬁcant at the 5% level).12 The interaction AQI ∗

12
We consider whether the beneﬁt of having analysts from other
brokerages present may stem directly from the presence of other, less
biased analysts. A natural approach to exploring this possibility is to examine whether the GroupV isit _Other ﬁnding is related to the adaptation
results described in Section 3.1.3. That is, does the presence of other analysts help because it potentially adds the perspective of a visitor who is
adapted to high pollution. To implement an empirical test of this idea, we
take the adaptation speciﬁcation, and ask whether the presence of others
from high pollution cities (and hence adapted to pollution) mitigates the
effect of pollution on pessimism, particularly for analysts that are

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

981

Table 9
The effect of analyst group visit on optimism.
Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from 2009 to 2015.
The dependent variable in all columns is F orecast _Optimism, which denotes the difference between annual EPS forecast issued within calendar days [1,15] of the site visit and realized EPS, scaled by price as of the trading day prior
to the forecast, multiplied by 100. AQI denotes the Air Quality Index of the visit city on the visit day, scaled by 10 0 0.
GroupV isit _Same is an indicator variable denoting that at least one other analyst from the same brokerage was present
during the visit. GroupV isit _Other is an indicator variable denoting that at least one other analyst from a different brokerage was present during the visit. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation,
W ind_Speed, log (Assets), Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num
and F orecast _Num, with output suppressed to conserve space. See the notes to Table 1 for detailed deﬁnitions of the
control variables. Signiﬁcance: ∗ signiﬁcant at 10%; ∗ ∗ signiﬁcant at 5%; ∗ ∗ ∗ signiﬁcant at 1%.
(1)

(2)

−3.864∗∗∗
(1.432)
−0.277
(0.222)

−3.768∗∗∗
(1.420)

Dependent variable
AQI
GroupV isit _Same
GroupV isit _Other

0.019
(0.166)

(3)
(4)
F orecast _Optimism
−3.864∗∗∗
(1.432)
−0.277
(0.222)
0.017
(0.165)

AQI ∗ GroupV isit _Same

−3.311∗∗
(1.525)
0.039
(0.349)

(5)

(6)

−8.064∗∗∗
(2.447)

6.150∗∗
(2.654)

−7.882∗∗∗
(2.459)
0.087
(0.343)
−0.580∗
(0.316)
−4.684∗
(2.842)
6.752∗∗
(2.656)

−0.536∗
(0.315)
−3.633
(2.930)

AQI ∗ GroupV isit _Other
Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Observations
R-squared

3824
0.609

3824
0.608

3824
0.609

3824
0.609

3824
0.609

3824
0.610

GroupV isit _Same is negative, though only marginally signiﬁcant (p-value = 0.100). The difference between the coeﬃcients on the two interactions is signiﬁcant at the 1%
level.
Overall, these results suggest that the “wisdom of the
crowds” effect may dominate for analysts from different
(competing) brokerages, while groupthink dominates for
visitors from the same brokerage. Naturally, these results
and their interpretation should be treated as speculative –
we have not attempted to model fully the decision to make
site visits, let alone modeling whether visits are conducted
by one or multiple analysts. We nonetheless believe these
results – and our heterogeneity results more generally – to
be provocative ﬁndings that may prompt further work in
this area.
4. Conclusion
In this paper we study how environmental conditions
impact sell-side analyst forecasts. We show that forecast
optimism is lower following site visits on heavily polluted days, consistent with a negative impact of pollution on analyst affect. We further show that this effect
themselves
from
low
pollution
locales
(i.e.,
we
interact
AQI(When AQI < 0) with a set of dummy variables denoting whether
or not there is a “high adaptation” (high pollution) analyst visiting on the
same date. In these speciﬁcations, none of the coeﬃcients approaches
signiﬁcance, which we suggest may result in large part because of the
inclusion of many highly correlated covariates.

is driven by the relation between pollution and forecasts issued soon after the site visit, suggesting that pollution’s impact on affect dissipates with time. We also
present suggestive evidence that the effect of pollution is
weaker for analysts who themselves are based in highly
polluted cities, consistent with analysts adjusting to the
effects of poor air quality, and evidence that the effect
of pollution is also weakened by the presence of analysts from other brokerage ﬁrms, suggesting that the “wisdom of the crowds” may mitigate the biases in individuals’
judgments.
Our ﬁndings indicate that even expert agents may be
inﬂuenced by apparently irrelevant environmental conditions, and furthermore, this takes place even in a high
stakes setting. While ﬁnance scholars have focused on the
impact of weather and pollution on stock prices and trading, it may be fruitful to extend this line of research to
consider whether and how decisions of experts in other
domains are impacted by environmental conditions: For
example, are more bank loans rejected, or do economic
forecasters issue more pessimistic macro predictions, on
cloudy or polluted days? We may also delve more deeply
into the conditions that lessen the inﬂuence of environmental factors, perhaps via required delays between environmental exposure and decision-making, or via a simple information treatment which informs decision-makers
about the relation between environmental conditions and
mood. We leave these avenues of inquiry for future
research.

982

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

Appendix A. Data set construction
We begin our sample construction by hand collecting disclosures on site visits to all ﬁrms traded
on the Shenzhen Stock Exchange. We obtained 22,200
such releases, covering 1481 ﬁrms (and 67,443 visitors,
including stock analysts, individual investors, mutual/hedge
fund managers, and also reporters), over the period of
2009–2015. Based on this initial dataset, we use the following seven steps to assemble our ﬁnal dataset which is
used for our empirical analyses.
Step 1: Since we are primarily interested in sell-side analysts who provide earnings-per-share (EPS) forecasts, we
only keep observations in which sell-side analysts released
at least one forecast report within 30 days after the visit,
leaving us with 5004 ﬁrm-visit × analyst level observations.
Step 2: We then merge in site-date level AQI and
weather information into the master dataset. For 486 out
of 5004 observations, we do not have corresponding AQI
information, leaving us with 4518 analyst site visits.
Step 3: Each analyst report potentially covers multiple forecasts for different horizons (current year, next year,
EPS in two years, and so forth). Because we wish to test
the relationship between forecast horizon and pollutioninduced bias, we treat each forecast as a distinct (though
non-independent) observation, leading to a total of 10,068
visit × analyst × EPS forecast level observations. Since
we need to calculate forecast optimism using the realized EPS data, we drop 2 observations for which the forecast ﬁscal year is later than 2016, the ﬁnal year of our
data.
Step 4: We merge in ﬁnancial information in year t − 1
for the listed ﬁrms in our sample. 448 observations (4.5%)
do not have matched pre-visit year ﬁnancial data, leaving
us with 9618 observations. Among these matched observations, 843 observations have missing ﬁnancial information on total assets, market/book value, intangible assets,
stock turnover, annual stock return and daily volatility (all
in year t − 1), leaving us with 8775 observations.
Step 5: We then merge in analyst-speciﬁc information,
including the number of ﬁrms the analyst follows, and
the number of forecast reports generated by the analyst,
in year t. 1613 (18.4%) observations do not have matched
analyst-level information at all, leaving us with 7162 observations.
Step 6: To control for the inﬂuence of weather, we
then merge in weather information on the site visit date,
including hours of sun, temperature, humidity, precipitation, and wind speed. We also further dropped 47 observations with missing values for weather variables (which
are recorded as missing by the meteorological station, and
attributed to equipment malfunction or human error). This
ﬁlter leaves us with 7115 observations.
Step 7: Finally, since we merge in information on each
analyst’ s city of employment during the three months
prior to the site visit. This ﬁlter further reduced the sample
by 2007 observations, leaving us with 5108 observations. In
our main analysis, we restrict our sample to EPS forecasts
released within 15 days of the site visit, giving us a ﬁnal
sample of 3824 for our main analysis.

Appendix B. The relation between air pollution and
forecast delay
Numbers in parentheses are standard errors clustered
by ﬁrm. The sample covers the period from 2009 to 2015.
The sample in columns 1 - 5 is conﬁned to the set of
earnings forecasts issued within 30 days of a site visit
(i.e., Delay ≤ 30), in column 6 the sample is limited
to foreacsts issued within 15 days. The dependent variable in columns 1–4 and in column 6 is Delay, which
denotes the number of days between the site visit and
the issuance of the forecast. The dependent variable in
column 5 is log (Delay). AQI denotes the Air Quality Index of the site visit city on the visit date, scaled by
10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets),
Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes
to Table 1 for detailed deﬁnitions of the control variables.
Signiﬁcance: ∗ signiﬁcant at 10%; ∗∗ signiﬁcant at 5%; ∗∗∗
signiﬁcant at 1%.
(1)

(2)

Dependent
variable
AQI

Observations
R-squared

(4)

4.320 1.186 6.515 4.681
(3.998) (4.155) (7.180) (7.213)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Delay ≤

(3)
Delay

(5)
(6)
log(Delay ) Delay
0.224
(0.873)

5.457
(4.066)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

30

30

30

30

30

15

5108
0.001

5108
0.025

5108
0.687

5108
0.690

5108
0.674

3824
0.755

Appendix C. Robustness tests for main regressions
without winsorizing
Numbers in parentheses are standard errors clustered
by ﬁrm. This table presents the results from Table 2, without winsorizing any of the continuous variables. The sample covers the period from 2009 to 2015. The dependent variable in all columns is F orecast _Optimism, which
denotes the difference between annual EPS forecast issued within calendar days [1,15] of the site visit and realized EPS, scaled by price as of the trading day prior
to the forecast, multiplied by 100. AQI denotes the Air
Quality Index of the visit city on the visit day, scaled by
10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets),
Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes
to Table 1 for detailed deﬁnitions of the control variables.
Signiﬁcance: ∗ signiﬁcant at 10%; ∗∗ signiﬁcant at 5%; ∗∗∗
signiﬁcant at 1%.

R. Dong, R. Fisman and Y. Wang et al. / Journal of Financial Economics 139 (2021) 971–984

Dependent variable
AQI

(1)
(2)
F orecast _Optimism
∗∗∗

3.199
(1.110)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Observations
R-squared

3824
0.002

∗

(3)

(4)
∗∗∗

F orecast _Num

4.291
(1.429)

4.515
(1.653)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

3824
0.425

3824
0.543

Appendix D. The relation between air pollution and
analyst forecast optimism
Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from
2009 to 2015. The dependent variable in all columns is
F orecast _Optimism, which denotes the difference between
annual EPS forecast issued within calendar days [1,15] of
the site visit and realized EPS, scaled by price as of the
trading day prior to the forecast, multiplied by 100. AQI denotes the Air Quality Index of the visit city on the visit day,
scaled by 10 0 0. See the notes to Table 1 for detailed definitions of the control variables. Signiﬁcance: ∗ signiﬁcant
at 10%; ∗∗ signiﬁcant at 5%; ∗∗∗ signiﬁcant at 1%.

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Observations
R-squared

Dependent variable

log(Horizon )
Hours_o f _Sun
Temperature
Humidity
Precipitation
W ind _Speed
log(Assets )
Market _to_Book
Intangible_Asset
Vol atil ity
T ur nover
Return
Analyst _At tent ion
F ol l ow_Co_Num

(3)

(4)

3.558∗∗∗
(1.072)

4.206∗∗∗
(1.322)

3.769∗∗∗
(1.420)
1.596∗∗∗
(0.095)
0.000
(0.002)
0.002
(0.001)
0.005
(0.006)
0.000
(0.001)
0.008
(0.008)
0.212
(0.132)
0.105
(0.065)
2.627
(2.600)
1.912
(18.856)
0.046
(0.054)
0.095
(0.162)
0.313∗∗
(0.133)
0.159
(0.331)

2.129∗
(1.104)

(continued on next page)

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes

3824
0.065

3824
0.443

3824
0.608

Numbers in parentheses are standard errors clustered by ﬁrm. The sample covers the period from
2009 to 2015. The dependent variable in all columns
is Management _Negat ivit y, which denotes the number of
negative words divided by total words of management answers during the Q & A session. AQI denotes the Air Quality Index of the site visit city on the visit date, scaled by
10 0 0. Controls include log (Horizon), Hours_o f _Sun, Temperature, Humidity, Precipitation, W ind_Speed, log (Assets),
Market _to_Book, Intangible_Asset, Volatility, Turnover, Return, Analyst _At tent ion, F ollow_Co_Num and F orecast _Num,
with output suppressed to conserve space. See the notes
to Table 1 for detailed deﬁnitions of the control variables.
Signiﬁcance: ∗ signiﬁcant at 10%; ∗∗ signiﬁcant at 5%; ∗∗∗
signiﬁcant at 1%.

AQI
(1)
(2)
F orecast _Optimism

3824
0.004

Yes
Yes

Appendix E. The relation between air pollution and
management negativity

Dependent variable

AQI

0.214
(0.245)

∗∗∗

1.967
(1.126)

3824
0.046

983

(1)
(2)
(3)
Management _Negat ivit y

(4)

0.011
(0.007)

Year-quarter FEs
Day of week FEs
Industry FEs
City FEs
Analyst FEs
Controls
Observations
R-squared

3086
0.003

0.004
(0.007)

0.016
(0.011)

0.020
(0.013)

Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes

3086
0.038

3086
0.754

3086
0.758

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==> RFS02 - Banking on Carbon: Corporate Lending and Cap-and-Trade Policy.txt <==
Ivan T. Ivanov
Federal Reserve Bank of Chicago, USA
Mathias S. Kruttli
Kelley School of Business, Indiana University, USA
Sumudu W. Watugala
Kelley School of Business, Indiana University, USA
We estimate the effect of carbon pricing policy on bank credit to greenhouse-gas-emitting
firms. Our analyses exploit the geographic restrictions inherent in California’s cap-andtrade bill and a discontinuity in the embedded free permit threshold of the federal WaxmanMarkey cap-and-trade bill. Affected high emission firms face shorter loan maturities, lower
access to permanent forms of bank financing, higher interest rates, and higher participation
of shadow banks in their lending syndicates. These effects are concentrated among private
firms, while credit terms of public firms are largely unaffected. Overall, we show that banks
respond quickly to realizations of transition risk. (JEL G20, G21, G28)
Received: June 1, 2021; Editorial decision: July 16, 2023
Editor: Ralph Koijen
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

We are particularly grateful for the comments of two anonymous referees and the Editor, Ralph Koijen.
We thank Ian Appel, Aymeric Bellon, Patrick Bolton, Sudheer Chava, Darwin Choi, John Coglianese, Piotr
Danisewicz, Andrew Ellul, Emilia Garcia-Appendini, Vidhan Goyal, Matthew Gustafson, Florian Heider,
Christoph Herpfer, Deniz Igan, Andrew Karolyi, Lorena Keller, Ryan Lewis, Tao Li, Kyle Meng, Justin Murfin,
Borghan Narajabad, Phong Ngo, David Ng, Sanjay Patnaik, Diane Pierret, Alexander Popov, Nagpurnanand
Prabhala, Tarun Ramadorai, Brigitte Roth Tran, Joâo Santos, Glenn Schepens, Hongyu Shan, Yu Shan, Mandeep
Singh, and Chi-Yang Tsou and seminar participants at Cornell University, European Central Bank, Federal
Reserve Bank of Chicago, Federal Reserve Board, Harvard University, University of Bristol, University of
Houston, University of Zurich, UNPRI, Virtual Seminar on Climate Economics, NFA, System Energy Meeting,
AFBC, Federal Reserve Week After Conference, MFA, SFS Cavalcade, FIRS, Sustainable Finance Forum,
NBER Summer Institute Risks of Financial Institutions, Federal Reserve System Banking Conference, OFR
Cleveland Fed Financial Stability Conference, Finance Down Under Conference, Swiss Winter Conference on
Financial Intermediation, HEC-McGill Winter Finance Workshop, University of Oklahoma Energy and Climate
Finance Research Conference, EBC Conference, Bank Regulation Research Conference, OCC Symposium
on Climate Risk in Finance and Banking, CEMA, MoFiR, CICF, and Chatham House for helpful comments.
We thank Kyle Meng for making data available on his website. Keely Adjorlolo provided excellent research
assistance. Part of this work was completed while Ivanov and Kruttli were at the Board of Governors of the
Federal Reserve System. The views stated herein are those of the authors and are not necessarily the views of
the Federal Reserve Bank of Chicago or the Federal Reserve System. Supplementary data can be found on The
Review of Financial Studies web site. Send correspondence to Mathias S. Kruttli, mkruttli@iu.edu.
The Review of Financial Studies 37 (2024) 1640–1684
© The Author(s) 2023. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
https://doi.org/10.1093/rfs/hhad085
Advance Access publication December 7, 2023

Downloaded from https://academic.oup.com/rfs/article/37/5/1640/7461198 by Mathematical Statistics user on 19 March 2025

Banking on Carbon: Corporate Lending and
Cap-and-Trade Policy

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

1 A survey conducted by the Bank of International Settlements in April 2020 reports that central

banks expect climate change to have potential financial stability implications for the banking system
(Bank of International Settlements, 2020).
2 Carney (2015, p. 6) defines transitions risks as “the financial risks which could result from the

process of adjustment towards a lower-carbon economy.” Legislation considered in the U.S. Senate
would require the Board of Governors of the Federal Reserve System to develop financial risk analyses relating to climate change. Transition risks are explicitly addressed in Section 3.8 of the bill
(https://www.congress.gov/bill/116th-congress/senate-bill/2903/text).

1641

Downloaded from https://academic.oup.com/rfs/article/37/5/1640/7461198 by Mathematical Statistics user on 19 March 2025

Regulators and investors alike anticipate climate change to pose significant
risks to the financial services industry, with potential adverse effects on
systemic stability.1 One source of risk is the adverse impact of climate change
regulations on greenhouse-gas (GHG) emitting firms and their creditors. The
implications of such “transition risks” are currently unknown because most
jurisdictions have not implemented climate change regulations on a large
scale.2 To the extent that financial institutions have large exposure to GHGemitting firms and limited flexibility to adjust such exposures, climate policies
may adversely affect financial stability. Conversely, if financial institutions
can quickly mitigate exposure to high-emitting firms in response to climate
policies, then the minimal impact of such risks on systemic stability should not
hinder regulatory action curbing GHG emissions.
We examine periods when major climate change policies in the United States
move through the legislative process and exploit quasi-exogenous variation in
regulatory requirements to identify their effect on corporate lending. To do
so, we combine facility-level GHG emissions data from the Environmental
Protection Agency (EPA) with comprehensive loan-level data on bank lending
to private and public firms in the United States from the Federal Reserve’s Y14
Collection (Y14) and the Shared National Credit (SNC) Program. Because capand-trade programs are arguably the most prominent climate policy solution
for curbing GHG emissions, we focus on the two main cap-and-trade bills
that passed or came close to passage in the United States: the California and
the federal Waxman-Markey cap-and-trade bills. Both of these bills introduce
a legally binding transition to a low-carbon economy and constitute two
independent natural experiments in our study, occurring at different points
in time, with emitting firms assigned to treatment and control groups along
different dimensions.
We first examine the introduction of California’s cap-and-trade bill. In
December 2011, California enacted the first major cap-and-trade bill of
any state in the United States, with the cap-and-trade program set to
be implemented in January 2013. After the passage of but before the
implementation of the program, GHG-emitting firms and their creditors face
increased risks. These risks stem from an expected increase in operating costs
as well as the uncertainty around such an increase due to the unknown impact of

The Review of Financial Studies / v 37 n 5 2024

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the cap-and-trade program. Our analysis will capture these two effects jointly.
Given this program only affects firms with GHG emissions in California, we
estimate the response of firm financing to cap-and-trade policy by exploiting
variation in the fraction of firm emissions in California. We study the response
of both public and private firms using quarterly corporate loan data from Y14.
We find evidence consistent with lenders negotiating loan contracts
following the passage of California’s cap-and-trade bill in a manner that
mitigates their exposure to affected firms. Firms with a large share of
GHG emissions in California experience a reduction in loan maturities of
approximately 5 months compared to firms with a small share of their
emissions in California. This reduction is considerable given the average
loan maturity of firms in our sample is about 30 months. The changes in
loan maturity are driven by both a decline in maturity within loan type and
a reduction in permanent forms of bank financing. Specifically, firms with
substantial GHG emissions in California exhibit an increased reliance on credit
line financing at the expense of term loan financing. The share of term loan
financing decreases by about 25 percentage points. While treated firms also
face higher loan interest rates, the total committed credit to these firms does
not change significantly.
These debt structure changes provide lenders with the ability to quickly
reduce exposure should firms face difficulties in operating under the capand-trade program. Short maturities allow lenders to frequently reevaluate
credit relationships (Diamond 1991; Rajan and Winton 1995). Unlike term
loans, the availability of credit lines is conditional on firms maintaining
high cash flow and low credit risk (Jimenez, Lopez, and Saurina 2009;
Sufi 2009; Acharya et al. 2014), and banks use discretion in preventing
small firms from drawing on their credit lines in times of economic and
financial stress (Greenwald, Krainer, and Paul 2021; Chodorow-Reich et al.
2022). Further, the higher interest rates are consistent with banks requiring
direct compensation for exposure to risks associated with the climate policy.
We complement our results on California’s cap-and-trade bill with an
analysis of the Waxman-Markey cap-and-trade bill. To date, the WaxmanMarkey bill is the federal cap-and-trade legislation that came closest to passage
in the United States with a peak probability of passage implied by prediction
markets at nearly 60% in 2009 (Meng 2017). The bill cleared the U.S. House of
Representatives in June 2009, and was under consideration by the U.S. Senate
until July 2010. Waxman-Markey carved out an exemption—a “free permit”
to emit GHGs—for manufacturing firms with energy intensity at or above the
prespecified 5% cutoff. This allows us to compare the financing outcomes of
manufacturing firms just above and below the free permit threshold at the end
of 2009 relative to 2008, when the bill had not yet passed the House. Our
research design is similar to Meng (2017), who studies the economic cost of the
Waxman-Markey cap-and-trade program using data on the equity valuations of
public firms.

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

3 See, for example, Tabuchi (2021).

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We conduct the Waxman-Markey analysis with data from the SNC as the
Y14 data are not available prior to 2011. The SNC data provide comprehensive
coverage of the U.S. syndicated loan market and allow us to measure the
same loan contracting outcomes as with the Y14 data with the exception of
loan interest rates. Importantly, although this empirical setting differs in terms
of when treatment occurs and how firms are assigned to treatment, we find
that lenders manage their exposure to covered firms in a qualitatively similar
way. Firms just below the free permit threshold experience a reduction in loan
maturities of up to seven months compared to firms just above the threshold
after the bill passed the U.S. House of Representatives. Also, firms without
free permits face a reduction in term loan share and a corresponding increase
in credit lines. These results are significantly stronger for the most affected
firms, that is, those closer to the 5% energy intensity cutoff.
We next examine the heterogeneity in the effects of these cap-and-trade
programs on corporate credit. Virtually all of the documented effects are concentrated within the subsample of private firms. By contrast, we observe few
significant changes in the debt structure of public firms. The differential effect
of cap-and-trade policies on private versus public firms is consistent with banks
expecting that private firms face relatively higher operating costs as a result of
cap-and-trade policies. Both anecdotal evidence and our data suggest that private firms have lower GHG emissions efficiency than their public counterparts,
which would make operating under a cap-and-trade program more costly.3 The
differential effects between private and public firms also could be driven by
greater financial constraints among private firms (Hadlock and Pierce 2010;
Saunders and Steffen 2011; Mortal and Reisel 2013; Erel, Jang, and Weisbach
2015; Ivanov, Pettit, and Whited 2022). Because private firms are typically
smaller than public firms, both firm size and ownership may explain our
results.
In addition to debt structure changes that are equilibrium outcomes of
contracting between banks and firms, banks can also take more unilateral
measures to reduce exposure to firms covered by impending cap-and-trade
programs, such as selling loans on the secondary loan market or monitoring
borrowers more closely. The SNC data allow us to analyze these two
dimensions for the Waxman-Markey cap-and-trade bill. We show that lenders
with large ex ante exposure to high GHG-emitting firms reduce syndicated
loan exposure to firms below the free permit threshold by a greater extent.
In response to this selling, some shadow banks, such as collateralized loan
obligations (CLOs), take a significantly larger loan share in the syndicates of
treated firms. Finally, firms below the free permit threshold are more likely to
have cash flow covenants in their contracts.

The Review of Financial Studies / v 37 n 5 2024

4 A separate asset pricing literature shows how equity and options markets price climate policy risks, for exam-

ple, Engle, Giglio, Kelly, Lee, and Stroebel (2020); Ilhan, Sautner, and Vilkov (2021); Bolton and Kacperczyk

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We also analyze whether firms experience significant changes in profitability, saving, and investment following the implementation of California’s capand-trade program. Using the financial statement information for both private
and public firms from Y14, we show that following program implementation,
private firms face reductions in profitability. They also increase cash holdings,
likely for precautionary reasons. In addition, private firms decrease capital
expenditures, suggesting that there are large adverse real effects on the
borrowers most affected by this cap-and-trade program.
Overall, by isolating periods around the passage of two major cap-andtrade bills, we show that the fluid nature of commercial lending relationships
allows banks to adjust their exposure to covered firms quickly through loan
renegotiation. In addition, our findings indicate that banks expect cap-and-trade
policy to place a larger burden on private firms. For regulators concerned with
financial stability, these results are reassuring as they show that bank lenders
actively manage exposure to transition risk realizations stemming from climate
policies. However, the results also show that financing conditions for covered
firms tighten at the same time as these firms face a price on carbon. Taken
together, these adverse effects may jeopardize the survival of some firms in
polluting industries. Understanding heterogeneity in the effect of cap-and-trade
programs on emitting firms is important for regulators designing climate policy.
The distinction our analysis documents between private and public firms
adds to the existing literature that focuses on public firms. Meng (2017)
finds that equity investors of public firms expect only modest economic
costs as a result of the Waxman-Markey cap-and-trade bill, which are at
the lower end of the distribution of estimates from government agencies
and privately funded studies. Studying the California cap-and-trade program,
Bartram, Hou, and Kim (2022) also document a modest impact on public firms
as financially constrained public firms are likely to move their emissions out of
California into other states. We complement these papers by showing that the
effects of cap-and-trade programs on privately held companies’ debt structure
are large.
An emerging literature investigates how climate policy risks affect
firm financing outcomes. Delis, de Greiff, Iosifidi, and Ongena (Forthcoming)
show that fossil fuel firms with reserves in countries that score high on climate
policy indices face higher interest rates on syndicated loans following the
adoption of the Paris Climate Agreement of 2015. Seltzer, Starks, and Zhu
(2022) find that the corporate bonds of firms with poor environmental
profiles that operate in U.S. states with stricter environmental regulations
pay higher yields and receive lower credit ratings after the Paris Climate
Agreement.4 Antoniou, Delis, Ongena, and Tsoumas (2022) show that when
firms are able to store pollution permits, their cost of debt can decrease

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

1. Background
Cap-and-trade programs are a key policy tool for transitioning to a lowercarbon economy. Cap-and-trade programs cap total GHG emissions at a
threshold that decreases over time. However, a cap-and-trade program does not
explicitly set a price on carbon. Firms get allocated emission permits or need to
purchase permits at auctions or the secondary market. The goal of a cap-andtrade program is to reduce total GHG emissions but let market mechanisms
determine the price on carbon.
1.1 California cap-and-trade bill
The most significant cap-and-trade bill that has been implemented in the United
States is California’s cap-and-trade program (see, e.g., Bartram, Hou, and Kim
(2022)). Another significant cap-and-trade program implemented in the
United States in 2009 is the U.S. Regional Greenhouse Gas Initiative that
covers a number of northeastern states but only caps emissions of utilities.
California’s cap-and-trade program is the only mandatory cap-and-trade
program introduced in any state within the United States. that covers the
majority of firms with high GHG emissions across industries.
The program requires all facilities with emissions of more than 25,000 metric
tons of carbon dioxide equivalents (CO2e) per year to obtain allowances for

(2021); Pástor, Stambaugh, and Taylor (2022). Finally, Chava (2014); Chen, Hsieh, Hsu, and Levine (2022);
Hsu, Li, and Tsou (2023) relate firms’ financing to their general environmental profile.
5 Papers that focus on nonenvironmental policies and firm financing are, for example, Alimon (2015);

Qiu and Shen (2017); Ivanov, Pettit, and Whited (2022). They find that regulations introducing additional costs
for corporate borrowers, such as labor protection laws or higher corporate taxation, lead to higher loan spreads,
tighter nonprice loan terms, and more diffuse loan ownership structure. Bae and Goyal (2009) find that weaker
legal protection is linked to tighter financial conditions.

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in the future if they preemptively acquire permits. Oehmke and Opp (2023)
develop a theoretical model and find that capital regulations in response to
climate risks can address financial risks but not necessarily reduce emissions.
Kacperczyk and Peydró (2022) study bank lending to polluting firms following
bank commitments to decarbonization. Other papers focus on the impact of
physical climate risks on the municipal bond or bank lending markets (Painter
2020; Goldsmith-Pinkham et al. 2023; Correa et al. 2023).
Our paper contributes to this literature in two major ways. First, we study
the response of firm financing to the introduction of two well-defined and
legally binding regulatory frameworks intended for transition to a lowercarbon economy.5 Second, our data allow us to distinguish between public
and private firms and to comprehensively measure debt contract structure in
addition to price for bilateral and syndicated bank lending, which is crucial
for understanding how banks manage their exposure around climate change
legislation.

The Review of Financial Studies / v 37 n 5 2024

6 See https://www.arb.ca.gov/regact/2010/capandtrade10/capandtrade10.htm.
7 See https://ww2.arb.ca.gov/our-work/programs/cap-and-trade-program.
8 Our conversations with the California Air Resources Board confirmed that the range of industries included in

the cap-and-trade regulation is so wide that virtually all facilities in California that emit more than 25,000 metric
tons of carbon dioxide equivalents per year are part of the cap-and-trade program. A list of the covered industries
can be found online (https://ww2.arb.ca.gov/sites/default/files/classic//cc/capandtrade/guidance/chapter2.pdf).
9 The economic analysis can be found online (https://ww2.arb.ca.gov/sites/default/files/barcu/regact/2010/capand

trade10/capv4appn.pdf).

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their emissions. Carbon dioxide equivalents are defined as the quantity of
carbon dioxide that for a given amount of GHGs or mixture of GHGs would
generate the same global warming potential. The regulation was approved by
the Office of Administrative Law on December 22, 2011.6 The California
Air Resources Board administers the cap-and-trade program and collects
and verifies data reported by each emissions facility through the Mandatory
Reporting Regulation program.7 Each firm receives some quantity of free
allowances to emit GHGs and must purchase the remaining allowances for their
operations from quarterly auctions or through other secondary market means.
The first phase of the program was implemented on January 1, 2013, and
covered all emitting firms other than fuel suppliers. Fuel suppliers were covered
starting on January 1, 2015. The few fuel suppliers operating in California, such
as Chevron and ExxonMobil, are generally large public firms. The covered
facilities come from a wide range of industries, such as cement producers,
electricity generation, and petroleum refining.8 The program’s emissions cap
was set to decrease by 2% annually in 2013 and 2014 relative to the emissions
level forecast for 2012. For subsequent years, the emissions cap was set to
decrease by 3% annually relative to the realized emissions level in 2012. The
goal of the cap-and-trade program was for California to return to 1990 emission
levels by 2020.
At the time of regulation enactment at the end of 2011, the expected
compliance costs for firms covered by the cap-and-trade program were highly
uncertain. The California Air and Resources Board released an economic
analysis ahead of the final vote stating on page 12 that: “Given the uncertainties
about the nature of these factors [for example, ease of switching to low-GHG
methods of production and pace of technological progress], it is impossible
to predict with precision the allowance price. ... In 2010, ARB conducted a
joint analysis of the AB 32 Climate Change Scoping Plan with Charles River
Associates and Professor David Roland-Holst of the University of California
Berkeley. The estimated price of CO2 in these three analyses ranged from about
$20/MTCO2e to $100/MTCO2e in 2020.”9
While this cap-and-trade program only covers a single state, the economic
activity in California is considerable. California had a GDP of $2.1 trillion
in 2012, and if California was a sovereign country, its economy would have

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

ranked in the top 10 of the largest economies in the world.10 Therefore, the
introduction of the California cap-and-trade program allows us to study the
response of corporate lending to a major economy transitioning away from
fossil fuels.

1.3 Climate policy and bank lending
The passage of cap-and-trade legislation increases the credit risk of polluting
borrowers. The credit risk framework, widely used in academia, industry, and

10 This is based on data from the Bureau of Economic Analysis (https://www.bea.gov/data) and the International

Monetary Fund (https://www.imf.org/en/Publications/WEO/weo-database/2022/October).
11 See https://www.congress.gov/bill/111th-congress/house-bill/2454/text.
12 The Economic Consequences of Waxman-Markey: An Analysis of the American Clean Energy and

Security Act of 2009, August 6, 2009. (https://www.heritage.org/environment/report/the-economicconsequences-waxman-markey-analysis-the-american-clean-energy-and).
13 Estimated Costs to Households From the Cap-and-Trade Provisions of H.R. 2454, June 20, 2009.

(https://www.cbo.gov/publication/24918).

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1.2 Waxman-Markey cap-and-trade bill
At the U.S. federal level, no GHG cap-and-trade program has yet been
implemented. The cap-and-trade program that came closest to passage was part
of the American Clean Energy and Security Act of 2009, also known as the
Waxman-Markey bill.11 The bill passed the U.S. House of Representatives on
June 26, 2009, and had a high probability of becoming law, while Democrats
held both a filibuster-proof majority in the Senate and the presidency. The bill
ultimately failed to pass in the Senate on July 22, 2010.
The centerpiece of the Waxman-Markey bill was a cap-and-trade program
in which the total amount of GHG emissions in a given year would be capped
relative to GHG emissions in 2005. The cap was set at 3%, 17%, 42%,
and 83% below the 2005 emissions level by 2012, 2020, 2030, and 2050,
respectively. Importantly for the identification strategy discussed in Section
3.2, approximately 15% of all emissions permits to emit GHG would be
given for free to selected manufacturing firms covered by the cap-and-trade
regulation.
At the time, the effect of the Waxman-Markey bill on firms as well as the
associated economic costs were highly uncertain. While under consideration by
the U.S. Congress, various sources reported widely diverging cost estimates,
reflecting the high uncertainty of the impact of the bill on firms. For example,
the Heritage Foundation estimated that: “Cumulative gross domestic product
(GDP) losses are $9.4 trillion between 2012 and 2035.”12 In addition, the
Congressional Budget Office estimated that “...the net annual economy wide
cost of the cap-and-trade program in 2020 would be $22 billion or about $175
per household.”13

The Review of Financial Studies / v 37 n 5 2024

bank regulation,14 defines expected loan loss from the perspective of the lender
as:
ExpectedLoss = P D ×LGD ×EAD,

(1)

14 See, for example, Plosser and Santos (2018) and Leitner and Yilmaz (2019), and a detailed description of

the Basel II capital framework (https://www.bis.org/publ/bcbs107.pdf) and its application to the U.S. setting
(https://www.federalreserve.gov/generalinfo/basel2/FinalRule_BaselII/).

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where P D denotes the firm’s probability of default, LGD denotes the loss
given default, and EAD denotes the lender’s exposure to the firm at default.
The cap-and-trade program can lead to a higher P D and LGD, which increase
expected loan losses.
The cap-and-trade program can reduce a firm’s cash flow because a price
on carbon increases its operating costs. The cap-and-trade program could also
increase the variance of cash flow. Importantly, both lower expected cash flow
and higher cash flow variance increase the likelihood that a firm’s cash flow
falls below the default threshold, leading to higher P D (Trueman and Titman
1988; Minton and Schrand 1999; Acharya, Davydenko, and Strebulaev 2012).
These adverse changes in the distribution of cash flow are also likely to affect
loan recovery rates in the event firms default. To the extent that the cap-andtrade program erodes the financial health of a large fraction of firms in polluting
industries, the collateral value of these firms is also likely to decline due to a
decrease in the resale value of, for example, equipment, which can also increase
LGD, ultimately increasing expected losses to the lender (Shleifer and Vishny
1997; Benmelech and Bergman 2011).
Right after the passage but before the implementation of a cap-and-trade
bill, it is unknown how binding the emissions cap would be for covered firms.
Lenders and firms are not (fully) aware of the extent to which firms would
have to modify production processes to reduce emissions, purchase emission
allowances to maintain current levels of emissions, or do both. Additionally,
the price of emissions allowances is still unknown at the time of bill passage,
because the cap-and-trade program does not set an explicit price but lets
the market determine it. As discussed in Sections 1.1 and 1.2, official cost
estimates and public commentary suggest that the impact on firms was highly
uncertain at the time of passage for both cap-and-trade bills.
Because of these unknowns, banks have to insure against the states of the
world in which the adverse effects on cash flow are substantial. The passage
of a cap-and-trade bill makes these states more likely. Lenders might cut credit
or renegotiate the loan contracts of affected firms to gain flexibility to reduce
exposure in the future, that is, to reduce EAD. The analysis in this paper
focuses on how banks manage EAD in response to realizations of transition
risk.

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

2. Data
In this section, we discuss the data used to analyze the impact of the cap-andtrade bills on corporate lending. The variables in our analyses are also described
in Table A1 in the appendix.

15 For more details of the Y14 data, see https://www.federalreserve.gov/apps/reportingforms/Download/Download

Attachment?guid=c4ef7d8e-9242-4384-bd8c-fe458e753bb2.

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2.1 Credit data
Our analysis combines GHG emissions data from the EPA with corporate
lending data from Y14 and SNC. Both data sets cover bank borrowing of a
wide range of private and public firms. The California cap-and-trade program
was signed into law in 2011 and implemented in 2013, which allows us to
use the Y14 data, spanning 2011 to present, for this analysis. These data
provide information on interest rates and capture bilateral lending in addition
to syndicated lending (the SNC data only capture the latter). In other words,
the Y14 data also allow us to observe smaller firms that are typically reliant
on bilateral lending. We use the SNC data for the Waxman-Markey analysis as
the bill was under consideration by the U.S. Congress in 2009-2010, when the
Y14 data are not available. In addition, while we can utilize the longer-time
series SNC data for the analysis of the California cap-and-trade bill, a number
of high GHG-emitting firms in California borrow only bilaterally, and are thus
not covered by the SNC Program.
The Y14 data come from Schedule H.1 of the Federal Reserve’s Y14Q
Collection, which covers 30 banks in the United States with total assets
exceeding $50 billion during our sample period. Banks provide granular loanlevel data on their corporate loans whenever a loan exceeds $1 million in
commitment amount, together with associated financial statement information
of the borrower (whenever available). For each loan facility, the Y14 reports
the identity of the borrower, loan commitment amount and type, loan interest
rate, origination date, maturity date, drawn amount in the case of credit
lines, and bank internal borrower rating. We exclude government entities,
financial firms, real estate firms, and offices of bank holding companies. We
also exclude capitalized lease obligations, fronting exposures, commitments
to commit, other real estate owned and other assets. Further, we discard
loans that are guaranteed by the federal government, associated with special
purpose vehicles, in default, not fully syndicated, for which the information
on commitment amount is missing, which remain outstanding on banks books
after maturity, or have remaining maturities exceeding 9 years. We winsorize
the variables other than the term loans ratio at the 1% level. Table 1 presents
the summary statistics for the Y14 data used in the analysis of the California
cap-and-trade bill.15

The Review of Financial Studies / v 37 n 5 2024

Table 1
Summary statistics for the California cap-and-trade bill analysis
Observations

Firms

Mean

SD

P10

P50

P90

2,929
1,418
2,929
2,929
2,929
2,929
1,046
1,136
1,119

878
538
878
878
878
878
699
734
736

327.960
3.126
34.234
0.152
0.518
0.067
3.496
8.331
12.375

549.367
1.660
18.389
0.266
0.500
0.229
10.116
12.112
8.931

7.400
1.360
7.061
0.000
0.000
0.000
−5.269
0.176
3.857

109.089
2.750
37.553
0.000
1.000
0.000
2.972
3.496
10.706

953.498
5.500
56.200
0.532
1.000
0.102
13.133
22.529
22.857

410
196
410
410
410
410
158
166
165

127
77
127
127
127
127
109
112
112

624.782
3.103
31.175
0.172
0.385
0.480
3.344
11.362
11.992

858.426
1.678
18.903
0.292
0.487
0.419
8.026
16.792
8.253

10.043
1.391
5.063
0.000
0.000
0.017
−5.116
0.247
3.315

203.557 1,963.848
2.819
5.257
33.189
55.735
0.026
0.633
0.000
1.000
0.309
1.000
3.093
10.046
4.329
29.414
10.802
21.164

A. Full sample

B. Firms with California emissions
Committed credit (in m US$)
Interest rates (in %)
Remaining maturity (in months)
Share of term loans
Private
CA emissions share
CapEx/Assets (in %)
Cash/Assets (in %)
EBITDA/Assets (in %)

This table reports the summary statistics of the firms included in our sample in our analysis of California’s capand-trade bill. The data are quarterly, except the balance sheet variables, which are at an annual frequency. For
each variable, the panels show the total observations and unique firm count, mean, standard deviation, and 10th ,
50th , and 90th percentiles.

The SNC data come from regulatory reporting associated with the SNC
Program, an inter-agency agreement among the three main federal banking
regulators—the Federal Reserve System, the Federal Deposit Insurance
Corporation, and the Office of the Comptroller of the Currency—to monitor
the syndicated loan market.16 The SNC program covers all syndicated
commitments that exceed $20 million and are held by three or more supervised
institutions as of the end of each calendar year, which accounts for virtually the
entire syndicated loan market in the United States.
The SNC data set contains loan-specific information as of the end of
each calendar year from 1992 through 2012. For each loan facility, the data
provide the identity of the borrower, including name, industry, and location,
loan type, loan commitment amount, origination date, maturity date, drawn
amount in the case of credit lines, and bank internal borrower rating. The SNC
data provide a unique opportunity to examine lender responses to cap-andtrade policies because they have complete coverage of the lending syndicate,
including shadow bank participation over the life of each loan. Unlike the Y14
data, the SNC data do not contain information on whether a firm is publicly
listed. We map SNC data to the historical Compustat data set to determine

16 SNC

Program description and guidelines dated May 5, 1998,
(https://www.occ.gov/news-issuances/bulletins/1998/bulletin-1998-21.html).

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Committed credit (in m US$)
Interest rates (in %)
Remaining maturity (in months)
Share of term loans
Private
CA emissions share
CapEx/Assets (in %)
Cash/Assets (in %)
EBITDA/Assets (in %)

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 2
Summary statistics for Waxman-Markey cap-and-trade bill analysis
A. Baseline bandwidth
Mean

SD

P10

P50

P90

414
414
414
143
414

467.161
34.993
0.264
0.441
0.568

671.574
17.064
0.376
0.498
0.496

45.000
13.510
0.000
0.000
0.000

216.915
34.775
0.000
0.000
1.000

1,279.458
56.327
0.947
1.000
1.000

236
236
236
105
236

60
60
60
38
60

B. Wide bandwidth

Committed credit (in m US$)
Remaining maturity (in months)
Share of term loans
Cash flow covenant
Private

Lead
Obs. Firms banks

Mean

SD

P10

P50

P90

805
805
805
264
805

470.035
34.741
0.247
0.496
0.532

684.228
15.978
0.365
0.501
0.499

47.153
14.093
0.000
0.000
0.000

211.491
34.500
0.000
0.000
1.000

1,250.000
54.720
0.903
1.000
1.000

469
469
469
196
469

75
75
75
49
75

C. Lender-firm exposure (0 to 1)

Baseline bandwidth
Wide bandwidth

Obs.

Firms

Lenders

Mean

SD

P10

P50

P90

19,358
38,121

236
469

2,891
3,975

0.040
0.035

0.142
0.127

0.000
0.000

0.005
0.005

0.057
0.054

This table reports the summary statistics of the firms included in our sample for the Waxman-Markey cap-andtrade bill analysis. The data are annual. Panels A and B show the data for the firm-level analysis within the two
bandwidths described in Section 3.2. Panel C shows the data for the lender-firm-level analysis in Section 5.1.
For each variable, the panels show the total number of observations, unique firm and lead bank/lender count,
mean, standard deviation, and 10th , 50th , and 90th percentiles.

public status in 2009. We winsorize variables other than ratios at the 1% level.
Table 2 presents the summary statistics for the SNC data used in the analysis
on the Waxman-Markey bill.
2.2 Greenhouse gas emissions
Since 2010, the EPA requires each production facility emitting more
than 25,000 metric tons of carbon dioxide equivalents per year to
report their emissions. The covered GHGs are carbon dioxide, methane,
nitrous oxide, and fluorinated GHGs. These data are publicly available
(https://www.epa.gov/ghgreporting), cover a wide range of industries, and
account for a substantial share of total U.S. emissions. Nearly 8,000 facilities
that belong to direct GHG emitters are required to annually report their
emissions, accounting for 3 billion metric tons of carbon dioxide equivalents
or roughly 50% of total U.S. GHG emissions as of 2012.17 To measure lending
to high GHG-emitting firms, we map firms in the EPA data to firms in the loan

17 The EPA data set also details the emissions of indirect GHG emitters. These facilities, such as large gas stations,

produce materials resulting in more than 25,000 metric tons of emissions when combusted. We exclude indirect
emitters (fuel suppliers) from our analysis because they were not covered at the start of the California cap-andtrade program (see Section 1.1).

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Committed credit (in m US$)
Remaining maturity (in months)
Share of term loans
Cash flow covenant
Private

Lead
Obs. Firms banks

The Review of Financial Studies / v 37 n 5 2024

3. Empirical Strategy
We examine the impact of the two cap-and-trade bills on firms’ credit
contracts along the following major dimensions: the firm’s total loan
commitments, commitment-weighted average remaining loan maturity, term
loan commitments as a share of total commitments, and the commitmentweighted average interest rates. Loan interest rates are only available in the
Y14 data used in the California analysis. Our analysis is conducted at the firm
level because the renegotiation process typically affects all loans to a given
borrower.

Figure 1
Emissions by county
This figure shows the 2012 GHG emissions by county based on the EPA data on high GHG-emitting firm
facilities. Only GHG emissions from firms in the Y14 data are included. Darker-shaded counties represent higher
emissions.

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data using the name and ZIP code of the parent company of each GHG-emitting
facility. As we use a fuzzy name match technique, we verify each potential
match manually. Internet Appendix Table IA-7 presents summary statistics by
year for the matched sample.
The California cap-and-trade program also covers emissions from California
electricity importers that occur out of the state and cannot be identified in the
EPA data. To capture these emissions, we obtain data from the California Air
and Resources Board.
Figure 1 depicts the county-level distribution of high GHG-emitting firms in
our Y14 sample as of 2012. For each county, we sum up the GHG emissions
of all facilities in that county. The figure shows that a substantial number of
high GHG-emitting facilities are located in California, as indicated by the large
number of darker-shaded counties. This geographic distribution suggests that
our analysis of California’s cap-and-trade regulation likely provides valuable
insights into the effect of carbon pricing policies on firm financing.

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

3.1 Research design for the California bill
We first test how the passage of California’s cap-and-trade bill affects the
availability and the terms of credit extended to firms covered by the cap-andtrade program. We use a difference-in-differences specification, in which we

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We test whether lenders reduce exposure to high GHG-emitting firms
to limit the expected loss on loans. Second, we test whether banks gain
additional flexibility to cut credit in the future. Shortening loan maturity
allows banks to maintain flexibility and greater bargaining power during loan
renegotiation (Flannery 1986; Diamond 1991; Rajan and Winton 1995). In
addition, banks can gain additional flexibility by lending via credit lines instead
of term loans, as credit lines generally have tight financial covenants and
their availability is conditional on firms maintaining high cash flow (Sufi
2009; Acharya et al. 2014). Further, Greenwald, Krainer, and Paul (2021) and
Chodorow-Reich et al. (2022) show that smaller firms may lose access to credit
lines in times of stress. Finally, lenders could also increase loan interest rates
as a compensation for lending to affected firms.
Bank lenders should have the ability to quickly respond to a cap-and-trade
bill because loan renegotiation occurs frequently. Roberts and Sufi (2009) and
Roberts (2015) show that, on average, commercial loans are renegotiated
once every 9 months, significantly changing contract terms, such as amounts,
maturities, interest rates, or financial covenants. Renegotiation is frequent for
a number of reasons. Financial covenants in loan contracts are set tightly and
are likely to be tripped, forcing renegotiations (Dichev and Skinner, 2002).
Additionally, firms can initiate loan renegotiation to ensure the ability to
take on investment projects. For example, capital expenditure covenants are
typically set tight and frequently renegotiated to allow firms to change current
investment projects or undertake new investments (Nini, Smith, and Sufi,
2009). Firms may also renegotiate debt contracts to relax borrowing base
restrictions and ensure availability under credit lines tied to accounts receivable
or inventory. We expect that whenever renegotiation happens around the
passage of a cap-and-trade bill, lenders are likely to require stricter loan
terms for firms covered by the cap-and-trade program. While firms may have
incentives to renegotiate less during times of an impending cap-and-trade
program, the highly state-contingent nature of bank loans described above is
unlikely to allow firms to significantly reduce renegotiation.
Importantly, changes to loan contract terms represent an equilibrium
outcome arrived at during the negotiation process between banks and firms.
While banks might try to gain additional flexibility to renegotiate contracts
in the future, firms would bargain for contract terms that are more likely to
insulate them at least in part against the uncertainty of operating under a capand-trade program. Therefore, the direction and magnitude of changes in loan
contract terms in response to the introduction of cap-and-trade programs is
ultimately an empirical question.

The Review of Financial Studies / v 37 n 5 2024

where ki denotes a facility of firm i, and Iki ∈CA is an indicator variable for
whether facility ki is located in California. This variable measures treatment
intensity as a firm with higher share of its total emissions in California would
have to pay the carbon price for a greater share of its total emissions under
the program. We also discretize the continuous variable to define treatment
whenever a firm’s GHG emissions in California are at least 50% of its total
emissions. Figure 2 illustrates the identification strategy.
We estimate the following regression with data from the Y14 collection:
yi,q =λCA_Emissions_Sharei,q ×IPost CA bill +β1 CA_Emissions_Sharei,q
+β2 Controlsi,q +ψi +φq,ind +i,q ,

(3)

where the dependent variable of interest, yi,q is one of the major loan contract
terms described above for firm i in quarter q. We restrict the quarterly
sample to a pre-period and a post-period that include the third and the fourth
quarters of 2011 and 2012, respectively. As the coverage of our data starts
in the third quarter of 2011, we exclude the first two quarters of 2012 to
avoid quarterly seasonal variation in commercial lending as documented by
Murfin and Petersen (2016). CA_Emissions_Sharei,q denotes the emission
share calculated using the annual EPA data for the year of quarter q. We
show in Internet Appendix Table IA-5 that using only 2011 emissions data
leads to qualitatively similar results. The coefficient of interest, λ, is employed
to compare the changes in contract terms for treated firms around the bill’s
passage relative to those of the control firms. The second half of 2012 captures
the time period when both firms and lenders faced significant uncertainty
as to the effect of the cap-and-trade program on firms’ future profitability.
Importantly, because any bill that is passed by a legislative body is to some
extent anticipated, our estimates around the passage of the California capand-trade bill should be considered a lower bound for the actual effects of the
cap-and-trade program on loan terms.
Given that California’s cap-and-trade bill covers fuel-supply emissions only
starting in 2015 instead of 2013, we exclude fuel suppliers from our estimation
sample. The control variables include borrower rating fixed effects representing
the most conservative rating assigned to each firm by its bank lenders. Our
rating measure relies on banks’ internal ratings for each borrower converted to
a five-grade S&P scale (AAA/AA, A, BBB, BB, and B or lower). We include
industry-quarter fixed effects based on the four-digit NAICS code of each firm

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split firms into a treatment group and a control group based on the geographic
location of each firm’s GHG-emitting facilities.
We define cap-and-trade program treatment in terms of each firm’s GHG
emissions in California as a share of total firm emissions:
Ki
ki =1 F acilityEmissionski ×Iki ∈CA
, (2)
CA_Emissions_Sharei =
Ki
ki =1 F acilityEmissionski

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

to estimate treatment effects within a given industry, which is important as the
GHG emissions of a production process vary widely by industry. We use the
four-digit NAICS code to ensure a sufficient number of observations in each
industry.
3.2 Research design for the Waxman-Markey bill
A federal cap-and-trade program is likely to be more binding than a state-level
program because firms may be able to avoid a state regulation by relocating
activity out-of-state (Giroud and Rauh 2019; Bartram, Hou, and Kim 2022).
Meng (2017) shows that after the bill passed in the House, prediction markets
implied a considerable probability, close to 60%, of the bill also passing in
the Senate. Under Waxman-Markey, a subset of manufacturing firms covered
by the cap-and-trade regulation would have received approximately 15% of
total permits of the cap-and-trade program for free. Following Meng (2017),

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Figure 2
Identification strategy for the California cap-and-trade bill analysis
Panel A illustrates the identification strategy that assigns firm treatment by exploiting the share of GHG emissions
in California for the analysis of California’s cap-and-trade bill. In this example, we consider treated firms as those
having at least 50% of their GHG emissions in California. In our empirical analyses, we also use a continuous
measure of the share of GHG emissions in California. Panel B shows the relevant pre/post timeline for the
analysis.

The Review of Financial Studies / v 37 n 5 2024

yi,t = λIi∈T reated ×It=2009 +Controlsi,t +ψi +φt +γb +i,t ,

(4)

where the sample is limited to 2008 and 2009 (the “pre” and “post” periods)
and the coefficient of interest, λ, measures the relative change in the outcomes
of interest between the treatment and control groups. Treatment, Ii∈T reated ,
takes the value of one if firm i does not receive free permits under WaxmanMarkey and is zero otherwise. The dependent variables of interest are again a
firm’s remaining maturity, share of term loans, and the natural log of a firm’s
total loan commitments. We consider two bandwidths around the free permit
threshold of 5% energy intensity. The baseline bandwidth includes firms
in six-digit NAICS manufacturing industries that have an energy intensity
between 2% and 8%. The wide bandwidth includes firms in six-digit NAICS
manufacturing industries with an energy intensity between 1% to 9%. Internet
Appendix Table IA-11 shows the energy intensity distribution across sectors.
The inclusion of firm and time fixed effects in the regression subsume the
uninteracted terms Ii∈T reated and It=2009 . The controls differ slightly from those
18 Energy intensity is defined in SEC.763(b)(2)(A)(ii)(II) of the Waxman-Markey bill as “... dividing the cost of

purchased electricity and fuel costs of the sector by the value of the shipments of the sector, ...”. Trade intensity
is defined in SEC.763(b)(2)(A)(ii)(II) of the Waxman-Markey bill as “... calculated by dividing the value of the
total imports and exports of such sector by the value of the shipments plus the value of imports of such sector,
...”.
19 The trade intensity threshold conditional on being above the 5% energy intensity threshold leaves too few

observation for a separate analysis (Meng, 2017).
20 The free permits are supposed to cover the firms cost from direct emissions and increased expenditures for

electricity until 2026, when they would be phased out. To the extent that firms receiving free permits are affected
by the cap-and-trade program through other channels, our estimates present a lower bound for the impact of
the cap-and-trade program on loan terms. Further, the phase out of the free permits in 2026 is unlikely to affect
creditor decisions in 2009, as the average maturity of syndicated loans is only around 3 years.

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we use this distinct feature of the bill granting free permits to manufacturing
sectors (based on six-digit NAICS codes) that had an energy intensity of at
least 5% and trade intensity of at least 15% between 2004 and 2006.18 This
feature of the bill allows us to estimate a difference-in-differences regression
constructing the treatment and control groups with firms close to the 5% energy
intensity threshold as certain manufacturing sectors fall just below and just
above the 5% energy intensity threshold, while being above the 15% trade
intensity threshold.19 Specifically, firms that do not receive free permits should
pose greater credit risks than firms that are granted free permits.20 Figure 3
illustrates our identification strategy.
We use the SNC data for this analysis. Given these data are annual and
reported as of year-end, we estimate a baseline regression with two time
periods, 2008 and 2009. At the end of 2008, the Waxman-Markey bill had not
been introduced in either chamber of the U.S. Congress. At the end of 2009,
the Waxman-Markey bill had just passed in the House of Representatives and
was under consideration by the U.S. Senate.
Our baseline regression is a difference-in-differences specification that takes
the following form:

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

in Equation (3) due to differences in the underlying data. The annual SNC
data only include firm ratings assigned by the lead lender (the administrative
agent) in the supervisory five-grade ratings scale. Therefore, we include
indicator variables that take the value of one whenever at least some fraction
of the commitments to a borrower are rated “special mention,” “substandard,”
“doubtful,” and “loss,” respectively, by the lead bank with “pass” being the
omitted category. As the lead bank is the primary relationship-holder with the
borrower in the syndicated loan market, we also include lead bank fixed effects.
We show in Internet Appendix Table IA-9 that omitting the lead bank fixed
effects leads to qualitatively similar results.
4. Baseline Results
In this section, we present our baseline estimates and discuss how the two capand-trade bills affect corporate lending to the covered firms.

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Figure 3
Identification strategy for the Waxman-Markey bill analysis
Panel A illustrates the identification strategy that assigns firm treatment by exploiting the free permit threshold
based on energy intensity for the analysis of the Waxman-Markey cap-and-trade bill. Firms below the 5% energy
intensity threshold do not receive free permits and are treated. We also conduct analyses allowing for differential
effects by energy intensity across the treated firms. Panel B shows the relevant pre/post timeline for the analysis.

The Review of Financial Studies / v 37 n 5 2024

Table 3
California’s cap-and-trade bill and credit
(1)

(2)

(3)

(4)

A. Log committed credit
CA_Emissions _Sharei ×IPost CA bill

−0.133
(0.113)

ICA_Emissions_Sharei ≥50% ×IPost CA bill

Observations
Adj R 2

−0.119
(0.111)
−0.122
(0.108)

2,929
.937

2,929
.937

−0.098
(0.102)

2,929
.938

2,929
.938

B. Remaining maturity (in months)
CA_Emissions _Sharei ×IPost CA bill

−4.514∗
(2.715)

ICA_Emissions_Sharei ≥50% ×IPost CA bill

Observations
Adj R 2

2,929
.659

−5.001∗∗
(2.506)

2,929
.660

−4.723∗
(2.641)

2,929
.659

−5.137∗∗
(2.391)

2,929
.660

C. Term loans share (0 to 1)
CA_Emissions _Sharei ×IPost CA bill

−0.220∗∗
(0.102)

ICA_Emissions_Sharei ≥50% ×IPost CA bill

Observations
Adj R 2

−0.219∗∗
(0.096)

−0.225∗∗
(0.099)

−0.225∗∗
(0.095)

2,929
.554

2,929
.558

2,929
.555

2,929
.559

No
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

For all panels
Controls
Uninteracted variables
Firm FE
Industry-quarter FE

This table reports estimates from Equation (3). The dependent variables are the log committed credit in panel
A, maturity (in months) in panel B, and the term loans share of total committed credit (0 to 1) in panel C.
IPost CA bill is an indicator variable that takes the value of one for the third or fourth quarter of 2012 and zero
for the third or fourth quarter of 2011. CA_Emissions _Sharei is a continuous variable (0 to 1) measuring a
firm’s California GHG emissions as a share of the firm’s total GHG emissions. ICA_Emissions_Sharei ≥50% is an
indicator variable that takes the value of one if the firm has at least 50% of its total GHG emissions in California
and zero otherwise. Firm and industry-quarter fixed effects are included. Uninteracted independent variables are
included in the regression or absorbed by fixed effects. Standard errors are clustered by industry and are reported
in parentheses. *p < .10; **p < .05; ***p < .01.

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4.1 California’s cap-and-trade bill and credit terms
We first examine how the passage of California’s cap-and-trade bill affects
firms’ loan contracting outcomes. Table 3 reports the estimates of Equation (3)
for all three outcomes of interest. Panel A shows that the loan commitments
coefficients are negative but insignificant with or without controls. This result
suggests that banks do not manage their exposure by immediately cutting credit
to firms with a high share of their GHG-emissions in California.
Panel B shows negative and significant estimates on the remaining maturity
(in months) of affected firms after the passage of the bill. The remaining
maturity of firms with a substantial share of their GHG emissions in California

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

4.1.1 Private and public firms The results in Table 3 show that banks
actively manage risks introduced by the cap-and-trade bill through the loan
contracting process, leading to less borrower-friendly loan terms. When
designing cap-and-trade programs, it is also important to understand potential
heterogeneity in banks’ responses. To do so, we examine whether private firms
are differentially affected compared to public firms.
While data on public firms are readily available through mandatory public
disclosures, our regulatory data sets are unique in their extensive coverage of
private firms. To our knowledge, we are the first to study the effects of climate
policy risks on corporate lending to private and public firms. In the emerging
climate finance literature, private firms are typically ignored because of a lack
of data. Exceptions are Shive and Forster (2020), who investigate private firms’
emissions based on Capital IQ data, which are available for larger private

21 The vast majority of loans in the Y14 data are either term loans or credit lines, as well as other types of

commitments, such as demand loans. To ensure that the reduction in term loans comes from an increase in
credit lines, in unreported tests we estimate the regression in Equation (3) with credit line share as the outcome
variable and find the increase in the credit line share to be very similar to the decrease in the term loans share.

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decreases by 4 to 5 months. This decrease is economically significant as the
average maturity in our sample is approximately 30 months, as shown in Table
1. We also find a negative and statistically significant effect on firms’ reliance
on term loans (panel C). Term loans as a share of total commitments decreases
by about 0.23 for firms with substantial GHG emissions in California, which
suggests that banks gain flexibility to potentially reduce exposure to such firms
by substituting permanent financing with cash flow contingent financing.21
Importantly, the changes in maturity are not driven by the shift from term
loans to credit lines. Internet Appendix Table IA-2 provides the results of the
maturity regression with the sample restricted to term loans, and we find
even stronger effects. This finding is consistent with banks perceiving their
exposure to the term loans of firms with a large share of their GHG emissions
in California as riskier than the credit lines of these firms.
Bartram, Hou, and Kim (2022) show that financially constrained public
firms shifted some of their GHG emissions out of California after the implementation of the cap-and-trade program. Consequently, it is important to assess
whether industries that are less able to “export” emissions across state lines
face tighter loan terms. The industry for which avoiding the price on carbon
is arguably the most challenging is electricity generation, because electricity
imports—electricity generated outside of California but sold in California—are
also covered by the cap-and-trade program. In Internet Appendix Table IA-4,
we present results that show how for the subsample of electricity generators, the
log commitment to electricity generators in California decreases by over 20%
after the enactment of the cap-and-trade bill, and this decrease is statistically
significant.

The Review of Financial Studies / v 37 n 5 2024

22 See Tabuchi (2021).
23 See

https://business.edf.org/insights/transferred-emissions-risks-in-oil-gas-ma-could-hamper-the-energytransition/.

24 See https://ww2.arb.ca.gov/resources/documents/faq-cap-and-trade-program#ftn24.

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firms that issue publicly traded debt. Our sample comprehensively covers a
wider range of private firms regardless of public capital markets access. Also,
De Haas and Popov (2023) analyze the emissions of Belgian firms around an
exogenous shock to the cost of equity and find that they reduce their emissions
after going public.
A cap-and-trade program is likely more expensive for private firms than for
public ones for several major reasons. First, private firms could be significantly
less emissions-efficient than their public counterparts due to limited disclosures
and regulation. Anecdotal evidence is consistent with this notion. According
to The New York Times in June 2021: “Oil and gas giants are selling off their
most-polluting operations to small private companies. Most manage to escape
public scrutiny.”22 Additionally, a report by the Environmental Defense Fund
in May 2022 states: “Assets [oil and gas] are flowing from public to private
markets at a significant rate.”23
We corroborate this idea using balance sheet information on private and
public firms from Y14. Based on these data, we construct three measures of
emissions inefficiency: total firm emissions divided by net sales, total assets,
or total debt. Figure 4, panels A–D, shows median emissions inefficiency as
of 2012 for both public and private firms in the four industries that account
for about 85% of our sample. All measures indicate that private firms are
substantially more emissions inefficient, emitting more GHGs per dollar of
revenue, assets, or debt than their public counterparts in the same industry.
Normalized emissions are about three times higher for private firms than public
firms across all four industries.
Second, size effects may also play a role in a differential impact of capand-trade programs on public and private firms. Private firms are smaller—the
median private firm in our sample has $600 million in assets compared $5,000
million for public firms. Thus, to the extent that there are economies of scale
in regulation compliance, such as upgrading old equipment or becoming more
emissions efficient, private firms may be more adversely affected by cap-andtrade programs. Indeed, the California Air and Resources Board concluded that
covered firms implemented process and efficiency upgrades in response to the
cap-and-trade program.24
Finally, private firms tend to be more financially constrained
than public firms (Hadlock and Pierce 2010; Saunders and Steffen
2011;
Mortal and Reisel
2013;
Erel, Jang, and Weisbach
2015;
Ivanov, Pettit, and Whited 2022). Therefore, cap-and-trade programs are
likely to adversely affect the already limited ability of private firms to obtain
the necessary funding from their lenders for their transition to a low emissions

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

A

B

Private

Public

0.9
0.8
0.7
0.6

0.4
0.3
0.2
0.1
0

C

Emissions/Revenues

Emissions/Assets

Emissions/Debt

D

Figure 4
Firm emissions inefficiency
This figure shows the median firm CO2e emissions (in kg) divided by revenues, assets, or debt (in $) in 2012 by
sector, for private and public firms separately.

regime. This can lead to additional bargaining power for bank lenders over
private firms during the loan negotiation process.
Given these substantial differences between private and public firms, in
Table 4 we present results separately for these two types of firms. We show that
the effects in Table 3 are concentrated within the subsample of private firms.
Private firms exhibit a weakly significant decrease in commitments (panel
A) but large and significant decreases in maturity (panel B) and term loan
share (panel C). Maturity decreases by 11 to 12 months for private firms with
substantial emissions in California as compared to 4 to 5 months for the full
sample. Similarly, the passage of the cap-and-trade bill translates to over 0.5
reduction in term loan share for private firms, roughly twice as large as in the
full sample.
By contrast, public firms see no change or even some improvement in credit
terms after the passage of the cap-and-trade program. For example, term loan
share increases significantly, while both commitments and remaining maturity
increase but are not statistically significant. These results are consistent

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0.5

The Review of Financial Studies / v 37 n 5 2024

Table 4
California’s cap-and-trade bill and credit for private and public firms
Private firms
(1)

(2)

Public firms

(3)

(4)

(5)

(6)

(7)

(8)

CA_Emissions _Sharei
×IPost CA bill

−0.334∗
(0.170)
−0.331∗∗
(0.167)

ICA_Emissions_Sharei ≥50%
×IPost CA bill

Observations
Adj R 2

−0.265
(0.161)

1,532
.902

0.067
(0.204)
−0.255
(0.157)

1,532
.902

1,532
.909

1,532
.909

0.080
(0.195)
0.117
(0.160)

1,397
.928

1,397
.923

0.130
(0.150)

1,397
.928

1,397
.924

B. Remaining maturity (in months)
CA_Emissions _Sharei −11.737∗∗∗
×IPost CA bill
(3.759)

−11.556∗∗∗
(3.640)

ICA_Emissions_Sharei ≥50%
×IPost CA bill

Observations
Adj R 2

−11.788∗∗∗
(3.914)

1,532
.724

1,532
.725

1.642
(2.857)

−11.461∗∗∗
(3.740)

1,532
.725

1,532
.725

1.984
(2.737)
0.203
(3.073)

1,397
.567

1,397
.567

0.593
(2.981)

1,397
.569

1,397
.569

C. Term loans share (0 to 1)
CA_Emissions _Sharei
×IPost CA bill

−0.522∗∗∗
(0.142)

−0.479∗∗∗
(0.135)

ICA_Emissions_Sharei ≥50%
×IPost CA bill

Observations
Adj R 2

−0.556∗∗∗
(0.126)

0.060∗∗
(0.024)

−0.510∗∗∗
(0.122)

0.060∗∗
(0.026)
0.050∗∗
(0.025)

0.052∗∗
(0.024)

1,532
.582

1,532
.586

1,532
.593

1,532
.596

1,397
.549

1,397
.549

1,397
.547

1,397
.547

No
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

No
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

For all panels
Controls
Uninteracted variables
Firm FE
Industry-quarter FE

This table reports estimates from Equation (3). The dependent variables are the log committed credit in panel
A, maturity (in months) in panel B, and the term loans share of total committed credit (0 to 1) in panel C.
IPost CA bill is an indicator variable that takes the value of one for the third or fourth quarter of 2012 and zero
for the third or fourth quarter of 2011. CA_Emissions _Sharei is a continuous variable (0 to 1) measuring a
firm’s California GHG emissions as a share of the firm’s total GHG emissions. ICA_Emissions_Sharei ≥50% is an
indicator variable that takes the value of one if the firm has at least 50% of its total GHG emissions in California
and zero otherwise. Firm and industry-quarter fixed effects are included. Uninteracted independent variables are
included in the regression or absorbed by fixed effects. Standard errors are clustered by industry and are reported
in parentheses. *p < .10; **p < .05; ***p < .01.

with lenders anticipating that private firms face a disproportionately larger
increase in operating costs than public firms as a result of the cap-and-trade
program, and that public firms are largely unaffected or might even benefit
from the adverse impact of the cap-and-trade program on their privately held
competitors.
It is difficult to empirically disentangle the extent to which the differential
effects between public and private firms are driven by firm ownership or

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A. Log committed credit

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

4.1.2 Interest rates Another key loan contract variable is the loan interest
rate. A bank might not only manage the expected loss of its loans to high
GHG-emitting firms by adjusting contract terms that allow them to mitigate
exposure at default if necessary but also require higher interest rates for such
loans. Given that the Y14 data provide information on loan interest rates, we
also estimate Equation (3) with weighted average loan interest rates paid by a
given borrower as the dependent variable. As interest rates in the Y14 data are
only reliably available for term loans, we estimate the interest rate regression
only for term loans. Table 5 shows that creditors price loans to private firms
with exposure to California’s cap-and-trade program higher, but we do not
find any effect for the subsample of public firms. The effect for private firms
is economically large with an estimated interest rate increase of up to 1.7
percentage points. For public firms, the interest rates stay the same, which
again suggests that banks expect public firms to be largely unaffected by the
cap-and-trade program. Overall, this result implies that banks require direct
compensation for bearing the risks related to the legislation in addition to the
increased contract flexibility.
4.2 The Waxman-Markey cap-and-trade bill and credit terms
In this section, we examine how loan contract terms respond to the passage
of the Waxman-Markey cap-and-trade bill in the House of Representatives as
described in Section 3.2. We report the estimates of Equation (4) in Table 6.
Overall, the difference-in-differences estimates of total credit commitments,
remaining maturity, and term loans share in panels A, B, and C, respectively,
are comparable to the effects we find in the California analysis and driven
by private firms. Credit commitments do not exhibit a differential response to
the bill for firms that fall below the free permit threshold. By contrast, private
firms just below the free permit threshold face a shortening of maturities of up
to 10 months relative to firms just above the threshold, which is considerable
given that the average maturity of loans to firms in the manufacturing sectors
near the free permit threshold is approximately 35 months over our sample

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size. Private ownership may allow firms to avoid market and regulatory
scrutiny, thereby reducing the incentives of private firms to improve emissions
efficiency. Also, private firms are more likely to be dependent on bank
financing because of a lack of access to public equity and bonds markets.
However, larger firms might be more emissions efficient because of the
economies of scale in production processes. Thus, the lack of adverse bank
financing effects among public firms may be a by-product of their size.
While the high correlation of size and public ownership makes it difficult to
disentangle the effects of the two, we show in Internet Appendix Table IA-6
that even the smallest public firms exposed to California’s cap-and-trade
program do not experience adverse changes to their lending terms. This finding
suggests that the results in Table 4 are at least partially driven by public status.

1,418
.733
Yes
Yes
Yes
Yes

0.798
(0.531)

(3)

1,418
.731
Yes
Yes
Yes
Yes

0.608
(0.420)

(4)

688
.820
No
Yes
Yes
Yes

688
.821
No
Yes
Yes
Yes

1.567∗∗
(0.689)
688
.834
Yes
Yes
Yes
Yes

(0.772)

(0.773)

(7)
1.661∗∗

(6)

1.606∗∗

(5)

Private firms

688
.835
Yes
Yes
Yes
Yes

1.598∗∗
(0.696)

(8)

730
.634
No
Yes
Yes
Yes

0.373
(0.947)

(9)

730
.633
No
Yes
Yes
Yes

0.022
(0.534)

(10)

730
.636
Yes
Yes
Yes
Yes

0.345
(0.838)

(11)

Public firms

730
.634
Yes
Yes
Yes
Yes

0.069
(0.487)

(12)

This table reports estimates from Equation (3) with the interest rate (in %) as the dependent variable. IPost CA bill is an indicator variable that takes the value of one for the
third or fourth quarter of 2012 and zero for the third or fourth quarter of 2011. CA_Emissions _Sharei is a continuous variable (0 to 1) measuring a firm’s California GHG
emissions as a share of the firm’s total GHG emissions. ICA_Emissions_Sharei ≥50% is an indicator variable that takes the value of one if the firm has at least 50% of its total
GHG emissions in California and zero otherwise. Only term loans are included in the sample. Firm and industry-quarter fixed effects are included. Uninteracted independent
variables are included in the regression or absorbed by fixed effects. Standard errors are clustered by industry and are reported in parentheses. *p < .10; **p < .05; ***p < .01.

1,418
.727
No
Yes
Yes
Yes

Observations
Adj R 2
Controls
Uninteracted variables
Firm FE
Industry-quarter FE

1,418
.729
No
Yes
Yes
Yes

0.577
(0.426)

0.858
(0.542)

ICA_Emissions_Sharei ≥50% ×IPost CA bill

CA_Emissions _Sharei ×IPost CA bill

(2)

Full sample

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1664

(1)

Table 5
California’s cap-and-trade bill and interest rates

The Review of Financial Studies / v 37 n 5 2024

414
.926

0.057
(0.073)

(1)

No
Yes
Yes
Yes

414
.640

−0.138∗∗
(0.066)

414
.656

−5.848
(4.001)

No
Yes
Yes
Yes

805
.641

−0.113∗
(0.064)

805
.703

−4.122
(3.708)

805
.930

0.063
(0.057)

(2)

Yes
Yes
Yes
Yes

414
.676

−0.123∗
(0.069)

414
.659

−6.062
(3.814)

414
.926

0.046
(0.073)

(3)

Yes
Yes
Yes
Yes

805
.643

−0.116∗
(0.061)

805
.704

−4.258
(3.676)

805
.930

0.071
(0.055)

(4)

No
Yes
Yes
Yes

223
.653

−0.279∗∗∗
(0.073)

223
.581

−9.995
(5.945)

223
.929

−0.035
(0.069)

(5)

No
Yes
Yes
Yes

393
.662

−0.238∗∗∗
(0.065)

393
.683

−8.115
(5.422)

393
.913

0.056
(0.068)

(6)

Yes
Yes
Yes
Yes

223
.704

−0.247∗∗∗
(0.068)

223
.603

−10.478∗
(5.230)

223
.930

−0.044
(0.065)

(7)

Private firms

Yes
Yes
Yes
Yes

393
.664

−0.230∗∗∗
(0.060)

393
.691

(4.966)

−8.474∗

393
.911

0.056
(0.066)

(8)

No
Yes
Yes
Yes

191
.655

0.021
(0.092)

191
.803

0.734
(2.857)

191
.873

0.120
(0.101)

(9)

No
Yes
Yes
Yes

412
.630

0.035
(0.080)

412
.740

2.265
(2.588)

412
.913

0.068
(0.076)

(10)

Yes
Yes
Yes
Yes

191
.654

0.018
(0.097)

191
.831

0.213
(2.674)

191
.871

0.128
(0.103)

(11)

Public firms

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1665

Yes
Yes
Yes
Yes

412
.659

0.023
(0.081)

412
.742

2.287
(2.675)

412
.917

0.083
(0.074)

(12)

This table reports estimates from Equation (4). The dependent variables are the log committed credit in panel A, maturity (in months) in panel B, and the term loans share of total committed credit
(0 to 1) in panel C. Ii∈T reated is an indicator variable that takes the value of one if the firm would not receive free permits under Waxman-Markey and zero otherwise. It=2009 is an indicator
variable that takes the value of one for year 2009 and zero for year 2008. The results are shown for all firms and the subsamples of private and public firms. Firm, year, and lead bank fixed
effects are included. Uninteracted independent variables are absorbed by fixed effects. Standard errors are clustered by industry and reported in parentheses. *p < .10; **p < .05; ***p < .01.

Controls
Firm FE
Year FE
Lead bank FE

For all panels:

Observations
Adj R 2

Ii∈T reatedW ide ×It=2009

Ii∈T reated ×It=2009

C. Term loans share (0 to 1)

Observations
Adj R 2

Ii∈T reatedW ide ×It=2009

Ii∈T reated ×It=2009

B. Remaining maturity (in months)

Observations
Adj R 2

Ii∈T reatedW ide ×It=2009

Ii∈T reated ×It=2009

A. Log committed credit

All firms

Table 6
Waxman-Markey cap-and-trade bill and credit
Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

The Review of Financial Studies / v 37 n 5 2024

yi,t =λ1 IEIi ∈[1,2) ×It=2009 +λ2 IEIi ∈[2,3) ×It=2009 +λ3 IEIi ∈[3,4) ×It=2009
+λ4 IEIi ∈[4,5) ×It=2009 +Controlsi,t +ψi +φt +γb +i,t ,

(5)

yi,t =λ1 IEIi ∈[1,3) ×It=2009 +λ2 IEIi ∈[3,5) ×It=2009
+Controlsi,t +ψi +φt +γb +i,t .

(6)

Panel A in Table 7 shows that firms in the 4% to 5% energy intensity
bucket face large and significant changes in maturity and insignificant impact
on term loan share, while firms in the lower energy intensity buckets face
large changes in term loan share and limited effect on loan maturity. Panel
B shows that the results are substantially stronger among private firms for both
regression specifications shown in Equations (5) and (6), respectively. Private
firms with the highest energy intensity below the free permit threshold face
reductions in both maturity and term loan share in addition to reductions in
loan commitments. These results are consistent with banks using different tools
to reduce exposure that vary with the expected impact of the cap-and-trade
program. Banks cut commitments to the most affected firms, while applying
reductions in term loans share and maturity more broadly to most other covered
firms.25
Because firms in our sample receive free permits based on energy intensity,
our difference-in-differences estimates could be confounded by developments
in the price of energy between 2008 and 2009. The narrow bandwidth around

25 Banks are known to actively and closely monitor firms, and thus, possess information unavailable to other

stakeholders (Diamond, 1984). We test whether the industries with the largest decrease in stock market valuations
due to the Waxman-Markey cap-and-trade bill, as measured by Meng (2017) and Meng and Rode (2019), also
experience the most stringent loan contracts and show in Internet Appendix Table IA-8 that the expectations of
the banks and stock market differ. To be able to conduct this analysis for private and public firms, we assume
that the heterogeneity of stock market expectations across industries is similar for private and public firms.

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period, as shown in Table 2. Additionally, for private firms below the free
permit threshold reliance on credit lines increases at the expense of term loans.
The difference is again economically significant as term loans share (credit
line share) is approximately 22-28 percentage points lower (higher) for firms
just below the free permit threshold than for those just above the threshold.
Syndicated loans in the SNC database are almost exclusively credit lines or
term loans, so an increase in the term loans share implies a lockstep decrease
in the credit lines share.
We also examine potential heterogeneity in the impact of the WaxmanMarkey bill on firms below the 5% free permit cutoff. Within the set of firms
that are just below the cutoff, those with higher energy intensities are more
likely to be affected by the cap-and-trade program as carbon pricing increases
energy expenditures for fuel and electricity. We estimate two specifications
that include separate coefficients for each energy intensity bucket below the
free permit threshold:

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 7
Waxman-Markey cap-and-trade bill and credit by energy intensity
Log committed

Remaining Maturity

Term loans share

(1)

(3)

(5)

(2)

(4)

(6)

IEIi ∈[1,2) ×It=2009
IEIi ∈[2,3) ×It=2009
IEIi ∈[3,4) ×It=2009
IEIi ∈[4,5) ×It=2009
IEIi ∈[1,3) ×It=2009

0.078
(0.055)
−0.014
(0.078)

IEIi ∈[3,5) ×It=2009

Observations
Adj R 2

−3.420
(3.727)
−5.268
(3.762)
−4.812
(4.138)
−7.380*
(3.759)

0.079
(0.056)
0.077
(0.072)
0.023
(0.078)
−0.111
(0.084)

805
.930

805
.930

805
.702

−4.148
(3.684)
−5.578
(3.937)

805
.703

−0.115∗
(0.065)
−0.111∗
(0.064)
−0.189∗∗∗
(0.061)
−0.058
(0.154)

805
.641

−0.113∗
(0.063)
−0.153∗∗
(0.072)

805
.642

B. Private firms
IEIi ∈[1,2) ×It=2009
IEIi ∈[2,3) ×It=2009
IEIi ∈[3,4) ×It=2009
IEIi ∈[4,5) ×It=2009
IEIi ∈[1,3) ×It=2009

0.149∗
(0.085)
−0.053
(0.070)
0.036
(0.090)
−0.189∗∗∗
(0.050)
0.068
(0.070)
−0.051
(0.091)

IEIi ∈[3,5) ×It=2009

Observations
Adj R 2

−7.188
(4.831)
−8.928∗
(5.301)
−15.208∗∗∗
(5.741)
−11.312∗∗
(4.823)

−7.854
(4.888)
−13.991∗∗
(5.486)

−0.217∗∗∗
(0.067)
−0.240∗∗∗
(0.067)
−0.281∗∗∗
(0.077)
−0.234∗∗∗
(0.053)

−0.226∗∗∗
(0.062)
−0.266∗∗∗
(0.065)

393
.913

393
.911

393
.690

393
.693

393
.657

393
.662

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

For all panels
Controls
Firm FE
Year FE
Lead bank FE

This table reports estimates from Equations (5) and (6). The dependent variables are the log committed credit,
maturity (in months), and the term loans share of total committed credit (0 to 1). IEIi ∈[a,b) is an indicator
variable that takes the value of one if the firm would not receive free permits under Waxman-Markey and the
energy intensity level of the firm is at least a% and less than b%, and zero otherwise. It=2009 is an indicator
variable that takes the value of one for year 2009 and zero for year 2008. The results are shown for all firms and
the subsample of private firms. Firm, year, and lead bank fixed effects are included. Uninteracted independent
variables are absorbed by fixed effects. Standard errors are clustered by industry and reported in parentheses. *p
< .10; **p < .05; ***p < .01.

the 5% energy intensity cutoff alleviates this concern because it ensures that
we compare firms that do not differ substantially in terms of energy intensity.
In addition, crude oil prices nearly doubled from December 2008 to December
2009—the Brent crude oil price increased from $43.72 on December 31, 2008,

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A. All firms

The Review of Financial Studies / v 37 n 5 2024

26 See, for example, Addoum, Ng, and Ortiz-Bobea (2020) and Kruttli, Roth Tran, and Watugala (2023) for a

description of the database.

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to $78.39 on December 31, 2009. Therefore, if anything, energy price changes
during this period works against the results we document: firms receiving
free permits—those with higher energy intensity—will see a greater increase
in operating costs due to higher energy prices relative to firms without free
permits, but obtain better financing terms according to our analysis, due to the
impact of the cap-and-trade bill.
The Waxman-Markey bill went through the legislative process in the
aftermath of the Global Financial Crisis, and thus, it is important to understand
whether the crisis may have differentially affected corporate lending to
manufacturing firms. Such confounding factors are likely to be differenced
out because we compare manufacturing firms above and below the freepermit threshold. Additionally, the placebo tests discussed in Section 5.3 and
shown in Figure 6 confirm that from the end of 2007 to the end of 2008—
the height of the Global Financial Crisis, but before the introduction of the
Waxman-Markey bill—we do not observe any differential effects around the
5% energy intensity threshold. Finally, we also assess this possibility using
sales and employment data from the National Establishment Time Series
database.26 Internet Appendix Table IA-10 shows no differential impact on
sales and employment around the energy intensity threshold during the height
of the Global Financial Crisis, suggesting that these industries were similarly
affected by that crisis.
The analyses presented so far show that firms’ total commitments are largely
unaffected by the passage of the cap-and-trade bills. However, this leaves
the possibility that firms’ outstanding (or utilized) commitments decrease as
firms shift reliance from term loans to credit lines. Particularly, in response to
cap-and-trade program uncertainty, firms may reduce leverage by increasing
the share of their credit line financing and utilizing less of their credit
commitments. To test for this possibility, Internet Appendix Table IA-1 shows
estimates of Equations (3) and (4) with the total utilized credit normalized by
total commitments amount as the dependent variable. For both the California
cap-and-trade bill and the Waxman-Markey cap-and-trade bill, the coefficient
estimates are economically small and statistically insignificant. These results
suggest that the shift from term loans to credit lines is not driven by firms
utilizing less credit.
As loan contract renegotiation between borrowers and lenders changes
contracts terms, such as amounts, maturities, interest rates, and credit line
share simultaneously with financial covenants (Roberts, 2015), it is important
to examine how cap-and-trade bills affect financial covenants. Specifically, it
is possible that banks relax the financial covenants of firms affected by capand-trade trade programs, while tightening remaining maturities and term loan
shares, thereby rendering the effect on loan contracts ambiguous. The SNC

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 8
Waxman-Markey cap-and-trade bill and cash flow covenants
(1)
Ii∈T reated ×It=2009

0.319∗∗
(0.129)

Observations
Adj R 2
Controls
Lead bank FE
Firm FE
Year FE

143
.606
No
No
Yes
Yes

0.264∗∗
(0.100)

264
.643
No
No
Yes
Yes

(3)
0.320∗∗
(0.136)

143
.613
No
Yes
Yes
Yes

(4)

0.234∗∗
(0.098)

264
.642
No
Yes
Yes
Yes

(5)
0.275∗∗
(0.130)

143
.657
Yes
No
Yes
Yes

(6)

0.289∗∗
(0.116)

264
.629
Yes
No
Yes
Yes

(7)
0.186
(0.114)

143
.674
Yes
Yes
Yes
Yes

(8)

0.245∗∗
(0.113)

264
.624
Yes
Yes
Yes
Yes

This table reports estimates from Equation (4). The dependent variable is an indicator variable that takes the
value of one if the firm has a cash flow covenant. Ii∈T reated is an indicator variable that takes the value of one
if the firm would not receive free permits under Waxman-Markey and zero otherwise. Ii∈T reatedW ide is the
equivalent variable for the wide bandwidth sample. It=2009 is an indicator variable that takes the value of one for
year 2009 and zero for year 2008. Firm, year, and lead bank fixed effects are included. Uninteracted independent
variables are absorbed by fixed effects. Standard errors are clustered by industry and reported in parentheses.
*p < .10; **p < .05; ***p < .01.

data allow us to measure whether any of the loans of a given borrower include
cash flow covenants.
We estimate Equation (4) with the cash flow covenant indicator as an
outcome variable. The sample is smaller than in our baseline Waxman-Markey
results because the cash flow covenant measure is only available for the subset
of loans/borrowers that are reviewed in the SNC exam. The SNC Program typically samples the largest and most complex syndicated loans for annual/semiannual examinations to assess systemic stability risks in the syndicated loan
market. During our sample period, this sample represents only up to 41% of
the total dollar amount of total SNC loans (Gustafson, Ivanov, and Meisenzahl,
2021). Therefore, we are unable to conduct subsample analyses for these tests.
The results in Table 8 show that firms just below the free permit threshold
are more likely to have a cash flow covenant in their loan contracts following
the passage of the Waxman-Markey bill in the House of Representatives. The
coefficient estimates imply that firms without free permits face between a 19and 32-percentage-point higher probability of having cash flow covenants in
their contracts after the passage of the program. Therefore, the strictness of
loan contracts increases even further once we consider financial covenants.
Overall, our analyses of the two independent natural experiments, the
California and the Waxman-Markey cap-and-trade bills, yield qualitatively
similar results. This is reassuring considering that both the time period and
the treatment assignment are different. The magnitude of the estimates are
also similar in the two sets of analyses, which might be surprising given
that the California cap-and-trade bill became a law, while the WaxmanMarkey cap-and-trade bill ultimately failed in the U.S. Senate. The significant
effect of the Waxman-Markey bill on firm financing is likely due to the
federal nature of the bill. A national cap-and-trade program is potentially
more stringent to firms than a single-state program because shifting GHG

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Ii∈T reatedW ide ×It=2009

(2)

The Review of Financial Studies / v 37 n 5 2024

emissions to less regulated jurisdictions is arguably more challenging and
a larger share of firms’ emissions would be covered. In line with this
idea, Martin, Muûls, Preux, and Wagner (2014) find that program avoidance
is limited for the Emissions Trading Scheme in the European Union.

This section presents analysis that helps us understand alternative ways
for banks to manage exposure to affected firms and the impact of the
cap-and-trade program on firms’ balance sheets. Further, it shows robustness
tests for our baseline results from Section 4. The analyses in this section rely
on either the SNC or the Y14 data, depending on data availability.
5.1 Lenders’ ex ante exposure and shadow banks
An important financial stability consideration is the extent to which risks are
concentrated within specific types of lenders. If lenders with high ex ante
exposure to the climate policy quickly transfer these risks to less exposed
lenders, systemic stability concerns are likely to be mitigated when a realization
of transition risk like the passage of a cap-and-trade bill occurs. We explore
this idea using lender-firm level data and test whether overall lenders’ total
exposure to high-emission firms affects lenders’ incentives to sell syndicated
loans when a cap-and-trade bill is passed. A wide range of lenders trade
syndicated loans on the secondary loan market and the richness of the SNC
data allow us to trace the evolution of lenders’ loan positions over time
(Irani and Meisenzahl, 2017).
We first compute a lender’s total exposure to a given firm as a fraction of the
lender’s total syndicated loans:
LenderF irmExposurei,l,t =

F irmLendingi,l,t
,
T otalLendingl,t

(7)

where the numerator is the total syndicated commitments of firm i held by
lender l at the end of year t, and the denominator is the total syndicated
commitments across all borrowers held by lender l in year t.
We also compute a lender’s exposure to high GHG-emitting firms as of
2008—the pre-period of the Waxman-Markey analysis:
LenderH ighEmissionExposurel =
N
i=1 F irmLendingi,l,2008 ×Ii∈H ighEmissionF irms
,
T otalLendingl,2008

(8)

where H ighEmissionF irms are all the firms that are included in the EPA data
set, as well as fuel suppliers from sectors covered by the proposed WaxmanMarkey cap-and-trade program. The EPA data are as of 2010, the first available
year in the data. Figure 5, panels A and B, shows the distribution of the

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5. Systemic Stability Implications and Robustness

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

LenderF irmExposurei,l,t = λ1 Il∈H ighEmissionLender ×Ii∈T reated ×It=2009
+ωi,l +Ωi,t +i,l,t ,

(9)

where the indicator variable Il∈H ighEmissionLender takes the value of one if
lender l had an above median LenderH ighEmissionExposurel as defined
in Equation (8). We also include firm × lender fixed effects, ωi,l , to ensure
that the estimates capture changes within a firm and lender, and firm × year
fixed effects, Ωi,t . These fixed effects subsume lower order interaction terms
as well as firm and lender fixed effects. The remaining variables are defined
the same way as for Equation (4), and the standard errors are double-clustered
by six-digit NAICS industry and lender.
Table 9 shows that the estimate of the high GHG emission exposure
interaction term is consistently negative and strongly significant. The estimates
range between −0.015 and −0.008 and imply a considerable economic
magnitude in light of the average LenderF irmExposurei,l,t shown in Table
2, panel C, ranging between 0.035 and 0.040. These results show that lenders’
current exposure to high GHG-emitting firms is an important factor in their
decision to sell the syndicated loans of firms that would not receive free permits
under the proposed Waxman-Markey cap-and-trade program.
Syndicated loans are held not only by banks but also by shadow banks,
for example, CLOs, pension funds, and hedge funds. Shadow banks hold a
significant share of syndicated loans (Irani et al., 2021), and may increase
exposure to polluting firms after the passage of a cap-and-trade regulation
because of different risk appetites. Understanding these dynamics is important,
because risks may accumulate in certain pockets of the nonbank financial sector
such as CLOs, pension funds, or other shadow banks, leading to a more fragile
financial system.
To test which shadow banks increase their holdings of the syndicated loans of
treated firms, we modify Equation (9) by including interaction terms between
Ii∈T reatedW ide ×It=2009 and indicators for each type of lender: bank, CLO,
collateralized debt obligations (CDOs), pension fund, insurance company,
bank-affiliated fund, nonfinancial company, investment fund (e.g., a mutual or
a hedge fund), and other credit institutions. We limit the sample to term loans as
shadow banks are unlikely to participate in credit lines. Firm-year fixed effects

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LenderH ighEmissionExposurel variable for all the lenders in our sample.
The median lender working with affected firms in the baseline or the wide
bandwidth specifications has portfolio exposure to high GHG-emitting firms
of about 9%.
We then test whether lenders with above median ex ante exposure to
high GHG-emitting firms (“high emission lenders”) are more likely to sell
the syndicated loans of treated manufacturing firms after the House of
Representatives passed the Waxman-Markey cap-and-trade bill using the
following regression specification:

The Review of Financial Studies / v 37 n 5 2024

A

1,000

Count

500

250

0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.9

1.0

Lending share to high−emission firms

B

Count

1,500

1,000

500

0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Lending share to high−emission firms
Figure 5
Lenders’ exposure to high GHG-emitting firms
This figure shows the distribution in 2008 of the lenders’ credit commitment to high GHG-emitting firms as a
share of total credit commitment, LenderH ighEmissionExposurel , defined in Equation (8). Panels A and B
include all lenders that lend to firms within the baseline and wide bandwidths of the Waxman-Markey analysis,
respectively. This variable is used in Equation (9), the estimates of which are presented in Table 9.

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750

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 9
Waxman-Markey cap-and-trade bill and lenders’ emission exposure
(1)
Ii∈T reated ×It=2009

(2)

0.000
(0.009)

−0.014∗∗∗
Ii∈T reated ×It=2009
×Il∈H ighEmissionLender (0.003)

−0.015∗∗∗
(0.003)

−0.013∗∗
(0.005)

19,358
.669
No
No
Yes
Yes
No

(5)

(6)

(7)

(8)

−0.001
(0.009)

0.000
(0.010)

Ii∈T reatedW ide ×It=2009
×Il∈H ighEmissionLender

(4)

38,121
.598
No
No
Yes
Yes
No

−0.008∗∗∗
(0.003)

−0.013∗∗
(0.005)

19,358
.672
Yes
No
Yes
Yes
No

38,121
.600
Yes
No
Yes
Yes
No

−0.012∗∗∗
(0.004)

−0.009∗∗∗
(0.003)

19,358
.806
No
Yes
No
No
Yes

38,121
.769
No
Yes
No
No
Yes

−0.012∗∗∗
(0.005)

19,358
.681
No
No
No
Yes
Yes

38,121
.611
No
No
No
Yes
Yes

This table reports estimates from Equation (9). The dependent variable is a lender-firm level variable given in
Equation (7), which measures the credit commitment between a firm and a lender as a share of the total credit
commitments of the lender. Ii∈T reated is an indicator variable that takes the value of one if the firm would not
receive free permits under Waxman-Markey and zero otherwise. Ii∈T reatedW ide is the equivalent variable for
the wide bandwidth sample. It=2009 is an indicator variable that takes the value of one for year 2009 and zero
for year 2008. Il∈H ighEmissionLender is indicator variable that takes the value of one if the lender has above
median exposure to high GHG-emitting firms in 2008. Lower order interaction terms that are not shown are
absorbed by fixed effects. Firm, year, and lender fixed effects are included separately or interacted. Standard
errors are double-clustered by industry and lender and reported in parentheses. *p < .10; **p < .05; ***p < .01.

account for time-varying firm-specific factors, such as the reduced term loan
reliance of firms without free permits under the proposed Waxman-Markey
cap-and-trade program, while the interaction terms help isolate how different
types of lenders change exposure to treated firms.
Table 10 shows that shadow banks, such as CLOs and CDOs, significantly
increase their holdings of the syndicated loans of firms without free permits
across specifications by nearly 3 percentage points. By contrast, insurance
companies sharply decrease their holdings of firms without free permits
although this result becomes insignificant once we compare insurance
companies only to banks (column 10). Overall, these results suggest that
banks not only change the loan terms of high GHG-emitting firms in light of
pending cap-and trade regulations but also transfer their risk exposure to other
participants in the syndicated loan market.
5.2 Balance sheet effects
The results presented in the previous sections are consistent with banks
tightening loan terms in response to the expected adverse cash flow effects
of carbon pricing. While the ultimate impact of a cap-and-trade program on
firms’ cash flow is unclear prior to implementation, banks are likely to insure
against the states of the world in which firms’ cash flow is substantially lower

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Ii∈T reatedW ide ×It=2009

Observations
Adj R 2
Controls
Lender FE
Year FE
Firm-lender FE
Firm-year FE

(3)
0.000
(0.008)

The Review of Financial Studies / v 37 n 5 2024

Table 10
Waxman-Markey cap-and-trade bill and shadow bank types
(1)
Ii∈T reatedW ide ×It=2009
×Il∈Bank

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(10)

0.028∗∗∗
(0.009)
0.018∗∗
(0.007)

Ii∈T reatedW ide ×It=2009
×Il∈CDO
Ii∈T reatedW ide ×It=2009
×Il∈P ensionsF unds

0.027∗∗∗
(0.007)
−0.001
(0.022)

0.008
(0.028)
−0.050∗∗
(0.020)

Ii∈T reatedW ide ×It=2009
×Il∈I nsurance
Ii∈T reatedW ide ×It=2009
×Il∈BankAff iliatedF unds

−0.038
(0.026)
−0.002
(0.014)

Ii∈T reatedW ide ×It=2009
×Il∈NonF inancialCompanies

0.008
(0.014)
−0.035
(0.066)

−0.028
(0.069)
−0.015∗∗∗
(0.005)

Ii∈T reatedW ide ×It=2009
×Il∈I nvestmentF unds

0.001
(0.012)
0.010 0.020∗∗
(0.011) (0.010)

Ii∈T reatedW ide ×It=2009
×Il∈Others
24,138
.561
Yes
Yes

24,138
.562
Yes
Yes

24,138 24,138
.561
.561
Yes
Yes
Yes
Yes

24,138
.562
Yes
Yes

24,138 24,138
.561
.561
Yes
Yes
Yes
Yes

24,138
.561
Yes
Yes

24,138 24,138
.561
.563
Yes
Yes
Yes
Yes

This table reports estimates from Equation (9) but interacting the independent variable with lender type. The
dependent variable is a lender-firm level variable given in Equation (7), which measures the credit commitment
between a firm and a lender as a share of the total credit commitments of the lender. Ii∈T reatedW ide is an
indicator variable that takes the value of one if the firm would not receive free permits under Waxman-Markey
and zero otherwise. It=2009 is an indicator variable that takes the value of one for year 2009 and zero for year
2008. Il∈A is an indicator variable that takes the value of one if the lender is of type “A” and zero otherwise.
In column 10, the reference lender type is “Bank,” which is thus dropped from the regression. Only term loans
are included in the sample. Lower order interaction terms are included in the regression or absorbed by fixed
effects. Firm fixed effects are interacted with year and lender fixed effects, respectively. Standard errors are
double-clustered by industry and lender and reported in parentheses. *p < .10; **p < .05; ***p < .01.

and more volatile. As discussed in Section 1.3, a lower or more volatile cash
flow increases the probability of default and the loss given default.
The Y14 data allow us to analyze how cap-and-trade programs affect
cash flow and other balance sheet outcomes in the context of California’s
cap-and-trade program. As these financial statement information are updated
annually or biennially, the data are well suited for studying the evolution of
firm balance sheet outcomes around the implementation of California’s capand-trade program. Consequently, we define the pre-period as 2011 and the
post-period as 2013, the first year of the implementation. We measure cash
flow with firms’ earnings before interest, taxes, depreciation, and amortization
(EBITDA) normalized by total assets and estimate the regression in Equation
(3) with this measure as the dependent variable.
Table 11, panel A, shows a significant reduction in EBITDA/Assets for firms
with a large emissions share in California after the implementation of the

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0.025∗∗∗
(0.006)

Ii∈T reatedW ide ×It=2009
×Il∈CLO

Observations
Adj R 2
Firm-lender FE
Firm-year FE

(9)

−0.011
(0.011)

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 11
California’s cap-and-trade program implementation and firm balance sheets
All firms

Private firms

Public firms

(2)

(3)

(4)

(5)

(6)

CA_Emissions _Sharei
×IPost CA Implementation

−3.940∗
(2.221)

−3.891∗
(2.203)

−6.177∗∗∗
(0.794)

−5.299∗∗∗
(1.358)

−3.323
(3.924)

−3.358
(3.929)

Observations
Adj R 2

1,117
.525

1,117
.520

480
.421

480
.411

637
.567

637
.572

CA_Emissions _Sharei
×IPost CA Implementation

3.003∗
(1.805)

3.193∗
(1.923)

6.909∗∗
(3.339)

5.748
(4.118)

1.232
(2.143)

1.612
(2.333)

Observations
Adj R 2

1,135
.738

1,135
.738

486
.705

486
.711

649
.738

649
.731

CA_Emissions _Sharei
×IPost CA Implementation

−2.666
(3.362)

−2.935
(3.480)

−4.738∗∗
(2.150)

−4.926∗
(2.693)

3.800
(2.760)

2.541
(2.748)

Observations
Adj R 2

1,045
.208

1,045
.200

452
.380

452
.354

593
.118

593
.116

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes
Yes
Yes
Yes

B. Cash/Assets

C. CapEx/Assets

For all panels:
Controls
Uninteracted variables
Firm FE
Industry-year FE

This table reports estimates from Equation (3) estimated with annual firm balance sheet data and 2013 as
the post-period. The dependent variables are EBITDA/Assets (panel A), Cash/Assets (panel B), CapEx/Assets
(panel C). IPost CA Implementation is an indicator variable that takes the value of one for 2013 and zero for 2011.
CA_Emissions _Sharei is a continuous variable (0 to 1) measuring a firm’s California GHG emissions as a share
of the firm’s total GHG emissions. Firm and industry-year fixed effects are included. Uninteracted independent
variables are included in the regression or absorbed by fixed effects. Standard errors are clustered by industry
and are reported in parentheses. *p < .10; **p < .05; ***p < .01.

cap-and-trade program. This result is again driven by private firms in
the sample. A one-standard-deviation increase in emissions in California
is associated with a decrease in EBITDA/Assets between 1.39 and 1.62
percentage points for private firms depending on the specification.27 While this
decrease is economically relevant compared to the average EBITDA/Assets of
around 12%, it might be lower than the banks expected as the ultimate price
on carbon was close to the price floor set by the California Air and Resources
Board. The settlement price of the auctions up to the end of 2013 ranged from
$10.09 to $14.00, and was thus very close to the price floor of the auctions,
which ranged from $10.00 to $10.71.

27 The standard deviation of private firms’ emissions share in California is 0.26.

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(1)
A. EBITDA/Assets

The Review of Financial Studies / v 37 n 5 2024

28 See https://ww2.arb.ca.gov/our-work/programs/cap-and-trade-program/cap-and-trade-program-data.
29 Auction settlement prices can be found here: https://ww2.arb.ca.gov/sites/default/files/2020-08/results_

summary.pdf. The median absolute change in firm emissions year-to-year is around 8,000 MTs of CO2e.

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This decrease in cash flow is consistent with higher firm operating costs
as a result of the program, particularly for the emissions inefficient private
firms. This effect is likely to have a direct component that comes from the
price on emissions stemming from the combustion of fossil fuels in production
processes. However, there is also an indirect supply chain effect where
electricity and potentially other inputs become more expensive as a result of
the price on carbon. While the supply chain effect is difficult to estimate, our
estimates of the decrease in cash flow are roughly in line with auction prices of
the emission allowances. Based on the coefficient estimates shown in Table
11, a one-standard-deviation move in a firm’s California emission share is
estimated to decrease EBITDA by around $8.5 million for private firms. Up
to the end of 2013, around $1.4 billion in allowances were sold in auctions,
which translates into about $6 million per firm.28
As discussed in Section 1.3, an increase in cash flow variance also leads
to an increase in the probability of default and the loss given default.
However, conclusively testing for changes in cash flow variance is challenging
because the low frequency of financial statements in our data do not allow
us to compare a firm’s cash flow variance around the implementation of
the California cap-and-trade program. Overall, the relative stability of the
quarterly auction settlement price on carbon and the limited year-to-year
changes in firm emissions suggest that the adverse effect on mean cash flow is
somewhat more pronounced than the effect on cash flow variance after program
implementation.29
Panel B shows that the potentially higher uncertainty in obtaining external
finance for private firms documented in Section 4.1 also translates to large
increases in cash balances normalized by assets, indicating an increase in
precautionary savings. A one-standard-deviation increase in emissions in
California amounts to a 1.8-percentage-point increase in the cash-to-assets
of affected private firms relative to the average and median cash-to-assets of
private firms of 9% and 3%, respectively. Finally, we find that the higher
uncertainty in accessing external capital markets and higher savings rates
also leads to lower investment as proxied by net capital expenditures (in
panel C) normalized by assets. Overall, we show that the highly uncertain
environment in the bank financing market for firms covered by California’s
cap-and-trade program has adverse real implications for these firms. This
reduction in investment and the increase in cash holdings could further impact
the profitability of private firms.
The firm balance sheet data allow us to investigate the additional robustness
of the baseline effects on total credit commitments in Section 4.1 as these
results are based only on commitments from banks subject to Y14 reporting.

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

5.3 Robustness tests
In this section, we discuss additional robustness tests. We first examine the
possibility of pre-trends in our difference-in-differences setting. This seems
unlikely as our estimates rely on two distinct natural experiments, with
treatment along different dimensions that occur at different points in time.
Nevertheless, the longer time series dimension of the SNC data allow us to test
for differences around the energy intensity threshold of the Waxman-Markey
bill before the bill’s passage by the House of Representatives in 2009. We also
examine whether the treatment effects reverse in 2010 after the bill failed in
the U.S. Senate.
We reestimate Equation (6) over the following year pairs: from (2004, 2005)
through (2011, 2012). The regression coefficients are plotted in Figure 6 with
the “post" year of each test on the x-axis. The dependent variables are those for
which we previously found a statistically significant effect: maturity, term loans
share, and the incidence of cash flow covenants from Section 4.2. Covenants
data are not available prior to 2006, so the first 2-year sample for which we can
estimate covenants effects is (2006, 2007). Also, because of the smaller number
of firms for which covenant data are available, Figure 6 plots the coefficient
estimate of Equation (4) for cash flow covenants.
For all three variables, estimates for the coefficient of interest are not
significantly different from zero in the placebo years prior to 2009. The
coefficients only show a significant effect in 2009, which is the actual treatment
year, when Waxman-Markey cleared the House of Representatives and was
under consideration by the Senate. This result is reassuring as the effects in
2009 do not appear to be driven by violations in the parallel trends assumption.
Interestingly, for all outcome variables, we find that the coefficient estimates
revert to pre-2009 levels in the years after the bill failed in the Senate, with the
reversion being statistically significant for the maturity and cash flow variables.
This result suggests a rebound in borrowers’ financial flexibility after the
Waxman-Markey cap-and-trade bill failed in the Senate in July 2010.
As the Y14 data coverage starts in 2011, we are unable to study pre-trends for
the California cap-and-trade setting. To alleviate concerns that our differencein-differences estimates may be driven by California-specific economic factors

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It is possible that private firms shift borrowing to nonbanks and small
banks that do not report to Y14 around the passage of the cap-and-trade
bill. Firms’ total balance sheet debt includes borrowing from all sources,
thereby allowing us to investigate whether such substitution occurs. We,
therefore, compare firms’ total debt in 2012 relative to total debt in 2011.
In Internet Appendix Table IA-3, we show similar results for firms’ total debt
as in our baseline commitment specifications in Table 4—while total debt
of private firms declines following the passage of California’s cap-and-trade
program, these results are not significantly different from zero—suggesting
limited substitution of borrowing sources.

The Review of Financial Studies / v 37 n 5 2024

B

C

D

E

F

Figure 6
Placebo tests for the Waxman-Markey cap-and-trade bill
This figure shows the difference between treated and control firms in the Waxman-Markey analysis for a range
of pre and post years based on the coefficient estimates from corresponding regressions using both the baseline
and wide bandwidth samples. Panels A and B cover maturity (in months) and panels C and D cover the term
loans share of total committed credit (0 to 1). They show coefficients for treated firms in the high energy intensity
bucket for regressions on private firms as given in Equation (6). Panels E and F cover cash flow covenants (0
or 1) and show coefficients for treated firms based on regressions as given in Equation (4). The regressions are
separately estimated for samples of 2 consecutive years: (2004, 2005), (2005, 2006), (2006, 2007), (2007, 2008),
(2008, 2009), (2009, 2010), (2010, 2011), and (2011, 2012). The year shown on the x-axis is the “post” year in
a specific test. The Waxman-Markey bill passed the U.S. House of Representatives in 2009 (red), but ultimately
failed in the U.S. Senate in 2010 (gray). The cash flow covenant variable is not available prior to 2006. The bands
show the 90% confidence interval.

that are unrelated to the cap-and-trade program, we estimate “falsification”
style regressions in which nonpolluting firms are treated proportionally to
the number of establishments they have in the state as a fraction of total
establishments for each firm. The data on firm establishments comes from the
National Establishment Time Series database. Similar to our main analysis, we
compare the time series evolution of loan commitments, maturity, term loan

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A

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table 12
California’s cap-and-trade bill and non-polluting firms
Log committed
(1)

(2)

Maturity
(3)

(4)

Term loans share
(5)

(6)

Interest rate
(7)

(8)

A. All firms

Observations
Adj R 2

40,907
.952

40,907
.952

40,894
.897

40,894
.897

40,894
.757

40,894
.757

11,931 11,931
.892
.892

B. Private firms
CA_Estab_Sharei ×IPost CA bill 0.040∗∗
−0.095
−0.162∗
−0.112
(0.019)
(0.907)
(0.093)
(0.112)
∗
∗
ICA_Estab_Sharei ≥50%
0.034
−0.192
−0.151
−0.108
(0.020)
(0.937)
(0.083)
(0.109)
×IPost CA bill

Observations
Adj R 2

39,188
.946

39,188
.946

39,175
.905

39,175
.905

39,175
.763

39,175
.762

11,178 11,178
.905
.905

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes

For all panels
Controls
Uninteracted variables
Firm FE
Industry-quarter FE

Yes
Yes
Yes
Yes

This table reports estimates from Equation (3), but for firms in nonpolluting sectors. The dependent variables
are the log committed credit, remaining maturity (in months), the term loans share of total committed credit (0
to 1), and the interest rate (in %), respectively. IPost CA bill is an indicator variable that takes the value of one
for the third or fourth quarter of 2012 and zero for the third or fourth quarter of 2011. CA_Estab_Sharei
is a continuous variable (0 to 1) measuring a firm’s California establishments as a share of the firm’s total
establishments. ICA_Estab_Sharei ≥50% is an indicator variable that takes the value of one if the firm has at
least 50% of its total establishments in California and zero otherwise. Firm and industry-quarter fixed effects
are included. Uninteracted independent variables are included in the regression or absorbed by fixed effects.
Standard errors are clustered by industry and are reported in parentheses. Results are shown for all firms (panel
A) and the subsample of private firms (panel B). *p < .10; **p < .05; ***p < .01.

share, and interest rates from the last two quarters of 2011 to those in 2012.
We restrict the sample to nonpolluting firms, which we define to be firms in
two-digit NAICS sectors with negligible GHG emissions. Each of these eight
major sectors accounts for less than 0.01% of emissions in the EPA data set. We
also exclude the agricultural sector because it is responsible for a considerable
share of GHG emissions that are not covered by EPA data.
Table 12 shows the results for both the full sample (in panel A) and private
companies (in panel B). The results in both panels paint a completely different
picture from those in our main specifications—nonpolluting firms with larger
presence in California do not see much of a change in maturity or interest rates
between late 2011 and 2012. In addition, loan commitments of nonpolluting
firms increase and term loans share decline between 2011 and 2012, albeit the
respective statistical and economic significance is mixed across specifications.
These patterns are consistent with debt contracts of nonpolluting firms in
California not changing materially between 2011 and 2012. These estimates

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CA_Estab_Sharei ×IPost CA bill 0.039∗∗
−0.259
−0.157∗
−0.161
(0.019)
(0.944)
(0.088)
(0.102)
∗
ICA_Estab_Sharei ≥50%
0.016
−0.530
−0.140
−0.142
(0.024)
(1.052)
(0.076)
(0.098)
×IPost CA bill

The Review of Financial Studies / v 37 n 5 2024

also stand in stark contrast with our main results in which high-emitting firms
in California face substantially stricter loan terms.
6. Conclusion

Appendix

Table A1
Variable descriptions
Variable name

Data source

Description

Borrower ratings SNC

SNC

Borrower ratings Y14

Y14

CA emissions share

EPA; Y14

Four indicator variables that take the value of one
whenever at least some fraction of the commitments
to borrower i in year t are rated “special mention,”
“substandard,” “doubtful,” and “loss,” respectively, by
the lead bank. Otherwise, the value of the indicator
variables are zero. “Pass” is the omitted category.
Four indicator variables based on the borrower i ’s credit
rating in quarter q . The borrowers’s credit ratings are
issued by the banks and aggregated across banks for
each borrower. As banks use different internal rating
scales, banks in the Y14 also convert their own internal
rating scale to an S&P scale in order for the measure
to be comparable across banks. AAA/AA is the omitted
category.
The emissions in California normalized by total emissions of firm i in year y .

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Despite widespread discussions of climate policy risk, we know little about
how lenders manage this risk and about the associated impact on emitting firms.
We use specific features of the two major cap-and-trade bills implemented
or considered in the United States thus far to identify effects and show
that cap-and-trade programs lead to significant changes in corporate lending
to affected firms. Firms face shortening in loan maturities, lower access to
permanent forms of bank financing such as term loans, higher interest rates,
and lower participation of banks in their lending syndicates with increased
participation of shadow banks. These effects are mainly concentrated among
private firms, suggesting banks are less concerned about the impact of cap-andtrade programs on public firms.
The fluid nature of commercial lending relationships allows banks to adjust
their credit exposure quickly through loan renegotiation. This paper shows
that they do so swiftly, in ways that mitigate their exposure to cap-and-trade
legislation. These findings suggest that, at least in the bilateral and syndicated
lending markets, legislation intended to curb GHG emissions and transition to
a low-carbon economy is unlikely to pose large, unmanageable risks to the
banking sector. The large differential response of private and public firms’
loan terms implies that private firms simultaneously face tighter loan terms
and a price on carbon, which has important implications for the design of such
programs.

Banking on Carbon: Corporate Lending and Cap-and-Trade Policy

Table A1
(Continued)
Data source

Description

CA establishment share

NETS; Y14

CapEx/Assets

Y14

Cash/Assets
Cash flow covenant

Y14
SNC

Committed credit

SNC; Y14

EBITDA/Assets
EI

Y14
Meng (2017); SNC

Interest rate

Y14

Lead bank fixed effects

SNC

Lender firm exposure

SNC

Lender high emission
exposure

SNC

Private

SNC; Y14

Remaining maturity

SNC; Y14

Term loans share

SNC; Y14

Treated

SNC

Treated wide

SNC

The number of establishments in California normalized
by total number of establishments of firm i in year y .
Net capital expenditure normalized by assets of firm i in
year t .
Cash normalized by assets of firm i in year t .
An indicator variable that takes the value of one when a
cash flow covenant is present in any of the commitments
to borrower i in year t .
Defined as the total dollar amount of loan commitments
(in millions of US$) of borrower i in year t (quarter q ).
EBITDA normalized by assets of firm i in year t .
Energy intensity based on firm i ’s 6-digit NAICS
industry.
The interest rate that borrower i pays on term loans in
quarter q .
These are indicator variables based on the different lead
banks in the sample.
The amount of firm i ’s syndicated loans held by lender
l in year t normalized by the total amount of syndicated
loans held by lender l in year t .
The amount of high-emission firms’ syndicated loans
held by lender l in year t normalized by the total amount
of syndicated loans held by lender l in year t .
An indicator variable that takes the value of one when the
borrower is private and zero when the borrower is public.
Defined as the average maturity of the loans of borrower
i in year t (quarter q ).
Defined as the share of total commitments to borrower i
in year t (quarter q ) in the form of term loans.
An indicator variable based on a firm i ’s industry that
takes the value of one (zero) if the industry has an energy
intensity of at least 2% and smaller than 5% (between 5%
and 8%).
An indicator variable based on a firm i ’s industry that
takes the value of one (zero) if the industry has an energy
intensity of at least 1% and smaller than 5% (between 5%
and 9%).

This table describes our variables. Some variables are in both the SNC and Y14 data sets, while others are only
available in one data set.

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==> RFS03 - Pricing Uncertainty Induced by Climate Change.txt <==
Pricing Uncertainty Induced by Climate
Change
Michael Barnett
Arizona State University

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William Brock
University of Wisconsin and University of Missouri
Lars Peter Hansen
University of Chicago
Geophysicists examine and document the repercussions for the earth’s climate induced by
alternative emission scenarios and model specifications. Using simplified approximations,
they produce tractable characterizations of the associated uncertainty. Meanwhile,
economists write highly stylized damage functions to speculate about how climate change
alters macroeconomic and growth opportunities. How can we assess both climate and
emissions impacts, as well as uncertainty in the broadest sense, in social decision-making?
We provide a framework for answering this question by embracing recent decision theory
and tools from asset pricing, and we apply this structure with its interacting components to
a revealing quantitative illustration. (JEL D81, E61, G12, G18, Q51, Q54)
Received December 7, 2017; editorial decision November 19, 2019 by Editor Harrison
Hong. Authors have furnished an Internet Appendix, which is available on the Oxford
University Press Web site next to the link to the final published paper online.

Global efforts to mitigate climate change are guided by projections
of future temperatures. But the eventual equilibrium global
mean temperature associated with a given stabilization level of
atmospheric greenhouse gas concentrations remains uncertain,
complicating the setting of stabilization targets to avoid potentially
dangerous levels of global warming.
– Allen et al. (2009)
We thank James Franke, Elisabeth Moyer, and Michael Stein of RDCEP for the help they have given
us on this paper. Comments, suggestions and encouragement from Harrison Hong and Jose Scheinkman
are most appreciated. We gratefully acknowledge Diana Petrova and Grace Tsiang for their assistance in
preparing this manuscript, Erik Chavez for his comments, and Jiaming Wang, John Wilson, Han Xu, and
especially Jieayo Wang for computational assistance. More extensive results and python scripts are available
at http://github.com/lphansen/Climate. The Financial support for this project was provided by the Alfred P. Sloan
Foundation [grant G-2018-11113] and computational support was provided by the Research Computing Center
at the University of Chicago. Send correspondence to Lars Peter Hansen, University of Chicago, 1126 E. 59th
Street, Chicago, IL 60637; telephone: 773-702-3908. E-mail: lhansen@uchicago.edu.
© The Authors 2020. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution
Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial
re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For
commercial re-use, please contact journals.permissions@oup.com
doi:10.1093/rfs/hhz144

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Introduction

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Our ambition, like that of other researchers, is to understand better the
macroeconomic consequences of climate change and conversely how the
economic activity will alter the climate in the future. We see this challenge
as a problem for which aggregate uncertainty is a first-order consideration and
not just a second-order afterthought as it often is in quantitative macroeconomic
analyses. Developing a modeling framework that could support policy
discussions requires that we quantify the associated uncertainty and assess
its impacts on policy design. Addressing this problem requires a structural
model in the sense of Hurwicz (1966) because we will be compelled to assess
possibilities that are not well represented by historical evidence. Economic
dynamics necessarily play a central role. To design, say, an optimal carbon tax
compels us to use measurements of the mechanism by which human activity
today will affect climate in the future and an assessment of the resultant damages
to human welfare. Uncertainty prevails in both the transmission mechanism
and the resultant social damages. While much of the economics literature
has focused on quantifying social damages, climate science investigates the
transmission mechanism by which carbon emissions alter the environment. As
is reflected in the Allen et al. (2009) quote, climate science quantifications
embed uncertainty, both across models and within any given model. This paper
pays particular attention to the interaction of the climate impacts and their
economic consequences.
We build and assess dynamic structural economic models using:
a. decision theory under uncertainty
b. nonlinear impulse response functions
c. dynamic valuation via asset pricing
In terms of item (a), we use a formal decision problem as a way to
conduct a meaningful sensitivity analysis. While much of decision theory
within economics is typically axiomatic in nature, for us the resultant recursive
representations are also of vital importance for implementation. In terms of item
(b), changes in emissions today alter the climate and hence economic damages
in current and future time periods. Our interest in the shadow price of the
human-induced externality on the climate leads us to use nonlinear counterparts
to impulse response functions familiar in macroeconomics and climate science.
In terms of item (c), we use asset pricing methods not only to impute market
valuations but also social valuations. Our asset pricing vantage point leads us
to view the shadow prices of interest as discounted expected values of the
impulse responses. As we know, asset prices are “marginal” in nature. In a
private market setting, they depend on the stochastic intertemporal marginal
rates of substitutions of investors. Because our interest is in social valuation,
the prices of interest use the marginal rates of substitution of the preferences
of the fictitious planner for stochastic discounting and the pertinent relative

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prices. In turn these are sensitive to the formulation of decision theory under
uncertainty that we use to represent these preferences. We provide mathematical
characterizations of the probability measures that adjust for ambiguity over how
much emphasis to place on the alternative models and for the potential impact
of model misspecification. Indeed, we use tools from items (a), (b), and (c) in
ways that are intertwined. While our main focus is to apply these tools in social
valuation to represent Pigouvian taxes that confront externalities in socially
efficient manners, an analogous approach can be developed to study the local
impacts of policy changes from socially inefficient allocations.
In this paper, we use the “social cost of carbon” as a target of measurement.
Featuring this entity as a tax on an externality is an overly simplified solution to
a complex policy problem, both politically and economically. Two challenges
in implementing such a tax are (1) what happens to the tax revenues and (2) how
do existing distortionary taxes alter an idealized choice of a carbon tax? These
challenges carry with them a variety of ramifications for implementation, from
determining how best to offset any undesirable distributional consequences to
ensuring that proceeds are allocated in ways that are not socially wasteful.1 Of
course, there are questions about how to coordinate any such policy across a
variety of political venues. These are all vital questions that are part of actual
policy discourse, but not ones that we address in this particular paper. Our aim
is to assess what sources of uncertainty matter the most. We use implications
for the social cost of carbon to guide those discussions, although we suspect
that some of the key uncertainty considerations here should also contribute to
other more complex and pragmatic approaches to policy.
Our analysis targets “sensitivity” to uncertainty and potential misspecification. We approach this in two ways. First, we take a preliminary stab at exploring
the uncertainty in the transmission mechanism from carbon emissions to the
climate (captured by us as temperature changes). Second, we show that the
“details” of the economic model can really matter, by conducting our analysis
within some different economic configurations of technology and preferences.
In this paper, we feature continuous-time models and corresponding pricing
methods that are familiar to financial economists. We will exploit the
continuous-time recursive representations of preferences to produce revealing
formulas for how alternative uncertainty components are reflected in valuation.
While the continuous-time diffusion model gives some pedagogically revealing
formulas, our approach has direct extensions to discrete-time models and
models with jump components, although we do not develop such connections
here.
1. Uncertainty and Approximation
We find it advantageous to explore three components to uncertainty:
1 Kevin Murphy and Bob Topel have emphasized these points in direct communication.

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• risk - uncertainty within a model: uncertain outcomes with known
probabilities
• ambiguity - uncertainty across models: unknown weights for alternative
possible models
• misspecification - uncertainty about models: unknown flaws of
approximating models

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The first of these components is captured in scientific discourse by
introducing random shocks or impulses into models. With known distributions,
this modeling approach captures risk. Economists often discuss risk and
aversion to that risk. We frame this discussion as one in which outcomes are not
known, but probabilities are. For instance economic agents “inside” rational
expectation models confront risk. The literature on long-run risk assumes
investors have preferences that respond to the intertemporal composition of
risk using the recursive formulation originally proposed by Kreps and Porteus
(1978). The long-run risk literature uses this framework in conjunction with
uncertainty in macroeconomic growth rates. See, for instance, Bansal and Yaron
(2004). As many previous researchers have noted, the human impact on the
climate is a potentially important source of uncertainty that could play out over
long horizons. See, for instance, Jensen and Traeger (2014), Cai et al. (2015),
Nordhaus (2017), Hambel, Kraft, and Schwartz (2018), and, especially, Cai,
Judd, and Lontzek (2017).
The second of these components, ambiguity, reflects the fact that there are
multiple models at the disposal of decision-makers motivating the question of
how much weight to assign to each of these models in terms of their credibility.
This is addressed by subjective probabilities within a Bayesian framework. The
robust Bayesian approach explores sensitivity to subjective inputs. Historical
data alone have only limited insights in terms of how we conceptualize climate
change uncertainty. Some of the potential adverse climate outcomes seem
best understood by using climate models designed to help us think through
the long-term consequences of human inputs into the climate system. For an
example of within model ambiguity, consider the findings reported in Olson
et al. (2012) for what they call the climate sensitivity parameter. Figure 3 of their
paper reports Bayesian posteriors using an uninformative prior and compares
this to an informative prior documenting substantial sensitivity, suggesting the
importance of the subjective prior in the analysis. This is not a parameter for
which “the evidence speaks for itself.” More generally, the interplay between
models and evidence seems vital if we are to think through the consequences
of uncertainty, broadly conceived. There are now a variety of climate models
with differing implications, so how to confront cross-model uncertainty seems
pertinent to an assessment of uncertainty.
In this paper, we apply an approach to model ambiguity that applies the
Hansen and Miao (2018) recursive implementation of the smooth ambiguity
model originally proposed and axiomatized by Klibanoff, Marinacci, and
Mukerji (2005). The smooth ambiguity model provides a differential

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preferential response to the uncertainty about models that is distinct from risk.
Examples motivated by climate science are given in Millner, Dietz, and Heal
(2013) and Lemoine and Traeger (2016), although their analyses are driven
by robustness considerations. Such considerations for subjective probabilities
have played an important role in Bayesian inferences. For instance, see Berger
(1984). Hansen and Sargent (2007), and Hansen and Miao (2018) provide a
link between the smooth ambiguity model and a recursive robust prior model.
This third component to uncertainty, potential model misspecification, is
necessitated by the underlying complexity of the environment to be understood
through the guises of insightful models. The climate environment, like the
economic one, is complex. Models that we constructed of their interactions
are necessarily abstractions designed to help us understand the underlying
phenomenon under consideration. They are necessarily misspecified because
of our desire for simplicity, and because our understanding of some of the
features of the environment is limited. Other model shortcomings may be
difficult to pinpoint ex ante. Interestingly, some well known climate models
are themselves sufficiently complicated that researchers construct simplified
approximations typically called emulators that capture some broad features
using relatively simple time-series models. See, for instance, Li and Jarvis
(2009) and Castruccio et al. (2014). Considerations like these lead us to consider
potential model misspecification as an important source of uncertainty.
In summary, we formulate a social decision planner problem that includes
concerns about the potential misspecification of alternative models and
ambiguity over how much weight to assign to each these models. In so doing,
we are following the Hansen and Miao (2018) continuous-time extension of
Hansen and Sargent (2007). As we will show, this approach gives revealing
continuous-time formulas for pricing uncertainty components to the SCC.
Since the formulas target social valuation, not market valuation, they do
not provide empirical predictions. Instead we use the SCC sensitivity to
alternative sources of uncertainty as a well-posed structural setting for our
quantitative investigation. This structural approach yields a probability measure
encapsulating the planner’s uncertainties and the corresponding aversions.
Finally, we illustrate the effect of ambiguity aversion on the SCC.
2. A Model with Reserves and Climate Damages
Our model consists of an information structure and the evolution of
endogenous state variables including reserves, cumulative emissions, capital,
and environmental damages, along with societal preferences. Figure 1 depicts
the economic model components without climate impacts and environmental
damages. This model has a Brownian motion information structure and,
like many in macroeconomics, is highly stylized. We use it to illustrate a
framework for doing dynamic policy analysis in the presence of uncertainty in
a numerically tractable setting. But we are cognizant of its limitations and hope

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Figure 1
Depiction of the economic model in the absence of climate and economic damages. The model includes Brownian
increment shocks, adjustment costs in capital accumulation and curvature in how investment in discovery
increases the stock of new reserves.

to add some complexity in future research. The continuous-time, Brownian
information structure simplifies some of the implications for social valuation,
but it is not essential to the overall approach.2
2.1 Information
To assist some of our characterizations, we presume a Brownian information
.
structure where W = {Wt : t ≥ 0} is a m-dimensional standard Brownian motion
.
and F = {Ft : t ≥ 0} is the corresponding Brownian filtration with Ft generated
by the Brownian motion between dates zero and t.
.
In what follows, we let Z = {Zt : t ≥ 0} be an exogenously specified,
stochastically stable, multivariate forcing process. We write its evolution
equation stochastically as
dZt = μZ (Zt )dt +σZ (Zt )dWt .
In our examples Z will be Ornstein-Uhlenbeck or Feller type processes with
affine mean dynamics and either constant or linear volatility dynamics.
2.2 State variable evolution
We consider an extended version of a model used by Brock and Hansen (2018).
Capital K evolves as




It
dKt = Kt ζK (Zt )dt +φ0 log 1+φ1
dt +σK ·dWt ,
Kt
2 Our continuous-time diffusion model is similar in some respects to two prior contributions. Hambel, Kraft, and

Schwartz (2018) build and analyze a DICE-type model and consider damage specifications in technology and
in technology growth. Our production specification is different, in particular, in our inclusion of reserves as a
state variable. The structure of our model, net of climate change, bears some similarity to the ? analysis of two
productive capital stock technologies with adjustment costs. Our two stocks, however, produce distinct outputs
with one being the stock of reserves.

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where It is investment and 0 < φ0 < 1 and φ1 > 1. For computational purposes,
we will use the evolution for logK:


It
|σK |2
d logKt = ζK (Zt )dt +φ0 log 1+φ1
dt −
dt +σK ·dWt ,
Kt
2
where the third dt term is the local lognormal adjustment implied by Ito’s
lemma.
Output is constrained by an AK model:
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Ct +It +Jt = αKt ,
where Ct is consumption, It is new investment in productive capital, Jt is
investment in new reserves, and α > 0 is a productivity parameter. So far, we
imposed the adjustment costs in the capital evolution. Alternatively, we could
posit the adjustment costs in the output constraint. This model is sufficiently
streamlined so that it allows for both interpretations.3
In contrast to standard DICE models, we introduce the possibility or
replenishing reserves through an investment J in exploration. We do this
because the stock of known reserves does change based on new discoveries
as has been captured in some models of oil reserves as we discuss below. As
we will see, allowing for reserve augmentation does have important quantitative
consequences for our analysis. The stock of reserves, Rt , can be at least partially
replenished and evolves according to
dRt = −Et dt +ψ0 (Rt )1−ψ1 (Jt )ψ1 dt +Rt σR ·dWt ,
where ψ0 > 0 and 0 < ψ1 < 1 and Et is the emission of carbon. For
computational purposes, we use the implied evolution for logR:
 ψ 1
 
Jt
Et
|σR |2
d logRt = −
dt +ψ0
dt −
dt +σR ·dWt .
Rt
Rt
2
Remark 2.1. This model of reserves has some features in common with others
in the literature. The well-known Hotelling (1931) specification is a special case
in which Jt is constrained to be zero and σR = 0. To elaborate, let
 +∞
Rt =
Et+s ds
0

be a total stock of reserves available from date t forward. Then dRt = −Et dt,
or
Et
d logRt = − dt.
Rt
While the Hotelling constraint would gives us some pedagogical simplicity
and is a revealing platform for illustration, historically the stock of reserves has
3 See the Online Appendix for an elaboration.

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been increasing over time because of new discoveries. This motivates why we
allow for productive resources to be engaged in exploration.
Another special case is when ψ1 = 1. With this specification, a nonnegativity
constraint on Jt may bind for a substantial fraction of time in the solution to
the planner’s problem. A similar model with these features was analyzed by
Casassus, Collin-Dufresne, and Routledge (2018). They treated the counterpart
of Jt as an “impulse control problem” whereby Jt is optimally set to zero over
time segments determined endogenously. While we view this as an interesting
special case, we choose not to address it in this paper.
As a third example, Bornstein, Krusell, and Rebelo (2017) have an industry
model of reserves with a counterpart to investment Jt with diminishing returns.
They allow for richer dynamics by including an additional state variable they
call exploration, whose evolution depends on Jt . Exploration increases the
reserve stock in a proportional manner. In contrast, we conserve on state
variables by having fossil fuel investment augment the reserve stock. We also
allow for the current stock of reserves to alter the productivity of investment Jt
in a manner that preserves a constant-returns-to-scale specification.
None of these three papers used their reserve model to explore adverse
social implications of carbon admissions. While many previous researchers
have imposed a Hotelling (1931)-type constraint, we are particularly interested
in the impact of including investment in the new discovery of fossil fuels.
2.3 Damages
Climate literature suggests an approximation that can simplify discussions of
uncertainty and its impact. Matthews et al. (2009) and others have purposefully
constructed a simple “approximate” climate model:
 t
Tt −T0 ≈ β Es ds = βFt ,
(1)
0

where the F evolution pertinent to this approximation is
dFt = Et dt.
Within this framework, emissions today have a permanent impact on
temperature in the future where β is a climate sensitivity parameter.
Of course, this is a rather stark approximation of a complex climate system,
and we will entertain some alternatives. A substantial literature in climate
science assesses for what purposes this is a revealing approximation, which
we will discuss subsequently. There are transient components to temperature
fluctuations not explicitly connected to emissions that are needed to capture
a more complete characterization of temperature dynamics. These could be
captured by an exogenous transient process added to βFt in our analysis.
We focus on the component that the Matthews et al. approximation is
meant to capture. Thus while actual temperature has transient departures, the

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contribution to temperature change that might be most pertinent to our analysis
of the economic impact of climate change could be the increment βEt . Even
with a richer specification of the climate dynamics, it could be advantageous to
feature the longer-term temperature changes induced by human activity as it is
not obvious why the transient components should be included when quantifying
damages induced by an externality induced by carbon emissions. In this paper
we use cumulative emissions, F , and not temperature, T, as the pertinent state
variable.
The simplicity of the Matthews et al. approximation is sometimes used
to reframe policy questions in terms of a carbon budget. Given knowledge
of the parameter β, a maximal allowable change in temperature implies an
intertemporal constraint on the amount of emissions and in effect could be
used to justify a Hotelling-type constraint on cumulative emissions. But when
there is substantial uncertainty about the climate sensitivity coefficient, β, there
is corresponding uncertainty about what constraint to impose on emissions.
Figure 2 depicts this uncertainty via a histogram and a smoothed density based
on evidence reported by MacDougall, Swart, and Knutti (2017). They find the
cross model mean value to be 1.72 degrees centegrade per one trillion tons
of carbon (TtC). The .05 quantile value is 0.88, which is about half the mean
value, and the .95 quantile is 2.52, showing the extensive range of parameter
values. When there is substantial uncertainty about β, there is uncertainty
about what constraint to impose on emissions. As an alternative, we could
impose the constraint on the realized temperature change or on the admissible
augmentation of carbon concentration.
Given our limited understanding of how to model damages and longterm uncertainty associated with the impact that emissions might have on
the economy, some scholars have doubted the value of building so called
integrated assessment models with ad hoc specifications of economic or social
damages. Instead some have suggested that the social policy objectives should
be framed in terms of temperature increases induced by carbon concentration
targets. For recent such arguments, see Morgan et al. (2017) and Pezzey
(2019). Imposing admissible temperature or concentration bounds can be
represented as an extreme form of damage or penalization function with infinite
damages or penalties when a threshold is exceeded. We could use this as our
specification for damages, but instead we follow much of the economics-climate
literature by penalizing large temperature changes through a so-called “damage
function” specified exogenously. Consistent with a more general view of carbon
budgeting, this damage function could be taken to be a penalty function instead
of a hard constraint where the magnitude of the penalty is dictated, at least
in part, by the implied climate outcomes. Recall that our aim is to assess
what aspects of uncertainty have the most adverse consequences, and we see
value in the modeling formalism. On the other hand, we share concerns about
the literal interpretation of ours and others of the computed social costs of
carbon.

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0.8
0.7

Density

0.6
0.5
0.4

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0.3
0.2
0.1
0
0

0.5

1

1.5

2

2.5

3

3.5

Climate Sensitivity Parameter
Figure 2
Climate sensitivity uncertainty. Histogram (red) and normal density approximation (blue) for the climate
sensitivity parameter β across models. The climate sensitivity parameter is in units of degrees centigrade per
teraton carbon. Figure based on evidence reported in Figure 3A by MacDougall, Swart, and Knutti (2017)
(© American Meteorological Society, used with permission) and constructed with data provided by the authors.

In this paper, we follow much of the previous literature in economics by
positing an ad hoc damage process to capture negative externalities on society
imposed by carbon emissions. Just as in the case of the climate approximation,
the damage specification we use is an obvious simplification. The economics
literature has explored alternative damage specifications typically expressed
as functions of temperature. By positing such an evolution we refrain
from modeling formally any dynamics associated with adaptation including
responses in advance of future temperature increases.4 While this model is
overly simplistic, the evolution of damages captures two forms of uncertainty
that interest us, one from damages that we as depict as uncertainty in the function
 and the other from climate uncertainty parameter β.
2.4 Consumption damages
In this specification, the instantaneous contribution to the social utility function
is
δ(1−κ)(logCt −logDt )+δκ logEt ,
where δ > 0 is the subjective rate of discount and 0 < κ < 1 is a preference
parameter that determines the relative importance of emissions in the
4 While the literature on modeling adaptation to climate change is limited, for a recent example focused on

agriculture, see Keane and Neal (2018).

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instantaneous utility function. Abstracting from damages, the instantaneous
utility is the logarithm of a Cobb-Douglas composite good that depends
on material consumption and an energy component that is proportional
to emissions. We incorporate damages into this analysis by presuming
that diminishes proportionately the material consumption component to the
composite good. While in this representation, damages enter the utility function,
we may equivalently think of this as a model with proportional damages to
production along the lines suggested by Brock and Hansen (2018).
We model the logarithm of damages as
 
f
logd = (βf )+ζD (z)·
,
1
 
f
1
potentially captures two forms of uncertainty in damage/climate sensitivity
by adding an exogenous shifter to the logarithm of damages. One component is
deliberately proportional to the temperature anomaly. The other component
could capture a distinct role for more transient changes in temperature on
damages or other technological contributions that could affect damages. As
we will see, this exogenous component opens the door to possible model
misspecification that is at least partially disguised by the Brownian increments
dWt . The other component could capture a distinct role for more transient
changes in temperature on damages or other technological contributions that
could affect damages. The implied evolution for logD is
 
 
F
E
d logDt = [∇](βFt )βEt dt +dζD (Zt )· t +ζD (Zt )· t dt,
(2)
1
0
where ζD is a two-dimensional vector. With this specification, ζD (z)·

where [∇] is the first derivative of the function .
In our subsequent illustration we parameterize  as

γ1 y + 21 γ2 y 2
0≤y <γ
(y) =
1
γ1 y + 2 γ2 y 2 + 21 γ2+ (y −γ )2
y ≥γ ,

(3)

where γ2+ ≥ 0. To illustrate the impact of damage uncertainty, we focus on the
parameter γ2+ . For a low damage specification, we set this parameter to zero and
for a high damage specification we set it to be a positive number. By setting γ2+
to an arbitrarily large number, we approximate a carbon budget constraint by
penalizing damages in excess of γ . While the construction of γ is suggestive
of a “tipping point,” previous literature has explicitly focused on tipping points
with uncertain consequences. Of course, other damage functions are also of
interest. Observe that the uncertainties about the economic damage function
, in general, or the parameter γ + , it particular, and the geophysics climate
sensitivity parameter β are in effect multiplicative as they contribute to social

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1

Low Damages

0.95

0.9

High Damages

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Proportional Reduction in Economic Welfare

Pricing Uncertainty Induced by Climate Change

Carbon Budget

0.85

0.8

0

1

2

3

4

5

Temperature Increment over Preindustrial Levels (˚C)
Figure 3
Economic damage uncertainty. The two curves plot D as a function of the temperature net of preindustrial levels
for two alternative damage configurations. The vertical axis gives the corresponding damage percentage.

welfare. Because of this interaction, it would be misleading to simply add
together the uncertainties from the two sources.
In our computational example, we use the two damage functions depicted
in Figure 3. The low damage specification is implemented by setting γ2+ = 0.
In terms of the previous environmental economics literature, we imagine the
case in which γ2+ = 0 as an approximation to Nordhaus (2018). One can see
from this figure that our 3◦ C percentage loss is approximately the same
as that of Nordhaus and Moffatt (2017), who say, “...the estimated impact
is −2.04(+2.21)% of income at 3◦ C warming... We also considered the
likelihood of thresholds or sharp convexities in the damage function and
found no evidence from the damage estimates of a sharp discontinuity or
high convexity...” Weitzman (2012) argues for a steeper degradation in the
damages and motivates his construction of an alternative damage function
on the basis of uncertainty considerations. Rather than simply impose an
approximation to Weitzman’s damage function we illustrate an uncertainty
adjustment by positing an alternative even steeper function over some of
the temperature increment region and consider the impact of weighting the
two possibilities. This allows us to characterize the uncertainty contribution
explicitly.
There are two interconnected forms of uncertainty in the evolution of
damages that we will capture in conjunction with Equation (2), one from the
specification of the damage function  and the other from climate uncertainty
parameter β.

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2.4.1 Damages to macroeconomic growth. Alternatively, suppose that
damages diminish growth in the capital evolution:5
 
F
d logKt =ζK (Zt )dt −(βFt )dt −ζD (Zt )· t dt
1


It
|σK |2
+φ0 log 1+φ1
dt −
dt +σK ·dWt .
Kt
2
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Not surprisingly, and as discussed in previous literature (see, for instance,
the recent discussion in Diaz and Moore 2017), this difference can have an
important impact on computations of the social cost of carbon.6 Examples of
empirical analyses that seek to bear on this issue are Dell, Jones, and Olken
(2012) and Burke, Hsiang, and Miguel (2015), who have different perspectives
on the importance of heterogeneity and nonlinearity based on reduced-form
panel data evidence. From our perspective, this reinforces the notion of damage
rate uncertainty.
Several researchers, including Dell, Jones, and Olken (2012), Burke, Hsiang,
and Miguel (2015), Burke, Davis, and Diffenbaugh (2018), and Colacito,
Hoffmann, and Phan (2019), have looked empirically at the relation between
macro growth and temperature. Dell, Jones, and Olken (2012) explore crosscountry evidence including lagged effects. They document the largest impacts
of temperature on macroeconomic growth occur for low income countries.
While they find evidence for a long-term impact, the quantitative magnitude
of the impact is much reduced. The climate-economic system potentially has
feedbacks in both directions and a single equation approach may be a flawed
way empirically to deduce the long-term impacts. The heterogeneity in the
impacts across economies at different stages of economic development does
seem to be both empirically and substantively important. Unfortunately our
simplified analysis in this paper is not designed to confront this heterogeneity,
although the consequences of uncertainty will remain for a more refined
analysis.
Figure 4 uses reported evidence from Burke, Davis, and Diffenbaugh (2018)
exploiting cross-country variation in development and temperature exposure.
They report cross-country evidence with temperature and its square regressors
(in addition to fixed effects.)7 Their featured econometric specification has a

5 Bansal, Kiku, and Ochoa (2017) and Hambel, Kraft, and Schwartz (2018) give alternative stochastic models of

damages to macroeconomic growth. Both use a recursive utility specification for preferences with a risk-based
approach where the decision-maker knows the probabilities.
6 The material in section 9 of Diaz and Moore’s (2017) supplementary online material directly speaks to this point.

See Moyer et al. (2014), who provide an initial illustration to show that modifying a DICE-type model to include
damages to the growth rate of productivity could have a big impact on the SCC.
7 Relatedly, Burke, Hsiang, and Miguel (2015) show how a quadratic specification for the temperature impact on

growth can capture the heterogenous temperature responses previously documented by Dell, Jones, and Olken
(2012) and others.

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Growth Rate Impact

0

−0.005

−0.01

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−0.015

−0.02
0

1

2

3

4

5

Temperature Increment over Preindustrial Levels (˚C)
Figure 4
Macroeconomic growth rate damages. The reported quintiles are constructed using estimates from Burke, Davis,
and Diffenbaugh (2018) provided by the authors. The blue solid line represents the probability .2 quintile, and
the red dot-dashed line represents the .8 quintile. The intermediate curves are the .4 and .6 quintiles.

homogeneous growth response to temperature and abstracts from more lagged
impacts that might emerge through adaptation.
Our growth damage function is constructed from the estimated coefficients
from Burke, Davis, and Diffenbaugh (2018). Our γ1 and γ2 roughly correspond
to the linear and quadratic temperature effects, respectively, on economic
growth in their global effect regression.8 There are nontrivial issues in
converting this evidence to a single region, say world, model, leading us to make
some ad hoc choices in how we report and subsequently use their evidence.9
As we will see this quadratic specification of temperature on economic
damages will have rather dramatic implications for the policy implications
of our climate-economic model, and we include this in large part to illustrate
the impact of damage uncertainty. We have some skepticism as to how far
one can go in using developing country responses to quantify more generally
global responses to temperature changes by extrapolating from lower income
countries in locations with higher temperature.10 Moreover, given historical
evidence alone it is likely to be challenging to extrapolate climate impacts on
a world scale to ranges in which many economies have yet to experience.
8 See Figure 1A and the estimated coefficients β and β from equation 1 in their methods section.
1
2
9 The preindustrial temperature level corresponds to a value of approximately 13◦ C in temperature levels as
measured by historical records. We use 13◦ C as the baseline for the construction of the temperature anomaly

values that arise in our model. This value is in line with the median no damage temperature value estimated in
Burke, Davis, and Diffenbaugh (2018). We thank Marshall Burke for answering our questions about their work
and directing us to the GitHub repository for the relevant inputs need for our computations. Neither he nor his
coauthors bear responsibility for how we used their very interesting evidence.
10 These studies do include fixed country and time effects.

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Both richer dynamics and alternative nonlinearities may well be essential
features of the damages that we experience in the future due to global warming.
Burke, Davis, and Diffenbaugh (2018) give a thoughtful treatment of the impact
of parameter uncertainty that we exploited when constructing Figure 4 and that
we draw on in our computations that follow.11
3. Implications of Hamilton-Jacobi-Bellman Equations
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We start by deducing the relatively standard optimization implications
of our model in the absence of ambiguity and model misspecification
concerns. The following notation will be used in setting up social planner
Hamilton-Jacobi-Bellman (HJB) equations. Let the state vector Xt include
logKt ,logRt ,logDt ,Ft ,Zt , and let the action vector At include KItt , KJtt and
Et
. Write the composite state equation as
Rt
dXt = μX (Xt ,At )dt +σX (Xt )dWt ,


where σX (x) σX (x) is nonsingular m by m matrix. Let n denote the number of
states. In what follows we use lower-case letters to denote potential realized
values. For instance, d is a possible realization of logDt , k is a possible
realization of logKt and r is a potential realized value of logRt . In terms of
the actions, i and j are possible realizations of the investment ratios KItt and KJtt
and e is a possible realization of emissions ERtt . We denote the value function
by V (x). For our alternative model specifications, some of the state variables
enter into the value function in ways that we can exploit for computational
simplicity.
3.1 Consumption damages
The HJB equation for this setup abstracting from robustness is

0 =max −δV (x)+δ(1−κ) log(α −i −j )+k −d +δκ (loge +r)
a∈A



2
∂V
1
 ∂ V
+
(x)σX (x) ,
(4)
(x)·μX (x,a)+ trace σX (x)
∂x
2
∂x∂x 
where A is a constraint set for the realized action or decision a. As part of a guess
and verify approach, the implied value function coefficient for the logarithm
of damages is κ −1. The pertinent terms for the first-order conditions for the
actions or controls are:

 

1
δ(1−κ) log(α −i −j ) +δκ loge +(κ −1) [∇](βf )β +ζD (z)·
eexp(r)
0
+Vf (x)eexp(r)+Vk (x)φ0 log(1+φ1 i)+Vr (x) −e +ψ0 exp[ψ1 (k −r)]j ψ1 .
11 While cross-country differences in the long-term impact of temperature on growth is likely to be pronounced,

interestingly Colacito, Hoffmann, and Phan (2019) also find that seasonal differences are important in an advanced
economy like that of the United States.

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The first-order conditions for i, j , and e are12
−

δ(1−κ) φ0 φ1 Vk (x)
+
= 0, (5)
α −i −j
1+φ1 i

δ(1−κ)
+Vr (x)(ψ0 ψ1 )j ψ1 −1 exp[ψ1 (k −r)] = 0, (6)
α −i −j

 
δκ
1
exp(r) = 0. (7)
+Vf (x)exp(r)−Vr (x)+(κ −1) [∇](βf )β +ζD (z)·
0
e
−

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We denote the solution for the investment-capital ratio as i ∗ (x) and for
the exploration-capital ratio as j ∗ (x). The first-order conditions for the
two investments can be solved separately from the first-order condition for
emissions. Moreover, there is a further simplification as the first-order condition
for investment in capital implies the affine relationship (conditioned on state
variables)
φ0 φ1 Vk (x) α −i ∗ −j ∗ = δ(1−κ)(1+ψ1 i ∗ ),
which can be exploited in computation.
3.1.1 Relative prices of capital and reserves. As is typical in the investment
literature, we define the relative price π , sometimes referred to as Tobin’s q, as
the marginal rate of substitution between capital and consumption:


α −i ∗ (x)−j ∗ (x)
1+φ1 i ∗ (x)
π(x) = Vk (x)
,
(8)
=
δ(1−κ)
φ0 φ 1
where the second relation follows from the first-order conditions (5) for
investment in new capital. While the first-order conditions are for the
investment-capital ratio, the value function argument is the logarithm of capital.
These two adjustments net out in our construction of π .
Analogously, we define the relative price ρ as the marginal rate of substitution
between the reserve stock and consumption:

 ∗ 1−ψ1
exp[ψ1 (r −k)]
α −i ∗ (x)−j ∗ (x)
j (x)
ρ(x) = Vr (x)
,
=
δ(1−κ)
ψ0 ψ1
where the second equality is implied by the first-order conditions (6) for
investment in new reserves.
In the construction of these prices, we use the marginal utility of
consumption. Depending on the interpretation of the model, we could use
either Ct or the damaged counterpart Ct /Dt as the numeraire good. Use of the
∗ (x)−j ∗ (x)
∗ (x)−j ∗ (x)
with α−i
latter replaces the marginal utility contribution α−i δ(1−κ)
δ(1−κ)exp(d)
in the price constructions. Thus, in both cases, the formulas would include an
additional multiplication by exp(d) under the second choice of numeraire good.
12 In imposing first-order condition (5), we allow for “disinvestment,” that is, we permit i < 0. This outcome is not

prevalent in our model solution, however.

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13 Following our earlier notational convention, [∇ 2 ] denotes the second derivative of  .

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3.1.2 Social cost of carbon. The social marginal rate of substitution between
emissions and consumption is commonly referred to as the social cost of carbon
(SCC). Thus it is a shadow price of the resource allocation problem for a
hypothetical planner. It could be implemented via a Pigouvian tax that would
correct the private shadow price for the externality, although we use this way to
assess the impact of uncertainty, when conceived broadly. Following previous
literature, we start by representing this social cost in terms of partial derivatives
of the value function of the social planner. We then apply an asset pricing
perspective to interpret components to this social cost. This follows in part
discussions in Golosov et al. (2014). Cai, Judd, and Lontzek (2017) have a more
ambitious exploration of the risk consequences for the social cost of carbon. We
also embrace an asset pricing interpretation, but we will show how to extend the
analysis to include forms of uncertainty other than risk. Our purpose in making
this asset pricing link goes beyond the particular example economy that we
posited. This same perspective also allows researchers to understand better the
components to the social cost applicable in more general settings.
The marginal utility of emissions as a function of the state vector is given by

 
δκ
Vr (x)
1
−V
(x)+(1−κ)
[∇](βf
)β
+ζ
(z)·
,
=
f
D
0
e∗ exp(r) exp(r)
which follows from the first-order conditions (7). Dividing by the marginal
utility of consumption gives



 
Vr (x)
α−i ∗ (x)−j ∗ (x)
1
scc(x) =
−Vf (x)+(1−κ) [∇](βf )β+ζD (z)·
.
0
exp(r)
δ(1−κ)
As with the constructions of q ∗ and r ∗ , the scaling by capital nets out when
forming the marginal rate of substitution used in the social cost of carbon
construction.
The social cost induced by the externality is captured by the two terms:

 
1
ecc(x) = −Vf (x)+(1−κ) [∇](βf )β +ζD (z)·
,
(9)
0
scaled by the current period marginal utility for consumption. Both of these can
in turn be expressed as expected discounted values of future social damages.
To motivate this representation, consider impulse response functions for the
logarithm of damages in the future induced by a marginal change in emissions
today. This is necessarily a nonlinear impulse response and hence will be state
dependent. The marginal emissions change induces an impact on logDt+u given
by13

   u
1
[∇](βFt )β +ζD (Zt )·
+
[∇ 2 ](βFt+τ )β 2 Et+τ dτ.
(10)
0
0
The first contribution in (10) occurs on impact and is independent of u because
emissions at t have an (approximately) permanent impact on the logarithm

Pricing Uncertainty Induced by Climate Change

of damages. The second term (10) reflects the nonlinear dependence of the
logarithm of damages on state variable f . It includes an integral because of
the accumulative impact of emissions on this state variable. Because these are
expressed as marginal utilities, we discount using the subjective rate δ. Using
a simple integration-by-parts argument, we write
 ∞

 2
2
ecc(x) = (1−κ)E
exp(−δτ ) ∇  (βFt+τ )β Et+τ dτ | Xt = x
0

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 
1
+[∇](βFt )β +ζD (Zt )·
0

(11)

divided by the current period marginal utility of consumption. In formula (11),
we use the notation E to denote the expectation operator.14 In the Online
Appendix we show that formulas (9) and (11) coincide.
Thus the ecc is an expected discounted impulse response of marginal
damages induced by current period emissions divided by the current period
marginal utility of consumption. The discounting here is with respect to the
subjective rate of discount because we are working with marginal utilities. This
overall approach of representing the ecc as a discounted expected value extends
to more complex models of climate dynamics. But so far, we have presumed
knowledge of the climate dynamics when constructing this cost. We will have
much more to say about uncertainty adjustments in the next section.
3.2 Damages to macroeconomic growth
We briefly describe the corresponding set of calculations of the model in which
there are damages to capital evolution. In this specification, we no longer make
reference to an explicit damage state variable. The pertinent terms from the
HJB equation for optimization are given by
δ(1−κ)log(α −i −j )+δκ loge +Vk (x)φ0 log(1+φ1 i)

+Vr (x) −e +ψ0 exp[ψ1 (k −r)]j ψ1 +Vf (x)eexp(r).
Even with the modifications, the first-order conditions for i and j remain the
same. The value function and its derivatives are different, however, as is the
first-order condition for e:
δκ
+Vf (x)exp(r)−Vr (x) = 0.
e

14 The second term in (11) also can be written as a discounted expectation of


 
1
δ [∇](βFt )β +ζD (Zt )·
,
0

which is the same for all τ ≥ 0.

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Thus the implied marginal utility for emissions satisfies
δκ
Vr (x)
=
−Vf (x).
e∗ exp(r) exp(r)

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We now think of −Vf divided by the marginal utility of consumption to be the
external contribution to the social cost of carbon. The instantaneous utility cost
induced by a marginal change in e is given by −Vk (x)[∇(βf )β], and as we
show in the Online Appendix:
 ∞

ecc(x) = E
exp(−δτ )Vk (Xt+τ )[∇(βFt+τ )β]dτ | Xt = x .
0

Changing the numeraires at each date from utils to consumption entails
replacing Vk by the relative price π ∗ as given by formula (8) so that the social
costs being discounted weight marginal damages by π ∗ .
4. Incorporating Additional Uncertainty Components
As formulated so far, the planner’s problem only features risk and not other
components of uncertainty. We now explore multiple ways to capture a broader
notion of uncertainty, beyond just risk, that exploit some simplifications
that emerge from our continuous-time formulation. In what follows, we
capture ambiguity and model misspecification concerns conveniently with
two parameters (ξp ,ξm ) following an approach suggested by Hansen and
Sargent (2007) and extended to continuous time by Hansen and Miao (2018).
From a computational/mathematical perspective, they act as penalization
parameters that restrain the sensitivity analysis of alternative models (ξp ),
and the exploration of the potential misspecification of those models (ξm ).
An outcome of the computation will be an alternative probability measure that
reflects aversions to model ambiguity and to the potential misspecification of
each of the models under consideration by the social planner. In constructing
such a measure, we borrow convenient mathematical tools used extensively
for pricing derivative claims. The measure emerges as part of our solution to
an HJB equation for the planner who designs policies that are aimed to be
sensibly robust in the presence of this uncertainty. In effect, this probability is
an uncertainty-based pricing measure. In this section, we derive this adjusted
probability measure under various settings of uncertainty and its implications
for social valuation, and Section 5 illustrates its impact in a quantitative
example.
4.1 Discounting, uncertainty, and pricing
Our analysis shows how an asset pricing perspective adds new twists to
the environmental economics literature. Discussions of the questions “what
should the discount rate be for social valuation?” have been extensive in the
environmental economics literature to date. This discourse sometimes alludes

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to ad hoc uncertainty adjustments. A detailed version of such an exploration
is provided in Gollier (2013), including references to ambiguity aversion as a
motivation for wanting to alter discount rates. The discussion of discount rates
often includes both a subjective discount rate contribution, δ in our model,
and a growth rate adjustment. While our formulas for the SCC only include
the former, this is because we expressed the costs to discounting in utility
units. Had we used instead a consumption numeraire, a consumption growth
adjustment would have been present in our analysis as well. But even here, the
theory of asset pricing typically uses a stochastic discount factor process when
there are shocks to the macroeconomy. Differential exposure to these shocks
should be discounted in different ways as encoded conveniently in stochastic
discount factors. It is perhaps more germane to ask “what should the social
stochastic discount factor be for social valuation?” Producing interest rate
counterparts over alternative horizons depends on both the price of uncertainty
and the exposure to that uncertainty, but these adjustments are a feature of the
joint properties of the stochastic discounting and the uncertain social costs
to be discounted. Consistent with Gollier’s reference to forward rates, the
compounding of stochastic discount factors over multiple periods of time can
have substantively important valuation consequences giving rise to a potentially
important term structure for risk prices.
We next provide an overview of how we incorporate a broad notion of
uncertainty into valuation. In a nutshell, our uncertainty measures adds an
important dimension to stochastic discounting and the remainder of this section
shows how to construct this measure.
4.2 An overview
We purposely limit our exploration of alternative probability measures to
those that are “disguised” from the planner and not trivially revealed through
observations.15 Roughly speaking, consider alternative probabilities that can be
represented as likelihood ratios. Because we focus on models with Brownian
information structures, it is most convenient to use changes of measures familiar
in mathematical finance justified mathematically by the Girsanov theorem. As
is well known from the theorem, the implied change of probability measure
includes a possibly history-dependent drift distortion within the Brownian
increment. That is, dWt under the alternative probability measure can be
expressed as
dWt = Ht dt +dWtH ,
(12)
where dWtH a Brownian increment under the change of measure and H =
{Ht : t ≥ 0} is a history-dependent drift distortion process. The drift distortion

15 We accomplish this formally by considering only alternative probability measures that are absolutely continuous

over finite intervals of time.

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allows for considerable flexibility, but this formulation is not “without loss of
generality.”16 It is a restriction enforced by the likelihood ratio formulation.
To implement concerns about misspecification, we necessarily penalize
or constrain the corresponding drift distortions. For our alternative ways
to depict ambiguity aversion and model misspecification, we show the
corresponding adjustments to the Hamilton-Jacobi-Bellman (HJB) equation of
the robust social planner. These adjustments introduce a minimization problem
to the HJB equation formulation so that the planner solves a max-min, or
equivalently a two-player, zero-sum game specified recursively rather than only
a maximization problem. The minimization is over alternative probabilities
represented conveniently as drift distortions. We then use the minimization
problem to construct a specific probability measure that gives the valuation
adjustment that we are looking for. For adding specificity, we start by describing
more formally the resultant preferences.
4.3 Continuation values
We use continuation values to define the preferences recursively. Continuation
values are prospective and computed by solving a forward stochastic differential
equation. As in dynamic programming, a terminal value along with a forwardlooking evolution equation imply continuation value processes for each
hypothetical decision or action process. Looking forward, for Markov decision
problems of the type we consider for a social planner, the equation for the
continuation value evolution alters the HJB equations previously described.
Let U = {Ut : t ≥ 0} denote the continuation value process posed in continuous
time. Write
dUt = μU,t dt +σU,t ·dWt ,
where a recursive representation of the value function implies the restriction:
0 = μU,t +υt −δUt .

(13)

This representation of preferences translates into an HJB equation once we use
the Markov structure and the Ito formula to depict the drift μU,t in terms of value
function derivatives and the local evolution of the Markov state. For an action
or decision process A and value function V , the local dynamic coefficients for
the continuation value process are:


2
∂V
1
 ∂ V
μU,t =
(Xt )σX (Xt )
(Xt )·μX (Xt ,At )+ trace σX (Xt )
∂x
2
∂x∂x 


∂V
σU,t =
(Xt ) σX (Xt ).
∂x
The instantaneous utility υt depends on the action as a function of the state.
Optimization leads us to include the maximization as in (4).
16 Although there are ways to further generalize some of the formulations which follow, these are beyond the scope

of this paper.

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Under the (local) change of measure captured by (12), this is modified to be:
0 = μU,t +υt +σU,t ·Ht −δUt .

(14)

Alternative specifications of aversions to uncertainty will lead us to restrain the
drift distortion processes H in different ways.

0 = minm μU,t +υt +σU,t ·h−δUt +
h∈R

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4.4 Model misspecification
Initially, we explore model misspecification for a single model. Allowing for
arbitrary misspecification leads to a degenerate outcome. Instead we consider
ways of penalizing distortions using a well-studied construct in the applied
probability literature called “relative entropy.” The approach has been used
previously in the literature on robust control theory. For instance, see James
(1992) for a continuous-time formulation. We use the adaptation and extension
by Hansen and Sargent (2001), and Hansen et al. (2006). Anderson, Brock, and
Sanstad (2018) used a discrete-time formulation of this approach to study an
alternative energy climate model with concerns for model misspecification.
As shown by Hansen and Sargent (2019b), this formulation can be viewed
as a special case of the recursive variational decision theory axiomatized by
Maccheroni, Marinacci, and Rustichini (2006). This approach introduces a
quadratic penalty in (14)
ξm
1
σU,t ·σU,t ,
h·h = μU,t +υt −δUt −
2
2ξm
(15)

where the minimized value is:
Ht∗ = −

1
σU,t .
ξm

Here, ξm determines how much the planner is concerned about misspecification.
Large values of ξm capture low concern about misspecification, while for small
values of ξm this concern is much more pronounced.
Next, we describe a more structured approach to parameter uncertainty.
4.5 Parameter ambiguity
Dynamic models typically have unknown parameters for which theory and data
are only partially informative. Recall from Figure 2, that there is substantial
uncertainty in the climate sensitivity parameter β used in the Matthews
et al. approximation. Similarly, Figures 3 and 4 illustrate uncertainty in the
specification of damages. There may be very little reason to commit to a specific
measure of central tendency in the case of Figures 2 and 4 or an arbitrary
weighting of the high and low damage specifications in Figure 4 when solving
the model. We could perform calculations based on imposing alternative values
on the fictitious social planner and check for sensitivity of the analysis. Here,

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we suggest an alternative strategy whereby the planner confronts parameter
ambiguity and model specification with caution.
Let θ denote a possible parameter configuration unknown to the planner in
a set . For each possible parameter realization θ, there is dynamic evolution
given by:
dXt = μX (Xt ,At | θ)dt +σX (Xt )dWt .
For a value function V and a decision process {At : t ≥ 0}
∂V
(Xt )·μX (Xt ,At | θ ).
∂x

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μU,t (θ) =

Let Pt (dθ ) be a date t reference prior/posterior over a set of possible values
of  conditioned on date t information. In a dynamic setting, the distinction
between a prior and posterior becomes blurred as “yesterday’s posterior” is
“today’s prior”. The values of θ can index unknown parameters or a discrete
set of models or both. Rather than fully embrace this posterior, the planner
explores deviations. Let Qt (θ ) be a relative density that satisfies:

Qt (θ)Pt (dθ ) = 1,


which is used to alter the posterior distribution. Let Gt (θ ) be a drift distortion
that can depend on the unknown parameter. Then the drift distortion that
interests us is an Ht that satisfies


σX (Xt )Ht =
[μX (Xt ,At | θ )+σX (Xt )Gt (θ )]Qt (θ)Pt (dθ )



−

μX (Xt ,At | θ)Pt (dθ ),

(16)



as a possible drift distortion for the Brownian motion. Notice that if Qt
is identically one, then Ht = Gt (θ)Pt (dθ ) solves this equation. Before
proceeding, there is one technical restriction that we must impose on how
the drift depends on the unknown parameter vector.
Remark 4.1. Recall that we allow for σX to be singular (e.g., m < n). Instead,
we restrict the m by m matrix (σX ) σX to be nonsingular. Allowing σX to have
more rows than columns requires some explanation because there may not
exist a solution Ht to the equation. We rule this problem out by presuming
that the parameter vector to be fully disguised by the local dynamics. Suppose
there is some (potentially conditional) linear combination of the n-dimensional
state vector that has locally predictable dynamics for which the Brownian
exposure is zero. We restrict the implied drift for this linear combination to be
independent of θ. For example, in our model there is no diffusion component to
the state dynamics for F . These same dynamics do not depend on an unknown
parameter.

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To accommodate this structured uncertainty, in restricting the local mean of
the continuation value, we now alter minimization problem (15) along the lines
suggested in the Hansen and Miao (2018):
0=

min

min −δUt +υt

q, q(θ)Pt (dθ )=1 g(θ )∈Rm

 

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
ξm
μU,t (θ)+σU,t ·g(θ )+ g(θ )·g(θ ) q(θ )Pt (dθ )
+
2


+ξp [logq(θ)]q(θ )Pt (dθ ),
(17)


where we have penalized the choice of density distortion q with a scaled version
of the relative entropy divergence:

[logq(θ )]q(θ )Pt (dθ ),


which has been used extensively in the applied probability and statistics
literature. Letting q be one makes this divergence zero, and letting the parameter
ξp become arbitrarily large restricts the posterior distortion q to be arbitrarily
close to unity.
This minimization has a very tractable quasi-analytical solution, which is
important for numerical implementation. The minimizing g(θ) does not depend
on θ and has a solution analogous to that for minimizing h for the model
misspecification problem:
G∗t (θ ) = −

1
σU,t .
ξm

The minimizing density distortion


exp − ξ1p μU,t (θ )

,
Q∗t (θ ) =
1
 exp − ξp μU,t (θ) Pt (dθ )

which tilts the resultant posterior toward θ ’s for which the value function drift
is relatively low. Substituting these solutions in to the objective in (17) gives:



1
ξm
(18)
−δUt +υt −ξp log exp − μU,t (θ ) Pt (dθ)− σU,t ·σU,t .
ξ
2
p

Remark 4.2. This approach, absent model misspecification, can be viewed
as a continuous-time version of a “smooth ambiguity” model. Klibanoff,
Marinacci, and Mukerji (2005) represent uncertainty as a two-stage lottery
whereby one stage is used to capture risk conditioned on a model θ, which for
us is depicted as a Brownian increment, and another stage to depict ambiguity

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over models (indexed by θ ). They suppose that there are distinct preference
representations of aversions associated with this two-stage lottery. In this paper,
we follow Hansen and Miao (2018) in our use of a continuous-time formulation
along with the robustness interpretation. To connect our formulation to that
of Klibanoff, Marinacci, and Mukerji (2005), notice that the outcome of the
minimization problem depicted in (18) includes a term given on the left-hand
side of the inequality




1
−ξp log exp − μU,t (θ) Pt (dθ ) ≤ μu,t (θ)Pt (dθ).
ξp


The term on the left is recognizable as the exponential certainty equivalent and
less than the posterior mean  μu,t (θ )Pt (dθ ). Hansen and Miao (2018) derive
this as a continuous-time limit of recursive smooth ambiguity preferences.
Remark 4.3. As an alternative ambiguity adjustment in a continuous-time
Brownian setting, Chen and Epstein (2002) propose an instant-by-instant
restriction on the potential subjective probabilities Qt (θ )Pt (dθ ) assigned to
the alternative models. The decision-maker is uncertain about Qt but instead
restricts it to be in the convex set that can be state-dependent. The Chen and
Epstein (2002) preference specification is a recursive implementation of the
max-min utility formulation axiomatized by Gilboa and Schmeidler (1989).
Hansen and Sargent (2019b) motivate state dependence in the date-by-date
constraint set as a form of time variation in parameters and show how to
construct such an ambiguity set using a refinement of relative entropy. The
formulation in Hansen and Sargent (2019b) combines this approach with
concerns that each of the models in the ambiguity set might be misspecified.
This amalgam is very much analogous to the extension of the smooth ambiguity
formulation we proposed here. The asset pricing methods that we describe in
what follows are also applicable to the uncertainty averse preferences proposed
in Hansen and Sargent (2019b).
4.6 Parameter learning
Learning adds state variables to the analysis. For sufficiently simple examples,
there could be sufficient statistics that make learning recursions straightforward
and tractable to implement recursively. These sufficient statistics would need
to be included among the set of state variables and the drift distortions to the
underlying Brownian motion would alter their evolution. Also, depending on
what coefficients are uncertain, the choice of action could affect the learning and
the social planner problem as we have posed it here, as the social planner might
have incentives to “experiment.” To the extent such a channel exists, designing
a policy with this incentive in mind would add controversy to the analysis, as
it does in macroeconomic policy in other settings.17 For some key climate
17 For example, see Cogley et al. (2008) for a discussion of robustness and experimentation in a monetary policy

setting with learning.

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parameters, learning can happen at best very slowly. In our computations
we will omit the learning channel altogether. Although this will substantially
simplify our calculations, there are also convincing climate science-related
reasons to embrace this approximation. For instance, Roe and Baker (2007)
write, “The envelope of uncertainty in climate projections has not narrowed
appreciably over the past 30 years, despite tremendous increases in computing
power, in observations, and in the number of scientists studying the problem...
foreseeable improvements in the understanding of physical processes, and in
the estimation of their effects from observations, will not yield large reductions
in the envelope of climate sensitivity.” This perspective is consistent with the
Bayesian computations of Olson et al. (2012) for what they call the climate
sensitivity parameter that we mentioned earlier.
4.7 HJB equation and implications
We now propose a modified HJB equation for the social planner that includes
concerns about model misspecification and ambiguity. In light of this evidence
of very slow learning, we use a time invariant probability P in place of Pt
as an approximation. The value function dynamics given in Equation (17)
imply a counterpart HJB Equation to (4) with damages entering preferences
(or equivalently scaling consumption):

0 = max
min
minm −δV (x)+δ(1−κ) log(α−i−j )+k−d +δκ (loge+r)
a∈A q>0, qP (dθ )=1 g∈R



∂V
(x)·
μX (x,a | θ)q(θ)P (dθ )+σX (x)g
+
∂x



2
1
 ∂ V
+ trace σX (x)
(x)σX (x)
2
∂x∂x 

ξm
+ g  g +ξp [logq(θ )]q(θ )P (dθ ).
(19)
2

See the Online Appendix for more details on our numerical implementation.18
This max-min problem provides a state-dependent action a ∗ as well as statedependent density q ∗ and a drift distortion g ∗ . We now show how to use
these latter two objects to construct an uncertainty adjusted probability by
constructing a corresponding drift for the state dynamics. The ambiguityadjusted probability over the parameter space  is q ∗ (θ | x)P (dθ ) and the drift
as a function of the Markov state is given by

∗
(20)
μ (x) = μX [x,a ∗ (x) | θ ]q ∗ (θ | x)P (dθ )+σX (x)g ∗ (x).


In Section 3, we represented the external contribution to the social cost of
carbon as expected discounted future marginal damages induced by a marginal
18 We also provide a Jupyter Notebook on https://github.com/lphansen/Climate with access to the code for the

project and a user interface with more details on the implementation and the resultant accuracy.

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change in emissions for all future time periods where the time t +τ contribution
is
(1−κ)[∇ 2 ](βFt+τ )β 2 Et+τ

 
1
+δ(1−κ) [∇](βFt )β +ζD (Zt )·
0

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scaled by the marginal utility of consumption. This same logic extends once
we incorporate the alternative uncertainty sources, but with qualification.
The expectation is now computed using the conditional ambiguity-adjusted
probability measure. Instead of computing this expectation directly, we may
infer it from our ambiguity-adjusted HJB solution to the planner’s problem as
δκ
Vr (x)
ecc∗ = ∗
−
,
e exp(r) exp(r)
where the right-hand side is the marginal utility emissions minus the private
contribution from the value function. As in Section 3.1.2, this follows from the
first-order condition for emissions from the planner’s HJB equation. See the
Online Appendix for an elaboration.
As an alternative to evaluating the discounted value using the ambiguityadjusted probability, suppose we use the original unadjusted probabilities to
evaluate the expected discounted value of the future marginal social costs. Call
this ecc(x). We take the difference between the two discounted expected values

ucc∗ (x) = ecc∗ (x)−ecc(x)
divided by the marginal utility of consumption or its damaged counterpart to
be the uncertainty component to the SCC of carbon, inclusive of both model
ambiguity and model misspecification adjustments.
We compute ecc and hence ucc∗ as follows:
i) integrate:
 
[∇](βf )β +ζD (z)·

(1−κ)


ii) integrate:



 
1
P (dθ );
0

[∇ 2 ](βf )β 2 e∗ exp(r)P (dθ );

(1−κ)


iii) solve a Feyman Kac equation to compute the discounted expected value
of the future damage flow given in (ii) using the baseline probability
measure;
iv) add the solution from part (i) to the solution from part (iii) to form ecc.

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We apply the analogous approach for the model in which damages alter
economic growth. This basic construct is much more generally applicable
including to models with richer climate dynamics.
The altered probability is not meant to represent the beliefs of the social
planner. This constructed probability gives the planner a way to confront more
general forms of uncertainty other than risk. Conveniently, the outcome of our
robustness analysis to alternative probabilities can be captured and computed by
specifying two parameters that serve as preference parameters for the decisionmaker, ξp and ξm . Although we do not dictate what these should be, we find
it revealing to look at the implied ambiguity-adjusted probabilities and the
corresponding relative entropies to assess what probabilities are of most concern
to the decision-maker.19
Remark 4.4. Since the writing of Good (1952), robust Bayesians have
suggested that an implied “worst-case probability” under which the decisionmaker optimizes is worthy of careful inspection. The ambiguity-adjusted
probability measure that emerges from the HJB equation is arguably difficult
to interpret in this light, because it depends on endogenous state variables. To
construct this worst-case probability, we appeal to a result from two-player,
zero-sum differential games. Just like in dynamic programming, there is a date
zero static game that the HJB equation provides a solution for. Provided that a
so-called “Bellman-Isaacs condition” is satisfied, the orders of maximization
and minimization can be exchanged as of date zero without altering the implied
value to the game. See Fleming and Souganidis (1989) for a formal discussion.
To compute the worst-case probability, exchange orders in the static game
by first maximizing conditioned on the probability and then minimizing over
probabilities subject to penalization. The outcome of this static minimization
with the order of extremization reversed gives the worst-case probability from a
robust Bayesian perspective. For further discussion, see Hansen et al. (2006).20
Remark 4.5. The term “social cost of carbon” can have different meanings
depending on the context. While we featured the Pigouvian taxation
interpretation, there is another construct that may be more pertinent to current
usage by governments, say as is reflected in the Green Book prepared by
HM Treasury (2018). Consider a marginal change in emissions from an
existing equilibrium that may not be socially efficient. To formalize this
with a similar perspective, we would impose the stochastic evolution of the
pertinent economic state variables specified exogenously in our HJB equation
formulation. For instance, we could solve for a competitive equilibrium

19 See Anderson, Hansen, and Sargent (2003), and Anderson, Brock, and Sanstad (2018) for alternative ways to

link the parameter ξm to entropy measures and to so-called “detection error probabilities” used to assess how
statistically close the ambiguity-adjusted probability measure is to the reference or baseline probability.
20 The material in appendix D of their paper is particularly relevant to this topic.

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abstracting from climate impacts and then impose the resultant actions on the
planner’s problem. Instead of computing the action “a” as in HJB Equation
(19), we would dispense with the maximization and impose the solution for
the action from the competitive problem. We would continue to solve the
minimization problem to produce an ambiguity adjusted probability to use
for social valuation. With this approach, we would still compute the social
marginal rate of substitution of emissions and consumption as an alternative
measure of the social cost of carbon. This cost also can be represented as the
valuation of a social cash flow for the implied economic damages using the
ambiguity adjusted probability measure from the altered HJB equation.
5. An Illustration
In this section, we illustrate our analysis. To provide a basic understanding of
the economic model, we start by investigating a steady-state version of our
model without climate impacts. Given the homogeneity imposed, this version
of the model possesses a steady state in the appropriate ratios of variables.
This was by design. We use these relations to gain an initial understanding of
our baseline parameter configuration and to set the stage for assessing how the
efficient allocation is altered by incorporating the climate externality. We then
we introduce a climate/damage externality and show how uncertainty alters
emissions and the social cost of carbon. As we will illustrate, the damage
specification acts similarly to a Hotelling-like constraint on emissions.
5.1 Steady state without climate impacts
To illustrate “how the model works” we start with a deterministic version of
the model without damages and investigate the steady-state implications.
Table 1 lists the technology and preference parameters, and Table 2 gives
the steady-state values associated with our parameters. The economic model
at this level of abstraction is difficult to calibrate in a fully convincing way.
Thus, this table is not the outcome of a formal moment matching approach
sometimes used in the macro calibration literature. In addition to its simplicity,
the notion of capital in our setup should be broad based in including human
capital and forms of intangible capital in addition to physical capital. Similarly,
the reserves in our models could include both oil and coal.21 See the Online
Appendix for more details.
The emissions trajectory implicit in this fixed point ignores the climate
externality in perpetuity, so the outcome essentially will be to “fry the planet.”
Absent climate impacts, by design our model has sufficient homogeneity

21 We formally imposed two steady-state targets in our parameter settings, one on the reserves to capital ratio and

the other on the growth rate of capital. Had we not included the possibility of investment for the discovery of new
reserves, we would have been led to a rather different “calibration strategy,” including some speculation about a
substantially larger stock of “potential reserves.”

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Table 1
Technology (top) and preference
(bottom) configurations.
Value

α
φ1
φ0
μK
ψ0
ψ1

.115
16.7
.060
−.035
.113
.143

δ
κ

.010
.032

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Parameter

Table 2
Steady states for the model specification without
climate impacts. The values with a superscript a
were imposed when setting the parameters.
Variable
Investment/capitala : i
Growth rate of capitala : η
Marginal value of capitala : π
Emissions/reservesa : e
Reserves/capitala : exp(r −k)
Exploration/capital: j
Consumption/capital: c
Marginal value of reserves: ρ

Value
.090
.020
2.50
.015
.980
2.72 ×10−4
.0247
.0545

whereby there is steady growth implying a fixed point in ratios. Under the
Matthews et al. (2009) approximation, temperature will grow without bound.
In the competitive steady state associated with our parameter settings, emissions
grow at 2% while the subjective discount factor is 1%. This implies that log
damages will grow at roughly 4% given our quadratic specification of log
damages. This means that the discounted future social costs will be infinite
at the deterministic steady state. The solution to the social planner’s problem
will avoid this extreme outcome as it will be desirable to limit the growth of
emissions and keep the damage integral finite.
5.2 Consequences of climate and damage uncertainty
Our first set of results are computed in a stochastic version of the model22
using the smooth ambiguity specification of preferences applied to both climate
sensitivity and to the damage uncertainty depicted in Figure 3. In particular, we
make the following modeling simplifications:
i) ξm = ∞,

 
F
ii) ζD (Zt )· t = ζD,2 (Zt ).
1
22 See the Online Appendix for more details on the volatility parameters.

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In regards to item (i), we do not mean to diminish the importance of
model misspecification and plan to do comparative analysis of the distinct
consequences of both uncertainty components in future research. We impose
the restriction in item (ii), to simplify computation, though it also removes
a potentially interesting source of variation for emissions. Moreover, as
we discussed in Section 4.4, activating both would open an interesting
additional channel for model misspecification concerns to affect prudent
climate/economics policy.
As we discussed previously, associated with this ambiguity adjustment are
altered probabilities assigned to the alternative damage specifications and
altered densities for the climate sensitivity parameter β. As we see no easy
way to give a “primitive interpretation” for the magnitude of the smooth
ambiguity parameter ξp , we instead look at the distributional consequences
of this parameter setting. With this in mind, we begin by looking at the implied
densities and probabilities.
We start by assigning baseline probabilities of one half to each of the damage
specifications. Once we introduce damages, there is no even approximate
stochastic steady state of interest. As a result, this induces state dependence
in the worst-case or adjusted probabilities that is prominently reflected in the
dynamic evolution of state variables. The dependence on the state variable f
that measures cumulative emissions turns out to have a particularly pronounced
impact on the worst-case densities. The altered probabilities become greater as
the emissions trajectories push towards relatively higher damages towards the
region where the two damage specifications depicted in Figure 3 diverge. This
pattern is evident in the second column of Table 3, where we report entropies
for a deterministic path simulated from the state initialization that matches
the steady states from the competitive model without climate impacts. The
entropies only start to have notable distortions on this path 50 years out. Prior
to this date, altering probabilities has little impact on the decision problem
because the two damage specifications agree. The simulated path for the state
variables is from the solution to the planner’s problem in which emissions are
relatively modest. Exposure to large environmental degradation is delayed until
well into the future under this trajectory.
Figure 5 depicts the distorted climate sensitivity densities that condition on
each of the damage function specifications. This figure gives three densities for
the climate sensitivity parameter β. One reproduces the normal approximation
from Figure 2 and the other two are the ambiguity adjusted densities conditioned
on each of the two damage specifications. These are shifted to the right to capture
the caution implicit in the ambiguity adjusted probabilities. The distortions are
notably larger conditioned on the high-damage specification, which is to be
expected. The high damage specification is of most concern to the planner
while the adjusted weights reported in Table 3 even up to 100 years are modest.
Conditioned on the high damage specification the adjusted density for β loads
up probability in the right-tail with the second mode of the density becoming
more prominent.

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Table 3
Entropies relative to the baseline normal density with a mean of 1.73 and a standard deviation of .493.
For the “weighted damage” specification, the baseline probabilities are one half for each damage
specification in Figure 3. The implied worst-case probabilities for the low damage specification are given
in parentheses. For the “low damage” specification, probability one is placed on the low damage
specification. The worst-case means and standard deviations are reported in parentheses. For the “high
damage” specification, probability one is placed on the high damage specification. The value used for ξp
1 .
is 4000
Weighted
damage (low damage prob)

Low
damage (mean, SD)

High
damage

0
25
50
75
100

.005 (.50)
.010 (.50)
.026 (.50)
.112 (.46)
.197 (.42)

.010 (1.80, .502)
.032 (1.86, .510)
.054 (1.89, .515)
.071 (1.91, .518)
.084 (1.93, .520)

.004
.008
.018
.087
.162

Probability Density

Year 50

Year 75

Year 100

0.8

0.8

0.8

0.7

0.7

0.7

0.6

0.6

0.6

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

0
1

2

3

Climate Sensitivity

4

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Year

0
1

2

3

Climate Sensitivity

4

1

2

3

4

Climate Sensitivity

Figure 5
Probability densities for the climate sensitivity parameter. The blue solid curves represent the baseline probability
density, the red dot-dashed curves represent the ambiguity-adjusted density conditioned on the low damage model,
and the green dashed curves represent the ambiguity-adjusted densities conditioned on the high damage model.

Figure 6 plots the implied social cost of carbon over a 100-year time
horizon. This figure also includes a contribution that quantifies the impact of
the uncertainty-adjusted probability measure. The private contribution to this
cost is relatively speaking, very small and can safely be ignored. In contrast,
the uncertainty component is substantial and accounts for roughly half of the
social cost of carbon for this example. Not surprisingly, given our depiction
of the adjusted densities in Figure 5, the relative importance of the uncertainty
adjustment (as well as the cost itself) becomes more prominent at say 100 years
out than at zero. The units are 2010 U.S. dollars per ton of carbon.
Figure 7 gives two emissions trajectories, one computed when we abstract
from ambiguity aversion and the other from the same social planner’s problem
as was used in the Table 3 and Figure 5. Both trajectories decay much like in
a Hotelling exhaustible resource allocation problem. However, this outcome
is not induced by the potential exhaustion of the resource because our model
allows for investment in new reserves. Instead, the potential for severe damages

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800

600

Total
Uncertainty

400

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Dollars per Ton of Carbon

1000

200

0
0

20

40

60

80

100

Years
Figure 6
Social cost of carbon decomposition. The units are 2010 U.S. dollars per ton of carbon. The costs are computed
at the socially efficient allocation. The blue solid curve represents the total social cost of carbon. The private
contribution is negligible relative to the other components and is not plotted. The red dashed curve represents
the uncertainty contribution.

12

Gigatons of Carbon

11

Ambiguity Neutral
10

9

8

7

Ambiguity Averse
6

5

4
0

20

40

60

80

100

Years
Figure 7
Emissions comparison. The figure reports emissions paths under ambiguity aversion (blue solid line) and
ambiguity neutrality (red dashed line). In each case, the socially efficient allocations are used under the respective
ambiguity preferences.

restrain the emissions for the fictitious planner because of the presence of the
climate externality.23 While the curves in Figure 6 hold fixed the emissions and

23 Note that the initial value of emissions is actually higher here than in our steady-state setting that ignores climate

impacts. This finding emerges because the initial decrease in the marginal social value of holding reserves

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800

Ambiguity Averse

600

400

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Dollars per Ton of Carbon

1000

Ambiguity Neutral
200

0

0

20

40

60

80

100

Years
Figure 8
Social cost of carbon trajectories computed under ambiguity aversion (blue solid line) and under ambiguity
neutrality (red dashed line). In each case the socially efficient allocations are used under the respective ambiguity
preferences. The units are 2010 U.S. dollars per ton of carbon.

other allocations implied by the model, in Figure 8, we report the total social cost
of carbon with and without the ambiguity averse preferences. Both trajectories
grow like the resource price in a Hotelling model, but not surprisingly, the social
cost of carbon is higher when the planner is averse to ambiguity.
We next report results from a “sensitivity to the prior” type analysis familiar
in robust Bayesian methods. We change rather substantially the ex ante weights
to the two damage specifications by focusing on two extremes. In the first one,
we simply embrace the “low damage” specification by assigning probability
one to this specification while continuing to focus on climate sensitivity. In the
second one, we feature the “high damage” specification by assigning all of the
weight on this specification.
In making these comparisons, we hold fixed the parameter ξp . Alternatively
we might hold fixed relative entropies at perhaps some date and adjust the
ξp parameter accordingly. This becomes an issue because for the fixed ξp the
relative entropies differ across damage function specifications as is evident
in Table 3. Consistent with the computation we reported earlier, Figure 9
shows that for the “high damage” configuration, the distortions become quite
pronounced with a fatter right-hand tail for the climate sensitivity for longer
time periods in the future.
Figures 10 and 11 depict the conditioning outcomes for emissions and the
social cost of carbon, respectively. The emissions and social cost of carbon
trajectories when the ex ante equal weights are used are quite similar to those

increases emissions over that in the steady-state economy. While at the outset this impact offsets the additional
climate-induced social costs, it is only a transient phenomenon.

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Low Damage Specification

Probability Density

Year 50

Year 75

Year 100

0.8

0.8

0.8

0.7

0.7

0.7

0.6

0.6

0.6

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

0
2

3

4

0
1

Climate Sensitivity

2

3

4

1

Climate Sensitivity

2

3

4

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1

Climate Sensitivity

High Damage Specification

Probability Density

Year 50

Year 75

Year 100

0.8

0.8

0.8

0.7

0.7

0.7

0.6

0.6

0.6

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

0
1

2

3

Climate Sensitivity

4

0
1

2

3

Climate Sensitivity

4

1

2

3

4

Climate Sensitivity

Figure 9
Conditional probability densities for the climate sensitivity parameter. The top panel presumes the low damage
specification occurs with probability one, and the bottom panel presumes the high damage specification occurs
with probability one. The blue solid curves represent the baseline probability density; the red dot-dashed curves
represent the ambiguity-adjusted densities for the low damage specification; and the green dashed curves represent
the ambiguity-adjusted densities for the high damage specification.

that emerge when we feature only the high damage specification. In contrast,
the emissions trajectory is higher and the social cost of carbon lower when
entertaining only the low damage specification. This finding is explicitly tied
to our parameter ξp . A larger relative entropy penalty pushes the one-half/onehalf outcomes closer to an intermediate location. Figure 8 illustrates this for
the limiting case in which the ambiguity/robustness parameter is infinite.
To understand the plotted outcomes it is revealing to compare the adjusted
probability densities. Of particular interest are the green densities reported
in Figure 5 and the corresponding ones reported in the bottom of panel of
Figure 9. For instance, consider what happens at year 100. In Figure 5, the
density for the climate sensitivity parameter conditioned on the high damage
specification is even more substantial than the corresponding curve in the lower
panel of Figure 9, where only the high damage specification is entertained by the
planner. But in the ex ante one-half/one-half case, the marginal density for the
climate sensitivity parameter averages over the two damage specifications and
adjustments conditioned on the low damage configuration are much smaller
than those that condition on the high damage specification. About 40% of
the ambiguity-adjusted weight goes to the low damage specification, making it

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14

12

10

8

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Gigatons of Carbon

Low Damage

6

Weighted
High Damage

4
0

20

40

60

80

100

Years
Figure 10
Emissions comparison. The values are computed at the socially efficient allocation simulated along a deterministic
path. The blue solid curve repeats the trajectory give in Figure 7. The green dashed curve conditions on the high
damage specification, and the red dot-dashed curve conditions on the low damage specification.

Dollars per Ton of Carbon

1000

High Damage
800

Weighted

600

400

200

0
0

Low Damage

20

40

60

80

100

Years
Figure 11
Social cost of carbon comparison. The values are computed at the socially efficient allocations simulated along
deterministic paths. The units are 2010 U.S. dollars per ton of carbon. The blue solid curve repeats the trajectory
give in Figure 8. The green dashed curve conditions on the high damage specification, and the red dot-dashed
curve conditions on the low damage specification.

important in the low damage contribution in the marginal density for the climate
sensitivity parameter. More generally, the marginal densities are similar for the
different time periods even though the densities conditioned on the high damage
specification differ in ways that are quantitatively important. Consistent with
the similarities in the ambiguity-adjusted densities, there is an overall similarity
in trajectories for both the emissions and the social cost of carbon, as reported
in Figures 10 and 11.

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Table 4
Emissions and social cost of carbon external and uncertainty contributions. The values are computed at
the socially efficient allocations for deterministic pathways. The top panel gives the values at 0, 50, and
100 years for the ambiguity-neutral setting of the growth damages model. The bottom panel gives the
values at 0, 50, and 100 years for the ambiguity-averse setting of the growth damages model.
Ambiguity neutral: ξp = ∞
Year

Emissions

SCC - total

SCC - uncertainty

Entropy

0
50
100

2.4
2.0
1.8

240
708
1,996

0
0
0

0
0
0

209
590
1,638

.15
.17
.19

0
50
100

1.4
1.2
1.1

411
1,168
3,244

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1
Ambiguity averse: ξp = 175

5.3 Climate change and growth damages
For the macroeconomic growth damage specification, we incorporate estimates
of Burke, Davis, and Diffenbaugh (2018) used as in the construction of Figure 4.
The results from this growth specification of damages are much more extreme
than those displayed in the previous figures. What follows are the impacts
observed in emissions and the external and uncertainty contributions to the
social cost of carbon.
Table 4 provides the implications for emissions and the social cost of carbon
along a simulated deterministic path for 100 years. As before, the initial states
for this path match the steady states from the competitive model without climate
impacts. For these comparisons, we hold fixed relative entropies at time 100 to
be close to those in the consumption damage ambiguity averse setting. Given
the specification differences, this compels us to adjust the ξp parameter.
The socially efficient emissions are remarkably small and the social cost
of carbon remarkably high even under ambiguity neutrality. The uncertainty
adjustment is substantial, making the numbers all the more extreme.
As we noted earlier, using growth damages from tropical, underdeveloped
regions may well overstate damages to growth for other economies for reasons
many economists have discussed (see, e.g., Sachs 2001). We conjecture
that, to use this evidence in a more revealing way, it requires explicit
regional heterogeneity coupled with a more complete accounting the economic
differences in the regions. Distinguishing long-run from short-run growth
responses could also change the nature of the evidence as suggested in the
earlier work of Dell, Jones, and Olken (2012).24 Hence, we view our growth
analysis as a call for more serious probes into the sources and consequences of
economic damages.

24 Dell, Jones, and Olken (2012) consider only linear specification for temperature on macroeconomic growth rates.

Nonlinearity could well alter their short-run/long-run decomposition.

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5.4 Discussion and extensions
We have shown how uncertainty can potentially matter for the social cost of
carbon. Our model is very stylized, and our calculations are no doubt sensitive
to some of the modeling details. Whenever one engages, like we have, in
quantitative storytelling, the outcome is in part about the model and in part about
the social problem that it addresses. We explicitly constructed the framework
to include multiple “stories.” In what follows, we conjecture about potential
extensions of our analysis.
Our social costs of carbon, and in particular, the uncertainty components,
are sensitive to the parameter ξp . Our particular choice of ξp is made for sake
of illustration, but by conveniently using relative entropy, we have reduced
the ambiguity aversion representation to a single parameter. Instead of being
committed to a single parameter value, we may think of our framework as
providing a disciplined way to perform a prior/posterior sensitivity analysis for
uncertain damage and climate sensitivity parameters indexed by the choice of
ξp .
The discount rate choice δ will matter as it does in other discussions of climate
policy. Changing the subjective discount rate will certainly alter our emissions
and cost numbers. Moreover, stochastic discounting in social valuation depends
on both the subjective rate of discount in preferences and the ambiguity-adjusted
probability measure that we characterized. Along a similar vein, we find it
revealing and advantageous to focus on distinct contributions to valuation as
well as quantifying their overall impact. While our example economy is special,
the decomposition we propose has much more general applicability.
One familiar observation about Hotelling-type models is that as the price
rises, backstop technologies become viable, which can give an upper bound on
the price. The analogous observation applies in our setting with the potential for
green energies to become profitable in the future. While such a technology is
absent in our model, extensions that incorporated this will also place a new
source of uncertainty and a new channel by which uncertainty affects the
economic performance in future time periods. While the model would have
to change and the computations would be altered, we suspect that uncertainty,
broadly conceived, would continue to play an important role in a quantitative
investigation. Relatedly, as carbon presents more of a challenge for society in
the future and as technology advances, carbon sequestration may become an
attractive form of mitigation. The potential for this and other forms of mitigation
to become socially productive would certainly alter our quantitative findings,
but they would also open the door to new sources of uncertainty.
While the computations in this section focused on model ambiguity, as we
argued earlier in the paper, potential model misspecification is also a concern.
This misspecification may be disguised by the Brownian increments making it
difficult for the planner to detect model deviations. In future work, we hope to
investigate misspecification concerns as a third component to the uncertainty
pertinent to climate change.

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In this paper, we abstracted from active learning and its impact on the
uncertainty adjustments. While learning about carbon sensitivity may be modest
in the current environment, if we experience more rapid climate change in the
future, learning also could be more pronounced. This is absent from our model,
but it could be an important consideration. This form of learning, however,
occurs in times of potentially high economic damages making it costly for
society to defer action while waiting to learn more. This said, we believe
learning to be an interesting extension of our analysis.
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6. Impulse-Response Approximation for Climate Dynamics
Recall that a central component to the social cost of carbon is the response
function or trajectory for damages to an emissions impulse. A variety of
papers in the climate science literature have used transfer function and impulse
response methods to approximate the much more complex output that emerges
from climate models. This approach aims to provide useful summaries of model
implications or syntheses to support tractable emulation and facilitate model
comparison. Some examples include Li and Jarvis (2009), Joos et al. (2013),
and Castruccio et al. (2014). The Matthews et al. (2009) approximation is a
particularly simple version of such a linearized response function. In what
follows, we describe some more recent model comparisons that we find to be
particularly revealing. These findings suggest further important research should
be done that incorporates model uncertainty from climate science and expose
further modeling challenges to be faced in embracing this evidence.
Carbon-climate dynamics are often represented in two component parts,
the dynamic response of CO2 concentration to a change in emissions and
the dynamic response of temperature to a change in CO2 concentration via
radiative forcing. Combining the two, as in the Matthews et al. approximation,
entails a convolution of these response trajectories. Nonlinearity plays a role
connecting the two components as it is typically the logarithm of ratio of current
concentration to the preindustrial counterpart that determines radiative forcing
that is used as an input into the dynamic mapping from CO2 concentration to
temperature. See, for instance, Pierrehumbert (2014).
Impulse response and transfer functions, while pedagogically and computationally convenient, are inherently linear tools of analysis. As discussed
in Joos et al. (2013), there is a nontrivial issue over what range of inputs
might serve as a good approximation. The impulse response functions that
contribute to the social cost of carbon can accommodate nonlinearity by
allowing for explicit state dependence in the responses and by calculating local
approximations evaluated at the stochastic outcome of the planner’s problem.
Indeed, a small change in emissions in a nonlinear stochastic system with
uncertain random consequences in the future can be pertinent to the social
valuation. Given a nonlinear stochastic diffusion evolution, these responses
could be computed recursively using what is called the first variation of the

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Pricing Uncertainty Induced by Climate Change

process. Such computations, while they have conceptual appeal, would seem to
be tractable only for small scale nonlinear stochastic systems. Perhaps nonlinear
emulation methods also would be valuable inputs into studies like ours.
7. Conclusion

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We have shown how to apply continuous-time decision theory and asset pricing
tools to confront multiple components of uncertainty for the purposes of social
valuation. The framework we developed incorporates both concerns about
model uncertainty and model misspecification. The resultant methods allow
for these broader notions of uncertainty to be integrated formally into decisionmaking. We apply these tools to study the economic impacts of climate change
through the lens of the social cost of carbon.
While the methods are more generally applicable, our example illustrates
the impact of the interacting uncertainty components coming from climate and
economic modeling. In effect, the impact of these uncertainties is multiplicative:
and when both are large, together their impact can be truly substantial. As a
result, the social cost of carbon shows notable increases when both sources
of uncertainty are acknowledged. This aspect of the analysis is particularly
pertinent when the decision-maker is averse to ambiguity over models and to
potential model misspecification. Just as risk aversion is theory of “caution,” so
too are preference-based concerns about ambiguity and misspecification.25 We
believe these components to be particularly relevant for assessing the economic
impacts of climate change, and we expect them to be pertinent for social
valuation applied in other settings.
We are sympathetic to concerns that readers might have of our seemingly
simplistic use of the social cost of carbon. Yet, for the purposes of this paper,
the social cost of carbon serves as a metric to guide our assessment of what
components of uncertainty are most impactful. The development of richer
models of the underlying economy that include research aimed at mitigation or
for the development of viable green technologies are appealing extensions of
our analysis.
For quantifying the consequences of uncertainty in revealing ways, we
suspect that we have scratched the surface so to speak. For purposes of
illustration, we have imposed overly simplified specifications of climate and
economic dynamics. Moreover, the approximate climate models we consider
potentially understate the importance of nonlinearities in the climate dynamics.
Within the confines of risk analyses, important research on climate tipping
points has been done by Lenton et al. (2008), Cai et al. (2015), Cai, Lenton, and
Lontzek (2016), and Cai, Judd, and Lontzek (2017). We suspect that adopting

25 Even for financial markets, what is called risk aversion may be better conceived as investor concerns about these

other components to uncertainty. For example, see Hansen and Sargent (2019a).

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a broader perspective on uncertainty could contribute productively to this line
of research.

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==> RFS04 - Carbon Tail Risk 2020.txt <==
Carbon Tail Risk
Emirhan Ilhan
Frankfurt School of Finance & Management

Grigory Vilkov
Frankfurt School of Finance & Management
Strong regulatory actions are needed to combat climate change, but climate policy
uncertainty makes it difficult for investors to quantify the impact of future climate regulation.
We show that such uncertainty is priced in the option market. The cost of option protection
against downside tail risks is larger for firms with more carbon-intense business models. For
carbon-intense firms, the cost of protection against downside tail risk is magnified at times
when the public’s attention to climate change spikes, and it decreased after the election of
climate change skeptic President Trump. (JEL G13, G32, Q54)
Received March 1, 2019; editorial decision May 17, 2020 by Editor Ralph Koijen. Authors
have furnished an Internet Appendix, which is available on the Oxford University Press
Web site next to the link to the final published paper online.

Scientists broadly agree that strong regulatory actions are needed to avoid the
potentially catastrophic consequences of climate change.1 Climate change is
mostly caused by the combustion of fossil fuels, so any regulation will have to
aim at significantly curbing firms’ carbon emissions. However, whether, how,
and when regulatory climate policies will be implemented is highly uncertain.

We are grateful to Ralph Koijen (the editor) and two anonymous referees. We also thank Tobias Berg, Patrick
Bolton, Mathijs Cosemans, Kathrin de Greiff, Philipp Krueger, Ulf Moslener, David Ng, Altan Pazarbasi, Paulo
Rodrigues, Johannes Stroebel, and Jakob Thomä and seminar participants at the Western Finance Association
Meetings in Huntington Beach, Frankfurt School of Finance & Management, the RSM Dynamics of Inclusive
Prosperity Conference, the European Commission Conference on Promoting Sustainable Finance, the European
Commission Summer School on Sustainable Finance, the New Challenges in Insurance Conference, the EFA
Doctoral Workshop on ESG, the EFA Panel on Sustainable Finance, and the 2nd CUHK Derivatives and
Quantitative Investing Conference for their helpful comments. Supplementary data can be found on The Review
of Financial Studies web site. Send correspondence to Zacharias Sautner, z.sautner@fs.de.
1 The Intergovernmental Panel on Climate Change (IPCC 2018) summarizes the current scientific consensus about

climate change. The IPCC is the United Nations’ intergovernmental body for providing scientific evidence related
to climate change.
The Review of Financial Studies 34 (2021) 1540–1571
© The Author(s) 2020. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
doi:10.1093/rfs/hhaa071
Advance Access publication June 27, 2020

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Zacharias Sautner
Frankfurt School of Finance & Management

Carbon Tail Risk

2 In this paper, the term “priced” means that option prices reflect that certain stocks are riskier than others, rather

than that the market compensates investors for taking a certain risk by offering an expected return. Likewise,
“uncertainty” is not to be understood strictly in the Knightian sense of the word. This wording follows the
meaning used in the related literature (Pastor and Veronesi 2013; Kelly, Pastor, and Veronesi 2016).

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Regulation to limit carbon emissions could be enforced via carbon taxes, capand-trade schemes, or emission limits, all of which have different impacts on
firms. Even in the case of carbon taxes, it is highly uncertain what the price for
carbon emissions should be (it ranges between $15 and $360 per ton of CO2 ,
depending on the model) (Financial Times 2019). Climate policy uncertainty
is further amplified because of fundamental uncertainty about how strongly
emissions have to be reduced to limit global warming (see Barnett, Brock, and
Hansen 2020).
Climate policy uncertainty has heterogeneous effects across firms in the
economy. Uncertainty is likely to be most relevant for carbon-intense firms, as
such firms will be most affected by policies that aim at curbing emissions. For
such firms, regulation that limits carbon emissions can lead to stranded assets or
a large increase in the cost of doing business (Litterman 2016). Carbon-intense
firms may also experience financing constraints if banks reduce funding because
of climate-related capital requirements. Yet the extent to which carbon-intense
firms will be affected by regulation is highly uncertain. This uncertainty makes
it difficult for investors to quantify the impact that future climate regulation
will have on firms in terms of large drops in stock prices or general increases
in volatility.
In this paper, we test whether climate policy uncertainty is priced in the
option market.2 Specifically, we explore whether the cost of option protection
against downside tail risks is larger for firms with more carbon-intense business
models. We also explore whether the cost of option protection against increases
in return volatility (variance risk) is larger for more carbon-intense firms.
Our analysis builds on prior work documenting that political or regulatory
uncertainty is priced in the option market. Notably, Kelly, Pastor, and Veronesi
(2016, KPV hereafter) show that options which provide insurance against tail
and variance risks are more expensive when general political uncertainty is
higher. The benefit of using options-based measures is that these measures
reflect forward-looking expectations of subjective or perceived risk.
Pastor and Veronesi (2013, PV hereafter) provide a theoretical framework
that helps us explain why political uncertainty about climate regulation
(“climate policy uncertainty”) may affect asset prices. In their model, the
government decides whether to change its current policy. Potential new policies
are heterogeneous ex ante; that is, agents expect different policies to affect
firms in unique ways and with varying degrees of uncertainty. The government
decides on adopting a new policy based on investors’ welfare and political
costs. A new policy is more likely to be adopted if its positive impact on
firms’ profitability is higher and if the political costs associated with it are

The Review of Financial Studies / v 34 n 3 2021

3

We follow the literature in using risk-neutral quantities as risk measure proxies. The benefit of option-implied
variables compared to equivalents under the physical probability measure is their forward-looking character,
while the cost includes a potential bias stemming from the risk premium effect (for discussions of related issues,
see, e.g., Chang, Christoffersen, and Jacobs 2013; Cremers, Halling, and Weinbaum 2015; DeMiguel et al. 2013).

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lower. While investors can only start learning about policy impacts when a new
policy is adopted, “political signals” allow them to learn about political costs
before the adoption of a new policy. Asset prices are affected by shocks that
originate from learning about the political costs of the new policies: as new
shocks occur, investors change their beliefs about expected future policies.
PV show that political uncertainty leads investors to demand compensation
for political events (debates, negotiations, or elections) as such events affect
beliefs about future policies. Hence, investors’ expectations about future policy
changes affect asset prices. A cross-sectional implication of PV’s model is that
the cost of protection against downside tail and variance risks associated with
climate policy events depends on the sensitivity of firms to potential climate
regulation.
Our analysis uses three option market measures for firms in the S&P 500
as well as for the economic sectors of the index. Our focal measure, SlopeD,
originates from KPV and identifies downside tail risk. The measure reflects
the steepness of the implied volatility slope, and it is created as the slope of a
function that relates left-tail implied volatility to moneyness (with moneyness
being measured by the option’s delta). The measure is on average positive,
because far out-of-the money (OTM) puts are typically more expensive (in
terms of implied volatilities) than puts that are less OTM. An increase in SlopeD
indicates that deeper OTM puts become more expensive, which reflects a
relatively higher cost of protection against downside tail risks. SlopeD measures
the properties of the risk-neutral probability distribution implied by option
prices, and, hence, takes into account both the physical distribution of a stock’s
returns and an adjustment for the risk premium associated with the stock’s risk.3
Our other two measures provide complimentary information from the option
market. The model-free implied skewness (MFIS) quantifies the asymmetry of
the risk-neutral distribution (Bakshi, Kapadia, and Madan 2003). By being the
third central moment of the distribution normalized by the risk-neutral variance
(raised to the power of 3/2), MFIS reflects the expensiveness of protection
against left tail events relative to the cost of exposure to right tail events. The
variance risk premium (VRP) allows us to evaluate the cost of protection against
general variance risk, and it is computed as the difference between the riskneutral expected and the realized variances (Carr and Wu 2009; Bollerslev,
Tauchen, and Zhou 2009).
We focus on measures constructed from options with 30 days to maturity.
Short-term options are traded more frequently and with lower effective
transaction costs compared to long-term derivatives. Hence, their prices adjust
faster to investors’ flow of information as well as to changes in perceived

Carbon Tail Risk

4 For example, Muravyev and Pearson (2020) document that investors trade options on S&P 500 constituents with

time to maturity less than 3 months 30% more often (in terms of stock-days) than options with maturities between
3 and 12 months. The bid-ask spreads, adjusted for execution timing based on a high-frequency trade analysis,
are on average about 50% higher for longer-term options than for shorter-term ones.
5 Bolton and Kacperczyk (2020) explain their finding with Gennaioli and Shleifer’s (2010) local thinking

hypothesis, whereby investors use a coarse categorization of firms within a given industry when evaluating
carbon risks.

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uncertainty and risks.4 Further, we aim to identify the cost of protection against
large price drops, and such tail events have the most pronounced pricing effects
for short-term options (Cont and Tankov 2004).
Our data on carbon emissions are collected by means of a survey by CDP,
formerly known as the Carbon Disclosure Project. We focus on Scope 1
emissions, which originate from the combustion of fossil fuels or from releases
during manufacturing. We scale carbon emissions by firms’ equity market
values to obtain a measure of carbon intensity. We perform this scaling as the
impact of the costs of future climate regulation should be considered relative to
market values; for a given amount of emissions, firms with high equity market
values are likely to suffer less from regulation than firms with low market
values. Our main measure is a firm’s industry carbon intensity, that is, Scope 1
emissions of all reporting firms in the industry divided by the market value of
all reporting firms in the industry. We use this measure as carbon intensities are
primarily driven by industry characteristics (as we will show). Recent evidence
also indicates that industry characteristics drive the effect of Scope 1 intensities
on returns and investor screening (Bolton and Kacperczyk 2020).5 We use a
selection model as firms disclose emissions voluntarily to CDP.
We find strong evidence that climate policy uncertainty is priced in the
option market. A one-standard-deviation increase in a firm’s log industry carbon
intensity increases the implied volatility slope (SlopeD) by 0.014, or by 10% of
the variable’s standard deviation. We confirm our finding for sector exchangetraded fund (ETF) options: the cost of option protection against downside tail
risks is higher for the more carbon-intense sectors of the S&P 500. These results
are highly robust. For example, they are unaffected if we drop oil and gas firms
(our regressions already control for oil betas), and we continue to find effects for
option maturities of up to one year. Overall, our estimates suggest that options
written on carbon-intense firms are relatively more expensive, especially for
the far-left tail region, as they provide protection against downside tail risks
associated with climate policy uncertainty.
Evidence for the two other measures is more mixed, but it complements the
picture presented by SlopeD. While we find some effects for MFIS at the sector
level, we cannot detect corresponding effects at the firm level. These weaker
results reflect that MFIS, different from SlopeD, does not directly capture left
tail risk. Instead, it measures distribution asymmetry by comparing left and
right tail risk, with the latter, as we show, also being higher for carbon-intense
firms. For VRP, we find effects at the firm level, but not at the sector level.

The Review of Financial Studies / v 34 n 3 2021

6 Full diversification is unlikely for sectors with a low number of constituents and for sectors with a skewed

distribution of value weights.
7 In the PV model, the probability of the adoption of new policies increases (a) when the impact of the current

policy is harmful to firm profitability and (b) when political costs associated with new policies are low. We are
agnostic about which of these components drives our assumption. Public attention on climate change is often
increased after natural disasters and climate summits or political events related to climate change. The former
likely reveals inadequacy of current climate policies and, thereby, their harmful impact, whereas the latter likely
reduces political costs of adopting pro-climate policies.
8 An explanation for the difference in results may be that the Engle et al. (2020) index captures downside aspects

associated with climate change more directly, as it focuses on negative news.
9 No or little change in the status quo under President Trump was likely, especially when compared to Clinton’s

plans, even though he campaigned on withdrawing from the Paris Agreement. However, as the Paris Agreement
did not have any in-built enforcement mechanisms and U.S. climate regulation had been lenient prior to his
election, the expected uncertainty of the set of potential new policies under a regime of President Trump should
still be lower than that under a Clinton regime.

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Hence, our results for all three measures combined indicate that higher climate
policy uncertainty increases at the firm level the likelihood of left and right tail
events, and it has some effect on firm-level uncertainty as measured by VRP.
On the sector level, however, where firm-specific risks are partially diversified
away,6 we observe that the effect is more systematic and concentrated in the
left tail.
In a next step, we investigate whether the effect of carbon intensities on
downside tail risk is amplified at times when public attention to climate change
is high. Our assumption is that high public attention to global warming increases
the probability that pro-climate policies are adopted.7 Importantly, as the
probability of a policy change rises, so does uncertainty about which specific
new policies will be selected and what their impact on firm profitability will be.
While this implies more certainty that a regulatory change occurs, pro-climate
policies are characterized by large uncertainties in terms of their impact on firm
profitability as such policies represent larger deviations from current practices.
The cost of option protection against downside tail risk should therefore be
magnified at times when public attention to climate change spikes. To obtain
proxies for attention to climate change, we use the negative climate change news
index developed by Engle et al. (2020) as well as Google search volume data for
the topic “climate change”. While we find that the effect of carbon intensities
on SlopeD is aggravated when there is more negative climate change news, we
cannot detect a corresponding effect for Google search data.8
Finally, we use the election of President Trump in 2016 as a shock that
reduced climate policy uncertainty in the short term. Advantages of the
election are that its outcome was unexpected to the market and that it featured
two candidates with opposing views on climate regulation. While President
Trump signaled in his campaigns that prevailing climate policies would not
become stricter, Hillary Clinton, to the contrary, promised pro-climate policies.
Hence, President Trump’s election meant little change in the status quo of
U.S. climate regulation, whereas Clinton’s election would have implied the
opposite if she were elected.9 The cost of insurance against downside tail risks

Carbon Tail Risk

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associated with climate policy uncertainty should therefore have declined after
President Trump’s election, especially for carbon-intense firms. Supporting
this prediction, SlopeD for highly carbon-intense firms decreased by 0.025
after President Trump’s election, relative to less carbon-intense firms, a decline
equal to 12% of the variable’s standard deviation during the event window. We
find similar effects for sector options.
Our findings contribute to two strands of literature. The first strand documents
that regulatory or political uncertainty affects asset prices. As mentioned, KPV
is most closely related to us as they show that options are more expensive if
they provide protection against risks associated with political events. Consistent
with their model, PV find that stocks are more volatile and command a
higher risk premium when political uncertainty is higher, measured using the
Baker, Bloom, and Davis (2016) index. Similar evidence is provided by
Brogaard and Detzel (2015). Brogaard et al. (2020) find that higher global
political uncertainty is associated with lower equity returns and higher volatilities around the world. Related evidence from the healthcare market comes from
Koijen, Philipson, and Uhlig (2016), who show theoretically and empirically
that political uncertainty related to medical approval regulation and
reimbursement policies affects the profit risk of healthcare firms. As a result,
healthcare firms need to compensate investors with a risk premium. Using data
on U.S. healthcare firms, they document a 4%–6% annual medical innovation
premium, which reflects investor uncertainty about healthcare regulation.
Only a few papers in finance study climate policy uncertainty. Barnett (2019)
shows that climate policies that restrict oil use can generate a run on oil, whereby
oil firms accelerate extraction. This leads to a decrease in the oil price and
the value of oil firms. He also shows that firms with high climate policy risk
benefited from President Trump’s election. Similarly, Ramelli et al. (2020)
show that stock prices of carbon-intensive firms positively reacted to President
Trump’s election. Delis, de Greiff, and Ongena (2020) find that climate policy
uncertainty started to be priced into syndicated loans, especially among fossil
fuel firms. Engle et al. (2020) develop a dynamic strategy that hedges news
about climate change, and Barnett, Brock, and Hansen (2020) provide a
decision theory framework to address how climate uncertainty affects asset
prices.
The second strand examines the effects of climate change on asset prices.
Hong, Li, and Xu (2019) find that stock prices of food companies do not
fully reflect climate risks. Bolton and Kacperczyk (2020) document that
firms with higher carbon intensities earn a carbon premium. This finding
is similar to Hsu, Li, and Tsou (2020), who find that firms that generate
many toxic chemical emissions earn higher returns. Görgen et al. (2020)
create a carbon factor to capture firms’ sensitivity to the transition to a lowcarbon economy. Matsumura, Prakash, and Vera-Munoz (2014) find that higher
emissions are associated with lower firm values. Similarly, Berkman, Jona,
and Soderstrom (2019) use a firm-specific climate risk measure that they
find is negatively related to firm value. Using aggregate market outcomes,

The Review of Financial Studies / v 34 n 3 2021

1. Hypotheses Development
Our hypotheses development is guided by PV, who provide a framework to
explain why political uncertainty affects asset prices. Asset prices in their
model are affected by political shocks, which are due to investors learning
about the political costs associated with new policies. As these costs are
uncertain, investors are unable to predict which policies will be chosen, and
investors change their beliefs once political shocks arise. Hsu, Li, and Tsou
(2020) build on PV to analyze how firms with toxic emissions are affected by
political uncertainty. In their model, the government learns about the welfare
costs of toxic emissions and decides between strong and weak regulatory
regimes. Strong regulation has a more negative effect on the profitability of
emission-intense firms, and, as a result, these firms face larger risks.
Our hypotheses are related to these papers because global warming generates
large climate policy uncertainty for carbon-intense firms. (We consider climate
policy uncertainty to be a specific form of political uncertainty.) As global
warming is primarily caused by the combustion of fossil fuels, regulation
must be aimed at significantly reducing carbon emissions. Importantly, it
remains highly uncertain whether, how, and when such regulation would be
implemented. How firm profitability would be affected by any new policies
is also highly unclear. Climate policy uncertainty matters most for carbonintense firms, as these firms are the most directly affected by policy instruments
that curb emissions, such as emission limits, cap-and-trade schemes, or
carbon taxes. These instruments would likely reduce future cash flows of
carbon-intense firms and may depress their valuations as a result.
In summary, climate policy uncertainty makes it difficult for investors to
quantify the impact of future climate regulation on carbon-intense firms, in
terms of both large stock price drops and general increases in return volatility.
Hence, the cost of option protection against downside tail and variance risks
associated with climate policy uncertainty should be larger for such firms:
Hypothesis 1. The cost of option protection against downside tail and
variance risks associated with climate policy uncertainty is higher at carbonintense firms.

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De Haas and Popov (2019) show that more equity-funded markets have lower
per capita emissions, as stock markets seem to reallocate investment toward
more carbon-efficient sectors. Bansal, Kiku, and Ochoa (2017) show that
equity portfolios have negative exposure to long-run temperature fluctuations,
and Daniel, Litterman, and Wagner (2016) calibrate the price of climate risk.
Giglio et al. (2018) study long-term discount rates to evaluate climate change
mitigation policies. Although most of these studies concentrate on underlying
price effects and risk premiums, we analyze whether the cost of protection
against climate policy uncertainty is priced in the option market.

Carbon Tail Risk

Hypothesis 2. The cost of option protection against downside tail risks
associated with climate policy uncertainty increases at times when public
attention to climate change is higher.
Finally, we exploit President Trump’s election in 2016 as a shock that
reduced climate policy uncertainty in the short term. The advantage of the
2016 presidential election is that it featured two candidates with opposing
views on climate change. While Hillary Clinton supported new pro-climate
policies, President Trump signaled that prevailing climate policies were likely
to stay. He dubbed climate change “a hoax” and tweeted that “the concept
of global warming was created by and for the Chinese in order to make U.S.
manufacturing non-competitive” (Trump 2012). His stance can be interpreted
as a desire to keep the lenient status quo intact, whereas Clinton’s position was
more radical with a desire to make forward progress in pro-climate regulation.
Therefore, the set of climate policies likely to be adopted under President
Trump should have a lower variance compared to that under Clinton. Hence,
his unexpected election should have reduced uncertainty about which climate
policies will be adopted after Election Day.11 This should reduce the cost of
insurance against downside tail risks associated with climate policy uncertainty
at carbon-intense firms. This leads to the following hypothesis:
Hypothesis 3. The cost of option protection against downside tail risks
associated with climate policy uncertainty declined after the election of
President Trump in 2016 at carbon-intense firms.
10 Pastor and Veronesi (2012) formally model impact uncertainty. Pastor and Veronesi (2012) differs from PV’s

model in a way that has implications for our hypotheses. Pastor and Veronesi (2012) assume that prior beliefs
about the impacts of potential policies are identical. In contrast, PV allow the impacts and uncertainties to vary
across potential policies. It is these a priori heterogeneous beliefs about potential policies in PV that induce an
endogenous increase in political uncertainty as the probability of a policy change rises. In a limiting case in
which the probability of policy change goes to zero, there is no political uncertainty since the status quo is sure
to remain.
11 An advantage to the analysis of President Trump’s election is that his victory was largely unexpected by the

market. On Election Day morning, online gambling company Betfair put the probability of a victory by President
Trump at 17% (Wagner, Zeckhauser, and Ziegler 2018). President Trump also lost the popular vote by almost 3
million votes.

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High public attention to global warming, which may be the result of climaterelated natural disasters or political summits on climate change, should make
new pro-climate policies and their adoption more likely. New pro-climate
regulations can take many different forms with varying levels of severity (as
modelled in PV), and this heterogeneity generates policy uncertainty.10 As the
probability of a policy change rises, so does the political uncertainty about
which new policies will be adopted and their impact on firm profitability. The
cost of protection against downside tail risks associated with climate policy
uncertainty therefore should be magnified at such times. This leads to the
following hypothesis:

The Review of Financial Studies / v 34 n 3 2021

2. Data

2.1.2 Variable measurement. We scale firms’ Scope 1 emissions by their
end-of-year equity market values to obtain a measure of carbon intensity.
We divide emissions by equity values because new regulation is likely to be
implemented via cap-and-trade mechanisms or carbon taxes, which implies
that the amount to be paid by a firm should be considered relative to its market
value. Specifically, the stock price of a firm with a large market value is likely
to be affected less by, for example, a carbon tax, compared to a firm with the
same emissions but a low market value. We show that results are robust if we
scale emissions by total assets instead.
We employ a firm’s industry carbon intensity as the main measure in our
regressions. First, Table 2 shows that high carbon intensities cluster within a few
industries (and sectors) and are highly skewed. Figure 2 confirms this pattern

12 CDP data are reliable. First, many CDP signatories are influential investors in the surveyed firms, so false reporting

could have major ramifications. Second, many institutions consider CDP data to be so trustworthy that they use
them for their own risk management (Krueger, Sautner, and Starks 2020), and leading ESG data providers use
them for rating models (e.g., MSCI ESG Research, Bloomberg, or Sustainalytics).

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2.1 Carbon emissions
2.1.1 Data source. We collect data on carbon emissions from CDP, formerly
known as the Carbon Disclosure Project. The data are collected by CDP
on behalf of institutional investors representing over $87tr in assets under
management in 2018.12 Firms submit their data to CDP at the end of June,
covering emissions of the prior calendar year (the deadline was changed to
mid-August for 2018 submissions). CDP then releases these data by the end of
October. We examine emissions generated between 2009 and 2016. We focus
on S&P 500 firms because CDP primarily covers these firms for its U.S. survey.
Figure 1 shows that participation in the CDP survey among S&P 500 firms has
increased over time, in terms of the number of reporting firms (Figure 1, panel
A) and as a fraction of the S&P 500 market capitalization (Figure 1, panel B).
The data include information on three types of emissions. Scope 1 emissions
are direct emissions, which originate from the combustion of fossil fuels or from
releases during manufacturing. Scope 2 emissions are indirect emissions from
the consumption of electricity or steam, and Scope 3 emissions are emissions
that occur in the value chain of a firm (both upstream and downstream). CDP
translates all greenhouse gases into carbon dioxide (CO2 ) equivalents. We focus
on Scope 1 emissions because they are directly owned and controlled by firms.
(We find no effects for Scope 2 emissions and do not use Scope 3 emissions,
because they are not controlled by firms.) Table 1 shows that Scope 1 emissions
are highly skewed. While the average S&P 500 firm that reports emissions data
produces almost 5 million tons of carbon, the median firm emits only about
118,000 tons.

Carbon Tail Risk

A

Figure 1
CDP disclosure over time
This figure reports how disclosure of carbon emissions to CDP by S&P 500 firms has evolved over time. Panel A
reports the number of S&P 500 firms disclosing (blue) and not disclosing (white) the carbon emissions generated
in a given year as a fraction of the number of firms in the S&P 500. Panel B reports the market capitalization of
firms disclosing (blue) and not disclosing (white) the carbon emissions generated in a given year as a fraction of
the total market capitalization of the S&P 500.

across the sample.13 Second, Table 3, panel A, documents that firms’ carbon
intensities are primarily driven by industry characteristics. The panel explains in
columns 1 and 2 a firm’s carbon intensity, log(Scope 1/MV firm). While column

13 Internet Appendix Table 1 shows that unscaled emissions are similarly skewed. In fact, the top-20 emitting firms

alone generate about 60% of all carbon emissions in the S&P 500, and 29% come from just five firms.

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B

The Review of Financial Studies / v 34 n 3 2021

1 uses a firm’s industry carbon intensity, log(Scope 1/MV industry), as the only
explanatory variables, column 2 adds firm characteristics and year fixed effects.
In column 1, the adjusted R 2 of the regression is .920, which demonstrates that
firm-level variation in carbon intensity is largely subsumed by industry-level
variation. In column 2, the adjusted R 2 increases only slightly, which indicates
that firm characteristics play only a modest role in explaining firm-level carbon
intensities. Columns 3 and 4 estimate the same regressions from columns 1
and 2 but rely on unscaled instead of scaled emissions. We report these two
regressions to ensure that our results are not affected by the use of market values
on both sides of the equations. Reassuringly, the regressions confirm the pattern
that is documented in the first two columns. Third, Bolton and Kacperczyk
(2020) show that the effects of Scope 1 intensities on returns and exclusionary
screening by investors are driven by industry characteristics.
Therefore, our variable of interest is Scope 1/MV industry, defined as total
Scope 1 carbon emissions (in metric tons of CO2 ) of all reporting firms in the
industry divided by the total market capitalization of all reporting firms in the
industry (in millions $). The measure is calculated at the SIC4 level because
emissions can vary substantially within the SIC2 level (Internet Appendix
Table 2).

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Figure 2
Distribution of carbon intensities across S&P 500 firms
This figure reports a histogram of log(Scope 1/MV firm). Scope 1/MV firm are a firm’s Scope 1 carbon emissions
(in metric tons of CO2 ) divided by the firm’s equity market value (in millions $). The sample includes S&P 500
firms with data on carbon emissions disclosed to CDP. The sample covers emissions generated between 2009
and 2016.

Carbon Tail Risk

Table 1
Summary statistics
Variable

STD

25th

Median

75th

Obs.

4,957,597
313.82
261.85
38.20
0.710

15,853,469
1,131.91
757.36
69.56
0.238

16,829
1.15
1.61
5.02
0.500

117,715
6.76
6.43
12.70
0.667

1,078,551
54.46
48.64
36.36
1.000

1,963
1,815
1,903
1,763
1,963

SlopeD
MFIS
VRP

0.176
−0.415
−0.002

0.136
0.271
0.087

0.100
−0.564
−0.011

0.135
−0.429
0.005

0.207
−0.284
0.021

1,959
1,959
1,959

Institutional ownership
log(Assets)
Dividends/net income
Debt/assets
EBIT/assets
CapEx/assets
Book-to-market
Returns
CAPM beta
Volatility
Oil beta

0.793
10.12
0.395
0.263
0.104
0.039
0.407
0.171
1.065
0.066
−0.018

0.130
1.33
0.516
0.157
0.072
0.038
0.286
0.270
0.531
0.028
0.169

0.711
9.12
0.165
0.149
0.053
0.013
0.202
0.008
0.671
0.046
−0.115

0.811
9.95
0.331
0.246
0.095
0.028
0.343
0.149
1.021
0.058
−0.034

0.883
10.88
0.522
0.362
0.143
0.055
0.562
0.307
1.390
0.079
0.057

1,916
1,963
1,949
1,960
1,963
1,959
1,815
1,963
1,963
1,963
1,963

Summary statistics are reported at the firm-year level. The sample includes all firms in the S&P 500 with data on
carbon emissions disclosed to CDP. Table A.1 defines all variables in detail. The sample period covers emissions
generated during the years 2009 to 2016 and option market measures from 2010 to 2017.

2.2 Option market measures
2.2.1 Data source. We use option market measures to identify the effects of
climate policy uncertainty. Option prices subsume expectations about investment opportunities (Vanden 2008), and option-based variables work well in
predicting future assets price dynamics (e.g., Christoffersen, Jacobs, and Chang
2013). Most importantly, options-based measures reflect expectations about all
possible future events, even the rarest ones. We use options data from the
Surface File of Ivy DB OptionMetrics. For sectors, we use options on State
Street Global Advisors’ ETFs (SPDR ETFs) as the underlying. The Surface
File contains daily Black-Scholes implied volatilities for standard maturities
and delta points (for absolute deltas from 0.2 to 0.8, with 0.05 delta increments).
The implied volatilities are created from closing options prices through interand extrapolation in the time and delta dimensions. Although these implied
volatilities do not correspond to traded option contracts and form a standardized
volatility surface, they reflect the consensus expectations of market participants
priced into the options. We select OTM calls and puts with absolute deltas
smaller than 0.5. Return and market capitalization data are from CRSP.14
We process the surface data to make them less discrete in the moneyness
(defined as strike over spot) dimension. For each underlying, maturity, and day,

14 We obtain the composition of the S&P 500 and its sectors from Compustat and merge these data with data from

CRSP through the CCM linking table using GVKEY and IID to link to PERMNO, following the second-best
method from Dobelman, Kang, and Park (2014). We match CRSP data with options data through the historical
CUSIP link, provided by Ivy DB OptionMetrics.

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Mean

Scope 1 firm
Scope 1/MV firm
Scope 1/MV industry
Scope 2/MV firm
Industry CDP disclosure

The Review of Financial Studies / v 34 n 3 2021

Table 2
Firms’ carbon intensities by industry and sector
A. Ranking of top-10 industries by Scope 1/MV firm
Industry name

SIC2

Mean

STD

25th

Median

75th

Obs.

1
2
3
4
5
6
7
8
9
10

Primary metal industries
Electric, gas, & sanitary services
Stone, clay, & glass products
Transportation by air
Water transportation
Petroleum & coal products
Oil & gas extraction
Railroad transportation
Paper & allied products
Auto repair, services, & parking

33
49
32
45
44
29
13
40
26
75

12,029
3,216
1,100
1,091
334
322
232
200
189
188

549
3,584
356
759
67
46
151
50
244
36

11,642
630
798
479
281
285
133
157
44
163

12,029
2,329
1,022
937
314
330
200
209
64
171

12,417
4,119
1,378
1,436
407
353
306
244
421
225

2
153
5
26
6
16
69
23
35
7

SPDR ETF

Mean

STD

25th

Median

75th

Obs.

XLU
XLE
XLB
XLI
XLP
XLY
XLV
XLK
XLF

2,396
324
292
54
19
16
4
1.2
0.8

572
45
59
5
3
12
2
0.7
0.3

1,880
290
280
51
16
8
3
0.6
0.5

2,602
314
304
53
19
11
4
1.1
0.8

2,883
355
327
57
21
21
6
1.8
1.0

8
8
8
8
8
8
8
8
8

B. Ranking of S&P 500 sectors by Scope 1/MV sector
Rank

Sector

1
2
3
4
5
6
7
8
9

Utilities
Energy
Materials
Industrials
Consumer staples
Consumer discretionary
Healthcare
Technology
Financials

Panel A reports firms’ Scope 1 carbon intensities for the top-10 industries. Statistics are reported at the firm-year
level across different SIC2 industries. Scope 1/MV firm are a firm’s Scope 1 carbon emissions (in metric tons of
CO2 ) divided by a firm’s equity market value (in millions $). We rank industries by the average carbon intensity
of firms in an industry. The sample includes all firms in the S&P 500 with data on carbon emissions disclosed to
CDP. The sample period covers emissions generated during the years 2009 to 2016. Not all firms are included in
our sample across all years, which explains why the number of observations in some industries falls below eight.
Panel B reports Scope 1 carbon intensities of the economic sectors of the S&P 500. Statistics are reported at the
sector-year level. Scope 1/MV sector are a sector’s Scope 1 carbon emissions (in metric tons of CO2 ) divided
by a sector’s equity market value (in millions $). We rank sectors by the average sector carbon intensity. The
sample includes 9 of the 11 sectors of the S&P 500. The sample period covers emissions generated during the
years 2009 to 2016.

we interpolate the observed implied volatilities as a function of moneyness
within the available data range using monotonic cubic splines (piecewise cubic
Hermite interpolating polynomials). We then fill in the implied volatilities
beyond the observed moneyness bounds with the volatilities on the bounds.
For OTM puts, we use the leftmost available data point (corresponding to a
Black-Scholes delta of -0.2), and for OTM calls, we use the rightmost available
data point (corresponding to a delta of 0.2). In this way, we produce 1,001
data points over the moneyness range from 1/3 to 3 (corresponding to equally
spaced points from a log-moneyness of -log 3 to log 3). Each of these data points
contains an implied volatility for a particular moneyness level and, hence, for
an option delta level.
2.2.2 Variable measurement.
2.2.2.1 Primary measure: Implied volatility slope. The implied volatility
slope (SlopeD), borrowed from KPV, is a function relating the left-tail

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Rank

Carbon Tail Risk

Table 3
Determinants of carbon intensities, carbon emissions, and carbon disclosure to CDP
A. Determinants of carbon intensities
or carbon emissions
log(Scope 1/
MV firm)

Dependent variable:

log(Scope 1/MV industry)

B. Disclosure
decision

log(Scope 1
firm)

(1)

(2)

0.969∗∗∗
(180.20)

0.940∗∗∗
(87.06)

log(Scope 1 industry)

CDP
disclosure
(4)

1.015∗∗∗
(148.91)

0.927∗∗∗
(50.36)
0.342∗∗∗
(8.77)
0.125∗∗
(2.44)
1.123∗∗∗
(4.19)
2.334∗∗∗
(3.85)
5.812∗∗∗
(3.98)
0.142
(0.93)
0.059
(0.33)
0.022
(0.09)
0.168∗∗
(2.57)
−8.362∗∗∗
(−4.45)
−0.341∗
(−1.86)
−0.029
(−1.37)

0.926∗∗∗
(113.84)
0.076∗∗∗
(11.69)
0.019
(1.35)
−0.067∗
(−1.75)
0.202∗∗
(1.99)
−0.121
(−0.88)
−0.104∗∗∗
(−2.85)
−0.051∗
(−1.89)
−0.084
(−1.35)
0.042∗∗∗
(3.16)
−0.530∗
(−1.70)
0.041
(1.23)
−0.006∗∗
(−1.97)

Industry CDP disclosure
log(Assets)

0.015
(0.89)
0.056∗
(1.78)
0.561∗∗∗
(3.80)
0.073
(0.23)
1.807∗∗
(2.27)
0.365∗∗∗
(3.82)
0.013
(0.16)
0.212
(1.26)
0.093∗∗∗
(2.98)
−2.444∗∗∗
(−3.05)
−0.096
(−1.13)
−0.006
(−0.70)

Dividends/net income
Debt/assets
EBIT/assets
CapEx/assets
Book-to-market
Returns
Institutional ownership
CAPM beta
Volatility
Oil beta
Time trend

(5)

Model

OLS

OLS

OLS

OLS

OLS

Year fixed effects
Level
Frequency

No
Firm
Annual

Yes
Firm
Annual

No
Firm
Annual

Yes
Firm
Annual

Yes
Firm
Annual

Obs.
Adj. R 2

1,815
.920

1,772
.922

1,963
.827

1,772
.850

3,206
.461

Regressions in panel A are estimated at the firm-year level. Scope 1/MV firm are a firm’s Scope 1 carbon emissions
(in metric tons of CO2 ) divided by the firm’s equity market value (in millions $). Scope 1/MV industry is the
Scope 1 carbon intensity of all firms in the same industry (SIC4) and year. It is defined as total Scope 1 carbon
emissions (metric tons of CO2 ) of all reporting firms in the industry divided by the total market capitalization
of all reporting firms in the industry (in millions $). Scope 1 firm are a firm’s Scope 1 carbon emissions (in
metric tons of CO2 ) (unscaled). Scope 1 industry are the Scope 1 carbon emissions (in metric tons of CO2 ) of
all firms in the same industry (SIC4) and year (unscaled). The sample includes all firms in the S&P 500 with
data on carbon emissions disclosed to CDP. The sample period covers emissions generated during the years
2009 to 2016. Regressions in panel B are estimated at the firm-year level. CDP disclosure equals one for a given
firm-year if a firm discloses data on the carbon emissions released during the year, and zero otherwise. Industry
CDP disclosure is the fraction of firms in the same SIC4 industry and year that discloses data on the carbon
emissions released during the year. The sample includes all firms in the S&P 500. The sample period is the same
as in the first panel. Table A.1 defines all variables in detail. t -statistics, based on standard errors clustered by
industry (SIC4) and year, are in parentheses. *p < .1; **p < .05; ***p < .01.

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(3)

The Review of Financial Studies / v 34 n 3 2021

2.2.2.2 Additional measures: Model-free implied skewness and variance
risk premium. MFIS is constructed following Bakshi, Kapadia, and Madan
(2003, BKM hereafter) and quantifies the asymmetry of the risk-neutral
distribution. It is computed using the standard formula for the skewness
coefficient, that is, as the third central moment of the risk-neutral distribution,
normalized by the risk-neutral variance (raised to the power of 3/2). By
being normalized, MFIS also provides information about the expensiveness
of protection against left tail events, though now relative to right tail events.
As changes in the distribution asymmetry are driven by the probability mass
in the downside relative to the upside region, MFIS is affected by both tails.
In terms of interpretation, more negative values of MFIS indicate a relocation
of probability mass under the risk-neutral measure (i.e., after adjusting for
preferences toward risk) from the right to the left tail. Like in BKM, MFIS at
time t for period τ is given by
MFIS(t,τ ) =

erτ W (t,τ )−3μ(t,τ )erτ V (t,τ )+2μ(t,τ )3
[erτ V (t,τ )−μ(t,τ )2 ]3/2

where V (t,τ ) and W (t,τ ) are prices of variance and cubic contracts,
respectively; r is the prevailing risk-free rate; and μ(t,τ ) is the risk-neutral
expectation of the underlying log return over the period τ . All unknown
ingredients (variance, cubic contracts, and expected log return) in the formula
are computed by integration of some functions of options prices over the
continuum of strikes for a given maturity (see BKM for details). We
approximate these integrals with finite sums using the interpolated volatility
surface (see above). As MFIS captures the distribution of the probability mass in
the left versus the right tail of the risk-neutral distribution, it can be interpreted

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implied volatility to moneyness, measured using the Black-Scholes delta.
Specifically, SlopeD is the slope coefficient from regressing implied volatilities
of OTM puts (deltas between -0.5 and -0.1) on the corresponding deltas
and a constant. Because far OTM puts (with smaller absolute deltas) are
typically more expensive, SlopeD usually takes positive values. A more
positive value of SlopeD indicates that deeper OTM puts are relatively more
expensive, suggesting a relatively higher cost of protection against downside
tail risks. Because SlopeD is defined as a regression slope, it measures relative
expensiveness and does not depend on the average level of the implied volatility.
This feature allows us to compare the measure across firms with different levels
of general risk. SlopeD is our preferred measure as it most directly captures the
relative cost of protection against downside tail risk. Intuitively, it quantifies the
cost of protection against extreme downside tail events relative to the cost of
protection for less extreme downside events. We derive our results from options
with 1-month maturities and provide results for maturities of up to 12 months
for robustness. (Internet Appendix B illustrates the information content of this
and the two other measures.)

Carbon Tail Risk

3. Empirical Model
3.1 Selection model and truncation rule
We estimate a selection model to mitigate the concern that our estimates are
biased because firms voluntarily disclose their carbon emissions to CDP. The
need for a selection model arises because firms only disclose their emissions
if the (unobservable) net benefit of disclosing is positive. As a result, we only
observe the emissions generated by firm i during year t if the firm discloses this
information to CDP (i.e., if CDP disclosurei,t = 1). In all other cases, data on
carbon emissions is missing (i.e., if CDP disclosurei,t = 0). We therefore jointly
estimate the following model:
OMMi,m,t+1 = β0 +β1 Log(Scope1/MV industry)i,t +xi,t β +ui,m,t+1 , (1)
CDP disclosurei,t = γ0 +γ1 Industry CDP disclosurei,t +xi,t γ +vi,t ,

(2)

whereby Equation (1) constitutes the outcome equation and Equation (2)
the selection equation. As explained, Equation (1) is only observed if CDP
disclosurei,t = 1. We relate a firm’s carbon intensity in year t to option market
measures (OMM i,m,t+1 ) in year t +1 as emissions of year t are only made public

15 We follow KPV to compute the ex post VRP as opposed to an ex ante VRP (which is used by, e.g.,

Bollerslev, Tauchen, and Zhou 2009). The reason for selecting the ex post version is that, by construction,
it reflects all the information flow from the observation date to the option maturity and can capture the reaction
of traders to particular events, while the ex ante version is based only on expectations formed before and on the
observation date, which implies that it can miss important information. We thank a referee for pointing out this
potential problem. Note that our results are robust to using either version of VRP.

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as the cost of protection against left tail events relative to the cost of gaining
positive realizations on the left tail.
VRP is computed as the difference between the risk-neutral expected and the
realized variance (Carr and Wu 2009; Bollerslev, Tauchen, and Zhou 2009).
As a proxy for the risk-neutral expected variance, we use the model-free
implied variance (MFIV t,t+M ) computed on day t for maturity M following
Britten-Jones and Neuberger (2000) by again approximating the respective
integrals with finite sums using the interpolated volatility surface observed
on day t for maturity M. The realized variance (RV t,t+M ) is computed from
daily log returns over a future window from t to t +M, that is, with a length
corresponding to the maturity of the options used for the risk-neutral variance.
The variance risk premium (VRPt,t+M ) for maturity M is computed in the ex
post version on each day t as MFIV t,t+M −RV t,t+M , and expressed in annual
terms.15
VRP captures the cost of protection against general uncertainty-related
volatility changes in down and up directions, whereas our other measures
capture the relative cost of protection against left tail risk (relative to “normal”
risks, SlopeD, or relative to the right tail, MFIS).

The Review of Financial Studies / v 34 n 3 2021

3.2 Outcome equation: Option market variables and carbon intensities
For firm i in month m and year t +1, each option market measure is calculated as
the average across daily values. We estimate regressions at the firm-month level
to increase power, to exploit that the options measures are available throughout
the year, and because emissions are relatively persistent within the firm-year.
Importantly, some of our tests also explore how the effect of emissions varies
when climate attention fluctuates within the year (monthly).
Scope 1/MV industryi,t is the Scope 1 industry carbon intensity of firm
i during year t. We use (one plus) the variable’s natural logarithm because
emission intensities are highly skewed. Results are unaffected by within-year
changes in equity market values (the denominator of the emissions variable) as
we scale emissions by end-of-year market capitalizations.
We control for firm characteristics that prior work identified as determinants of firm risk, notably log(Assets), Dividends/net income, Debt/assets,
EBIT/assets, CapEx/assets, Book-to-market, Returns, CAPM beta, and
Volatility (unless we explain the VRP). We also control for Institutional
ownership, Oil beta, and a time trend. Control variables are measured at year t.
3.3 Selection equation: CDP disclosure decision
CDP disclosureit equals one if firm i discloses data to CDP on the carbon
emissions released during year t and zero otherwise. Equation (2) includes the

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by CDP in year t +1 (at the end of October). Consequently, information about
emissions generated in year t is only available to investors in the 12-month
period starting from November of year t +1. For our sample period, this implies
that we estimate the effect of emissions generated between 2009 and 2016
on option market variables measured between November 2010 and December
2017. Note that we employ a firm-level selection model even though carbon
intensities are at the industry level. The reason is that, for some industries, no
firms within the S&P 500 disclose any emissions data. This makes industry
carbon intensities unobserved for some firms and may bias ordinary least
squares (OLS) estimates.
We estimate our model using full-information maximum likelihood (FIML)
with the assumptions that (ui,m,t+1 ,vi,t ) is bivariate normal with zero means
and nonzero variances; ui,m,t+1 is uncorrelated over m within a given firmyear; and Cov(ui,m,t+1 ,vi,t ) is nonzero. Joint normality of the error terms is
more restrictive than the assumptions required by the Heckman (1979) twostep procedure. However, the FIML estimator has the advantage that it is more
efficient (Wooldridge 2010) and that it produces standard errors that can be used
directly. Our setting differs from a standard selection model in that Equations
(1) and (2) operate at different observation levels. While the decision to disclose
carbon emissions is at the firm-year level (i.e., (i,t)), the option market measures
are the firm-month-year level (i.e., (i,m,t +1)). Internet Appendix C discusses
how this affects the FIML estimator. A similar FIML model with data from
different observation levels is also estimated in Brav et al. (2019).

Carbon Tail Risk

4. Empirical Results
4.1 Carbon intensity and downward option protection: Cross-sectional
results
4.1.1 Firm- and sector-level evidence: Main results. Table 4, panel A, tests
Hypothesis 1 and reports firm-level regressions of the effects of log(Scope 1/MV
industry) on option market measures. Column 1 shows that a firm’s industry
carbon intensity has a positive and significant effect on SlopeD. A one-standarddeviation increase in a firm’s log industry carbon intensity (2.28) increases
SlopeD by 0.014, which equals 10% of the variable’s standard deviation.
In comparison, a one-standard-deviation decrease in a firm’s profitability
(EBIT/assets) increases SlopeD by 0.013 or 10% of the variable’s standard
deviation. SlopeD is generally lower for firms that are larger, that are more
profitable, invest less, and have lower volatility. It is higher for firms with
higher leverage and with higher book-to-market ratios.
Column 2 shows that we cannot detect that a higher carbon intensity is
associated with a more negatively skewed risk-neutral distribution of a firm’s
stock return (MFIS). The weaker results for MFIS may reflect that this measure
does not directly capture left tail risk. Instead, MFIS captures the cost of
protection against left tail events relative to right tail events. In fact, Internet
Appendix Table 3 shows that carbon-intense firms also have higher right tail
risk (as reflected in the negative coefficient on SlopeU), which may explain
why we do not find effects for MFIS. In column 3, we find that carbon-intense
firms exhibit a higher variance risk premium (VRP): a one-standard-deviation
increase in log industry emissions increases the VRP by 0.002, or 3% of the
standard deviation.

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same control variables as the outcome regression, but additionally controls for
the disclosure level in firm i’s industry in year t (Industry CDP disclosureit ).
We include this variable to capture the effects of peer pressure on the decision to
disclose emissions. As more firms within an industry disclose their emissions,
nondisclosers likely feel greater pressure to disclose their CO2 footprints too.
Like with Matsumura, Prakash, and Vera-Munoz (2014), for our purposes, this
variable constitutes the excluded instrument in Equation (2), so it is omitted
in Equation (1). Internet Appendix D discusses potential violations of the
exclusion restriction.
Table 3, panel B, reports the selection regression. The estimates show that the
propensity for a firm to report emissions significantly increases if other firms
in the same industry disclose their data as well. In column 5, a one-standarddeviation shock in Industry CDP disclosure (0.32) increases the probability to
disclose emissions by 30%, a large number relative to the unconditional mean of
51%. The estimates in Table 3, panel B, confirm the importance of accounting
for selection bias. Firms that disclose emissions are larger, have lower leverage,
higher earnings, lower book-to-market ratios, higher betas, and lower volatility.

The Review of Financial Studies / v 34 n 3 2021

Table 4
Carbon intensities and option market variables: Main results
A. Firm-level regressions
Dependent variable:

MFIS
(2)

VRP
(3)

0.006∗∗∗
(3.85)
−0.029∗∗∗
(−9.22)
0.009
(1.54)
0.038∗∗
(2.28)
−0.187∗∗∗
(−4.59)
−0.374∗∗∗
(−5.13)
0.077∗∗∗
(8.10)
−0.018∗∗
(−2.13)
−0.045∗
(−1.75)
0.010
(1.42)
−0.687∗∗∗
(−6.48)
−0.008
(−0.50)
−0.000
(−0.29)

−0.002
(−0.70)
−0.043∗∗∗
(−8.04)
−0.014
(−1.26)
0.062∗∗
(2.00)
−0.078
(−1.02)
0.216∗
(1.75)
0.122∗∗∗
(5.21)
−0.054∗∗∗
(−2.95)
−0.085
(−1.59)
−0.033∗∗∗
(−3.18)
1.926∗∗∗
(8.27)
−0.003
(−0.10)
0.033∗∗∗
(9.93)

0.001∗∗∗
(3.79)
−0.005∗∗∗
(−7.10)
−0.000
(−0.00)
0.003
(0.71)
−0.018
(−1.60)
−0.060∗∗
(−2.35)
0.016∗∗∗
(4.30)
−0.010∗
(−1.93)
−0.008
(−1.20)
−0.001
(−0.44)

Model

Heckman

Heckman

Heckman

Year-by-quarter fixed effects
Level
Frequency

Yes
Firm
Monthly

Yes
Firm
Monthly

Yes
Firm
Monthly

Obs.
Adj. R 2

18,664
n/a

18,664
n/a

18,664
n/a

log(Scope 1/MV industry)
log(Assets)
Dividends/net income
Debt/assets
EBIT/assets
CapEx/assets
Book-to-market
Returns
Institutional ownership
CAPM beta
Volatility
Oil beta
Time trend

−0.020∗∗∗
(−2.73)
−0.001∗
(−1.67)

(Continued)

If industry characteristics largely capture investors’ perceptions of firms’
carbon intensities, then we should be able to also identify effects at the sector
level. We next use option measures directly derived from S&P 500 sector
ETF options. To calculate a sector’s carbon intensity, Scope 1/MV sector, we
aggregate emissions of all CDP-disclosing S&P 500 firms in a sector and divide
them by the respective firms’ equity market values. To do this, we first identify
the sectors to which each disclosing firm belongs. As sector weights vary with
stock market performance, we then construct monthly sector weights (averages
of daily weights) for each firm. Subsequently, we multiply these weights by the
emissions of each sector constituent, using only disclosing firms. We use the
resultant weighted average emissions as a proxy for sector-level emissions.16

16 The sector-level analysis does not allow us to estimate a selection model. However, bias from selective disclosure

could be plausibly less of a concern in this analysis, as there are only a few S&P 500 sectors.

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SlopeD
(1)

Carbon Tail Risk

Table 4
(Continued)
B. Sector-level regressions
SlopeD
(1)

MFIS
(2)

VRP
(3)

log(Scope 1/MV sector)

0.037∗∗∗
(2.80)

−0.067∗
(−1.92)

0.003
(1.46)

OLS

OLS

OLS

Yes
Sector
Monthly

Yes
Sector
Monthly

Yes
Sector
Monthly

774
.138

774
.366

774
.005

Model
Sector fixed effects
Level
Frequency
Obs.
Adj. R 2

Regressions in panel A are estimated at the firm-month level. SlopeD measures the steepness of the function
that relates implied volatility to moneyness (measured by an option’s Black-Scholes delta) for OTM put options
with 30 days maturity. MFIS is a measure of the model-free implied skewness. VRP is a measure of the variance
risk premium. Scope 1/MV industry is the Scope 1 carbon intensity of all firms in the same industry (SIC4) and
year. It is defined as total Scope 1 carbon emissions (metric tons of CO2 ) of all reporting firms in the industry
divided by the total market capitalization of all reporting firms in the industry (in millions $). The sample
includes all firms in the S&P 500 with data on carbon emissions disclosed to CDP. We estimate the effect of
emissions generated between 2009 and 2016 on option market variables measured between November 2010 and
December 2017. t -statistics, based on standard errors clustered by industry (SIC4) and year, are in parentheses.
Regressions in panel B are at the sector-month level. The option variables are calculated for S&P 500 sector
options. Scope 1/MV sector is the Scope 1 carbon intensity of a sector. It is defined as a sector’s Scope 1 carbon
emissions (in metric tons of CO2 ) divided by a sector’s equity market value (in millions $). The sample includes
9 of the 11 sectors of the S&P 500. The sample period is the same as in the first panel. t -statistics, based on
standard errors clustered by sector and year, are in parentheses. Table A.1 defines all variables in detail. n/a, not
applicable. *p < .1; **p < .05; ***p < .01.

A similar procedure is used to compute the equity market values of each sector,
using again only disclosing firms. Our sample includes 9 of the 11 sectors of
the S&P 500. Sector intensities are largest in the Utilities and Energy sector, as
displayed in Table 2, panel B.
Table 4, panel B, documents in column 1 that sector carbon intensities remain
positively and statistically related to SlopeD. A one-standard-deviation increase
in a sector’s log carbon intensity (2.35) increases SlopeD by 0.09, almost 1.4
times the risk variable’s standard deviation. Results are again weaker for the
other two measures. While we now find a weakly significant effect for MFIS in
column 2, the effect for VRP in column 3 is insignificant with a t-stat of 1.46.
Taken together, the results indicate that higher climate policy uncertainty
increases the firm-level likelihood of left and right tail events, and it has some
effect on firm-level VRP. On the sector level, where firm-specific risks are
diversified away, we observe an effect that is more systematic and concentrated
in the left tail. (One other reason sector-level results may differ from those at the
firm level is that sector carbon intensities are noisier as we do not have carbon
emissions for all firms in a given sector; this may introduce measurement error.)
4.1.2 Firm versus industry carbon intensities: Relative importance.
The firm-level analysis raises the question of whether firms with carbon
intensities that are lower (higher) than those of their industry peers exhibit

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Dependent variable:

The Review of Financial Studies / v 34 n 3 2021

Table 5
Firm versus industry carbon intensities: Relative importance
Dependent variable:

SlopeD
(1)

log(Scope 1/MV firm)

0.006∗∗∗
(3.39)

Residual log(Scope 1/MV firm)

SlopeD
(2)

SlopeD
(3)

0.003
(0.81)

Heckman

Heckman

Controls
Year-by-quarter fixed effects
Level
Frequency

Yes
Yes
Firm
Monthly

Yes
Yes
Firm
Monthly

Yes
Yes
Firm
Monthly

Obs.
Adj. R 2

18,664
n/a

18,664
n/a

18,664
n/a

log(Scope 1/MV industry)

Regressions are estimated at the firm-month level. SlopeD measures the steepness of the
function that relates implied volatility to moneyness (measured by an option’s BlackScholes delta) for OTM put options with 30 days maturity. Scope 1/MV firm are a
firm’s Scope 1 carbon emissions (in metric tons of CO2 ) divided by the firm’s equity
market value (in millions $). Scope 1/MV industry is the Scope 1 carbon intensity of
all firms in the same industry (SIC4) and year. It is defined as total Scope 1 carbon
emissions (metric tons of CO2 ) of all reporting firms in the industry divided by the
total market capitalization of all reporting firms in the industry (in millions $). Residual
log(Scope 1 MV/firm) is the residual of an OLS regression with log(Scope 1/MV firm)
as the dependent variable and log(Scope 1/MV industry) as the independent variable.
The regressions in the table control for log(Assets), Dividends/net income, Debt/assets,
EBIT/assets, CapEx/assets, Book-to-market, Returns, Institutional ownership, CAPM
beta, Volatility, Oil beta, and a time trend (not reported). The sample includes all firms
in the S&P 500 with data on carbon emissions disclosed to CDP. We estimate the effect
of emissions generated between 2009 and 2016 on option market variables measured
between November 2010 and December 2017. t -statistics, based on standard errors
clustered by industry (SIC4) and year, are in parentheses. Table A.1 defines all variables
in detail. n/a, not applicable. *p < .1; **p < .05; ***p < .01.

less (more) downside tail risk once we account for industry effects. To this
end, Table 5 evaluates the relative importance of firm- versus industry-level
carbon intensities. As a starting point, column 1 documents that firm-level
carbon intensities, log(Scope 1/MV firm), are also positively and significantly
related to SlopeD. The economic magnitudes of the effects are also similar.
Nevertheless, to what extent this finding reflects firm, rather than industry,
effects is unclear. We therefore evaluate in the next two columns whether
there is information in firm-level carbon intensities beyond what is captured in
industry-level variation. We first estimate a regression in which we calculate for
each firm-year the part of firm-level carbon intensities that is unexplained by
industry-level intensities. By construction, the estimated regression residual
is positive (negative) for firm-years where firm-level carbon intensities are
above (below) those of the industry peers. Columns 2 and 3 of Table 5 replace
log(Scope 1/MV firm) with this regression residual. The estimates show that
firm-level residual carbon intensities are unrelated to SlopeD, when we both
do and do not control for industry-level emissions. Importantly, log(Scope
1/MV industry) remains positively and significantly related to SlopeD, even

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Model

0.005
(1.06)
0.006∗∗∗
(3.76)
Heckman

Carbon Tail Risk

after accounting for the firm-level residual. This confirms that the market’s
perception of a firm’s exposure to climate policy uncertainty is driven by its
industry affiliation.

4.2 Carbon intensity, downward option protection, and attention to
climate change
To test Hypothesis 2, we allow the effect of carbon intensities to vary with
two proxies for public attention to climate change. To create the first proxy,

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4.1.3 Firm- and sector-level evidence: Robustness. Internet Appendix
Tables 4 and 5 address different concerns with our analysis. Internet Appendix
Table 4, panel A, shows that our firm-level results for SlopeD are highly robust.
In column 1, results are unchanged if we scale emissions by total assets instead
of equity values. In column 2, results are unaffected when we estimate a
regression at the firm-year level using annual values of SlopeD. Column 3
shows that results are similar for OLS regressions. In column 4, the magnitude
of the effects increases with firm fixed effects. In column 5, results hold after
dropping oil and gas firms, indicating that results are not driven by the decline in
oil prices between 2014 and 2016. In columns 6 to 8, we continue to find effects
if we calculate SlopeD from options with 3- to 12-month maturities. Column 9
shows that Scope 2 intensities are unrelated to SlopeD. In panel B, we continue
to find mostly insignificant effects for MFIS when using 30-day options (the
point estimates for most specifications remain negative). Interestingly, we do
however observe significant coefficients for longer maturities. Thus, the cost of
left tail protection relative to right tail gains seems to be growing with an option’s
horizon. Short-term options instead seem to be used mostly to take firm-specific
(volatility) bets in both directions. In panel C, the firm-level results for VRP
remain largely robust.
Internet Appendix Table 5, panel A, shows that the sector results for
SlopeD remain highly robust. Apart from scaling by assets and using annual
values, the robustness tests include a variety of alternative fixed effects as
well as option maturities of up to one year. Panel B confirms the sector-level
evidence for MFIS from the main analysis: the point estimates are negative
in almost all cases, though highly significant coefficients appear rarely. In
panel C, results continue to be mostly insignificant for VRP, as in the main
analysis.
Our emissions data from CDP are only available for the years between 2009
and 2016, but options data exist for much longer. To analyze results for the
more distant past, we use a prediction model and backfill Scope 1/MV firm
for the years 1995 to 2008. Using predicted carbon intensities, we observe a
statistically insignificant effect of carbon intensities on SlopeD (see Internet
Appendix Table 6). This suggests that climate policy uncertainty was priced
to a lower extent in the more distant past, assuming that our prediction model
delivers reasonable emission estimates.

The Review of Financial Studies / v 34 n 3 2021

4.3 Effect of the 2016 election of President Trump: Event study results
To test Hypothesis 3, we use President Trump’s election in 2016 as an event
that reduced climate policy uncertainty in the short term. President Trump’s
election was unexpected and, unlike his opponent Hillary Clinton, his positions
on climate policies were mostly about preserving the status quo, which was
characterized by a lack of strict climate regulation. His election on November
9, 2016, therefore, should have lowered the cost of option protection for carbonintense firms. To quantify the effect of President Trump’s election, we estimate a
difference-in-differences (DiD) model, using daily option data around Election

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we use an index developed by Engle et al. (2020) which captures the share
of news articles in outlays, such as Wall Street Journal, The New York Times,
or Yahoo News, that are about “climate change” and have been assigned to
a “negative sentiment” category. We capture the time-series effects of climate
attention by creating Negative climate change news high, which equals one if the
Engle et al. (2020) index is above the median, and zero otherwise.
To create the second proxy, we use Google’s search volume index (SVI) for
the search topic “climate change.” The index takes values between 0 and 100,
with 100 corresponding to the month with the highest number of searches on
climate change topics during our sample period. We use monthly U.S. search
data. We then create the dummy variable Climate change SVI high, which
equals one if the search index is above the median, and zero otherwise. Search
activity on Google plausibly proxies for attention by investors, as shown by
Da, Engelberg, and Gao (2011). Choi, Gao, and Jiang (2020) show that search
volume on climate change topics surges when investors experience abnormally
high temperatures.
The regressions in Table 6 then interact each of these two variables with
log(Scope 1/MV industry). Column 1 provides the results for the Engle et al.
(2020) index, and column 2 those for Google’s SVI. The estimates in column
1 show that log(Scope 1/MV industry) has a positive and significant effect on
SlopeD during low-attention times (i.e., when Negative climate change news
high is zero). Importantly, the coefficient estimate on the interaction term, which
is positive (0.002) and significant (t-stat of 1.67), reveals that the effect of carbon
intensities on SlopeD increases by 40% during high-attention times. During
such times, the total effect of log(Scope 1/MV industry) on SlopeD equals
0.007(= 0.002+0.005), which is also statistically significant. In column 2, using
Google’s SVI as the proxy for attention, we continue to find a positive effect of
log(Scope 1/MV industry) on SlopeD during periods of low and high climate
change attention. However, the interaction term that reflects the difference
between these two states of the world is statistically insignificant (though it has
the predicted positive sign). Overall, the results in Table 6 therefore provide
only weak evidence in support of Hypothesis 2.

Carbon Tail Risk

Table 6
Carbon intensities and option market variables: Effects of public attention to climate change
Dependent variable:

SlopeD
(1)

log(Scope 1/MV industry) x Negative climate change news high

0.002∗
(1.67)

log(Scope 1/MV industry) x Climate change SVI high
log(Scope 1/MV industry)
Negative climate change news high

0.005∗∗∗

Climate change SVI high
0.007∗∗∗

0.001
(0.45)
0.006∗∗∗
(3.61)
−0.005
(−1.01)

Estimated slope if Negative climate change news high = 1
Estimated slope if Climate change SVI high = 1
Model

Heckman

0.007∗∗∗
Heckman

Controls
Year-by-quarter fixed effects
Level
Frequency

Yes
Yes
Firm
Monthly

Yes
Yes
Firm
Monthly

Obs.
Adj. R 2

18,664
n/a

18,664
n/a

Regressions are estimated at the firm-month level. SlopeD measures the steepness of the function that relates
implied volatility to moneyness (measured by an option’s Black-Scholes delta) for OTM put options with
30 days maturity. In column 1, we measure attention to climate change using Negative climate change news
high, which is a dummy variable based the CH Negative Climate Change News Index developed in Engle
et al. (2020) (as in their paper, we use monthly averaged AR(1) innovation of the index). Negative climate
change news high equals one if the index is above the median, and zero otherwise. In column 2, we measure
attention to climate change using monthly values of Google’s SVI for the search topic “climate change.”
SVI is a relative index and takes values between 0 and 100. The highest number of searches in a month
takes the value of 100 and values for other months are relative to this number. Climate change SVI high
equals one if Google’s SVI is above the median, and zero otherwise. Scope 1/MV industry is the Scope
1 carbon intensity of all firms in the same industry (SIC4) and year. It is defined as total Scope 1 carbon
emissions (metric tons of CO2 ) of all reporting firms in the industry divided by the total market capitalization
of all reporting firms in the industry (in millions $). The regressions control for log(Assets), Dividends/net
income, Debt/assets, EBIT/assets, CapEx/assets, Book-to-market, Returns, Institutional ownership, CAPM
beta, Volatility, Oil beta, and a time trend (not reported). The sample includes all firms in the S&P 500 with
data on carbon emissions disclosed to CDP. We estimate the effect of emissions generated between 2009 and
2016 on option market variables measured between November 2010 and December 2017. t -statistics, based
on standard errors clustered by industry (SIC4) and year, are in parentheses. Table A.1 defines all variables in
detail. n/a, not applicable. *p < .1; **p < .05; ***p < .01.

Day 2016. We estimate the following model for firm i at day t:
OMMi,t = γ0 +γ1 Post Trump electiont ×Scope 1/MV industry highi
+γ2 Scope 1/MV industry highi +γ3 Post Trump electiont
+xi,t−1 γ +i,t

(3)

In this regression, Post-Trump election equals one for all firm-day
observations after Election Day on November 9, 2016, and zero for all firmday observations before. To identify treatment firms for which climate policy
uncertainty likely declined the most after President Trump’s election, we create
Scope 1/MV industry high, which equals one for the ten industries with the
highest carbon intensities, and zero otherwise (see Table 2, panel A). We use

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(3.47)
−0.003
(−0.82)

SlopeD
(2)

The Review of Financial Studies / v 34 n 3 2021

17 We want to exclude potentially confounding effects related to the generally higher uncertainty around elections,

which are reflected in options spanning those days (see KPV).
18 Wagner, Zeckhauser, and Ziegler (2018) find that firms with high effective tax rates and large deferred tax

liabilities benefitted from President Trump’s election.

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SlopeD as the proxy for OMM and employ a relatively wide event window of
[−250; +250] days as daily option measures for single names tend to be noisy
and driven by idiosyncratic effects. For robustness, we exclude in some tests
the [−50; +50] days around Election Day.17 We report results with different
sets of fixed effects.
Our test relies on the sharp climate policy differences between President
Trump and Hillary Clinton. Other policy differences may confound our results
if they are correlated with the treatment status. Two such important differences
are tax and healthcare policies. With respect to tax policies, Clinton supported an
increase in taxes on high-income earners, whereas President Trump campaigned
on large corporate tax cuts.18 To ensure that expected tax changes do not
contaminate our results, we control for firms’ effective tax rates (interacted
with the post-election dummy). With respect to healthcare policies, President
Trump campaigned on repealing Obamacare, whereas Clinton did not announce
any plans to do so. To verify that results are not driven by an increase in
SlopeDamong healthcare firms (which have low emissions and are part of the
control group), we exclude such firms in a robustness test.
Table 7 shows that γ1 in Equation (3), the DiD estimator, is negative and
statistically significant across all specifications. This indicates that the cost of
downward protection at highly carbon-intense firms significantly decreased
after President Trump’s election, relative to less carbon-intense firms. In
economic terms, column 1 implies that SlopeD of firms in carbon-intense
industries decreased by 0.025 after the election, relative to firms in industries
with low carbon intensities. This decline equals 12% of the variable’s standard
deviation during the event window. Results are similar in Columns 2 to 4,
which add different sets of fixed effects to the model. The point estimate of
the DiD effect is largest in Column 5, in which we exclude the narrow window
directly surrounding the election. Results are unaffected if we drop healthcare
firms in column 6. The estimates further indicate that tail risk generally declined
after President Trump’s election (negative coefficients on Post-Trump election),
which may reflect that policies are more business friendly under a Republican
government.
We perform several further robustness tests. Internet Appendix Table 7 shows
that SlopeD exhibits parallel trends for high- and low-emission firms prior to
the election. Internet Appendix Table 8, panel A, shows that results are similar
for longer and shorter event windows. However, the statistical significance gets
weaker once we move to a shorter window. Internet Appendix Table 8, panel
B, verifies that our results do not reflect a seasonal pattern in early November.
To this end, we generate a series of placebo dates with the same day and month

Carbon Tail Risk

Table 7
Effect of the election of President Trump in 2016 on option market variables
Dependent variable:

SlopeD

SlopeD

SlopeD

SlopeD

Event window:

[−250;
+250]

[−250;
+250]

[−250;
+250]

[−250;
+250]

(1)

(2)

(3)

(4)

Model
Controls
Day fixed effects
Firm fixed effects
Industry fixed effects
Level
Frequency
Obs.
Adj. R 2

SlopeD
[−250; +250],
[−250; +250], excl. [−50;
excl.
+50], excl.
[−50; +50]
Healthcare
(5)

(6)

−0.022∗∗∗
(−4.33)

−0.037∗∗∗
(−2.63)
0.046∗
(1.88)
−0.036∗∗∗
(−5.97)

−0.035∗∗
(−2.45)
0.043∗
(1.72)
−0.041∗∗∗
(−6.13)

−0.025∗∗∗ −0.020∗∗
(−2.88)
(−2.20)

DiD

DiD

DiD

DiD

DiD

DiD

Yes
No
No
No
Firm
Daily
200,897
.062

Yes
Yes
No
No
Firm
Daily
200,897
.091

Yes
Yes
Yes
No
Firm
Daily
200,897
.294

Yes
No
No
Yes
Firm
Daily
200,897
.184

Yes
No
No
No
Firm
Daily
159,041
.061

Yes
No
No
Yes
Firm
Daily
139,635
.060

Regressions are estimated at the firm-day level. We report results from difference-in-differences regressions
around the date of President Trump’s election on November 9, 2016. SlopeD measures the steepness of the
function that relates implied volatility to moneyness (measured by an option’s Black-Scholes delta) for OTM put
options with 30 days maturity. Post-Trump election equals one for all days after President Trump’s election, and
zero for all days before the election. Scope 1/MV industry high equals one for firms that operate in the top-10
industries based on Scope 1/MV industry, and zero otherwise (see Table 2, panel A). The regressions control
for Effective tax rate, Effective tax rate × Post-Trump election, log(Assets), Dividends/net income, Debt/assets,
EBIT/assets, CapEx/assets, Book-to-market, Returns, Institutional ownership, CAPM beta, Volatility, and Oil
beta (not reported). The sample includes all firms in the S&P 500 with data on carbon emissions disclosed to
CDP. Column 6 excludes firms in the healthcare industry (SIC4 codes 2834, 3841, 6324, 3826, 3842, 2836, 5122,
3845, 8062, 8071, 5912, 2835, 3851, 3844, 3843, and 5047). t -statistics, based on standard errors double clustered
by firm and day, are in parentheses. Table A.1 defines all variables in detail. *p < .1; **p < .05; ***p < .01.

as the election date, but from all other sample years. These seven pseudo-DiD
estimators are all statistically insignificant. Internet Appendix Table 8, panel
C, uses regressions at the sector level. At the sector level, we are able to use a
shorter event window of [−100, +100] days as daily sector options are less noisy.
To identify treatment sectors, we create Scope 1/MV sector high, which equals
one for the two sectors with the highest sector carbon intensities (Utilities and
Energy), and zero otherwise (see Table 2, panel B). The results are consistent
with those in Table 7: SlopeD of the highly carbon-intense sectors decreased
after President Trump’s election, relative to less carbon-intense sectors.19

19 The noninteracted effect of Scope 1/MV sector high is negative, which is surprising, though it is only weakly

significant (while Scope 1/MV industry high has the expected positive direct effect in Table 7). A reason for the
differences may be that the number of observations (sectors) we are identifying the effects off is smaller at the
sector level (two vs. seven sectors). Moreover, sector intensities may be noisier, since not all sector constituents
disclose their emissions.

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Post-Trump election x
−0.025∗∗ −0.029∗∗
Scope 1/MV industry high (−2.18)
(−2.43)
Scope 1/MV industry high
0.041∗
0.043∗
(1.67)
(1.77)
∗∗∗
Post-Trump election
−0.025
(−4.63)

SlopeD

The Review of Financial Studies / v 34 n 3 2021

5. Conclusion

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Strong regulatory actions are needed to avoid the potentially catastrophic
consequences of climate change. As climate change is mostly caused by the
combustion of fossil fuels, new regulation will have to aim at significantly
curbing firms’ carbon emissions. Whether, how, and when regulatory climate
policies will be implemented is highly uncertain, and firms with carbon-intense
business models will be most affected by this uncertainty.
We show that climate policy uncertainty is priced in the option market.
Specifically, the cost of option protection against downside tail risk is larger
for more carbon-intense firms. A one-standard-deviation increase in a firm’s
log industry carbon intensity increases the implied volatility slope, which
captures protection against downside tail risk, by 10% of the variable’s
standard deviation. We confirm our results using sector options. The cost of
downward option protection is magnified when public attention to climate
change spikes. Moreover, it significantly decreased at highly carbon-intense
firms after President Trump’s election in 2016, relative to other firms.

Carbon Tail Risk

Appendix
Table A.1
Variable definitions
Definition

SlopeD

Steepness of the function that relates implied volatility to moneyness
(measured by an option’s Black-Scholes delta) for OTM put options
with a 30-day maturity. It is constructed as the slope coefficient from
regressing implied volatilities of OTM puts (deltas between -0.5 and
-0.1) on the corresponding deltas and a constant. Because far OTM
puts (with smaller absolute deltas) are typically more expensive, the
variable usually takes positive values. We also construct similar
measures using 91-, 182-, and 365-day maturities. To construct the
variable, we follow Kelly, Pastor, and Veronesi (2016). The variable
is constructed at the monthly level (average of daily values) or the
daily level (indicated accordingly).
Model-free implied skewness for options with a 30-day maturity. It is
computed as the third central moment of the risk-neutral distribution,
normalized by the risk-neutral variance (raised to the power of 3/2).
To construct the variable, we follow Bakshi, Kapadia, and Madan
(2003). The variable is constructed at the monthly level (average of
daily values).
Ex post variance risk premium for options with a 30-day maturity. It is
computed for each day t as the difference between the risk-neutral
expected variance for the period from t to t +30 calendar days and the
realized variance measured from daily log returns for the same period
[t , t +30] (Carr and Wu 2009; Bollerslev, Tauchen, and Zhou 2009).
As a proxy for the risk-neutral variance, we use the model-free
implied variance computed like in Britten-Jones and Neuberger
(2000). The variable is constructed at the monthly level (average of
daily values).
Annual Scope 1 carbon intensity of all carbon-disclosing firms in the
same industry (SIC4) and year. It is computed as total Scope 1 carbon
emissions (metric tons of CO2 ) of all reporting firms in the industry
divided by the total market capitalization of all reporting firms in the
industry (in millions $).
Dummy variable that equals one for firms that operate in the top-10
industries based on Scope 1/MV industry, and zero otherwise. The
industries are listed in Table 2, panel A.
Annual Scope 1 carbon intensity of the firm itself. It is computed as a
firm’s total Scope 1 carbon emissions (metric tons of CO2 ) divided
by the firm’s equity market value (in millions $) at the end of the year.
Annual Scope 1 carbon intensity of a sector. It is computed as a sector’s
total Scope 1 carbon emissions (in metric tons of CO2 ) divided by a
sector’s equity market value (in millions $) at the end of the year.
Dummy variable that equals one for the two sectors in the S&P 500
with the highest mean values of Scope 1/MV sector, and zero
otherwise. The sectors are listed in Table 2, panel B.
Defined as Scope 1/MV industry but for Scope 2 carbon emissions
instead of Scope 1 carbon emissions.
Dummy variable that equals one for a given firm-year if a firm
discloses to CDP data on the carbon emissions released during the
year, and zero otherwise.
Fraction of firms in the same SIC4 industry and year that discloses data
to CDP on the carbon emissions released during the year.
Dummy variable that equals one if the CH Negative Climate Change
News Index is above the median, and zero otherwise. CH Negative
Climate Change News Index is developed in Engle et al. (2020) and
captures the share of all news articles that are about “climate change”
and have been assigned to a “negative sentiment” category. As in
their paper, we use monthly averaged AR(1) innovation of the index.

MFIS

VRP

Scope 1/MV
industry

Scope 1/MV
industry high
Scope 1/MV firm

Scope 1/MV
sector
Scope 1/MV
sector high
Scope 2/MV
industry
CDP disclosure

Industry CDP
disclosure
Negative climate
change news
high

Source
OptionMetrics

OptionMetrics

OptionMetrics

CDP,
Compustat

CDP,
Compustat
CDP,
Compustat
CDP,
Compustat
CDP,
Compustat
CDP

CDP
Engle et al.
(2020)

(Continued)

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Variable

The Review of Financial Studies / v 34 n 3 2021

Table A.1
(Continued)
Variable
Climate change
SVI high

Dividends/ net
income
Debt/assets

EBIT/assets

CapEx/assets

Book-to-market

Returns

Institutional
ownership
CAPM beta

Oil beta

Volatility

Time trend
Effective tax rate

Post-Trump
election

Source
Google
Trends

Standard deviation of monthly stock returns, computed for each month
with a rolling window of 12 months. We use averaged values over the
year. Winsorized at the 1% level.
Linearly increasing variable that takes different integer values for each
year in the sample, starting with zero.
Cash taxes paid (Compustat data item TXPD) divided by current year
pretax income (Compustat data items PI). Pretax income is adjusted
for special items (Compustat data items SPI).
Dummy variable that equals one for all days after President Trump’s
election on November 9, 2016, and zero for all days before the
election.

Compustat
Compustat

Compustat

Compustat

Compustat

Compustat,
CRSP

CRSP

ThomsonReuters
Kenneth
French’s
data library

U.S. Energy
Information
Administration,
Kenneth
French’s
data library
CRSP

Selfconstructed
Compustat

Selfconstructed

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Assets

Definition
Dummy variable that equals one if Google’s search volume index (SVI)
for the search topic “Climate change” is above the median, and zero
otherwise. We use monthly values of the index during our sample
period. The index is a relative index and takes values between 0 and
100. The highest number of searches in a month takes the value of
100, and values for other months are relative to this number.
Total assets (Compustat data item AT) at the end of the year.
Winsorized at the 1% level.
Dividends (Compustat data item DVT) at the end of the year divided by
net income at the end of the year (Compustat data item NI).
Winsorized at the 1% level.
Sum of the book value of long-term debt (Compustat data item DLTT)
and the book value of current liabilities (DLC) at the end of the year
divided by total assets at the end of the year (Compustat data item
AT). Winsorized at the 1% level.
Earnings before interest and taxes (Compustat data item EBIT) at the
end of the year divided by total assets at the end of the year
(Compustat data item AT). Winsorized at the 1% level.
Capital expenditures at the end of the year (Compustat data item
CAPX) divided by total assets at the end of the year (Compustat data
item AT). Winsorized at the 1% level.
Difference between common equity (Compustat data item CEQ) and
preferred stock capital (PSTK) at the end of the year divided by the
equity market value (MKVALT) at the end of the year. Winsorized at
the 1% level.
Stock price at the end of the year (Compustat data item PRCC_F)
divided by the stock price at the end of the previous year, minus 1.
Winsorized at the 1% level.
Fraction of outstanding shares owned by institutional investors at the
end of the year. Winsorized at the 1% level.
Sensitivity of monthly stock returns to monthly S&P 500 returns. The
variable is computed for each month with a rolling window of 60
months. For each firm i , the variable corresponds to the β1 coefficient
in the regression Returnsit = constant + β1 Market Returnst . We use
averaged values over the year. Winsorized at the 1% level.
Sensitivity of monthly stock returns to monthly WTI oil returns after
controlling for monthly market returns. The variable is computed for
each month with a rolling window of 60 months. For each firm i , the
variable corresponds to the β2 coefficient in the regression
Returnsit = Constant + β1 Market returnst +β2 Oil returnst . We use
averaged values over the year. Winsorized at the 1% level.

Carbon Tail Risk

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==> RFS05 - Is Capital Structure Irrelevant with ESG Investors.txt <==
Peter Feldhütter
Copenhagen Business School, Denmark
Lasse Heje Pedersen
AQR Capital Management, Copenhagen Business School,
Denmark and CEPR
This paper examines whether capital structure is irrelevant for enterprise value and
investment when investors care about environmental, social, and governance issues, which
we refer to as “ESG-Modigliani-Miller” (ESG-MM). Theoretically, we show that ESGMM holds with linear pricing and additive ESG. ESG-MM means that issuing low-yielding
green bonds does not lower the overall cost of capital because it makes the issuer’s other
securities browner. Hence, a firm’s incentive to make a green investment does not depend
on its financing choice. We provide suggestive evidence of failure of ESG-MM, implying
that firms and governments can exploit inconsistent ESG attribution or segmented markets.
(JEL E22, G12, G32, G4, H23, Q56)
Received: October 27, 2022; Editorial decision: May 18, 2024
Editor: Stefano Giglio
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

In the presence of ESG investors, a firm can lower its cost of capital by polluting
less, but can the cost of capital also be reduced by the design of the capital
structure? For example, many companies and governments issue green bonds
and other “labeled” securities,1 but does such labeling lower the issuer’s overall
cost of capital? We show empirically that the answer appears to be “yes.”
We are grateful for helpful comments from Viral Acharya, Nicolae Garleanu, Markus Ibert and Lukasz Pomorski,
as well as seminar participants at Copenhagen Business School and the 25th Annual Portfolio Management
Conference: Fresh Perspectives for Institutional Investment in a Fragile Environment. AQR Capital Management
is a global investment management firm, which may or may not apply similar investment techniques or methods
of analysis as described herein. We gratefully acknowledge support from the Center for Big Data in Finance
[grant no. DNRF167] and the Danish Finance Institute (DFI). The views expressed here are those of the authors
and not necessarily those of AQR. Supplementary data can be found on The Review of Financial Studies web
site. Send correspondence to Lasse Heje Pedersen, lhp.fi@cbs.dk.
1 The most common labeled securities are green bonds (earmarked for environmental projects), blue bonds

(earmarked for projects related to healthy oceans), social bonds (earmarked for projects with positive social
outcomes), sustainable bonds (earmarked for sustainable projects), and sustainability-linked bonds (where terms
like the interest payments depend on reaching certain sustainability goals).
The Review of Financial Studies 00 (2024) 1–24
© The Author(s) 2024. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction
in any medium, provided the original work is properly cited.
https://doi.org/10.1093/rfs/hhae059
Advance Access publication October 14, 2024

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Is Capital Structure Irrelevant with ESG
Investors?

The Review of Financial Studies / v 00 n 0 2024

2 Industry and regulatory tools for reporting a portfolio’s carbon footprint often consider each firm’s carbon

intensity computing in different ways based on the enterprise-level figures (see, e.g., Frankel et al. 2015).

2

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This answer is surprising since labeling certain securities as “green” need
not in itself lower the firm’s or government’s emission, for example. Indeed,
we show theoretically that the issuer’s cost of capital should not be affected
by capital structure, including labeling of securities, under certain conditions.
These results have implications for whether green bonds create an incentive,
or distort the incentive, to lower carbon emissions.
Understanding how security design affects the cost of capital and enterprise
value is an old question in finance. Indeed, the Modigliani-Miller (MM)
“propositions are the finance equivalents of conservation laws” of physics, as
noted in the Nobel Lecture of Miller (1990). MM show that the total value of
the firm is the same for all capital structures under two conditions: (i) market
pricing is linear in cash flows (also called “perfect markets” or the “law of one
price”) and (ii) the cash flows attributed to all liabilities add to the asset’s total
cash flows.
We generalize this insight to an economy in which investors care about ESG,
for example, carbon emissions. If investors care about carbon, then a greener
firm has a lower cost of capital — but, given how green a firm is, does issuing
green bonds lower the cost of capital? Our ESG-MM result says “no”: the
enterprise value is the same for all capital structures, including all choices of
labeling of securities, under two generalized conditions: (i) linear pricing of
cash flows and ESG and (ii) additive cash flows and ESG.
This ESG-MM result is a benchmark, not a certainty. We test the ESG-MM
empirically, finding evidence against it. Nevertheless, just like the original
MM, the ESG-MM benchmark can help investors and regulators evaluate
whether an investment approach or regulation is consistent in the sense that
it aggregates to the firm level.
Let us first understand each of the two conditions ((i) and (ii)) that underlie
ESG-MM. Condition (i) states that prices are linear in cash flows and ESG,
generalizing the same notion for the standard MM. This condition means that,
if a firms’ profits double, then its value doubles, everything else equal; and,
likewise, if its pollution doubles, then the resultant value discount doubles.
Condition (ii) is that cash flows are additive—just as in the standard MM—
and, also, ESG is additive, meaning that the externalities attributed to all
liabilities add to the total externality imposed by all the firm’s activities. For
example, some pension funds use various tools to estimate their portfolio’s
overall “carbon footprint,” and, to measure this footprint, investors must
attribute a certain amount of emission to each security, for example the number
of tons of carbon dioxide (CO2 ) attributed to each security. The simplest
way to do this attribution is to assume that each security has the same
“carbon intensity,” measured as CO2 per market value (or sales), as the overall
enterprise.2 In any event, investors must attribute the firm’s emission to the

Is Capital Structure Irrelevant with ESG Investors?

Recall that the standard MM theorem says that, even though debt has a lower
cost of capital, increasing debt does not lower the WACC because it makes
equity riskier. Similarly, our ESG-MM says that, even though green bonds have
lower cost of capital, issuing green bonds does not lower the WACC because
it makes the equity browner. In other words, since issuing green bonds does
not in itself reduce the firm’s overall carbon emission, it should not affect its
overall cost of capital.
When investors have green preferences, a green investment has a lower cost
of capital, encouraging such investments. However, under ESG-MM, a firm’s
incentive to pursue a green project does not depend on the financing method,
for example, whether the project is financed by green bonds. This may seem
surprising since green bonds may have an especially low cost of capital. But,
again, the cost of capital for the other liabilities adjusts accordingly, making
the net present value independent of financing decisions under ESG-MM. Said
differently, if the WACC is the same for all sources of financing, we have:




enterprise value and WACC
investment
ESG-MM
... =⇒
=⇒
.
same for all capital structures
independent of financing
Does ESG-MM hold in practice? Before we address this question with
evidence, we note that ESG investing and sustainable finance regulation are
starting to affect a large part of the financial system,3 and we find that ESGlabeled bonds are a large fraction of all new issues of all government bonds in
some countries and of all corporate bonds in some sectors.
Do real-world investors and regulators assess ESG, for example, carbon, in
an additive way? Most ESG ratings are done at the firm level, and applying

3 As a proxy for how widespread ESG investing is, the asset under management of signatories of the Principles

of Responsible Investment (PRI) is worth about half the combined market value of global equity markets and
global fixed income markets. As a proxy for sustainable finance regulation, a group of 121 global central banks
and financial supervisors have joined the “Network of Central Banks and Supervisors for Greening the Financial
System,” and these regulators come from 90 countries, which cover 91% of global GDP (Pedersen 2023).

3

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various securities, and we say that these attributed emissions are additive
if the total attributed CO2 emission is the same for all capital structures,
that is, add to the same as the firm’s actual total emissions. For example,
Partnership for Carbon Accounting Financials (2022, p. 40) states that one
of their recommended ways of attributing carbon emissions to securities has
the benefit that it “ensures 100% attribution of emissions over equity and debt
providers and avoids double counting”; that is, additive ESG is satisfied.
When markets have linear pricing of additive ESG, then our ESG-MM result
implies that the weighted-average cost of capital (WACC) is the same for all
capital structures. In summary, the ESG-MM result can be presented as follows:



 

linear
additive cash flows ESG-MM enterprise value and WACC
=⇒
.
+
same for all capital structures
pricing
additive ESG

The Review of Financial Studies / v 00 n 0 2024

4 For example, Capital Monitor reports that AkademikerPension “aims to more than treble its near 7% allocation

to green assets to 22.5% by 2030” (Mair 2021).
5 For example, on January 3, 2023, the EU made a statement titled “Sustainable Finance: Commission welcomes

political agreement on European green bond standard” in which the Commissioner for Financial Services,
Financial Stability and Capital Markets Union, Mairead McGuinness, said: “Led by Europe and European
issuers, the green bond market is growing into an important source of funding for companies that need to fund
large-scale climate-friendly investments, such as renewable energy, clean transportation, and energy-efficient
buildings. With the European Green Bond Standard, we are creating a new gold standard available to those
companies that want to be at the forefront of the sustainability transition.”
6 The German Federal Ministry of Finance states that “the use of proceeds from Green German Federal Securities

always corresponds to federal expenditure from the previous year” (https://www.bundesfinanzministerium.de/
Content/EN/Standardartikel/Topics/Priority-Issues/Climate-Action/green-german-federal-securities-restricted/
green-german-federal-securities.html). The Danish Ministry of Finance writes that “upon signing of the
annual Budget Act, the Ministry of Finance will inform Danmarks Nationalbank of the amount of eligible
green expenditures in the coming year.” (https://fm.dk/media/25347/kingdom-of-denmark-green-bondframework.pdf).

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the same firm-level score across all the firm’s securities is consistent with
additivity. As noted above, Partnership for Carbon Accounting Financials
(2022, p. 50) puts forth a method of attributing carbon emissions that is
additive, but then later states that green bonds “are not covered” by this
methodology. If investors consider green bonds as different—for example,
wholly green—then this can lead to a violation of additive ESG, depending on
how the carbon is attributed to the rest of the securities. As another example,
Funk (2020) presents a range of carbon attribution methods, where several
do not satisfy additivity. Further, some pension funds consider both their
carbon footprint and the fraction of their assets invested in green securities.4
Considering the green securities as a fraction of all assets means that ESG
is evaluated in a binary way (green vs. nongreen), which leads to a failure
of ESG additivity: the same firm can choose a capital structure where all
liabilities are nongreen or another where some liabilities are green and others
are not. Similarly, sustainable finance regulation may encourage investors and
creditors to support green bonds.5 In summary, in the real world, investors, data
providers, and regulators use a variety of methods for attributing ESG—some
additive, some not—so it is ultimately an empirical question whether ESG-MM
holds.
Turning to the evidence, when firms issue green bonds, their stock price
tends to increase (Flammer 2021). This finding could suggest a violation
of ESG-MM, but such corporate issuances of green bonds coincide with
new green projects, and these new projects can also change the value of the
enterprise and its cost of capital, making a test of ESG-MM difficult.
Green government bond issuances of Germany and Denmark are, however, a
natural place to test the ESG-MM. When these countries issue green bonds, the
bonds finance part of the government’s budget for the previous year.6 Hence,
the projects are already signed into law, so the issuance of green bonds does
not coincide with new green projects. If the green bonds finance the green part
of the budget, then the remaining (nongreen) bonds must finance the nongreen
projects. Hence, these bonds are less green than they would be if they financed

Is Capital Structure Irrelevant with ESG Investors?

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the entire budget (i.e., in the absence of green bonds). If investors recognize
this “conservation of green,” then the country’s cost of capital should be the
same with only one type of bond (medium green, medium cost) or with two
types of bonds, green (low cost) and nongreen (more brown, higher cost).
However, the data suggest otherwise. When governments issue green bonds,
these green bonds trade at a lower yield than perfectly matched standard bonds.
This lower yield is not in itself a violation of ESG-MM, because it could be
compensated by a rise in the yield of the standard bonds. For Danish bonds,
we find that the overall cost of capital falls, providing suggestive evidence
against ESG-MM, but the yield change is statistically insignificant in our
overall sample of sovereign bonds.
We find stronger evidence against ESG-MM in connection with events in
which firms reclassify their bonds as green. During such events, we see that
both the firm’s bonds and equity increase in value, on average.
If these empirical findings mean that some investors consider green bonds as
fully green without making the remaining securities browner, then this could
have broader implications. For example, suppose that a firm’s assets consist of
half coal and half wind turbines. The firm considers two alternative capital
structures: (a) all equity, evaluated as half brown and half green; (b) green
bonds financing the wind turbines, evaluated as all green, and equity, evaluated
based on the enterprise-level ESG score, making it half green and half brown.
Here, (b) corresponds to a much greener capital structure with lower cost of
capital. Indeed, with capital structure (b), half of the liabilities (debt) are all
green and the other half (equity) are half brown, making the liabilities only one
quarter brown in total. In essence, capital structure (b) allows the firm to get rid
of half its carbon emissions on paper in this hypothetical example — without
actually reducing its real emissions!
Our paper is related to several literatures. First, our model of capital markets
with ESG-motivated investors follows Pástor et al. (2021), Pedersen et al.
(2021), and Zerbib (2022). Second, the empirical relation between ESG and
stock returns is considered by Hong and Kacperczyk (2009), Bolton and
Kacperczyk (2021), Pedersen et al. (2021), and Eskildsen et al. (2024) while the
relation between ESG ratings and bond returns is considered by Polbennikov
et al. (2016). Gormsen et al. (2023) find that green firms have lower perceived
costs of capital and discount rates than brown firms.
The yield of corporate green bonds has been found to be lower than
corresponding bonds without this label (Zerbib (2019), Baker et al. (2022),
Caramichael and Rapp (2024)), although Flammer (2021) questions this
finding because of the difficulties in matching green and nongreen bonds. Our
data on sovereign bonds provide clear evidence of a lower yield for green bonds
with perfectly matched standard bonds, echoing similar findings for German
government bonds by Pástor et al. (2022) and D’Amico et al. (2022).
Our paper is also related to the broader literature on corporate social responsibility (CSR). In particular, Zivin and Small (2005) derive a conservation

The Review of Financial Studies / v 00 n 0 2024

1. Theory: Capital Structure Irrelevance with ESG
Just like the standard MM results, our ESG-MM results rely on a notion of
linear pricing (sometimes called perfect capital markets). To set the stage for
our MM results, we first make precise what linear pricing means and how
it can arise with ESG (Section 1.1). We then present our ESG-MM results
(Section 1.2) and how they can break down (Section 1.3).
1.1 Capital markets with ESG-motivated investors
We consider an economy with n = 1,..., N risky securities and a risk-free rate,
r f . Each security n has a future cash flow, vn , and an externality, sn . Here,
sn > 0 is a positive social impact while sn < 0 is a negative externality such as
carbon emission (measured in tons of carbon, say). The price pn in a capital
market with linear pricing can be written as
η
sn ,
(1)
pn = E(mvn )+
1+r f
where m is the pricing kernel and η ≥ 0 is the value of externalities.
While such a linear pricing scheme holds in many models,7 we present here
a simple example for concreteness. The economy has i = 1,..., I investors,
where investor i chooses her portfolio xi ∈ R N , measuring the numbers of
shares of each risky security. This portfolio choice generates a future wealth
of Wi = W̄i (1+r f )+ xi′ (v − p(1+r f )) and an ESG exposure of xi′ s, where W̄i is
the initial wealth, v is the vector of security payoffs, p is the vector of prices,
and s is the vector of ESG. The investor maximizes her expected utility
γi
(2)
E(Wi )− Var(Wi )+ηi xi′ s
2
with risk aversion γi and ESG preference ηi . The optimal portfolio follows from the first-order condition, 0=E(v)−(1+r f ) p −γi V xi +ηi s, with
V =Var(v):

1
xi = V −1 E(v)−(1+r f ) p +ηi s .
(3)
γi
7 See Pástor et al. (2021), Pedersen et al. (2021), and Zerbib (2022).

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result, showing that firms’ charitable giving does not affect firm value when it
is a perfect substitute for investors’ own charitable giving, while Baron (2007)
presents limitations and extensions.
We complement all these literatures by considering the effects of capital
structure choices on the overall firm value in the presence of ESG-motivated
investors. While the cited literature considers each type of security in isolation,
we show theoretically if and how ESG choices affect the overall cost of capital
for a government or firm, and we provide evidence that labeling of securities
can lower the cost of capital.

Is Capital Structure Irrelevant with ESG Investors?

The vector of equilibrium prices is therefore
E(v)−γ V xm
η
p=
+
s,
(5)
f
1+r
1+r f
P
where γ is the aggregate risk aversion defined by γ1 = i γ1i and η is the
P
aggregate ESG preference defined by γη = i ηγii . So we see that (1) holds with
′

xm
.
m = 1−γ (v−E(v))
1+r f
Lastly, each security has a return of rn = vpnn −1 and an expected return,
r̄n = E(rn ), given by
sn
r̄n =r f +γ pm Cov(rn ,rm )−η
(6)
pn

where pm = p ′ xm and rm = vpxmm −1 is the market return. Applying this
expression for the market and combining with (6) yields a natural ESG-adjusted
capital asset pricing model (CAPM) relation:
sn
r̄n =r f +λβn −η ,
(7)
pn
′

n ,rm )
and λ = r̄m −r f +η spmm is the risk premium with sm = s ′ xm .
where βn = Cov(r
Var(rm )

1.2 ESG-Modigliani-Miller theorems
Next, we consider a firm (or government) with assets (A) that deliver future
cash flows of v A with an overall externality of s A . The firm considers its choice
of capital structure. A capital structure consists of a set of securities, which
are claims to the firm’s overall cash flows and externalities. For simplicity,
we consider a firm with two securities, debt (D) and equity (E), although the
results naturally extend to any set of securities. These securities are attributed
cash flows v D and v E , which add to the total cash flow, v D +v E = v A . In close
parallel, these securities are attributed externalities s D and s E , which add to the
total externality (“additive ESG”):
s D +s E = s A .

(8)

For example, if the firm has 100 tons of carbon emissions, then the carbon
emissions attributed to all securities should remain 100 tons. If debt is 60% of
liabilities, then Partnership for Carbon Accounting Financials (2022, fig. 4-2)
attribute 60 tons to debt and 40 tons to equity, yielding an additive attribution.
Such additive ESG scores together with linear pricing ensure capital structure
irrelevance, as seen from the next proposition.
Proposition 1 (ESG-MM I). With linear pricing (1) and additive ESG scores
(8), the total enterprise value is equal to the value of cash flows and externalities
and is not affected by capital structure.

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In equilibrium, the total demand for shares must equal the supply, given by xm :
X1
X

V −1 E(v)−(1+r f ) p +ηi s .
(4)
xi =
xm =
γ
i
i
i

The Review of Financial Studies / v 00 n 0 2024

That is, the enterprise value equals that of an unleveraged firm for any capital
■
structure.
The standard MM result is also presented in terms of cost of capital in the
typical textbook, so we next present a similar result with ESG. For any security
with price pn and cash flow vn , the corresponding cost of capital (or expected
n)
return) is r̄n = E(v
−1, and the firm’s weighted-average cost of capital (WACC)
pn
is defined as
pE
pD
WACC =
r̄ E +
r̄ D .
(10)
pE + pD
pE + pD
Proposition 2 (ESG-MM II). With linear pricing (1) and additive ESG scores
(8), the WACC is independent of capital structure, including each security’s
ESG label. Increasing the ESG of debt (s D ) decreases the cost of debt capital
(r̄ D ) and raises the cost of equity capital (r̄ E ) for given v A and s A . Similarly,
increasing s E decreases r̄ E and raises r̄ D .
Proof. Since p E + p D = p A and future cash flows are distributed among debt
and equity, we have
p E r E + p D r D = ( p E + p D )r A
which shows that WACC is always the same as r̄ A :
pE
pD
r̄ E +
r̄ D = r̄ A .
pE + pD
pE + pD

(11)

(12)

D)
−1 =
Further, r̄ D is decreasing in s D since (1) implies that r̄ D = E(v
pD

E(v D )
−1. Clearly, r̄ E is decreasing in s E for the same reason. Since
E(mv D )+ η f s D
1+r

s D +s E = s A , we see that increasing the ESG rating of one security comes
at the expense of lowering that of the other security. We also see that
■
r̄ E = r̄ A + ppDE (r̄ A − r̄ D ) as in the usual MM.
To make carbon emissions comparable across firms of different sizes, investors
and regulators often look at carbon emission as a fraction of firm value, denoted
“carbon intensity” (or as a fraction of sales or other financial ratios). So, in the
case where s A is the (negative) of carbon emissions, the corresponding carbon
intensity is ŝ A = spAA .
More broadly, suppose that investors assign a relative ESG score (such as
a carbon intensity), ŝn , to any security n, such that sn = ŝn pn . Then the pricing
equation (1) becomes
η
ŝn pn .
(13)
pn = E(mvn )+
1+r f

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Proof. For any capital structure, the total value of the firm is
η
η
η
s E +E(mv D )+
s D = E(mv A )+
sA = pA.
p E + p D = E(mv E )+
1+r f
1+r f
1+r f
(9)

Is Capital Structure Irrelevant with ESG Investors?

Further, the cost of capital (7) can now be written as
r̄n =r f +λβn −ηŝn ,

(15)

which shows how carbon intensity (or relative ESG) affects required returns.
A common market practice (when no securities are labeled) is to assign the
same relative ESG to all securities, namely the relative ESG of the issuer’s
overall assets. Our next result shows that the ESG-MM conservation result
continues in this case.
Proposition 3 (ESG-MM with relative ESG or carbon intensity). With
linear pricing (14) and if all the firm’s securities receive the same relative ESG
(e.g., carbon intensity) as unleveraged assets, then total enterprise value and
WACC are not affected by capital structure.
Proof.
pD + pE =

1
1
1
E(mv D )+
E(mv E ) =
E(mv A ) = p A .
1− 1+rη f ŝ A
1− 1+rη f ŝ A
1− 1+rη f ŝ A
(16)

When the enterprise value is unaffected, then so is the WACC. We can also see
this directly via (15), which shows that the WACC is
pE
pD
(r f +λβ E −ηŝ A )+
(r f +λβ D −ηŝ A ) =r f +λβ A −ηŝ A . (17)
pE + pD
pE + pD
■
So far, we have been considering a firm with fixed assets, but it is also
interesting to consider a firm’s incentive to invest, for example, in a green
project. The firm has assets in place, v A ,s A , and now also considers investing
in a new project with cash flow va and externality sa at a cost of c.
The investment cost c is financed by issuing new securities. The new
securities have cash flows v ′ and externalities s ′ . These new securities must
be able to just finance the cost of the investment, that is, c = E(mv ′ )+ 1+rη f s ′ .
Naturally, the owners of the old securities are therefore left with cash flows of
v A +va −v ′ and externalities s A +sa −s ′ .
Defining the net present value of the investment as NPV = E(mva )+ 1+rη f
sa −c, we have the following irrelevance result:
Proposition 4 (Investment). With linear pricing (1) and additive ESG scores
(8), consider an investment financed by issuing new securities. Regardless of
its financing, the post-investment enterprise value is the same, and the value of
existing liabilities increase by the investment’s NPV.

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We see that the price is on both sides of the equation, but we can rewrite this
relation as
1
E(mvn ).
(14)
pn =
1− 1+rη f ŝn

The Review of Financial Studies / v 00 n 0 2024

Proof. The post-investment enterprise value is:
η
(s A +sa ).
1+r f

(18)

The post-investment value of the existing liabilities minus their pre-investment
value is


η
η
′
E(m(v A +va −v ′ ))+
(s
+s
−s
)−
E(mv
)+
s
a
A
A
A
1+r f
1+r f
η
= E(mva )+
sa −c = NPV
(19)
1+r f
for any choice of v ′ ,s ′ satisfying the financing condition c = E(mv ′ )+ 1+rη f s ′ .
■
So we see that, under the conditions of ESG-MM, making a green investment
is not more attractive if it can be financed by green bonds. Such a green
investment is attractive, simply if its NPV is positive. While the NPV
calculation takes into account investors’ preference for green, it does not matter
whether the investment is financed by green new bonds or financed in a way
that makes all the liabilities greener. For example, if the firm issues very green
bonds (high s ′ ), then it needs only sell fewer of them (low v ′ ), but the remaining
liabilities are browner (lower s A +sa −s ′ ). If it sells standard bonds (s ′ at the
enterprise level), it needs to sell more, but the existing liabilities become
greener.
1.3 Deviations from ESG-Modigliani-Miller
We have seen that ESG-MM follows from additive ESG measures (8) and linear
pricing (1). Next, we discuss how a failure of either of these conditions can
lead to a failure of ESG-MM. In other words, we highlight some potentially
empirically relevant ways in which firms can increase their enterprise value
via their choice of capital structure and ESG labeling.
1.3.1 Exploiting nonadditive ESG scores Suppose that linear pricing holds,
(1) or (14), but ESG scores do not add up as in (8). In this case, a firm can
benefit from choosing a capital structure that is perceived as particularly green,
as shown in the following proposition.
Proposition 5 (Nonadditive ESG). Consider a firm with existing liabilities
that are assigned the same relative ESG (e.g., carbon intensity) as the overall
enterprise. The firm makes a new investment financed by issuing green bonds
with higher ESG scores. Then the post-investment enterprise value (and the
value of the existing liabilities) are increasing in the green bond’s ESG score.
Therefore, the hurdle rate of the new investment is lower if it can be financed
by greener bonds (or a larger fraction of green bonds).

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E(m(v A +va ))+

Is Capital Structure Irrelevant with ESG Investors?

1+r f

where ŝ ′ is the relative ESG score assigned to green bonds (based on (14)).
The post-investment enterprise value is the sum of the new value of existing
liabilities and the value of the green bonds:
E(m(v A +va ))
E(m(v A +va −v ′ ))
E(mv ′ )
≥
+
,
η
η
′
1− 1+r f ŝ post
1− 1+r f ŝ
1− 1+rη f ŝ post

(20)

where ŝ post is the post-investment relative ESG score at the enterprise level.
Clearly the post-investment enterprise value, the left-hand side of (20),
increases in ŝ ′ . Hence, the inequality follows from ŝ ′ ≥ ŝ post . The postinvestment value of the existing liabilities is the new enterprise value less the
value of the green bonds, c. Hence, if the post-investment enterprise value
increases by more, then so does the value of existing liabilities. Finally, when
the green bonds have the same relative ESG score as the rest of the postinvestment firm (the right-hand side of (20)), then existing liabilities increase
with the investment’s NPV (Proposition 4), so the increase is higher with higher
ESG scores. Therefore, a firm that maximizes the market value of the enterprise
(or the equity) can use a lower hurdle rate for investments that can be financed
by more green bonds—because these bonds require a lower coupon and, under
the stated assumptions, do not make the rest of the liabilities browner (as they
■
should under ESG-MM).
To understand this result, consider the following example. A firm n has assets
that are partly green and partly brown. The firm considers a new investment of
the same type as the existing assets. The firm’s relative ESG score is therefore
the same before and after the investment, ŝ. If the investment is financed using
nonlabeled securities that are evaluated based on the project’s relative ESG
score, then the cost of capital is r f +λβn −ηŝ using (15).
If instead the firm finances the project using a fraction w of green securities
and the rest 1−w with nonlabeled securities, then the cost of capital is lowered.
In particular, if the green securities have a relative ESG score of ŝ ′ > ŝ, then
these green securities have a lower cost of capital of r f +λβn −ηŝ ′ . If the other
securities still have the same relative ESG score as the firm, then the total cost
of capital for the project is
r f +λβn −ηŝ −wη(ŝ ′ − ŝ).

(21)

We see that the cost of capital is lower when the fraction of green bonds w is
higher.
1.3.2 Exploiting nonlinear pricing: Segmented markets Another potential
source of failure of the ESG-MM theorems is that markets are segmented such
that (1) does not hold. For example, markets can be segmented in the sense that

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Proof. Using the notation from Propositions 3 and 4, given investment cost c,
the green bonds must be assigned a cash flow v ′ satisfying c = 1− 1η ŝ ′ E(mv ′ ),

The Review of Financial Studies / v 00 n 0 2024

0 = E(v)−(1+r f ) p −γi V xi +ηi s +θi ,

(22)

where θi ∈ R+N is the vector of Lagrange multipliers for the constraints xi ≥ 0
of agent i. The vector of equilibrium prices is therefore
p=

η
θ
η
E(v)−γ V xm +θ
+
s = E(mv)+
+
s,
1+r f
1+r f
1+r f 1+r f

(23)

where θ ∈ R+N is the aggregate shadow cost of short-sale constraints for each
P
security, defined by γθ = i γθii . These security-specific shadow costs, θ , depend
on the ESG scores, s, in equilibrium. Hence, prices are not linear in payoffs and
externalities in the equilibrium with short-sale constraints (23), and some firms
can potentially exploit the nonlinearity coming from θ .
For example, suppose that a firm considers two different capital structures:
(i) issuing securities with average ESG scores and no binding constraint, that
is, θn = 0 for all their liabilities, or (ii) issuing green bonds with θgr een > 0 and
equity with no binding constraint. Even with additive ESG scores (8), the
θgr een
second capital structure raises the enterprise value by 1+r
f due to the extra
premium on green bonds.
1.3.3 Alternative hypotheses: Signaling, commitment, and preferences In
our empirical tests, we look for evidence against ESG-MM. In this connection,
it is relevant to consider alternative hypotheses (i.e., effects unrelated to failure
of linear pricing and additive ESG) that could also lead to issuance of green
bonds and associated repricing of the issuer’s securities.
One alternative hypothesis is that the issuance of a green bond signals
valuable green projects. To understand the signaling story, consider the
issuance of a green bond to finance a green investment when ESG-MM holds
or fails. Failure of ESG-MM (Proposition 5) means that green bonds are
issued at a low yield and the existing liabilities (e.g., equities) increase in
value, even if the investment is zero NPV, consistent with the evidence of
Flammer (2021). However, if the investment has positive NPV, then the existing
liabilities increase in value even if ESG-MM holds (Proposition 4). So the
signaling story is that the issuance signals a positive NPV, which makes it
difficult to test ESG-MM. Empirically, we seek to address this challenge by
studying sovereign issues related to past budgets and relabeling of existing
bonds.

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different investor clienteles buy different types of securities at differing pricing
schemes. In this case, a firm can increase its enterprise value by creating the
securities that each clientele (over)values the most.
As a specific example, segmentation can arise from short-sale constraints
that “sideline” non-ESG investors when green investors pay a high enough
premium for green securities. To see how this works, we introduce short-sale
constraints in the capital markets of Section 1.1. With short-sale constraints,
the investor’s first-order condition becomes

Is Capital Structure Irrelevant with ESG Investors?

2. Empirical Results: Testing ESG-MM
This section tests our ESG-MM result using data on sovereign bond issuance
events (Section 2.3) and corporate bond relabeling events (Section 2.4). Before

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A broader version of the signaling story is that the issuance of a green bond
signals more green behavior in the future, which could be a sign of more
positive NPV projects to come or a lower cost of capital due to future green
behavior. However, since a green bond issue is related to a current investment,
it seems unclear why the issuer could not make such promises in a more
effective way.
Another alternative hypothesis is commitment: The firm wants a favorable
ESG rating for a green project, but the market is afraid that, once the money
is raised, it will be spent in a less green fashion. In this case, the green bonds
can be a way to contractually commit to spending the money in a specific way
(Chowdhry et al. (2019), Oehmke and Opp (2024)). Commitment is a relevant
issue, which can also help explain the use of sustainability-linked bonds. So,
to distinguish this effect from a violation of ESG-MM, we must search for
specific examples with less commitment problems. In particular, our study of
sovereign green bonds exploits that these bonds are financing the past budget,
which is already signed into law.
Yet another alternative hypothesis is related to the nature of investors’ ESG
preferences. The linear pricing (1) is based on the idea that investors have a
separate nonfinancial motive to hold green assets, consistent with the evidence
of Riedl and Smeets (2017). Further, additive ESG means that investors
attribute the firm’s actions across its securities, but investors might alternatively
consider the “impact” of their investments (Moisson 2022). In particular,
Oehmke and Opp (2024) consider a large social fund with an “impact mandate,”
meaning that it “incorporates social costs relative to a counterfactual scenario
in which the SR fund does not invest in a given firm.” In this case, the firm’s
capital structure could influence investors’ ability to have impact, in particular
through the commitment argument above.
However, consistent with our model, Bonnefon et al. (2022) find experimental evidence that “non-pecuniary benefits of firms’ externalities only accrue
through stock ownership, not through the actual impact of investment decisions.” Further, Bonnefon et al. (2022) find that “non-pecuniary preferences
are linear and additive,” consistent with our model.
Lastly, a behavioral story is that the issuer’s green activities simply become
more salient to investors when issuing a green bond. In other words, if investors
have limited attention and become more aware of the issuer’s green projects
when they see a green bond issue, then the cost of capital could be reduced if
the perceived social value s increases in the mind of some investors, increasing
their valuation or broadening the investor base.

The Review of Financial Studies / v 00 n 0 2024

2.1 Data
2.1.1 Sovereign bonds To test the ESG-MM in the sovereign bond market,
we use data on green sovereign bonds, paired with identical nongreen bonds
in terms of coupon and maturity issued by the same country. Flammer (2021)
argues that imperfect matching between green and nongreen bonds has led to
conflicting results in the literature regarding the existence and size of a potential
green bond premium, so focusing on perfectly matched twin bonds allows us
to address this issue.
In addition to studying the spread between green and standard bonds, we
are also interested in their weighted average yield (in the spirit of the WACC).
Since yields also change for reasons unrelated to green bond issuance events,
we look at yield spreads relative to a “control bond,” which is a similar bond
from another country. We collect end-of-day mid yields for all the bonds from
Bloomberg BGN from January 1, 2019, to February 5, 2024.
Table 1 shows the bonds included in our study. There are seven pairs
of green-and-standard bonds issued by Germany and two pairs issued by
Denmark. As control bonds, we use matched government bonds from the
Netherlands, a nearby EU country with the same AAA rating as Denmark and
Germany.8 While the twin bonds are perfectly matched in terms of maturity
and coupon, the control bonds are slightly different.
All bonds are later reopened after their initial issuance, meaning that
additional bonds are issued into the same bond series, and the sample consists
of 9 new-issue events and 20 reopening events, for a total of 29 event dates.
The green bond’s share of the total issue is between 7% and 24%. The auction
is announced 6 business days before in Germany and at least 3 business
days before in Denmark. The settlement date is 2 business days later in both
countries. In addition to the actual auction date, we therefore also investigate a
broader event window from 6 days before to 3 days after the auction.
2.1.2 Corporate bonds In the corporate bond market, we test the ESG-MM
using a subset of firms that reclassify all their existing brown bonds as green.
We manually search for firms that convert all their existing bonds into green
bonds, and Table 2 shows the cases. The reclassified bonds have been issued
at least 5 months before the announcement and some as far back as 2016. The
table shows that debt-to-equity is between 16% and 72%, so debt is a significant
part of the capital structure and a reclassification of debt could materially affect
the greenness of equity. We collect daily adjusted closing prices for bonds and
equity from Bloomberg in the period around the announcement date.
8 The government of Netherlands issued a green bond on May 19, 2019, and October 17, 2023, and the dates of

issuances and reopenings do not occur in any of our event windows.

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we present these tests, we introduce our data (Section 2.1) and show that ESGrelated bonds are becoming prevalent globally (Section 2.2).

Is Capital Structure Irrelevant with ESG Investors?

ISIN

Coupon

Issue date

Maturity

Danish 10-year bond I
Green bond
Standard bond
Control bond

DK0009924375
DK0009924102
NL00150006U0

0
0
0

January 19, 2022
January 20, 2021
February 11, 2021

November 15, 2031
November 15, 2031
July 15, 2031

Danish 10-year bond II
Green bond
Standard bond
Control bond

DK0009924615
DK0009924532
NL0015001AM2

2.25
2.25
2.5

September 26, 2023
February 8, 2023
February 16, 2023

November 15, 2033
November 15, 2033
July 15, 2033

German 5-year bond I
Green bond
Standard bond
Control bond

DE0001030716
DE0001141828
NL0015031501

0
0
0

November 4, 2020
July 8, 2020
May 28, 2020

October 10, 2025
October 10, 2025
January 15, 2027

German 5-year bond II
Green bond
Standard bond
Control bond

DE0001030740
DE0001141869
NL0012171458

1.30
1.30
0.75

August 31, 2022
June 28, 2022
February 6, 2017

October 15, 2027
October 15, 2027
July 15, 2027

German 10-year bond I
Green bond
Standard bond
Control bond

DE0001030708
DE0001102507
NL0014555419

0
0
0

September 2, 2020
June 17, 2020
March 12, 2020

August 15, 2030
August 15, 2030
July 15, 2030

German 10-year bond II
Green bond
Standard bond
Control bond

DE0001030732
DE0001102564
NL00150006U0

0
0
0

September 10, 2021
June 18, 2021
February 11, 2021

August 15, 2031
August 15, 2031
July 15, 2031

German 10-year bond III
Green bond
Standard bond
Control bond

DE000BU3Z005
DE000BU2Z007
NL0015001AM2

2.3
2.3
2.5

April 25, 2023
January 11, 2023
February 9, 2023

February 15, 2033
February 15, 2033
July 15, 2033

German 30-year bond I
Green bond
Standard bond
Control bond

DE0001030724
DE0001102481
NL0015614579

0
0
0

May 11, 2021
August 21, 2019
September 24, 2020

August 15, 2050
August 15, 2050
January 15, 2052

German 30-year bond II
Green bond
Standard bond
Control bond

DE0001030757
DE0001102614
NL00150012X2

1.8
1.8
2.0

June 13, 2023
October 11, 2022
September 29, 2022

August 15, 2053
August 15, 2053
January 15, 2054

This table shows the twin bond pairs used in the event study as well as the control bond used to calculate changes
in the overall cost of capital.
Table 2
Corporate bonds and green bond relabeling
Firm
Merlin Properties
Gecina SA
Colonial Group
Covivio SA
Energy Harbor Corp.
PSP Swiss Property

# bonds

Size
(bill.)

D/E

Currency

Announcement
date

Equity
index

Bond
index

6
12
7
7
2
10

3.100
6.150
3.225
2.894
1.000
1.830

61%
70%
72%
46%
16%
38%

EUR
EUR
EUR
EUR
USD
CHF

April 25, 2022
April 14, 2021
December 22, 2021
April 14, 2021
October 23, 2022
November 11, 2022

IBEX
CAC
IBEX
CAC
S&P 500
SMI

Spain
France
Spain
France
U.S.
Swiss

This table shows summary statistics for six events where the firm relabeled all existing outstanding corporate
bonds from ordinary bonds to green bonds. “# bonds” is the number of bonds outstanding at the announcement
date, and “Size (bill.)” is the combined notional amount outstanding in local currency. “D/E” is the notional
amount outstanding of bonds divided by the market value of equity the day before the announcement. “Equity
index” is the stock market index used in calculation of excess equity returns, and “Bond index” is the local
Treasury index used when calculating bond excess returns. Data are from Bloomberg.

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Table 1
Government bonds and green bond issuance

The Review of Financial Studies / v 00 n 0 2024

2.2 How prevalent are green and other ESG-related bonds
Before we analyze whether a green bond issuance is associated with a failure
of ESG-MM, it is interesting to consider how prevalent such bonds are. To
address this issue, Figure 1 shows the fraction of ESG-related bond issuance
for, respectively, corporations and governments. For corporate bonds, Figure 1
shows that ESG-related bonds issuance is growing rapidly and already a
nontrivial fraction of all issues globally (panel A) and a large part of all issues
in some industries (panel B). Panel C shows that a large part of government
bond issues are green for several developed countries.
Additionally, ESG loans is also rising fast, approximately 11.7% of global
loans issuance in 2022 based on data from Refinitiv Eikon. More broadly, a
large part of financial systems is becoming affected by sustainable finance
regulation (see Footnote 3).
We note that, since ESG-related bonds are a relatively new phenomenon,
they are still a modest part of all bonds outstanding in most cases. Figure 2
shows the fraction of ESG-related bonds to total bonds outstanding. Globally,
although increasing rapidly, ESG corporate bonds were around 3.5% of all
corporate bonds outstanding in 2022 (panel A). Yet, they are already a
significant fraction in some sectors (panel B). Although the fraction of green
bonds outstanding is still modest for governments (panel C), Figure A.2 (in
the internet appendix) shows that the fraction of ESG bonds outstanding is
significant in some African countries. In other words, since investors only
recently started to price ESG, any failure of the ESG-MM could only have
started recently. Even if ESG already affects the cost of capital of firms and
governments, ESG first affects new issues since issuers only change their total
capital structure sluggishly.
2.3 Testing ESG-MM using green government bonds
Before we analyze whether green bonds affect the overall cost of capital, we
consider whether green bonds have a lower yield than comparable standard
bonds. Figure 3 shows a measure of the “green bond premium” for each pair
of twin bonds in our study. Specifically, the figure shows the time series of the
standard-minus-green yield spread, ytS − ytG , where ytS is the yield-to-maturity
of the standard bond, and ytG is the yield-to-maturity of the corresponding
9 We downloaded the issuance data on June 30, 2023, and it appears that the amount issued is the total amount

outstanding at download date. While this corresponds to amount issued in most cases, it may be different for
some bonds in case of reopenings and buybacks. We downloaded the amount outstanding data on February 5,
2024, and defined the amount outstanding at a date as all bonds issued before the date and maturing after the date.

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2.1.3 Issuance and outstanding amounts We use data from Refinitiv Eikon
to calculate the fraction of issued and amount outstanding ESG bonds relative
to all bonds. They provide for each bond their amount issued converted to USD,
the industry classification and a green bond and/or ESG bond indicator.9

Is Capital Structure Irrelevant with ESG Investors?

green bond. (We note that the reverse spread, ytG − ytS , is sometimes denoted
as the bond greenium.)
As seen in Figure 3, the green bond premium is positive for all the bonds
we study at almost all times (only 6 of 4,444 observations are negative). The
consistently positive green bond premium is statistically significantly different
from zero, as seen in Table 3. Given that these pairs of standard and green bonds
are perfectly matched, these results provide strong evidence that green bonds
have a lower cost of capital than corresponding standard bonds.

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Figure 1
ESG bond issuance
Panel A shows the percentage of ESG or green corporate bonds of the total amount issued globally. Panel B
shows the percentage of ESG corporate bonds of the total amount issued globally for the five sectors that had
the highest ESG bond percentage in 2022. Panel C shows the percentage of sovereign green bonds of the total
amount issued globally for the four countries with the highest green bond issuance percentage in 2022 as well
as Germany.
ALT TEXT: The issuance of ESG and green bonds has tended to increase over the past decade.

The Review of Financial Studies / v 00 n 0 2024

The fact that green bonds face lower costs of capital opens the door for
such bonds also lowering the overall cost of capital, which is our main object
of interest. In other words, does issuing green bonds lower the government’s
cost of capital? This conclusion clearly does not follow by default. Instead, the
yield of the government’s other bonds could adjust such that the overall cost of
capital remains unchanged.

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Figure 2
ESG bonds outstanding
Panel A shows the percentage of ESG or green corporate bonds of the total amount outstanding at the end of the
year. Panel B shows the percentage of ESG corporate bonds of the total amount outstanding at the end of the
year for the five sectors that had the highest ESG issuance percentage in 2022. Panel C shows the percentage of
sovereign green bonds of the total amount outstanding. The data are from Refinitiv Eikon.
ALT TEXT: The total amount outstanding of ESG and green bonds has increased over the past decade.

Is Capital Structure Irrelevant with ESG Investors?

We examine this ESG-MM conservation property in Table 4. For each
issuance event of twin bond i with green bond yield yti,G , we consider the
following three metrics in a time window around each issuance event: (1) the
yield, yti,S , of the corresponding standard bond in excess of the yield, yti,C , of
the control bond from the Netherlands, that is, yti,S − yti,C ; (2) the weightedaverage cost of capital, (1−wti )yti,S +wti yti,G − yti,C , across the twin pair (in
excess of the control bond), where wti is the green bond’s fraction of the
combined outstanding of the twin bonds; and (3) the weighted-average yield of
all government bonds issued by this country (green and standard) in excess of
the control bond. These results are averaged across, respectively, (a) all events,
(b) all events in Denmark, and (c) all events in Germany.
As seen in Table 4, when looking across all events in both countries, the
yield changes are not significant. The yield of the standard bond goes down on
average, not up as predicted by the theory if these standard bonds become less
green, but the magnitude is economically small and statistically insignificant
overall. In the sample of Danish bonds, the effects is significant, however. For
the Danish bonds, we see that the standard bond yields go down around the
issuance event, as does the average twin pair yield and also because the green
bonds become a larger fraction of the pair. The point estimate of the average
yield across all Danish bonds is smaller, since most of the bonds are not part

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Figure 3
Green bond premium
For each pair of twin bonds we plot the time series of ytS − ytG where ytS is the yield-to-maturity of the standard
bond and ytG is the yield-to-maturity of the green bond.
ALT TEXT: The yield difference between ordinary and green bonds is nearly always positive for Danish and
German twin bonds.

The Review of Financial Studies / v 00 n 0 2024

Mean

Median

Min

Max

N

Danish 10-year I

2.90∗∗∗

2.80

0.00

6.20

532

Danish 10-year II

1.71∗∗∗

1.70

−1.20

4.20

91

German 5-year I

(0.12)
6.18∗∗∗

5.80

0.20

29.30

848

German 10-year I

(0.39)
3.19∗∗∗

2.50

−0.40

7.30

889

German 10-year II

(0.23)
1.72∗∗∗

1.50

−0.10

4.60

628

German 30-year I

(0.14)
2.35∗∗∗

2.00

0.40

4.60

713

German 5-year II

(0.15)
4.79∗∗∗

5.55

0.20

9.10

372

German 30-year II

(0.42)
1.07∗∗∗

1.10

0.60

1.50

168

German 10-year III

(0.04)
0.96∗∗∗

1.00

0.40

1.40

203

Average

(0.06)
3.37∗∗∗

3.28

1.30

7.33

889

(0.16)

(0.12)

This table shows descriptive statistics for the green bond premium, ytS − ytG , for each of the twin bond pairs.
“Mean” is the average difference in yield between the standard and green bond, with standard errors in
parentheses (estimated using Newey-West with 12 lags). “Average” is the average daily premium. The time
period is from September 8, 2020, to February 5, 2024. * p < .1; ** p < .05; *** p < .01.

Table 4
Yield reaction around green bond issuance
All

Denmark

Germany

Standard

Pair

All

Standard

Pair

All

Standard

Pair

All

CYR(0)

0.07

−0.02

−0.06

0.33

0.24

−0.33

−0.02

−0.12

0.04

(0.19)

(0.18)

(0.17)

(0.54)

(0.52)

(0.53)

(0.16)

(0.17)

(0.14)

CYR(0,3)

−0.21

−0.38

−0.02

−1.07∗

−1.31∗∗

−0.63

0.12

−0.02

0.21

(0.38)

(0.39)

(0.34)

(0.27)

0.03

(1.04)
−0.80∗

(0.47)

−0.34

(0.59)
−2.45∗∗∗

(0.46)

−0.27

(0.56)
−2.20∗∗∗

0.47

0.47

0.35

(0.48)

(0.50)

(0.32)

(0.59)

(0.56)

(0.46)

(0.54)

(0.56)

(0.40)

29

29

29

8

8

8

21

21

21

CYR(−6,3)
N

The table shows the average cumulative yield reaction (CYR) around N green bond issuance events,
1 P N CYR . For each choice of event window, CYR is calculated as CYR (S,T ) = PT (y i − y i,C )−
i
i
i
t
t=S t
i=1
N

i − y i,C ), where time t is measured in event time, y i is the cost of capital, and y i,C is the yield of the
(yt−1
t
t
t−1

control bond. In the column “standard,” yti = yti,S is the yield of the existing standard twin bond, in column
“pair” yti is the weighted average yield, yti = (1−wti )yti,S +wti yti,G , where yti,S is the yield of the standard bond,

yti,G is the yield of the green bond, and wti is the green bond’s fraction of the combined outstanding of the twin
P
bonds. In the column “all” yti is the weighted average yield, yti = Nj=1 wti yti , where N is the number of bonds

outstanding around the event and wti is the bond’s fraction of the combined outstanding of all N bonds. Standard
q
PN
errors are calculated as std(CY R) = N 1−1 i=1
(CY Ri −CY R)2 ). * p < .1; ** p < .05; *** p < .01.

of this pair. These results provide suggestive evidence that ESG-MM may be
violated, at least for Danish bonds, but the magnitude is small relative to the
amount of noise in the data.
As in any event study, the interpretation of the result depends on when the
market knows what. As described in Section 2.1, the event window includes the

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Table 3
Green bond premium.

Is Capital Structure Irrelevant with ESG Investors?

2.4 Relabeling of corporate bonds to green bonds
As an alternative test of ESG-MM, we next consider events in which firms
relabel standard corporate bonds into green bonds. Table 2 describes our
sample of such events, which is admittedly small since such events are a new
phenomenon.
For each event, we calculate the abnormal returns on bonds and equity using
the market model in an event window of 3 days before to 3 days after the
announcement of the relabeling.10 For equities, we use 30 days with available
prices before the event window to compute regression coefficients (β̂0 , β̂1 ) from
the regression
rti = β0 +β1rtm +ϵt ,t = −32,...,−4,

(24)

where rti is the daily return (including dividends) of firm i ′ s equity and rtm is
the daily return of the local equity index. The abnormal equity return on day t
in the event window is then computed as arti =rti −(β̂0 + β̂1rtm ).
For corporate bonds, we must address that each firm has multiple
corporate P
bonds. Therefore, we first calculate each firm’s overall bond
b, j
return as Nj=1 w j rt , where N is the number of bonds outstanding at the
b, j

announcement, rt

Amount issued j

is the return of bond j, and w j = P N

n=1 Amount issuedn

are

weights based on each bond series’ issuance size. Based on these firm-level
corporate bond returns, we calculate abnormal bond returns in the same way
as abnormal equity returns by regressing the firm-level bond return on the local
Treasury index return.
Table 5 shows the abnormal returns of equity and bonds during the event
window. As seen in the table, there is a significant positive equity price reaction
10 A day in the event study is a day for which we observe the firm equity price in Bloomberg, and any days with

missing firm equity returns drop out of the sample. Likewise, days without firm bond-returns drop out of the
sample when studying abnormal bond returns.

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announcement of the issuance (days -6 to -1), the auction date (day 0), and the
settlement date (day 2). So, if the market did not know for sure whether such a
green bond issue would happen, then the reduction in the cost of capital violates
ESG-MM. However, the market may be able to anticipate these bond issues,
especially since the government has already passed into law the budget for the
previous year and computed how much of the budget is eligible as green. If
the market already knew that the green issue would happen, then the standard
bond prices may have already reflected that they are browner, which would
imply no change in their yield — so even under this interpretation, the drop in
the yield of standard Danish bonds is inconsistent with ESG-MM. To justify
ESG-MM, we would need to assume that the market was surprised at how
small the green issuance was, but this interpretation seems a stretch given that
an actual issuance event would normally increase the expected total issuance
amount.

The Review of Financial Studies / v 00 n 0 2024

Event day

−3

−2

−1

0

1

2

3

Equity

0.83

−0.26

0.75

0.14

0.98∗∗

0.04

−0.33

(0.80)

(0.39)

(0.51)

(0.72)

(0.49)

(0.65)

(0.57)

Bonds

−0.09

−0.00

0.08

−0.07

0.10

0.03

0.07∗

(0.12)

(0.04)

(0.10)

(0.10)

(0.11)

(0.07)

(0.04)

The table shows the average abnormal excess return around six announcements ( N = 6) of all existing bonds
being relabeled to green bonds. For each announcement i , we calculate the abnormal equity return using the
market model on event day t as arti =rti −(β̂0 + β̂1 rtm ), where rti is the equity return of firm i , rtm is the local
country index, while (β̂0 , β̂1 ) are the regression coefficients from the regression rti = β0 +β1 rtm , t = −32,...,−4.
The “Equity” row shows the average abnormal equity return for each event day. For each announcement, we also
calculate the abnormal corporate bond return as artb,i =rtb,i −(β̂0 + β̂1 rtbm ), where rtb,i is the bond return of firm i ,
rtbm is the local government bond index return, while (β̂0 , β̂1 ) are the regression coefficients from the regression
P
b, j
rtb,i = β0 +β1 rtbm , t = −32,...,−4. The firm bond return is calculated as nj=1 w j rt , where n is the number
b, j

of bonds outstanding at the announcement, rt

ai

is the return of bond j and the weights are w j = P N j

where ai j is the amount issued of bond j . Standard errors are calculated as
** p < .05; *** p < .01.

j=1 ai j

q

,

1 PN
2
N −1 i=1 (ari −ar ) ). * p < .1;

of 0.98% on the day following the announcement. The fact that the effect comes
the day following the announcement is likely because the announcements occur
after the close of the stock market (our data does not include the time of the
announcement).
Turning to the effects on the corporate bonds, Table 5 also shows positive
bond returns. The largest point estimate of the bond reaction is at day 1, and
there is also a large reaction on day 3, which is statistically significant at the
10% level. The delayed reaction on day 3 is likely because corporate bonds are
less liquid than equities and therefore prices may be stale.
These findings appear inconsistent with ESG-MM, since they imply
that the overall enterprise value (bonds plus equity) increases around the
announcement. Said differently, if the bonds increase in value because they
are perceived as greener after the relabeling, then, according to ESG-MM, the
equity should become browner, resulting in a negative equity reaction, not the
observed positive equity reaction.
The relabeling is a violation of ESG-MM in as much that it is simply a
reclassification of existing securities, but we must consider the alternative
hypothesis that the event signals a positive NPV project as in Proposition 4.
The relabeling is part of the firm’s ESG strategy, but, the announcement
of a new ESG strategy typically comes before the announcement of the
bond reclassification. For example, Merlin Properties announced the bond
conversion the week after it presented its plan to become a net zero emissions
company by 2050. The internet appendix describes each event, explaining that
four out of six events happen after an ESG strategy announcement and the
remaining two events do not appear to have any value-related information. Our
results are similar if we leave out the two latter events, as also shown in the
internet appendix.

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Table 5
Equity and bond returns around green bond relabeling

Is Capital Structure Irrelevant with ESG Investors?

3. Conclusion
We show theoretically that, when the market has linear pricing and allocates
ESG characteristics such as CO2 emissions additively across securities, then
the overall cost of capital should only depend on the overall cash flows and
overall emissions, regardless of capital structure or security labels. Therefore,
an issuer’s incentive to pursue a green project should not depend on how the
project is financed. Said differently, a firm’s cost of capital should depend on
its total pollution, not on whether certain nonpolluting elements are financed
with green bonds.
Empirically, finding a clear causal link between asset prices and security
characteristics is challenging, but we find evidence suggesting a violation of
this ESG-MM property in that an issuer may lower its cost of capital by
issuing green bonds. Future research should further explore whether labeling
of securities complements or distorts the more meaningful task of reducing
overall emissions and externalities.
Code Availability: The replication code and data are available in the Harvard
Dataverse at https://doi.org/10.7910/DVN/BQFHNQ.
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==> RFS06 - Attention to Global Warming.txt <==
Attention to Global Warming
Darwin Choi, Zhenyu Gao and Wenxi Jiang
CUHK Business School

Received December 7, 2017; editorial decision March 27, 2019 by Editor Andrew Karolyi.
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

Introduction
President Donald Trump, who has called global warming a “hoax” on multiple
occasions, wrote the following message on Twitter on December 28, 2017,
when unusually cold temperatures were expected to hit the Eastern United
States:
In the East, it could be the COLDEST New Year’s Eve on
record. Perhaps we could use a little bit of that good old Global
Warming that our Country, but not other countries, was going to
pay TRILLIONS OF DOLLARS to protect against. Bundle up!
— Donald J. Trump (@realDonaldTrump)
We thank Andrew Karolyi (the Editor), Vikas Agarwal, Laura Bakkensen, Zhi Da, Andrew Ellul, Harrison
Hong, Roger Loh, Pedro Matos, Abhiroop Mukherjee, Adriaan Perrels, Jose Scheinkman, Wing Wah Tham,
Bohui Zhang, and Dexin Zhou; three anonymous referees; and seminar participants at the 2nd International
Conference on Econometrics and Statistics (EcoSta), 8th Helsinki Finance Summit on Investor Behavior, 10th
Annual Volatility Institute Conference: A Financial Approach to Climate Risk, Asian Bureau of Finance and
Economic Research (ABFER) 6th Annual Conference, China International Conference in Finance 2018, Review
of Financial Studies Climate Finance Workshop 2017 and Climate Finance Conference 2018, Society for Financial
Studies (SFS) Cavalcade Asia-Pacific 2018, Cheung Kong Graduate School of Business, Chinese University of
Hong Kong, Hong Kong Baptist University, Hong Kong Polytechnic University, Renmin University of China,
and University of Melbourne for helpful comments. Jingxuan Chen, Haojun Xie, and Hulai Zhang provided
excellent research assistance. We acknowledge the General Research Fund of the Research Grants Council of
Hong Kong (Project Number: 16516616) for financial support. Supplementary data can be found on The Review
of Financial Studies Web site. Send correspondence to Darwin Choi, Department of Finance, CUHK Business
School, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; telephone: (852) 3943-5301. E-mail:
dchoi@cuhk.edu.hk.
© The Author(s) 2020. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
doi:10.1093/rfs/hhz086

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We find that people revise their beliefs about climate change upward when experiencing
warmer than usual temperatures in their area. Using international data, we show that
attention to climate change, as proxied by Google search volume, increases when the
local temperature is abnormally high. In financial markets, stocks of carbon-intensive firms
underperform firms with low carbon emissions in abnormally warm weather. Retail investors
(not institutional investors) sell carbon-intensive firms in such weather, and return patterns
are unlikely to be driven by changes in fundamentals. Our study sheds light on peoples’
collective beliefs and actions about global warming. (JEL D83, G12, G14, G15, Q54)

Attention to Global Warming

1 In this paper, we use the term “abnormally warm” to refer to cases in which a city’s temperature is significantly

higher than the historical average temperature at the same point in the year. Our Google data capture the search
activity in each city and cover different languages. See Section 1 for a list of papers that study the Google search
volume of global warming in the United States.

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Pierre-Louis (2017) of The New York Times points out that President
Trump’s tweet made the mistake of confusing local weather with climate.
This misunderstanding about climate change is indeed a common mistake.
Global warming is a long-term trend usually not visible on a personal level.
In contrast, the local temperature in a given month or year is more noticeable,
even though it can be caused by reasons unrelated to global warming, for
example, ocean oscillations, such as the El Niño Southern Oscillation, ENSO
(Intergovernmental Panel on Climate Change, IPCC 2014; Schmidt, Shindell,
and Tsigaridis 2014). For example, a record-breaking warm month of July in
New York City provides negligible information about the increase in the average
global temperature in the following decade, but the local temperature in July is
much more visible to New Yorkers than the 10-year global trend.
In this paper, we test how people react to abnormal local temperatures by
examining their attention to climate change and stock prices. Our data cover
seventy-four cities in the world with major stock exchanges. The advantage of
using international attention and financial data is that we can estimate people’s
opinions in different parts of the world at a high frequency (unlike surveys)
and study their follow-up actions, as investors trade on their beliefs and move
stock prices. Humans’ collective belief and effort are important determinants of
the efficacy of climate policies and campaigns. Our study aims to empirically
identify how the general public realizes and responds to the impacts of global
warming.
Because their attention is limited, people are likely to focus on attentiongrabbing weather events and personal experiences. The local weather
conditions are people’s first-hand experience. The impact of local weather
also can be amplified through communication channels and the media (media
attention to climate change appears to be higher in the record-breaking warmest
years than in nonrecord years) (Schmidt 2015). Extreme local temperatures
therefore serve as “wake-up calls” that alert investors to climate change. Our
paper tests this idea in two steps: first, we test whether people pay more attention
to climate change when experiencing abnormally warm weather. The second
set of analyses examines whether this experience affects financial markets;
because of the home bias (see, e.g., the review by Karolyi and Stulz 2003), the
prices of local stocks are affected by local investors’ trading behavior.
Our results show that during abnormally warm months in a particular city,
the volume of Google searches for the topic of “global warming” in that
city increases.1 Our analysis controls for time fixed effects, and therefore the
relationship originates from geographical variation. Not all parts of the world
are equally warm in a given month; people tend to seek more information

The Review of Financial Studies / v 33 n 3 2020

2 Data on the quarterly equity positions of blockholders (who hold 5% or more of the total number of shares)

and of institutional investors who hold less than 5% of total shares are obtained from DataStream and FactSet,
respectively. The complement of these holdings gives us an estimate of retail investors’ positions.

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about global warming if they live in cities that have relatively higher abnormal
temperatures than other cities in that month. This effect is the most prominent
when the local abnormal temperature is in the city’s top quintile, as this weather
experience is more salient.
If investors revise their beliefs about global warming, they may buy stocks
with lower climate sensitivities and sell stocks with higher climate sensitivities
such that the former outperform the latter. We sort stocks into those with high
and low sensitivities using proxies for greenhouse gas emission levels. Firms
are classified as high-emission firms if they belong to industries that the IPCC
identifies as major emission sources. These companies tend to be more sensitive
to climate change if their future cashflows are adversely affected by higher
production costs and tighter environmental regulations or if socially responsible
investors avoid holding their stocks.
We find evidence that carbon-intensive firms earn lower stock returns than
other firms when the local exchange city is abnormally warmer in that month.
The effect is again more prominent when the abnormal temperature is in
the city’s top quintile. An increase in the city’s abnormal temperature from
the coolest quintile to the warmest quintile is associated with a reduction
of 48 bps in the long-short emission-minus-clean portfolio. In an alternative
specification, we define high- and low-emission firms according to their MSCI
Carbon Emission Scores, which capture individual companies’ emission levels
relative to their industry peers, and achieve similar results. We do not find
any significant return reversal in the longer term (up to a year). The return
patterns are observed in both energy and nonenergy high-emission sectors and
are robust to size adjustments. Furthermore, we do not obtain the same results
in a “placebo” test that uses an earlier sample period, 1983–2000, when global
warming was less of an issue.
To better understand the mechanism through which temperature affects
prices, we examine proxies for different investors’ trading behavior.2 We
focus on local blockholders, local institutional investors, and retail investors
(the majority of which are local) because they are exposed to the same
temperature. Which of these investors decrease their holdings of high-emission
firms in an abnormally warm quarter? Consistent with our conjecture that
individuals are more prone to limited attention and drawn to notable events,
we find evidence that retail investors sell high-emission firms and buy lowemission firms. Institutional investors (local and foreign) do not respond
systematically to abnormal temperatures. More interestingly, we find that local
blockholders trade in the opposite direction of retail investors. Therefore, local
abnormal temperatures do not appear to adversely affect all carbon-intensive
firms’ operations in a fundamental manner, as blockholders of these firms are

Attention to Global Warming

3 Although we cannot rule out the possibility that local blockholders revise their beliefs about global warning

downward in an abnormally warm quarter (which would be puzzling), our preferred interpretation is that these
blockholders respond to the decrease in stock prices, similar to the model developed by Hong, Wang, and Yu
(2008). Hong, Wang, and Yu (2008) argue that firms are buyers of last resort for their own stocks. They repurchase
shares when prices drop below their fundamental value.

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generally buying shares and household investors should be less informed than
blockholders.3 We conclude that unusually warm weather is a salient event that
affects individual investors, and we run a series of tests and find no evidence
that the price impact is a result of belief updates about firms’ future cashflows.
Rather, people seem to avoid holding high-emission firms as they become more
aware of climate risk, similar in spirit to avoiding “sin” stocks (companies
involved in producing alcohol, tobacco, and gaming).
Recent literature on climate change also examines people’s beliefs and
personal experience. Zaval et al. (2014), Akerlof et al. (2013), and Myers
et al. (2012) show that personal experience with global warming, as reported in
surveys, leads to an increased perception of climate risk in the United States;
this finding is confirmed by Broomell, Budescu, and Por (2015) and Howe
et al. (2013) using international surveys. Konisky, Hughes, and Kaylor (2016),
Borick and Rabe (2014), and Joireman, Truelove, and Duell (2010) find a
similar relationship using objective measures of weather experience, such as
outdoor temperature, snowfall, and occurrences of floods and hurricanes. Li,
Johnson, and Zaval (2011) further show that perceived deviations from normal
temperature not only alter beliefs but also are followed by actions: participants
are more likely to donate their earnings to a global warming charity. Surveys
measure beliefs about global warming in all these studies. In contrast, our paper
uses objective proxies for attention to capture the learning process, and we
can examine how updated aggregate beliefs are reflected in prices and trading
behavior. Our findings are related to experiential learning, in which people
begin the learning process based on concrete experience and form abstract
concepts by observing and analyzing information before acting (Boud, Keogh,
and Walker 1985; Kolb 1984). In our context, we can see whether people read
more about global warming (on the Internet) after they are personally affected
by the local weather.
This paper complements previous empirical findings on reactions to climate
and other external conditions. Chang, Huang, and Wang (2018) find that more
health insurance contracts are sold when the air is polluted, but they are more
likely to be canceled if air quality improves shortly afterward. Busse et al.
(2015) and Conlin, O’Donoghue, and Vogelsang (2007) show that the choice
to purchase warm- or cold-weather vehicle types and cold-weather clothing,
respectively, depends on the weather at the time of purchase. Hong, Li, and
Xu (2019) document underreaction of food companies’ stock prices to trends
in droughts that are exacerbated by global warming. Using a comprehensive
database of coastal home sales in the United States, Murfin and Spiegel
(forthcoming) find that real estate prices do not factor in the risk of sea level

The Review of Financial Studies / v 33 n 3 2020

rise. Our results are also in line with general underreaction to global warming.
Finally, the finding that people pay more attention and our observation of the
differential impacts on the cross-section of stocks distinguish our work from
the literature that links weather-induced investor mood and the stock market
(Goetzmann et al. 2015; Kamstra, Kramer, and Levi 2003, among others).
1. Methods and Hypotheses

Temperatureit = Aver_Tempit +Mon_Tempit +Ab_Tempit ,

(1)

where Aver_T empit is the average monthly local temperature in city i over the
120 months prior to t; Mon_T empit is the average deviation of this month’s
temperature from the average, that is, the average temperature in city i in
the same calendar month over the last 10 years minus Aver_T empit ; and
Ab_Tempit is the remainder. Our focus is how local abnormal temperatures
affect changes in attention (as proxied by the change in SV I , adjusted for
4 See the official Google Search blog for details: https://search.googleblog.com/2013/12/an-easier-way-to-explore

-topics-and.html.

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We would like to identify investor reaction to global warming in times
of unusually warm local weather. Given that climate change is a global
phenomenon, we conduct our study in a broad international setting to
understand people’s collective beliefs and reactions. The international setting
also gives us an identification advantage: climate science research shows that
extreme temperatures rarely occur simultaneously in both the Northern and
Southern Hemispheres (see, e.g., Neukom et al. 2014).
The reaction is first measured by the monthly Google Search Volume Index
(SV I ) of the topic “global warming” in a city, which proxies for people’s
attention. Google offers SV I for topics and search terms. We use topics
instead of search terms because the former addresses misspellings and searches
in different languages, as Google’s algorithms can group different searches
that have the same meaning under a single topic.4 Our idea follows Da,
Engelberg, and Gao (2011), who use SV I of tickers to study investor attention.
Several other papers also examine Google search volume for global warming
and climate change and relate it to local weather conditions: e.g., Lineman
et al. (2015), Cavanagh et al. (2014), Herrnstadt and Muehlegger (2014),
Lang (2014), and Kahn and Kotchen (2011). These studies focus on U.S.
data, whereas our paper covers more than seventy cities worldwide and many
different languages.
To understand the learning process, we decompose local temperatures into
three components, which account for predictable, seasonal, and abnormal
patterns. Specifically, for each city i in month t, we calculate the monthly
Temperatureit by taking the average of daily average temperatures in our data.
Then we define

Attention to Global Warming

2. Data
In the following, we describe the various databases we use, as well as the
variables we obtain and examine in our analyses (the databases used in the
Internet Appendix are described there).
2.1 Weather
We obtain daily weather data from the Global Surface Summary of Day
Data, which are produced by the National Climatic Data Center (NCDC). The
input data used in building these daily observations are the Integrated Surface

5 In large countries, such as China, India, Russia, and the United States, population (and therefore local investors)

are more dispersed, and the exchange city’s temperature is a weaker proxy for the effect of weather on investors.
Table 5 shows a weaker relationship between the exchange city’s abnormal temperature and returns in the ten
largest countries in our sample.

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seasonality). Even though a city’s monthly Ab_Temp provides little fundamental
information about the future global climate, it represents new experience and
is a salient event for people in the city.
Then we turn to investor reaction in the stock market. We study monthly sizeadjusted stock returns under abnormally warm weather in the exchange city.
The size-adjusted return is defined as the stock return minus the average return
of stocks in the same size quintile in the exchange in the same month. Exchange
cities are important cities in which many investors are located, and prices are
affected by domestic investors (see, e.g., Chan, Hameed, and Lau 2003).5 We
examine the cross-section of firms with different sensitivities to climate change.
If investors begin recognizing the effect of climate on financial markets and buy
low-climate-sensitivity and sell high-climate-sensitivity firms, the former will
earn higher returns than the latter. The short-term and the long-term patterns
are examined. Without reversal or with some continuation in the long run, it is
consistent with belief updating. A reversal indicates that the short-term price
changes overshoot and investors overreact.
The effect of abnormally warm weather on stock prices can occur through
multiple channels. First, climate-unfriendly firms may be fundamentally
damaged. Second, people may update their own valuation of firms when they
revise their beliefs about climate change upward. Investors may think that
high-emission firms’ future cashflows are adversely affected because climate
change can hurt firms’ production functions, impose higher costs for future
emissions, or induce tighter regulations on emissions. Third, and finally, on
recognizing the risk of global warming, socially responsible investors may
stay away from firms that are climate unfriendly, similar to the way in which
“sin” stocks are shunned by some investors (Hong and Kacpercyzk 2009).
Sections 3.4 and 3.5 present a series of tests to distinguish between these
channels.

The Review of Financial Studies / v 33 n 3 2020

2.2 Google Search Volume Index
The data source for internet search activity is Google Trends, which provides
a Search Volume Index (SV I ) of the search topic of “global warming.” We
download the monthly SV I in each of the seventy-four locations from 2004
(when Google Trends began to provide data) to 2017. We examine search
activity at both the city and country levels (except for some small countries for
which the search volume data are available only at the country level).7

2.3 Stock and company information
Stock returns, market capitalization, and industry information are available
from Thomson Reuters DataStream. For U.S. stocks, we use return and market
capitalization data from CRSP (we obtain a list of U.S. stocks from DataStream
and match them to CRSP using ISIN and CUSIP). DataStream covers more than
100,000 equities in nearly 200 countries from 1980 onward. We can observe the
firms’ countries of domicile (from the NATION variable) and their exchange
cities, but not the locations of firms’ establishments. The literature notes that
DataStream may suffer from data errors. We winsorize raw returns at the top
and bottom 2.5% in each exchange in each month. Following Hou, Karolyi,
and Kho (2011) and Ince and Porter (2006), we remove all monthly returns that
are above 300% and reversed within 1 month, as well as zero monthly returns
(DataStream repeats the last valid data point for delisted firms).

6 Our conclusion remains the same if we use other similar test periods in the twenty-first century.

Climate change became a global concern in the early twenty-first century. For example, in its
Third Assessment Report released in 2001, the IPCC claims that “there is new and stronger
evidence that most of the observed warming of the past 50 years is attributable to human activities” (https://archive.ipcc.ch/graphics/speeches/robert-watson-november-2001.pdf). In 2001, national science
academies of many different countries issued a joint statement stating that “IPCC represents the consensus
of the international scientific community on climate change science” (Science 2001).
7 We also download the monthly SV I for the topic “climate change,” but the search traffic for this topic is much

lower than that of “global warming” in the first few years of our sample period. In more recent years, the SV I s
of the two topics are highly correlated. In the paper, we report the results using the SV I of “global warming.”

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Data (ISD), which contain weather records from over 9,000 stations globally
since 1973 (the coverage was considerably lower before 1973). The weather
conditions include temperature, wind speed, cloudiness, precipitation, snow
depth, etc. By identifying the location coordinates, we select the closest weather
station to the address of the exchange. We collect the daily records of seventyfour cities with major stock exchanges from 1973 to 2017. Our main test period
is from 2001 to 2017, when climate change is a global phenomenon.6 As noted
in Section 1, abnormal temperatures require 10 years of data to calculate. We
use the period from 1983 to 2000, when few people recognized climate change,
to conduct a “placebo” test.

Attention to Global Warming

2.5 Carbon emission
We identify high-emission firms in two ways. First, we adopt the industry
definitions provided by the Intergovernmental Panel on Climate Change
(IPCC), the leading international body for the assessment of climate change.
Five major industry sectors are identified as major emission sources: Energy;
Transport; Buildings; Industry (such as chemicals and metals); and Agriculture,
Forestry, and Other Land Use (AFOLU). Each sector is further divided into
subcategories (Krey et al. 2014 offers a full list). We hand-match the IPCC
subcategories with the industry names provided by DataStream.9 All firms in
the matched industries are classified as high-emission firms.
Second, we obtain firms’ carbon emission estimates from MSCI ESG
Ratings, which analyzes companies’ environmental, social, and governance
issues. Specifically, MSCI ESG studies greenhouse gas (GHG) emissions of
companies worldwide. A Carbon Emission Score is given to each firm annually
since 2007, on a scale of 0–10. Companies with better performance on this issue
score higher. The score is adjusted by industry and is thus comparable for two
firms from different industries. We define high- (low-) carbon emission firms
as firms whose MSCI Carbon Emission Scores in the previous calendar year
are lower than 3 (higher than 7).
The two definitions identify high-emission firms differently. For example,
Toyota Motor Corporation, listed on the Tokyo Stock Exchange, belongs to
the Automobiles industry in DataStream (which is mapped to the Transport
Equipment industry, IPCC code = 1A2f2). According to the first method, it is
classified as a high-emission firm. The average MSCI score of Toyota Motor
Corporation in our sample period is 9.4, and the second method places it in

8 In other words, we do not directly measure retail ownership, and the proxy is subject to measurement errors.

Several other papers also define the complement of U.S. institutional holdings as a proxy for individual U.S.
investors’ demand: for example, DeVault, Sias, and Starks (2019), Agarwal, Vashishtha, and Venkatachalam
(2018), Malmendier and Shanthikumar (2007), Griffin, Harris, and Topaloglu (2003), and Cohen, Gompers, and
Vuolteenaho (2002).
9 For example, Coal (DataStream Industry Classification Benchmark ICB code = 1771), Gold Mining (DataStream

ICB code = 1777), and General Mining (DataStream ICB code = 1775) are matched with Mining and Quarrying
(IPCC code = 1A2f4). Table IA.1 in the Internet Appendix provides the map.

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2.4 Stock ownership
DataStream provides the aggregate ownership in a stock by domestic and
foreign blockholders (who hold more than 5% of shares outstanding) in
every quarter. Quarterly holdings by institutional investors and their locations
(at the country level) are obtained from FactSet, which covers 33 of our
74 exchange cities. We use the SAS code provided by Ferreira and Matos
(2008), available on WRDS, to calculate the ownership by institutional
investors, excluding blockholders. Then we define retail ownership as (100%
− DataStream blockholders’ ownership − FactSet institutional ownership
excluding blockholders).8

The Review of Financial Studies / v 33 n 3 2020

the low-emission group in all years. One can interpret that the company is a
relatively clean firm in a high-emission industry. Throughout the paper, we
primarily use IPCC definitions because they are available for all firms and for
a longer period. MSCI covers only a subset of firms in a small number of
exchanges. It may have a selection issue and the results should be interpreted
with caution.10

3. Empirical Results
Our tests aim to investigate two questions: (1) whether people’s attention varies
with local temperatures and (2) if so, how experiences of local temperatures
affect the stock price of local firms and investors’ trading behavior. Table 1
shows the list of 74 stock exchange cities. It reports the number of unique
stocks, number of foreign firms (whose country of domicile information is
available and is different from that of the exchange city), number of emission
firms and foreign emission firms (defined using the IPCC classification), as
well as average retail and blockholder ownerships in each city in our sample.
In all regressions below, all standard errors are clustered by exchange city and
year-month (or year-quarter for regressions of changes in ownership).
3.1 Attention and local temperatures
To capture changes in attention, we first calculate the log monthly change in the
Google Search Volume Index, DSV I . DSV Iit is the log change in SV I in city
i in month t, adjusted for seasonality.11 Panel A of Table 2 shows the summary
10 MSCI collects data once a year from the most recent corporate resources, such as annual reports and corporate

social responsibility reports. When direct disclosure is not available, MSCI uses GHG data reported by the Carbon
Disclosure Project or government databases. Note that MSCI does not assign a score to every public firm. The
number of firms with a valid MSCI Carbon Emission Score in our data increases from 1,888 in 2007 to 11,239 in
2017, as shown in Table IA.2 in the Internet Appendix. Although MSCI also issues other climate-change-related
scores to companies, such as the Climate Change Theme Score, the Carbon Emission Score is available for the
longest period.
11 DSV I is defined as the residuals from the regression of the log change in the monthly SV I on month-of-the-year

dummies. The residuals are then winsorized at the top and bottom 2.5% tails. Two cities, Shenzhen and Shanghai,

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2.6 Price of carbon and environmental regulatory regime index
The price of carbon is measured by carbon futures prices. EUA Futures
Contracts, traded on the Intercontinental Exchange (ICE) Futures Europe,
are contracts in which the traders are obliged to make or take the delivery
of 1,000 emission allowances. Each allowance is an entitlement to emit
one ton of carbon-dioxide-equivalent gas. We download the data from
Bloomberg (symbol: MO1 Comdty), beginning in April 2005. We also use the
environmental regulatory regime index developed by Esty and Porter (2001).
The index is a ranking of countries’ regulatory stringency, structure, subsidies,
and enforcement; it represents the quality of the environmental regulatory
system.

Attention to Global Warming

Table 1
List of exchange cities
City

Country/area

Continent

#
#
#
#Foreign %
%
Firms Foreign Emission emission Retail Blockholder
0
10
0
0
4
1
1
0
3
0
1
0
2
0
0
4
0
4
1
69
1
0
0
1
0
646
0
0
14
0
0
12
0
1
3
1
0
440
3
2
0
0
8
0
1
2
0
0
324
4
0
52
37
3
0
0
2
0

56
68
141
315
11
2
27
8
63
146
23
58
466
79
81
71
123
24
17
462
9
258
27
70
181
650
167
233
196
153
61
574
39
55
85
38
51
940
8
97
99
67
152
259
1,908
18
41
47
1,026
36
46
234
382
40
72
100
136
613

0
2
0
0
3
1
1
0
0
0
0
0
1
0
0
3
0
3
1
17
0
0
0
1
0
251
0
0
4
0
0
3
0
0
3
0
0
165
0
1
0
0
4
0
0
0
0
0
121
0
0
45
6
0
0
0
2
0

51.47
59.12

2.67
0.69

72.86

2.16

41.55

0.53

48.30

3.27

54.03
76.86
43.06
49.19

8.30
0.01
0.94
1.73

51.70

2.89

38.95

0.38

55.97

1.57

36.73

0.73

58.34
58.09
45.97

2.15
0.45
0.33

46.68

0.55

46.02
55.26

1.12
3.54

66.50
30.26

0.69
11.08

62.59
39.39
40.98

0.04
2.74
0.85

(Continued)

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Amman
Jordan
Asia
228
Amsterdam
Netherlands
Europe
247
Athens
Greece
Europe
364
Bangkok
Thailand
Asia
796
Berlin
Germany
Europe
54
Bern
Switzerland
Europe
18
Bogota
Colombia
South America 74
Bratislava
Slovakia
Europe
25
Brussels
Belgium
Europe
280
Bucharest
Romania
Europe
272
Budapest
Hungary
Europe
77
Buenos Aires
Argentina
South America 97
Busan
Korea
Asia
1,006
Cairo
Egypt
Africa
198
Colombo
Sri Lanka
Asia
294
Copenhagen
Denmark
Europe
285
Dhaka
Bangladesh
Asia
410
Dublin
Ireland
Europe
76
Dusseldorf
Germany
Europe
58
Frankfurt
Germany
Europe
1,735
Hamburg
Germany
Europe
65
Hanoi
Vietnam
Asia
400
Harare
Zimbabwe
Africa
71
Helsinki
Finland
Europe
208
Ho Chi Minh
Vietnam
Asia
340
Hong Kong
Hong Kong
Asia
2,064
Istanbul
Turkey
Europe
461
Jakarta
Indonesia
Asia
592
Johannesburg
South Africa
Africa
663
Karachi
Pakistan
Asia
410
Kiev
Ukraine
Europe
83
Kuala Lumpur
Malaysia
Asia
1,207
Kuwait
Kuwait
Asia
177
Lagos
Nigeria
Africa
160
Lima
Peru
South America 140
Lisbon
Portugal
Europe
97
Ljubljana
Slovenia
Europe
137
London
United Kingdom
Europe
3,558
Luxembourg
Luxembourg
Europe
38
Madrid
Spain
Europe
298
Manila
Philippines
Asia
283
Mexico City
Mexico
North America 183
Milan
Italy
Europe
519
Moscow
Russia
Europe
349
Mumbai
India
Asia
4,806
Munich
Germany
Europe
90
Muscat
Oman
Asia
98
Nagoya
Japan
Asia
116
New York City United States North America 3,874
Nicosia
Cyprus
Europe
143
Osaka
Japan
Asia
140
Oslo
Norway
Europe
446
Paris
France
Europe
1,578
Prague
Czechia
Europe
71
Riyadh
Saudi Arabia
Asia
182
Santiago
Chile
South America 236
Sao Paulo
Brazil
South America 297
Shanghai
China
Asia
1,180

The Review of Financial Studies / v 33 n 3 2020

Table 1
(Continued)
China
Singapore
Macedonia
Bulgaria
Sweden
Germany
Australia
Taiwan
Israel
Japan
Canada
Austria
Poland
New Zealand
Croatia
Switzerland

Asia
Asia
Europe
Europe
Europe
Europe
Oceania
Asia
Asia
Asia
North America
Europe
Europe
Oceania
Europe
Europe

2,024
920
40
157
1,102
55
2,888
1,023
785
3,656
841
166
1,075
229
73
367

0
140
0
0
27
5
93
34
7
2
39
2
23
5
0
15

1,093
443
20
41
292
12
1,502
556
251
1,465
395
65
339
62
27
119

0
70
0
0
7
3
37
19
0
0
27
0
8
1
0
2

40.36

0.62

59.45
40.86
72.78

2.86
0.64
0.59

70.39
49.02
31.80
29.39

0.52
6.54
0.47
3.49

63.68

0.68

This table lists the seventy-four exchange cities (and their countries/areas and continents) that we use in analyses
and the number of unique firms, number of foreign firms (whose home country information is available and is
different from that of the exchange city), number of emission firms and foreign emission firms (defined by the
IPCC classification), and average retail and blockholder ownerships in each city during the sample period, from
2001 to 2017.

statistics of DSV Iit , as well as those of Aver_T empit , Mon_T empit , and
Ab_Tempit , the decomposition of temperature in city i in month t according
to Equation (1). The mean DSV I is close to zero (−0.02%), whereas the
mean Aver_T emp, Mon_T emp, and Ab_Temp are 61.9◦ F, 0.16◦ F, and 0.27◦ F,
respectively.
Then we run the following regression:
DSVI it = α +β1 Ab_Tempit +t YearMontht +it ,

(2)

Our coefficient of interest is β1 . Table 2, panel B, reports the results. In Column
1, the coefficient estimate of Ab_Temp is significantly positive (t-stat = 2.3),
which suggests that people pay more attention to global warming when they
are experiencing an abnormally high temperature. The regression includes
year-month fixed effects, meaning that the relationship is observed from the
geographic variation (in a given month, when a city is abnormally warm relative
to other places, people in that city tend to search about global warming more
than people in other places).
In Column 2, we rank all months into quintiles based on Ab_Tempit in city i
and use these quintile dummies in the regression instead of Ab_Temp. The
coefficients of the quintile dummies indicate that the temperature effect is
nonlinear: the coefficients of quintiles 2, 3, and 4 are not significantly different
from zero, while the coefficient of quintile 5 is 4.84 (t-stat = 2.6). Thus, our

are dropped from the analysis, because Google Trends returns no valid local data for them. Table IA.3 in the
Internet Appendix examines changes in attention at daily, weekly, and quarterly levels. The results are weaker. A
day or week of abnormal temperatures may not shift beliefs, whereas a month is more likely to. It may also take
an extended period of warm weather for the media effect to come into play. (At the quarterly level, the results
are also weaker, but the average extreme temperature within a quarter is attenuated.)

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Shenzhen
Singapore
Skopje
Sofia
Stockholm
Stuttgart
Sydney
Taipei
Tel Aviv
Tokyo
Toronto
Vienna
Warsaw
Wellington
Zagreb
Zurich

Attention to Global Warming

Table 2
Google search volume for “global warming” and abnormal temperature
A. Summary statistics
Variable
Obs
DSVI(city)
DSVI(country)
Aver_Temp
Mon_Temp
Ab_Temp
#Exchange cities

11,603
10,366
11,603
11,603
11,603
72

Mean

SD

P10

P25

P50

P75

P90

−0.017
0.047
61.861
0.155
0.265

66.484
77.578
12.454
10.837
2.679

−51.333
−57.793
48.334
−15.185
−2.794

−23.129
−24.908
51.655
−8.069
−1.201

−0.604
−1.506
59.458
0.259
0.238

22.652
22.644
72.406
8.178
1.696

51.584
59.254
81.695
15.506
3.419

Ab_Temp

0.536∗∗
(2.26)

Ab_Temp Q2

Ab_Temp Q4
Ab_Temp Q5
Yes
11,603
.020

(4)
DSVI(country)

0.724∗∗
(2.43)
−0.279
(−0.16)
−1.787
(−1.00)
−1.149
(−0.47)
3.539
(1.66)

0.630
(0.34)
1.220
(0.84)
1.074
(0.58)
4.841∗∗
(2.57)

Ab_Temp Q3

Year × Month FEs
Obs.
Adj. R 2

(3)
DSVI(country)

Yes
11,603
.020

Yes
10,366
.015

Yes
10,366
.015

This table reports the results of analyses on the effect of abnormal temperatures on the search volume of the topic
of “global warming” on Google. Panel A presents summary statistics of the variables. DSVI(city) is the monthly
log change of Google’s search volume index (SVI) of the topic “global warming” in the exchange city and adjusted
for seasonality, and DSVI(country) is calculated using the SVI in country of the city. Aver_Temp is the average
monthly temperature (in Fahrenheit degrees) of the exchange’s city over the previous 120 months. Mon_Temp
is the city’s average temperature in the same month of the year over the previous 10 years minus Aver_Temp.
Ab_Temp is the city’s temperature in this month minus Aver_Temp and Mon_Temp. Panel B represents the result
of regressing DSVI(city) (Columns 1 and 2) and DSVI(country) (Columns 3 and 4) on city-level temperature
measures. For each exchange city, months are sorted into quintiles based on Ab_Temp, and Ab_Temp Q2-Q5 are
quintile dummies that equal one if the month belongs to quintiles 2–5, respectively. The sample is from 2004 to
2017. Standard errors are clustered by exchange city and by year-month, and the corresponding t -statistics are
reported in parentheses. *p < .1; **p < .05; ***p < .01.

results suggest that Google search volume increases with the highest abnormal
local temperatures, which are the most salient. This idea is similar in spirit to
the “frog in the pan” hypothesis proposed by Da, Gurun, and Warachka (2014),
who show that investors pay more attention to infrequent dramatic changes than
to frequent gradual changes.
The economic magnitude is worth noting. Based on the estimation in Column
2, compared to the 20% abnormally coolest months, in the 20% abnormally
warmest months people search more about global warming by 4.8%, or about
7.3% of its standard deviation (which is 66.5%, as shown in panel A).
Finally, we repeat all the regressions by replacing SV I in city i with SV I
in the country (for countries with more than one stock exchange, we pick
the exchange city with the largest total market capitalization; the regressions
include sixty-three countries). Panel A of Table 2 shows that the summary
statistics of the two SV I s are similar. Columns 3 and 4 report the regression

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B. Regression of DSVI on abnormal temperature
(1)
(2)
DSVI(city)
DSVI(city)

The Review of Financial Studies / v 33 n 3 2020

3.2 Stock returns and local temperatures
Next, we examine whether local weather affects stock prices, focusing on the
differential reactions in the cross-section of firms. We first form two portfolios
according to the IPCC definitions described in Section 2. In each city i from
2001 to 2017, portfolio EMI SSI ONi includes all firms whose DataStream
industry group is mapped with the IPCC sectors. All remaining firms in city
i are assigned to portfolio CLEANi . A long-short portfolio EMCi (which
stands for Emission Minus Clean) is formed by buying EMI SSI ONi and
selling CLEANi . We construct all portfolios using equal weights and value
weights. Panel A of Table 3 shows the summary statistics. Size-adjusted returns
are reported.12 Figure 1 plots the average equal-weighted EMC size-adjusted
returns and the confidence intervals across five temperature quintiles in the
12 We use size-adjusted returns, because the market capitalization data obtained from DataStream have better

coverage than other financial data. Other models can calculate adjusted returns (e.g., a factor model based on
momentum and cashflow-to-price) (Hou, Karolyi, and Kho 2011). One disadvantage is that the sample size
would be greatly reduced when requiring other company information. Specifically, we check the availability of
the following variables in the Worldscope database: book/market, dividend/price, earnings/price, and long-term
debt/common equity. Requiring at least one of these variables will reduce the number of observations in our main
regression by 81%. Twelve of our seventy-four exchange cities have zero observations, and fifty-eight cities have
less than 10% of the observations remaining.

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results, which are qualitatively similar to those at the city level. In later tests, we
have only country-level information on investor locations. Most exchange cities
are important cities with high populations, concentrated capital, and extensive
media coverage. Because abnormal temperature in the exchange city is strongly
associated with people’s attention at the country level, it seems reasonable to
use the city’s temperature to proxy for people’s experience in the country.
The Internet Appendix examines whether institutional investor and media
attention also change with local abnormal temperatures. We follow BenRephael, Da, and Israelsen (2017) to measure abnormal institutional investor
attention (AI A). AI A tracks how frequently Bloomberg users, who are likely
financial institutions, search and read information about a certain stock. While
we do not have users’ location, we can obtain information at the stock level
(in 45 exchanges). Table IA.4 shows the results. We do not find evidence that
abnormally warm weather leads to different levels of institutional attention
to high-emission and low-emission firms in the exchange. This finding is
in line with our trading results in Section 3.5 and our hypothesis that local
weather mostly affects retail investors. Using data from Raven Pack News
Analytics, Table IA.5 finds that media attention to high-emission firms do not
vary with local abnormal temperatures. However, most data from Raven Pack
News come from English-speaking media (which may not be located in the
exchange city) and are available at the stock level (so that generic stories about
climate change will not be captured). Future research can revisit these questions
if there are better measures of international institutional investor and media
attention.

Attention to Global Warming

exchange city. We see a general decrease in EMC returns as we move up
the temperature quintiles, with statistically significant underperformance in the
warmest quintile. Summary statistics for raw returns (not adjusted for size) and
longer-term returns (up to 12 months) of EMC are also shown in panel A.
Similar in spirit to Hirshleifer and Shumway (2003) and Saunders (1993),
who examine the relationship between morning sunshine in a city and index
returns, we capture investors’ experience by using local abnormal temperature
in the city. We run the following regression:
(3)

where EMCit is the value-weighted or equal-weighted, size-adjusted or raw
return of the EMC portfolio in city i in month t (from 2001 to 2017), and
Ab_Tempit is the abnormal temperature in city i in month t based on the
decomposition in Equation (1). Year-month fixed effects are included.13
Panels B (equal-weighted) and C (value-weighted) of Table 3 offer the results.
Column 1 of Panel B shows that higher abnormal temperature is associated
with significantly lower EMC size-adjusted returns. A 1-standard-deviation
increase in Ab_Temp corresponds to a decrease of 16 bps in EMC return
(= −0.060×2.676). Column 2 replaces Ab_Temp with the quintile dummies
based on the city’s abnormal temperature. It shows that the negative effect on
EMC returns is the strongest in the highest temperature quintile, consistent
with our Google SV I results in Section 3.1. The economic impact is sizeable,
with a change from temperature quintile 1 (coolest) to quintile 5 (warmest)
corresponding to a drop of 48 bps (t-stat = −4.0) in size-adjusted return.
The results are similar when we consider raw returns (Columns 3 and 4).
Finally, Columns 5 and 6 study EMI SSI ON and CLEAN portfolio sizeadjusted returns, respectively. Relative to the city’s coldest temperature quintile,
EMI SSI ON (CLEAN ) earns significantly lower (higher) returns in the
warmest quintile, at the 1% significance level. Therefore, both portfolios
contribute to the low EMC returns in the warmest months. The results using
value-weighted returns are generally similar, as shown in panel C.
Next, we examine the long-term performance subsequent to an abnormally
warm month:
EMC i,t+1,t+n = α +β1 Ab_Tempit +t YearMontht +it ,

(4)

where n = {3,6,12} and the returns are measured from month t +1 to month
t +n. Year-month fixed effects are included. If β1 is negative or zero, it is
consistent with slow belief updating; investors with limited attention generally
overlook climate risk but recognize it when reacting to attention-grabbing
weather events. Otherwise, if β1 appears to be positive, it implies that part

13 Table IA.6 in the Internet Appendix runs these regressions at weekly and quarterly levels. We obtain similar

results that are statistically weaker.

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EMC it = α +β1 Ab_Tempit +t YearMontht +it ,

The Review of Financial Studies / v 33 n 3 2020

Table 3
Emission-minus-clean portfolio return and abnormal temperature
Mean

SD

P10

P25

P50

P75

P90

Equal-weighted
EMC
EMC(raw)
EMISSION
CLEAN
EMCt+1,t+3
EMCt+1,t+6
EMCt+1,t+12

12,614
12,614
12,614
12,614
12,614
12,614
12,614

0.044
0.060
0.022
−0.022
0.057
0.122
0.276

4.867
5.728
3.269
2.002
6.614
9.089
12.908

−3.528
−4.189
−2.060
−1.391
−5.605
−8.379
−12.533

−1.464
−1.692
−0.829
−0.605
−2.269
−3.326
−4.969

0.000
0.112
0.000
0.000
0.142
0.272
0.672

1.657
1.926
0.957
0.535
2.663
4.157
6.601

3.819
4.519
2.251
1.368
5.821
8.532
13.078

Value-weighted
EMC
EMC(raw)
EMISSION
CLEAN

12,614
12,614
12,614
12,614

0.100
0.117
0.032
−0.068

5.999
6.710
4.263
3.108

−5.155
−5.628
−3.545
−2.936

−2.210
−2.415
−1.536
−1.348

0.047
0.121
0.001
−0.019

2.507
2.713
1.693
1.192

5.609
6.096
3.776
2.813

Ab_Temp

12,614

0.307

2.676

−2.776

−1.142

0.306

1.746

3.446

B. Equal-weighted EMC returns
(1)

(2)

(3)

EMC
Ab_Temp

−0.060∗∗∗
(−3.34)

−0.068∗∗∗
(−2.67)
−0.148
(−1.16)
−0.125
(−0.88)
−0.145
(−1.27)
−0.481∗∗∗
(−4.04)

Ab_Temp Q2
Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Year × Month FEs
Obs.
Adj. R 2

Yes
12,614
.020

C. Value-weighted EMC returns
(1)

Ab_Temp Q4
Ab_Temp Q5
Year × Month FEs
Obs.
Adj. R 2

Yes
12,614
.036

−0.297∗
(−1.69)
−0.316
(−1.60)
−0.212
(−1.63)
−0.614∗∗∗
(−3.82)

−0.035
(−0.44)
−0.041
(−0.41)
−0.094
(−1.52)
−0.285∗∗∗
(−3.35)

0.113∗
(1.90)
0.084
(1.47)
0.051
(0.90)
0.196∗∗∗
(3.95)

Yes
12,614
.014

Yes
12,614
.022

Yes
12,614
.018

(2)

(3)

(4)

(5)

(6)

EMISSION

CLEAN

−0.317
(−1.37)
−0.522∗∗
(−2.23)
−0.441∗∗
(−2.42)
−0.574∗∗∗
(−2.81)

−0.069
(−0.63)
−0.202∗
(−1.77)
−0.174
(−1.64)
−0.324∗∗∗
(−3.10)

0.142
(1.34)
0.135
(1.33)
0.136
(1.52)
0.152
(1.60)

Yes
12,614
.033

Yes
12,614
.028

Yes
12,614
.032

EMC(raw)
−0.066∗∗
(−2.00)

−0.211
(−1.13)
−0.337∗
(−1.79)
−0.310∗
(−1.78)
−0.476∗∗∗
(−3.06)

Ab_Temp Q3

(6)
CLEAN

Yes
12,614
.018

−0.055∗∗
(−2.08)

Ab_Temp Q2

(5)
EMISSION

Yes
12,614
.020

EMC
Ab_Temp

(4)
EMC(raw)

Yes
12,614
.036

Yes
12,614
.033

At the beginning of month t , EMI SSI ON and CLEAN portfolios are formed based on firms’ industry code.
High-carbon-emission industries are defined following the IPCC’s report. Portfolio return (as a percentage) equals
the average adjusted return of stocks at month t , equal weighted or value weighted. Adjusted return equals raw
return minus the average return of stocks in the same size quintile by each exchange. EMC equals EMI SSI ON
minus CLEAN . EMC(raw) is calculated using raw returns. EMCt+1,t+3 , EMCt+1,t+6 , and EMCt+1,t+12
are calculated using adjusted returns over months t +1 to t +3, t +1 to t +6 and t +1 to t +12, respectively.
Panel A reports summary statistics. Panel B reports the results of regressions of EMC on contemporaneous
temperature variables using equal-weighted portfolio returns, and panel C uses value-weighted returns. The
sample is from January 2001 to December 2017. Standard errors are clustered by exchange city and year-month,
and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p < .01.

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A. Summary statistics
Variable
Obs

-.4

1

2

3
Quintile of Ab_Temp

4

5

Figure 1
EMC on abnormal temperature, 2001–2017
The figure presents the average EMC returns (equal-weighted and adjusted for year-month fixed effects, as a %)
by Ab_Temp quintiles with 95% confidence intervals using the sample for 2001–2017.

of the belief update in month t is irrational (overreaction) as the previous
price pattern has reversed. Table 4 presents the results. For brevity, only equalweighted EMC size-adjusted returns are reported in the main text. The Internet
Appendix (Table IA.7) reports value-weighted returns.
As shown in Columns 1, 3, and 5, the coefficients of Ab_Temp are statistically
insignificant. The coefficients of temperature quintiles in Columns 2, 4, and 6 do
not show a systematic pattern and are generally statistically insignificant. These
results indicate that there is no strong continuation or reversal in the 3 to 12
months after month t. (It is certainly possible that there is a return reversal after
12 months. With 17 years of data, longer term reversals are statistically difficult
to detect. We encourage future research to test whether the belief updating
process is rational or irrational with longer sample periods.)
A concern about the IPCC industry classification is that we may pick up
some industry effects. Although it is not obvious why such effects would
vary with local abnormal temperatures, we conduct three additional tests to
further confirm our previous results. First, we rerun the return regressions in
Equation (3) using an earlier sample period, 1983 (the beginning year of our
abnormal temperature measures) to 2000. Unlike panel B of Table 3 (in which
the sample period is 2001–2017), Columns 1 and 2 of Table 5 do not show any
systematic difference in EMI SSI ON and CLEAN portfolio returns under
different abnormal temperatures. Climate change was less of a global concern
and the scientific evidence was less conclusive before the 21st century. It is not

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-.2

EMC
0

.2

.4

Attention to Global Warming

The Review of Financial Studies / v 33 n 3 2020

Table 4
Long-term EMC returns subsequent to abnormal temperature
(1)

(2)
EMCt+1,t+3

Ab_Temp

−0.048
(−1.40)

Ab_Temp Q3
Ab_Temp Q4

−0.012
(−0.38)

Yes
12,614
.034

Yes
12,614
.034

(5)
−0.001
(−0.01)

−0.070
(−0.26)
−0.050
(−0.21)
−0.127
(−0.50)
−0.061
(−0.26)

Yes
12,614
.048

(6)

EMCt+1,t+12

Yes
12,614
.047

−0.005
(−0.01)
−0.126
(−0.31)
−0.138
(−0.33)
0.348
(0.82)

Yes
12,614
.053

Yes
12,614
.053

The table reports the results of regressions of EMCt+1,t+3 , EMCt+1,t+6 , and EMCt+1,t+12 on abnormal
temperature variables at month t . All EMC returns are calculated using the equal-weighted average of adjusted
returns. The sample is from January 2001 to December 2017. Standard errors are clustered by exchange city and
year-month, and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p < .01.

surprising that we observe the return pattern globally only after 2001 if this is
due to the awareness of climate risk.
Second, some high-emission industries’ returns may be correlated with
fluctuations in oil prices. Columns 3 to 6 separately examine all energy firms
(which are in the IPCC Energy sector) and other high-emission firms (which are
in the remaining four IPCC sectors). Both groups underperform when the city
is abnormally warm. The results observed among nonenergy industries confirm
that investors are more likely to react to different carbon emission levels than
to oil prices.
Our third test defines high- and low-emission firms by their MSCI carbon
emission scores. Because these scores are industry-adjusted, it is now possible
to have both high- and low-emission firms in the same industry, and this test
will not be driven by industry effects. Note that this analysis is performed with
a smaller sample (with 14 exchanges), as MSCI scores are only available since
2007 and cover only a subset of exchanges and firms. The results in Columns
7 and 8 are in line with those of our previous tables. EMC earns lower returns
when the city’s Ab_Temp is high, especially when it is in the highest quintile.
In Column 7, a 1-standard-deviation increase in Ab_Temp corresponds to a
decrease of 38 bps in EMC size-adjusted return (t-stat = −2.6).
Columns 9 and 10 of Table 5 conduct another robustness check. Some
exchange cities are small in total market capitalization and contain fewer firms.
The tests in Section 3.5 require equity ownership data from FactSet, which
generally covers larger stock exchanges. The EMC return results using this
subset are similar to those in the full sample. Finally, Columns 11 and 12
include dummy variables that indicate the country of the exchange city is the
ten largest in size in our sample. In our return regressions (Equation (3)),
we use the exchange city’s temperature to proxy for people’s experience in

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Ab_Temp Q5

(4)

EMCt+1,t+6

−0.303
(−1.41)
−0.189
(−1.44)
−0.431∗∗
(−2.64)
−0.358
(−1.56)

Ab_Temp Q2

Year × Month FEs
Obs.
Adj. R 2

(3)

(2)

(3)

Placebo
Ab_Temp

Ab_Temp Q4
Ab_Temp Q5

(6)

−0.048∗∗
(−2.26)
−0.126
(−0.55)
−0.282
(−1.30)
−0.198
(−1.07)
−0.402∗
(−1.89)

0.117
(0.54)
0.146
(0.60)
0.115
(0.65)
−0.035
(−0.18)

Ab_Temp Q3

(5)

(7)

Nonenergy

−0.084∗∗
(−2.58)

0.000
(0.01)

Ab_Temp Q2

(4)
Energy

(8)

(9)

MSCI
−0.143∗∗
(−2.60)

−0.168
(−1.25)
−0.076
(−0.51)
−0.116
(−0.94)
−0.491∗∗∗
(−3.60)

(10)
FactSet

(12)
Top-10 areas

−0.058∗∗
(−2.16)
−0.415
(−0.68)
−0.853∗
(−1.92)
−0.151
(−0.36)
−0.935∗
(−1.99)

(11)
−0.075∗∗∗
(−3.66)

−0.083
(−0.79)
0.028
(0.11)
−0.136
(−0.92)
−0.569∗∗
(−2.50)
−0.033
(−0.26)
0.079∗∗
(2.36)

Top10_Area
Ab_Temp × Top10_Area
Ab_Temp Q5 × Top10_Area
Year × Month FEs
Obs.
Adj. R 2

−0.149
(−1.17)
−0.126
(−0.88)
−0.146
(−1.28)
−0.507∗∗∗
(−3.66)
−0.036
(−0.29)

0.156
(0.63)
Yes
8,997
.015

Yes
8,997
.015

Yes
10,744
.041

Yes
10,744
.040

Yes
12,537
.015

Yes
12,537
.015

Yes
784
.258

Yes
784
.255

Yes
5,788
.034

Yes
5,788
.035

Yes
12,614
.020

Yes
12,614
.020

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This table presents results of several robustness tests of the analysis in Table 3. Columns 1 and 2 are placebo tests: regressions of EMC on contemporaneous temperature variables from
January 1983 to December 2000. EMI SSI ON and CLEAN portfolios are formed based on firms’ industry codes. High-carbon-emission industries are defined following the IPCC’s report.
Portfolio return (as a percentage) is the equal weighted average adjusted return of stocks at month t . Adjusted return equals raw return minus the average return of stocks in the same size
quintile by each exchange. EMC equals EMI SSI ON minus CLEAN . In Columns 3 to 6, the EMI SSI ON portfolio is divided by Energy and Nonenergy firms, and EMC portfolio returns
are calculated for each group. In Columns 7 and 8, EMI SSI ON and CLEAN firms are categorized using MSCI ratings: EMI SSI ON includes stocks with carbon emission scores lower
than 3, whereas the CLEAN portfolio consists of stocks with carbon emission scores higher than 7. This sample is from January 2008 to December 2017 and includes only exchanges with
more than thirty stocks covered by MSCI. In Columns 9 and 10, the sample includes only exchanges in the FactSet database. Columns 11 and 12 include dummy variables that indicate
the country of the exchange city is the ten largest in size in our sample (the countries are Russia, Canada, China (two exchanges), United States, Brazil, Australia, India, Argentina, and
Saudi Arabia). In all columns, standard errors are clustered by exchange city and year-month, and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p < .01.

Attention to Global Warming

(1)

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Table 5
EMC return and abnormal temperature: Robustness tests

The Review of Financial Studies / v 33 n 3 2020

3.3 Belief updating process
Overall, our findings suggest that the EMC return is negative in abnormally
warm weather. One might wonder why, after many years, we still see a
reaction in a warm month—why is this update so slow? We offer two potential
explanations. First, there is perhaps some reversal in beliefs. While we do not see
a statistically significant return reversal in the 12 months after the abnormally
warm month, this does not mean that there is no reversal in beliefs at all (it
may simply not be strong enough to be detected in the return data). Figure 1
offers more suggestive evidence: when we sort EMC portfolio returns into
five abnormal temperature quintiles, Quintile 1 (the coolest quintile) shows a
positive return, although it is not significant at the 5% level. We think some
people revise their beliefs downward in an abnormally cool month, for example,
President Donald Trump, as noted in the Introduction.
Additionally, it is possible that the learning process occurs at different times
in different countries, and hence we see a generally slow update when we study
exchange cities all over the world. The impact of climate change could have been
felt in a small subset of countries even before it became a global issue. Following
Hong, Li, and Xu (2019), we focus on countries that experienced increasing
drought trends (that were possibly exacerbated by rising temperatures) in the
second half of the 20th century. For example, in that period, Peru experienced
disrupted water supplies, especially in dry seasons, as the tropical glaciers of
the Cordillera Blanca shrank rapidly (Baraer et al. 2012). We identify these
countries by estimating the time trend of the Palmer Drought Severity Index

14 Table IA.8 in the Internet Appendix runs the return regressions by dropping all firms listed in the United States

(on the New York Stock Exchange), which constitute a large part of our sample and have geographically diverse
investor base. Our main results are robust to dropping firms listed in the United States.

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the country. In larger countries where the population is more dispersed, this
proxy will be weaker. We find that the relationship between the city’s abnormal
temperature and emission-minus-clean portfolio returns is indeed weaker in
large countries.14
We explore other variables in our weather data in the Internet Appendix
(Tables IA.9 and IA.10): average wind speed, maximum wind speed,
precipitation, and snow depth. Abnormal weather conditions are defined in
the same way as in Equation (1). There is no evidence that Google DSV I
and EMC returns vary with these local conditions in a systematic manner.
While some contemporaneous research establishes a link between institutional
investors’ increased perception of climate risk and extreme weather events
in the United States (Gibson and Krueger 2018; Alok, Kumar, and Wermers
Forthcoming), we acknowledge that our current variables do not perfectly
capture the occurrences of hurricanes (or typhoons), floods, and droughts. We
invite future research to test these links again using better data on international
extreme weather.

Attention to Global Warming

Table 6
EMC return and abnormal temperature: Additional tests

Ab_Temp
Drought
Ab_Temp × Drought

(2)
Late

(3)
Early

(4)
Late

0.035∗
(1.81)
0.144
(0.96)
−0.153∗
(−1.84)

−0.054∗∗
(−2.32)
0.102
(0.88)
0.015
(0.43)

0.329
(1.50)

0.028
(0.28)

0.087
(0.35)
0.225
(0.83)
0.192
(1.04)
0.290
(1.47)
−1.237∗∗
(−2.02)

−0.100
(−0.93)
−0.087
(−0.53)
−0.161
(−1.42)
−0.549∗∗∗
(−3.29)
0.416
(1.49)

Yes
7,804
.019

Yes
9,131
.034

Ab_Temp Q2
Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Ab_Temp Q5 × Drought
Year × Month FEs
Obs.
Adj. R 2

Yes
7,804
.019

Yes
9,131
.034

At the beginning of month t, EMISSION and CLEAN portfolios are formed based on firms’ industry codes. Highcarbon-emission industries are defined following the IPCC’s report. Portfolio return (as a percentage) equals the
equal-weighted average adjusted return of stocks. Adjusted return equals the raw return minus the average return
of stocks in the same size quintile by each exchange. EMC equals EMISSION minus CLEAN. See Table 2 for
definitions of Ab_Temp and Ab_Temp Q2-Q5. Drought equals one if the country is ranked in the bottom quintile
based on long-term drought trends. Each country’s long-term drought trend is estimated based on the Palmer
Drought Severity Index (PDSI) from 1900 to 2014 following the method in Hong, Li, and Xu (2019). Columns 1
and 3 labeled as “Early” refers to a regression using the sample from January 1983 to December 2000, whereas
“Late” refers to January 2001 to December 2017. In all regressions, standard errors are clustered by exchange
city and year-month, and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p <
.01.

(PDSI) provided by Dai, Trenberth, and Qian (2004). The index measures
drought intensity based on a model developed by Palmer (1965). Regression
Equation (3) is run again with an interaction term of Ab_Temp and Drought,
using Early (1983–2000) and Late sample periods (2001–2017). Drought is
a dummy variable indicating countries that have a PDSI time trend in the lowest
quintile and that experience worsening droughts. (These countries are Austria,
Brazil, Israel, Italy, Japan, Peru, Saudi Arabia, Taiwan, and Venezuela.)
Table 6 shows the results. Column 1 shows that EMC returns react to
Ab_Temp more negatively among Drought countries in the period 1983–2000.
Column 3 presents similar findings in the highest Ab_Temp quintile. In 2001–
2017, the point estimates in Columns 2 and 4 suggest that these countries
show a slightly weaker response in EMC returns to high Ab_Temp. While our
full-sample results in Table 3 show that people typically update their beliefs
under warmer-than-usual temperatures in the period 2001–2017, countries that
have reacted earlier may now show weaker reactions—as most people in these
countries might have already become aware of climate change.15
15 A median of 74% of people across countries in Latin America agree that climate change is a very serious

problem in a 2015 survey conducted by The Pew Research Center (Stokes, Wike, and Carle 2015), compared

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(1)
Early

The Review of Financial Studies / v 33 n 3 2020

with a global median is 54% (and 45% of Americans). Stokes, Wike, and Carle (2015) also note that fears of
drought are particularly prevalent in Latin America. One can link our main findings to the reaction to stale or
redundant information (Tetlock 2011; Huberman and Regev 2001). The scientific evidence of climate change is
abundant, whereas abnormal local temperatures carry little new information. In Drought countries, the reaction
to redundant information is weaker as people generally know more about the impact of climate change.
16 We do not construct EMC portfolios here, because most countries have too few foreign firms. We also run

stock-level regressions with the full sample in Table IA.11 in the Internet Appendix. The results are broadly
consistent with those of the portfolio regressions.

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3.4 Mechanism of the pricing effect
The above sections suggest that some investors are reacting to local weather
conditions. Google search activity mostly originates from households, so we
expect that retail investors (the majority of whom are local) have limited
attention and react to abnormally warm local temperatures rather than to
fundamental information. Upon recognizing the effect of climate change,
they can update their beliefs about firms’ valuation or stay away from
climate-unfriendly stocks, as discussed in Section 1.
We confirm our conjecture in this section and the next section. First, we show
that the return patterns are not entirely attributed to fundamental information
about firms’ valuation. Using high-emission firms in exchange cities with at
least one foreign firm (forty-three cities), Columns 1 and 2 in Table 7, panel A,
run a stock-level regression on local abnormal temperatures and check whether
foreign firms listed on the local exchange show the same results.16 Firms whose
major operations are located in a foreign country will not see their production
harmed by local weather conditions, but their returns are still influenced by local
sentiment (see, e.g., Chan, Hameed, and Lau 2003). Although the stock-level
results are weaker than EMC portfolio results in Table 3, we see high-emission
firms’ stock returns significantly decrease with Ab_Temp. More important, there
is no significant difference between local and foreign firms in their price reaction
to abnormal temperatures. Columns 3 and 4 repeat the tests using ten exchange
cities with the highest proportion of foreign firms (10% of all listed firms
across these exchanges are foreign firms, and therefore the test of the difference
between local and foreign firms has higher statistical power). Again, there is no
significant difference, suggesting that the returns are driven by local investors.
Addoum, Ng, and Ortiz-Bobea (forthcoming) find that high temperature
shocks can negatively affect companies’ earnings in some industries. In
particular, the following industries’ earnings are harmed by extremely
warm temperatures: Electric Utilities, Leisure Products, Construction and
Engineering, Capital Markets, Gas Utilities, and Machinery. Four (Electric
Utilities, Construction and Engineering, Gas Utilities, and Machinery) of these
six industries are classified as high-emission industries according to our IPCC
classifications.
In Columns 1 and 2 of Table 7, panel B, we form the EMI SSI ON
portfolio using only firms in the above four industries (the CLEAN portfolio

Attention to Global Warming

Table 7
EMC return and abnormal temperature: Additional tests
A. Local and foreign firms
(1)
Dep. var.: Return

(2)

(3)

All exchanges with foreign firms
−0.021∗
(−1.79)
−0.493∗
(−1.97)
−0.024
(−0.91)

Ab_Temp
Foreign
Ab_Temp × Foreign

−0.029∗
(−2.09)
−0.390
(−1.47)
−0.008
(−0.32)

−0.496∗
(−1.95)

Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Ab_Temp Q5 × Foreign
Year × Month FEs
Obs.
Adj. R 2

Yes
808,211
.006

−0.139
(−1.00)
−0.149
(−1.36)
−0.033
(−0.25)
−0.228
(−1.48)
0.070
(0.62)

Yes
808,211
.006

Yes
515,466
.009

B. High-emission firms that may be harmed by extremely warm temperatures
(1)
(2)
(3)
Dep. var.: EMC
Ab_Temp

Harmed

Ab_Temp Q4
Ab_Temp Q5
Year × Month FEs
Obs.
Adj. R 2

(4)

−0.048∗∗∗
(−2.76)
−0.356
(−1.47)
−0.309∗∗
(−2.55)
−0.398∗
(−1.92)
−0.590∗∗∗
(−3.10)

Ab_Temp Q3

Yes
11,789
.006

Yes
515,466
.009

Not harmed

−0.086∗∗∗
(−2.94)

Ab_Temp Q2

−0.407
(−1.46)

Yes
11,789
.006

−0.146
(−1.08)
−0.113
(−0.73)
−0.081
(−0.65)
−0.441∗∗∗
(−3.68)

Yes
12,513
.019

Yes
12,513
.019
(Continued)

remains the same).17 Columns 3 and 4 form the EMI SSI ON portfolio using
firms in all the remaining high-emission industries according to our IPCC
classifications. While the first set of high-emission firms may suffer from
negative earnings shocks, the second set is unlikely to be significantly affected
by high temperatures. We obtain statistically significant results in both tests.

17 They correspond to the following ICB industry codes in our paper: 7535 (Conventional Electricity), 2353

(Building Materials & Fixtures), 2357 (Heavy Construction), 3728 (Home Construction), 7573 (Gas Distribution),
and 2757 (Industrial Machinery).

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−0.036
(−0.43)
−0.195∗∗
(−2.46)
−0.021
(−0.28)
−0.135
(−1.29)
−0.008
(−0.06)

Ab_Temp Q2

(4)

Top-10 exchanges

The Review of Financial Studies / v 33 n 3 2020

Table 7
(Continued)
C. Carbon prices and environmental regulation scores
(1)
EMC
Ab_Temp
Ab_Temp × High_Price

(2)
EMC

(3)
EMC
−0.096∗
(−1.86)

−0.038
(−1.32)
−0.015
(−0.27)

Reg_High
Ab_Temp × Reg_High
−0.186
(−1.26)
−0.148
(−0.84)
−0.090
(−0.66)
−0.325∗∗
(−2.07)
−0.086
(−0.42)

Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Ab_Temp Q5 × High_Price

−0.045
(−0.32)
−0.090
(−0.55)
−0.171
(−1.45)
−0.435∗∗
(−2.29)

Ab_Temp Q5 × Reg_High
Year × Month FEs
Obs.
Adj. R 2

0.064
(0.50)

−0.075
(−0.22)

Yes
9,541
.016

Yes
9,541
.016

Yes
10,590
.023

Yes
10,590
.022

Panel A of this table reports results of regressions of individual stocks’ adjusted returns on contemporaneous
abnormal temperate. Adjusted return equals raw return minus the average return of stocks in the same size
quintile by each exchange. Foreign equals one if it is a foreign firm listed on the local exchange, and zero if it is
a local firm (firms with missing home country information are dropped). See Table 2 for definitions of Ab_Temp
and Ab_Temp Q2-Q5. Columns 1 and 2 include exchanges with foreign firms, and Columns 3 and 4 use ten
exchange cities with the highest proportion of foreign firms (Hong Kong, Singapore, London, Oslo, New York
City, Toronto, Frankfurt, Taipei, Sydney, and Stockholm). In panel B, at the beginning of month t, EMISSION
and CLEAN portfolios are formed based on firms’ industry codes. In Columns 1 and 2, high-carbon-emission
industries include Electric Utilities, Construction and Engineering, Gas Utilities, and Machinery. In Columns
3 and 4, high-carbon-emission industries include all the remaining high-emission industries according to the
IPCC’s report. Portfolio return (as a percentage) equals the equal-weighted average adjusted return of stocks.
EMC equals EMISSION minus CLEAN. In Panel C, High_Price is a dummy variable that equals one if the
carbon price is in the upper half of all months. Reg_High is a dummy variable that equals one if the regulation
environment score in the country is positive (twenty-seven countries), and zero if it is negative (twenty-five
countries); countries with missing scores are dropped. The sample is from January 2001 to December 2017. In
all regressions, standard errors are clustered by exchange city and year–month, and the corresponding t -statistics
are reported in parentheses. *p < .1; **p < .05; ***p < .01.

Taken together, panels A and B of Table 7 suggest that our overall findings are
not purely driven by adverse earnings news.18
However, investors may still update their private beliefs about firms’
valuation as they become more aware of climate risk, even if in the absence

18 The reaction is net of firms’ hedging activities. Addoum, Ng, and Ortiz-Bobea (forthcoming) design a test using

city-specific weather derivative introduction and discontinuation dates from the CME Group. They find that
hedging activities using weather derivatives in the United States have a small impact on earnings sensitivities
to temperatures. We believe that hedging activities of international firms have an even smaller impact, given
the absence of weather derivatives in most countries. (It is possible to hedge climate change risk using other
securities. For example, Engle et al. (forthcoming) propose to use a large panel of equity returns to build climate
change hedge portfolios.)

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0.041
(0.30)
0.045
(0.74)

Ab_Temp Q2

(4)
EMC

Attention to Global Warming

3.5 Trading behavior
Next, we turn to additional data to help us study the trading activity of
different types of investors. As described in Section 2, we obtain data on
blockholders’ ownership and institutional ownership from DataStream and
FactSet, respectively. Retail investors’ ownership is defined as (100% −
Blockholders’ ownership − Institutional ownership excluding blockholders).
Note that we do not observe retail ownership directly and the estimate is subject
to measurement errors.
Trading activity is the change in ownership between two quarters. For
example, if the retail ownership in a particular stock increases from 75% to
77% (of total shares outstanding), we infer that retail investors buy 2% in this
quarter. Similar to returns, we calculate the EMC_ for each type of investors,
defined as the average change in ownership in high-emission firms minus that
in low-emission firms. Panel A of Table 8 reports the summary statistics.
We run regressions similar to Equation (3):
EMC_it = α +β1 Ab_Tempit +t YearQuarter t +it ,

(5)

where EMC_it is the average net buy across all high-emission firms (in
exchange city i) minus the average net buy across all low-emission firms in
19 The index is calculated based on information available in 2001. Investors may react to expected changes in

future regulations instead. Table IA.12 in the Internet Appendix studies some of the most important international
events, namely, the establishment of the Copenhagen Agreement in December 2009 and the Paris Agreement in
November 2015 and the release of the IPCC Reports in February 2007 and September 2013, which might trigger
tighter future regulations because of coordinated efforts and advances in scientific research. We do not observe
a stronger link between EMC and Ab_Temp after these events.

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of any real change in firms’ valuation. While such beliefs are not observable,
we examine cases in which future cashflows of high-emission firms are more
harmed by climate change. If investors revise their estimates about future
cashflows, the revisions would be more prominent under these situations, and
we would observe a stronger negative link between high-emission firms’ returns
and local abnormal temperatures.
Table 7, panel C, analyzes two examples of these situations. Columns 1 and
2 study periods when the carbon futures price is above the sample median.
When the price of carbon is high, the production costs of carbon-intensive
firms increase. Columns 3 and 4 use the environmental regulatory regime index
developed by Esty and Porter (2001). We define a dummy variable, Reg_H igh,
to denote countries in which the index is positive (the index is positive in 35
exchange cities from 27 countries; the quality of the environmental regulatory
system is good in these countries). Tighter regulations in these places make
it more costly to emit carbon. We do not observe stronger reactions in EMC
returns to Ab_Temp when the carbon price is high and when the quality of
regulations is good.19 Therefore, there is no evidence that investors update
their beliefs about firms’ future cashflows in unusually warm months.

Obs

Mean

SD

P10

P25

P50

P75

P90

EMC_Retail
EMC_Institution
EMC_DomInstitution
EMC_ForInstitution
EMC_Blockholder
EMC_DomBlockholder
EMC_ForBlockholder
#Exchange cities

2,008
2,008
2,008
2,008
2,008
2,008
2,008
33

−0.007
0.006
−0.004
0.009
−0.003
0.000
−0.012

2.345
0.317
0.222
0.199
2.344
2.098
1.320

−0.942
−0.229
−0.114
−0.138
−0.917
−0.761
−0.214

−0.315
−0.070
−0.032
−0.038
−0.271
−0.201
−0.025

−0.015
0.000
0.000
0.000
0.000
0.000
0.000

0.298
0.076
0.025
0.052
0.279
0.194
0.034

0.924
0.245
0.107
0.161
0.884
0.698
0.174

B. Stock trading on abnormal temperature
(1)

(2)

(3)

EMC_Retail
Ab_Temp

−0.080∗
(−2.01)

Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5

Page: 1136

Year × Quarter FEs
Obs.
Adj. R 2

Yes
2,008
.006

(5)

Yes
2,008
.003

0.077∗∗
(2.08)
0.012
(0.89)
−0.001
(−0.05)
0.005
(0.31)
0.037∗
(1.76)

Yes
2,008
.021

(6)
EMC_Blockholder

0.003
(0.84)
−0.102
(−0.67)
−0.165
(−1.18)
−0.316∗∗
(−2.22)
−0.396
(−1.62)

Ab_Temp Q2

(4)
EMC_Institution

Yes
2,008
.021

0.064
(0.40)
0.132
(0.96)
0.303∗∗
(2.32)
0.362
(1.50)

Yes
2,008
.003

Yes
2,008
.001
(Continued)

The Review of Financial Studies / v 33 n 3 2020

A. Summary statistics
%

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Table 8
EMC of trading and abnormal temperature

EMC_DomInstitution
Ab_Temp

0.002
(0.99)

Ab_Temp Q2

Ab_Temp Q4
Ab_Temp Q5
Yes
2,008
.013

(4)

EMC_ForInstitution

Yes
2,008
.016

(5)

0.002
(0.24)
−0.017
(−1.19)
0.018∗∗
(2.07)
−0.001
(−0.07)

Yes
2,008
.012

(6)

EMC_DomBlockholder
0.047∗
(1.94)

0.001
(0.46)
0.007
(1.08)
0.017
(1.25)
−0.010
(−1.11)
0.039
(1.66)

Ab_Temp Q3

Year × Quarter FEs
Obs.
Adj. R 2

(3)

Yes
2,008
.013

(7)

0.023
(0.94)
0.003
(0.02)
0.147
(1.69)
0.277∗
(1.83)
0.128
(1.31)

Yes
2,008
−.006

(8)

EMC_ForBlockholder

Yes
2,008
−.007

0.036
(0.39)
−0.040
(−0.48)
−0.006
(−0.08)
0.172
(1.03)

Yes
2,008
.005

Yes
2,008
.005

1112–1145

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At the beginning of quarter t, EMISSION and CLEAN portfolios are formed based on firms’ industry codes. High-carbon-emission industries are defined following the IPCC’s report.
EMC_Retail refers to the difference in the average changes in retail investors’ ownership over the quarter between emission and clean firms (as a percentage). EMC_Institution
and EMC_Blockholder refer to changes in ownership by institutional investors and blockholders, respectively. Blockholders are those who own more than 5% of shares outstanding,
whereas institutional investors include mutual funds, banks, and others but exclude those who are blockholders. Institutional investors and blockholders are further divided into
domestic and foreign investor categories. Panel A reports the summary statistics of key variables, and panels B and C report the results of regressions of the EMC of ownership
changes on abnormal temperature variables, which are defined in Table 2. In all regressions, year-quarter fixed effects are also included. The sample is from January 2001 to
December 2016. Standard errors are clustered by exchange city and year-quarter, and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p < .01.

Attention to Global Warming

C. Stock trading for domestic and foreign investors
(1)
(2)

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Table 8
(Continued)

(1)

(2)

(3)

EMC_Retail
Ab_Temp

−0.075
(−1.65)

Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Year × Quarter FEs
Obs.
Adj. R 2

Yes
312
.019

(5)

Yes
312
.006

0.061
(1.36)
0.037
(0.33)
−0.140
(−1.03)
−0.054
(−0.48)
−0.067
(−0.42)

Yes
312
−.003

(6)
EMC_Blockholder

0.006
(0.24)
−0.215
(−0.79)
0.028
(0.12)
−0.175
(−0.81)
−0.289∗∗∗
(−3.21)

Ab_Temp Q2

(4)
EMC_Institution

Yes
312
−.007

0.244
(1.09)
0.189
(0.91)
0.156
(0.79)
0.296
(1.74)

Yes
312
.018

Yes
312
.005
(Continued)

The Review of Financial Studies / v 33 n 3 2020

A. Using MSCI carbon emission scores

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Table 9
EMC of trading and abnormal temperature: Robustness test

Energy
EMC_Retail
Ab_Temp

−0.046∗
(−1.77)

0.019∗∗
(2.55)
−0.030
(−0.16)
−0.287∗∗
(−2.06)
−0.127
(−0.53)
−0.393∗
(−1.72)

Ab_Temp Q2
Ab_Temp Q3
Ab_Temp Q4
Ab_Temp Q5
Year × Quarter FE
Obs.
Adj. R 2

EMC_Institution

Yes
1,708
.016

Yes
1,708
.016

Nonenergy
EMC_Blockholder

−0.082∗
(−1.89)

0.028
(1.02)
−0.016
(−0.09)
0.265
(1.62)
0.052
(0.22)
0.337
(1.56)

0.026
(0.48)
0.008
(0.19)
0.058
(1.19)
0.067
(1.43)

Yes
1,708
.006

Yes
1,708
.003

EMC_Retail

Yes
1,708
.019

Yes
1,708
.020

EMC_Institution

−0.085
(−0.57)
−0.145
(−1.05)
−0.308∗∗
(−2.29)
−0.366
(−1.51)

Yes
2,008
.003

Yes
2,008
.000

EMC_Blockholder
0.080∗
(2.03)

0.001
(0.22)
0.006
(0.45)
−0.010
(−0.44)
−0.003
(−0.15)
0.029
(1.23)

Yes
2,008
.018

Yes
2,008
.018

0.053
(0.33)
0.113
(0.79)
0.302∗∗
(2.46)
0.338
(1.43)

Yes
2,008
−.000

Yes
2,008
−.003

1112–1145

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In panel A, EMI SSI ON and CLEAN firms are categorized using MSCI ratings: EMI SSI ON includes stocks with carbon emission scores lower than 3, whereas the
CLEAN portfolio consists of stocks with carbon emission scores higher than 7. EMC_Retail refers to the difference in average changes of retail investors’ ownership
over the quarter between emission and clean firms (as a percentage). EMC_Institution and EMC_Blockholder refer to changes in ownership by institutional investors and
blockholders, respectively. Blockholders are those who own more than 5% of shares outstanding, whereas institutional investors include mutual funds, banks, and others but
exclude those who are blockholders. In panel B, EMI SSI ON and CLEAN firms are categorized based on firms’ industry codes. High-carbon-emission industries are defined
following the IPCC’s report. The EMI SSI ON portfolio is divided into energy and nonenergy firms, and the EMC portfolio is calculated for each group. In both panels, the
EMC of ownership changes is regressed on abnormal temperature variables, which are defined in Table 2, with year-quarter fixed effects. The sample is from January 2001 to
December 2016. Standard errors are clustered by exchange city and year–month, and the corresponding t -statistics are reported in parentheses. *p < .1; **p < .05; ***p < .01.

Attention to Global Warming

B. Stock trading for energy/nonenergy firms

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Table 9
(Continued)

The Review of Financial Studies / v 33 n 3 2020

20 Possibly, some institutions are net buyers and some are net sellers, and they appear constant when we sum

them. In a survey to institutional investors around the world (Krueger, Sautner, and Starks forthcoming), most
respondents believe that climate risks have financial implications for their portfolios. Examining whether this
subset of investors reacts to local weather conditions will be interesting.
21 Blockholders’ trading patterns can be potentially explained two ways. First, high-emission firms are shunned by

some retail investors; like sin stocks, they should earn high expected returns (Hong and Kacpercyzk 2009). Table 3,
panel A, shows that EMI SSI ON firms earn higher size-adjusted returns than CLEAN firms unconditionally
(2.2 bps per month vs. −2.2 bps (equal-weighted) and 3.2 bps vs. −6.8 bps (value-weighted)). Second, attentioninduced price pressure reverses in the long run (although we cannot identify significant reversals in our tests).
To examine the second explanation, Table IA.13 in the Internet Appendix checks whether the price reaction to
abnormal temperatures is stronger under high investor attention. The evidence is mixed.
22 While retail investors may not fully understand the nuance of industry-adjusted MSCI scores, we believe that

they can identify some clean and emission firms, at least within some industries. For example, Toyota Motor
Corporation (Virgin America) is a CLEAN (EMI SSI ON ) firm according to MSCI scores. Toyota is widely
recognized for its efforts to reduce vehicle CO2 emissions, and it ranked top in Carbon Clean 200, a list of world’s
top clean companies. On the other hand, Virgin America has been criticized for its fuel efficiency by the media.
A study by the International Council for Clean Transport shows that Virgin America produces more greenhouse
gas emissions per passenger than other domestic U.S. carriers. Perhaps unsurprisingly, Japanese and U.S. retail
investors can recognize these firms relative to their industry peers, given the media reports. Nevertheless, we
urge the reader to interpret the results with caution.

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quarter t, Ab_Tempit is the abnormal temperature in city i in quarter t (defined
in the same way as monthly Ab_Temp), and Y earQuartert are year-quarter
fixed effects. A separate regression is run for each type of investors. We also
run regressions by replacing Ab_Temp with abnormal temperature quintile
dummies.
Panel B of Table 8 reports the results for retail investors (Columns 1 and
2), institutional investors excluding blockholders (Columns 3 and 4), and
blockholders (Columns 5 and 6). In line with our expectation, retail investors
reduce their holdings in high-emission firms under abnormally warm weather;
in Column 1, the coefficient of Ab_Temp is negative and statistically significant
(t-stat = −2.0). Column 2 shows that retail investors reduce their EMC holdings
by 0.40% in the warmest temperature quintile compared to the coldest quintile.
We do not find evidence that institutional investors alter their EMC holdings
systematically according to local abnormal temperatures.20
Blockholders seem to respond to the decrease in stock prices and buy highemission firms as Ab_Temp increases. This finding is similar to the idea that
firms are buyers of last resort for their own stocks, and they repurchase shares
when prices drop below their fundamental value (Hong, Wang, and Yu 2008).21
Panel C of Table 8 shows the regressions for domestic institutions (Columns
1 and 2), foreign institutions (Columns 3 and 4), domestic blockholders
(Columns 5 and 6), and foreign blockholders (Columns 7 and 8). Only domestic
blockholders significantly increase their EMC ownership when the abnormal
temperature increases.
Table 9 repeats the tests using MSCI scores (instead of IPCC industries) to
define emission levels (panel A) and separately studies energy and nonenergy
high-emission sectors (panel B). Similarly, retail investors reduce their holdings
of high-emission firms in unusually warm quarters.22 Because retail investors
should not be more informed than domestic blockholders, we do not think

Attention to Global Warming

retail investors are reacting to fundamental changes (confirming our argument
in Section 3.4: the return results are not entirely driven by negative cashflow
shocks). We interpret this as evidence that retail investors’ changes in beliefs
about climate risk move stock prices—they avoid holding high-emission firms
as they become more aware of global warming. Institutional investors and
blockholders, on the other hand, do not appear to update their beliefs in
abnormally warm weather.

Surveys of the scientific literature show a 97%–98% consensus among scientists
that humans are causing global warming (Cook et al. 2016, 2013; Anderegg et al.
2010; Oreskes 2004). Anthropogenic influence is evident from the emission
of greenhouse gases such as CO2 from human activities. Despite all these
scientific facts, not everyone treats climate risk seriously and reacts to it—a
U.S. survey (Marlon et al. 2016) estimates that only 70% of adults believe that
global warming is happening, and 40% think it will harm them personally.23
Global warming is an important long-term issue that requires collective action
from humans, not just from climate scientists, to address. Our paper aims to
understand how people update their beliefs about climate change.
One reason for the discrepancy between scientific findings and aggregate
beliefs is that people have limited attention. The effects of climate risk are
usually overlooked in normal times because they focus on attention-grabbing
weather events and personal experiences. Consistent with this idea, we show
that people revise their beliefs upward when the local temperature is abnormally
warm. Google search activity on the topic “global warming” is greater. In
financial markets, carbon-intensive firms underperform in the month in which
the exchange city is warmer than usual. We find that retail investors, rather
than institutional investors and blockholders, shun climate-unfriendly stocks
and seem to be responsible for these price patterns. While climate change is
a long-term trend, local temperatures are more noticeable even though they
contain negligible information about the global trend. Retail investors react
to salient but uninformative weather events, and their beliefs and actions are
reflected in prices and trading activity.
We document evidence that people in countries where the impact of climate
was more prominent in the past suffer less from limited attention. To increase
public awareness and the efficacy of climate campaigns, policies that reduce the
information gaps between the scientific community and the general public will

23 Opinions vary across different parts of the United States, which are reflected in housing prices in the neighborhood

(Baldauf, Garlappi, and Yannelis Forthcoming). Global surveys also suggest that climate change deniers are
present all over the world and that the proportion of deniers varies by country. Only 42% of surveyed adults
worldwide (53% in the United States, 57% in the United Kingdom, and 50% in France) see global warming as
a serious threat (results come from Gallup surveys in 111 countries in 2010). The Gallup report is available at
https://news.gallup.com/poll/147203/Fewer-Americans-Europeans-View-Global-Warming-Threat.aspx.

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4. Conclusion

The Review of Financial Studies / v 33 n 3 2020

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==> RFS07 - Climate Change and Long-Run Discount Rates: Evidence from Real Estate.txt <==
Climate Change and Long-Run Discount
Rates: Evidence from Real Estate
Stefano Giglio
Yale University, NBER, and CEPR

Krishna Rao
Zillow
Johannes Stroebel
Stern School of Business, New York University, NBER, and CEPR
Andreas Weber
Stern School of Business, New York University
We show that housing markets provide information about the appropriate discount rates
for valuing investments in climate change abatement. Real estate is exposed to both
consumption and climate risk and its term structure of discount rates is downward sloping,
reaching 2.6% for payoffs beyond 100 years. We use a tractable asset pricing model that
incorporates features of climate change to show that the term structure of discount rates
for climate-hedging investments is thus upward sloping but bounded above by the risk-free
rate. At horizons at which risk-free rates are unavailable, the estimated housing discount
rates provide an upper bound. (JEL G11, G12, R30)
Received June 9, 2020; editorial decision January 26, 2021 by Editor Stijn Van
Nieuwerburgh. Authors have furnished an Internet Appendix, which is available on the
Oxford University Press Web site next to the link to the final published paper online.

We thank several referees, Arthur van Benthem, Robert Barro, John Campbell, Thom Covert, Simon Dietz, Robert Engle, Xavier
Gabaix, María Pilar Martínez-García, Kenneth Gillingham, Christian Gollier, Michael Greenstone, Ben Groom, Bob Hall, Lars
Hansen, Geoffrey Heal, Larry Karp, Derek Lemoine, Martin Lettau, Antony Millner, Stijn van Nieuwerburgh, William Nordhaus,
Monika Piazzesi, Nick Stern, Thomas Sterner, Christian Traeger, Martin Weitzman, and numerous conference and seminar
participants. We thankfully acknowledge generous research support from the Harvard Weatherhead Center for International Affairs,
the Center for the Global Economy and Business, the Fama-Miller Center, the Initiative on Global Markets, the Norwegian Finance
Initiative, NBIM, and the Global Risk Institute. We thank Zillow, iProperty, and Rightmove for sharing part of their data, and
Konhee Chang, Hongbum Lee, Sung Lee, Gil Nogueira, and Andreas Schaab for excellent research assistance. Supplementary data
can be found on The Review of Financial Studies web site. Send correspondence to Johannes Stroebel, johannes.stroebel@nyu.edu.

The Review of Financial Studies 34 (2021) 3527–3571
© The Author(s) 2021. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
doi:10.1093/rfs/hhab032
Advance Access publication March 25, 2021

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Matteo Maggiori
Stanford University, NBER, and CEPR

The Review of Financial Studies / v 34 n 8 2021

Any consideration of the costs of meeting climate objectives
requires confronting one of the thorniest issues in all climatechange economics: how should we compare present and future
costs and benefits? [...] A full appreciation of the economics of
climate change cannot proceed without dealing with discounting.
— William Nordhaus1

1 Quotation comes from Nordhaus (2013).
2 See also Kaplow, Moyer, and Weisbach (2010), Schneider, Traeger, and Winkler (2012), and Weisbach and

Sunstein (2009) for discussions of normative and descriptive approaches to discounting.

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Much of the economics literature on the optimal policy response to climate
change focuses on the trade-off between the immediate costs and the potentially
uncertain long-run benefits of reducing carbon emissions. Discount rates play
a central role in this debate, since even small changes in discount rates can
dramatically alter the present value of investments that pay off over long
horizons. For example, assume that an investment to reduce carbon emissions
costs $3 billion, and is expected to avoid environmental damages worth $100
billion in 100 years. At a discount rate of 3%, the present value of those
damages is $5.2 billion, and the project should be implemented. At a slightly
higher discount rate, such as 5%, the present value of the investment drops to
$760 million and the investment is no longer attractive. However, despite the
importance of these discount rates for optimal policy design, economists and
policy makers do not agree on what discount rates should be used to value
investments in climate change mitigation.
In this paper, we make progress on this question by exploring the information
that private market discount rates contain about how to appropriately value
investments in climate change abatement. First, we provide new evidence on
the term structure of discount rates for an important asset class, real estate,
up to the extremely long horizons that are relevant for analyzing climate
change (hundreds of years). Second, we combine these new facts with insights
from asset pricing theory to discipline the debate on the appropriate choice of
discount rates for an investment in climate change abatement, which involves
similar horizons as the housing asset but has a different risk profile.
Much of the prior debate on the appropriate discount rates for climate change
investments has either relied on theoretical arguments or tried to infer discount
rates from the realized returns of traded assets, such as private capital, equity,
bonds, and real estate. For example, in the context of the dynamic integrated
climate-economy (DICE) model, Nordhaus (2013) chooses a discount rate of
4% to reflect his preferred estimate of the average rate of return to capital.2
We show that this common practice of valuing investments in climate change
abatement by discounting cash flows using the average rate of return to some
traded asset often ignores important considerations regarding the maturity and
risk properties of such investments.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

3 van Binsbergen, Brandt, and Koijen (2012) provide evidence of a downward-sloping term structure of discount

rates for equities over a 1- to 10-year horizon. van Binsbergen and Koijen (2017) review related evidence across
a number of asset classes.

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In particular, asset pricing theory shows that the rate at which a particular
expected cash flow should be discounted depends on the state of the world in
which the cash flow is realized; cash flows that materialize in bad states are
more desirable, and hence less risky for the investor. They should therefore
be discounted at a lower rate. In addition, different assets pay off their cash
flows at different maturities. Because risk in the economy is different for
different horizons and preferences for risks can vary with the horizon as well,
horizon-specific discount rates must be used when evaluating investments with
different maturity profiles. The average rate of return to a particular asset, for
example, capital, only reflects the discount rate appropriate for that particular
stream of cash flows. It is thus generally not informative for determining the
appropriate discount rate for another asset, such as an investment in climate
change abatement, which has benefits that tend to be delayed until much longer
horizons and which have very different risk properties.
In theory, then, to understand the appropriate discount rate for investments
in climate change abatement we would want to look at traded assets with
similar riskiness and horizons. While this is difficult in practice, we show that
researchers can still extract relevant information from the observed private
market returns of assets, such as real estate. This information can then be used
together with asset pricing models to adjust for the maturity and riskiness of
cash flows of investments in climate change abatement.
Our first empirical contribution is to provide estimates of the term structure
of discount rates for an important asset class, real estate, over a horizon of
hundreds of years. This represents the first data-driven characterization of a
term structure of discount rates for any asset over the horizons relevant for
investments in climate change abatement.3 Using a variety of approaches, we
estimate the average return to real estate to be around 6%. This contributes to
a recent research effort to better document the return properties of residential
real estate as an asset class (e.g., Favilukis, Ludvigson, and Van Nieuwerburgh
2017; Jordà et al. 2019; Chambers, Spaenjers, and Steiner 2019; Eichholtz et al.
2020). At the same time, recent estimates from Giglio, Maggiori, and Stroebel
(2015) show that the discount rate for real estate cash flows 100 or more years in
the future is about 2.6%. This combination of high average (expected) returns
and low long-run discount rates implies a downward-sloping term structure of
discount rates for real estate. Intuitively, since real estate assets are claims to
cash flows (rents) at all horizons, their expected rate of return is an average
of the discount rates on short-run and long-run cash flows. If average returns
are higher than long-run discount rates, then short-run discount rates must be
higher than long-run discount rates (and higher than average returns).

The Review of Financial Studies / v 34 n 8 2021

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These findings reinforce the problems of using the average rate of return to
traded assets to discount investments in climate change abatement. Even if we
assumed that climate-change-abatement investments and real estate had similar
risk properties at all horizons, using an average rate of return would suggest that
such investments should be discounted at 6%. Instead, the appropriate discount
rate for the long-run benefits of these investments should be much lower, and
their present value much higher.
Of course, this simple comparison ignores potential differences in risk
properties of investments in climate change abatement and real estate. We thus
also document the risk properties of real estate. We first show that real estate
is indeed a risky asset: its returns are positively correlated with consumption
growth, and therefore with the marginal utility of consumption, and it performs
badly during consumption disasters, financial crises, and wars. This is consistent
with the average return to real estate of about 6%, which is above the real riskfree rate, and thus includes a risk premium to compensate investors for bearing
risk.
We then document that real estate is exposed specifically to climate change
risk, and that this risk is reflected in house prices. This is an important step in
helping us link the discount rates applicable to real estate and the discount rates
for investments in climate change abatement. For this analysis, we work with a
proprietary data set of housing transaction prices as well as for-sale and for-rent
listings for properties located in the coastal states of Florida, New Jersey, North
Carolina, and South Carolina. Properties in these states are exposed to climate
change risk due to both rising sea levels and hurricanes. To obtain a measure of
each property’s physical exposure to climate risk, we geo-code the addresses
of all properties to identify those properties that will be flooded with a 6-feet
increase in the sea level, as measured by NOAA.
Since physical exposure to climate risk is correlated with unobserved
property amenities, such as beach access, we cannot simply compare the prices
across properties that are differentially exposed to such risk in order to estimate
the price impact of climate risk. Instead, we test whether the prices of properties
that are more exposed to climate change decline in relative terms when the
perception of climate risk increases. We measure perception of climate risk
in the housing market by performing a systematic textual analysis of the forsale listings to measure the frequency with which climate-related text (e.g.,
mentions of hurricanes or flood zones) appears in the written description of
the listed properties. The fraction of listings that include such texts is the basis
for a “Climate Attention index” that we construct at both the ZIP-code-quarter
and ZIP-code-year levels. Our interpretation of this index is that it reflects
households’ perceptions of the risk of future climate change on the cash flows
from real estate in those locations.
We use data on the universe of property transactions from these states
to conduct hedonic regressions that explore how the transaction prices of
properties in the flood zone vary differentially when the “Climate Attention

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

4 Other research has explored the extent to which other asset classes, such as equities and fixed-income assets, are

exposed to climate risk (Engle et al. 2020; Huynh and Xia 2020; Painter 2020). See Giglio, Kelly, and Stroebel
(2020) for a review of this literature.
5 This modeling approach relates to exciting new work that mixes physical elements of climate change (tipping

points, increasing ocean levels, etc.) with the likely response of economic activity (technological innovation,
geographic relocation of production, etc.) as undertaken by Crost and Traeger (2014), Lemoine (2021), Lemoine
and Traeger (2014), and others.

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index” changes, controlling for property characteristics and various fixed
effects. Our analysis shows that when the fraction of property listings that
mention climate change doubles, there is a 2% to 3% relative decrease in the
prices of properties that are in the flood zone compared to otherwise comparable
properties in the same ZIP code that are not in a flood zone. This result survives
in a specification with property fixed effects, which only identifies the pricing
of climate risks from multiple transactions of the same property in periods
with differential perceptions of these risks. Furthermore, we show that annual
rents of exposed and non-exposed properties do not vary differentially with
movements in our “Climate Attention index.” This confirms that our estimates
of differential price movements are not driven by differential changes in the
flow utilities, but instead result from a differential change in the risks associated
with future cash flows.
Based on these findings, we conclude that real estate prices directly reflect
climate risk, making it a particularly interesting asset to study the valuation of
investments to mitigate such risks. These findings are consistent with a quickly
growing literature in finance that has documented the exposure of real estate
to physical climate risk factors, such as rising sea levels and wildfires (e.g.,
Hallstrom and Smith 2005; McKenzie and Levendis 2010; Atreya and Ferreira
2015; Bakkensen and Barrage 2017; Gibson, Mullins, and Hill 2017; Eichholtz,
Steiner, and Yönder 2019; McCoy and Walsh 2018; Ortega and Taspinar 2018;
Bernstein, Gustafson, and Lewis 2019; Garnache and Guilfoos 2019; Baldauf,
Garlappi, and Yannelis 2020).4 Relative to much of this literature, our use of
time- and space-varying measures of climate risk attention and our focus on
rents in addition to home sales allow us to address a number of alternative
interpretations of the observed relative price differences between properties
that are differentially exposed to climate risk.
To explore the implications of the downward-sloping term structure of risky
real estate for valuing investments in climate change abatement, we build a
tractable asset pricing model that incorporates crucial features of climate change
and its related risks. Our aim is not to provide an entirely new asset pricing
model, nor is it to fully incorporate the micro foundations of physical models of
climate change. Rather, we aim to provide a transparent and portable framework
to show how the insights of modern asset pricing theory can be used together
with inputs from a physical model of climate change to inform the appropriate
discount rates for investments in climate change abatement.5

The Review of Financial Studies / v 34 n 8 2021

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Our baseline model builds on the view that climate change is a form of disaster
risk (see, Weitzman 2012; Barro 2015 for prominent articulations of this view):
it is a rare event with potentially devastating consequences for the economy. We
embed this view in a general equilibrium model with a representative agent and
complete markets based on the endowment economy studied by Lucas (1978).
We further modify this classic setup to reflect two important messages of the
climate change literature.
First, we incorporate feedback loops between the state of the economy
and the time-varying probability of a climate disaster. In particular, we allow
the probability of a disaster to increase endogenously over time when the
economy grows at a faster rate. Intuitively, this feature captures the notion that
faster growth accumulates more environmental damages, such as greenhouse
gas emissions and pollution, thereby increasing the probability of adverse
climatic events, akin to tipping points (see, Alley et al. 2003, Lemoine and
Traeger 2014). These damages in turn might feed on themselves, for example,
because rising temperatures lead to even more carbon emissions for the same
level of production. Our model captures these vicious cycles by allowing
the probability of a further disaster to increase after a disaster occurs (see,
Cox et al. 2000).
Second, we allow for economic growth to pick up temporarily after a disaster.
This feature captures the potential adaptation of the economy following a
disaster, and reflects a variety of adaptation measures, including relocating
production to less affected areas, investments to prevent further damages (e.g.,
sea walls), and investments, such as air conditioning, that allow for productive
work despite adverse climate conditions (see the discussions in, Brohé and
Greenstone 2007; Desmet and Rossi-Hansberg 2015; Burke and Emerick 2016;
Barreca et al. 2016). While we only capture these forces in reduced form, we
show that they play a crucial role in capturing a more realistic evolution of the
economy in response to climate change. In addition, this mean reversion of
cash flows allows the model to match our data on the term structure of risky
real estate. For assets exposed to the disaster risk, the partial mean reversion
of the economy after a disaster implies that short-term cash flows are riskier
than long-term cash flows, which only occur after the economy has partially
recovered. This mechanism is central to generating downward-sloping term
structures of discount rates: the riskier short-term cash flows are discounted at
higher rates than the safer long-term cash flows.
Since climate change is a form of disaster risk, investments in the mitigation
of this risk are hedges: similar to insurance policies, they pay off primarily in
bad states of the world, and are thus particularly valuable. This has a number
of implications for the discount rates used to value their cash flows. The
first implication is that the shape of the term structure of discount rates for
investments to abate climate change is the opposite of what we estimate for the
term structure of housing, a risky asset. In fact, the term structure for abatement
investments should be upward sloping: hedging against effects of the disaster

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

6 The literature in climate change economics has sometimes motivated a downward slope in the discount rates

for investments in climate change abatement with an extension of the Ramsey rule to include uncertainty about
consumption growth that increases with the horizon. This would have the effect of pushing down the longrun risk-free rate due to a precautionary savings motive that increases in the horizon (see, Arrow et al. 2013).
However, the predictions of this framework are inconsistent with the relatively flat term structure of real interest
rates observed in the data. Moreover, the Ramsey framework does not consider the riskiness of cash flows and
therefore has no predictions on the term structure of risk premiums. Consistent with this, the guidance on discount
rates provided by governments recommending declining discount rates for cost-benefit analysis, usually does
not indicate that the discount rate should vary with the risk properties of the investments.

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on short-term cash flows is more valuable than hedging the effects on long-term
cash flows, since these long-term cash flows are affected less due to adaptation.
Importantly, however, this upward-sloping term structure does not imply
that the level of discount rates for investments in climate change abatement
is high at any horizon. In fact, it should be below the risk-free rate at all
horizons, reflecting the investment’s hedge characteristics. For shorter horizons,
we can observe the real risk-free rate (given by real bond yields) directly in
the data, providing us with a tight upper bound (1% – 2%) on the discount
rate for short-term cash flows from investments in climate change abatement.
For longer horizons, there are no reliable estimates of the level of the risk-free
interest rate. However, our model suggests that the very long-run discount rate
of 2.6% for risky real estate provides an upper bound on the risk-free rate, and
therefore also on the discount rates for long-term cash flows from investments
in climate change abatement. This simple upper bound is a powerful result
that challenges a wide range of estimates previously used in the literature. For
example, this bound is substantially below the 4% rate suggested by Nordhaus
(2013). Quantitatively, it is more in line with long-run discount rates that are
close to the risk-free rate, as suggested by Weitzman (2012), or the 1.4%
suggested by Stern (2006). It is also close to the average recommended longterm social discount rate of 2.25% elicited by Drupp et al. (2015) in a survey
of 197 experts.
Note that our finding that the appropriate term structure to discount cash
flows from climate change abatement is low but upward-sloping contrasts
with a number of papers that have argued for using declining discount rates
for valuing investments in climate change abatement (Arrow et al. 2013;
Cropper et al. 2014; Farmer et al. 2015; Traeger 2014). These arguments have
motivated policy changes in France and the United Kingdom, which have
adopted a downward-sloping term structure of discount rates for evaluating
long-run investments, including those in climate change abatement. While these
differences do not have a substantial effect on the actual discount rates used to
value the long-run cash flows from such investments (they are relatively low, at
approximately 2%, both under the term structures used in those countries and
under our upward-sloping term structure), the two have substantially different
implications for the economic mechanisms to create these low long-run discount
rates.6 In addition, they have substantially different implications for evaluating
the payoffs from climate abatement investments that may accrue at shorter

The Review of Financial Studies / v 34 n 8 2021

1. Risk and Return Properties of Real Estate
As described in the introduction, private market discount rates have the potential
to inform the valuation of investments in climate change abatement. In this
section, we discuss a number of reasons why real estate discount rates are
particularly valuable from this perspective. First, we show that real estate is both
risky in general (i.e., it pays off more in good states of the world) and exposed to
climate risk in particular. Second, we show that, for real estate, private markets
reveal information about the term structure of discount rates for horizons of up
to hundreds of years. This feature of real estate is particularly beneficial to learn
about the valuation of investments in climate change abatement, for which the
potential benefits can stretch over very long time periods.

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horizons. The calibration of our model suggests that climate disasters cause
the most damage immediately after they hit, making it most valuable to hedge
the immediate costs. As a result, the correct discount rates for investments
that yield shorter-term protection against climate change disasters should be
substantially below the risk-free rate of 1%-2%. In contrast, the downwardsloping term structures used in France and United Kingdom suggest discount
rates of 4% and 3.5%, respectively, for the first 30 years of a project’s cash
flows.
Finally, in addition to exploring the discount rates appropriate for climate
change mitigation within our disaster-risk view of climate change risk, we can
use our model to understand discounting of climate investments in alternative
models of climate change risk. In particular, our specification for the economy
and climate change dynamics is general enough to also nest, under a different
parametrization, an important alternative view of climate change: that of the
DICE models of Nordhaus and Boyer (2000) and Nordhaus (2008), in which
(a) climate change acts as a tax on output and climate damages are higher
when the economy is doing well, and (b) uncertainty about the path of the
economy is the main driver of uncertainty about climate change. Under this
parameterization, climate change mitigation investments pay off mostly in
good states of the world (when the economy is expanding). The appropriate
discount rates for these risky investments are thus above the risk-free rate.
In this class of models, the climate “tax rate” can be increasing with the
level of economic activity, so that the damages are disproportionally higher
during booming economies. In our framework, such a feature implies discount
rates for investments in climate change abatement that are high and increasing
with the horizon. Intuitively, this occurs because a bad shock to the economy
lowers both climate damages and the growth rate of damages over time. Our
framework explains why the “disaster” view and the “tax” view of climate
change have diametrically opposed predictions for the appropriate discount
rates for investments in climate change abatement.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

1.1.1 Data construction. Our empirical analysis builds on a number of data
sets. Our baseline data contain the universe of for-sale and for-rent property
listings from Zillow, a major online real estate data provider. We obtained
listings from four coastal states with properties that are potentially exposed
to climate risk through rising sea levels: Florida, New Jersey, North Carolina,
and South Carolina. For each listing, we observe the textual description of the
property provided by the real estate agents, in addition to the listing date and
listing price. The For-rent listings cover the period between the first quarter of
2011 and the second quarter of 2017. The For-sale listings extend back to the
first quarter of 2008.
Our second data set contains the universe of public record assessor and
transaction deeds data for the same states since the start of 2008. These data
include detailed property characteristics, such as information on the property
size and the number of bathrooms and bedrooms, as well as transaction prices
and dates for all property sales.
To measure different properties’ exposures to climate risk, we geo-code their
addresses and map them to geographic shapefiles provided by the National

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1.1 The riskiness of housing: Exposure to climate risk
We first provide direct evidence that climate risk is priced in real estate markets,
with increased climate risk leading to relatively lower prices for more exposed
properties. Our analysis has to overcome a number of empirical challenges.
First, when comparing prices of properties that are differentially exposed to
climate risk, it is difficult to control for all amenities that might be correlated
with exposure to climate risk. For example, beachfront properties are more
exposed to climate risk than properties further inland—they are more likely to
be flooded when sea levels rise—but they might still sell at a premium because
of the value of the beach access. Controlling for such difficult-to-measure
amenities in hedonic regressions is challenging, which introduces concerns
about omitted variable bias.
To overcome this challenge, we therefore investigate how the prices of
properties that are differentially exposed to climate risk change in response
to a change in that climate risk. As long as the amenity value of beach access
does not change when climate risk changes, this analysis is informative about
the pricing of climate risk in housing markets. However, such a “differences-indifferences” analysis presents a second challenge: true climate risk is a relatively
slow-moving object that does not provide much of the time-series variation
required to identify how it is priced. Our approach is to instead exploit the much
more substantial time-series variation in the attention paid to climate risk in
the housing market. Indeed, even though true climate risk might not change
much from year to year, we show that the extent to which homebuyers focus
on these risks changes much more frequently, and we would thus expect the
pricing implications of climate risk to be particularly strong when households
pay more attention to these risks.

The Review of Financial Studies / v 34 n 8 2021

Oceanic and Atmospheric Administration (NOAA) that indicate which regions
will be flooded should sea levels rise by 6 feet or more. While flooding risk
is only one of a number of climate risk factors, it is an important and easily
measurable risk for properties in the coastal regions of the states analyzed in our
study. Properties that are more exposed to climate risk on this measure tend to be
closer to the waterfront, but there is substantial variation in exposure to climate
risk across properties in the same narrow geography (see Figure 1, which shows
the variation in our measure of climate risk exposure for downtown Miami).
We use our property listings data to build a novel measure of attention to
climate risk. We construct this “Climate Attention index” by calculating the
proportion of for-sale listings with property descriptions that contain climate
change-related words and phrases such as “hurricanes,” “FEMA,” “floodplain,”
and “flood risk.” Most of the flagged listings include descriptions that highlight
that a specific property is less exposed to climate risk (e.g., “Not in a flood
zone, it’s high and dry!”). We believe that this is sensible: if you are selling
a property with particular exposure to climate risk, for example, because it
sits in a flood zone, you would not want to highlight this negative feature in
a property listing. However, if you are selling a house that is not exposed
to climate risk, this is something worth highlighting in a property listing, in
particular in areas and at times when potential buyers pay more attention to
these risks. Internet Appendix A.2 provides more details on the construction
of the Climate Attention index, which we make publicly available to other
researchers in the replication package associated with this paper.
There is substantial spatial and time-series variation in this measure of
climate risk attention. The top panel of Figure 2 provides a heatmap of the
Climate Attention index for Florida, pooling across all listings in our sample
at the ZIP code level (the Internet Appendix includes corrsponding maps for

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Figure 1
Illustration of identifying properties in the flood zone
This figure illustrates how we identify properties in the flood zone of downtown Miami, Florida. On the left, we
plot each property as a green dot and overlay the NOAA’s flood map. Then, on the right, we geo-code to identify
the properties that fall under the flood zone and represent them as red dots. As seen above, properties closer to
the coastal line are more likely to be situated in the flood zone.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

White areas have insufficient observations

Climate Attention Index for NJ

0

.03

.01

.04

.05

.02

.06

.03

.07

.04

Climate Attention Index for FL

2008q1

2011q1

2014q1

2017q1

2008q1

2011q1

Period
State Level

2014q1

2017q1

Period

Zip Codes w/ Properties in Flood and Non-Flood Zones

State Level

.04
.03
.02

0

.01

.02

.04

.06

.05

Climate Attention Index for SC

.08

Climate Attention Index for NC

Zip Codes w/ Properties in Flood and Non-Flood Zones

2008q1

2011q1

2014q1

2017q1

2008q1

2011q1

Period
State Level

Zip Codes w/ Properties in Flood and Non-Flood Zones

2014q1

2017q1

Period
State Level

Zip Codes w/ Properties in Flood and Non-Flood Zones

Figure 2
Climate attention index in the cross-section and time series
The top panel visualizes a heatmap of our Climate Attention index in Florida at the ZIP code level. The Climate
Attention index is defined as the fraction of for-sale listings whose description includes climate-related text for
the period from 2008Q1 to 2017Q2. The other panels illustrate the quarterly time series of the Climate Attention
index aggregated at the state level as well as for ZIP codes that include at least some properties in the flood zone.

the three other states). Properties near the coast are more susceptible to climate
risk. Consistent with this, the Climate Attention index is substantially higher
for these properties in the cross-section. The other panels of Figure 2 illustrate
the time series of the Climate Attention index for each of the four states in our
sample, both for the whole state (black solid line) and only for ZIP codes that
include at least some properties in a flood zone (blue dashed line). Consistent
with the heatmap, the attention paid to climate risk is substantially higher in ZIP

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Attention Index
(0.04,1.00]
(0.03,0.04]
(0.02,0.03]
(0.01,0.02]
[0.00,0.01]

The Review of Financial Studies / v 34 n 8 2021

codes that are located in parts of the country where properties will be flooded
if sea levels rise substantially. There is also sizable time-series variation in
the Climate Attention index within geographies. For example, in New Jersey,
the Climate Attention index nearly tripled between 2011 and 2013, around the
time of Hurricane Sandy, which rendered more than 20,000 homes in the state
uninhabitable.

log(P rice)i,h,g,t
= α +βlog(I ndexg,t )×F loodZh +γ F loodZh +δXh +φg ×ψt +i,h,g,t . (1)
The unit of observation is a transaction i, of property h, in ZIP code g, at time t.
The dependent variable is the log of the transaction price. We flexibly control for
various property characteristics in Xh . We also include ZIP code-quarter fixed
effects, φg ×ψt , to capture differential house price movements across ZIP codes
and time. We interact the log of the Climate Attention index, log(I ndexg,t ),
with the Flood Zone indicator, F loodZh .7 This allows us to estimate the effects
of changing climate attention for properties that are differentially exposed
to physical climate risks. We also include the Flood Zone indicator directly,
allowing us to control for the unconditional price effect of being located in a
flood zone as well as of any unobserved property amenities that are correlated
with this measure of exposure to climate risk.
Column 1 of Table 1, panel A, shows estimates from this regression when
we measure the Climate Attention index at the ZIP-code-year level. All else
equal, properties that lie in the flood zone trade at a (statistically insignificant)
premium to properties that are not in the flood zone, consistent with those
properties also having more attractive amenities, such as proximity to the beach.
More importantly, we estimate a statistically significant negative β-coefficient.
A doubling in the Climate Attention index is associated with a relative 2.4%
decline in the transaction prices of properties in the flood zone. The direct effect
of increasing climate attention on all properties is absorbed by the ZIP-codequarter fixed effects.8 Column 2 measures the Climate Attention index at the
ZIP-code-quarter level, and presents similar estimates. In columns 3 and 4 of
Table 1, panel A, we include property fixed effects in the regressions from
columns 1 and 2. In these specifications, the estimates of β are identified off

7 To deal with the (small) number of ZIP-code-years with no listing mentioning climate change, we add a small

constant (0.01) to the Climate Attention index before taking logs. Our results are robust to variation in the constant
added and to the linear (instead of log-linear) inclusion of the Climate Attention index.
8 While the coefficients for the control variables are not of primary interest in this study, Internet Appendix A.2.2

shows that they are consistent with estimates from the literature (e.g., Kurlat and Stroebel 2015; Stroebel 2016):
for example, larger and more recently upgraded homes trade at a premium.

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1.1.2 Empirical analysis. Next, we estimate how climate risk is priced in
real estate markets. Our baseline hedonic regression is given by Equation (1):

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

Table 1
Transaction prices and rent prices: Hedonic analysis
A. Transaction prices
Dependent variable:
log(transaction prices)

Flood Zone

(2)
0.014
(0.013)
−0.020∗∗∗
(0.004)







.
.585
7,287,000

.
.585
7,233,113

(3)

−0.029∗∗
(0.010)

.



.721
3,485,238

(4)

(5)

(6)

0.085∗∗∗
(0.006)
−0.021∗∗
(0.007)

.



.721
3,443,265

−0.210∗∗
(0.071)


.
.585
7,233,113

−0.367∗∗∗
(0.091)
.


.721
3,443,265

(5)

(6)

B. Rent prices
Dependent variable:
log(rent prices)

Flood Zone
log(Index by ZIP-Year)
× Flood Zone
log(Index by ZIP-Quarter)
× Flood Zone
Index by ZIP-Quarter
× Flood Zone
Property controls
ZIP × Quarter FE
Property FE
R-squared
N

(1)

(2)

0.041∗∗∗
(0.012)
0.018∗∗∗
(0.004)

0.033∗∗
(0.011)
0.015∗∗∗
(0.004)







.
.728
2,142,433

.
.728
2,142,240

(3)

(4)

−0.034∗∗∗
(0.006)
0.005
(0.005)
0.003
(0.003)

.



.942
1,191,657

.



.942
1,191,642

0.415∗∗∗
(0.072)


.
.728
2,142,240

0.016
(0.042)
.


0.942
1,191,642

This table shows results from Regression 1. The dependent variable is the log of the transaction price in panel
A and the log of the rental listing price in panel B. In columns 1, 2, and 5, we control for various property
characteristics, such as the property size, property age, and the number of bedrooms. In columns 3, 4, and 6, we
include property fixed effects. The Flood Zone indicator and the property controls are naturally dropped in these
regressions due to perfect multicollinearity. Index by ZIP-Year and Index by ZIP-Quarter represent the fraction
of listings whose description includes climate-related texts at the ZIP-code-year level and the ZIP-code-quarter
level, respectively. Standard errors are clustered at the ZIP-code-quarter level and in parentheses. ∗ p < .05; ∗∗
p < .01; ∗∗∗ p < .001.

properties that we observe transacting more than once. The estimates are nearly
identical, suggesting that our baseline findings are not driven by unobserved
property characteristics. In columns 5 and 6, we include the raw Climate
Attention index rather than the log of the index. Interpreting the magnitudes
suggests that a 1 percentage point increase in the number of listings that suggest
particular attention to climate risk is associated with a 0.2% – 0.4% decrease
in the transaction price.
One concern with the estimates presented above is that they might not
just capture the pricing of future climate change risk, but that our estimates
also might be picking up changes in the flow utility of climate risk-exposed
properties that could be correlated with climate risk attention. For example,

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log(Index by ZIP-Year)
× Flood Zone
log(Index by ZIP-Quarter)
× Flood Zone
Index by ZIP-Quarter
× Flood Zone
Property controls
ZIP × Quarter FE
Property FE
R-squared
N

(1)
0.004
(0.015)
−0.024∗∗∗
(0.005)

The Review of Financial Studies / v 34 n 8 2021

1.1.3 Key takeaways. The evidence provided above shows that real estate
has substantial exposure to climate risk, and thus fulfills an important criterion
for us to use housing discount rates to learn about how to value investments in
climate change abatement.
1.2 The riskiness of housing: Exposure to consumption risk
Next, we show that in addition to being exposed to climate risk, real estate
is exposed to consumption risk: its returns are higher in states of the world
where the marginal utility of consumption is lower. To show this, we analyze
the behavior of real house prices during financial crises and periods of rare
consumption disasters; we also estimate the correlation between house prices
and consumption as well as personal disposable income.
Panel A of Figure 3 shows the average reaction of real house prices during
financial (banking) crises. The analysis is based on dates of financial crises in
Schularick and Taylor (2012), Reinhart and Rogoff (2009), and Bordo et al.
(2001) for 20 countries for the period 1870-2013, and on our own data set
of historical house price indexes for these countries. Internet Appendix A.3.1
provides the details of the crisis dates and the house price series. The beginning
of a crisis is normalized to be time zero. The house price level is normalized to
be one at the onset of the crisis. House prices rise on average in the three years
prior to a crisis, achieve their highest level just before the crisis, and fall by as
much as 7% in the three years following the onset of the crisis. This fall in house
prices during crisis periods, which are usually characterized by high marginal
utilities of consumption, contributes to the riskiness of real estate as an asset.
Panel B of Figure 3 shows the average behavior of house prices during the rare
consumption disasters as defined by Barro (2006). The consumption disaster

9 The positive effect on rents that we observe in some of these specifications could, for example, be the result of

general equilibrium effects in the housing market. Increased attention to climate risk makes individuals who are
interested in living near the coast less likely to want to buy a house. Individuals who choose instead to shift into
the rental market could be driving up rents.

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it could be that climate risk attention rises after damaging storms that have a
particularly strong direct effect on the utility of living in properties located in
flood zones. To show that such a confounding story is not driving our results,
panel B of Table 1 runs regressions similar to Equation (1), but now uses
the log of the rental listing price as the dependent variable. In contrast to the
transaction price regression, rental prices of properties exposed to climate risk
increase during periods of increasing attention paid to climate risk, though the
effect declines and is not statistically significant when we include property fixed
effects. This is reassuring, because it suggests that our findings for transaction
prices are not the result of a decline in the flow utility of these properties when
climate risk increases. Instead, the decline in transaction prices most likely
results from the increased present discounted cost of climate risk.9

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

B

.95

Real House Prices Relative to Crisis
.9
.92
.94
.96
.98
1

Real House Prices and Consumption
1
1.05 1.1 1.15 1.2 1.25 1.3

1.02

A

.88

-3
-3

-2

2

-2

3

-1
0
1
Years Relative to Consumption Trough
Real House Prices

Financial crises

2

3

Real Consumption

Consumption disasters

D

2

Real House Prices (Log Scale)
4
6
8

Real House Prices (Log Scale)
200
400
600

10

12

800

C

1960

1970

1980

1990

2000

2010

1970

1980

House prices: U.K.

1990

2000

2010

House prices: Singapore

E
1

1913

1914

1939

Real House Prices
.8
.9

1940
1915
1916
1941
1942
1944

1945

1917
1943

.7

1918

0

2
4
Years Since Start of War
World War I

6

World War II

House prices during the World Wars

Figure 3
House price riskiness
Panel A shows average real house price movements relative to those during financial crises. Panel B shows average
real house price movements and average real consumption relative to the trough of consumption disasters. Panels
C and D show the evolution of real house prices in the United Kingdom and Singapore, respectively. Shaded
regions represent financial crises. Panel E shows the evolution of real house prices for countries with available
house price time series during World War I and World War II. See Internet Appendix A.3.1 for a description of
the data series.

dates for the 20 countries included in our historical house price index data set
are those defined by Barro and Ursua (2008). The dotted line tracks the level
of consumption: following the start of a disaster, consumption falls for three
years before reaching its trough (normalized to be time zero) and recovers in
the subsequent three years. The solid line tracks the house price level: house
prices fall together with consumption over the first three years of the disaster

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-1
0
1
Years Relative to Crisis

The Review of Financial Studies / v 34 n 8 2021

10 All crisis dates are from Reinhart and Rogoff (2009), except for the periods 1997-1998 and 2007-2008 for

Singapore. The latter dates have been added by the authors and correspond to the Asian financial crisis of
1997-1998 and the global financial crisis of 2007-2008.
11 Despite extensive efforts to collect an exhaustive database. We are still limited by the relatively small number

of crises for which house price data are available and by the relatively low quality of house price series before
1950. In addition, rental data are generally unavailable, preventing us from performing a comprehensive study
of the riskiness of the underlying cash flows of housing. Nevertheless, our results suggest that real estate is an
asset that has relatively lower payoffs during economic crises. Note that our results are likely to underestimate
the riskiness of real estate and housing because of three effects. (1) House price indexes are generally smoothed
and therefore underestimate the true variation in house prices. (2) We only consider the behavior of house price
changes (capital gains) and have not considered the behavior of rents (dividends). For the two countries for which
long high-quality time series of rental indexes are available (France for the period 1949-2010 and Australia for
the period 1880-2013), we find rent growth to be positively correlated with consumption growth (0.36 and
0.15, respectively). (3) A sizable part of the housing stock is often destroyed during wars. Thus, the return to a
representative investment in real estate would be lower than the fall in index prices as it would incorporate the
physical loss of part of the asset.

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but fail to recover over the subsequent three years. The fall in house prices
during these rare disasters also contributes to the riskiness of real estate as an
asset class.
Panels C and D of Figure 3 show the time series of house prices and crisis
years for the United Kingdom and Singapore—the countries with the best data
on the term structure of housing discount rates (see below).10 The pattern of
house price movements during crises in these two countries is similar to the
average pattern described above. House prices peak and then fall during major,
crises such as the 2007-2008 global financial crisis. The 1984 banking crisis in
the United Kingdom is the sole exception with increasing house prices.
Panel E of Figure 3 shows the performance of house prices during World War
I and World War II (WWI and WWII). In both cases, time zero is defined to be
the start date of the war period, 1913 and 1939 for WWI and WWII, respectively.
The dotted line tracks house prices of five countries with data availability for
the duration of WWI (1913-1918): Australia, France, Netherlands, Norway,
and the United States. House prices fell throughout the war with a total decline
in real terms of around 30%. Similarly, the solid line tracks house prices of six
countries—now also including Switzerland—for the duration of WWII (19391945). House prices fell by 20% in real terms from 1939 to 1943 and then
stabilized for the last two years of the war, 1944-1945. Overall, we find wars
to be periods of major declines in real house prices, which further contributes
to the riskiness of real estate as an asset.11
We also investigate the average correlation between consumption and house
prices over the entire sample rather than just during crisis periods. Table 2
reports the correlation of house price changes with consumption changes as
well as consumption betas over the entire sample and for each country. The
correlation is positive for all 20 countries, except for France (−0.05), and
often above 0.5. Accordingly, consumption betas are also positive except for
France (−0.10) and often above 1.0. The estimated positive correlation between
house prices and consumption and the positive consumption betas reinforce
the evidence that real estate is a risky asset: it has low payoffs in states of

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

Table 2
Real house price growth and real consumption growth
Real cons. growth

Mean

SD

Mean

SD

Correlation

Cons. beta

1901-2009
1975-2009
1975-2009
1975-2009
1975-2009
1840-2009
1975-2009
1975-2009
1975-2009
1814-2009
1975-2009
1830-2009
1975-2009
1975-2009
1975-2009
1975-2009
1952-2009
1937-2009
1952-2009
1890-2009

2.51%
2.92%
2.38%
1.99%
2.17%
2.06%
−0.45%
1.28%
0.02%
2.79%
2.46%
1.77%
7.18%
1.13%
0.58%
3.14%
1.55%
0.47%
2.89%
0.49%

12.1%
6.06%
7.69%
9.24%
8.70%
11.8%
2.33%
8.10%
4.45%
20.8%
8.09%
11.6%
19.5%
10.1%
7.93%
8.07%
6.04%
7.17%
9.55%
7.36%

1.51%
1.59%
1.61%
0.98%
2.07%
1.49%
1.64%
1.75%
1.97%
1.57%
1.00%
1.78%
3.43%
0.92%
4.62%
1.56%
1.63%
1.48%
2.26%
1.84%

4.99%
1.51%
1.73%
2.71%
2.79%
6.32%
1.52%
2.18%
1.60%
7.49%
2.30%
3.83%
4.03%
3.02%
4.49%
2.60%
1.99%
3.82%
2.11%
3.41%

.102
.439
.433
.538
.710
−.054
.494
.165
.503
.078
.580
.243
.348
.707
.370
.593
.536
.187
.700
.148

0.248
1.761
1.929
1.838
2.214
−0.101
0.755
0.614
1.394
0.215
2.044
0.737
1.685
2.365
0.652
1.837
1.627
0.350
3.169
0.320

The table shows the time-series properties of annual growth rates of real house prices (as described in Internet
Appendix A.3.1) and real consumption, as collected by Barro and Ursua (2008). Column 1 shows the sample
considered. Columns 2 and 3 show the mean and standard deviation of real house price growth. Columns 4 and
5 show the mean and standard deviation of real consumption growth. Column 6 shows the correlation of real
house price growth and real consumption growth. Column 7 shows the consumption beta of house prices.

the world in which consumption falls and marginal utility is high. We also
investigate the correlation between house price growth and alternative measures
of economic activity by using data from Mack and Martínez-García (2011), and
report the correlation between annual real house price growth and real personal
disposable income growth in a panel of 23 developed and emerging countries
(see Table 3). The average correlation is 0.33 and positive for all 23 countries,
except for Croatia (−0.35), otherwise with a minimum of 0.04 for Norway
and a maximum of 0.62 for Japan. The “personal disposable income beta” is
positive for all countries, except Croatia (−0.16), and often above 1.0 again.
Overall, this evidence further corroborates the fact that real estate returns are
risky.
1.3 The term structure of real estate discount rates
Next, we provide evidence on an important and previously unexplored
dimension of real estate data: the term structure of housing discount rates.
We first present our analysis of expected real estate returns, which we find
to be relatively high, between 5.5% and 7.4%. We then combine these new
data with the estimates of Giglio, Maggiori, and Stroebel (2015) to provide
evidence for the slope of the term structure of real estate discount rates. Our
analysis suggests that this term structure is downward sloping, and thus cautions
against using real estate’s average rate of return to infer discount rates for very
long-run benefits associated with investments in climate change abatement. In

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Australia
Belgium
Canada
Denmark
Finland
France
Germany
Italy
Japan
Netherlands
New Zealand
Norway
Singapore
South Africa
South Korea
Spain
Sweden
Switzerland
U.K.
U.S.

Real HP growth
Period

The Review of Financial Studies / v 34 n 8 2021

Table 3
Real house price growth and personal disposable income growth
Real HP growth
SD

Mean

SD

Correlation

PDI beta

3.54%
2.53%
2.91%
1.12%
0.07%
1.73%
−0.09%
1.90%
2.28%
3.47%
3.36%
0.33%
−0.39%
0.64%
4.16%
2.31%
2.65%
2.90%
2.00%
1.36%
0.49%
1.16%
3.05%

6.67%
5.50%
7.49%
4.58%
2.52%
8.58%
10.6%
7.71%
5.13%
8.49%
9.44%
8.15%
4.24%
7.36%
6.40%
9.12%
6.92%
7.73%
7.01%
3.88%
9.13%
12.3%
8.83%

1.37%
0.92%
1.35%
1.17%
1.28%
1.13%
0.81%
1.92%
1.12%
2.05%
1.89%
0.89%
1.49%
3.97%
2.76%
0.74%
2.22%
1.13%
1.40%
1.59%
0.34%
8.79%
2.74%

2.10%
2.30%
2.18%
1.53%
1.64%
2.29%
2.27%
2.97%
1.61%
2.26%
3.33%
2.48%
1.44%
4.38%
3.63%
3.01%
2.05%
3.41%
2.39%
1.54%
2.37%
27.0%
7.37%

.156
.431
.466
.425
.237
.224
.409
.470
.332
.420
.574
.363
.622
.245
.067
.467
.037
.486
.467
.322
.474
−.345
.129

0.495
1.031
1.604
1.275
0.365
0.839
1.909
1.219
1.056
1.575
1.627
1.195
1.835
0.412
0.117
1.414
0.126
1.103
1.371
0.812
1.824
−0.158
0.155

This table shows the time-series properties of quarterly frequency annual growth rates of real house prices and
personal disposable income between 1975 and 2016, as collected by Mack and Martínez-García (2011). Columns
1 and 2 show the mean and standard deviation of real house price growth. Columns 3 and 4 show the mean and
standard deviation of real personal disposable income growth. Column 5 shows the correlation of real house
price growth with real personal disposable income growth. Column 6 shows the personal disposable income beta
of house prices.

subsequent sections, we will use insights from asset pricing theory to inform
what can be learned from the downward-sloping term structure of risky real
estate cash flows about the optimal discount rate for investments in climate
change abatement.
1.3.1 Average rate of return to housing and rental growth rate. We employ
two complementary approaches to estimate the average return to real estate.
The first approach, which we call the price-rent approach, starts from a pricerent ratio estimated in a baseline year and constructs a time series of returns
by combining a house price index and a rental price index: Without loss of
generality, suppose we know the price-rent ratio at time t = 0. We can then
derive the time series of the price-rent ratio as
Pt
Pt Dt Pt−1
D1
=
;
given,
(2)
Dt+1 Pt−1 Dt+1 Dt
P0
where P is the price index and D the rental index. Note that, given a baseline
price-rent ratio, only information about the growth rates in prices and rents is
necessary for these calculations. Gross real housing returns are then


Dt+1 Pt+1 πt
G
Rt,t+1
=
+
,
(3)
Pt
Pt πt+1

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Australia
Belgium
Canada
Switzerland
Germany
Denmark
Spain
Finland
France
U.K.
Ireland
Italy
Japan
South Korea
Luxembourg
Netherlands
Norway
New Zealand
Sweden
U.S.
South Africa
Croatia
Israel

Real PDI growth

Mean

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

where π is a price level index to adjust for inflation. To compute expected
net returns E[R], we subtract maintenance costs and depreciation (δ) and any
tax-related decreases in returns (τ ):
E[R] = E[R G ]−δ −τ.

(4)

Rt,t+1 =

Vt+1 +N It+1 πt St
,
Vt
πt+1 St+1

(5)

where V is the value of the housing stock, N I is net capital income on housing,
π is a price level index that adjusts for inflation, and S is the stock of housing.
To adjust for the quality and quantity of the housing stock, we use several
complementary approaches. In our first approach, we proxy for the change in
the housing stock by population growth. In alternative specifications, we control
for the change in the housing stock with the growth in residential housing units
or the growth in residential floor space. In our most conservative approach,
we rely on (constant-quality) quantity indexes, which allows us to directly
control for quality as well as “pure” quantity changes in the housing stock
at the same time. For the United States, we can also draw on holding gains
from the national revaluation accounts, which directly hold the aggregate stock
of housing constant. Finally, even though our main interest lies in net returns
to housing, the national accounts also allow us to estimate maintenance costs
and depreciation (δ) and tax-related decreases in returns (τ ), and hence gross
returns to housing E[R G ], which we compare to our results from the price-rent
approach.
Table 4 presents estimates of the return to housing for three countries. We
explore data from the United Kingdom and Singapore, since we are able to
measure very long-run discount rates for these countries (see below); we also
provide estimates for the United States for comparison, since they have been
the subject of an extensive literature (e.g., Flavin and Yamashita 2002; Lustig
and van Nieuwerburgh 2005; Piazzesi, Schneider, and Tuzel 2007). Internet
Appendix A.4 provides the details of our approach and the underlying data
sources.
United States. For the United States, our preferred estimates using the
price-rent approach are based on a price-rent ratio from Trulia that includes
a utilities correction (column 2); our preferred results using the balance-sheet

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The second approach, which we label the balance-sheet approach, follows
Favilukis, Ludvigson, and Van Nieuwerburgh (2017) and Piketty and Zucman
(2014): We obtain data on the value of the residential housing stock from
countries’ national accounts to estimate the value of the housing stock (i.e., its
price), and data on the net capital income earned on the housing stock (i.e., the
“dividend” earned on the housing stock). Since we are only interested in the
return to a representative property, we need to control for changes in the total
housing stock to derive the net return to housing in each period as

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Trulia
CS
CPI-S

Baseline-P/R
Price index
Rent index
-

Bal
CS
CPI-S

Trulia−
CS
CPI-S
-

0.7%

8.9%
8.1%
0.8%
2.5%
0.67%
5.7%

0.7%

9.7%
8.9%
0.8%
2.5%
0.67%
6.5%

(3)

-

Trulia−
FHFA
CPI-S

0.7%

9.4%
8.9%
0.5%
2.5%
0.67%
6.3%

(4)

1953-2016

-

Trulia−
CS
PCE-H

0.9%

10.0%
9.0%
1.0%
2.5%
0.67%
6.8%

(5)

Pop

-

-

9.7%
7.1%
2.7%
2.3%
1.1%
6.3%

(6)

Units

-

-

9.3%
7.1%
2.3%
2.3%
1.1%
5.9%

(7)

Floor

-

-

9.1%
7.0%
2.1%
2.3%
1.1%
5.7%

(8)

-

-

8.9%
7.0%
1.8%
2.3%
1.1%
5.5%

(9)

Reval

Balance sheet

QI

-

-

8.7%
7.0%
1.6%
2.3%
1.1%
5.2%

(10)

-

Bracke
LR
CPIH

1.4%

9.5%
6.8%
2.7%
2.5%
0%
7.0%

(11)

-

Bal
LR
CPIH

Pop

-

-

10.2%
7.0%
3.3%
2.4%
0%
7.9%

(13)

Units

-

-

9.9%
6.9%
3.0%
2.4%
0%
7.6%

(14)

Balance sheet

1988-2016

1.4%

9.6%
6.9%
2.7%
2.5%
0%
7.1%

(12)

Price/rent

United Kingdom

QI

-

-

9.7%
6.9%
2.8%
2.4%
0%
7.4%

(15)

1990-2016

-

iProp
URA
URA

−0.4%

9.9%
5.6%
4.2%
2.5%
0.6%
6.8%

(16)

Price/rent

Singapore

This table shows our estimates for net real returns to housing and real rent growth in the United States, the United Kingdom, and Singapore based on the price-rent approach and the
balance-sheet approach. The price-rent approach starts from a price-rent ratio estimated in a baseline year and constructs a time-series of returns by combining a house price index and a
rental price index. Baseline-P/R is the source of the baseline price-rent ratio, either a direct estimate or based on the balance-sheet approach (Bal). In the United States, Trulia− includes an
adjustment for utilities possibly included in Trulia’s gross rents. CS is the Case-Shiller house price index; FHFA is the FHFA house price index; CPI-S is the shelter component of the CPI; and
PCE-H is the housing component of the PCE price index. In the United Kingdom, LR stands for Land Registry, and CPIH is the housing component of the consumer price index including
housing. In Singapore, iProp stands for iProperty.com, and URA stands for Urban Redevelopment Authority. In the balance-sheet approach, the total value of the residential housing stock
is used to estimate the value of housing, and net capital income earned on the housing stock is used to estimate net rents. To estimate the return on a representative property, we control
for changes in the total housing stock by the growth in population (Pop), housing units (Units), housing floor space (Floor), or quality-adjusted quantity indexes (QI). The U.S. Financial
Accounts also publish aggregate holding gains for each sector in the economy in the revaluation accounts (Reval), which directly hold the aggregate stock of housing constant. See Internet
Appendix A.4 for further details on the estimation procedures and the underlying data sources used. Numbers may not add up due to rounding.

Sample

-

0.7%

Rent growth

Stock adj.

10.2%
9.5%
0.8%
2.5%
0.67%
7.1%

Gross return
Rental yield
Capital gain
Depreciation
Taxes
Net return

(2)

Price/rent

United States

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(1)

Table 4
Expected returns and rental growth

The Review of Financial Studies / v 34 n 8 2021

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

United Kingdom. Columns 11 to 15 of Table 4 report the estimates for the
real estate market in the United Kingdom The price-rent and the balance-sheet
approaches produce similar estimates for the average annual real gross return
(E[R G ]): 9.5% for the price-rent approach and 9.7% for the balance-sheet
approach. We estimate a maintenance and depreciation cost of 2.4% using the
balance-sheet approach and maintain a calibration of 2.5% for the price-rent
approach. There are no property taxes to be considered in the United Kingdom
Average real net returns in the United Kingdom real estate market are therefore
between 7.0% and 7.4%.12
Singapore. Column 16 in Table 4 reports our price-rent approach estimate
for the Singapore real estate market at 9.9%. We assume the cost of maintenance
and depreciation to be 2.5%, in line with our estimates for the United States,
and the property tax impact to be 0.6%. Our estimate of the real net return in the
Singapore real estate market is thus 6.8%. We do not calculate complementary
balance-sheet approach estimates for Singapore for two reasons: First, more
than three quarters of residential dwellings are not in the private housing market
but publicly governed and developed by the Housing and Development Board
(HDB). Unfortunately, the national accounts data do not allow us to separate
these out with sufficient accuracy. Second, the national accounts data do not
allow us to determine the total consumption of real estate services excluding
relevant costs, that is, net rents, with sufficient accuracy.

12 Numbers for the balance sheet approach may not add up due to rounding when moving from gross to net returns.

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approach use direct holding gains from the revaluation accounts (column
9). We also provide robustness checks that use alternative price and rental
indexes as well as alternative price-rent ratios for the price-rent approach, and
various corrections for the growth in the housing stock for the balance-sheet
approach. Both approaches provide similar estimates for the average annual
real gross return (E[R G ]): 9.7% based on the preferred estimate from the
price-rent approach and 8.9% based on the preferred estimate from the balancesheet approach. We estimate a maintenance and depreciation impact of 2.3%
using the balance-sheet approach and calibrate the impact of maintenance and
depreciation at 2.5% for the price-rent approach based on prior results from
Harding, Rosenthal, and Sirmans (2007). Our balance-sheet estimates imply
a tax impact of 1.1%, and we assume a property tax impact of 0.67% for
a representative household for the price-rent approach. This results in average
real net returns of between 5.5% and 6.5% for the United States housing market.
These estimates are similar to the estimates in Flavin and Yamashita (2002),
who find a real return to real estate of 6.6%, and the estimates in Favilukis,
Ludvigson, and Van Nieuwerburgh (2017), who find a real return of 9%-10%
before netting out depreciation and property taxes.

The Review of Financial Studies / v 34 n 8 2021

Growth rate of rental income. Finally, we estimate the average real growth
rate of rental income using the same data sources, which we denote by g.
For all three countries, the estimated real growth rate of rents is low. For the
United States, we estimate g = 0.7%, an estimate in line with that of Campbell
et al. (2009), who obtain a median growth rate of 0.4% per year. We obtain
a slightly higher estimate of g = 1.4% for the United Kingdom and a slightly
lower estimate of g = −0.4% for Singapore (largely driven by a few deflationary
periods). These results are consistent with Ambrose, Eichholtz, and Lindenthal
(2013), who find very low real rental growth in a long time series of rents for
Amsterdam, and with Shiller (2006), who estimates long-run real house price
growth rates to be very low, often below 1% (the equivalence of these two
long-run growth rates is necessary for rental yields to be stationary).
1.3.2 Long-Run housing discount rates. In recent work, Giglio, Maggiori,
and Stroebel (2015) use unique data from the United Kingdom and Singapore
to estimate how much value households attach to future real estate cash flows
accruing over a horizon of hundreds of years (see also Giglio, Maggiori, and
Stroebel 2016). In these real estate markets, residential properties trade either
as freeholds, which are permanent ownership contracts, or as leaseholds, which
are prepaid and tradable ownership contracts with finite maturity. The initial
maturity of leasehold contracts generally varies between 99 years and 1,000
years. By comparing the relative prices of leasehold and freehold contracts for
otherwise identical properties, the authors estimate the present value of owning
a freehold after the expiration of the leasehold contract. They show how this
present value is informative about the discount rate attached to real estate cash
flows that occur in the very long run.
The red bars in Figure 8 represent the estimates from Giglio, Maggiori,
and Stroebel (2015). They show the price discount of leaseholds with varying
maturities compared to freeholds for otherwise identical properties. For
the United Kingdom estimates, for example, the bucket with leaseholds of

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Average rate of return: summary. Overall, these estimates show that
expected real returns for real estate are around 6% or higher for the countries
we consider. These estimates are robust to the different methodologies we use.
They are also in line with contemporaneous work from Jordà et al. (2017) that
finds average returns to housing of around 7% before taxes across a number
of countries. Our estimates are also consistent with the notion that average
house price growth over extended periods of time is relatively low, as argued
by Shiller (2006), with high rental yields being the key driver of real returns to
real estate and housing. In fact, our estimated average capital gains are positive
but relatively small for all three countries, despite focusing on samples and
countries that are often regarded as having experienced major growth in house
prices. Consistent with our results from Section 1.2, our estimates of average
returns to real estate imply a positive real estate risk premium.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

1.3.3 Takeaway: The term structure of discount rates in the housing
market. In this section, we show that (a) real estate has a real expected rate
of return of above 6% per year, and (b) the relative pricing of freeholds and
leaseholds implies discount rates of around 2.6% for rents 100 years or more in
the future. Since the average return on real estate is simply a weighted average
of the average returns of all of its cash flows (at all maturities), these two facts
together are informative about the shape of the term structure of discount rates
for the housing asset. It needs to be low at the long end, in order to match the
2.6% discount rate applied to the long-term housing claims. But it needs to be
high enough at the short end to imply an average discount rate of 6%. In other
words, the term structure of discount rates for the housing asset needs to be
downward sloping in order to explain the data. In the next section, we introduce
an asset pricing model of real estate that is able to match these moments, and
discuss its implications for valuing investments in climate change abatement.
2. Valuing Investments in Climate Change Abatement in a World with
Declining Discount Rates for Risky Assets
The previous section provided evidence that the term structure of discount rates
for real estate, a risky asset, is downward sloping, and that real estate is an asset
class that is directly exposed to climate change risk. In this section, we introduce
a general equilibrium model to study the link between climate change risk, the
term structure of discount rates for real estate, and consumption. Our model
has two objectives: First, it provides a quantitative framework, calibrated to
asset markets and our new evidence on the term structure of housing discount
rates, from which one can extract appropriate discount rates for climate-changeabatement investments at any horizon. Second, it allows us to nest, in reduced
form, a number of different approaches to modeling the economic impact of

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remaining maturity between 100 and 124 years shows that households are
willing to pay 11% less for a leasehold with that maturity than for a freehold.
Interpreted differently, 11% of the value of a freehold property is due to cash
flows that accrue more than 100 years into the future. In general, leasehold
discounts are strongly associated with maturity, with shorter leaseholds trading
at bigger discounts: between 17.6% for leaseholds with remaining maturity of
80-99 years and 3.3% for remaining maturities of 150-300 years. Leaseholds
with more than 700 years remaining maturity trade at the same price as
freeholds. Pricing patterns are similar for properties in Singapore. The authors
provide a detailed investigation of the institutional setup of leasehold and
freehold contracts, and examine a number of possible explanations for the
observed leasehold discounts. They conclude that leasehold price discounts are
tightly connected to the contracts’ maturity and that discount rates of around
2.6% for cash flows more than 100 years in the future are necessary to match
the data from both countries.

The Review of Financial Studies / v 34 n 8 2021

climate change, ranging from the “tax view” in the spirit of Nordhaus and Boyer
(2000) and Nordhaus (2008), to the “disaster view” in the spirit of Weitzman
(2012, 2014). This allows us to understand these views’ different predictions
for the discount rates of investments in climate change abatement.

Model setup.

We assume that aggregate consumption follows
ct+1 = μ+xt −Jt+1 ,

(6)

xt+1 = μx +ρxt +φJt+1 ,

(7)

where ct is the log of aggregate consumption; since the economy is closed
and does not feature investment, ct also corresponds to aggregate output in
equilibrium.13 Jt is a jump process that takes value ξ ∈ (0,1) with probability
λt in each period, and value 0 otherwise. We interpret J as climate risk: a rare
but possibly large negative shock to output. The climate disaster probability
λt depends endogenously on the dynamics of the economy (see below).14 The
process xt captures persistent changes in the growth rate of consumption and
plays a key role in determining the term structure of discount rates.
As is standard in financial economics, we allow for a separate cash flow
process, dt , for risky assets—which in our model corresponds to the rents of
real estate—to capture the idea that asset markets only reflect a subset of total
economic activity. The process for these rent cash flows is similar to the one
for aggregate consumption:
dt+1 = μd +yt −ηJt+1 ,

(8)

yt+1 = μy +ωyt +ψJt+1 .

(9)

13 Note that we assume complete markets, so all risk is shared perfectly across households. The equilibrium effects

of incorporating heterogeneity and incomplete risk-sharing in asset pricing models has been studied in a long
literature (see, e.g., Constantinides and Duffie 1996). We leave the exploration of the specific implications of
climate change risks to future research.
14 Our model is designed to help researchers and policy makers understand how to value investments in climate

change abatement. We thus remove any risk sources not related to climate risk. Other shocks could be added
without changing the qualitative implications of the model.

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2.1 A general equilibrium model with climate change risks
Our model builds on a modified version of the Lucas (1978) representativeagent economy with power utility preferences. To provide a simple analytical
framework for climate change, we introduce a production sector that, while
exogenous, allows for important feedback effects between the growth rate of
the economy and the probability of rare and adverse climate shocks that destroy
parts of the output. The setup is rich enough to allow for key climate-related
dynamics in the economy, including an endogenous relationship between
consumption and climate risk, while also being stylized enough to be solved in
closed form up to simple recursive expressions.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

λt+1 = μλ +αλt +νxt +χ Jt+1 .

(10)

In designing this process, we aim to capture some of the main features of
physical models of climate change, while at the same time maintaining a
tractable solution to the asset pricing model. Two features of this process make
it particularly useful for bringing climate risk into an asset pricing framework:
1. The disaster probability λt is an endogenous function of the growth
rate of the economy. Since xt —which captures the expected deviation
of the growth rate of the economy from the trend—enters additively
and positively (ν > 0) in Equation (10), the probability of a disaster
increases over time when the economy grows at a faster rate. Intuitively,
this feature captures the notion that faster growth accumulates
more environmental damages, such as greenhouse gas emissions and
pollution, thereby increasing the probability of adverse climatic events,
akin to tipping points (see, Alley et al. 2003; Lenton et al. 2008;
Overpeck and Cole 2006; Lemoine and Traeger 2014; Franklin and
Pindyck 2018).

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The main difference between real estate rents and consumption is the larger
exposure of rents to the underlying economic shocks, represented by climate
risk J . This is captured by the multiplier η > 1. In our case, η reflects the
empirical observation that housing has an above-average exposure to climate
risk, primarily due to the immovability of land. Analogous to xt , the process
yt captures persistent changes in the growth rate of rents. Having different
processes for xt and yt allows for flexibility in the calibration of this model to
different specific settings.
Our setup allows for partial mean reversion in the growth rate of consumption
and rents after a disaster. Formally, after a disaster strikes, the growth rate of the
economy increases (ψ > 0,φ > 0) and this increase is persistent (ρ > 0,ω > 0).
As we show below, this partial mean reversion plays a crucial role in explaining
the term structure of discount rates for risky assets (see also Gourio 2008; Lettau
and Wachter 2011; Nakamura et al. 2013; Belo, Collin-Dufresne, and Goldstein
2015; Hasler and Marfe 2016). In the context of climate risk modeling, the
partial mean reversion captures the notion that economic activity picks up
after a climate disaster as the economy adapts to new climatic circumstances.
Numerous papers have highlighted the importance of such adaptation processes,
including Brohé and Greenstone (2007), Deschênes and Greenstone (2011),
Desmet and Rossi-Hansberg (2015), Burke and Emerick (2016), and Barreca
et al. (2016). Yet, since there have not been many global climate disasters
(especially in modern data), such feature remains a possibility rather than an
empirical regularity.
The last component of our model is an endogenous climate disaster
probability, λt :

The Review of Financial Studies / v 34 n 8 2021

Disaster probability
0.2

t

: log deviation from long-run mean

0.1

t

Log Deviations

Trend Growth
Above-Trend Growth

0.15

0.05

0
5

10

15

20

25

30

35

40

45

50

35

40

45

50

55

60

Years
Rents

1.2

Rents

1
0.8
0.6
0.4
Trend Growth
Above-Trend Growth

0.2
0
5

10

15

20

25

30

55

60

Years

Figure 4
Sample paths: Trend growth and above-trend growth
The figure shows two sample paths of the economy under our baseline calibration. The top panel reports the log
deviation of the climate disaster probability, λt , from its mean. The bottom panel reports the path of log rents,
dt . The dotted line represents the baseline path along which the economy grows at its deterministic trend. The
solid line represents a temporary deviation from the trend in which growth accelerates.

2. The climate disaster probability λt increases following the occurrence
of a disaster (χ > 0), thus allowing climate shocks to induce a selfreinforcing cycle in which each shock increases the probability of the
next shock (see, e.g., Cox et al. 2000; Melillo et al. 2017). Note that, in
contrast to the mean reversion in cash flows described above, this is a
force that pushes toward making long-run cash flows more risky.
To illustrate the richness of these patterns, Figures 4 and 5 plot two sample
paths of the economy. Figure 4 shows a path in which no disaster occurs, but
the economy grows above trend for a sustained period of time, starting in year
10.15 The top panel shows log deviations of the disaster probability λt from its
steady-state value. We set the steady state value to 3% to reflect the Barro (2006)
estimate of the average probability of a consumption disaster. The bottom panel
shows the path of log rents, dt , over time: rents (and the economy overall)
increase at a decreasing rate, reaching a permanently higher level as a result
of the growth spurt. This sustained economic expansion induces a progressive
increase in the probability of a climate disaster until the economy returns to its
steady-state growth rate. The lags of the effect of greenhouse gas emissions and
pollution on the disaster probability can be substantial: The disaster probability
15 As we will discuss in Section 2.2, trend growth is calibrated at 2%. We assume that in period 10, growth of

both consumption and rents increases to 5% and then slowly reverts to long-run trend growth. Since growth is a
persistent process in the model, growth is above trend for approximately 20 years in this sample path.

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1.4

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

Disaster Probability t : Log Deviation From Long-Run Mean

0.4

0.2

t

Log Deviations

Above-Trend Growth / No Disaster
Above-Trend Growth / With Disaster

0.3

0.1

0
5

10

15

20

25

30

35

40

45

35

40

45

50

55

60

Years
Rents

1.2

Rents

1
0.8
0.6
0.4
Above-Trend Growth / No Disaster
Above-Trend Growth / With Disaster

0.2
0
5

10

15

20

25

30

50

55

60

Years

Figure 5
Sample paths: Above-trend growth, with and without a disaster
The figure shows two sample paths of the economy under our baseline calibration. The top panel reports the log
deviation of the climate disaster probability, λt , from its mean. The bottom panel reports the path of log rents, dt .
The dotted line represents a path along which the economy grows at its deterministic trend, then experiences an
increase in growth (the same as the solid line in Figure 4). The solid line represents an alternative path along which
the increased probability of disasters due to the temporary acceleration in the economy leads to the occurrence
of a disaster after year 25.

reaches its maximum approximately 7 years after the growth spurt has started.
Since the model is stationary, the disaster probability ultimately reverts to its
mean, but the half-life of the shock is extremely long at 14 years.
Figure 5 instead shows a path in which the economy expands above trend,
starting in year 10 (exactly as before), but with a climate disaster occurring
after year 25. This disaster induces a large drop in consumption and rents. The
dynamics of climate risks are particularly interesting. As before, the disaster
probability increases as the economy accelerates. Once the disaster hits, the
probability of a future disaster increases further. It takes almost 40 years (in a
sample path chosen to have no further disasters) from the original growth spurt
shock for the probability of a disaster to revert to its long-run mean. The bottom
panel of Figure 5 also illustrates the mean reversion in the growth rate of the
economy. After a disaster strikes, the growth rate of the economy increases
(ψ > 0) and this increase is persistent (ω > 0).
The term structure of discount rates for risky assets. Despite the richness
of the underlying dynamics of the economy, we are able to solve quasianalytically for the term structure of housing risk premiums and the risk-free
rate. We derive these objects assuming the existence of a representative agent
who maximizes lifetime utility and faces a complete set of financial instruments.
In our baseline model, the period utility function features constant relative-risk

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1.4

The Review of Financial Studies / v 34 n 8 2021

aversion (γ ) as in Lucas (1978):
1−γ

U (Ct ) = δ t

Ct
,
1−γ

(11)

Pt(n) =

Et [Dt+n ]
.
(1+r nt )n

(12)

As we show in Internet Appendix A.5, the term structure of discount rates r nt is
closely linked to the term structure of one-period expected returns. Intuitively,
the appropriate discount rate for cash flows of horizon n is simply the average
(n)
across one-period expected returns Et [Rt,t+1
] for claims to cash flows at each
horizon up to n, where the holding-period returns over the next period are given
(n)
(n−1)
by Rt,t+1
= Pt+1
/Pt(n) . More formally, this can be written as17
1
(k)
ln(Et [Rt,t+1
]).
n k=1
n

r nt 

(13)

(n)
The expected one-period return for the n-maturity claim, Et [Rt,t+1
], can in
f
turn be thought of as the sum of the one-period risk-free rate, Rt,t+1 , which is
f
(n)
]−Rt,t+1 ,
independent of the maturity of the claim, and a risk premium, Et [Rt,t+1
which varies with the horizon n. While Internet Appendix A.6 provides the full
solution of the model, and while the calibrated results presented below use this
full solution, we next focus on a simple approximate solution that captures the
main forces that shape the term structure of one-period excess returns in our
model here:
f

(n)
(n)
]−Rt,t+1  γ Covt [rt,t+1
, ct+1 ]
Et [Rt,t+1


= γ η −ψed,n−1 −φbd,n−1 −χfd,n−1 ξ 2 λt (1−λt ).

(14)

The first equality above uses the fact that the log stochastic discount factor under
power utility preferences is mt,t+1 = logδ −γ ct+1 , and the second equality
16 We label objects that relate to single cash flows at a specific maturity n by superscript (n). The set of claims to a

single cash flow at maturity n that we are interested in is a subset of a more general class of assets with maturity
n that could pay cash flows, such as rents at any point in time up to that maturity. We denote prices and returns
of claims to more general classes of assets with maturity n with superscript n.
17 See Internet Appendix A.5.1 for a derivation. The result holds exactly when the term structure of discount rates is

constant over time (though it can have any shape over maturities n). For example, a flat term structure of discount
rates implies a flat term structure of expected one-period returns across maturities, and vice versa.

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where δ is the rate of time preference. In Internet Appendix A.6, we derive
the prices of claims to consumption and rents at different horizons. Here, we
focus on the crucial forces determining the term structure of housing discount
rates. Formally, we are interested in the per-period discount rate of maturity n,
denoted r nt , that equates the price of a single cash flow Et [Dt+n ] of maturity n,
denoted Pt(n) , with its present discounted value:16

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

ed,n =

1−ωn
.
1−ω

(15)

Since this term enters negatively in Equation (14), positive values for both ψ
and ω imply a declining term structure of risk premiums for rents. Recall that ψ
determines the degree of mean reversion of the growth rate of the economy after
a climate disaster, and ω captures the persistence of this growth rate increase.
When ψ > 0, as in our baseline calibration below, rents (partially) mean-revert
after a climate disaster. This mean reversion in cash flows implies that the
occurrence of a disaster is worse for short-term claims than it is for long-term
claims because immediate short-term cash flows drop by more than cash flows
that are further in the future.

Remark on preferences. The previous discussion highlights that, in our
setting, the observed downward-sloping term structure of risk premiums for
housing is generated by the dynamics of the cash flows (risk quantities) rather
than by the term structure of risk prices, which are flat. One might wonder
whether more sophisticated preferences, such as Epstein-Zin preferences that
are popular in both the asset pricing and climate change literatures, could also
generate this downward slope. We discuss in Internet Appendix A.5.3 that this
is not the case. In fact, introducing Epstein-Zin preferences would push the
slope of the term structure of discount rates for risky assets upward. To match
the data on a downward-sloping term structures of discount rates for risky real

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represents the solution to the model, where bd , ed and fd solve recursive
equations derived analytically and reported in Equations (A.14c) to (A.14e)
in Internet Appendix A.6.
Equation (14) highlights the components that drive the downward-sloping
term structure of discount rates for risky assets (i.e., housing) in our framework.
The level of the term structure is determined by the aggregate amount of risk
in the economy, ξ 2 λt (1−λt ), and by the agent’s risk aversion, γ . Neither has a
differential effect on the risk premiums of cash flows with different maturities
(there are no n-subscripts).
The shape of the term structure is determined by the terms inside the bracket.
The term bd arises from the term structure of risk-free assets (term premia) and
is essentially constant in realistic calibrations of the model that match the flat
term structure of risk-free rates in the data. The term fd is a quantitatively small
adjustment for the risk that arises from changes in the disaster probability λt .
The component that quantitatively dominates the shape of the term structure
of housing risk premiums is ψed,n−1 , which captures the term structure of
exposures of claims of different maturity to the climate disaster (and the ensuing
recovery). The model is parsimonious enough to admit an analytical solution
for ed,n (see Equation (A.14e) in the Internet Appendix):

The Review of Financial Studies / v 34 n 8 2021

estate, we would thus require an even stronger mean reversion in cash flows.18
More generally, we are not aware of a standard representation of preferences
that would push toward a downward-sloping term structure of discount rates for
risky assets, such as real estate. As a result, capturing the observed downward
slope through the dynamics of risk quantities, as we do in our model, seems like
the natural approach to us, in particular given that the required dynamics are
highly consistent with empirical research on the adaptation to climate change.

2.2.1 Baseline calibration. Whenever possible, we calibrate parameters
following the existing asset pricing literature. The remaining parameters are
calibrated to match some of our new moments estimated in Section 1. For
example, we follow the asset pricing literature and set risk aversion γ = 10, the
drop in consumption following a disaster ξ = 21%, and the exposure of risky cash
flows to the climate shock η = 3 (see Bansal and Yaron 2004; Barro 2006; Barro
and Jin 2011). Average consumption growth in the absence of a disaster is set
to μ = 2%. The remaining parameters of the consumption process are chosen to
generate a recovery in consumption growth after disasters (φ > 0), and persistent
growth rates (ρ > 0). The magnitude of these parameters (φ = 0.025, ρ = 0.85)
targets a term structure of real interest rates that is slightly upward sloping with
a level of around 1%, matching our empirical estimates based on the U.K. gilts
real yield curve between 1998 and 2016 reported in Figure 6. These data show
that the U.K. real yield curve is approximately flat on average, with a real yield
close to 1% for maturities between 1 and 25 years.19
In our calibration, rents are not only correlated with consumption but also
share many dynamics with consumption, including recovery after disasters
18 The long-run risk model of climate change by Bansal, Kiku, and Ochoa (2013) and the model of Cai, Judd, and

Lontzek (2013) both use Epstein-Zin preferences.
19 Figure 6 plots the average shape of the real U.K. gilts curve for the period 1998-2016, as well as for two subperiods:

1998-2007 and 2008-2016. The level of the yield curve shifted down during this latter period and the yield curve
became hump shaped. More recently, as more and more U.K. government bonds with longer maturities have
been issued, reliable prices for such longer maturities have also become available. In 2016, the Bank of England
therefore started to extend the real yield curve up to maturities of 40 years. For the short time period, when data
on such long maturities are available, the yield curve is essentially flat for these longer maturities as well.

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2.2 Calibration
In this section, we turn to calibrating our model. The objective of our calibration
is not to quantitatively match all conceivable moments of real and financial
variables; since our model is only driven by a single climate disaster shock,
J , we would certainly fail in such an exercise along many dimensions.
Furthermore, history and scientific evidence only provide incomplete and
uncertain guidance on many key parameters related to climate events. What we
strive for instead is a reasonable calibration that can match core moments of the
data as they relate to the discounting of climate-change-abatement investments
and, in particular, match our new evidence on the risk and return properties of
real estate, including the term structure of discount rates from Section 1.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

3
Real yield curve, 1998-2007
Real yield curve, 2008-2013
Real yield curve, 1998-2013

2.5
2

Yield

1.5
1

0
-0.5
-1

4

6

8

10

12

14

16

18

20

22

24

Maturity (years)
Figure 6
U.K. gilts real yield curve
The figure plots the real yield curve for U.K. gilts as computed by the Bank of England for the period
1998-2016, as well as for two subperiods: 1998-2007 and 2008-2016. It is available at http://www.
bankofengland.co.uk/statistics/Pages/yieldcurve/archive.aspx, last accessed July 2017. Until 2015, the U.K.
government debt also included some perpetual bonds: war loans and annuities. These bonds composed a negligible
part of the outstanding U.K. government debt (£2.6bn out of £1.5trn of debt outstanding) and were classified
as small and illiquid issuances by the U.K. Debt and Management Office. In 2015, following the passage of
the Finance Act, all outstanding perpetuities were called in by the British government. They are excluded from
our analysis, not only because they are nominal and we only use data on U.K. real gilts but also because their
negligible size, scarce liquidity, and callability make it difficult to interpret their prices in terms of discount rates.

(ψ > 0) and persistent rent growth (ω > 0). The magnitudes of these parameters
(ψ = 0.24, ω = 0.915) are chosen to match the shape and the level of the observed
term structure of discount rates in the housing market as described in Section
1. Finally, we set the steady-state conditional probability of disasters, λ, to 3%
per year, following the estimates in Barro (2006). The remaining parameters
for the λt -process are chosen to obtain economically reasonable interactions
between the real economy and the disaster probability, while at the same
time matching the term structure of the risk-free rate. The risk-free rate is
directly affected by the disaster probability dynamics through the precautionary
savings channel; an increase in the disaster probability decreases the rate
by increasing precautionary savings. In particular, the disaster probability is
persistent (α = 0.75), increases after a jump (χ = 0.05), and increases when
expected consumption growth xt is above its trend (ν = 0.1). Finally, we impose
that rents and consumption have the same long-run growth rate and that xt and
yt have mean zero.20

20 The resultant parameter restrictions are μ = μ+(η −1)λ̄ξ , μ = −λ̄φξ , and μ = −λ̄ψξ . See Internet
x
y
d

Appendix A.6 for details.

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0.5

The Review of Financial Studies / v 34 n 8 2021

0.1
Risk-Free
Housing
Damages ( =1/10)
Damages ( =1/2)
Damages ( =1)

Discount Rate

0.05

0

-0.1

100

200

300

400

500

600

700

800

900

1000

Years

Figure 7
Discount rates for risk-free bonds, housing, damages
The figure shows the per-period discount rate corresponding to different assets for maturities 1 to 1,000 years, in
our baseline model calibration. The top line represents the term structure of discount rates for the risky housing
asset. The dashed line below it represents the real risk-free asset, that is, the real yield curve. The three black
lines in the bottom represent different calibrations of the damage process with θ ∈ {1, 0.5, 0.1}.

2.2.2 Calibration-implied housing term structure and climate risk
elasticities. Figure 7 plots the term structure of discount rates that the
calibrated model implies for risk-free and risky assets. The model is able to
match the approximately flat term structure of risk-free rates observed in the
data with an average level of around 1.0%. The model also produces a strongly
declining term structure of discount rates for real estate, starting around 10% per
year at short horizons and decreasing to around 3% per year at long horizons,
matching the declining term structure of discount rates that we estimated for
housing. To further assess how well we match our estimates of the real estate
data, the two panels of Figure 8 report the leasehold price discounts estimated
for housing in the United Kingdom and Singapore, together with the ones
implied by the calibrated model, to highlight the close fit between the model
and the data. The model also matches the average rate of return on housing (at
around 5.5%) that we have independently estimated in the data.
Our model also helps rationalize the cross-sectional regularity that houses
that are differentially exposed to climate risk have different price elasticities
with respect to news about climate change. This is qualitatively consistent
with the evidence reported in Section 1.1. That section focused on increase
perception of climate risk, that is, future climate affecting future rents, but not
current rents. Of course, current prices react immediately since they correspond
to the present value of future rents. In our calibration, a house with a 1%
higher exposure to climate change (i.e., higher η), responds to a one percentage
point increase in the probability of a climate disaster (λt ) with a price decline

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-0.05

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

A

UK

0

-0.05

Discount

-0.1

-0.2

Model
Data

-0.25
80-99

100-124

125-149

150-300

700+

Leasehold Maturity

Leasehold discounts in the United Kingdom

B

SG

0

-0.05

-0.1

Discount

-0.15

-0.2

-0.25

-0.3

-0.35

-0.4
Model
Data

-0.45
50-70

71-85

86-90

91-95

96-100

800+

Leasehold Maturity

Leasehold discounts in Singapore
Figure 8
Leasehold discounts
The figure shows the discount rates for housing assets predicted by the model (left bars) and in the data (right
bars), for the United Kingdom (upper panel) and Singapore (lower panel). The discounts are estimated from a
hedonic regression and reported in log points.

that is 0.4 percentage points larger relative to a house with lower exposure.
Unfortunately, these magnitudes are not directly comparable to the estimates
from Section 1.1, since such a comparison would require us to map changes in
our Climate Attention index to (perceived) changes in λt .

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-0.15

The Review of Financial Studies / v 34 n 8 2021

2.3 Valuing investments in climate change abatement
We start this section by using our calibrated model to derive appropriate
discount rates for various types of investments in climate change abatement.
Since our model nests the key ideas of a variety of standard models in climate
change economics, we then proceed to show how our results compare to and
improve upon the implications of two key views in climate change economics:
the “tax” view, pioneered by Nordhaus and Boyer (2000) and Nordhaus (2008),
and the “disaster view,” pioneered by Weitzman (2012, 2014).

qt+1 = μq −yt +ηJt+1 .

(16)

Intuitively, the occurrence of a climate disaster in our model induces an
immediate destruction of rents (ηξ ), but these damages revert over time as the
economy adapts (captured by yt ).21 Investments in climate change abatement
provide a payoff that at least partially offsets the damages. Specifically, we
assume that an insurance contract insures a fixed proportion θ of the growth
rate of damages: θ qt+1 . Values of θ range from 1 (full insurance) to close
to zero (no insurance). Of course, it is possible to specify alternative types of
climate change mitigation investments, for example, some that mitigate the
long-run damages more strongly than in this specification. One advantage of
our fully specified model is that it allows researchers to explore different types
of climate interventions.
Figure 7 reports the appropriate discount rates for investments in climate
change abatement of different maturity for three values of θ: 1, 0.5, and 0.1.
Higher values of θ correspond to lower black lines.22 The figure highlights a
number of crucial results from our model:
1. Appropriate discount rates for investments in climate change
abatement are always below the risk-free rate. This feature comes

21 We set μ = μ −2λ̄ηξ so that damages and rents have the same long-run growth rate.
q
d
22 In some calibrations, the appropriate discount rates are negative, especially at shorter maturities. This is not

surprising given the insurance contract nature of the investments; investors are simply willing to pay a price
today that is above the expected payoff of the project.

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2.3.1 Valuing investments in the benchmark model. To derive the
appropriate discount rates for investments in climate change abatement, we
need to model their cash flows and their relation with the climate shocks.
We model climate change investments as assets that compensate the investor
for future damages to production and rents due to climate change, akin to
insurance policies on climate change. Climate change mitigation investments
in our framework are not large enough to affect equilibrium consumption;
they are infinitesimal investments that are therefore informative about marginal
valuations. We denote the process of damages to rents due to climate change
by Qt and model its (log) dynamics as

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

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from these investments being a hedge: they pay off following a climate
disaster, and therefore in states of the world with high marginal utility.
For relatively short horizons, we have estimated a real risk-free rate
of about 1%, providing us with a tight upper-bound on the appropriate
discount rates.
2. At long horizons, the term structure of housing discount rates
provides an upper bound on the appropriate discount rate. While
the risk-free rate provides a theoretically tight upper bound at all
horizons, no reliable data exist on risk-free rates beyond horizons of
about 30 years. This makes direct measurements of the risk-free-rate
upper bound at horizons relevant for investments in climate change
abatement infeasible. However, Section 1 described observed discount
rates on risky housing for such long horizons, allowing us to bound the
long-run discount rates for assets that are safer than real estate, including
investments in climate change abatement, to be below 2.6%.
Importantly, a discount rate below 2.6% (and even more so 1%)
is lower than many estimates used in the existing literature and by
policymakers for discounting investments in climate change abatement.
For example, it is substantially below the 4% suggested by Nordhaus
(2013). Quantitatively, it is more in line with long-run discount rates
that are close to the risk-free rate, as suggested by Weitzman (2012),
or the 1.4% suggested by Stern (2006), or results by Barro (2015). It is
also close to the average recommended long-term social discount rate
of 2.25% elicited by Drupp et al. (2015) in a survey of 197 experts, and
falls within the range of 1% to 3% that more than 90% of these experts
are comfortable with. Moreover, in light of the general disagreement
in the literature regarding the appropriate discount rate, the interagency
group tasked by the U.S. government to value reductions in CO2 chose
three certainty-equivalent constant discount rates: 2.5%, 3%, and 5% per
year. Our estimates provide a tight bound that is only consistent with the
lowest rate of 2.5% for investments providing a long-run hedge against
climate disasters. Greenstone, Kopits, and Wolverton (2013) report the
cost of 1 metric-ton of CO2 to be $57 when using the suggested 2.5%
discount rate, but only $11 when using a 5% discount rate, illustrating
the impact of this bound on climate-change-related welfare calculations.
3. The term structure of discount rates for investments in climate
change abatement is upward sloping, making the housing discount
rates a tighter bound for longer horizons. Appropriate discount
rates for investments in climate change abatement increase with the
horizon, which disproportionally tightens our upper bound as the horizon
increases. This feature is driven by the same mean reversion in cash flows
that generates the downward slope in the term structure of risky assets
(such as real estate): since cash flows that are further in the future are

The Review of Financial Studies / v 34 n 8 2021

reduced less by a climate disaster, the benefits of reducing its effects are
smaller, too.

2.3.2 Alternative models: The “tax” view versus the “disaster” view of
climate change. Modeling climate change risk and its effects on the economy
is a daunting task, both because the physical processes driving climate change
are not fully understood and because of the sparsity of historical data to predict
how climate change will affect the economy. It is unsurprising, therefore, that
the literature has approached the modeling of climate change and its effects on
the economy in many different ways.
One view, pioneered by Nordhaus and Boyer (2000) and Nordhaus (2008),
thinks of climate change akin to a tax on output. When output is high, pollution
and the costs of climate change are also high. In this view, the main source
of uncertainty about the future of climate is the future path of the economy. If
the economy does well, pollution and climate change damages will be high; if
the economy deteriorates, pollution and damages will be low. Investments in
climate change abatement are thus risky, as they pay off in states of the world
in which the economy is already doing well.
The alternative view follows Weitzman (2012, 2014): climate change is
a disaster-type risk that, if it materializes, causes output to drop (see also,
Barro 2015; Lemoine 2021; Wagner and Weitzman 2015). In this “disaster”
interpretation, climate change itself represents the main source of uncertainty,
and is itself a source of aggregate risk for the economy. Alternatively, this

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Note that the implied low but upward-sloping term structure of discount rates for
investments in climate change abatement contrasts with a number of papers that
have argued for using declining discount rates for valuing investments in climate
change abatement (Arrow et al. 2013; Cropper et al. 2014; Farmer et al. 2015;
Traeger 2014). These arguments have motivated policy changes in France and
the United Kingdom, which have adopted a downward-sloping term structure
of discount rates for evaluating long-run investments, including those in climate
change abatement. While this disagreement about the term structures does not
have a substantial effect on the actual level of discount rates to value the long-run
cash flows—they are relatively low, at approximately 2%, under both the term
structures used in those countries and under our estimated upward-sloping term
structure—the two rely on different economic mechanisms. Importantly, they
also make substantially different predictions for evaluating the payoffs from
abatement investments that may accrue at shorter horizons. The calibration of
our model suggests that climate disasters cause the most damage immediately
after they hit, making it most valuable to hedge the immediate costs. As a
result, the discount rates are substantially below the risk-free rate of 1%-2%. In
contrast, the downward-sloping term structures used in France and the United
Kingdom suggest discount rates of 4% and 3.5%, respectively, for the first 30
years of a project’s cash flows.

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

qt+1 = μq −πq yt +ηq Jt+1 .

(17)

Different parameters of the model primitives under either the “tax view”
or the “disaster view” map onto different values of μq , πq , and ηq in this
general specification. For example, by setting πq = 1 and ηq = η, we recover
our benchmark specification in Equation (16). To illustrate the discounting
implications of the two different views, we compute the implied term structure
of discount rates for a benchmark investment in climate change abatement that
provides partial insurance. We assume the investment’s payoff process to follow
qt+1 /10, thus hedging 10% of the innovation in climate change damages.
The basic “disaster” view of climate change. Our framework can be
made consistent with the core of Weitzman’s original argument if we set
the probability of a climate disaster to be constant (λt = λ̄), remove the mean
reversion in the economy (xt = yt = 0), and set πq = 0 and ηq = η in Equation (17).
The climate-change-damages process then follows:
qt+1 = μq +ηJt+1 .

(18)

Figure 9 reports the term structure of discount rates for the climate-changeabatement investment described above in this Weitzman-type model (lowest
solid line). We can see that the original Weitzman logic implies discount rates
that are low, indeed lower than the risk-free rate, but also invariant across
horizons. This invariance across horizons clearly conflicts with our evidence
on horizon-dependent term structures of discount rates for assets exposed to
climate risk (such as housing).
Relative to this original Weitzman view, our model adds two features that
allow us to capture richer dynamics in climate change damages and to match
the empirically-observed horizon-dependent term structure of discount rates:
mean reversion (adaptation) in the economy, and climate risk that depends

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“disaster" view of climate change can also represent the case in which
uncertainty about the future path of the economy (and not uncertainty about
the climate per se) is the dominant source of uncertainty, but nonlinearities
in the feedback from the economy to climate change are so pronounced that
sufficiently high economic expansion might ultimately lead to a disaster (if
a tipping point is reached). In these cases, investments in climate change
abatement are then hedges that reduce aggregate risk, because they pay off
when consumption is low (after a climate disaster materializes).
Our own calibrated model is a special case of this “disaster” view of climate
change. However, our framework is general enough to nest both of these
views and to shed light on the very different implications they have for the
appropriate discount rates for investments in climate change abatement. To
highlight this, Equation (17) presents a generalized version of the dynamics of
climate damages (Equation (16) in our calibrated baseline specification):

The Review of Financial Studies / v 34 n 8 2021

0.045

0.04

0.035

0.03

Discount Rate

0.025

0.02

0.015

0.005
Risk-Free Rate
Tax View of Climate Change (Constant)
Tax View of Climate Change (Increasing)
Disaster View of Climate Change (No Adaptation)
Disaster View of Climate Change (Adaptation)

0

-0.005
100

200

300

400

500

600

700

Years

Figure 9
Leading models of climate change: Predictions for discount rates
The figure shows the per-period discount rate appropriate for climate-change-abatement investments under
different models of climate change damages. In all these models, climate damages follow the process q =
μq −πq yt +ηq Jt+1 ; the discount rates in the figure correspond to those applied to an investment whose payoff
is q/10. The “constant tax view” of climate change views damages as a constant fraction of output, so that
μq = μd , ηq = −η, and πq = 0. The “increasing tax view” views damages as a fraction of output that increases
in good times, so that μq = μd , ηq = −η, and πq = k . The “disaster view” with no mean-reversion views climate
change damages as inducing a drop in output, so that μq = 0, ηq = η, and πq = 0. Finally, the “disaster view” with
mean reversion corresponds to our baseline case, with μq = 0, ηq = η, and πq = 1.

endogenously on the growth rate of the economy as well as the occurrence
of climate shocks. To illustrate, if we reintroduce mean reversion as in
our benchmark calibration into this Weitzman economy, the climate-changeabatement investment starts to pay off whenever a climate disaster occurs
(captured by the term ηJt+1 ), and continues to pay off at a declining rate in future
periods (captured by the term −πq yt ), reflecting higher economic growth due
to adaptation. The lowest dashed line in Figure 9 indeed replicates our baseline
results from Figure 7 and confirms that the discount rates for this investment
are below the risk-free rate at all horizons, but increase with the horizon.
The basic “tax” view of climate change. We can also use our framework
to explore the “tax” view of climate change elaborated on most prominently
by Nordhaus. For exposition, we start by considering a simplified environment
in which the tax rate that climate change imposes on the economy is constant,
and the fundamental source of uncertainty stems from shocks to the economy.
Such a setup corresponds to a linear damage function in the DICE model.
The payoff to an investment in climate change abatement is then equivalent
to the tax revenue from the climate tax, which can be captured by setting
Qt = τ Dt , where τ is the climate tax rate. We keep all other processes in our
economy unchanged, but remove the mean reversion (xt = yt = 0) to stay within

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0.01

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

the neoclassical-growth-model spirit of Nordhaus’ DICE model.23 Since the
tax is constant, the payoff to climate-change-abatement investments behaves
exactly like output. In particular, we can parameterize Equation (17) by setting
μq = μd , πq = 0, and ηq = −η. The process for damages from climate change
then becomes
qt+1 = dt+1 = μd −ηJt+1 .
(19)

23 In Weitzman’s work, and in our benchmark model, the shocks J
t+1 are a direct manifestation of climate change

disasters, and we parametrized them accordingly. In Nordhaus’ work, climate change is a tax on the economy,
and the shocks Jt+1 are to be interpreted as not directly related to climate change (e.g., they may capture shocks
to productivity instead). We focus on showing how the views of Nordhaus and Weitzman can be mapped into our
model and highlight their starkly different predictions for discount rates here. Since the difference in predictions
is stark in a qualitative sense already (i.e., different signs of the covariance of climate risk with consumption), we
thought it best not to recalibrate shocks when analyzing the implications of Nordhaus’ view in our framework.
24 That is, we are implicitly defining the tax rate to follow [ln(1−τ
t+1 )−ln(1−τt )]−[ln(1−τt )−ln(1−τt−1 )] =

μy +ω{[ln(1−τt1 )−ln(1−τt−1 )]−[ln(1−τt−1 )−ln(1−τt−2 )]}+ψJt+1 .

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It follows immediately that investments in climate-change abatement in this
setting are risky, since their payoff is positively correlated with consumption
(see also Gollier 2013). This is reflected by the negative loading on Jt+1 in the
above equation (ηq = −η). Note that this loading is positive in the corresponding
equation for the “disaster” view (Equation (18)); these different loadings are
at the core of the starkly different predictions that these two views offer for
discounting investments in climate change abatement. Indeed, Figure 9 shows
that in the “tax” view (in which shocks to the economy are the fundamental
source of uncertainty and the relationship between production and climate
change is not very nonlinear), discount rates are high, above the risk-free rate,
and invariant across horizons (solid black line). The first implication, high
discount rates, is a key characteristic of the “tax” view of climate change. The
second implication, a flat term structure, derives from our assumption of a
constant tax rate.
A richer model in the spirit of Nordhaus (2008) allows for the tax rate
to increase with economic activity, such that damages are disproportionally
higher when the output of the economy is higher. Yet, the nonlinearities are
not sufficiently strong to actually imply lower consumption in paths of high
economic growth compared with paths of low economic growth (as in the
tipping point literature captured by the “disaster" view). We capture the essence
of this argument by assuming that tax proceeds follow Qt = τt−1 Dg,t , where τt−1
increases when output is high as specified below. We obtain that
(20)
Dt = Dg,t (1−τt−1 ),
where Dg,t are rents in the absence of climate damages, which we refer to as
gross rents, and Dt are net rents. We assume that gross rents follow dg,t+1 =
μd −ηJt+1 as before. Net of the climate tax, rents then follow


(21)
dt+1 = dg,t+1 + ln(1−τt )−ln(1−τt−1 ) = dg,t+1 +yt ,


where yt = ln(1−τt )−ln(1−τt−1 ) follows the same process as specified in
Equation (9).24 As we can see, this richer Nordhaus view still implies an output

The Review of Financial Studies / v 34 n 8 2021

The above process is now a special case of Equation (17), in which μq = μd ,
πq = k, and ηq = −η. As in the simpler constant-tax version of the Nordhaus
view discussed above, investments in climate change abatement are risky (their
payoffs are still positively correlated with output, ηq = −η). However, as shown
in Figure 9, the increasing tax rate (captured by −kyt ) now induces the discount
rates for climate-change-abatement investments not only to be high (above
the risk-free rate) but also to be increasing with the horizon (dashed black
line). Intuitively, when the economy does badly, expected climate damages
are persistently low, thus making long-term investments in climate-change
abatement even riskier than short-term investments.
2.4 Key takeaways
The evidence in Section 1 uncovered a downward-sloping term structure of
discount rates for real estate, an asset that has substantial exposure to both
consumption risk and climate risk. The general equilibrium model developed
in this section is able to match this downward-sloping term structure of discount
rates by leveraging a simple mechanism: mean reversion in cash flows as
the economy adapts after a climate disaster. The implication of this mean
reversion is declining risk exposures of higher-maturity cash flows, since a
climate disaster that strikes today has larger effects on immediate cash flows
than on distant cash flows.
Our modeling exercise has allowed us to establish a number of simple yet
powerful results on appropriate discount rates for investments in climate change
abatement that hedge disaster-type climate risks: (a) that these discount rates

1−τ̄
25 We use the approximation lnτ −lnτ
t
t−1 ≈ −kyt and choose k = τ̄ . Recall that yt = ln(1−τt )−ln(1−τt−1 ) ≈
τt−1 −τt
τt −τt−1
1−τt−1
1−τt−1 , so that lnτt −lnτt−1 ≈ τt−1 = −yt τt−1 . Since we do not want the loading on yt to be time
τ̄
varying, we set k = 1−
τ̄ , where τ̄ is the steady-state tax rate.

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process that can (approximately) be nested in Equation (8) of our baseline
model; the only difference lies in the interpretation of some of these processes.
Note that this setup now also generates mean reversion in cash flows. However,
while mean reversion in cash flows comes from adaptation to climate events in
our baseline model, mean reversion is mechanically induced by the increasing
schedule of the climate-change tax rate (τ ) with respect to the level of economic
activity in the present setup. As we will see, this leads to starkly different
implications for discount rates.
damages in this setup are given by qt+1 = dg,t+1 +
 Climate-change

lnτt −lnτt−1 . These damages are similar to those in the simpler Nordhaus

setup in Equation (19), but now include an extra term, lnτt −lnτt−1 , that
derives from time variation in the climate tax rate. To preserve the linearity and
tractability of our model, we capture these damages in approximate form:25


qt+1 = dg,t+1 + lnτt −lnτt−1 ≈ dg,t+1 −kyt = μd −kyt −ηJt+1 .
(22)

Climate Change and Long-Run Discount Rates: Evidence from Real Estate

3. Conclusion
In this paper, we showed how discount rates estimated from private markets,
such as the housing market, can be informative about appropriate discount rates
for investments in climate change abatement. While much is still unknown
about the dynamics of climate change and its impacts on the economy, the
seminal work by Nordhaus, Weitzman, Gollier, and others has substantially
advanced our understanding of these issues. Our empirical and structural
analysis contributes to this line of work, furthers our understanding of existing
models, and provides new challenges for the next generation of models hoping
to capture the interaction of climate change, asset markets, and the economy.
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==> RFS08 - Welfare Consequences of Sustainable Finance.txt <==
Harrison Hong
Columbia University, USA and NBER
Neng Wang
Columbia University, CKGSB, ABFER, and NBER, USA
Jinqiang Yang
School of Finance, Shanghai University of Finance and Economics, China
and Shanghai Institute of International Finance and Economics
We model the welfare consequences of mandates that restrict investors to hold firms with
net-zero carbon emissions. To qualify for these mandates, value-maximizing firms have
to accumulate decarbonization capital. Qualification lowers a firm’s required return by its
decarbonization investments divided by Tobin’s q, that is, the greenium or the dividend yield
shareholders forgo to address the global-warming externality. The welfare-maximizing
mandate approximates the first-best solution, yielding welfare gains compared to laissezfaire by mitigating the weather disaster risks resulting from carbon emissions. Our model
generates optimal transition paths for decarbonization that we use to evaluate proposed
net-zero targets. (JEL G30, G12, E20, H50)
Received November 15, 2021; editorial decision February 20, 2023 by Editor Stefano
Giglio. Authors have furnished an Internet Appendix, which is available on the Oxford
University Press Web site next to the link to the final published paper online.

We thank Stefano Giglio (Editor) and two anonymous referees for helpful comments. We also thank Lars
Peter Hansen (discussant), John Hassler (discussant), Martin Oehmke (discussant), Marcus Opp (discussant),
Lukas Pomorski (discussant), Chester Spatt (discussant), Luke Taylor (discussant), Patrick Bolton, Darrell
Duffie, Jack Favilukis, Ron Giammarino, Robert Heinkel, Marcin Kacperczyk, Ali Lazrak, Bob Litterman,
Fabio Natalucci, Bob Pindyck, Rafael Repullo, Tom Sargent, Jim Stock, Felix Suntheim, Paul Tetlock, Jerome
Vandenbussche, Xavier Vives, Michael Woodford, and seminar participants at American Finance Association
Meetings, BI Norwegian Business School Conference, CEBRA Annual Conference, Columbia University,
Confronting Uncertainty in Climate Change (University of Chicago), IESE Banking Conference, IMF Policy
Workshop, Korean University Business School, Luohan Academy Conference, National Taiwan University, New
York Federal Reserve Bank, Oklahoma University Energy Conference, Peking University, Stanford University,
UBC Sauder Business School, University of Edinburgh, University of Virginia, UN-PRI Conference, and
Virtual Seminar on Climate Economics (San Francisco Fed) for helpful comments. Neng Wang acknowledges
support from CKGSB Research Institute. Yang acknowledges the support from the National Natural Science
Foundation of China [Grants 71772112, 71972122, and 72072108] and Shuguang Program of Shanghai
Education Development Foundation. Send correspondence to Neng Wang, neng.wang@columbia.edu.
The Review of Financial Studies 36 (2023) 4864–4918
© The Author(s) 2023. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
https://doi.org/10.1093/rfs/hhad048
Advance Access publication June 1, 2023

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Welfare Consequences of Sustainable
Finance

Welfare Consequences of Sustainable Finance

1 The European Union and likely the Security Exchange Commission are addressing greenwashing by requiring

investors to disclose the carbon emissions of firms in their portfolios.
2 The first model analyzing the impact of green mandates on the required rate of return is cast in a static constant

absolute risk aversion (CARA) setting (Heinkel, Kraus, and Zechner 2001). Hong and Kacperczyk (2009) show
how ethical investing mandates affect costs of capital for sin companies. Recent work, for example, Pastor,
Stambaugh, and Taylor (2021) and Pedersen, Fitzgibbons, and Pomorski (2021), has modeled how nonpecuniary
tastes of green investors influence cross-sectional asset prices in a capital asset pricing model (CAPM) setting
or in a setting with financial constraints (Oehmke and Opp 2020). While exits or screens are the predominant
form of mandates, mandates need not only be passive but also be active via voting for environmentally friendly
policies (Gollier and Pouget 2014; Broccardo, Hart, and Zingales 2020).

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Sustainable finance mandates, whereby asset portfolios are restricted to firms
that can meet net-zero emissions targets, are increasingly embraced by the
financial sector. Prominent mandates include the Glasgow Financial Alliance
for Net Zero, which has commitments from 450 financial firms across 45
countries with $130 trillion of assets under management (Eaglesham and
Benoit 2021) and the Network for Greening the Financial System, which
supports net-zero pledges by central banks.
These mandates are meant to address the global-warming externality by
influencing the firms’ costs of capital, thereby incentivizing them to reform.
Following Intergovernmental Panel on Climate Change (IPCC) mitigation
pathways (Rogelj et al. 2018), major corporations have announced audited
plans to meet net-zero emissions targets by accumulating decarbonization
capital, including renewables, afforestation and reforestation, soil carbon
sequestration, bioenergy with carbon capture and storage (BECCs), and direct
air capture (DAC).1
While prior work on socially responsible investing has indicated that
divestment and the cost-of-capital channel can be a material incentive for firms
to reform,2 challenging questions remain about the welfare consequences of
these mandates. First, how close to the first-best outcomes can these mandates
get us when it comes to mitigating global warming? Put another way, can
mandates be a viable tool to address the global-warming externality when
the risk of a climate tipping point is imminent? A climate tipping point is
an absorbing state characterized by more frequent weather disasters (Lenton
et al. 2008; Collins et al. (2019); National Academy of Sciences 2016) that
significantly increase the social cost of carbon (Cai et al. 2015; Cai and
Lontzek 2019). Second, how should the corporate sector optimally decarbonize
given trade-offs between the costs of accumulating decarbonization capital and
the benefits of averting catastrophic consequences of global warming for the
society as a whole?
To address these issues, we introduce decarbonization capital into a dynamic
stochastic general-equilibrium model with the standard capital stock, which
serves as both the input for producing a homogeneous good and also the source
of carbon emissions (Nordhaus 2017; Jensen and Traeger 2014). Decarbonization capital only offsets carbon emissions, has no productive role, comes at
the expense of forgone corporate investments or dividend payouts, and faces

The Review of Financial Studies / v 36 n 12 2023

3 Models with time-varying disaster arrival rates (Gabaix 2012; Gourio 2012; Collin-Dufresne, Johannes, and

Lochstoer 2016; Wachter 2013) have been shown to be quantitively important in simultaneously explaining
business cycles and asset price fluctuations.
4 The decarbonization capital, which is unproductive and does not contribute to output, sits in the firm’s assets but

is not priced by markets other than through the mandate qualification mechanism.

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capital adjustment costs. More decarbonization relative to productive capital
delays a climate tipping point, which is modeled as a Poisson jump process
from a “Good” climate state with infrequent weather disasters to an absorbing
“Bad” climate state with frequent weather disasters (Lontzek et al. 2015).
Weather disasters in both “Good” and “Bad” climate states, also modeled
as jump processes with time-varying arrival rates, destroy both productive
and decarbonization capital stocks and lead to significant welfare losses for
households with Epstein-Zin recursive utility (Rietz 1988; Barro 2006; Pindyck
and Wang 2013; Martin and Pindyck 2015).3 To effectively manage climate
tipping-point risk, more decarbonization capital stock, which also mitigates
weather disasters in both climate states, is needed for an economy with a larger
productive capital stock.
Since the firm bears the costs of decarbonization, but the benefits of
decarbonization are enjoyed by society in the form of a lower aggregate risk,
there is an externality in the economy that can be addressed by sustainable
finance mandates. A mandate comprises the fraction of aggregate wealth that
is restricted for sustainable investment and a qualification standard for each
firm choosing to be sustainable. In equilibrium, a sufficiently large fraction of
ex ante identical firms choose to meet the qualification standard so that they
are included in the representative investor’s sustainable-firm portfolio.
Our analysis has three main sets of results. First, the required rate of return
for a sustainable firm is lower than that for an unsustainable firm. The wedge
between the two types equals the required mitigation spending (to fund the
aggregate decarbonization capital accumulation) for a sustainable firm divided
by its Tobin’s q, that is, the dividend yield a sustainable firm’s shareholders
forgo to address the global-warming externality or greenium. This required rate
of return formula is due to the equilibrium result that Tobin’s q, for sustainable
and unsustainable firms must be the same so that firms are indifferent between
being sustainable or not.4 Additionally, sustainable and unsustainable firms
invest and hence grow at the same rate (path by path) over time. This is because
(1) investment is connected to Tobin’s q via first-order conditions (FOCs)
for both types of firms (Hayashi 1982) and (2) both types of firms have the
same Tobin’s q. Finally, sustainable firms must lower their payouts to their
shareholders in order to fund their mitigation spendings in order to enjoy lower
costs of capital and keep the growth of all firms the same.
The premium for sustainable stocks (i.e., greenium) in our model arises for
a reason different from the standard mechanism in the literature (e.g., Heinkel,
Kraus, and Zechner 2001; Hong and Kacperczyk 2009). In these papers, a

Welfare Consequences of Sustainable Finance

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group of investors who are financially unconstrained have to be indifferent
between investing in sustainable firms or not in equilibrium at the margin.
Mandates force these unconstrained investors to take concentrated positions in
unsustainable firms. To the extent stocks are imperfect substitutes, for example,
because of idiosyncratic shocks, unconstrained investors will demand a higher
required rate of return for unsustainable firms. In contrast, our model does not
have idiosyncratic risk, and portfolio shares are fixed. The reason the mandate
has an effect in our model is that value-maximizing firms have to be indifferent
between being sustainable or not.
Second, we compare households’ welfare in a competitive-markets economy
augmented with welfare-maximizing mandates with that in the first-best
economy. Whereas the planner jointly chooses mitigation and productive
investments, firms in the market economy with welfare-maximizing mandates
choose productive investments taking as given the mitigation spending required
by the welfare-maximizing mandate path. The welfare-maximizing mandate
in general depends on the climate state, the productive capital stock and
the ratio of decarbonization-to-productive capital. Given a sufficiently large
fraction of aggregate wealth that is restricted to mandates, we solve for the
optimal required firm mitigation spending that maximizes welfare in the market
economy. There tends to be too much investment and too little consumption in
the welfare-maximizing mandated market economy compared to the first-best
economy.
We prove that incorporating another policy instrument, for example, an
investment tax, into the market economy with optimal mandates (discussed
above) can attain the first-best. Quantitatively, we show introducing the
welfare-maximizing mandate alone into the market economy well approximates the first-best outcomes. In other words, the optimal mandate can be a
useful tool to address the global warming externality.
Third, our model generates transitions to steady-state decarbonization-toproductive capital ratios that can be used to evaluate the optimality net-zero
targets proposed by policymakers. When the adjustment costs of productive
and decarbonization capital are close, the optimal path in the mandated
market economy implies a rapid transition to a high steady-state ratio of
decarbonization-to-productive capital stock, much in the way that policy
makers are hoping with 2030 or 2050 net-zero targets in the Paris agreement.
Even though decarbonization capital is entirely unproductive, its disasterrisk mitigation benefits are such that as the mandated market economy
decarbonizes, the aggregate risk of economic growth is reduced. Hence,
investment, growth, and household welfare increase over time as the economy
reaches steady state. Asset prices, including the stock-market risk premium
and the aggregate Tobin’s q, also favorably respond to the lower aggregate risk
resulting from the accumulation of decarbonization capital. Our model offers
a rationale for positive growth over the net-zero transition that does not require
assumptions that renewables are highly cost effective (see, e.g., the European

The Review of Financial Studies / v 36 n 12 2023

1. Model
1.1 Climate state
Consider the following climate-transition model. Let St denote the climate state
at time t. The economy starts from the good climate state (G) and stochastically
transitions to the bad state (B) at a stochastic rate of ζt > 0. Moreover, we
assume that this climate transition is permanent in that the B state is absorbing.
In both climate states, weather disaster shocks, for example, hurricanes and
wildfires, destroy capital too. But the good climate state (G) has less-frequent
weather disasters than does the bad state (B). We model these weather disaster
shocks and the climate state transition via jumps to be discussed in detail later.
Next, we introduce the production side of the economy.

1.2 Firm production and productive capital (K) accumulation
There is a continuum of firms endowed with the same production function and
capital accumulation technology. In both climate states (G and B), each firm’s
output at time t, Yt , is proportional to its contemporaneous productive capital
stock, Kt :
Yt = AKt ,

(1)

where A > 0 is a constant that defines productivity. This is a version of widely
used AK models in macroeconomics and finance. This simplifying assumption

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Union’s [2022] projections). But even modestly higher adjustment costs for
accumulating decarbonization capital result in a dramatically slower transition
to a much lower steady-state decarbonization-to-capital ratio.
Our paper differs from the two-sector model of Eberly and Wang (2009),
where investors’ preferences for portfolio diversification is the key force. Our
paper builds on Hong, Wang, and Yang (2022), who model the regional-level
mitigation of weather disasters, and the optimal capital tax to stimulate the
first-best level of flow spending for preparedness. Our paper contributes to
the emerging climate-finance literature on the role of the financial system
in addressing global warming (for an overview, see Hong, Karolyi, and
Scheinkman 2020). Bansal, Ochoa, and Kiku (2017) use a long-run risk model
to evaluate the impact of higher temperature on growth stocks. Barnett, Brock,
and Hansen (2020) provide an asset pricing framework to confront climate
model uncertainty. Engle et al. (2020) develop a method to hedge climate risks
through trading of stock portfolios. Piazessi, Papoutsi, and Schneider (2022)
develop a deterministic multisector growth model with climate externalities
and financial frictions to study the environmental impact of unconventional
monetary policy.

Welfare Consequences of Sustainable Finance

makes our model tractable and allows us to focus on the impact of the financial
investment mandate on equilibrium asset pricing and resource allocation.5

dKt = (It− ,Kt− )dt +σ Kt− dWt −(1−Z)Kt− dJt .

(2)

As in Lucas and Prescott (1971), Hayashi (1982), and Jermann (1998), we
assume that (I,K), the first term in (2), is homogeneous of degree one in
I and K, and thus
(I,K) = φ(i)K ,

(3)

where i = I /K is the investment-capital ratio and φ(·) is increasing and
concave. This specification captures the idea that changing capital stock rapidly
is more costly than changing it slowly. The installed capital earns rents in
equilibrium so that Tobin’s q, the ratio between the value and the replacement
cost of capital exceeds one. The second term captures continuous (Brownian
motion) shock to capital {Wt } (common to all firms) and the parameter σ is
the diffusion volatility. Next, we will introduce disaster shocks.
1.2.2 Weather disaster (jump) shocks. In both climate states (G and B), the
firm’s capital stock K is subject to an aggregate jump shock due to weather
disasters. We capture weather disaster shocks via the third term in (2), where
{Jt } is a (pure) jump process driving weather disaster arrivals with a climatestate-dependent arrival rate {λSt t } process.
An arriving jump (dJt = 1) permanently destroys a stochastic fraction (1−Z)
of the firm’s capital stock Kt− , as Z ∈ (0,1) is the recovery fraction. (If a shock
destroyed 15% of capital stock, for example, we would have Z = 0.85.) There is
no limit to the number of these weather disaster shocks. If a jump does not arrive
in state St , that is, dJt = 0, the third term disappears. Let (Z) and ξ (Z) denote
the cumulative distribution function (cdf) and probability density function (pdf)
of the recovery fraction, Z, conditional on a jump arrival, respectively. We
assume that the cdf (Z) and pdf ξ (Z) are time invariant. In a given climate
state St (B or G) at time t, we model the stochastic damage upon the arrival of
a weather disaster by assuming that the recovery fraction, Z ∈ (0,1), of capital
stock is governed by the following cdf (Barro and Jin 2011; Pindyck and Wang
2013):
(4)
(Z) = Z β ,
where β > 0 is a constant. To ensure that our model is well defined (and
economically relevant moments are finite), we require β > max{γ −1,0}. That
5 To ease the exposition, we assume that all firms start with the same initial capital stock level, K , although our
0

model can be generalized to allow for heterogeneous levels of initial K0 . We could also generalize our model by
introducing idiosyncratic shocks across firms. Our aggregation results would remain valid as long as firms can
also perfectly hedge idiosyncratic shocks at no cost.

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1.2.1 Investment. Let It denote a firm’s investment. Also in both B and G
climate states, the firm’s productive capital stock, Kt , evolves as

The Review of Financial Studies / v 36 n 12 2023

is, the damage caused by a weather disaster arrival follows a fat-tailed powerlaw function (Gabaix 2009).

Yt = AKt = It +CFt +Xt .

(5)

We use boldfaced notations for aggregate variables. Next, we introduce emissions, emission removals, and the dynamics of the aggregate decarbonization
capital stock N.
1.3 Aggregate emissions, emission removals, and decarbonization capital
stock N
We assume that aggregate emissions Et is proportional to the aggregate
productive capital stock Kt :
(6)
Et = eKt ,
where e > 0 is a constant. The aggregate capital stock Kt and emissions
Et equal the sum (integral)
 of each firm’s capital stock Kt and emissions
Et : Kt = Ktν dν and Et = Etν dν, respectively.6 That is, aggregate emissions
increase linearly with the size of the production sector of the economy, which
is measured by the aggregate capital stock K, or equivalently gross domestic
product (GDP) (AK). Similarly, we assume that the aggregate emission
removals Rt is proportional to the aggregate decarbonization capital stock Nt :
Rt = Nt ,

(7)

where > 0 is a constant. Both aggregate emissions Et and carbon removals
Rt are given by an “AK”-type of technology, as we can see from (6) and (7).
equals
Let Xt denote the aggregate mitigation spending (investment), which

the sum of mitigation spending contributions by all firms: Xt = Xtν dν. The
aggregate decarbonization capital stock N evolves as follows:
dNt
Nt−

= ω(Xt− /Nt− )dt +σ dWt −(1−Z)dJt .

(8)

The control Xt− /Nt− in (8) for N accumulation at the aggregate level is
analogous to the investment-capital ratio It− /Kt− in (2) for productive capital
(K) accumulation at the firm level. That is, absent jumps, ω(Xt− /Nt− ), the drift
6 We integrate capital stock and emission over a continuum of firms with respect to the measure ν . See Sun (2006)

for technical conditions under which we can construct the associated probability and agent measures that allow
one to invoke a law of large numbers.

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1.2.3 Firm investment, dividends, and mitigation spending (contribution).
At any time t, the firm uses its output AKt to finance investment It , pay
cash flows (dividends) CFt to shareholders, and make mitigation spending
Xt contributing to the aggregate decarbonization capital accumulation to be
described in detail soon. Therefore,

Welfare Consequences of Sustainable Finance

nt =

Nt
.
Kt

(9)

Using Ito’s lemma, we obtain the following dynamics for nt :
dnt
= [ω(xt− /nt− )−φ(it− )]dt .
nt−

(10)

Note that there is no uncertainty for the dynamics of nt in our model. This is
because productive and decarbonization capital stocks are subject to the same
jump-diffusion growth shocks.8 Next, we will introduce the climate tippingpoint and weather disaster arrival rates.
1.4 Tipping-point arrival and weather disaster arrival rates
Let Jt denote the climate tipping-point arrival process. Conditional on being
in the good climate state at time t, St = G, global warming increases the arrival
rate of the climate tipping point. As state B is assumed to be absorbing, there
are no further climate-state transitions once the economy is in state B. (For
notional convenience, we will sometimes write the arrival rate of the climate
tipping point as ζtSt with the understanding that ζtG > 0 and ζtB = 0.)
First, we assume that the tipping-point arrival rate ζtG is increasing in the
aggregate emissions Et and decreasing in the aggregate emissions removals
Rt . Similarly, we assume that the weather disaster arrival rates in both climate
states, λGt , and λB
t , are also increasing in the aggregate emissions Et and
decreasing in the aggregate emissions removals Rt . As Et = eKt and Rt = Nt
(see Equations (6) and (7)), we may write the three transition rates, (ζtG , λGt ,
and λB
t ), as functions that are increasing in Kt and decreasing in Nt .
7 In our model, whether firms do mitigation spending on their own (e.g., planting trees by themselves) or contribute

resources to the planner who plants trees on behalf of all firms, the solution is the same. This is because a firm’s
mitigation spending yields only public benefits and no firm-specific benefit. We choose to specify an aggregate
decarbonization capital accumulation process throughout our paper.
8 Note that n is continuous even when the climate state transitions from G to B.
t

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of dNt /Nt− , is analogous to φ(It− /Kt− ), the drift of dKt /Kt− . We assume that
ω(·) is increasing and concave as we do for φ(·). This specification captures
the idea that changing N rapidly is more costly than changing it slowly. As we
show later, the adjustment costs for Nt has first-order implications on welfare
implications and the transition path toward the net-zero target.7
Equation (8) implies that the growth rate for the decarbonization capital
stock N, dNt /Nt− , is subject to the same diffusion and jump shocks as the
growth rate of the aggregate productive capital stock K, dKt /Kt− . Recall that
the productive capital stock at the aggregate level follows the same process
as at the firm level: dKt /Kt− = dKt /Kt− path by path, for example, for each
realized jump and recovery fraction Z.
Let nt denote the aggregate decarbonization-productive capital ratio:

The Review of Financial Studies / v 36 n 12 2023

1.5 Sustainable investment mandate
The sustainable investment mandate requires the representative agent to
invest a constant fraction (α > 0) of the entire portfolio (aggregate wealth) in
sustainable firms, referred to as type-S firms, at all time t when allocating
assets.
On the supply side, a portfolio of S firms and a portfolio of U firms will
arise endogenously in equilibrium, which we refer to as the S portfolio and U
portfolio, respectively. For a firm to qualify to be type-S, it has to spend at least
Mt = mt Kt at all time t. That is, a firm at least spends mt for each unit of its
productive capital Kt on mitigation by contributing to the accumulation of the
aggregate decarbonization capital stock, which delays the tipping-point arrival
and reduces the weather disaster shock arrival rates. A firm is then qualified to
be included in the S-portfolio, if and only if its mitigation spending Xt satisfies
Xt ≥ Mt .

(11)

Otherwise, it is a type-U unsustainable firm.
The S and U portfolios include all the S and U firms, respectively. Let QSt
and QUt denote the aggregate market value of the S portfolio and of the U
9 To make the dependence of ζ St and λSt on n and S explicit, we write ζ St = ζ (n ; S ) and λSt = λ(n ; S ).
t
t
t t
t t
t
t
t
t

This homogeneity assumption is consistent with sustainable long-term balanced growth.

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We assume that the effects of Kt and Nt on the three transition rates (ζtG , λGt ,
G
G
B
and λB
t ) can be summarized via nt . That is, ζt , λt , and λt are all homogeneous
of degree zero in Kt and Nt . We thus write these rates as functions of the scaled
aggregate decarbonization stock nt = Nt /Kt : ζtG = ζ (nt ;G), λGt = λ(nt ;G), and
9
B
λB
t = λ(nt ;B). Recall ζt = ζ (nt ;B) = 0.
As decarbonization probabilistically delays the tipping point and reduces
the weather-disaster arrival rates, we assume ζ  (nt ;G) < 0, λ (nt ;G) < 0,
and λ (nt ;B) < 0. Additionally, we assume that the marginal benefits (e.g.,
decreasing the climate tipping-point arrival rate and reducing the frequencies
of weather disaster shocks) of accumulating decarbonization capital stock
decreases as nt increases: ζ  (nt ;G) > 0, λ (nt ;G) > 0, and λ (nt ;B) > 0. That
is, the absolute value for the derivative of the climate tipping-point arrival rate,
|ζ  (nt )|, decreases with nt . Similarly, the marginal effect (magnitude wise) of
N on the change of λSt decreases as N increases in that λ (nt ;St ) > 0.
Finally, to capture the idea that weather disasters are more frequent in the B
state than in the G state conditional on nt , we assume λt (nt ;G) < λt (nt ;B) for
all nt . We specify the functional forms for λt (nt ;G), λt (nt ;B), and ζ (nt ;G) in
Section 5.
As climate transition and weather disaster shocks are aggregate, how
much each individual firm spends on mitigation does not affect its own
payoff. Therefore, absent mandates or other incentive programs, firms have
no enticements to mitigate on their own in a competitive market economy.

Welfare Consequences of Sustainable Finance

portfolio at t, respectively. The total market capitalization of the economy, Qt ,
is given by Qt = QSt +QUt . In equilibrium, the investment mandate requires that
the total capital investment in the S portfolio, QSt , has to be at least an α fraction
of the total stock market capitalization Qt :
(12)

Next, we will turn to the demand side of the economy.
1.6 Dynamic consumption and asset allocation
The representative agent makes consumption, asset allocation, and risk
management decisions. We use individual and aggregate variables for the
agent interchangeably as we have a continuum of identical agents (with unit
measure). For example, the aggregate wealth, Wt , is equal to the representative
agent’s wealth, Wt , in equilibrium. Similarly, the aggregate consumption, Ct ,
is equal to the representative agent’s consumption, Ct .
The representative agent has the following investment opportunities: (a) the
S portfolio, which includes all the sustainable firms; (b) the U portfolio, which
includes all other firms that are unsustainable; and (c) the risk-free asset that
pays interest at a risk-free interest rate r f process determined in equilibrium.10
Preferences. We use the Duffie and Epstein (1992) continuous-time version
of the homothetic recursive preferences developed by Epstein and Zin (1989)
and Weil (1990), so that we may express the agent’s value-function process,
{Vt ;t ≥ 0}, as follows:
 ∞

f (Cs ,Vs )ds ,
(13)
Vt = Et
t

where f (C,V ) is known as the normalized aggregator given by
−1

f (C,V ) =

C 1−ψ −((1−γ )V )χ
ρ
.
1−ψ −1
((1−γ )V )χ−1

(14)

Here, ρ is the rate of time preference, ψ the elasticity of intertemporal
substitution (EIS), γ the coefficient of relative risk aversion, and we let χ =
(1−ψ −1 )/(1−γ ). Unlike expected utility, recursive preferences as defined by
(13) and (14) disentangle the coefficient of relative risk aversion from the
EIS. An important feature of these preferences is that the marginal benefit
−1
of consumption is fC = ρC −ψ /[(1−γ )V ]χ−1 , which depends on not only
current consumption but also (through the value function V ) the trajectory of
future consumption.

10 To be precise, as markets are dynamically spanned, the economy also has actuarially fair insurance claims for

each weather disaster arrival (with every possible recovery fraction Z ) and the insurance contracts contingent on
climate transition as well as diffusion shocks. But we suppress these zero-net-supply claims since they do not
change allocations in the economy as shown in Pindyck and Wang (2013) and Hong, Wang, and Yang (2022).

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QSt ≥ αQt .

The Review of Financial Studies / v 36 n 12 2023

1.7 Competitive equilibrium with mandates
Let Yt , Ct , It , and Xt denote aggregate output, consumption, investment,
and mitigation spending, respectively. Using an individual firm’s resource
constraint (5), and adding across all type-S and type-U firms, we obtain the
aggregate resource constraint in the economy:
Yt = Ct +It +Xt .

(15)

We define the competitive equilibrium subject to the investment mandate
introduced earlier as follows: (a) the representative agent dynamically chooses
consumption and asset allocation among the S portfolio, the U portfolio, and
the risk-free asset subject to the investment mandate; (b) each firm chooses its
status (S or U ) via mitigation spending and investment I to maximize its market
value; (c) all firms that choose sustainable investment policies are included in
the S portfolio and all remaining (unsustainable) firms are included in the U
portfolio; and (d) all markets clear.
The market-clearing conditions at each time t include (i) the representative
agent’s demand for the S portfolio equals the total supply by firms choosing to
be sustainable; (ii) the representative agent’s demand for the U portfolio equals
the total supply by firms choosing to be unsustainable; (iii) the net supply of the
risk-free asset is zero; and (iv) the goods market clears, that is, the aggregate
resource constraint given in (15) holds.
1.8 Comments on the model assumptions
We highlight three key sets of assumptions that have been made to gain
tractability.
1.8.1 Firm decarbonization technology. Following the carbon-externality
literature, we assume that it does not matter which firm does the cleanup
(Salanie 2000). In principle, we can allow firms to have different emission
11 If γ = ψ −1 so that χ = 1, the recursive utility (13) turns into the standard constant relative-risk aversion (CRRA)

expected utility, represented by the additively separable (normalized) aggregator:
f (C,V ) =

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−ρ V .
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This more flexible utility specification is widely used in asset pricing
and macroeconomics for at least two important reasons: (1) conceptually,
risk aversion is very distinct from the EIS, which this preference is able to
capture, and (2) a quantitative and empirical fit with various asset pricing facts
are infeasible with standard CRRA utility but attainable with this recursive
utility, as shown by Bansal and Yaron (2004) and the follow-up long-run risk
literature.11

Welfare Consequences of Sustainable Finance

2. Equilibrium Solution with Mandates
In this section, we obtain and analyze the equilibrium solution with the
sustainable finance mandate. A firm has to spend the minimal required mt
fraction of its productive capital stock Kt to qualify as a sustainable firm at time

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intensities. Any firm could be sustainable and spend on cleanup. For
decarbonization technologies, such as direct air capture (DAC), this seems a
good assumption since these DAC plants could be built by many firms in many
industries (e.g., DAC investments made by Microsoft). But other technologies
might be more efficient for firms in certain industries (e.g., dirty industries) to
execute. In this instance, the investment mandate would also naturally depend
on the types of industries that firms are in, among other factors.
1.8.2 Carbon cycle and damage function. We have made simplifying
assumptions regarding the carbon cycle and damage functions in our model.
Below we discuss these simplifications and some potential generalizations.
First, in reality, emissions increase the stock of carbon which affects
temperature with a delay. In our model the stock of carbon is assumed to
immediately influence the climate tipping-point and weather disaster arrivals.
We can generalize our model by allowing for a lag between the time at which
an investment in the decarbonization capital N is made and the time at which
this decarbonization investment has a risk-mitigating effect. Introducing this
time lag will introduce additional technical complications into our analysis.
This is because we need to keep track of both the decarbonization capital that
is mitigating the aggregate risk as well as other accumulated decarbonization
stock N that will mitigate in the future.
Second, the climate tipping-point arrival rate ζt depends on cumulative
emissions in the atmosphere. We assume that this cumulative emissions is
well approximated using n = N/K in our model. An alternative specification
is that the arrival rate ζt depends on (Kt −Nt ). Climate science does not offer
guidance on which approximation is more sensible per se. How important the
functional form assumption is also depends on the underlying decarbonization
technologies. But the latter level-based specification is not tractable in our
growth stationary economy where economic damages of disasters increase
with K.
1.8.3 Exposures of productive and decarbonization capital to disaster
shocks. Weather disaster shocks in our model are assumed to affect the
stochastic growth of productive and decarbonization capital equally. This is
a simplification since it makes the dynamics of nt deterministic. This property
allows us to conveniently analyze the transition dynamics toward net-zero
target over time. If we were to allow the stochastic growth of productive and
decarbonization capital stocks to respond differently to jump and diffusion
shocks, nt would be stochastic, but we still have the homogeneity property
and hence will not lose much tractability.

The Review of Financial Studies / v 36 n 12 2023

2.1 Firm optimization
A value-maximizing firm chooses whether to be sustainable or unsustainable
taking the sustainable investment mandate into account. First, we pin down
mitigation spending by both types of firms: XtU and XtS . As mitigation spending
has no direct benefit for the firm, if the firm chooses to be U , it will set XtU = 0
for all t. Moreover, even if a firm chooses to be an S firm, it has no incentive
to spend more than Mt , that is, (11) always binds for a type-S firm. That is, it
is optimal for a sustainable firm to set xtS as
XS
xtS = tS = m(nt ;St ),
(16)
Kt
where mt = m(nt ;St ) is the minimal threshold level of a firm’s Mt /Kt above
which it is qualified to be sustainable. By meeting this mandate, the firm lowers
its required rate of return.
Firms are indifferent between the two options in equilibrium. To solve for
the equilibrium, first, we solve the following problem for a type-j firm:
 ∞ 

t j
e− 0 r (nv ;Sv )dv CF j (nt ;St )dt .
(17)
max E
I j ,Xj

0

In Equation (17), r j (nt ;St ) is the expected cum-dividend return for a type-j
firm in equilibrium12 and CF j (nt ;St ) is type-j firm’s cash flow at t given by
CF S (nt ;St ) = AKtS −ItS (nt ;St )−XtS (nt ;St ) and
(18)
CF U (nt ;St ) = AKtU −ItU (nt ;St ).
Since the fraction of total wealth allocated to meet the sustainability
investment mandate is α ∈ (0,1], the scaled aggregate mitigation spending, xt ,
is given by
Xt αXtS
xt =
=
= αxtS = αm(nt ;St ).
(19)
Kt KtS
Exploiting our model’s homogeneity property, we conjecture and verify that
j
the equilibrium value of a type-j firm, Qt , at time t must satisfy:
j
j
Qt = q j (nt ;St )Kt ,
(20)
j
where q (nt ;St ) is Tobin’s q for a type j -firm as a function of nt and climate
state St .
12 Additionally, we impose the standard transversality condition for (17).

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t. While spending on aggregate risk mitigation yields no monetary payoff for
the firm, doing so allows it to be included in the S-portfolio. We work within the
set of mt specifications where we can write mt as a function of nt and climate
state St : mt = m(nt ;St ). We assume that a firm’s mitigation is observable and
contractible. We first solve for the equilibrium in Subsections 2.1-2.3 for a
given mt process and then solve for the welfare-maximizing mt in Section 2.4.
Finally, we comment on our model assumptions and equilibrium in Section 2.5.

Welfare Consequences of Sustainable Finance

Next, we consider the firm’s investment problem when it takes the sustainability mandate {mt = m(nt ;St ) : t ≥ 0} as given. The following HamiltonJacobi-Bellman (HJB) equation characterizes the firm’s value function in
climate state S:13
Ij

1
j
+ (σ K j )2 QKK (K j ,n;S)
2
+[ω(x(n;S)/n)−φ(i(n;S))]nQjn (K j ,n;S)
+λ(n;S)E Qj (ZK j ,n;S)−Qj (K j ,n;S)
+ζ (n;S)(Qj (K j ,n;S  )−Qj (K j ,n;S)),

(21)

where S = {G,B}, and S  denote the other state. For example, if S = G, then
S  = B.14
The left side of (21) is the (cum-dividend) expected return r j (n;S) times the
market value of type-j firm. The first term on the right side is the dividend (cash
flow) payment. The second and third terms are the capital accumulation and
diffusion volatility effects on the expected capital gains. The last two terms
capture the effects of weather disaster arrivals and the climate tipping point
arrival on the expected capital gains. The conditional expectation E[·] in (21)
operates with respect to the distribution of recovery fraction Z and CF j (n;S)
is the cash flow for a type-j firm in climate state S given by (18).
Let cf j (n;S) = CF j (n;S)/K j denote the scaled cash flow for a type-j firm.
j
j
By using our model’s homogeneity property, Qt = q j (nt ;St )Kt for S =
j
{G,B}, we obtain the following ODE for q (n;S), the Tobin’s q in the climate
state S:
r j (n;S)q j (n;S) =max cf j (n;S)+(φ(i j )−λ(n;S)(1−E(Z)))q j (n;S)
ij

+[ω(x(n;S)/n)−φ(i(n;S))]nqnj (n;S)
+ζ (n;S)(q j (n;S  )−q j (n;S)).

(22)

The investment FOCs for both S and U firms implied by (22) in both G and
B states are the following well known conditions in the q-theory literature:
1
.
(23)
q j (n;S) =  j
φ (i (n;S))

 u −  t r j (nv ;Sv )dv
− u r j (nv ;Sv )dv j
0
CF j (nt ; St )dt +e 0
Qu is a
0 e
martingale under the physical measure, where r j (n; S ) is the required rate of return that the firm takes as given.
The firm also takes the scaled aggregate decarbonization capital stock n, aggregate mitigation spending x(n; S ),
and aggregate investment i(n; S ) as given.

13 A type-j firm’s objective (17) implies that

14 Recall that ζ (n; B) = 0.

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j

r j (n;S)Qj (K j ,n;S) = max CF j (n;S)+(I j ,K j )QK (K j ,n;S)

The Review of Financial Studies / v 36 n 12 2023

g j (n;S) = φ(i j (n;S))−λ(n;S)(1−E(Z))−ζ (n;S)

q j (n;S)−q j (n;S  )
. (24)
q j (n;S)

The first term captures the investment effect, the second term describes the
weather disaster effect, and the last term gives the effect of the climate tippingpoint arrival on growth.
As x S (n;S) = m(n;S) and x U (n;S) = 0, we have cf S (n;S) = A−i S (n;S)−
m(n;S) for a type-S firm and cf U (n;S) = A−i U (n;S) for a type-U firm.
2.2 Representative agent’s optimization
To solve the portfolio-allocation problem, we first introduce the investment
opportunities.
j

2.2.1 Return dynamics of S and U portfolios. Let Qt denote the market
value of the type-j portfolio, which includes all type-j firms, where j =
j
{S,U }. Let Dt denote the dividends of the type-j portfolio. We will later
show that the equilibrium cum-dividend return for the type-j portfolio in state
S is
j

j

dQt +Dt− dt
j

Qt−

= r j (nt− ;S)dt +σ dWt −(1−Z)(dJt −λ(nt− ;S)dt)
qj (nt− ;S  )−qj (nt− ;S) 
d Jt −ζ (nt− ;S)dt .
qj (nt− ;S)
j

+

(25)

The diffusion volatility equals σ as in (2). The third term on the right side of
(25) captures the effect of disasters on return dynamics.
The fourth (last) term describes the effect of climate transition from the G
state to the absorbing B state.15 Upon the arrival of the tipping point (d Jt = 1),
the percentage change of the portfolio value equals the percentage change of
Tobin’s q caused by the climate state transition. This is because unlike the
weather disaster shock dJt , the climate state transition shock Jt does not
change Kj .

15 Note that the last term in (25) is zero in the B state.

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A type-j firm’s marginal benefit of investing equals its marginal q, q j (n;S),
multiplied by φ  (i j (n;S)). The investment FOC (23) states that this marginal
benefit, q j (n;S)φ  (i j (n;S)), equals one, the marginal cost of investing. The
homogeneity property implies that a firm’s marginal q is equal to its average q
(Hayashi 1982).
Let g j (n;S) denote a type-j firm’s expected growth rate including the effect
of jumps.
In state S, the expected growth rate is

Welfare Consequences of Sustainable Finance

2.2.2 Wealth dynamics. Let Wt denote the representative agent’s wealth. Let
HtS and HtU denote the dollar amount invested in the S and U portfolios,
respectively. Let Ht denote the agent’s wealth allocated to sustainable and
unsustainable firm equity at time t. That is, Ht = HtS +HtU . The dollar amount
invested in the risk-free asset is then given by (Wt −Ht ).
In state S, the agent’s wealth evolves as
S
U
dWt = r f (nt− ;S)(Wt− −Ht− )−Ct− dt + r S (nt− ;S)Ht−
dt
+r U (nt− ;S)Ht−

q(nt− ;S  )−q(nt− ;S)
+σ Ht− dWt − (1−Z)(dJt −λ(nt− ;S)dt)−
q(nt− ;S)

(26)
× d Jt −ζ (nt− ;S)dt Ht− .

The first term in (26) is the interest income from savings in the riskfree asset minus consumption. The second term is the expected capital gains
from investing in the S and U portfolios. Note that the expected returns are
different: r S (n;S) and r U (n;S) for the S and U portfolios, respectively. The
third and fourth terms contain the diffusion and two jump martingales for
the stock market portfolio. This is because the stochastic components of the
returns (diffusion and jumps) for the S and U portfolios are identical path by
path.16
In equilibrium, the dollar allocation to the S portfolio (HtS ), as a fraction
of the agent’s total dollar allocations to the risky assets (Ht = HtS +HtU ),
πtS = HtS /Ht = HtS /Wt , equals the fraction of aggregate wealth mandated for
investment in the S portfolio: π S = α. The remaining 1−π S fraction of Ht
is allocated to the U portfolio. That is, we have HtS = αWt = QSt = αQt , HtU =
(1−α)Wt = QUt = (1−α)Qt , and Wt = Qt = QSt +QUt .
Let Vt = V (Wt ,nt ;St ) denote the agent’s value function. The HJB equation
for the value function in state S, V (W,n;S), satisfies (see Appendix A.1 for

16 Here, to ease the exposition, we use the equilibrium result that all firms have the same average q in equilibrium,

which we show in Proposition 1 in the Section 2.3.

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In addition to the diffusion volatility term, the two jump terms are also
martingales. This is why the first term on the right side of (25), r j (nt− ;S),
is the expected cum-dividend return. Because all firms have the same
Tobin’s q, the S and the U portfolios have the same shock processes and
the only difference between the two portfolio is the expected return term:
r j (nt− ;S) for the type-j portfolio. We verify these equilibrium results in
Appendix A.

The Review of Financial Studies / v 36 n 12 2023

details):
0 =max f (C,V ;S)+ r S (n;S)α +r U (n;S)(1−α) W −C
C

+ζ (n;S)

q(n;S)−q(n;S  )
W VW +[ω(x(n;S)/n)−φ(i(n;S))]nVn
q(n;S)

σ 2 W 2 VW W
+λ(n;S)E[V (ZW,n;S)−V (W,n;S)]
2
 


q(n;S  )

+ζ (n;S) V
W,n;S −V (W,n;S) .
q(n;S)
+

(27)

The FOC for consumption C in both climate states is given by
fC (C,V ;S) = VW (W,n;S).

(28)

This is the standard consumption FOC for recursive utility. We can show that
the value function V (W,n;S) is homogeneous with degree 1−γ in W :
V (W,n;S) =

1
(u(n;S)W )1−γ ,
1−γ

(29)

where u(n;S) is a welfare measure proportional to the representative agent’s
equilibrium certainty equivalent wealth to be determined.
Substituting (29) into the FOC (28) yields the following linear consumption
rule with a time-varying MPC that depends on n and S:17
C(W,n;S) = ρ ψ u(n;S)1−ψ W .

(30)

Substituting (30) and (29) into the HJB equation (27), we obtain the following
ODE for u(n;S) in state S:
0=

ρ ψ u(n;S)1−ψ −ρ
+αr S (n;S)+(1−α)r U (n;S)−ρ ψ u(n;S)1−ψ
1−ψ −1
+ λ(n;S)(1−E(Z))+ ω(x(n;S  )/n)−φ(i(n;S  ))
−

nu (n;S)
u(n;S)

γ σ 2 λ(n;S)
+
E(Z 1−γ )−1
2
1−γ

q(n;S)−q(n;S  ) ζ (n;S)
+
+ ζ (n;S)
q(n;S)
1−γ



u(n;S  )q(n;S  )
u(n;S)q(n;S)

1−γ


−1 . (31)

17 Since our model is a representative-agent framework, the aggregate financial wealth, W , is equal to W for all
t
t

t . We thus simply use these two interchangeably. See Pindyck and Wang (2013) for a similar consumption rule
in their model.

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+λ(n;S)(1−E(Z))W ]VW

Welfare Consequences of Sustainable Finance

Note that the last two terms are only present in state G, but not state B. The
reason is that a stochastic transition only occurs from state G to state B, as B
is an absorbing state.18

Proposition 1. For a given scaled aggregate decarbonization capital stock n
and the climate state S, all firms have the same average Tobin’s q, which in
equilibrium is also the average Tobin’s q for the aggregate economy (q):
q S (n;S) = q U (n;S) = q(n;S).

(32)

The investment-capital ratio for all firms is the same and equal to the aggregate
investment-capital ratio i(n;S):
i S (n;S) = i U (n;S) = i(n;S).

(33)

1
The investment-q equation also holds at the aggregate: q(n;S) = φ  (i(n;S))
. The
cash flow wedge between a U and an S firm equals the firm’s mandated
mitigation spending m(n;S):

cf U (n;S)−cf S (n;S) = m(n;S),

(34)

where cf U (n;S) = A−i(n;S) is the scaled cash flow for a U firm.
As a firm can choose to be either sustainable or not, it must be indifferent
between the two options at all time. Hence, all firms have the same average
Tobin’s q. Equations (23) and (32) imply that all firms must also have the same
investment-capital ratio.
2.3.1 Cash flow wedge and required rate of return wedge. Importantly,
U firms generate more free cash flows and hence pay more dividends to
shareholders. How can the two types of firms have the same market valuation
(Tobin’s q) when one type pays more dividends than the other? This is because
U firms that pay more dividends also have to compensate investors with higher
expected rates of returns than S firms. Next, we summarize the required rate
of return wedge between S and U firms.

18 We first solve the ODE for climate state B and then solve the ODE for climate state G using the equilibrium

objects in state B.

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2.3 Market equilibrium
f
The equilibrium risk-free rate (rt ), the expected returns for the S and U
S
U
portfolios (rt and rt ), and average Tobin’s q (qt ) for all firms are functions
of nt given the climate state St . For brevity, and when doing so will not cause
confusion, we suppress the dependence on the climate state S.
Proposition 1 summarizes equilibrium outcomes for S versus U firms.

The Review of Financial Studies / v 36 n 12 2023

That is, by being sustainable, a firm lowers its required rate of return from
r U (n;S) to r S (n;S) by m(n;S)
. This is one of the key predictions of our model.
q(n;S)
2.3.2 Scaled aggregate mitigation, investment, and consumption. The
next proposition summarizes the results for x(n;S), i(n;S), and c(n;S).
Proposition 3. The relation between the firm-level (scaled) mitigation
spending m(n;S) and the aggregate (scaled) mitigation spending x(n;S) =
X(n;S)/K is given by:19
x(n;S)
≥ x(n;S).
(36)
m(n;S) =
α
The aggregate investment-capital ratio i(n;S) satisfies
(A−i(n;S)−x(n;S))φ  (i(n;S))−ρ
0 =
+φ(i(n;S))
1−ψ −1
γ σ 2 λ(n;S)
+
E(Z 1−γ )−1 +[ω(x/n)−φ(i(n;S))]
2
1−γ


1 ni (n;S)+nx (n;S)
ψ nq (n;S)
−
×
1−ψ q(n;S)
1−ψ A−i(n;S)−x(n;S)
⎤
⎡
 1−γ

ζ (n;S) ⎣ (A−i(n;S  )−x(n;S  ))q(n;S)ψ 1−ψ
+
−1⎦ . (37)
1−γ
(A−i(n;S)−x(n;S))q(n;S  )ψ
−

The aggregate (scaled) consumption c(n;S) is equal to the aggregate (scaled)
dividend cf(n;S):
c(n;S) = cf(n;S) = A−i(n;S)−x(n;S).

(38)

Since each S firm spends m(nt ;St )KtS units on mitigation and all firms are
the same, the mitigation spending mandate for a firm, m(n;S), is 1/α times
the aggregate scaled mitigation, x(n;S), where α is the fraction of S firms in
equilibrium (see Equation (36)). The last term in (37) captures the effect of
climate-state transition on the aggregate investment ratio i(n;S). The aggregate
consumption equals the aggregate dividend, which is the residual cash flows
from operations after we subtract the aggregate investment and mitigation
spending.
19 This is the case provided that the firm-level mitigation spending is feasible in that m(n; S ) can be funded.

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Proposition 2. Given that the sustainable firm spends m(n;S) for each unit of
its productive capital on mitigation, the required rate of return wedge between
a U and an S firm is given by
m(n;S)
.
(35)
r U (n;S)−r S (n;S) =
q(n;S)

Welfare Consequences of Sustainable Finance

2.3.3 Aggregate average Tobin’s q, q(n;S), and asset pricing implications.
In the next proposition, we summarize the key predictions for the asset market
in the economy.

q(n;S) =

1
φ  (i(n;S))

.

(39)

The aggregate stock-market risk premium in state S, r M (n;S)−r f (n;S), is
given by
r M (n;S)−r f (n;S) = γ σ 2 +λ(n;S)E (1−Z)(Z −γ −1)
q(n;S)−q(n;S  )
+ ζ (n;S)
q(n;S)



q(n;S  )
q(n;S)

−γ


−1 .
(40)

The equilibrium interest rate in state S, r f (n;S), is given by
nq (n;S)
c(n;S)
+φ(i(n;S))−γ σ 2 +[ω(x(n;S)/n)−φ(i(n;S))]
q(n;S)
q(n;S)


q(n;S)−q(n;S  ) q(n;S  ) −γ
.
−λ(n;S)E (1−Z)Z −γ −ζ (n;S)
q(n;S)
q(n;S)
(41)

r f (n;S) =

While the Tobin’s q result for the aggregate economy is similar to the
standard FOC for corporate investment as in the q-theory literature, this result
in our model is an outcome of both individual firm’s optimization and market
clearing. The equilibrium market risk premium and interest rate formulas
generalize those in Pindyck and Wang (2013) and Hong, Wang, and Yang
(2022) by incorporating the effect of decarbonization capital stock and the
climate transition risk. The first term on the right side of (40) is the standard
diffusion shock contribution to the equity risk premium. The second term is
the weather-disaster-shock contribution to the equity risk premium. The third
term, which only exists in state G, is the risk premium due to the stochastic
tipping-point arrival.
Similarly, the last two terms on the right side of (41) for the risk-free rate
r f (n;S) capture the effects of weather-disaster and climate-transition shocks
on r f (n;S). The fourth term in (41) captures the effect of decarbonization
capital accumulation and the first three terms are the standard terms (because of
dividends, productive capital accumulation, and diffusion shocks) on r f (n;S)
as in Pindyck and Wang (2013) and Hong, Wang, and Yang (2022).

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Proposition 4. Tobin’s q for the aggregate economy, q(n;S), and the
aggregate investment, i(n;S), satisfy the same equation as the investment-q
relation at the firm level:

The Review of Financial Studies / v 36 n 12 2023

J (K,N;S) = V (W,n;S) =

1
(b(n;S)K)1−γ ,
1−γ

(42)

where b(n;S) is a welfare measure given by
b(n;S) = u(n;S)×q(n;S).

(43)

For brevity, we suppress S whenever doing so causes no confusion.
Equation (43) follows from the equilibrium result that W = q(n;S)K as
all households’ wealth is in the stock market, which is valued at q(n;S)K.
Substituting W = q(n;S)K into the agent’s value function V (W,n;S) given in
(29) for the market economy yields J (K,N;S) given in (42) and (43). Note that
b(n;S) equals the product of u(n;S) appearing in the agent’s objective (29)
and the equilibrium (aggregate) Tobin’s q, q(n;S). That is, b(n;S) captures
information from both the agent’s and the representative firm’s optimization
problems. The function b(n;S) can be naturally interpreted as a welfare
measure proportional to certainty equivalent wealth (scaled by the size of the
economy K).
2.4.1 Differential equations and FOCs for states G and B. Using the
optimal consumption rule (30), the investment FOC (39), and the resource
constraint c(n;S) = A−i(n;S)−x(n;S), we obtain the following equilibrium
condition:
 −1

A−i(n;S)−x(n;S) −ψ
= φ  (i(n;S))b(n;S),
(44)
ρ
b(n;S)
which reflects information from both the firm’s and the agent’s optimization
decisions. In Appendix A, we show that b(n;S) = u(n;S)×q(n;S) also satisfies

20 Broadly speaking, our mandate choice is related to the optimal fiscal and monetary policy literature (e.g., Lucas

and Stokey 1983) in macroeconomics. See Ljungqvist and Sargent (2018) for a textbook treatment.

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2.4 Market economy with the welfare-maximizing mandate
For a given level of α, we endogenize the qualification standard, characterized
by the mitigation threshold Mt = m(nt ;St )Kt , for a firm to be sustainable. To be
precise, at time 0, the planner announces the criterion {Mt ; t ≥ 0} and commits
to the policy with the goal of maximizing the representative agent’s utility
given in (13). The representative agent and firms optimize taking the planner’s
mandate as given.20
Consider the agent’s optimization problem. First, the homogeneity property
of our model implies that the agent’s value function is homogeneous of degree
1−γ in wealth W . Second, in equilibrium the agent’s wealth is all invested in
the stock market and therefore W is proportional to the aggregate capital stock
K. Taking these two observations together, we may write the agent’s value
function as follows:

Welfare Consequences of Sustainable Finance

the following ordinary differential equation (ODE):


 −1
A−i(n;S)−x(n;S) 1−ψ
ρ
0=
−1
1−ψ −1
b(n;S)

(45)

This ODE for b(n;S) summarizes information about both u(n;S) and q(n;S).
Having obtained the agent’s value function and optimal policies, we turn to the
planner’s problem of choosing x to maximize J (K,N;S). It is equivalent to
maximize b(n;S) given in (45), which yields:
 −1

A−i(n;S)−x(n;S) −ψ
= ω (x/n)b (n;S).
(46)
ρ
b(n;S)
2.4.2 Steady States for G and B. Let nss (S) denote the steady-state value of
n in state S, where the drift of n is zero. Therefore, by setting (10) to zero, we
obtain the following relation linking aggregate investment iss (S) and mitigation
spending xss (S):
ω(xss (S)/nss (S))−φ(iss (S)) = 0.

(47)

Additionally, substituting the zero-drift condition (47) into (45), we obtain the
following equation at the steady state:


 −1
A−iss (S)−xss (S) 1−ψ
ρ
γσ2
ss
0 =
−1
+φ(i
(S))−
1−ψ −1
b(nss (S);S)
2



b(nss (S);S  ) 1−γ
λ(nss (S);S)
ζ (nss (S);S)
1−γ
E(Z )−1 +
+
−1 .
1−γ
1−γ
b(nss (S);S)
(48)
2.4.3 Solution summary. At the steady state at which dnt = 0, the scaled
decarbonization capital stock nss (S), iss (S), xss (S), and the welfare measure
b(nss (S);S) jointly solve the four pairs of equations (for G and B): the FOC
(46) for xss (S), the FOC (44) for iss (S), the zero-drift condition (47) for nss (S),
and (48) for b(nss ;S).21
21 We conjecture and verify the steady-state solution as follows. First, we hypothetically fix the steady-state value
of nss in state S at 
nss . Solving the three-equation system given by (44), the zero-drift condition (47), and (48),
we obtain a triple, which we write as (b(
nss ),
iss ,
xss ). We perform this calculation for a range of positive values
for 
nss ). Among all these triples, only one triple
nss (from zero to a large number) and then obtain the implied b (
satisfies (46). This pins down the steady-state values of nss (S ), iss (S ), xss (S ), and b(nss (S ); S ).

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nb (n;S)
+φ(i(n;S))
b(n;S)



γ σ 2 λ(n;S)
b(n;S  ) 1−γ
ζ (n;S)
1−γ
−
+
E(Z )−1 +
−1 .
2
1−γ
1−γ
b(n;S)
+ [ω(x(n;S)/n)−φ(i(n;S))]

The Review of Financial Studies / v 36 n 12 2023

2.5 Comments on a competitive market economy with mandates
2.5.1 Relation between α and firm qualification standards m. It is worth
highlighting a few key properties of our welfare-maximizing mandate. In our
model, the parameter α is given. Provided that α is large enough so that a firm
choosing to be sustainable can afford spending m = x/α per unit of its capital
stock on mitigation spending, the equilibrium aggregate mitigation spending x
of the market economy with optimal mandates can be implemented. Note that
the welfare-maximizing mandate, or equivalently the qualification standard for
firms to be sustainable, adjusts: when α is larger, the qualification standards
m = x/α for each firm become lower since more firms are sustainable. This
is possible because, given the assumptions about decarbonization technology,
it is irrelevant which firms, or how many, invest in decarbonization. That is,
it is sufficient to have a set of firms doing all of the decarbonization capital
investments, as long as the sum of their contributions allow the economy to
reach the aggregate Xt target we set. Put differently, our market economy with
an optimal mandate only pins down xt or equivalently, the product of α and
firm-level mitigation spending m. Additional information would be needed to
pin down α and m separately. For instance, if we knew in the data what m was,
we could maximize welfare by choosing α. In Section 5.3, we discuss these
issues in detail and solve for the model using this alternative setup.
2.5.2 Sustainable finance tax: Mandated market economy with α = 1.
What if the investment mandate requires all investors to be sustainable: α = 1?
This is in effect a sustainable finance tax where firms have no choice but to be
sustainable. Our welfare-maximizing economy yields the same outcomes as an
economy with capital (or equivalently sales) taxation with probability one. Let
τt denote the tax rate at which the government levies on each firm’s capital or
equivalently sales as Y = AK and A is a constant.
We define the competitive equilibrium with sustainable-finance taxation as
follows: (1) the representative agent dynamically chooses consumption and
asset allocation among the U portfolio, S portfolio, and the risk-free asset;
(2) each firm chooses its investment policy I to maximize its market value by
solving (17) where the firm’s cash flow at t, CF (nt ;S), is given by CF (nt ;S) =
AKt −It (nt ;S)−τt Kt ; and (3) all markets clear.

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For the transition dynamics, the scaled mitigation spending xt , the
investment-capital ratio it , and the welfare measure bt are all functions of
the scaled decarbonization capital stock nt and the climate state St . We fully
characterize the solution for the transition dynamics as follows. The functions
x(n;S), i(n;S), and b(n;S) for both G and B states jointly solve the ODE
system of the following three pairs of equations: the FOC (44) for i = i(n;S), the
FOC (46) for x = x(n;S), and the ODE (45) for b(n;S) subject to the boundary
conditions at the steady state summarized above.

Welfare Consequences of Sustainable Finance

The government sets the tax rate for capital stock as follows:
τt = τ (nt ;St ) = x(nt ;St ).

(49)

2.5.3 Heterogenous-agents model: Sustainable versus unsustainable
investors. We may also equivalently interpret our representative-agent model
(with portfolio restrictions) as a model with heterogeneous agents in which
some investors have sustainability investment mandates (e.g., some large
asset managers and sovereign wealth funds) and others face no sustainability
mandates nor preferences for being sustainable.
Specifically, consider a model with two types of investors: S investors whose
wealth constitutes an α fraction of the economy-wide total wealth and U
investors who hold the remaining wealth in the economy. Importantly, the U
investors are not allowed to short sale stocks issued by S firms.23
Since S investors are mandated to hold S stocks, they hold the entire S
portfolio. Even though S firms pay fewer dividends than U firms under all
circumstances, the valuation of the two types of firms are the same because
U investors cannot make arbitrage profits as they are unable to short S
stocks. We can also show that the equilibrium resource allocation and asset
prices in this heterogeneous-agents model are the same as in our (baseline)
representative-agent model.
Despite the difference in the expected return between unsustainable and
sustainable firms, investors in unsustainable firms would not dominate the
economy in the long run because Tobin’s q for unsustainable and sustainable

22 See Chamley (1986) and Judd (1986) for seminal contributions.
23 In our heterogeneous-agents model, we need to impose the short-sale constraints for the S firms’ equity.

Otherwise, there is no equilibrium. This is because investor can pocket the profits by taking a long position
in the U firm and a short position in the S firm. This is a textbook arbitrage example as investors with this
position take no risk at all but make sure profits, as S and U firms are driven by identical shocks path and path,
the prices for the two types of firms are the same, but the dividends of U firms strictly dominate the dividends
of S firms.

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As a result, this economy attains the same resource allocation as the welfaremaximizing economy with investment mandate α = 1. The intuition is as
follows. Because taxes are mandatory for all firms, using taxation, the
government effectively makes all firms “sustainable.” Since the government
is benevolent maximizing the representative agent’s welfare, it simply sets the
sustainable-finance tax rate τ (n;S) to the same aggregate mitigation spending
x(n;S) as in the economy with the socially optimal investment mandate.
While taxation typically distorts decisions and hence is inefficient,22 taxation
proceeds in our model allow the government to fund the accumulation
of decarbonization capital, substantially reducing the weather-disaster and
climate tipping-point arrival rates so that the equilibrium resource allocation
with taxation is much closer to the first-best solution, which we will later show.

The Review of Financial Studies / v 36 n 12 2023

3. First-Best Solution
In this section, we summarize the first-best solution where the planner chooses
aggregate C, I, and X to maximize the representative agent’s utility defined in
(13)-(14). Using the homogeneity property, we work with scaled variables at
the aggregate level, it = It /Kt , xt = Xt /Kt , and ct = Ct /Kt . In Appendix B, we
show that x(n;S) and i(n;S) for both climate states (S = G,B) satisfy the
following simplified FOCs:


A−i(n;S)−x(n;S)
ρ
b(n;S)

ρ

−ψ −1

+φ  (i(n;S))nb (n;S) = φ  (i(n;S))b(n;S)

A−i(n;S)−x(n;S)
b(n;S)

−ψ −1

(50)
= ω (x(n;S)/n)b (n;S) .

(51)

The welfare measure (proportional to certainty equivalent wealth) in state S,
b(n;S), solves the following ODE:


 −1
A−i(n;S)−x(n;S) 1−ψ
ρ
−1
0=
1−ψ −1
b(n;S)
nb (n;S)
+φ(i(n;S))
b(n;S)



γ σ 2 λ(n;S)
b(n;S  ) 1−γ
ζ (n;S)
1−γ
−
+
E(Z )−1 +
−1 .
2
1−γ
1−γ
b(n;S)
+[ω(x(n;S)/n)−φ(i(n;S))]

(52)

Because state B is absorbing, we first solve the triple, b(n;B), i(n;B), and
x(n;B), for state B by using (50), (51), and (52). Then, we solve the triple,
b(n;G), i(n;G), and x(n;G), for state G by using (50), (51), (52), and the b(n;B)
solution obtained earlier.
At the first-best steady state nFB (S) for both G and B states, we have
ω(xFB (S)/nFB (S))−φ(iFB (S)) = 0.

(53)

Moreover, if ω(·) = φ(·), that is, the investment efficiency functions for the two
types of capital stocks are the same, the investment-capital ratio for K equals

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firms are the same. There are no feasible gains from trade, and unsustainable
investors cannot make arbitrage profits given the short-sales constraint.
Our no-trade and equilibrium pricing reasoning is similar to that in the
equilibrium asset pricing model with agency conflicts (between the controlling
and outside minority shareholders) in Albuquerque and Wang (2008). Note that
the homogeneity property (in our setting with Epstein-Zin utility and geometric
processes) is key for the no-trade result.

Welfare Consequences of Sustainable Finance

γ σ 2 λ(nFB (S);S)
+
E(Z 1−γ )−1
2
1−γ


1−γ
b(nFB (S);S  )
ζ (nFB (S);S)
+
−1 .
1−γ
b(nFB (S);S)
−

(54)

Solution Summary. At the first-best steady state at which dnt = 0, the scaled
decarbonization capital stock nFB (S), iFB (S), xFB (S), and the welfare measure
b(nFB (S);S) jointly solve the four pairs of equations (for states G and B): the
FOC (51) for xFB (S), the FOC (50) for iFB (S), the zero-drift condition (53)
for nFB (S), and (54) for b(nFB ;S).
For the transition dynamics, the scaled mitigation spending xt , the
investment-capital ratio it , and the welfare measure bt are all functions of
the scaled decarbonization capital stock nt and the climate state St . We fully
characterize the solution for the transition dynamics as follows. The xt =
x(n;S), it = i(n;S), and b(n;S) processes jointly solve the ODE system of the
following three pairs of equations: the FOC (50) for i(n;S), the FOC (51) for
x(n;S), and the ODE (52) for b(n;S) for the two states (G and B) subject to the
boundary conditions (for nFB (B) and nFB (G)) at the steady state summarized
above.
4. Comparing the Welfare-Maximizing Mandate Economy to the First-Best
We proceed in two steps in this section. First, we show in Section 4.1 why
the market economy with the welfare-maximizing mandate cannot attain the
first-best outcome. Then, we show how the planner can attain the first-best
outcome by introducing an investment tax into the market economy with
the welfare-maximizing mandate in Section 4.2. The key insight is that by
optimally designing the sustainability investment mandate and setting taxes
on the deviation of corporate investment (from the average level), the planner
can attain the first-best by ensuring that the aggregate decarbonization capital
accumulation stays on the socially efficient path at all time.
4.1 A market economy with the welfare-maximizing mandate does not
attain the first-best
As no private agent has incentives to spend resources to accumulate the
decarbonization capital stock, our market economy is Pareto inefficient.
Although using the optimal investment mandate as a function of nt , xt =

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that for decarbonization capital N at nFB (S). Substituting (53) into (52) yields
the following steady-state condition in S:
⎤
⎡

1−ψ −1
FB
FB
A−i
(S)−x
(S)
ρ
⎣
−1⎦ +φ(iFB (S))
0=
1−ψ −1
b(nFB (S);S)

The Review of Financial Studies / v 36 n 12 2023

4.1.1 Investment distortions. By comparing the solution for the mandated
market economy given in (44)-(46) with the solution for the planner’s economy
given in (50)-(52), we see that the different resource allocations in the two
economies arise from different investment (I) functions. Specifically, the
i(n;S) equation (44) for the mandated market economy is different from the
i(n;S) Equation (50) in the first-best economy. Why does this difference exist
given optimal investment mandates in the market economy? We answer this
question in two steps.
First, consider the planner’s problem. Increasing investment I has two
effects at the aggregate level: (1) a direct effect of reducing the resources
for the representative household’s consumption as I crowds out C = Y−I−X,
captured by the first term on the left side of (50); and (2) an indirect effect
of decreasing the scaled aggregate decarbonization capital stock, n = N/K, in
the future as the firm’s future K is higher due to current investment. The latter
effect is captured by the second term on the left side of (50).
In contrast, firms in the mandated market economy do not take the indirect
long-term effect of investment on future n into account. Indeed, this second
term on the left side of (50) is absent in the investment equation (44) in the
mandated market economy.
The indirect long-run effect of investment on n in the planner’s economy
makes investment more costly than in the mandated market economy, ceteris
paribus. By comparing (44) and (50), we can conclude that i(nt ;St ) in the firstbest economy is lower than in the mandated market economy.25
24 Taking the optimal tax as given, the representative agent’s and the firm’s own incentives give rise to the first-best

trade-off between consumption and investment in the marketplace. This is the main argument underpinning the
calculation for the social cost of carbon in the climate economics literature.
25 We use the property b (n; S ) > 0, the investment optimality (FOCs), and the concavity of φ(·) (equivalently

convex adjustment costs).

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x(nt ;S), improves welfare, the planner cannot attain the first-best by solely
relying on the optimal mandate. Why? First recall that in a static economy
with one source of market failure, the planner can attain the first-best by
imposing the optimal Pigouvian tax to fund the first-best mitigation spending
(or equivalently decarbonization capital stock). This is because the private
sectors’ incentives are fully aligned with the planner’s once the optimal
Pigouvian tax is chosen in a static setting.24
However, this simple one-instrument-for-one-market-failure argument in a
static setting is invalid in our dynamic model. This is because the planner needs
at all time t and for all contingencies, which
to choose the socially optimal XFB
t
is an infinite dimensional problem.
A priori, there is no reason the optimal sustainability investment mandate
xt = x(nt ;S) in a dynamic setting allows the planner to attain the first-best. Next,
we will lay out the specific differences between the mandated market economy
and the planner’s first-best economy.

Welfare Consequences of Sustainable Finance

4.2 Restoring the first-best
To achieve the first-best in the market economy of our model, it is necessary and
sufficient that at all t and for all nt and St the following two conditions hold:
(a.) each firm chooses the first-best investment policy at all time and (b.) the
society as a whole collects resources to fund the first-best aggregate mitigation
spending.
To ease the exposition, we first show how to attain the first-best by properly
using the following two state-contingent instruments: (1) taxing all firms at the
rate of τt = xt introduced in Section 2.5 for each unit of capital and (2) taxing
a firm’s investment if its investment-capital ratio it exceeds the economy-wide
it .
Then, we can conclude that the first-best outcome also can be attained by
using a combination of the sustainability mandate mt = xt /α and a tax on the
wedge between a firm’s investment and the economy-wide, it . This follows
from our result on the equivalence between taxing a firm’s capital at the rate of
aggregate mitigation spending xt and using a qualification standard mt = xt /α
for firms to be sustainable.26
The capital tax instrument is to fund the first-best mitigation spending Xt .
The second instrument eliminates firms’ incentives to over-invest in their own
capital stocks so that the aggregate productive capital accumulation K and
decarbonization N follow the first-best trajectories. To achieve this goal, we
j
tax firm j at the rate of 
τ j (nt ;St )Kt , where

τ j (n;S) = φ(i j )−φ(i(n;S)) q(n;S)

nb (n;S)
.
b(n;S)

(55)

In (55), i(n;S) and q(n;S) are the equilibrium aggregate investment-capital
ratio i and average q in state S, respectively, and b(n;S) = u(n;S)×q(n;S)
26 This equivalence result holds provided that α is large enough so that m = x/α is feasible at the firm level given

its resource constraint (as discussed in Section 2.5).

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In sum, firms have incentives to spend more on investment in a market
economy (even with optimal mandates) than socially desirable. That is, our
mandated economy still features over-investment compared with the first-best.
This is because the planner takes both direct and indirects costs of investing
into account while firms in (mandated) market economies only take the direct
effect of investing on n into account.
With both (direct and indirect) effects of a firm’s investment on equilibrium
resource allocations, we at least need two instruments to attain the first-best
outcome. Next, we show that two optimally chosen instruments are sufficient
to attain the first-best: one to collect proceeds from investors to fund socially
desirable first-best aggregate mitigation spending and the other for the society
to eliminate firms’ incentives to over-accumulate capital, which in turn implies
that the society can ensure that the nt process follows the first-best trajectory.

The Review of Financial Studies / v 36 n 12 2023

τ j (n;S)
r j (n;S)q j (n;S) =max cf j (n;S)−
ij

+(φ(i j )−λ(n;S)(1−E(Z)))q j (n;S)
+[ω(x(n;S)/n)−φ(i(n;S))]nqnj (n;S)
+ζ (n;S)(q j (n;S  )−q j (n;S)),

(56)

where 
τ j (n;S) is given in (55).
Importantly, using (55) for 
τ j (n;S), we obtain the following investment
FOC for firm j :


nb (n;S)
 j
j
.
(57)
1 = φ (i ) q −q(n;S)
b(n;S)
Then using the equilibrium results i U = i S = i and q U = q S = q, we obtain the
following equation for the aggregate investment-capital ratio i:


A−i(n;S)−x(n;S)
ρ
b(n;S)

−ψ −1

+φ  (i(n;S))nb (n;S) = φ  (i(n;S))b(n;S), (58)

which is the same as the FOC (50) in the first-best economy. The second term
on the left side of (58) arises from the formula for the tax rate 
τ j (n;S), which
j
depends on the investment wedge φ(i )−φ(i(n;S)) . This investment wedge
tax allows us to attain the first-best outcome. For brevity, we relegate some
details of the proofs (e.g., verifying the value functions, policy functions, and
the equivalence between the two implementations) to Appendix C.2.
5. Quantitative Analysis
In this section, we calibrate our model to study how well mandates approximate
the first-best. We focus on the parameter region where the planner chooses to
act now to decarbonize, that is, where the planner makes significant annual
mitigation spending contributions and smoothly ramps up to a high steady-state
decarbonization-to-productive capital ratio nss .

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is a measure of welfare (proportional to the household’s certainty equivalent
wealth). The only term in (55) that firm j chooses is φ(i j ). If its investment i j
exceeds the economy-wide average i, firm j pays a tax 
τ j (n;S) given in (55) for
each unit of its capital. This tax discourages corporate investment, mitigating
 (n;S)
over-investment in K and under-investment in N. The multiple q(n;S) nbb(n;S)
for the wedge φ(i j )−φ(i(n;S)) in (55) is necessary to attain the first-best
outcome.
Below, we further explore our model’s mechanism by highlighting a few key
equations in our proof. First, firm j ’s average q, q j (n;S), satisfies the following
ODE in state S:

Welfare Consequences of Sustainable Finance

5.1 Functional form specifications
We begin by specifying various functional forms in our model.

φ(i) = i −

ηK i 2
−δK ,
2

(59)

where ηK measures the degree of adjustment costs and δK is a constant that
can be viewed as the depreciation rate.
Similarly, at the aggregate level, we assume that the controlled drift for the
aggregate decarbonization capital stock N takes the same form as that for firmlevel capital stock K:
ω(x/n) = (x/n)−

ηN (x/n)2
−δN ,
2

(60)

where ηN is the adjustment cost parameter for the aggregate decarbonization
capital N. Note that x/n = X/N is the aggregate investment X in the
decarbonization capital scaled by N, which is analogous to a firm’s investment
level scaled by its capital stock: i = I /K.
Delaying the tipping point arrival. By accumulating decarbonization
capital stock, the society decreases the tipping-point arrival rate from ζ0 > 0
to
(61)
ζ (n;G) = ζ0 (1−nζ1 ),
where 0 < ζ1 < 1. (Recall that ζ (n;B) = 0.) For a given n, the lower the value
of ζ1 the more efficient the decarbonization capital stock is at curtailing the
tipping-point arrival.27
5.1.2 Conditional Damage and Weather-disaster Arrival Rates. In a given
climate state S, decarbonization capital N can also ameliorate the damage to
economic growth by reducing the frequencies of weather-disaster (e.g., hightemperature) events. Specifically, we use the following specification for the
weather-disaster arrival rate λ(n;S) in state S:
λ(n;S) = λS0 (1−nλ1 ),

(62)

where λS0 > 0 is the arrival rate absent any decarbonization capital stock (n =
0) in climate state S and λ1 ∈ (0,1) measures how efficient the aggregate
decarbonization capital stock reduces the weather-disaster arrival rate λ(n;S).
For brevity, we assume that λ1 is the same in the two climates states G and

27 This follows from ∂ζ (n; G )/∂ζ = −ζ nζ1 ln(n) > 0 as n < 1.
1
0

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5.1.1 Firm-level capital K and aggregate decarbonization capital N. As in
Pindyck and Wang (2013), we specify a firm’s investment-efficiency function
φ(i) as

The Review of Financial Studies / v 36 n 12 2023

Table 1
Parameter values
Parameters

Value

ψ
ρ
γ

1.5
4.2%
8

A
ηK
ηN
σ
δK = δN

26%
5
5
9%
6%

Jump arrival baseline parameter from state G to B
Jump arrival sensitivity parameter from state G to B

ζ0
ζ1

0.02
0.1

Power-law exponent
Jump arrival baseline parameter with n = 0 in state G
Jump arrival baseline parameter with n = 0 in state B
Mitigation technology parameter

β
λG
0
λB
0
λ1

39
0.05
2
0.3

Productivity for K
Adjustment cost parameter for K
Adjustment cost parameter for N
Diffusion volatility for N and K
Depreciation rates for N and K

All parameter values, whenever applicable, are continuously compounded and annualized.

B. Similar to the effect of ζ1 on the tipping-point arrival, a lower value of λ1
is associated with a more efficient decarbonization technology reducing the
weather disaster arrival rate, ceteris paribus.
The expected aggregate growth rate in state S, g(n;S), is
g(n;S) = φ(i(n;S))−λ(n;S)+ζ (n;S)

q(n;S  )−q(n;S)
,
q(n;S)

(63)

where , the expected fractional capital loss conditional on a jump arrival, is
given by
1
.
(64)
 = E(1−Z) =
β +1
Note that a lower value of β is associated with a more damaging and also more
fat tailed disaster. The first term in (63), φ(i(n;S)), is the expected growth in
state S absent jumps and the second term adjusts for the effect of weatherdisaster arrivals. The last term in (63) captures the effect of the climate-state
transition from state G to B on the expected growth rate in state G. Finally, the
last term is zero in state B as state B is absorbing: ζ (n;B) = 0.
5.2 Baseline calibration
Our model has 15 parameters in total. Next, we will choose parameter values
based on known key macrofinance moments and empirical studies on climate
mitigation pathways involving decarbonization. Our calibration exercise is
intended to highlight the extent to which mandates can approximate the social
planner’s solution when the planner wants to act now to decarbonize the
economy. We summarize the values of these parameters for our baseline
analysis in Table 1.

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Symbol

Elasticity of intertemporal substitution
Time rate of preference
Coefficient of relative risk aversion

Welfare Consequences of Sustainable Finance

5.2.2 Parameters for productive and decarbonization capital. We set
the productivity parameter A = 26% per annum and the capital adjustment
parameter ηK = 5 to target an average q of 2.5 and an average growth rate
of 2.2% per annum in the pre-climate-change sample. The values of A =
26% and ηK = 5 are within the range of empirical estimates (Stokey and
Rebelo 1995; Eberly, Rebelo, and Vincent (2012)). Decarbonization capital
has no productivity but faces adjustment costs as physical capital. We set the
decarbonization capital adjustment cost parameter ηN = ηK = 5 for parsimony
and also under the premise that direct air capture and plants are themselves
a form of physical capital. We set the annual diffusion volatility at σ = 9%
(Pindyck and Wang 2013) to target a historical stock market risk premium of
about 6% per annum (Hansen and Singleton 1982; Mehra and Prescott (1985)).
The annual depreciation rate for productive δK = 6%, is in line with the literature
cited above as well. Again, for parsimony, we set δN = δK .
5.2.3 Parameters for delaying the tipping point of climate transition.
Recent studies have indicated that tipping points in the climate system can
occur even at current levels of warming (Lenton et al. 2019). To generate a
sizeable act-now effect, we set the expected arrival rate of a tipping point to be
once every 50 years: ζ0 = 0.02. We then build on estimates from Gates (2021),
who proposes that spending around $5 trillion dollars each year on carbon
capture can forever eliminate the problem of global warming (this estimate
is based on $100 per ton cost of capture and there are 51 billion tons of carbon
emissions per year).29 We consider a modest scenario similar to that of de Pee
et al. (2018). In the de Pee et al. (2018) model, spending a couple of trillion
dollars per year on decarbonizing heavy industries can substantially reduce the
tipping point arrival rate from 2% per annum (1/ζ0 = 50) to around 0.5% per
annum (with an implied expected arrival in 200 years). This calibration yields
a value of ζ1 = 0.1.30
28 Estimates of the EIS ψ in the literature vary considerably, ranging from a low value near zero to values as high

as two. Vissing-Jørgensen and Attanasio (2003) estimate the elasticity to be above unity for stockholders, while
Hall (1988), using aggregate consumption data, obtains an estimate near zero. Guvenen (2006) reconciles the
conflicting evidence on the elasticity of intertemporal substitution from a macro perspective. In the long-run risk
literature, it is critical to choose an EIS value larger than one.
29 Reforestation also has the potential to contribute to keeping global temperatures from breaching the 1.5◦ Celsius

barrier. This adjustment process is also expensive like building direct air capture plants (Bastin et al. 2019;
Griscom et al. 2017).
30 At the steady state in G, ζ (nss ; G ) = ζ (1−(nss )ζ1 ) = 0.02×(1−6.13%0.1 ) ≈ 205 years.
0

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5.2.1 Preferences parameters. We choose a value for the time rate of
preferences within the standard range: ρ = 4.2% per annum. We set the
coefficient of relative risk aversion at γ = 8 and the EIS at ψ = 1.5, both of which
are within the standard ranges used in the long-run risk literature (Bansal and
Yaron 2004).28

The Review of Financial Studies / v 36 n 12 2023

5.3 Comparing laissez-faire, markets with optimal mandate, and
first-best economies
We first provide a quantitative comparison across the steady-state solutions for
the three economies: laissez-faire, market economy with welfare-maximizing
mandate, and first-best.
5.3.1 Comparing steady-state solutions. We summarize the steady-state
results in state G in the three columns of Table 2. The column labeled “laissezfaire” reports the results for the laissez-faire economy (i.e., α = 0). The column
labeled “mandate” reports the solution for the mandated market economy, and
the column labeled “first-best” reports the first-best solution.
In the laissez-faire economy, as firms have no incentives to provide public
goods (aggregate risk mitigation), there is no mitigation spending (x = 0) and
31 This panel regression approach initially focused on how weather affects crop yields (Schenkler and Roberts

2009) by using location and time fixed effects. But it is now applied to many other contexts, including economic
growth and productivity. The main idea is that abnormally high annual temperature fluctuations are plausibly
exogenous shocks that causally trace out the impact of higher temperatures on output. Burke, Hsiang, and Miguel
(2015) find that the effects of temperature on growth is nonlinear. But we stay with the linear specification of
Dell, Jones, and Olken (2012).

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5.2.4 Parameters for weather disasters and conditional damage functions.
Since weather disasters, for example, droughts, are associated with high
temperatures, we calibrate the parameter λG0 describing the arrival rate of
weather disasters in state G and the parameter β measuring the expected
damages conditional on arrival,  = (β +1)−1 , using a set of panel regressions
documenting the adverse effects of weather shocks in the form of extreme
temperatures for economic growth (Dell, Jones, and Olken 2012).31
First, we calibrate β as follows. For the median country in the Dell, Jones,
and Olken (2012) sample, extreme weather disasters in the form of extremely
high temperatures lowers the GDP growth rate by 2.5% per annum. To match
this moment, we set β = 39 as the implied reduction of GDP growth conditional
on a disaster arrival is  = 1/(β +1) = 1/40 = 2.5% per annum. Second, using
again the Dell, Jones, and Olken (2012) sample, we infer that the weather
disaster arrival rate in state G is low: around λG0 = 0.05 per annum in the
pre-climate-change sample. In other words, such weather disaster events are
uncommon, occurring in five percent of the country-year (annual) observations.
Our analysis is most apt for the median country in their sample. But our model
can be recalibrated for any subset of countries. For state B, we set λB
0 = 2,
a forty times increase in weather disaster frequencies, following studies of
tipping points cited in the Introduction. Third, we set λ1 = 0.3 for the arrival
rate λ(n;S) in both states G and B so that the decarbonization-to-productive
capital ratio n, which lowers temperatures, not only delays the tipping-point
arrival but also reduces the frequency of weather disasters, as is often modeled
in climate science and integrated assessment models.

Welfare Consequences of Sustainable Finance

Table 2
Comparing across the laissez-faire, the mandated market, and the first-best economies in state G
xss
nss
iss
qss
css
gss
r f,ss
rp ss
bss

Laissez-faire

Mandate

First-best

0
0
11.83%
2.45
14.17%
2.04%
1.10%
6.73%
0.0542
0

0.76%
6.13%
12.41%
2.64
12.82%
2.44%
0.73%
6.58%
0.0826
10.9

0.78%
6.48%
12.07%
2.52
13.15%
2.30%
0.91%
6.60%
0.0830
10.0

The steady-state value of n in state G is nss = 0.0613.

thus nss = 0. In the market economy with optimal investment mandates, the
aggregate decarbonization capital stock is nss = 6.13%, which falls only slightly
short of the first-best level: nFB = 6.48%. The annual contribution of mitigation
spending is also only slightly under the first-best: xss = 0.76% < xFB = 0.78%.
Also, note that firms facing optimal mandates still over-invest in capital
accumulation compared to the first-best: iss = 12.41% > iFB = 12.07%. In contrast and as expected, firms under-invest in the laissez-faire economy compared
to first-best: iss = 11.83% < iFB = 12.07%, as the laissez-faire economy is
riskier. Because the value of capital, the aggregate q, moves in lockstep with
the investment-capital ratio i, the steady-state Tobin’s q is the highest in the
economy with mandates and lowest in the laissez-faire economy. The transition
time to the steady state (conditional on remaining in state G at all time) in the
market economy with the mandate is 10.9 years compared to 10.0 years for the
planner’s economy.
Now we quantify the society’s willingness to pay (in units of consumption
goods/dollars) for an optimal mandate. The optimal mandate generates a 52%
welfare gain at the steady state where nss = 6.13% and bss = 0.0826, which is
almost identical to the first-best solution. This follows from a comparison with
the laissez-faire economy in which there is no decarbonization capital stock in
equilibrium (nss = 0) and the steady-state equilibrium value of bss = 0.0542. In
sum, mitigation spending and macroeconomic variables in the market economy
with mandates closely track the first-best.
5.3.2 Comparing optimal policies and the welfare measure b. In Figure 1,
we examine the optimal mitigation x, investment i, consumption c, and
a welfare measure (proportional to the certainty-equivalent wealth) b as
functions of n in state G. All these aggregates are functions of n in a given
climate state S. For all four panels, the solid lines represent the market economy
solution under welfare-maximizing mandates, and the dashed lines represent
the planner’s first-best solution. We compare how closely the policy functions
in the market economy with welfare-maximizing mandates track the social
planner’s first-best policies.

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Scaled mitigation spending
Scaled decarbonization stock
Scaled aggregate investment
Average Tobin’s q
Scaled aggregate consumption
Expected GDP growth rate
(Real) risk-free rate
Stock market risk premium
Aggregate welfare measure
Time from n = 0 to 0.99nss in G

The Review of Financial Studies / v 36 n 12 2023

A

D

Figure 1
Aggregate mitigation spending x, investment i, consumption c, and welfare measure b as functions of the scaled
decarbonization capital stock n in state G. Table 1 reports the parameter values.

Panel A shows that the solution for the market economy with mandates
closely tracks the planner’s first-best all the way up to the steady-state: nss =
6.13%. It also shows that the first-best solution features a higher steady-state
value: nFB = 6.48%, which we discussed earlier. That is, even in the long run,
the welfare-maximizing mandates still fall short of achieving the first-best.
Panel B shows that investment i is higher in the market economy with
mandates than in the first-best economy in state G. As we discussed earlier,
firms in the market economy even with mandates do not fully take into account
the impact of their capital accumulation decisions on the aggregate variables.
At the margin, firms still over-invest relative to the first-best level. In contrast,
the planner fully takes into account that more decarbonization capital stock N
is necessary to effectively protect a larger economy (with a larger K).
Since the resource constraint requires that the sum of i, c, and x equals the
constant productivity A, consumption c is lower in the market economy with
mandates than the first-best (panel C). This is because firms over-invest in the
mandated market economy relative to the first-best and mitigation spending
in the two economies are very close. Also as both x and i increase over time,
scaled consumption c falls over time.
Panel D shows that the welfare measure b(n;G) (proportional to certainty
equivalent wealth) for the market economy with optimal mandates is almost

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B

Welfare Consequences of Sustainable Finance

5.3.3 Constrained mitigation spending: xt ≤ x. Thus far, we have imposed
no constraints on how much budget a firm can set aside for its mitigation
spending. But in reality, often there are limits on how much a firm can
contribute. Without loss of generality, we assume that the aggregate mitigation
spending satisfies xt ≤ x at all t, where x is the parameter measuring how tight
this constraint is. This constraint applies to both the market economy with
welfare-maximizing mandates and the planner’s economy.
For our quantitative analysis, we set x = 0.35%. As the steady-state annual
mitigation contribution is xss = 0.76% in the market economy with optimal
mandates, this constraint is reasonably tight as x = 0.35% is about 54% lower
than the unconstrained steady-state annual mitigation spending xss = 0.76%
with optimal unconstrained mandates.
Figure 2 plots the optimal policy functions and welfare measure b for both
the market economy with welfare-maximizing mandates and the planner’s
economy in state G with the aggregate mitigation spending satisfying the
xt ≤ x = 0.35% constraint. Panels A and D show that the market economy
with welfare-maximizing mandates uses almost the same mitigation policy x
and attains almost the same level of welfare as the planner facing the same
xt ≤ x = 0.35% constraint. However, as for our baseline case without mitigationspending constraints, the two economies generate different i and x dynamics.
Panels B and C again confirm our earlier results that firms invest more in the
market economy (even with mandates) than the planner’s economy and hence
households consume less in the mandated market economy than in the planner’s
economy.
5.3.4 Required m and the required rate of return wedge for a given α.
Figure 3 plots the mandate m(n;G) and the required rate of return wedge
r U (n;G)−r S (n;G) in panels A and B, respectively, for three levels of α
(fraction of wealth pledged to the mandate): 0.1,0.2,0.3.32 The aggregate
mitigation constraint x ≤ x = 0.35% implies that a firm’s scaled mitigation
spending m must satisfy the constraint: m ≤ 0.35%/α. For the α = 0.1, α = 0.2,

32 Gadzinski, Schuller, and Vacchino (2018) estimate that the market value of global capital stock (including

housing) in 2019 is close to $800 trillion. Assuming the average Tobin’s q for global capital stock is around
2, we infer that the stock of capital K is about $400 trillion. To fund the net-zero pledges of $100 trillion, the
implied mandate requires 25% of aggregate wealth to be committed to sustainable firms.

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identical to that in the first-best economy for all the levels of n up to the
steady-state level of nss = 6.13%. This is good news as mandates are effectively
incentivizing firms to contribute to decarbonization. However, the market
economy with mandates still falls short of delivering the planner’s first-best
steady-state level of nFB = 6.48%, which is about 5.4% higher than nss = 6.13%,
as we discussed earlier.

The Review of Financial Studies / v 36 n 12 2023

B

C

D

Figure 2
Aggregate mitigation spending x, investment i, consumption c, and welfare measure b in state G for both the
planner’s and mandated market economies with x = 0.35%. Table 1 reports all other parameter values.

and α = 0.3 cases, the implied individual firm’s constraints are m ≤ 3.5%, m ≤
1.75%, and m ≤ 1.17%, respectively.
Panel A of Figure 3 shows that m(n;G) increases with n but is capped for
n ≥ 0.02 for all three cases. This is because x increases with n but is capped at
x for n ≥ 0.02. The higher the level of α, the less each firm has to contribute to
mitigation spending. For example, as we increase the total capital commitment
to sustainable investment by 50% from α = 0.2 to α = 0.3, each firm’s required
contribution m(n;G) decreases by one third. For example, when the aggregate
mitigation constraint x ≤ x = 0.35% binds for n ≥ 0.02, each firm’s mitigation
spending decreases from 1.75% to 1.17% per annum.
Recall that the required rate of return wedge r U (n;G)−r S (n;G) equals a
firm’s mitigation spending m(n;G) divided by its average q, q(n;G). Because
average q is much less sensitive to n than mitigation spending m(n;G), the
change of r U (n;G)−r S (n;G) mostly tracks the change of m(n;G), which can
be seen by comparing the two panels of Figure 3.
5.3.5 Required α and required rate of return wedge for a given m. We
have characterized the welfare-maximizing mandate by (a) taking the total
capital that can be committed to sustainable investment (α) as given and (b)

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Welfare Consequences of Sustainable Finance

A

B

A

B

Figure 4
Capital pledge for sustainable investment α(n; G ) and the required rate of return wedge r U (n; G )−r S (n; G )
for the m = 0.01,0.02,0.03 cases in the market economy with welfare-maximizing mandates and the aggregate
mitigation constraint: xt ≤ x = 0.35%. Table 1 reports the parameter values.

choosing the firm-level mandate m so that the economy can fund the aggregate
level of mitigation spending x. We could also derive the welfare-maximizing
policy by (a) taking each firm’s mitigation spending m as given and (b) solving
for the required capital commitments in the aggregate economy α to fund the
aggregate mitigation spending x. Whether we solve for α taking m as given or
we solve for m taking α as given yields the same welfare-maximizing aggregate
mitigation spending x, as long as the x ≤ x constraint is the same.
Figure 4 reports the necessary capital pledge α for various levels of firmlevel (scaled) mitigation spending m. In this figure, we continue to impose
the same aggregate mitigation spending constraint x ≤ x = 0.35% as in Section
5.3.4. Panel A shows that if each firm can spend 1% of its capital toward
mitigation (m = 0.01), we then need 35% of the aggregate wealth to fund
the maximal aggregate mitigation spending x = 0.35%, that is, α = 35%. The

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Figure 3
Firm-level mitigation spending mandate m(n; G ) and the required rate of return wedge r U (n; G )−r S (n; G ) for
the α = 0.1,0.2,0.3 cases in the market economy with welfare-maximizing mandates and the aggregate mitigation
constraint: xt ≤ x = 0.35%. Table 1 reports all other parameter values.

The Review of Financial Studies / v 36 n 12 2023

5.4 Optimal transition under a welfare-maximizing mandate
In this subsection, we discuss the optimal transition under a welfaremaximizing mandate (the model analyzed in Section 2.4).
5.4.1 Decarbonization-to-productive capital ratio nt . Figure 5 plots the
transition path of nt over time t conditional on no climate transition from state
G to B before reaching the steady state nss (G) in state G. Because of adjustment
costs, nt gradually rises to the steady-state level nss . We plot the transition paths
for three different values of the adjustment cost parameter: ηN = 5 (red dashed
line), ηN = 5.5 (solid line) and ηN = 5.85 (dotted line). We are interested in
comparing the transition path in the market economy under optimal mandates
with the planner’s solution under a relatively pessimistic tipping point scenario
(where the tipping point is expected to arrive in 50 years absent intervention,
that is, under the business-as-usual policy).
When ηN = 5, the steady state of nt is nss = 6.13% in the mandated market
economy and it takes about 11 years for nt to reach 0.99×nss = 6.07%, the 99%
of the steady-state value. When we increase ηN from 5 to 5.5 the steady state
decarbonization capital stock N decreases to 4.3% of the contemporaneous
aggregate capital stock K, that is, nss = 4.3% and the transition time to 99%
of the steady-state value, 0.99×nss = 4.26, increases to 20 (almost doubling
from 11 years). Finally, when we further increase ηN to 5.85, we see a dramatic
change in the transition path. The steady-state value of n drops to less than 1%
and the transition time it takes to reach 0.99×nss is around 50 years. In sum,
the optimal transition path is highly sensitive to the decarbonization capital
adjustment cost ηN .
5.4.2 Mitigation, investment, consumption, and welfare bt under mandates. In Figure 6, we examine the optimal mitigation xt , investment
it , consumption ct , and a welfare measure (proportional to the certaintyequivalent wealth) bt transition dynamics conditional on being in state G. In
panel A, xt rises over time, reflecting the gradual buildup of decarbonization

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mitigation spending constraint xt ≤ x = 0.35% binds when n > 0.02. If each firm
can spend more toward mitigation (m = 0.03), the minimal level of required
capital commitments (α) drops to around 12% at the steady state. Naturally,
the required rate of return difference is lower when m is low (e.g., m = 0.01)
since more capital (35% of total wealth) is committed to sustainable investing.
But when m is high (e.g., m = 0.03), only about 11.7% of firms are committed
to being sustainable in equilibrium and therefore these firms need a lower
required rate of return in compensation, as we see in panel B. At the steady
state, the required rate of return wedge is 1.14% per annum if the firm-level
mandated (scaled) mitigation spending m is 1%, but drops significantly to only
0.38% per annum if the firm-level mandated mitigation spending m increases
to 3%.

Welfare Consequences of Sustainable Finance

capital in the economy.33 The higher is the adjustment cost of decarbonization
capital relative to productive capital, the lower the level of mitigation spending.
For ηN = 5, the aggregate mitigation spending {xt } reaches the steady-state
value of xss = 0.76%. The steady-state annual contributions for the ηN = 5.5 case
equals xss = 0.59%, which is a 22% decrease from xss = 0.76% for the baseline
ηN = 5 case. For the ηN = 5.85 case, xss = 0.14%, which is 82% lower than
xss = 0.76% for the baseline ηN = 5 case! In sum, the decarbonization capital
adjustment cost is a critical parameter for our model.
In panel B, it increases over time t as nt increases over t. This is because
the climate transition risk falls, which in turn makes the returns to investment
rise. The lower is the adjustment cost of decarbonization capital, the higher the
level of it , since decarbonization capital is accumulating and there is less risk.
In panel C, we see that consumption c falls over time as mitigation
and investment ramp up due to the resource constraint as ct = A−it −xt .
Additionally, consumption rises as the adjustment cost increases since there
is less spending on mitigation but also fewer investments. Panel D plots our
measure of social welfare, bt , which is proportional to the agent’s certainty
equivalent wealth, over time conditional on being in state G. Naturally, the
higher is the adjustment cost of decarbonization capital, the lower the value of
b. Moreover, the welfare measure b rises significantly over time as the economy
33 While x increases over time, the mitigation spending/decarbonization capital stock ratio x /n decreases over
t
t t

time conditional on being in state G. This is because nt is low in the early transition period.

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Figure 5
The transition path of nt in the market economy with optimal mandates conditional on being in state G. Table 1
reports the parameters.

The Review of Financial Studies / v 36 n 12 2023

A

D

Figure 6
Aggregate mitigation spending (xt ), investment (it ), consumption (ct ) and welfare measure (bt ) dynamics
conditional on being in state G. The parameter values are reported in Table 1.

decarbonizes. Focusing on the ηN = 5 case, we see that bt rises from 0.06 at t = 0
to the steady-state value of 0.083. This 40% welfare gain is obviously very
large.
Even at ηN = 5.5, we still obtain large welfare gains. However, for the ηN =
5.85 case, the welfare gain (again measured via the percentage change of b)
is substantially lower as we transition from our current situation to the steady
state. This is consistent with our earlier calculations in Figure 5 showing that
the buildup of decarbonization capital is very sensitive to the adjustment cost
of decarbonization capital relative to productive capital.
5.4.3 Mandated spending for qualifying firms, and the required rate of
return wedge. In Figure 7, we present the optimal mandate mt and the
required rate of return wedge rtU −rtS for the same three cases: ηN = 5,5.5,5.85.
Panels A and B show that both the qualifying standard for a firm (mt ) and
the required rate of return wedge (rtU −rtS ) increase with time t. Consider the
ηN = 5 case (dotted red lines). The mandate for a qualifying firm mt peaks
at the steady-state value of around 3.8% per annum.34 That is, a firm would
need to spend 3.8% of its capital stock per year on decarbonization to qualify

34 This follows from mss = xss /α = 0.76%/20% = 3.8%.

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B

Welfare Consequences of Sustainable Finance

A

B

for the sustainable portfolio at the steady state. The sustainable firms are
then compensated for their contributions with a significant required rate of
return wedge rtU −rtS = 1.4% at the steady state in the market economy with
mandates.35
Recall that as we increase the adjustment costs of decarbonization capital
ηN , both the steady-state nss and the required aggregate mitigation spending
x decrease significantly. Therefore, the qualification standard for firms to be
sustainable naturally falls and so do the required rate of return wedges. Note
that the optimal ramping-up schedules of both m and required rate of return
wedge r U −r S are nonlinear.
5.4.4 Tipping-point arrival (ζt ), weather-disaster arrival (λt ), and growth
(gt ). Next, we will highlight the mechanism for why social welfare is rising
over the net-zero transition period. In panels A and B of Figure 8, we see that
the tipping-point arrival rate and the disaster arrival rate λt falls over time t,
as the society builds up the decarbonization capital. As the economy becomes
more resilient, the expected growth rate gt rises over time (panel C). Three
forces determine gt : the investment channel i, the expected loss given a disaster
arrival and the expected value destruction due to the expected tipping-point
arrival, which can be seen from (63). Quantitatively, the investment channel
φ(it ) dominates growth. Note that when the decarbonization capital adjustment
costs ηN are high, gains from aggregate risk mitigation become much lower.
This is because it is much more costly to mitigate risk and thus optimal for the
society to reduce risk mitigation.
Even though the accumulation of decarbonization capital is entirely
unproductive, economic growth can nonetheless rise in the net-zero transition
due to the disaster-risk mitigation benefits of decarbonization. The logic behind
35 This follows from r U −r S = xss /(αqss ) = 1.4%.

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Figure 7
Mitigation spending mandate (mt ) and the required rate of return wedge rtU −rtS dynamics conditional on being
in state G. Table 1 reports the parameters.

The Review of Financial Studies / v 36 n 12 2023

A

B

C

A

B

C

Figure 9
f
Transition dynamics of the equilibrium interest rate (rt ), stock market risk premium (rpt ), and average Tobin’s
q for the aggregate capital stock (qt ) conditional on being in state G. Table 1 reports the parameter values.

this takeaway differs from the logic behind the projections from the European
Union on the net-zero transition. The most recent climate briefing by European
Union (2022) also sees positive growth projections from the net-zero transition.
But their projection follows from its assumption that renewables will be highly
efficient.
5.4.5 Asset pricing and valuation (Tobin’s q). The benefit of decarbonizing
the economy and reducing the damage of climate risks to physical capital stock
is reflected in some of the asset prices. Panel B of Figure 9 shows that the
market risk premium rp declines over time as the economy decarbonizes, while
panel C shows that Tobin’s q modestly increases over time. However, the riskfree declines with t in panel A even though disaster risk is falling over the
transition. In sum, asset prices (risk premium and Tobin’s q) reflect the benefits
of decarbonizing the economy and reducing climate disaster risks. But again,
when adjustment costs of decarbonization is relatively higher, the impact on
asset prices, government policies, and welfare are far weaker.

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Figure 8
Transition dynamics of tipping-point arrival rate (ζt ), weather disaster arrival rate (λt ), and the expected growth
rate (gt ) conditional on being in state G. Table 1 reports the parameters.

Welfare Consequences of Sustainable Finance

6. Conclusion

Appendix
A. Market Economy with Optimal Mandates
In this appendix, we provide additional technical details for the market economy with optimal
Markovian mandates in Section 2. First, we provide key intermediate steps for the household’s
problem.
A.1 Household’s Optimization Problem
Using the household’s wealth dynamics in state S given in (26), we obtain the following HJB
equation for the household’s value function V (W,n;S):
0 = max

C,π S ,H

r f (n;S)W −C+ r S (n;S)π S +r U (n;S)(1−π S )−r f (n;S) H +λ(n;S)(1−E(Z))H VW

+ f (C,V ;S)+[ω(x/n)−φ(i)]nVn +

q(n;S)−q(n;S  )
σ 2 H 2 VW W
+ζ (n;S)
H VW
2
q(n;S)

+ λ(n;S)E[V (W −(1−Z)H,n;S)−V (W,n;S)]


 
q(n;S)−q(n;S  )
H,n;S  −V (W,n;S) ,
+ ζ (n;S) V W −
q(n;S)

(A.1)

subject to the investment mandate π S ≥ α. In (A.1), we use the equilibrium property that the Sand the U -portfolio equilibrium returns have the same (diffusion and jump) risk exposures with
probability one. Using (A.1), W = H , and π = α, we obtain (27).36 The FOC for consumption C is

36 Suppose that r S > r U were true, the optimality condition for π S would imply counterfactually π S → ∞, as (A.1)
is linear in π S . Since π S → ∞ cannot be an equilibrium, r S ≤ r U is necessary in equilibrium. Moreover, we can

show that in equilibrium r S < r U holds, which implies that the short-sale constraint π S ≥ α has to bind. This is
because investors have incentives to short S firms otherwise. By combining the equilibrium condition H = W ,
we thus conclude that the household’s value function satisfies the simplified HJB equation (27).

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Sustainable finance mandates have grown significantly in the last decade in
lieu of government failures to address climate-disaster externalities. Firms that
spend enough resources on mitigating these climate-disaster externalities qualify for sustainable finance mandates. These mandates incentivize otherwise ex
ante identical unsustainable firms to become sustainable in order to lower their
costs of capital. We present and solve a dynamic stochastic general-equilibrium
model featuring the gradual accumulation of nonproductive but protective
decarbonization capital to study the welfare consequences of sustainable
finance.
Using our tractable model, we highlight some key takeaways by introducing
the welfare-maximizing mandate into an otherwise laissez-faire market
economy. Despite being entirely unproductive, the disaster-risk mitigation
benefits of decarbonization capital are such that investment, growth, and
welfare are rising over time (and risk premiums falling) as we approach the
steady state. But the optimal transition path is highly sensitive to the relative
adjustment costs of decarbonization to productive capital.

The Review of Financial Studies / v 36 n 12 2023

the standard condition given by (28). The FOC for the portfolio allocation to the risky asset, H , is
given by


q(n;S  )−q(n;S)
0 = αr S (n;S)+(1−α)r U (n;S)−r f (n;S)+λ(n;S)(1−E(Z))+ζ (n;S)
VW
q(n;S)

+ζ (n;S)



q(n;S  )−q(n;S)
q(n;S)−q(n;S  )
VW W −
H,n;S  .
q(n;S)
q(n;S)

(A.2)

Later, we will use (A.2) to derive the equilibrium market return r M . Next, we will derive
equilibrium prices and allocations in the mandated market economy.
A.2 Market Equilibrium for a Given Mandate
First, a sustainable firm has no incentive to spend more on mitigation for its sustainability
S

qualification than the minimal requirement m, which implies x S = X S = m. Second, in equilibrium,
K
the representative household invests her entire wealth in the stock market and holds no riskS
U
free asset: H = W and W = Q +Q . Third, the representative agent’s dollar-amount investment
in the S portfolio equals the total market value of sustainable firms (π S = α) and her dollar-amount
investment for the U portfolio equals the total market value of the U portfolio which includes all
unsustainable firms (π U = 1−α). Finally, goods market clears. As in Pindyck and Wang (2013) and
Hong, Wang, and Yang (2022), the risk-free asset holding is zero, H = W = QS +QU = q S (n;S)KS +
q U (n;S)KU = q(n;S)(KS +KU ) = q(n;S)K, and W J = ZW . Additionally, using π S = α and the
portfolio allocation rule given in (A.2), we obtain
r M (n;S) = r f (n;S)+γ σ 2 +λ(n;S)E (1−Z)(Z −γ −1)
+ζ (n;S)

q(n;S)−q(n;S  )
q(n;S)



q(n;S  )
q(n;S)

−γ


−1

= αr S (n;S)+(1−α)r U (n;S).

(A.3)

As all firms have the same Tobin’s q in equilibrium, using the investment FOCs (23) and (22) we
conclude that both S and U firms invest at the same rate: i S (n;S) = i U (n;S) = i(n;S) and
A−i(n;S)−m(n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S)
q(n;S) =
r S (n;S)−g(n;S)
A−i(n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S)
,
r U (n;S)−g(n;S)
where the expected growth ate is
=

g(n;S) = φ(i(n;S))−λ(n;S)(1−E(Z))−ζ (n;S)

q(n;S)−q(n;S  )
.
q(n;S)

(A.4)

(A.5)

Using αr S (n;S)+(1−α)r U (n;S) = r M (n;S), x = αm(n;S), and (A.4), we obtain
A−i(n;S)−x(n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S)
r M (n;S)−g(n;S)
=

α(A−i(n;S)−m(n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S))
αr S (n;S)+(1−α)r U (n;S)−g(n;S)
+

=

4908

(1−α)(A−i(n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S))
αr S (n;S)+(1−α)r U (n;S)−g(n;S)

αq(n;S)(r S (n;S)−g(n;S))+(1−α)q(n;S)(r U (n;S)−g(n;S))
= q(n;S). (A.6)
α(r S (n;S)−g(n;S))+(1−α)(r U (n;S)−g(n;S))

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+σ 2 H VW W −λ(n;S)E[(1−Z)VW (W −(1−Z)H,n;S)]

Welfare Consequences of Sustainable Finance

The optimal consumption rule given in (30) implies
c(n;S) =

C C
= q(n;S) = ρ ψ u(n;S)1−ψ q(n;S).
K W

(A.7)

0

=

1
1−ψ −1



 

c(n;S)
c(n;S)
−ρ + αr S (n;S)+(1−α)r U (n;S)−
+λ(n;S)(1−E(Z))
q(n;S)
q(n;S)


nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
ζ (n;S)
+
−1
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

=

1
1−ψ −1



 

c(n;S)
c(n;S)
−ρ + r M (n;S)−
+λ(n;S)(1−E(Z))
q(n;S)
q(n;S)


nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
ζ (n;S)
−1 .
+
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

(A.8)

By using (A.6) and the goods market clear condition, we obtain
c(n;S) M
nq (n;S)
= r (n;S)−g(n;S)−[ω(x(n;S)/n)−φ(i(n;S))]
.
q(n;S)
q(n;S)

(A.9)

Substituting (A.9) into (A.8) and using c(n;S) = A−i(n;S)−x(n;S) and (A.7), we obtain
1
1−ψ −1





A−i(n;S)−x(n;S)
γ σ 2 λ(n;S) 
−ρ +φ(i(n;S))−
+
E(Z 1−γ )−1
q(n;S)
2
1−γ

⎤
⎡
 1−γ

ζ (n;S) ⎣ (A−i(n;S  )−x(n;S  ))q(n;S)ψ 1−ψ
+
−1⎦
1−γ
(A−i(n;S)−x(n;S))q(n;S  )ψ

+[ω(x(n;S)/n)−φ(i(n;S))]


1 ni (n;S)+nx (n;S)
ψ nq (n;S)
−
,(A.10)
1−ψ q(n;S)
1−ψ A−i(n;S)−x(n;S)

which implies (37). Finally, we obtain the equilibrium risk-free rate formula (41) by substituting
r M (n;S) = r f (n;S)+γ σ 2 +λ(n;S)E (1−Z)(Z −γ −1) +ζ (n;S)

×

q(n;S  )
q(n;S)

−γ

q(n;S)−q(n;S  )
q(n;S)


−1

into (A.9). Next, we provide details on how to obtain the ODE (45) for b(n;S), which equals the
product of u(n;S) and q(n;S). Then, we can obtain the welfare-maximizing mandate by choosing
x to maximize b(n;S).

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And then substituting c(n;S) given by (A.7) and the value function given in (29) into the HJB
equation (27), we obtain

The Review of Financial Studies / v 36 n 12 2023

A.3 Welfare-maximizing Markovian Mandate
Using (29) and W = q(n;S)K in equilibrium, we may rewrite the ODE (31) for u(n;S) as:

 

c(n;S)
c(n;S)
1
S
U
−ρ
+
αr
(n;S)+(1−α)r
(n;S)+λ(n;S)(1−E(Z))−
0 =
1−ψ −1 q(n;S)
q(n;S)

(A.11)

1
Then using (44) and q(n;S) = φ  (i(n;S))
, we obtain

0

⎤
⎡

1−ψ −1
1
⎣ A−i−x
−ρ ⎦ + αr S (n;S)+(1−α)r U (n;S)+λ(n;S)(1−E(Z))
1−ψ −1
b(n;S)

=


c(n;S)
nu (n;S) γ σ 2 λ(n;S) 
+[ω(x(n;S)/n)−φ(i(n;S))]
−
+
E(Z 1−γ )−1
q(n;S)
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+
−1 .
(A.12)
+ζ (n;S)
q(n;S)
1−γ
u(n;S)q(n;S)

−

Using (A.9) and (A.5) to simplify (A.12), we obtain:
⎤
⎡

1−ψ −1



ρ
u(n;S  )q(n;S  ) 1−γ
A−i−x
⎦ +φ(i(n;S))+ ζ (n;S)
⎣
0=
−1
−1
1−ψ −1
b(n;S)
1−γ
u(n;S)q(n;S)

+(ω(x(n;S)/n)−φ(i(n;S)))



nu (n;S) nq (n;S)
γ σ 2 λ(n;S) 
+
−
+
E(Z 1−γ )−1 .
u(n;S)
q(n;S)
2
1−γ
(A.13)

Finally, using b(n;S) = u(n;S)×q(n;S), we obtain (45).

B. First-Best
The following HJB equation for state S = G,B characterizes the planner’s optimization problem:
0 = max f (C,J ;S)+φ(i)KJK +ω(x/n)NJN +
C,i,x

K2 JKK +2NKJKN +N2 JNN 2
σ
2

+λ(n;S)E[J (ZK,ZN;S)−J (K,N;S)]+ζ (n;S) J (K,N;S  )−J (K,N;S) ,

(B.1)

subject to the aggregate resource constraint at time t:
AKt = Ct +it Kt +xt Kt .

(B.2)

The FOC for the scaled investment i is
fC (C,J ;S) = φ  (i)JK (K,N;S).

(B.3)

The FOC for the scaled aggregate mitigation spending x is
fC (C,J ;S) = ω (x/n)JN (K,N;S),

4910

(B.4)

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
nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+ζ (n;S)
−1 .
+
q(n;S)
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

Welfare Consequences of Sustainable Finance

for the economically interesting case where the first-best mitigation spending is strictly positive:
x > 0.37 The FOCs (B.3) and (B.4) imply the following condition:
ω (x/n) JK (K,N;S)
=
.
φ  (i)
JN (K,N;S)

(B.5)

C. A Market Economy with Mandates versus the First-Best
In this appendix, we first show why the optimally mandated market economy does not generate
the first-best outcome (Section C.1) and then provide details on how to attain the first-best by
introducing optimal investment taxes into the mandated market economy (Section 4.2).
C.1 Differences between the Optimally Mandated Market Economy and the First-Best
First, we summarize the key equations for the optimally mandated market and first-best economies.
C.1.1 First-best. The planner chooses i and x to maximize the welfare measure b(n;S) given
by the following ODE:
0

=

⎤
⎡

1−ψ −1

S
)−x(n;
S
)
ρ
γ σ 2 λ(n; S ) 
A−i(n;
⎣
−1⎦ +φ(i(n; S ))−
+
E(Z 1−γ )−1
b(n; S )
2
1−γ
1−ψ −1

+[ω(x(n; S )/n)−φ(i(n; S ))]

nb (n; S ) ζ (n; S )
+
b(n; S )
1−γ





b(n; S  ) 1−γ
−1 ,
b(n; S )

(C.1)

which implies the following FOC for investment:

ρ

A−i(n;S)−x(n;S)
b(n;S)

−ψ −1

= φ  (i(n;S))b(n;S)−φ  (i(n;S))nb (n;S),

(C.2)

and the FOC for mitigation spending x given in (51).
C.1.2 Mandated market economy. In contrast, in the mandated market economy, an individual
firm chooses i to maximize its market value, that is, q(n;S), taking the aggregate mitigation
spending x and the evolution of the scaled decarbonization capital stock n as well as asset
prices as given. Then, in equilibrium, an individual firm’s investment-capital ratio i equals i, the
aggregate investment-capital ratio in the economy. Substituting the equilibrium results q S (n;S) =
q U (n;S) = q(n;S) and i S (n;S) = i U (n;S) = i(n;S) into (22), we obtain the following equation for
the aggregate Tobin’s q, q(n;S):
r j (n;S)q(n;S) =max cf j (n;S)+(φ(i)−λ(n;S)(1−E(Z)))q(n;S)
i

+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S)+ζ (n;S)(q(n;S  )−q(n;S)).
(C.3)
Since the preceding equation applies to both S and U firms, we may multiply α and 1−α on both
sides of the preceding equation for type-S and type-U firms, respectively. Doing so yields two

37 Otherwise, x = 0 as mitigation cannot be negative.

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The left side of (B.5) is the ratio between the marginal investment efficiency for N, ω (x/n), and the
marginal investment efficiency for K, φ  (i). The right side of (B.5) is the ratio between the marginal
(utility) value of N and the marginal (utility) value of K. Substituting the agent’s value function
(42) into the FOCs (B.3)-(B.4) and the HJB equation (B.1) and simplifying these equations, we
obtain (50), (51), and (52) for state S = G,B.

The Review of Financial Studies / v 36 n 12 2023

equations. Summing up these two equations yields an equation for q(n;S). Dividing the two sides
of this new equation and rearranging terms, we obtain:
0 =max
i

A−i −x
+φ(i)−λ(n;S)(1−E(Z)))−r M (n;S)
q(n;S)
nq (n;S)
q(n;S  )−q(n;S)
+ζ (n;S)
.
q(n;S)
q(n;S)

(C.4)

Next, substituting (29) into (27) and using the equilibrium condition W = q(n;S)K, we obtain the
following equation for u(n;S):
⎤
⎡

1−ψ −1
c
ρ
c
⎣
0 = max
−1⎦ +r M (n;S)+λ(n;S)(1−E(Z))−
c 1−ψ −1
u(n;S)q(n;S)
q(n;S)

nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+
−1 ,
+ζ (n;S)
q(n;S)
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

(C.5)

Substituting the resource constraints c = A−i −x into (C.5), we obtain:
⎤
⎡

1−ψ −1
A−i −x
ρ
A−i −x
⎣
−1⎦ +r M (n;S)+λ(n;S)(1−E(Z))−
0 = max
i 1−ψ −1
u(n;S)q(n;S)
q(n;S)

nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+
−1 .
+ζ (n;S)
q(n;S)
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

(C.6)

Summing up (C.4) and (C.6), we obtain the following:
⎡
⎤
 

1−ψ −1

nu (n; S ) nq (n; S )
ρ
A−i
−x
⎣
0 = max
−1⎦ +φ(i)+(ω(x(n; S )/n)−φ(i(n; S )))
+
u(n; S )q(n; S )
u(n; S )
q(n; S )
i 1−ψ −1

−


 ζ (n; S )  u(n; S  )q(n; S  ) 1−γ
γ σ 2 λ(n; S ) 
−1 .
+
E(Z 1−γ )−1 +
2
1−γ
1−γ
u(n; S )q(n; S )

(C.7)

Now using b(n;S) = u(n;S)×q(n;S), we obtain
⎤
⎡

1−ψ −1
A−i
−x(n;S)
ρ
nb (n;S)
⎣
−1⎦ +φ(i)+[ω(x(n;S)/n)−φ(i(n;S))]
0 = max
−1
i 1−ψ
b(n;S)
b(n;S)

−


 ζ (n;S)  b(n;S  ) 1−γ
γ σ 2 λ(n;S) 
+
E(Z 1−γ )−1 +
−1 .
2
1−γ
1−γ
b(n;S)

(C.8)

The firm’s investment FOC for i implied by (C.8) is

ρ

4912

A−i −x(n;S)
b(n;S)

−ψ −1

= φ  (i)b(n;S).

(C.9)

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+ [ω(x(n;S)/n)−φ(i(n;S))]

Welfare Consequences of Sustainable Finance

Since in equilibrium firm-level’s investment i equals the aggregate i. Therefore, the following
equation characterizes i:

 −1
A−i(n;S)−x(n;S) −ψ
ρ
= φ  (i(n;S))b(n;S).
(C.10)
b(n;S)

−


 ζ (n;S)  b(n;S  ) 1−γ
γ σ 2 λ(n;S) 
+
E(Z 1−γ )−1 +
−1 .
2
1−γ
1−γ
b(n;S)

(C.11)

While the two ODEs, (C.1) and (C.11), at the aggregate level for the mandated market and firstbest economies are the same, the two equations for i, (C.2) and (C.10), are different.38 Therefore,
the resource allocations in the two economies are different. Importantly, in a market economy
regardless of mandates, a firm takes the evolution of the scaled aggregate decarbonization capital n
as given. In contrast, in the first-best economy, when choosing investment i the planner internalizes
the impact of aggregate i on the n process. The aggregate investment i in the optimally mandated
market economy differs from that in the first-best economy because firms does not internalize the
benefit of aggregate risk mitigation. Next, we prove that by introducing an optimally chosen tax
that depends on the difference between a firm’s investment-capital ratio i and the aggregate i into
the market economy with optimal mandates restores the first-best.
C.2 Introducing Investment Taxes into the Mandated Market Economy Restores the
First-Best
Consider introducing the following optimal tax given in (55) as

τ j (n;S) = φ(i j )−φ(i(n;S)) q(n;S)

nb (n;S)
,
b(n;S)

(C.12)

into the market economy with mandates. The following HJB equation characterizes the firm’s value
function in climate state S:
j

r j (n;S)Qj (K j ,n;S) = max CF j (n;S)−
τ j (n;S)K j +(I j ,K j )QK (K j ,n;S)
Ij

1
j
j
+ (σ K j )2 QKK (K j ,n;S)+[ω(x(n;S)/n)−φ(i(n;S))]nQn (K j ,n;S)
2
+λ(n;S)E Qj (ZK j ,n;S)−Qj (K j ,n;S)
+ζ (n;S)(Qj (K j ,n;S  )−Qj (K j ,n;S)).

(C.13)

Using the homogeneity property of our model, we obtain the following ODE for q j (n;S):
r j (n;S)q j (n;S) = max cf j (n;S)+(φ(i j )−λ(n;S)(1−E(Z)))q j (n;S)
ij

− φ(i j )−φ(i(n;S)) q(n;S)

(C.14)

nb (n;S)
j
+[ω(x(n;S)/n)−φ(i(n;S))]nqn (n;S)
b(n;S)

+ζ (n;S)(q j (n;S  )−q j (n;S)).

(C.15)

38 Note that the FOCs (functional forms) for mitigation spending x in the mandated market economy and the first-

best economy are the same (that is, (46) and (51) are the same.)

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In equilibrium, the welfare measure b(n;S) then satisfies
⎤
⎡
1−ψ −1

ρ
nb (n;S)
A−i−x(n;S)
⎣
0=
−1⎦ +φ(i)+[ω(x(n;S)/n)−φ(i(n;S))]
−1
1−ψ
b(n;S)
b(n;S)

The Review of Financial Studies / v 36 n 12 2023

The FOC for investment i j is given by



nb (n;S)
.
1 = φ  (i j ) q j −q(n;S)
b(n;S)

(C.16)

r j (n;S)q(n;S) = cf j (n;S)+(φ(i(n;S)))−λ(n;S)(1−E(Z)))q(n;S)
+[ω(x(n;S)/n)−φ(i(n;S))]nq (n;S)+ζ (n;S)(q(n;S  )−q(n;S)),

(C.17)

which implies (A.4) and (A.6) are still held. Since i U = i S = i and q U = q S = q in equilibrium, the
following equilibrium condition between the aggregate investment-capital ratio (i) and Tobin’s q
for the aggregate capital stock (q) holds:


nb (n;S)
1 = φ  (i(n;S))q(n;S) 1−
,
(C.18)
b(n;S)
which implies
b(n;S)
= φ  (i(n;S)) b(n;S)−nb (n;S) .
q(n;S)

(C.19)

Rewriting the optimal consumption rule (30) and using the equilibrium restrictions, we obtain
c(n;S) =

C C
= q(n;S) = ρ ψ u(n;S)1−ψ q(n;S) = ρ ψ u(n;S)−ψ b(n;S),
K W

(C.20)

b(n;S)
b(n;S)
b(n;S)ψ
= ρψ
.
= ρψ
q(n;S)ψ
c(n;S)
A−i(n;S)−x(n;S)

(C.21)

which implies

And then combining (C.19) and (C.21), we obtain the FOC in equilibrium at the aggregate level
for i is then given by (58), which is the same at the optimal investment under FB as given in (C.2).
Next, we verify that the ODE for b(n;S) in the mandated market economy with investment taxes
is the same as the ODE (52) for b(n;S) in the first-best economy. Recall that in the representative
agent’s optimization problem, we have the following ODE for u(n;S):
0

=

ρ ψ u(n;S)1−ψ −ρ
+αr S (n;S)+(1−α)r U (n;S)−ρ ψ u(n;S)1−ψ +λ(n;S)(1−E(Z))
1−ψ −1

nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+
+ζ (n;S)
−1 .
q(n;S)
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

(C.22)

Using (30) and the equilibrium result W = q(n;S)K, we may rewrite the ODE (C.22) as


1
c(n;S)
c(n;S)
0 =
−ρ
+αr S (n;S)+(1−α)r U (n;S)+λ(n;S)(1−E(Z))−
1−ψ −1 q(n;S)
q(n;S)

nu (n;S) γ σ 2 λ(n;S) 
−
+
E(Z 1−γ )−1
u(n;S)
2
1−γ



u(n;S  )q(n;S  ) 1−γ
q(n;S)−q(n;S  ) ζ (n;S)
+
+ζ (n;S)
−1 .
q(n;S)
1−γ
u(n;S)q(n;S)

+[ω(x(n;S)/n)−φ(i(n;S))]

Then using (58) and q(n;S) =

4914

 , we obtain
1

φ  (i(n;S)) 1− nb (n;S)
b(n;S)

(C.23)

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Substituting i U = i S = i and q U = q S = q into (C.14), we obtain the following equilibrium pricing
equation for q:

Welfare Consequences of Sustainable Finance

0

=

⎤
⎡
1−ψ −1



ρ
⎣ A−i(n; S )−x(n; S )
−1⎦ + αr S (n; S )+(1−α)r U (n; S )+λ(n; S )(1−E(Z))
−1
b(n;
S
)
1−ψ

nu (n; S ) γ σ 2 λ(n; S ) 
c(n; S )
+[ω(x(n; S )/n)−φ(i(n; S ))]
−
+
E(Z 1−γ )−1
q(n; S )
u(n; S )
2
1−γ

+ζ (n; S )

q(n; S )−q(n; S  ) ζ (n; S )
+
q(n; S )
1−γ





u(n; S  )q(n; S  ) 1−γ
−1 .
u(n; S )q(n; S )

(C.24)


)
Using (A.6) and g(n;S) = φ(i(n;S))−λ(n;S)(1−E(Z))−ζ (n;S) q(n;S)−q(n;S
to simplify
q(n;S)
(C.24), we obtain:

0=

⎤
⎡

1−ψ −1

ρ
γ σ 2 λ(n; S ) 
⎣ A−i−x
−1⎦ +φ(i(n; S ))−
+
E(Z 1−γ )−1
−1
b(n;
S
)
2
1−γ
1−ψ

+(ω(x(n; S )/n)−φ(i(n; S )))





nu (n; S ) nq (n; S )
u(n; S  )q(n; S  ) 1−γ
ζ (n; S )
−1 . (C.25)
+
+
u(n; S )
q(n; S )
1−γ
u(n; S )q(n; S )

Finally, using b(n;S) = u(n;S)×q(n;S), we can simplify (C.25) to the following ODE for b(n;S):

0

⎡
⎤

1−ψ −1
A−i(n;S)−x(n;S)
ρ
nb (n;S)
⎣
−1⎦ +[ω(x(n;S)/n)−φ(i(n;S))]
−1
1−ψ
b(n;S)
b(n;S)

=

+φ(i(n;S))−


 ζ (n;S)  b(n;S  ) 1−γ
γ σ 2 λ(n;S) 
+
E(Z 1−γ )−1 +
−1 .
2
1−γ
1−γ
b(n;S)

(C.26)

This ODE is the same as the ODE for b(n;S) given in (52) for the first-best economy. In sum, we
have shown that by introducing the investment tax (55) into the mandated market economy allows
us to attain the first-best outcomes.

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==> RFS09 - The Importance of Climate Risks for Institutional Investors.txt <==
The Importance of Climate Risks for
Institutional Investors
Philipp Krueger
University of Geneva and Swiss Finance Institute

Laura T. Starks
McCombs School of Business, University of Texas at Austin
According to our survey about climate risk perceptions, institutional investors believe
climate risks have financial implications for their portfolio firms and that these risks,
particularly regulatory risks, already have begun to materialize. Many of the investors,
especially the long-term, larger, and ESG-oriented ones, consider risk management and
engagement, rather than divestment, to be the better approach for addressing climate risks.
Although surveyed investors believe that some equity valuations do not fully reflect climate
risks, their perceived overvaluations are not large. (JEL G11, G2, G3, Q54)
Received December 7, 2017; editorial decision August 4, 2019 by Editor Andrew Karolyi.
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

Climate risks have potentially large effects on investors’ portfolio companies.
Some companies face direct costs related to changes in the climate, originating
from extreme weather events or a general rise in sea levels. Examples include
insurance companies’ exposures to higher losses from insured properties in
coastal areas and food producers’ exposures to sustained drought spells.
Other companies can be negatively affected from policies and regulations
implemented to combat climate change. Fossil fuel firms, for instance, can

We benefited from the comments of Andrew Karolyi (the Editor) and four anonymous referees. We also thank
Marco Becht, Patrick Bolton, Claudia A. Bolli, Sebastian Ebert, Miguel Ferreira, Monika Freyman, Harrison
Hong, Ulf von Lilienfeld-Toal, Karl Lins, Karsten Löffler, Pedro Matos, Wilhelm Mohn, Ulf Moslener, Jose
Scheinkman, Olaf Stotz, and Kerrie Waring and seminar participants at the RFS Workshop on Climate Risk at
Columbia University, at the RFS Climate Finance Conference with Imperial College Business School at the First
Asset Pricing Conference at Collegio Carlo Alberto, Darden School of Business at the University of Virginia,
Dauphine University, the University of Queensland, and Copenhagen Business School. We thank Valentin
Jouvenot for excellent research assistance. Supplementary data can be found on The Review of Financial Studies
web site. Send correspondence to Zacharias Sautner, Frankfurt School of Finance & Management, Adickesallee
32-34, 60322 Frankfurt am Main, Germany; telephone: +49 69 154008-755. E-mail: z.sautner@fs.de.
© The Author(s) 2020. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
doi:10.1093/rfs/hhz137

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Zacharias Sautner
Frankfurt School of Finance & Management

The Review of Financial Studies / v 33 n 3 2020

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be adversely affected by carbon pricing or limits on carbon emissions.
Technological innovations related to climate change also threaten the business
models of some portfolio firms that operate in traditional industries. For
example, electric or fuel-cell-powered vehicles could disrupt traditional car
manufacturers. These risks to portfolio companies, which can broadly be
categorized into physical, regulatory, and technological climate risks, have the
potential to adversely affect the outcomes for many investment management
clients, pension beneficiaries, and shareholders of institutional investors. At
the same time, climate change also provides investment opportunities for the
portfolio companies and their institutional investors, for instance, in the areas
of renewable energy or energy storage.
A nascent literature in finance provides theoretical and empirical evidence
that institutional investors should consider climate risks in their investment
decisions. Notably, recent asset pricing models highlight the importance of
climate risks as a long-run risk factor (Bansal, Kiku, and Ochoa 2017) and the
importance of carbon risks and environmental pollution in the cross-section of
stock returns (Bolton and Kacperczyk 2019; Hsu, Li, and Tsou 2019). Growing
evidence indicates that climate risks may be mispriced in financial markets
(Hong, Li, and Xu 2019; Daniel, Litterman, and Wagner 2017; Kumar, Xin,
and Zhang 2019). At the firm level, Addoum, Ng, and Ortiz-Bobea (2019) show
that extreme temperatures can adversely affect corporate earnings, Pankratz,
Bauer, and Derwall (2019) provide evidence that increasing exposure to high
temperatures reduces revenues and operating income, and Kruttli, Tran, and
Watugala (2019) show that extreme weather is reflected in stock and option
market prices. Moreover, evidence suggests significant changes for firms after
the Paris Agreement. For example, greater climate risk leads to lower firm
leverage with firms decreasing their demand for debt and lenders reducing their
lending to firms with the greatest risk (Ginglinger and Moreau 2019); banks
began to price carbon risk into their loans after the Paris Agreement (Delis,
de Greiff, and Ongena 2019); and credit ratings and yield spreads changed for
polluting firms (Seltzer, Starks, and Zhu 2019). In addition, studies conclude
that firms can lower their cost of capital and increase value by improving their
environmental policies (Sharfman and Fernando 2008; Chava 2014; El Ghoul
et al. 2018). On the investor side, archival studies show that better environmental
policies are related to lower downside and overall portfolio risk (Hoepner et al.
2019; Gibson Brandon and Krueger 2018). In a similar spirit, Jagannathan,
Ravikumar, and Sammon (2019) argue that investors can reduce portfolio risk
by incorporating climate criteria into their investment processes and Rameli
et al. (2019) provide evidence that investors react to political events related to
firms’ climate strategies.
Despite the growing empirical evidence that investors should take climate
considerations into account, integrating climate risks into the investment
process can prove to be challenging, with investment tools and best practices
not yet well established. For example, many market participants, including

The Importance of Climate Risks for Institutional Investors

1 See Barnett, Brock, and Hansen (Forthcoming) for the challenges to price uncertainty induced by climate change.

Engle et al. (2019) and Andersson, Bolton, and Samama (2016a) discuss strategies to hedge climate risks.

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institutional investors, find climate risks difficult to price and hedge, possibly
because of their systematic nature, a lack of disclosure by portfolio firms, and
challenges in finding suitable hedging instruments.1
In this study we use a survey instrument to better understand whether and
how institutional investors consider climate risks in their investment decisions.
As such, we examine the ways in which investors view and manage climate
risks and whether systematic cross-sectional variation exists in their opinions
about climate risks and their strategies to manage these risks. Through this
analysis we contribute to the emerging archival research that suggests investors
should consider climate risks. Our study also contributes to the knowledge on
how institutional investors engage with their portfolio companies on climate
risk matters, adding to the findings in Dimson, Karakaş, and Li (2015, 2018)
and McCahery, Sautner, and Starks (2016). Understanding the specific role of
institutional investors is important, as they are increasingly viewed as catalysts
in driving firms to reduce their carbon emissions and to prepare for a low-carbon
economy (Andersson, Bolton, and Samama 2016b; OECD 2017).
The 439 survey respondents should be knowledgeable about the role of
climate risks for their institutions, as one-third hold executive-level positions in
their institutions. Further, our sample includes 48 respondents from institutions
with more than $100 billion in assets under management. This sizeable
representation of very large investors is useful, because such institutions could
have particularly strong influences on their portfolio firms’ climate policies.
The respondents’ institutions are located throughout the world, which allows
us to provide a global perspective on the role of climate risks. Our survey
addresses four key areas: the role of climate risks in investment decisions;
climate risk management; shareholder engagement related to climate risks;
and the implications of climate risks for asset pricing.
With regard to the first set of questions focused on the importance of climate
risks in comparison to other risks, we find that our respondents deem traditional
financial risks to be the most important risks they face, followed by operating,
governance, and social risks. Climate risks and environmental risks are ranked
fifth and sixth, respectively. However, this low relative rank does not imply that
climate risks are considered as financially immaterial. The investors believe
that climate risks have significant financial implications for portfolio firms.
This concern is also reflected in their climate expectations: the vast majority
of investors expect a rise in global temperature by the end of this century, and
four in ten even predict an increase that exceeds the Paris 2◦ C target. These
expectations reflect the possibility of very negative effects on financial assets
(Dietz et al. 2016).
A major challenge to investors can be the uncertainty of the time horizon
(Barnett, Brock, and Hansen Forthcoming; Andersson, Bolton, and Samama

The Review of Financial Studies / v 33 n 3 2020

2 We note that respondents with more sophisticated tools would have been more likely to participate in the survey.

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2016a) over which climate risks will materialize. Consequently, we also
evaluate the investors’ views on the horizons over which they expect climate
risks to materialize financially. Despite the potential horizon uncertainty, our
respondents do not view climate risks as a theme of the distant future. Fewer
than 10% believe that climate risks will materialize only in 10 years or more,
whereas 50% state that climate risks related to regulation have already started
to materialize.
Considerations of climate risks arise from both financial and nonfinancial
motivations. Purely financial motivations include how climate risks can affect
returns and risks. For example, Bénabou and Tirole (2010) posit that one
view of being environmentally responsible would be that of “doing well by
doing good,” under which investors take a long-term view and maximize
intertemporal profits. Some argue that climate change results in the stranding of
assets, which will lower portfolio values (Litterman 2013). Others maintain that
numerous investors consider climate risks primarily because of nonpecuniary
motives. Examples include the preferences of their clients or those of their
investment managers (Riedl and Smeets 2017; Hong and Kostovetsky 2012).
Other suggested motivations include regulatory requirements (FIR 2016), peer
pressure, or moral obligations.
Our survey demonstrates that no single motivation strongly commands
investors’ perspectives on the incorporation of climate risks into their
portfolio decisions. Agreement is strongest for three motives: the protection
of the investors’ reputations, their moral/ethical considerations, and their
legal/fiduciary duties, two of which (protection of reputation and legal/financial
duties) have both financial and nonfinancial implications (e.g., Fombrun
and Shanley 1990). The next highest-frequency motivations are more purely
financial: the ideas that incorporating climate risks into the investment process
improves investment returns and reduces portfolio risks.
The second and third areas of the survey focus on implementation aspects, in
particular, risk management and shareholder engagement. A survey is a useful
approach for studying these topics as implementation techniques are difficult
to detect using archival methods, because they are generally unobservable to
the researcher. For example, without asking investors, it is difficult, if not
impossible, to understand their use of scenario analyses, hedging activities,
and behind-the-scenes engagement practices. Our survey shows that investors
take a wide variety of approaches to managing climate risks, with only a small
percentage (7%) having chosen no approach to manage their climate risks
during the 5 years preceding the survey.2 Although large variation exists in
their approaches, the two major approaches are to conduct analyses of portfolio
firms’ carbon footprints and stranded asset risks, which are employed by 38%
and 35% of the respondents, respectively. Some of the respondents take these

The Importance of Climate Risks for Institutional Investors

3 To engage with portfolio firms, institutional investors are increasingly banding together over climate-focused

initiatives, such as Climate Action 100, the Portfolio Decarbonization Project, the Global Investor Coalition
on Climate Change, and CDP. For example, CDP—a nongovernmental organization that collects data on how
publicly listed firms manage climate risks—has support from investors who represented over $87 trillion in assets
under management in 2018.

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approaches one step further by attempting to reduce the carbon footprints
(29%) or stranded asset risks (23%) of their portfolios. Investors also use other
forms of climate risk management, such as incorporating climate risks into
their valuation models (26%) or hedging against climate risks (25%). From
the list of 12 possible approaches, the least frequently used tool is to divest
problematic portfolio firms, which is employed by 20% of the investors. The
large heterogeneity across investors suggests that the industry is still in the
process of finding the most effective ways to manage climate risks.
Our cross-sectional analyses indicate that institutions more concerned about
the financial costs of climate risks use a wider range of tools to manage risks
associated with climate change. Additionally, investors with longer horizons,
and institutions with a higher fraction of holdings subject to ESG analysis, also
engage in more climate risk management.
Institutional investors can also mitigate climate risks by engaging with
their portfolio firms.3 Through survey questions we examine the investors’
engagement strategies as well as their portfolio firms’ responses. We find a
generally high level of engagement by our respondent group as only 16% had
taken no engagement actions over the previous 5 years. This percentage is
comparable to the percentage in the McCahery, Sautner, and Starks (2016)
survey on shareholder engagement, in which they find that only 19% of
the respondents did not engage with their portfolio firms. The respondents
typically use multiple channels to engage over climate risks. Having discussions
with management is cited as the most frequently used channel (43% of
respondents used this approach, with 32% proposing specific actions to
management on climate risk issues). Close to 30% of the investors submitted
shareholder proposals on climate risk issues, and a similar fraction voted against
management on proposals because of climate risk concerns. These numbers
are consistent with a recent trend of successful votes on climate shareholder
proposals submitted to major oil and gas firms (Lemos Stein 2018).
Most firms responded to the investors’ engagements, although a number of
the firms simply acknowledged an issue rather than successfully resolving it.
Successful engagements are reported by 25% of respondents. If portfolio firms
did not respond to engagement or showed resistance, then the investors typically
refrained from further actions rather than initiating more engagement, trying
to hedge the climate risk issue or divesting from the firm. In fact, divestment
was the least used course of action when investors were dissatisfied with firm
responses to their engagement (only 17% exited under such circumstances).
This observation, together with the low prevalence of divestment for risk
management purposes, is interesting in light of the debate about whether

The Review of Financial Studies / v 33 n 3 2020

4 Nevertheless, even small adjustments can significantly affect asset values. A 5% market capitalization correction

among the world’s ten largest oil firms would imply a $65 billion value loss, based on data from May 2018.

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divestment or engagement is more effective in combating climate change,
particularly given that divestment is the approach recommended by a number of
activists and followed by an increasing number of institutions (Mooney 2017).
We find that investors that are more concerned about the financial effects
of climate risks engage firms along more dimensions. Larger investors also
engage firms across a wider range of channels, possibly because they have more
resources to engage and they have larger firm holdings. The latter reduces freerider concerns and implies stronger engagement incentives (Dimson, Karakaş,
and Li 2018).
The survey’s fourth section addresses the implications of climate risks for
asset pricing. Understanding institutional investors’ perceptions of any potential
mispricing is particularly relevant as they likely act as marginal investors,
thereby affecting equity prices. We elicit investors’ beliefs regarding whether
equity markets over- or underprice climate risks. To achieve meaningful
responses, we employ a sector-level approach including both directions of
mispricing, as climate risks may cause some sectors to be overvalued and others
to be undervalued.
Our respondents believe that equity valuations do not fully reflect the
risks from climate change, although the overvaluations are not perceived as
being very large. Not surprisingly, the oil sector is considered as the most
overvalued sector overall, followed by traditional car manufacturers and electric
utilities. Yet, the perceived misvaluation of these sectors relative to other
sectors seems modest.4 We find little evidence for a systematic link between
investor characteristics and their beliefs about the mispricing of climate risks.
That is, there exists little cross-sectional variation in the investor types with
the exception of two characteristics. We observe that the investor types that
view more underpricing of climate risks are those with a larger share of their
portfolios oriented to ESG standards and those that engage portfolio firms along
more dimensions (which may explain their engagement activities).
We also asked the investors for their opinions on whether climate change
causes assets in certain sectors to become stranded (Litterman 2013). We find
the largest percentages of respondents (25% and 21%) consider this stranded
asset risk to be very high in the coal and unconventional oil producer sectors,
respectively.
In terms of generalizability of our findings, we should note that our
respondent group is likely biased toward investors with a relatively high
awareness of climate risks, and possibly with higher credentials in climate risk
management. The reason is that such investors are probably more disposed
to participate in a climate risk survey. In addition, some of our responses
were obtained at ESG conferences. Nevertheless, understanding the views and
actions of such investors is particularly important, because they are more likely

The Importance of Climate Risks for Institutional Investors

1. Methodology and Research Design
1.1 Survey development
Our survey focuses on questions that are difficult to answer based on archival
data. Whenever possible, we generated our questions on the basis of theories
that make predictions about different aspects of climate risks. Internet Appendix
B provides the survey instrument.5 We used an iterative process for developing
the survey. As part of this process, we revised the survey based on the feedback
from two referees, several academics, and practitioners. We then presented the
survey instrument at a conference at Columbia University. After this event, we
further revised the survey based on feedback by a discussant and conference
participants. We also ran beta tests with practitioners to ensure the wording
and questions would be clear. Finally, we had a professional survey designer
review the wording, the ordering of the questions, and the length of the survey.
We then programmed an online version with random orderings of response
choices. An iterative process in designing a survey has been found to be

5 The survey also contained questions on methods to evaluate the consequences of climate risks for the investors’

portfolios, questions on the climate risk disclosure, and questions on the portfolio holdings relative to a lowcarbon benchmark. These questions are not covered in this paper because of space considerations. However, they
are discussed in Ilhan et al. (2019).

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to shape corporate climate policies and to guide future practices of integrating
climate issues into investment management.
Our paper contributes to a better understanding of the treatment of climate
risks in financial markets. By designing our survey in order to analyze
conceptual and empirical questions that are not directly testable through
archival research, we contribute to several literatures. We contribute to a better
understanding of the uncertainties of pricing of climate risk (e.g., Hong, Li,
and Xu 2019; Bansal, Kiku, and Ochoa 2017; Daniel, Litterman, and Wagner
2017) through documenting the importance institutional investors place on
climate risks, their forecasts of the probability of temperature changes, their
assessments of the relative mispricing in the industrial sectors most exposed
to climate risks, and how these attributes are related to investor characteristics.
Additionally, we contribute to the literature on risk management, particularly
the management of climate risk exposure (e.g., Andersson, Bolton, and Samama
2016a; Engle et al. 2019) by showing the extent to which institutional investors
use various risk management techniques and how investor characteristics
can explain these behaviors. We contribute to the literature on shareholder
engagements on environmental issues (e.g., Dimson, Karakaş, and Li 2015;
Dimson, Karakaş, and Li 2018; Hoepner et al. 2019; Barko, Cremers,
and Renneboog 2019) through our analyses of which investors engage, the
engagement channels they use to combat climate risk, and by providing
evidence on how firms typically respond to such engagements.

The Review of Financial Studies / v 33 n 3 2020

beneficial (Krosnick and Presser 2010). Surveys are increasingly used in the
finance literature, enabling better understandings of such topics as managers’
corporate-finance choices (Graham and Harvey 2001), institutional investor
activism (McCahery, Sautner, and Starks 2016), investor relations (Karolyi and
Liao 2017), ESG investing (Amel-Zadeh and Serafeim 2018), and barriers to
cross-border investing (Harvey et al. 2014).

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1.2 Survey delivery
We used both an online and a paper version of the survey that we distributed
through four delivery channels. First, we personally distributed the paper
version at four institutional investor conferences: the Sustainable Investment
Conference in Frankfurt on November 9, 2017; the ICGN Paris Event on
December 6 and 7, 2017; the Asset Management with Climate Risk Conference
at Cass Business School in London on January 23, 2018; and the ICPM
Conference in Toronto on June 10–12, 2018. We used the responses from
Frankfurt and Paris as beta tests to further improve the design. As a result, some
of the questions in the final survey were not included in these beta versions,
and some beta questions were dropped eventually. We obtained a total of 72
responses from these four conferences.
Second, we distributed the survey to a list of investment professionals
compiled by a survey service provider that manages a global panel of more
than 5m registered participants. The panel contains detailed data on individuals’
industries, job titles, and age to identify relevant panel subsamples. The service
provider has several mechanisms in place to ensure the authenticity of the
participants. Based on this panel we identified 1,018 individuals that work
in senior functions at institutional investors. The provider then invited these
panelists in March 2018 to participate in the online survey. To encourage
participation, the panelists received a small gift when filling in the survey (a
voucher or donation to charity). We obtained 410 initial responses from this
channel. To mitigate concerns over careless responses, we excluded participants
that took less than five minutes to complete the survey and participants for which
basic checks yielded logical inconsistencies in the responses (Meade and Craig
2012). We eliminated 90 responses in this process leaving 320 responses of
good quality. These respondents took on average 15 minutes to complete the
survey.
Third, in April 2018, we emailed invitations to participate in the survey
to a list of institutional investors that cooperate with a major asset owner on
climate risk topics through CERES and IIGCC. The asset owner ranks among
the world’s largest investors and wrote a supporting letter on our behalf. We
obtained 28 responses through this channel. The investor neither influenced the
survey design nor the analysis of responses. The investor also did not ask for
or receive access to the survey responses.
Fourth, we sent invitations to participate in the online survey to personal
contacts of the authors who work at different institutional investors, yielding

The Importance of Climate Risks for Institutional Investors

19 additional responses. In total we received 439 responses across the four
delivery channels.

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1.3 Respondent characteristics
Table 1 provides an overview of the characteristics for our survey respondents.
The largest numbers of respondents are fund/portfolio managers (21%),
followed by executive/managing directors (18%). About one-third of the
sample hold executive level positions in their institutions, such as CIO (11%),
CEO (10%), or in related functions (10%). Remaining respondents include
investment analysts/strategists (16%) and ESG/RI specialists (10%). Most
respondents work for asset managers (23%) and banks (22%), followed by
pension funds (17%), insurance companies (15%), and mutual funds (8%).
The remaining 15% work for other institutions, including sovereign wealth
funds, endowments or hedge funds. Our sample includes 19% of respondents
that work for institutions with less than $1 billion in assets under management,
32% with assets between $1 billion and $20 billion, 23% with assets between
$20 billion and $50 billion, and 16% with assets between $50 billion and $100
billion. A total of 48 respondents, or 11%, work for institutions with more than
$100 billion in assets.
We asked the respondents to report the typical holdings periods for their
investments. Respondents could classify holding periods into short (less than
6 months), medium (6 months to 2 years), long (2 years to 5 years), and very
long (more than 5 years). Only 5% of respondents’ institutions typically hold
investments for less than 6 months, 38% have medium holding periods, 38%
have long holding periods, and the remaining 18% typically hold investments
for more than 5 years. The headquarters of the institutions for which our
respondents work are located in different world regions: 32% are in the United
States, 17% in the United Kingdom and Ireland, 12% in Canada, 11% in
Germany, 7% in Italy, 5% in Spain, and the rest in other parts of the world. We
also collected information on the institutions’ investment structures. Across the
institutions the average portfolio share that incorporates ESG aspects is 41%,
they invest on average 47% in equities (43% in fixed income), and an average
of 38% of their assets is passively invested. Finally, we asked which positions
at their firms would be responsible for the implementation of climate risks in
the investment process (they could indicate more than one). The results indicate
that climate risks have become a topic with C-level responsibility at more than
50% of the investors: CIOs are responsible for implementing climate risks at
36%, and CEOs at 23%, of the institutions.
Because our respondents are anonymous, one question could be whether
we have redundancy in responses. However, we are confident that in the vast
majority of cases we have only one observation per institutional investor.
The reason is that, for 87% of the observations, we have sufficient data
to determine that none of the following identifying characteristics coincide:
location, assets under management, institutional investor type, investor horizon,

The Review of Financial Studies / v 33 n 3 2020

Table 1
Survey and respondent characteristics
Distribution channels (N = 439)
Panel
Conferences
Asset owner
Personal
Respondent position (N = 428)

Percentage
73
16
6
4

Investor horizon (N = 432)

Percentage

Short (less than 6 months)
Medium (6 months to 2 years)
Long (2 to 5 years)
Very long (more than 5 years)

5
38
38
18

Region (N = 429)

Percentage

21
18
16
11
10
10
10
2

United States
United Kingdom
Canada
Germany
Italy
Spain
The Netherlands
France

32
17
12
11
7
5
4
3

Institutional investor type (N = 439)

Percentage

Others (<3%)

9

Asset manager

23

Investment structure of portfolio

Mean

Bank
Pension fund
Insurance company
Mutual fund

22
17
15
8

ESG share (N = 415)
Equity share (N = 400)
Fixed income share (N = 402)
Passive share (N = 419)

40.6
47.0
43.1
38.2

Other institution

15

Positions responsible for climate
risk (N = 439)

Percentage

Assets under management (N = 430)

Percentage

Less than $1 billion
Between $1 billion and $20 billion
Between $20 billion and $50 billion
Between $50 billion and $100 billion
More than $100 billion

19
32
23
16
11

CIO

36

Fund/portfolio manager
Investment analyst/strategist
CEO
ESG/RI specialist
CFO/COO/chairman/other
Executive/managing director

29
26
23
23
19
18

This table provides summary statistics on the survey distribution channels and the characteristics of the 439
individuals that participated in our survey. As not all respondents provided information on all investor or
investment characteristics, the number of observations used in the different parts of the table can fall below
439. We report data on the distribution channel, position of the responding individuals (Question G8), type
of institution (Question G1), institution size (Question G6), investment horizon (Question G2), geographic
distribution (Question G7), ESG shares (Question G5), equity and fixed income shares (Question G3), passive
shares (Question G4), and institutional responsibility for climate risk policies (Question D3).

ESG share (±10% variation in the variable), equity share (±10%), and passive
share (±10%). In 9% of the observations we cannot exclude the possibility
that respondents work for the same institutional investors, as identifying
observations coincide. However, the responses are sufficiently different among
these respondents to discount that possibility with some degree of assurance.
In the remaining observations we have insufficient information to determine
whether characteristics coincide.
Internet Appendix Table 1 compares the respondents’ characteristics across
distribution channels. Most responses from our personal contacts were
ESG specialists, while respondents linked to the asset owner were mostly
executive/managing directors. The conference channel yielded mostly asset
managers or asset owners (especially pension funds), partially because they

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Percentage

Fund/portfolio manager
Executive/managing director
Investment analyst/strategist
CIO
CEO
CFO/COO/chairman/other executive
ESG/RI specialist
Other

The Importance of Climate Risks for Institutional Investors

were the demographics targeted by the conferences. The panel respondents
and those related to the asset owner work in smaller institutions; the panel
institutions further have shorter horizons. ESG portfolio shares are largest
among the asset owner’s partners and smallest for the panel. We use distributiontype fixed effects in all of our subsequent regression analyses to account
for systematic differences in the responses across the four distribution
channels.

6 Some part of the difference in the ESG shares may be explained by the growing trend of considering ESG topics

in investment mandates. Although our study captures investment characteristics survey as of 2018, the survey by
Amel-Zadeh and Serafeim (2018) was executed in 2016.

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1.4 Response bias
Any survey faces the risk that respondents answer strategically or untruthfully.
To mitigate this concern, we guaranteed anonymity, did not ask for names
or employers, and collected only limited information on the respondents’
institutions. The limitations of this approach are that we are unable to link
the survey responses to the institutions’ portfolio holdings and that some of
the collected investor characteristics may be too coarse to allow us to obtain
significant results in our cross-sectional tests.
We are unable to fully assess the potential response bias in our sample,
such as how our responses would change if we had a random set of investors.
However, we can provide some assessment of nonresponse bias by comparing
characteristics of responding investors to those of the population at large,
following, for example, Karolyi and Liao (2017). We compare the FactSet
population of institutional investors to our sampled population and find that
pension funds and banks are somewhat overrepresented in our sample (see
Internet Appendix Figure 1). In contrast, mutual funds and asset managers
are somewhat underrepresented. In terms of geographic distribution, our
respondents are more likely to work for institutions in North America and
Europe, compared to the universe of investors.
Overall, our respondent group is potentially biased toward investors with
a relatively high awareness of ESG topics and relatively higher credentials in
climate risk management. This outcome is a result of the fact that such investors
can be expected to be more disposed to participate in a climate survey, and
it is potentially also due to our delivery methods (especially the conference
channel). This potential sampling bias is reflected in our respondents’ high
average ESG share of 41%, which exceeds the percentages reported in other
studies. Amel-Zadeh and Serafeim (2018), for example, report an average
ESG share of less than 15% in their sample of institutional investors.6 We
also have an oversampling of large investors. However, as pointed out earlier,
understanding the views and actions of large investors with more sophisticated
climate risk policies is instructive due to their role as leaders in guiding
climate policies at portfolio companies, and other institutional investors.

The Review of Financial Studies / v 33 n 3 2020

In Internet Appendix Table 2, we evaluate the direction of the response bias
between institutional investors with high and low ESG share, and between large
and small institutions. We discuss these in Section 6.
2. Climate Risks in the Investment Process

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2.1 Expectations about climate change
For climate risks to be important in the investment process requires that
investors believe that climate change represents a risk. Thus, we first examine
whether investors view climate change itself as being a significant possibility
for the future. We ask their expectations regarding global temperature increases
at the end of the century. We anchored expectations by referring to the 2◦ C
target of the Paris Climate Accord and then requested the respondents’ own
expectations.
Figure 1A illustrates the respondents’ climate expectations in total and by
region. The figure shows a widespread belief in climate change. Across all
respondents, only 3% do not expect any temperature increase, 16% expect an
increase by up to one degree, and 30% by up to 2◦ C. Moreover, four in ten
respondents expect a temperature rise that exceeds the Paris 2◦ C target, with
12% expecting an increase of more than 3◦ C. Illustrating the consequences
of a temperature rise beyond 3◦ C , Thomas Buberl, CEO of insurer AXA has
expressed the view that “we can clearly say that at a scenario between 3◦ C
and 4◦ C, it’s not insurable anymore” (Hirtenstein 2018). These expectations
suggest that many of our respondents view very damaging climate scenarios to
be likely, which implies that at least some of our respondents should have deep
concerns about the effects of climate change on their portfolios. Examining the
differences across regions, we find that similar proportions of respondents from
North America and Europe expect temperature increases above 2◦ C. In addition,
North American respondents have more pessimistic expectations when it comes
to the most extreme scenario.
Because of the large uncertainty concerning climate change and its
consequences (Barnett, Brock, and Hansen Forthcoming; Andersson, Bolton,
and Samama 2016a), we asked the respondents to detail their confidence in
the reported expectations. Figure 1B illustrates their responses to this question.
Overall, there exists a large degree of confidence in expectations about global
warming given that 45% reported that they are relatively confident in their
expectations and another 34% are more or less confident. The figure also
indicates some heterogeneity in confidence levels across world regions, as
the percentage of relatively confident respondents varies between 36% and
51% with confidence levels being highest among North American respondents.
Internet Appendix Table 3 shows that respondents that expect a stronger
increase in temperatures also believe that climate change will have larger
consequences for firms, which indicates internal validity across responses for
some of the key climate variables we collected.

The Importance of Climate Risks for Institutional Investors

A 40%
35%
30%
25%
20%
15%
10%
5%
None
All Regions

Up to 1 degree Up to 2 degrees Up to 3 degrees More than 3
degrees
North America

Connental Europe

Do not know

United Kingdom

Rest of world

United Kingdom

Rest of world

B 60%
50%
40%
30%
20%
10%
0%
All Regions

North America

Relavely conﬁdent

Connental
Europe

More or less conﬁdent

Not very conﬁdent

Figure 1
Institutional investor climate change expectations
Figure 1A provides respondents’ expectations for the global temperature rise by the end of this century. We
report results for the full sample and by region. Regions include North America (United States and Canada),
Continental Europe, the United Kingdom and Ireland, and Rest of World. We anchored expectations by referring
in our question to the 2◦ C target of the 2016 Paris Climate Accord. Respondents were asked to state their own
climate expectations (Question D1) and to provide us with a confidence level for their assessment (Question D2).
Figure 1B provides responses on the confidence level, again reported for the full sample and by region.

2.2 Importance of climate risks
Recent asset pricing models highlight the importance of climate risks as a
long-run risk factor (Bansal, Kiku, and Ochoa 2017). However, it is unclear to
what extent investors consider climate risks to be important in their investment
decisions relative to other risks, and even whether they incorporate climate
risks into those decisions at all. To establish a benchmark for the investors’ risk
considerations, we asked the survey participants to state the relative importance
of six major risks when making investments in portfolio firms. Respondents
were required to rank these investment decision risks from one (most important
risk) to six (least important) (Question A1). Investors had to rank all six risks
and tied ranks were not allowed. Table 2, panel A, shows the percentage of

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0%

The Review of Financial Studies / v 33 n 3 2020

Table 2
Importance of climate risks and investor characteristics
A. Ranking of importance of investment risks (N = 406)

Percentage top risk
Mean ranking

Financial
risk

Operating
risk

Governance
risk

Social
risk

Climate
risk

Other environ.
risk

51
2.2

15
2.9

12
3.3

11
3.7

10
4.0

4
4.6

B. Financial materiality and materialization of climate risks
Financial
materiality

Regulatory climate
risk (N = 393)

Physical climate
risk (N = 393)

Technological climate
risk (N = 393)

Mean ranking

2.2

2.5

2.2

Regulatory climate
risk (N = 406)

Physical climate
risk (N = 401)

Technological climate
risk (N = 369)

55%
19%
17%
5%
2%
0%
1%

34%
32%
15%
9%
7%
1%
2%

33%
19%
26%
11%
7%
3%
1%

Risk
horizon
Already today
< 2 years
2 to 5 years
5 to 10 years
10 to 25 years
> 25 years
Never

(Continued)

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respondents that rank a specific risk as most important as well as each risk’s
mean importance rank. As the table illustrates, investors consider standard
financial risks (e.g., risks related to earnings or leverage), as most important,
followed by operating risks (e.g., changes in demand), corporate governance
risks (e.g., board structure), and social risks (e.g., labor standards). Climate
risks are ranked fifth, with only other environmental risks, such as air pollution
placing sixth. We find that 10% of the respondents consider climate risks as the
most important risk. Overall, the ranking across risks appears in line with the
focus on traditional investment risks in most of the finance literature. It also
reflects that most investors currently concentrate resources in the investment
process on risks other than climate risks (Blackrock 2016).
The low relative ranking of climate risks does not imply that the effects
of climate change are perceived as financially irrelevant. To understand
expectations of the financial effects of climate risks for portfolio firms, we
asked our participants in Question A2 to rate the financial materiality of three
sources of climate risks: physical risks (changes in the climate), regulatory risks
(changes in regulation), and technological risks (climate-related technological
disruption). Respondents were asked to rate each of these climate risks on a
scale of one (“very important”) to five (“not at all important”). Table 2, panel
B, shows that the respondents on average rate the financial consequences of all
three climate risks between 2.2 and 2.5, which means that the respondents regard
the financial materiality of climate risks to be somewhere between “important”
and “fairly important.” The effects of regulatory and technological risks are
seen as somewhat more important overall than those of physical risks (the

The Importance of Climate Risks for Institutional Investors

Table 2
(Continued)
C. Climate risks and investor characteristics
Climate
risk
ranking

Climate
risk
top 2

Climate risk
relative to
financial risk

Regulatory
climate
risk

Physical
climate
risk

Technological
climate
risk

(2)

(3)

(4)

(5)

(6)

−0.36
(−0.66)
−0.45
(−0.70)
0.08
(1.03)
0.89
(1.19)
0.39
(1.03)
−0.17
(−0.52)
2.10
(0.94)

−0.18
(−0.40)
0.12
(0.20)
−0.15∗
(−1.83)
−1.46∗∗∗
(−3.83)
−0.64
(−1.21)
0.26∗
(1.83)
−1.73
(−1.02)

−0.18
(−0.31)
−0.68
(−1.31)
−0.08
(−0.71)
−0.39
(−0.84)
−0.10
(−0.14)
−0.09
(−0.58)
2.17
(1.06)

−0.46
(−0.89)
−0.91∗∗
(−2.20)
−0.16∗
(−1.95)
−1.22∗∗∗
(−3.02)
−0.08
(−0.27)
0.37∗
(1.88)
3.03∗∗∗
(7.58)

−0.60
(−1.44)
−0.86∗∗
(−2.28)
−0.06
(−0.46)
−0.92∗∗∗
(−3.81)
−0.08
(−0.14)
−0.07
(−0.58)
1.93
(1.54)

Respondent position FE
Distribution channel FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Pseudo R -sq.

365
.013

365
.048

360
.029

373
.025

373
.040

373
.023

Long horizon
Assets under
management
ESG share (x100)
Passive share (x100)
Independent
institution
HQ country norms

Panel A reports the respondents’ rankings of six major investment risks. We asked respondents to rank the six
risks from one to six, where one is the most important risk and six the least important risk (Question A1). The
panel reports the percentages of respondents that rank a risk as the most important risk. We also report the
mean response, calculated as the average rank across respondents. Panel B reports the respondents’ ratings of
the financial materiality of different components of climate risk with respect to their portfolio firms (Question
A2). The responses can vary between one (very important) and five (not at all important). The panel additionally
reports the time horizons over which the respondents expect different climate risks to materialize financially
(Question A3). Panel C reports ordered logit regressions (probit in Column 2) relating the perceived importance
of climate risks to investor characteristics. We use five dependent variables: Climate risk ranking is the absolute
ranking of the importance of climate risks (see panel A). The variable ranges from one (most important risk)
to six (least important risk). Climate risk top 2 equals one if climate risk is ranked as the most or second most
important risk, and zero otherwise. Climate risk relative to financial risk is the difference in the ranking between
climate risk and financial risk. The smaller the difference the closer climate risk is ranked relative to financial risk.
Regulatory, physical, and technological climate risk measure the financial materiality of regulatory climate risk,
physical climate risk and technological climate risk (Question A2). All three variables can range between one
(very important) and five (not at all important). We use the following independent variables: Medium horizon;
Long horizon; Assets under management; ESG share; Passive share; Independent institution; and HQ Country
Norms (larger numbers reflect a stronger belief in the importance of environmental issues in an institutions’
country). Table A1 defines all variables in detail. t -statistics (reported in parentheses) are based on standard
errors that are clustered at the investor-country level. *p < .1; **p < .05; ***p < .01.

differences are statistically significant at the 1% level but relatively small in
magnitude).
The perception that climate risks matter financially conforms with evidence
from studies that use archival data to examine the financial effects of climate
risks. Ilhan, Sautner, and Vilkov (2019), for example, document that regulatory
climate risks increase tail risks in stock prices, and Addoum, Ng, and OrtizBobea (2019) find that extreme temperatures affect firm performance. Baldauf,
Garlappi, and Yannelis (2019) and Bernstein, Gustafson, and Lewis (2019)

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(1)
0.20
(0.35)
0.39
(0.66)
−0.16∗
(−1.93)
−0.60
(−1.20)
−0.30
(−0.73)
0.17
(1.18)
−1.20
(−0.78)

Medium horizon

The Review of Financial Studies / v 33 n 3 2020

7 Painter (2019) finds that investors seem to incorporate climate change into municipal bond pricing only for

long-term bonds.

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show that expected sea level rises affect real asset values in coastal areas,
although Murfin and Spiegel (2019) reach the opposite conclusion in their
analysis. Akey and Appel (2018) and Bartram, Hou, and Kim (2019) show that
pollution has real effects on firm decisions. Additional papers examine how fund
managers (Kumar, Shashwat, and Wermers Forthcoming) and other investors
(Choi, Gao, and Jiang Forthcoming) react to physical climate risk realizations.
Similarly, Gibson Brandon and Krueger (2018) find that institutional investors’
environmental policies change after extreme weather events and Painter (2019)
shows that climate change considerations affect municipal bond prices. Further
evidence regarding investor responses to climate risks lies in the fact that green
bonds have become increasingly important (Baker et al. 2018; Flammer 2018;
Tang and Zhang 2018; Zerbib 2019).
We expand this literature by evaluating investors’ expectations regarding the
horizons over which climate risks are expected to materialize. A challenge to
investor decision-making is that the horizon by which climate risks materialize
is highly uncertain (Barnett, Brock, and Hansen Forthcoming).7 Although one
usually assumes that physical risks mostly materialize over the longer term,
regulatory risks can have a much shorter time frame. We elicit investors’ views
on the time period over which they consider the climate risks will materialize
financially (Question A3).
Table 2, panel B, shows that the respondents overall believe that climate
risks have already become important concerns. Very few respondents, less than
10%, believe that the three components of climate risk will have a delayed
materialization of 10 years or more. In fact, a majority of the sample agrees
that regulatory risks are already important concerns today. Fewer investors,
but still more than 30%, believe that physical (and technological) risks are also
relevant today, consistent with some of the evidence in the research cited earlier.
Overall, our numbers indicate that the respondents consider climate risks
to matter for their institutions’ short-term as well as their long-term assets.
Moreover, their answers are consistent with the arguments of Weitzman (2012)
and Barro (2013) that climate change corresponds to disaster risk. As Giglio
et al. (2018) point out, climate change constitutes “a rare event with potentially
devastating consequences for the economy.”
The widespread perception that climate risks have begun to materialize raises
the question of when, if at all, investors began to incorporate these risks into
their investment processes. That is, how long have they been concerned about
these risks? Internet Appendix Figure 2 shows that for most investors this
is a relatively recent phenomenon. More than half of the respondents that
incorporate climate risks started to do so within the past 5 years. On the other
hand, a significant minority of investors have been long concerned about this

The Importance of Climate Risks for Institutional Investors

risk as 21% incorporated the risks into their investment process in some form
more than 10 years ago.8

8 It should be noted that this number could reflect a high awareness for climate risks among our respondents.

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2.3 Investors’ climate risk perceptions and investor characteristics
Next, we examine more closely the variation in perceptions of climate risks
across investors. Temperature-augmented long-run risk models, such as that of
Bansal, Kiku, and Ochoa (2017), imply that climate risks should be a bigger
concern for long-term investors, who are more likely to bear the consequences
of adverse climate risk realizations. In addition, recent research based on
archival data suggests that long-term investors care more about ESG issues
(Starks, Venkat, and Zhu 2018), and that environmental issues matter more
for investment performance when institutions are long-term oriented (Gibson
Brandon and Krueger 2018). These findings support the implication that
long-term investors should be more concerned about climate risks than shorterterm investors. Related evidence comes from Shive and Forster (2019), who
document a positive association between firm-level pollution and pressure from
short-term investors.
The largest institutional investors often own a slice of the world economy
through their sizeable holdings, and, thus, they are sometimes referred to as
universal owners. Such investors become more exposed to externalities from
climate change, causing them to be potentially more concerned about climate
risks. Much like the universal owners, other institutional investors with highly
diversified and more passively managed portfolios also should be more exposed
to climate risks, as they have less scope to divest assets with large climate risk
exposure. In addition, we expect investors who incorporate ESG factors also
to be more concerned about climate risks, given that they explicitly consider
environmental risks in their investment processes.
To test these cross-sectional predictions, we run regressions of the perceived
importance of climate risks on several investor characteristics. The results,
reported in Table 2, panel C, have several different proxies for investor
perceptions of climate risk as dependent variables. The dependent variable
in Column 1 is each respondents’ absolute ranking of climate risk. In Column
2 the dependent variable is a dummy that equals one if climate risk is ranked as
the most or second-most important risk. In Column 3, Climate risk relative to
financial risk is the difference in the ranking between climate risk and financial
risk, with smaller values of the variable indicating that a respondent has ranked
climate risk closer to financial risk. In Columns 4 to 6 the dependent variables
are the respondents’ assessments of the materiality of regulatory, physical, and
technological climate risks, respectively. These three variables range between
one (very important) and five (not at all important).
We include a set of independent variables to evaluate the predicted
relationships between perceptions of climate risks and investor characteristics.

The Review of Financial Studies / v 33 n 3 2020

9 As argued in Ferreira and Matos (2008) and Dyck et al. (2019), independent institutions are more likely to collect

information, have fewer potential business relationships with portfolio firms, and are therefore anticipated to
be more involved in monitoring management. We classify mutual funds, asset managers, hedge funds, private
equity funds, and public pension funds as independent institutions.

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Medium horizon (Long horizon) equals one if the typical holding period of
an investor is between 6 months and 2 years (above 2 years). Assets under
management equals one (less than $1bn); two (between $1 billion and $20
billion); three (between $20 billion and $50 billion); four (between $50
billion and $100 billion); or five (more than $100 billion). ESG share is the
percentage of the investor’s portfolio reported as incorporating ESG issues,
and Passive share is the fraction of the portfolio that is passively invested. We
additionally control for the institutional investor type (Independent institution)
and for the environmental norms in an institution’s home country (HQ Country
Norms). Independent institution equals one if an investor is considered to be
an independent institution and is zero otherwise.9 We control for HQ Country
Norms as the environmental norms in the country in which institutions are
headquartered are important determinants for their CSR preferences (see Dyck
et al. 2019). We also add fixed effects for the respondents’ positions in the firm
and for the survey distribution channel. These latter two aspects could affect
the responses.
In Columns 1 to 3 we cannot detect that medium- or long-term investors differ
from short-term investors in their perceptions of the importance of climate risk.
We find as shown in Columns 1 and 3 that larger investors rank climate risks
higher relative to other risks, possibly because such investors are more exposed
to externalities from climate change. We do not find a systematic link between
the importance of climate risk and the tendency of an institution to invest
passively. However, we do find in Column 3 that investors with higher ESG
shares rank climate risk closer to financial risk in terms of its overall importance
(reflected in a smaller distance in the rank importance of climate risk relative
to financial risk), which is consistent with the main investment thesis of ESG
oriented investors.
In Columns 4 to 6, we further find that several differences exist across
investors in terms of the perceived financial materiality of the three climate
risk components. Long-term investors find climate risks, in particular physical
and technological risks, to be substantially more financially material than do
other investors. Given that the average rankings (as shown in Table 2, panel B) of
these risks are either 2.2 or 2.5, the implied estimated differences in rankings of
around one-half for physical and technological risks are economically sizeable.
Large institutions consider physical risks in Column 5 as more financially
material, which is consistent with the idea that such investors bear greater costs
related to climate change. However, larger investors do not differ from other
investors in their assessments of the importance of regulatory and technological
risks. As would be expected, institutions with a greater proportion of ESG

The Importance of Climate Risks for Institutional Investors

investments regard physical and technological climate risk as more financially
relevant than do other investors.

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2.4 Motives for incorporating climate risks
Investors’ motivations for incorporating climate risks into their investment
decisions can be financial, nonfinancial, or a combination of both. Financial
motives include a quest for higher returns (possibly through mitigating the costs
of climate change), or lower risks (e.g., lower portfolio and tail risk). Bénabou
and Tirole (2010) propose several views on firm managements’ motivations
to engage in corporate social responsibility. One view is that institutional
investors take a long-term view and seek to maximize inter-temporal profits.
With regard to climate risks, this view implies that incorporating these risks into
the investment process is beneficial, because of higher returns or lower risks.
Gibson Brandon and Krueger (2018) and Hoepner et al. (2019) use archival
data in support of this view, but our survey allows for a more decisive answer
regarding investor motivations through a direct question about the financial
merits of incorporating climate risks.
Climate risk considerations can also arise because of nonfinancial
motivations. For example, considerations about climate risks may reflect the
investment managers’ personal preferences or their perceived moral or ethical
obligations. Hong and Kostovetsky (2012), for instance, show that political
preferences of investment managers predict their investments in socially
responsible stocks. A related view posits that investment managers consider
climate risks because it benefits them at the expense of their beneficiaries
(Bénabou and Tirole 2010). Further rationales include a combination of
financial and nonfinancial motivations, such as regulatory requirements,
protecting their reputations, and peer pressure.
We evaluate the relative importance of these nonmutually exclusive
motivations through Question A4 in which respondents could indicate their
agreement with different possible motives on a scale of one (“strongly
disagree”) to five (“strongly agree”). Table 3 reports the percentage of
respondents that “strongly agree” with each statement as well as the mean
response score. We also report the results of t-tests of the null hypothesis that
each mean score is equal to three (neither agree nor disagree) and that the mean
score for a given reason is equal to the mean score for each of the other reasons.
The table shows that agreement is strongest for two motives: the protection
of the investor’s reputation (30% strongly agree), which can arise from both
financial and nonfinancial motives, and moral/ethical reasons to consider
climate risks (27.5%), which would be a purely nonpecuniary motive.
Institutions also tend to agree with the motive of incorporating climate risks due
to a legal obligation/fiduciary duty (27%). Purely financial motives also score
relatively high, especially the idea that incorporating climate risks is beneficial
to returns (25% strongly agree) and reducing portfolio risk (24%) or tail risk
(21%).

The Review of Financial Studies / v 33 n 3 2020

Table 3
Motivation to incorporate climate risks
% with 5
(“strongly agree”) Mean
score
score

N

H0 :
Significant
Mean
differences in mean
score = 3
score vs. rows

(1)

(2)

(3)

(4)

(5)

(1)
(2)
(3)
(4)
(5)
(6)

29.7
27.5
27.0
25.2
23.5
22.6

4.03
3.88
3.87
3.85
3.85
3.88

417
415
415
417
417
416

∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗

2-11
1, 8-11
1, 8-11
1, 9-11
1, 9-11
1, 8-11

21.4
19.7

3.81
3.77

416
412

∗∗∗
∗∗∗

1, 9-11
1-3, 6, 10-11

18.5
18.2

3.69
3.68

411
390

∗∗∗
∗∗∗

1-7
1-8

15.6

3.68

416

∗∗∗

1-8

Protects our reputation
Is a moral/ethical obligation
Is a legal obligation/fiduciary duty
Is beneficial to investment returns
Reduces overall portfolio risk
Reflects our asset owners’
investment preferences
(7) Reduces tail risks
(8) Allows us to address
negative spillovers
(9) Helps attract fund flows
(10) Is increasingly stressed by
proxy voting advisors
(11) Follows the concerns of
other institutional investors

This table reports responses on the statements regarding possible motivations to incorporate climate risks into
the investment process (Question A4). Respondents could indicate their agreement on a scale of one (“strongly
disagree”) through five (“strongly agree”). Column 1 presents the percentage of respondents indicating strong
agreement to the statement. We rank results based on this measure. Column 2 reports the mean score, where
higher values correspond to stronger agreement. Column 3 reports the number of respondents. Column 4 reports
the results of a t -test of the null hypothesis that each mean score is equal to 3 (neither agree nor disagree). Column
5 reports the results of a t -test of the null hypothesis that the mean score for a given reason is equal to the mean
score for each of the other reasons, where significant differences at the 10% level are reported. ***p < .01.

3. Climate risk management
3.1 Approaches to climate risk management
Managing climate risks poses challenges to institutional investors because
of difficulties in pricing and hedging these risks. In addition, there are few
generally agreed upon methodologies as to how climate risks could and should
be managed. Through a survey we can develop a better understanding of how
institutional investors are approaching these issues. We collect information
on risk management tools currently employed by investors, which allows us to
evaluate current practices and to identify dimensions along which impediments
may exist. The academic literature on climate risk management at this point
is still in early stages, but Andersson, Bolton, and Samama (2016a) and Engle
et al. (2019) show that in principle investors can hedge climate risks, although
others argue that they are difficult to hedge in practice (CISL 2015). Another
form of risk management would be to avoid problematic firms as pointed out
theoretically by Heinkel, Kraus, and Zechner (2001) and empirically tested
by Fernando, Sharfman, and Uysal (2017). Focusing on a more established
mechanism, Dimson, Karakaş, and Li (2015) show that engagement on climate
risks can enhance shareholder value, and Dimson, Karakaş, and Li (2018)
study coordination in shareholder engagement on ESG issues. Our survey is

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Motivation to incorporate climate
risks into the investment process

The Importance of Climate Risks for Institutional Investors

Table 4
Climate risk management approaches
Percentage
that took
this measure

N

Significant
differences in mean
response vs. rows

Classification of
approaches
for Table 5

(1)

(2)

(3)

(4)

(1)

38.0

410

4-14

Passive

34.6
33.9
31.7
29.3

410
410
410
410

5-14
6-14
6-14
1-2, 10-14

Passive
Passive
Passive
Active

25.9

410

1-4, 12-14

Passive

25.6
25.1
24.6
23.7
22.9
20.2
7.1
3.7

410
410
410
410
410
410
410
410

1-4, 12-14
1-4, 12-14
1-4, 13-14
1-5, 13-14
1-5, 13-14
1-8, 12-14
1-12, 14
1-13

Passive
Active
Passive
Active
Active
Active
n/a
n/a

(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)

Analyzing carbon footprint
of portfolio firms
Analyzing stranded asset risk
General portfolio diversification
ESG integration
Reducing carbon footprint
of portfolio firms
Firm valuation models that
incorporate climate risk
Use of third-party ESG ratings
Shareholder proposals
Hedging against climate risk
Negative/exclusionary screening
Reducing stranded asset risk
Divestment
None
Other

This table reports the percentage of respondents that in the previous 5 years took a given approach to incorporate
climate risks into the investment process (Question B1). Responses were not mutually exclusive. We rank results
based on their relative frequency. Column 1 presents the percentage of respondents that took a certain measure.
Column 2 reports the number of respondents. Column 3 reports the results of a t -test of the null hypothesis that
the percentage for a given approach is equal to the percentage for each of the other approaches, where only
differences significant at the 10% level are reported. Column 4 classifies the motives into more active and more
passive approaches for the analysis in Table 5.

additionally informative because it allows to evaluate which risk management
techniques a broad spectrum of investors uses.
Question B1 is designed to determine which approaches the respondents’
institutions had taken in the previous 5 years to incorporate climate risks
into their investment processes. Table 4 reports the percentage of respondents
that employed a particular approach. Strikingly, only a very small percentage
(7%) of respondents had not taken any measures, which could be influenced
to some extent by our sample selection. The responses also indicate that
investors employ a wide spectrum of approaches without one approach being
strongly dominant. The fact that there does not exist an overwhelming dominant
approach could reflect the immaturity of the developed approaches to climate
risks. That is, investors are still learning how to deal with these risks.
The most frequently used current techniques have been analyses of firms’
carbon footprints and stranded asset risks, employed by 38% and 35% of the
investors, respectively. Thirty-two percent of the respondents deal with climate
risks by integrating ESG more generally into their investment processes. The
flipside of these numbers is that they indicate about two-thirds of investors
currently do not even use these basic approaches to manage climate risks.
Some investors indicate that they incorporate climate risks prior to making
investments, especially through screening (24%).

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Climate risk management approaches
taken in the past 5 years

The Review of Financial Studies / v 33 n 3 2020

3.2 Climate risk management and investor characteristics
To better understand institutions’ climate risk management, we develop an
index that reflects the spectrum of risk management techniques employed.
Climate risk management counts the different approaches an investor has taken
in the previous 5 years. In our survey we cover 13 possible techniques, implying
that the index can vary between 0 and 13. The index is designed to capture
the extent to which investors used different types of risk management tools,
rather than the degree to which they used any one type. Thus, we are capturing
the breadth of approaches rather than the depth or intensity. Conditional on
performing some sort of climate risk management, the median investor in our
sample uses three different approaches.
Additionally, we use two refinements of the index to explore which
investors use more active or more passive risk management techniques.
Active approaches counts the number of more active approaches used
(shareholder proposals, negative/exclusionary screening, reducing carbon

10 See Faust (2013). A related discussion is provided in Shancke et al. (2014).

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Regarding actions taken to manage climate risk after investments have been
made, 29% (23%) of respondents strive to reduce the carbon footprint (stranded
asset risk) of their portfolios, and 25% use some form of climate risk hedging.
The low percentage of investors who hedge climate risks may be in part a result
of the difficulty in differentiating among the uncertainty components of risk,
ambiguity, and misspecification (Barnett, Brock, and Hansen Forthcoming) as
well as further difficulties to hedging pointed out by Engle et al. (2019). Hedging
against climate risks requires not only understanding the fundamentally longlived risk of climate change, but also dealing with the difficulty of identifying
shocks, the proper horizon, and identifying the assets that correlate with the
outcomes, which overall results in the lack of existence of derivatives to engage
in hedging for climate change.
The least frequently used approach is divestment, although there still exists a
significant minority of investors (20%) who take this approach. The relatively
small number of investors who choose divestment informs the debate regarding
whether divestment or engagement is the more effective method for reducing
climate risk. We show in further analysis below that our investors have a higher
propensity to engage over climate risks than to avoid it by divesting. This
is consistent with the stated views of the Harvard endowment: “we maintain a
strong presumption against divesting investment assets” as the endowment is “a
resource, not an instrument to impel social or political change.”10 The lack of use
of divestment is consistent also with Bessembinder’s (2017) analysis indicating
significant costs to investors who divest fossil fuel companies. These costs
include reduced diversification, ongoing compliance costs, and transaction
costs.

The Importance of Climate Risks for Institutional Investors

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footprint, divestment, reducing stranded asset risk), while Passive approaches
counts the number of more passive approaches used (analyzing carbon
footprint, general diversification, ESG integration, valuation models, analyzing
stranded asset risk, hedging). We also explore which investor characteristics
are related with ex ante screening, exit (divestment) and voice (shareholder
proposals), three important but very different approaches to actively address
climate risks.
Given the uncertainty regarding how to manage climate risks, we expect
investors who are more concerned about the consequences of climate change
to engage in more climate risk management by using a greater breadth
of approaches. Similarly, investors who expect climate risks to materialize
earlier should also engage in more risk management techniques. Traditionally,
economists and others have assumed that climate risks are likely to be more
severe over the long term, which implies a prediction that long-term investors
would use a wider range of tools to manage these risks. In contrast, Giglio
et al. (2018) argue that short-term cash flows are riskier because they bear
the full brunt of a climate disaster, whereas long-term cash flows are less
exposed because the economy can recover. Thus, whether the breadth of risk
management approaches is higher among long-term or short-term investors
poses an empirical question. Given their role as universal investors, it is likely
that large investors employ more risk management, as they are more exposed to
climate externalities. Additionally, such investors should have more resources
to develop and use risk management tools. The role of the passive portfolio
share is more ambiguous. Investors with high passive holdings may use more
risk management as they cannot easily divest because of index tracking or
tracking error considerations. However, the low-cost business model of passive
investors may imply that they do not invest resources to actively manage climate
risks.
The results in Table 5 partially support our hypotheses. As expected, we find
in Column 1 that investors more concerned about the financial implications
of climate risks use a more diverse set of risk management tools. (Note
that smaller numbers for Climate risk materiality indicate that the investor
perceives climate risk as being more financially important.) In Column 2
we find no difference in the number of tools used between investors who
expect climate risks to materialize sooner versus those that expect them to
materialize later. Column 3 shows that investors with longer horizons engage
in a wider range of tools to manage climate risks. In fact, the estimates imply
that investors with a medium (long) horizon use 0.8 (1) more approaches, a
large number relative to the median of three approaches. Consistent with our
hypothesis, we find in Column 4 that larger investors manage climate risks
more broadly. Once we use a more complete specification in Column 5, we find
that some of the effects weaken, but most of the conclusions remain valid. In
particular, long-term investors still use about 30% more tools than the median
investor. Columns 6 and 7 show that medium-term and long-term investors

(1)
Climate risk materiality

(2)

Screening

Divestment

Shareholder
proposals

(9)

(10)

(5)

(6)

(7)

(8)

−0.45∗∗∗

−0.30∗∗

−0.41∗∗∗

−0.15∗∗∗

(−7.77)

(−5.78)
−0.01
(−0.03)
0.58
(1.52)
0.84∗∗
(2.07)
0.09
(1.32)
1.18∗∗∗
(3.12)
−0.25
(−0.61)
0.50∗∗
(2.21)
−0.24
(−0.15)

(−2.50)
0.06
(0.30)
0.57
(1.47)
0.42
(1.05)
0.04
(0.36)
1.59∗∗∗
(3.98)
−0.10
(−0.28)
0.15
(0.41)
0.30
(0.18)

(−3.40)
−0.10
(−0.64)
0.46
(1.31)
0.78∗∗
(2.02)
0.10
(1.13)
0.45
(1.41)
−0.37
(−1.00)
0.57∗∗∗
(3.02)
−0.97
(−0.65)

(−2.64)
0.04
(0.31)
−0.09
(−0.33)
−0.25
(−0.70)
−0.10∗∗∗
(−3.02)
0.84∗∗∗
(3.36)
0.03
(0.09)
−0.18
(−1.63)
0.19
(0.16)

0.01
(0.12)
0.12
(1.36)
0.45
(0.74)
0.77
(1.43)
0.07
(1.08)
0.53∗∗
(2.18)
0.38
(1.39)
0.46
(1.45)
−1.71∗∗
(−2.53)

−0.13∗∗
(−2.19)
−0.19∗∗
(−1.97)
0.59
(1.33)
0.41
(0.92)
0.04
(0.90)
0.83∗∗∗
(2.92)
−0.12
(−0.35)
0.21
(1.35)
−1.68
(−1.12)

−0.12
(−0.71)

Medium horizon
Long horizon

0.66∗∗
(2.24)
0.93∗∗∗
(3.07)

(4)

Passive
approaches

−0.49∗∗∗

Climate risk horizon

(3)

Active
approaches

1.23∗∗∗
(3.30)
−0.18
(−0.51)
0.44∗∗
(1.98)
0.09
(0.05)

1.43∗∗∗
(3.94)
−0.26
(−0.90)
0.44∗
(1.85)
−0.68
(−0.40)

1.25∗∗∗
(4.17)
−0.32
(−1.20)
0.49∗∗
(2.37)
0.07
(0.04)

0.14∗∗
(2.05)
1.22∗∗∗
(4.22)
−0.21
(−0.71)
0.45∗∗
(2.02)
0.22
(0.11)

Respondent position FE
Distribution channel FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Pseudo R -sq.

374
.050

393
.041

398
.036

399
.035

370
.051

370
.052

370
.051

367
.142

367
.080

367
.113

Assets under management
ESG share (x100)
Passive share (x100)
Independent institution
HQ country norms

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This table reports ordered logit and probit regressions relating climate risk management approaches to investor characteristics. Climate risk management counts the number of approaches
used in the past 5 years to incorporate climate risks into the investment process (Question B1). The remaining dependent variables capture subsets of this index. Active approaches counts the
number of active approaches used (shareholder proposals, negative/exclusionary screening, reducing carbon footprint, divestment, reducing stranded asset risk). Passive approaches counts the
number of passive approaches used (analyzing carbon footprint, general portfolio diversification, ESG integration, valuation models, analyzing stranded asset risk, hedging). Screening equals
one if an institutional investor used negative/exclusionary screening to manage climate risks, and zero otherwise. Divestment equals one if an institutional investor divested to manage climate
risks, and zero otherwise. Shareholder proposals equals one if an institutional investor submitted shareholder proposals to manage climate risks, and zero otherwise. We use the following
independent variables: Climate risk materiality (smaller numbers reflect greater perceived importance); Climate risk horizon (smaller numbers indicate that climate risks are expected to
materialize sooner); Medium horizon; Long horizon; Assets under management; ESG share; Passive share; Independent institution; and HQ country norms (larger numbers reflect a stronger
belief in the importance of environmental issues in an institutions’ country). Table A1 defines all variables in detail. t -statistics (reported in parentheses) are based on standard errors that are
clustered at the investor-country level. *p < .1; **p < .05; ***p < .01.

The Review of Financial Studies / v 33 n 3 2020

Climate risk management

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Table 5
Climate risk management approaches and investor characteristics

The Importance of Climate Risks for Institutional Investors

4. Shareholder Engagement on Climate Risks
4.1 Approaches to and success rates of climate risk engagements
Next, we assess how investors engage portfolio firms over climate risks, whether
such engagements are considered effective by the investors, and what actions
the investors take when their engagements are deemed unsuccessful. The benefit
of a survey is that because many engagements take place behind the scenes, it
is difficult to measure the effectiveness of engagement using archival data. We
asked the participants in Question B2 which measures of direct engagement
over climate risks they had taken with portfolio firms over the previous 5 years.
Table 6 presents evidence of a generally high level of engagement by our
respondent group: only 16% had not taken any actions over the past 5 years.
The respondents indicate that they used multiple channels to engage portfolio
firms over climate risks. Discussions with management were most frequent,
with 43% indicating that they had used the approach. The percentage compares
with 63% of the respondents in the McCahery, Sautner, and Starks (2016)
survey who used private discussions to engage management on governance
issues. The widespread use of private investor intervention regarding climate
topics supports the interpretation from their article that many investors first
engage firms through negotiations and take public actions only once the private
interventions fail. These results are also similar to the typical anatomy of
the engagement sequences analyzed in Dimson, Karakaş, and Li (2015), in
which engagements most often start with discussions between management
and shareholders and then potentially escalate depending on how the initial

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focus primarily on passive tools to address climate risks. The regressions in
Columns 6 and 7 also show that investors who deem climate risk as being more
important do not distinguish between active and more passive approaches but
use both approaches more broadly. Across Columns 1 through 5 we find that
investors with higher ESG shares use more climate risk management tools for
their investments. Unsurprisingly, high-ESG-share investors focus primarily on
active approaches to manage climate risks. In terms of our control variables, we
find that independent institutions engage in a wider range of primarily passive
tools to manage climate risks.
Turning to the specific tools used by the investors, Column 8 shows that
screening is more frequently used by smaller investors and by investors with
higher ESG shares, which seems intuitive because large investors are probably
more constrained in terms of screening and screening is probably one of the
most important forms of implementing ESG investing. The decision to divest
is unrelated to investor characteristics, with the exception that investors with
high ESG shares are more likely to exit due to climate concerns. Column 9
shows that more investors with higher ESG shares are also more likely to make
shareholder proposals on climate topics, which is also the case for the investors
who believe that climate risks are more important and will materialize earlier.

The Review of Financial Studies / v 33 n 3 2020

Table 6
Climate risk engagement

N

Direct engagement over climate risk issues in the past 5 years

(1)

(2)

(3)

(1)

43

406

2-10

32

406

1, 6-10

30

406

1, 6-10

30

406

1, 6-10

30

406

1, 6-10

20

406

1-5, 9

19

406

1-5, 9

18

406

1-5, 9

1
16

406
406

1-8, 10
1-9

(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)

Holding discussions with management regarding
the financial implications of climate risks
Proposing specific actions to management on
climate risk issues
Voting against management on proposals over
climate risk issues at the annual meeting
Submitting shareholder proposals on climate risk
issues
Questioning management on a conference call
about climate risk issues
Publicly criticizing management on climate risk
issues
Voting against reelection of any board directors due
to climate risk issues
Legal action against management on climate risk
issues
Other
None

Significant
difference in mean
response vs. rows

This table reports the percentage of respondents that haven taken a particular approach of direct engagement over
climate risk issues in the past 5 years (Question B2). We rank results based on their relative frequency. Responses
were not mutually exclusive. Column 1 presents the percentage of respondents that took a certain approach.
Column 2 reports the number of respondents. Column 3 reports the results of a t -test of the null hypothesis that
the percentage for a given approach is equal to the percentage for each of the other approaches, where significant
differences at the 10% level are reported.

discussions are received. Table 6 also indicates that a striking one-third of the
investors used these discussions to propose specific actions to management
about the firm’s climate policies. This result implies that a number of
institutional investors are actively involved with companies in combatting the
problems from climate change.
Climate risks are increasingly a controversial topic at annual shareholder
meetings. About one-third of the respondents have submitted shareholder
proposals on climate risk issues, and a similar fraction voted against
management proposals because of climate risk concerns. These numbers
are consistent with a recent trend of successful shareholder proposals at oil
companies. A proposal at Exxon Mobil, for example, asked management to
examine and disclose how climate risks would affect the company in the future.
The measure passed in 2017 with 62% of the vote.11 More confrontational
engagements are also taking place: 20% state that they publicly criticized the
management of portfolio firms over climate risk issues, 19% voted against

11 See Olson (2017) or Bauer, Moers, and Viehs (2015), who provide additional evidence on engagement success

with their finding that environmental proposals are more likely to be withdrawn, particularly if the sponsoring
shareholder is an institutional investor.

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Percentage
that used
this approach

The Importance of Climate Risks for Institutional Investors

4.2 Climate risk engagement and investor characteristics
Next, we study the determinants of investors’ propensity to engage over climate
policies. As with our risk management index, we create a variable that sums
the different engagement channels used by an investor. Our survey covers nine
intervention channels, implying that the index can vary between zero and nine.
Larger numbers indicate a stronger tendency to engage along multiple channels.
A caveat of our index is that it equally weights the different measures without
accounting for the severity of the actions taken (e.g., initiating a lawsuit is
probably a more severe action than holding discussions with management).
The index also does not account for the investor effort or cost associated with
using a specific engagement channel. To partially address these caveats, we
also individually examine how investor characteristics relate to the three most
frequent approaches as well as to the most hostile one (lawsuits).
Similar to our arguments for risk management, investors that are more
concerned about climate risks, and those that expect the risks to materialize
earlier, should engage along more dimensions. Investors with longer horizons
12 See Hodges, Leatherby, and Mehrotra (2018). This article also documents that litigation against firms over climate

change massively increased in the last few years.

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the reelection of directors because of their handling of climate risks, and 18%
initiated legal measures over climate risks. Reflecting an increasing trend of
climate litigation risk, BP’s CEO recently refused to disclose climate targets
and to answer questions from activist investors because of the fear of legal
actions.12 The median investor in our sample engaged through two channels
only.
A benefit of a survey is that it allows the direct measurement of whether
engagement—especially when private—is successful. Thus, we asked how
portfolio firms typically responded to engagement over climate risks (Question
B3). Targeted firms responded in most cases (71%) to the climate risk
engagement by their investors (Figure 2A), although the typical response was
acknowledging an issue rather than successfully resolving it (Figure 2B).
A successful completion of a typical engagement is reported by 25% of
respondents. Figure 2C further shows that if portfolio firms did not respond to
an engagement or showed resistance, then investors usually gave up and did not
take further actions (40%) (Question B4). Only 17% indicate that they divested
when being dissatisfied with portfolio firms’ responses. The remaining investors
either initiated the next level of engagement (21%) or tried to hedge the risk
(23%). These numbers corroborate our prior result that climate risks usually do
not trigger divestment, at least among most investors in our sample. Most of our
investors’ actions appear consistent with the view that divestment would reduce
investor influence to improve climate policies. As Marcel Jeucken, managing
director of responsible investment at PGGM observed, “if we divest, other
investors will buy the stock and nothing will change” (see Nicholls 2015).

The Review of Financial Studies / v 33 n 3 2020

A 80%

71%

70%
60%
50%
40%
29%
30%
20%
10%
Firm did not respond

Firm responded

B 40%
35%
30%
25%

20%
15%
12%
10%

9%
3%

0%
Resistance
(against
issues raised)

Issues were
Issues
were
acknowledged,
acknowledged but no acons
were taken

C 45%

Acons were
iniated, but
not
successfully
implemented

Acons were
successfully
implemented

Other

40%

40%
35%
30%
25%

21%

20%

23%

17%

15%
10%
5%
0%
No further acons
taken

Selling of
Iniated next level of Tried to hedge the
shares/divestment
engagement
climate-risk issue

Figure 2
Responses to climate risk engagement
Figure 2A reports whether the management of portfolio companies typically responded to the investor’s
engagement over climate risk issues (Question B3). Figure 2B reports the portfolio companies’ typical responses
to such engagements (also Question B3). Figure 2C reports the investors’ responses if the portfolio companies
either did not respond to the engagement (see Figure 2A) or showed resistance (see Figure 2B) (Question B4).

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0%

The Importance of Climate Risks for Institutional Investors

5. Pricing of Climate Risks across Industries
Recent research suggests that climate risks can significantly affect equity
markets. In Bansal, Kiku, and Ochoa (2017) rising temperatures negatively
affect the economy by increasing economic risk and reducing growth. Daniel,
Litterman, and Wagner (2017) calibrate the price of climate risk and suggest
that potentially large deadweight costs exist from delays in climate change
mitigation. In a similar spirit, Litterman (2011) argues that carbon emissions
should be priced at high levels immediately, primarily due to the risk of
catastrophic damages. In line with these approaches, Andersson, Bolton, and
Samama (2016a) assume that markets overvalue carbon-intensive assets to
derive hedging strategies. Empirical evidence supporting the mispricing of
climate risks exists as well. For example, Hong, Li, and Xu (2019) conclude
that the exposure of food stocks to drought risks are incorrectly valued by
markets. Similarly, Kumar, Xin, and Zhang (2019) present evidence that firms’
exposures to climate risks predict returns, which implies that stock markets

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should also have stronger engagement incentives, as they benefit more from
improving climate policies. Larger investors have more resources and larger
holdings in firms, reducing free-rider concerns and implying also stronger
engagement incentives. For the reasons provided above, ESG investors should
have stronger incentives to engage. The role of the passive portfolio share is
again more ambiguous, for the same arguments provided in the previous section
on the management of climate risks.
Table 7 reports our tests of these hypotheses. Consistent with our hypotheses,
we find that the investors who consider the effects of climate change to be
more financially material and use more engagement channels (see Column
1). Further, as predicted, larger investors also engage firms along more
dimensions (see Columns 4 and 5), although we have no evidence that long-term
investors use more engagement channels. Some evidence suggests, however,
that investors with medium investment horizons engage using more channels
(see Column 3). As expected, investors with a greater share of ESG-oriented
investments use a wider variety of engagement channels. We find that investors
with more passive holdings tend to use fewer engagement channels.
When we explore individual engagement channels, we find that more passive
institutions have a lower propensity to engage in discussions with management
(see Column 6). The institutions that expect climate to materialize earlier
are more likely to propose specific actions to management (see Column 7).
Moreover, the investors that are more concerned about the financial effects
of climate risks, and those that expect them to materialize earlier, are more
likely to vote against management. The same holds for larger institutions and
institutions with larger ESG shares. The willingness to file a lawsuit because
of climate issues is higher among larger institutions but otherwise unrelated to
investor characteristics.

(1)
Climate risk materiality

(2)

(3)

(4)

(5)

Holding
discussions

Proposing
actions

Voting against
management

Legal
action

(6)

(7)

(8)

(9)

−0.47∗∗∗

−0.56∗∗∗

−0.53∗∗∗

(−5.30)

(−4.39)
−0.15
(−1.02)
0.52
(1.44)
0.09
(0.16)
0.15∗∗
(2.11)
1.06∗∗∗
(3.03)
−1.04∗
(−1.71)
0.36∗∗∗
(2.70)
0.44
(0.32)

0.05
(1.01)
0.01
(0.10)
0.61∗
(1.85)
0.39
(0.66)
0.02
(0.44)
0.36
(1.05)
−0.88∗∗∗
(−4.12)
0.19
(1.14)
−1.22
(−1.38)

−0.09
(−1.29)
−0.22∗∗
(−2.08)
−0.02
(−0.08)
0.24
(0.67)
0.05
(1.09)
−0.12
(−0.63)
−0.23
(−0.65)
−0.11
(−1.19)
−1.69
(−1.20)

(−10.02)
0.21∗∗
(2.56)
0.61∗
(1.78)
0.17
(0.42)
0.10∗∗∗
(2.63)
0.61∗∗
(2.06)
−0.02
(−0.09)
0.31∗∗
(2.27)
−0.17
(−0.19)

−0.04
(−0.38)
−0.09
(−0.57)
0.06
(0.20)
−0.03
(−0.05)
0.19∗
(1.75)
0.55
(1.25)
0.13
(0.25)
0.07
(0.33)
−0.19
(−0.10)

−0.25
(−1.59)

Climate risk horizon
Medium horizon
Long horizon

0.97∗∗∗
(3.50)
0.57
(1.31)

1.16∗∗∗
(3.87)
−1.04∗
(−1.77)
0.37∗∗∗
(2.87)
0.47
(0.37)

1.43∗∗∗
(4.36)
−1.00∗∗
(−2.43)
0.37∗∗∗
(2.81)
−0.70
(−0.64)

1.37∗∗∗
(4.24)
−0.97∗∗
(−2.52)
0.35∗∗∗
(2.90)
0.11
(0.08)

0.25∗∗
(2.41)
1.24∗∗∗
(4.64)
−0.92∗∗
(−1.99)
0.38∗∗∗
(3.02)
−0.01
(−0.01)

Respondent position FE
Distribution channel FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Pseudo R -sq.

374
.054

393
.042

398
.046

399
.048

370
.057

364
.069

364
.056

364
.158

317
.069

Assets under management
ESG share (x100)
Passive share (x100)
Independent institution
HQ country norms

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This table reports ordered logit and probit regressions relating climate risk engagement channels to investor characteristics. Climate risk engagement counts the number of different direct
engagement channels that an investor has taken in the past 5 years (Question B2). The remaining dependent variables used in this table are individual components of this index. Holding
discussions equals of one if an institutional investor held discussions with management regarding climate risks, and zero otherwise. Proposing actions equals one if an institutional investor
proposed specific actions to management on climate risk issues, and zero otherwise. Voting against management equals one if an institutional investor voted against management on climate
risk issues and zero otherwise. The variable Legal actions equals one if an institutional investor took legal actions against management on climate risk issues, and zero otherwise. We use
the following independent variables: Climate risk materiality (smaller numbers reflect greater perceived importance); Climate risk horizon (smaller numbers indicate that climate risks are
expected to materialize sooner); Medium horizon; Long horizon; Assets under management; ESG share; Passive share; Independent institution; and HQ country norms (larger numbers reflect
a stronger belief in the importance of environmental issues in an institutions’ country). Table A1 defines all variables in detail. t -statistics (reported in parentheses) are based on standard
errors that are clustered at the investor-country level. *p < .1; **p < .05; ***p < .01.

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Climate risk engagement

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Table 7
Climate risk engagement and investor characteristics

The Importance of Climate Risks for Institutional Investors

13 See Hjort (2016) for a review of earlier climate risk papers.

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misprice climate risks. On the other hand, through their theoretical analysis,
Bansal, Kiku, and Ochoa (2017) show that equity portfolios have negative
exposures to long-run temperature fluctuations, which suggests that financial
markets may be able to price climate risks at least to some extent.13
We are able to contribute additional findings to this limited, and somewhat
mixed, evidence through questioning our investors directly in order to
understand the extent to which they believe that stock markets price climate risks
correctly. To examine investor beliefs on this issue, we asked the participants
whether they believe that current equity valuations correctly reflect the risks
and opportunities related to climate change (Question C1). As the exposure to
climate risks likely varies across the economy, we asked for their beliefs across
a range of industries. This sector approach, with both directions of mispricing,
is critical because the direction of mispricing is not known. The degree to
which climate risks are not recognized in valuations could vary by sector with
some sectors expected to be overvalued (e.g., the oil or coal sectors) and other
sectors expected to be undervalued (e.g., battery producers or water utilities).
This approach is supported by the prior research that indicates climate risks are
likely to vary across industries, depending on factors such as carbon emissions
or stranded assets (see Krueger 2015). Because of space and time constraints
for our participants, the survey does not cover all industries but only those
for which prior analysis indicates that climate change is likely to have a large
effect (Mercer 2015). As estimates about mispricing are uncertain, we take a
Bayesian approach and allow respondents to specify the confidence in their
estimates (Question C2). This enables us to evaluate how results change once
we put more weight on the responses accompanied with higher confidence
levels. That is, some respondents may provide more informed estimates given
their level of information.
Responses for each industry, reported in Table 8, can range between plus two
(“valuation much too high”; underpricing) and minus two (“valuations much
too low”; overpricing). Column 1 reports the mean score per industry, and
Column 2 reports the standard deviations of the means. Column 3 displays a
measure of relative misvaluation, which we construct as the industry mean score
relative to the mean score across all industries. We report in Columns 4 and 5
the percentages of respondents that indicate valuation levels that are “much too
high” or “much too low.” Column 6 reports the mean scores only for “relatively
confident” respondents. Although we directly asked about misvaluations related
to climate change, a caveat to our approach is that some respondents’ opinions
might reflect their views of general industry misvaluations at the time of the
survey.
The table reveals two principal findings. First, a mean valuation score of zero
would indicate a fair valuation. In contrast, we find the mean valuation scores to

Mean
score

STD

Relative industry
misvaluation

Percentage with score
of +2 (much too high)

Percentage with score
of -2 (much too low)

Mean score
(Confident respondents)

N

Page: 1098

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Oil
Automotive (traditional)
Electric utilities
Information technology
Insurance

0.52
0.48
0.47
0.47
0.46

1.03
0.94
0.91
0.98
0.91

37%
25%
25%
23%
21%

17
14
13
16
14

3
2
3
3
1

0.59
0.53
0.48
0.50
0.39

352
352
353
353
352

Natural gas
Coastal real estate
Gas utilities
Transportation
Construction

0.44
0.43
0.40
0.40
0.39

0.91
0.96
0.94
0.92
0.90

17%
13%
6%
4%
3%

11
14
11
12
10

2
3
4
3
3

0.51
0.43
0.38
0.37
0.44

352
350
353
351
351

Banking
Telecommunications
Water utilities
Infrastructure
Nuclear energy

0.38
0.38
0.37
0.37
0.35

0.96
0.88
0.96
0.93
1.05

0%
−1%
−2%
−3%
−7%

13
11
13
12
14

4
2
3
3
5

0.40
0.40
0.46
0.35
0.37

351
353
353
351
351

Chemicals
Coal mining
Automotive (electric)
Renewable energy
Raw materials (excluding coal)

0.35
0.35
0.33
0.31
0.27

0.96
1.07
0.92
0.98
0.90

−8%
−9%
−14%
−17%
−28%

12
16
11
11
7

3
5
2
3
3

0.40
0.35
0.36
0.30
0.34

350
351
352
351
350

Battery producers
Agriculture
Forestry and paper

0.27
0.27
0.27

0.97
1.02
0.97

−28%
−28%
−29%

11
13
9

4
5
4

0.30
0.39
0.36

349
349
351

Mean (across all industries)

0.38

12

3

0.41

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This table reports survey responses to a question that asked respondents to evaluate to what extent equity valuations of firms in different industries reflect the risk and opportunities related to
climate change (Question C1). Responses for each industry can range between plus two (valuations much too high) and minus two (valuations much too low). The table reports in Column 1
the mean scores across all respondents and in Column 2 the corresponding standard deviations. Column 3 reports a measure of relative misvaluation across industries. It is constructed as the
mean industry score divided by the mean score across all industries, minus 1. We also report in Columns 4 and 5 the percentage of respondents that indicate valuation levels that are “much
too high” or “much too low.” Column 6 reports the mean score only for those respondents that indicate that they are “relatively confident” about their valuation assessment (Question C2). We
rank responses by the mean score in Column 1.

The Review of Financial Studies / v 33 n 3 2020

Industry

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Table 8
Pricing of climate risks across industry sectors

The Importance of Climate Risks for Institutional Investors

14 The mean misvaluation score across all sectors of the economy is likely to be lower, as the sectors we selected

for our survey are probably more affected by climate change than the sectors that we did not include.
15 The authors point out that investors could have not been as concerned, because they considered alternatives, such

as carbon capture and sequestration, and other technological advances, changes in government energy policies,
whether oil and gas demand could actually be scaled back “within an economically meaningful horizon,” or the
lack of investor information about firms’ positions.

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exceed zero for every industry sector included in the survey. Thus, the average
respondent believes that the equity valuations of the sectors a priori most
exposed to climate risk do not fully reflect this risk. Rather the scores indicate
that investors believe valuations are somewhat too high, which suggests an
aggregate investor belief of climate risk underpricing.14 However, the responses
for most sectors are around 0.4, indicating that although investors believe
in widespread overvaluations, they are only modest overvaluations. Those
participants with more confidence in their assessments of relative valuation
show a slightly higher belief in mispricing. That is, mispricing is slightly
larger if we condition responses on participants with “relatively confident”
assessments. Another important finding is that investors’ answers do not reflect
precise estimates as substantial uncertainty exists around the mean estimates
(standard deviations range between 0.9 and 1.1).
The second principal finding is that relative sector mispricing is largest among
oil firms, traditional car manufacturers, and electric utilities. Yet, the magnitude
of sector-level mispricing is surprisingly low: the misvaluation of the three most
overpriced sectors is around 0.5 only, while the mean across all sectors is 0.38.
These numbers lead to a need for further research to better understand whether
the numbers reflect the broad belief that markets have already started to account
for the relative pricing of climate risks, or, instead, whether greater mispricing
exists but our investors do not recognize it. (Alternatively, it also could be
that our question simply did not capture relative mispricing well.) The first
possibility is consistent with the conclusions of Griffin et al. (2015) regarding
their findings of limited negative stock market reactions to concerns about a
carbon bubble and stranded assets for the largest oil and gas firms.15
To understand the responses to our mispricing question better, we examine
whether they vary systematically with certain investor characteristics. To
conduct this test, we create two indexes designed to capture the aggregate
mispricing. The first index, Climate risk underpricing, approximates an
investor’s aggregate view about overvaluation by averaging positive mispricing
scores (negative scores are set to zero). The index ranges between plus two
(strong average overvaluation) and zero (no average overvaluation). Our second
index measure, Climate risk mispricing, is nondirectional and is designed to
capture the general mispricing of climate risks by averaging the absolute values
of all mispricing scores. We additionally report regressions that explain the
underpricing of climate risks in the three industries that our investors believe
are the most mispriced. We use the same independent variables as in previous
tables and add the risk management and engagement indexes.

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The regressions in Table 9 provide little evidence of a widespread
systematic link between mispricing and investor characteristics. However,
two characteristics emerge as being particularly relevant. First, investors with
larger ESG shares generally view assets as being subject to more mispricing
(especially underpricing), possibly a reason that such investors promote
ESG factors to begin with. Second, investors that engage firms along more
dimensions believe that climate risks are more underpriced, which may explain
their engagement.
Assets are “stranded” if firms are unable to recover their investment cost,
implying a loss of value for investors (Carbon Tracker 2015). Many of those
concerned about climate risks consider stranded assets to be a particularly
significant risk for investors. McGlade and Ekins (2015), for example, estimate
that one-third of oil reserves, half of gas reserves, and over 80% of coal reserves
must remain unused until 2050 if countries are to meet the targets stipulated
in the Paris climate agreement. Thus, we question our investors on the risk
that climate change causes specific assets to become stranded (Question C3).
Table 10, panel A, reports how the investors consider this risk for six industry
subsectors, which we selected based on prior research (McGlade and Ekins
2015). Respondents could indicate their views on stranded assets using a scale
of one (“low”) through four (“very high”); they could also indicate “Do not
know.” For each industry subsector we report the percentage of respondents
that consider stranded asset risks to be “very high.”
We find that stranded asset risks are largest among coal producers, followed
by unconventional oil producers (tar sands or fracking). Yet, even for the
coal producers, which have the highest percentage of respondents believing
that they face stranded asset risks, only 25% believe this risk is very high.
However, the average response is 2.73 (out of 4), which suggests that a tendency
exists for investors to believe that stranded asset risk is present in the coal
sector.
Somewhat different from the cross-sectional analysis on mispricing, we find
in Table 10, panel B, evidence that the perception of stranded asset risks is
related to investor characteristics. Notably, investors that are more concerned
about the financial effects of climate risks believe that stranded asset risks are
higher among oil and natural gas producers. As before, investors who engage
firms more over climate topics, and those with larger ESG shares, perceive
higher stranded asset risks across most of the selected assets. Further, investors
with a higher share of passive investments perceive more stranded asset
risk.
Thus far, our analysis has mostly focused on downside risks associated with
climate change. However, climate change is likely to generate winners as well.
Understanding the associated opportunities is important for investors allocating
capital in the future. To identify how the institutional investor respondents
consider the potential opportunities, we asked them through an open question
to tell us which areas they see as providing the biggest opportunities from

Climate risk horizon
Medium horizon
Long horizon
Climate risk engagement

Climate risk mispricing

Average across all sectors

Average across all sectors

Climate risk underpricing
Oil

Automotive
(traditional)

Electric utilities

(1)

(2)

(3)

(4)

(5)

(6)

(7)

0.00
(0.08)
−0.00
(−0.09)
−0.07
(−0.50)
−0.06
(−0.43)
0.04∗∗
(2.18)

−0.01
(−0.18)
−0.01
(−0.29)
−0.06
(−0.46)
−0.05
(−0.43)

−0.03
(−1.10)
0.05
(0.87)
−0.01
(−0.05)
−0.01
(−0.09)
0.03∗∗
(2.87)

−0.04
(−1.57)
0.04
(0.75)
0.00
(0.03)
−0.00
(−0.00)

−0.06
(−0.37)
0.05
(0.45)
0.08
(0.17)
−0.14
(−0.28)
0.02
(0.21)

0.03
(0.25)
−0.09
(−0.68)
−0.86
(−1.61)
−1.07∗∗
(−2.29)
0.11
(1.61)

0.08
(0.43)
0.31∗
(1.81)
0.36
(0.46)
0.12
(0.11)
0.20∗∗∗
(3.54)

−0.06
(−0.67)
0.67
(1.30)
1.23∗∗∗
(2.67)
0.15
(0.61)
0.50
(0.47)

0.25∗∗∗
(3.14)
0.91∗
(1.86)
0.28
(0.51)
0.16
(0.53)
−0.07
(−0.09)

0.14
(1.54)
0.55
(1.48)
0.30
(0.42)
−0.12
(−0.44)
−0.25
(−0.16)

Climate risk management
0.03
(1.42)
0.28∗∗
(2.78)
0.02
(0.22)
−0.05
(−0.73)
−0.18∗
(−1.93)

0.01
(1.01)
0.03
(1.59)
0.29∗∗∗
(2.95)
−0.00
(−0.00)
−0.04
(−0.60)
−0.19∗
(−1.88)

−0.00
(−0.24)
0.19∗∗
(2.16)
−0.01
(−0.06)
−0.04
(−0.70)
−0.29
(−1.64)

0.00
(0.54)
−0.00
(−0.03)
0.22∗∗
(2.51)
−0.03
(−0.27)
−0.04
(−0.53)
−0.31∗
(−1.85)

Respondent position FE
Distribution channel FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Pseudo R -sq.

343
.035

343
.023

343
.012

343
.000

340
.041

340
.055

341
.040

Assets under management
ESG share (x100)
Passive share (x100)
Independent institution
HQ country norms

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This table reports OLS and ordered logit regressions relating perceptions of climate risk pricing to investor characteristics. The dependent variables capture the respondents’ views on
mispricing of climate risks (Question C1). Climate risk underpricing averages positive mispricing scores (negative scores are set to zero). The variable ranges between plus two (strong average
overvaluation) and zero (no average overvaluation). Climate risk mispricing averages the absolute values of all mispricing scores. We also report regressions that explain the underpricing of
climate risks in the three industries perceived to be most mispriced (oil, utilities and traditional automotive). We use the following independent variables: Climate risk materiality (smaller
numbers reflect greater perceived importance); Climate risk horizon (smaller numbers indicate that climate risks are expected to materialize sooner); Medium horizon; Long horizon; Climate
risk engagement; Climate risk management; Assets under management; ESG share; Passive share; Independent institution; and HQ country norms (larger numbers reflect a stronger belief in
the importance of environmental issues in an institutions’ country). Table A1 defines all variables in detail. t -statistics (reported in parentheses) are based on standard errors that are clustered
at the investor-country level. *p < .1; **p < .05; ***p < .01.

The Importance of Climate Risks for Institutional Investors

Climate risk materiality

Climate risk underpricing

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Table 9
Climate risk pricing across industry sectors and investor characteristics

The Review of Financial Studies / v 33 n 3 2020

Table 10
Stranded asset risk
A. Importance of stranded asset risks
% with 4
(“very high”)
score

Mean
score

% with
“do not
know”

N

(1)

(2)

(3)

(4)

(1)
(2)
(3)
(4)
(5)
(6)

25.1
21.3
16.7
11.9
11.7
10.5

2.78
2.69
2.64
2.46
2.40
2.42

3
3
4
3
5
4

371
371
371
370
369
371

Coal producers
Unconventional oil producers
Conventional oil producers
Natural gas producers
Iron and steel producers
Conventional electricity producers

Significant
differences in mean
score vs. rows

(5)

(6)

∗∗∗

2-6
1, 4-6
1, 4-6
1-3, 5
1-4
1-3

∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗

B. Stranded asset risk and investor characteristics
Stranded asset risk “very high”
Coal
producers

Unconventional
producers

Conventional
producers

Natural
gas
producers

Iron and
steel
producers

Conventional
electricity
producers

(1)

(2)

(3)

(4)

(5)

(6)

−0.23
(−1.26)
0.34∗∗
(1.98)
−0.80
(−0.99)
−0.99
(−1.18)
0.13
(1.07)
−0.05
(−0.33)
−0.30
(−0.80)
2.10∗∗∗
(3.65)
−0.26
(−1.49)
−2.66
(−1.50)

−0.60∗∗∗
(−3.14)
0.03
(0.18)
0.17
(0.21)
0.01
(0.02)
0.14∗
(1.86)
−0.17∗∗
(−2.16)
1.38∗∗∗
(4.13)
2.36∗∗∗
(5.61)
0.08
(0.26)
−5.09∗∗
(−2.42)

−0.66∗∗∗
(−2.87)
−0.19
(−1.02)
−0.42
(−0.53)
−1.26
(−1.53)
0.18∗∗
(2.15)
−0.13
(−1.61)
0.61
(0.97)
1.79∗∗∗
(5.25)
−0.88∗∗∗
(−2.60)
−0.44
(−0.24)

−0.57∗∗∗
(−4.18)
0.07
(0.37)
−1.93∗∗∗
(−2.66)
−1.84∗∗
(−1.97)
0.22∗
(1.92)
0.22∗∗∗
(3.27)
1.06
(1.45)
2.22∗∗∗
(3.75)
−0.28
(−0.65)
2.86∗∗
(2.02)

−0.18
(−1.11)
0.06
(0.38)
−1.09
(−1.36)
−0.33
(−0.44)
0.22∗∗
(2.22)
−0.25
(−1.59)
1.78∗∗∗
(2.73)
0.86
(1.11)
0.71∗∗
(2.44)
0.24
(0.14)

−0.18
(−0.94)
0.17
(0.72)
−0.64
(−0.76)
−1.08
(−0.94)
0.27∗∗∗
(3.90)
0.12
(0.46)
1.57∗∗∗
(2.79)
1.39∗∗
(2.18)
0.09
(0.25)
4.61∗∗∗
(4.27)

Respondent position FE
Distribution channel FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Pseudo R-sq.

345
.200

345
.175

343
.172

346
.177

337
.134

343
.143

Climate risk materiality
Climate risk horizon
Medium horizon
Long horizon
Climate risk engagement
Assets under management
ESG share (x100)
Passive share (x100)
Independent institution
HQ country norms

Panel A reports the investors’ responses to the question of how large they consider the risk that climate change
causes some assets to become stranded, that is, unable to recover their investment cost, with a loss of value for
investors (Question C3). We listed in the survey six industries for which we asked the respondents to evaluate
this risk. Respondents could indicate their views on a scale of one (“low”) through four (“very high”). They
could also indicate “Do not know.” In panel A, Column 1 presents the percentage of respondents indicating that
stranded asset risk is “very high.” We rank results based on this measure. Column 2 reports the mean score,
where higher values correspond to higher stranded asset risk. Column 3 presents the percentage of respondents
indicating “Do not know.” Column 4 reports the number of respondents. Column 5 reports the results of a t -test
of the null hypothesis that each mean score is equal to 1 (low stranded asset risk). Column 6 reports the results
of a t -test of the null hypothesis that the mean score for a given reason is equal to the mean score for each
of the other reasons, where significant differences at the 10% level are reported. Panel B in this table reports
ordered logit regressions relating perceptions of stranded asset risks to investor characteristics. The dependent
variables equal one if the respondent stated that stranded asset risks are “very high” and zero otherwise. We drop
observations where respondents indicated “Do not know.” We use the following independent variables: Climate
risk materiality (smaller numbers reflect greater perceived importance); Climate risk horizon (smaller numbers
indicate that climate risks are expected to materialize sooner); Medium horizon; Long horizon; Climate risk
engagement; Assets under management; ESG share; Passive share; Independent institution; and HQ country
norms (larger numbers reflect a stronger belief in the importance of environmental issues in an institutions’
country). Table A1 defines all variables in detail. t -statistics (reported in parentheses) are based on standard
errors that are clustered at the investor-country level. *p < .1; **p < .05; ***p < .01.

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Stranded asset risk

H0 :
Mean
score = 1

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Figure 3
Investment opportunities from climate change
This figure displays in a word cloud the responses that were given to an open question that asked the respondents to indicate in which areas, if any, they see the biggest investment opportunities
resulting from climate change (Question D4). The size of the words in the cloud corresponds to the frequency of their occurrence, with larger font sizes reflecting that an investment opportunity
was more frequently stated. We only list the top-15 words. N=378.

The Importance of Climate Risks for Institutional Investors

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The Review of Financial Studies / v 33 n 3 2020

climate change (Question D4). We classified the answers and report in Figure 15
the fifteen most frequent responses. The word cloud displays in larger font
those responses that were more frequent. Our respondents identify opportunities
mostly in renewable energy, but also in the areas of water (including water
supplies and management), electric vehicles, and technology.
6. Direction of Response Bias

7. Conclusions
We survey institutional investors to gain a better understanding of whether,
why, and how they consider climate risks in their investment decisions. We find
that the survey respondents generally think that climate risks have important
financial implications for their portfolio firms. Further, the majority believes
that climate risks, especially those related to regulation, have already started
to materialize. These beliefs are also reflected in the respondents’ climate
expectations: the vast majority expect a significant rise in global temperature
by the end of this century. Such expectations indicate that at least a significant
proportion of our respondents should have deep concerns about the effects
of climate change on their portfolios. The opinion that climate risks matter
financially conforms with evidence from studies that use archival data to
examine the financial effects of climate risks.
No single motive dominates the investors’ explanations for why they
incorporate climate risks into their investment processes. The most common
motives provided by the investors are to protect their reputations, moral/legal

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To evaluate the direction of potential response bias, we compare key survey
responses across different cuts of the data. Internet Appendix Table 2 reports
this comparison. We focus on contrasting the results between institutional
investors with high and low ESG share and between large and small institutions.
Additionally, we report a comparison of key results between the panel
respondents and the other three distribution channels. In panel A we find only
small differences across the subsamples in terms of the importance of climate
risks (high-ESG institutions rank climate risks only slightly higher than lowESG institutions). High-ESG-share and larger institutions generally also believe
that the financial materiality of the different sources of climate risks is higher. In
panel B we find high-ESG-share institutions, large institutions, and institutions
that were not part of the panel more strongly agree that they incorporate climate
risks because of financial and nonfinancial motives. Consistent with this finding,
panels C and D show that high-ESG-share and large institutions have a higher
propensity to conduct climate risk management and engagement. As we have an
oversampling of larger institutions and institutions with more ESG funds, these
differences support the possibility that our responses may be biased toward
investors with more developed climate risk polices.

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considerations, and the belief that climate risks affect portfolio risk and returns.
These findings imply that institutional investors consider climate risks both
because of nonfinancial and financial reasons.
Most of the respondents have taken at least first steps toward managing
climate risks, although the two most common approaches (analyses of carbon
footprints and stranded asset risks) have been used by less than half of
them. Divestment is the least frequently used approach overall. This finding
is interesting in light of the current debate about whether divestment or
engagement is more effective in combating climate change. Investors with
longer horizons generally use a wider range of tools to manage risks associated
with climate change. When investors engage portfolio firms over climate risks,
they usually prefer private discussions with management. The widespread use
of private intervention over climate topics implies that many investors first
engage firms through negotiations and take public actions only once these
private interventions failed. Larger investors generally engage firms along more
dimensions.
The average respondent believes that equity valuations do not fully reflect
the risks from climate change. Overvaluations are considered to be largest
among oil firms, followed by traditional car manufacturers, and electric utilities,
although the magnitudes of the overvaluations seem to be modest. Respondents
with larger ESG shares, and those that engage portfolio firms along more
dimensions, generally see more underpricing of climate risks.
Overall, our evidence indicates that investors consider climate risks as
important investment risks. While investors have already started to integrate
climate risks, the industry as a whole is still at early stages of incorporating
these risks into their investment processes. For example, many investors still do
not consider the basic approaches to identify and manage carbon and stranded
asset risks. In general, the long-term and larger investors appear better prepared
for the transition to a low-carbon economy.
Our analysis contributes to research that documents that investors should
consider climate risks. We hope that our findings help to spur additional
theoretical and empirical research in the area.

The Review of Financial Studies / v 33 n 3 2020

Appendix
Table A.1
Variable definitions
Variable

Definition

Survey question

Climate risk ranking

This variable is the absolute ranking of the
importance of climate risks. The variable ranges
from one (if climate risks are considered the
most important risk) to six (if they are
considered the least important risk).
This variable equals one if climate risk is ranked as
the most or second-most important risk and zero
otherwise.
This variable is calculated as the difference
between the ranking of the importance of climate
risk and the ranking of the importance of
financial risk.
This variable measures the financial materiality of
regulatory climate risk. The variable can range
between one (very important) and five (not at all
important).
This variable measures the financial materiality of
physical climate risk. The variable can range
between one (very important) and five (not at all
important).
This variable measures the financial materiality of
technological climate risk. The variable can
range between one (very important) and five (not
at all important).
This variable averages the responses to three
questions about the financial materiality of
regulatory, physical, and technological climate
risk. Each of these three variables can range
between one (very important) and five (not at all
important).
This variable counts the number of approaches
used in the past 5 years to incorporate climate
risks into the investment process.
This variable counts the number of active
approaches used (shareholder proposals,
negative/exclusionary screening, reducing
carbon footprint, divestment, reducing stranded
asset risk, and/or hedging).
This variable counts the number of passive
approaches used (analyzing carbon footprint,
general portfolio diversification, ESG
integration, valuation models, and/or analyzing
stranded asset risk).
This variable equals one if an institutional investor
used negative/exclusionary screening to manage
climate risks and zero otherwise.
This variable equals one if an institutional investor
divested to manage climate risks and zero
otherwise.
This variable equals one if an institutional investor
made submitted shareholder proposals to
manage climate risks and zero otherwise.
This variable averages the responses to three
questions about when the risk related to climate
change will materialize financially. Smaller
numbers indicate that the risks will materialize
sooner.
This variable counts the number of different direct
engagement channels that an investor has taken
in the past 5 years.

Question A1

Climate risk top 2

Regulatory climate risk

Physical climate risk

Technological climate risk

Climate risk materiality

Climate risk management

Active approaches

Passive approaches

Screening

Divestment

Shareholder proposals

Climate risk horizon

Climate risk engagement

Question A1

Question A2

Question A2

Question A2

Question A2

Question B1

Question B1

Question B1

Question B1

Question B1

Question B1

Question A3

Question B2

(Continued)

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Climate risk relative to financial risk

Question A1

The Importance of Climate Risks for Institutional Investors

Table A.1
(Continued)
Variable

Definition

Survey question

Holding discussions

This variable equals one if an institutional investor
held discussions with management regarding
climate risks and zero otherwise.
This variable equals one if an institutional investor
proposed specific actions to management on
climate risk issues and zero otherwise.
This variable equals one if an institutional investor
voted against management on climate risk
issues, and zero otherwise.
This variable equals one if an institutional investor
took legal actions against management on
climate risk issues and zero otherwise.
This variable averages positive mispricing scores
(negative scores are set to zero). The variable
ranges between plus two (strong average
overvaluation) and zero (no average
overvaluation).
This variable averages the absolute values of all
mispricing scores.
This variable equals one if the indicated typical
holding period of an institutional investor is
between 6 months and 2 years and zero
otherwise.
This variable equals one if the indicated holding
period of an institutional investor is above 2
years and zero otherwise.
This variable indicates the size of an institutional
investor and equals one (assets under
management less than $1 billion); two (between
$1 billion and $20 billion); three (between $20
billion and $50 billion); four (between $50
billion and $100 billion); and five (more than
$100 billion).
This variable is the percentage of the institution’s
portfolio that incorporates ESG issues.
This variable is the percentage of the institution’s
portfolio that is passively managed.
This variable equals one if an institutional investor
is considered to be an independent institution,
and zero otherwise. As in Ferreira and Matos
(2008) and Dyck et al. (2019), independent
institutions are more likely to collect
information, have fewer potential business
relationships with the corporations they invest in,
and therefore are anticipated to be more involved
in monitoring management. We classify mutual
funds, asset managers, hedge funds, private
equity funds, and public pension funds as
independent institutions.
This variable captures the importance of
environmental issues in the country in which an
institutional investor is headquartered. The data
are from Dyck et al. (2019), who construct the
variable based on the Environmental
Performance Index obtained from the Yale
Center for Environmental Law (Yale University)
and the Center for International Earth Science
Information Network (Columbia University) for
2004. Larger numbers reflect a stronger common
belief in the importance of environmental issues.

Question B2

Proposing actions

Voting against management

Climate risk underpricing

Climate risk mispricing
Medium horizon

Long horizon

Assets under management

ESG share
Passive share
Independent institution

HQ country norms

Question B2

Question B2

Question C1

Question C1
Question G2

Question G2

Question G6

Question G5
Question G4
Question G1

Question G7

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Legal actions

Question B2

The Review of Financial Studies / v 33 n 3 2020

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==> RFS10 - Corporate Climate Risk: Measurements and Responses.txt <==
Qing Li
Warrington College of Business, University of Florida, United States
Hongyu Shan
China Europe International Business School, China and Fordham University,
United States
Yuehua Tang
Warrington College of Business, University of Florida, United States
Vincent Yao
J. Mack Robinson College of Business, Georgia State University, United
States
This paper conducts a textual analysis of earnings call transcripts to quantify climate risk
exposure at the firm level. We construct dictionaries that measure physical and transition
climate risks separately and identify firms that proactively respond to climate risks. Our
validation analysis shows that our measures capture firm-level variations in respective
climate risk exposure. Firms facing high transition risk, especially those that do not
proactively respond, have been valued at a discount in recent years as aggregate investor
attention to climate-related issues has been increasing. We document differences in how
firms respond through investment, green innovation, and employment when facing high
climate risk exposure. (JEL G12, G31, G32, Q54)
Received: December 2, 2021; Editorial decision: June 30, 2023
Editor: Itay Goldstein
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

We thank Itay Goldstein (the editor), two anonymous referees, William Cong, Gustavo Cortes, Kris Gerardi, Gerard
Hoberg, Joel Houston, Chris James, Sehoon Kim, Nitish Kumar, Hao Liang, Tim Loughran (discussant), Xin Liu
(discussant), Kevin Mullally, Veronika Penciakova, Jay Ritter, Christoph Schiller (discussant), Jenny Tucker, and Baolian
Wang and conference/seminar participants at the 2021 AFA, the 2021 Second Sustainable Finance Forum, the 2021
RiskLab/BoF/ESRB Conference on Systemic Risk Analytics, the 2021 China International Risk Forum, the 2021 Rising
Star Conference, the 2020 NFA, the 2020 FMA, the 2020 Shanghai Green Finance Conference, Auburn University, the
Federal Reserve Bank of Atlanta, Fordham University, the University of Florida, and UT Dallas for helpful comments
and suggestions. We are grateful to Söhnke Bartram, Kewei Hou, and Sehoon Kim for sharing the GHGRP-Compustat
linktable and Pedro Matos for sharing the Global Corporate Patent data set. We also thank Osama Mahmood, Xiaoxiao
(Ray) Sun, Da Tian, and Mingyin Zhu for excellent research assistance. Vincent Yao gratefully acknowledges financial
support from Hong Kong Institute for Monetary and Financial Research. This paper represents the authors’ views, which
are not necessarily the views of the Hong Kong Monetary Authority, Hong Kong Academy of Finance Limited, or Hong
Kong Institute for Monetary and Financial Research. All remaining errors are our own. Supplementary data can be found
on The Review of Financial Studies web site. Send correspondence to Yuehua Tang, yuehua.tang@warrington.ufl.edu.

The Review of Financial Studies 37 (2024) 1778–1830
© The Author(s) 2024. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
https://doi.org/10.1093/rfs/hhad094
Advance Access publication January 16, 2024

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Corporate Climate Risk: Measurements and
Responses

Corporate Climate Risk: Measurements and Responses

1 For instance, a recent Standard & Poor’s (S&P) Ratings report reveals that the terms “climate” and “weather”

combined were among the most-frequently discussed topics in earnings calls among executives in S&P 500
companies—even more common than “Trump,” “the dollar,” “oil,” and “recession” (S&P Global Ratings 2018).

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Climate change poses severe challenges to businesses and society at large. Scientists predict that climate change will lead to increased incidence and severity
of both chronic and acute climate and weather events, leading to unprecedented
risks and disruptions that will affect corporations, the financial system, and
the aggregate economy (Litterman et al. 2020). Following the pioneering work
of Nordhaus (1977), many economists have studied interactions between
climate change and the economy (e.g., Golosov et al. 2014; Nordhaus 2019);
however, climate finance topics, such as how to assess, mitigate, and hedge
climate risk across firms and asset classes, have received limited attention
until recently. A major challenge to advancing this research agenda is the
lack of credible measures of climate risk exposure across asset classes, in
particular measures of equity assets (Hong, Li, and Xu 2019; Engle et al. 2020;
Giglio, Kelly, and Stroebel 2021).
Several factors contribute to the above-mentioned lack of measures of
firm-level climate risk exposure. First, in spite of stricter mandates imposed
by regulators and investor demand, firms remain reluctant to disclose their
climate risk exposure. For example, the most-common carbon emissions data
have been available for only a limited number of traditional sectors (e.g.,
manufacturing and utilities), and firms often omit the indirect costs of carbon
in supply chains (Shapiro 2021). Second, climate change is ever evolving, and
it remains unclear how the climate will eventually change and affect firms,
thus introducing significant uncertainty in government and corporate decisionmaking (Barnett, Brock, and Hansen 2020). Third, while historical emissions
data are needed to assess a firm’s past business models, data capturing forwardlooking views will be more useful in evaluating the firm’s climate exposure and
adaptability in the transition toward an environmentally sustainable economy,
an important goal for climate finance research (Giglio, Kelly, and Stroebel
2021).
In this paper, we fill this gap by quantifying, for the first time, climate risk
exposure at the individual firm level, using earnings call transcript data for
U.S. public companies. We use textual information from earnings calls in our
analysis for several reasons. First, the vast majority of U.S. public firms hold
regular earnings conference calls with their analysts and investors to discuss
performance and factors related to performance, and, a point that is critical
to this study, earnings calls contain detailed discussions with valuable and
insightful information about the climate risks a firm faces beyond those that
stem from public sources.1 Second, unlike other firms’ disclosures, such as
regulatory filings that are highly scripted and may lack informativeness and
timeliness (e.g., Brown and Tucker 2011), the content contained in quarterly
earnings transcripts is timelier and could vary significantly from quarter to

The Review of Financial Studies / v 37 n 6 2024

2 Humans are better at correctly teasing out the nuances of how the language of climate issues is used in a

particular context (e.g., earnings calls). Our choice builds on the premise that no algorithm understands the
context of human conversations better than human beings. See, for example, studies based on the most advanced
conversational AI algorithms, such as Google Meena (Adiwardana et al. 2020) and Facebook BlenderBot
(Roller et al. 2020; Xu, Szlam, and Weston 2021). See Section 3.1 for additional discussion of the advantages
of our approach of relying on human-constructed dictionaries over ML methods.

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quarter, allowing us to measure climate risk more accurately in real time.
Third, discussions in earnings calls are inherently weighted by importance as
an earnings conference call is a relatively short meeting where various parties
can discuss only what they view as material factors—a feature that is key to
measuring the importance of climate risks to firms. Finally, earnings calls also
include discussions on how firms respond to climate risks, which enables us
to capture firms’ proactiveness in addressing climate issues—a unique and
important innovation in our study.
We measure the climate risk faced by a given firm at a given time based
on the share of earnings calls conversations that are centered on physical
climate risk and transition risk, respectively. Our approach is similar to those
used by prior studies (e.g., Baker, Bloom, and Davis 2016; Hassan et al. 2019,
2023, 2020). More importantly, we also measure whether or not the company’s
attitude or response is proactive regarding the rise of climate risk by analyzing
the verbs used in climate risk discussions. To do so, we overcome several
challenges in applying standard textual analysis methods. The first is that
any such analysis must account for multiple categories of climate risk (e.g.,
Giglio, Kelly, and Stroebel 2021; Stroebel and Wurgler 2021), which can be
broadly classified as (a) physical climate risks, which are related to the
physical impacts of acute climate events (e.g., hurricanes and wildfires) or
chronic conditions (e.g., abnormal winter) and (b) transition risks. Given the
multifaceted nature of climate risk, it is challenging to create a single measure
that can capture all aspects of a firm’s climate risk exposure. Instead, we
measure distinct climate risks separately using a dictionary-based approach.
The second challenge faced when measuring climate risk is that a wellconstructed dictionary of climate-related keywords is not readily available in
the literature, and a significant number of false positive and false negative cases
arise if we apply a set of commonly known weather or climate keywords to a
large set of transcripts. We adopt the dictionary approach over the machine
learning (ML) method, with careful human supervision to minimize the
occurrence of false positives and negatives. This approach allows researchers
to make careful and deliberate judgment calls when classifying text based on
complex concepts, such as climate risks, while preserving transparency and
replicability.2 Through careful selection over many iterations, we construct
three comprehensive dictionaries consisting of over 1,600 climate keywords
that are not directly related to either energy costs or general environmental
risks.

Corporate Climate Risk: Measurements and Responses

3 Note that mentioning a well-publicized weather/climate event alone, without explicitly mapping onto a firm’s

risk profile, could reflect attention or shifting blame, but these factors do not contribute to our physical climate
risk measures.

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To construct climate risk measures, we require the respective physical
climate risk keywords to appear in the vicinity (±1 sentence) of at least one
risk synonym to ensure that firms are indeed exposed to uncertainty related
to climate-related events (as in Hassan et al. 2019).3 Transition risk differs
in that it may not materialize in the short term and is thus measured based
on discussions of keywords in our transition risk dictionary without having
to appear near a risk synonym. Our approach produces three climate risk
measures for each firm at quarterly frequency. In addition, using a list of
verbs that capture firms’ proactive attitudes when discussing transition risk,
we decompose our transition risk measure into proactive and nonproactive
components.
After establishing our measures, we conduct a battery of analyses to validate
that they indeed capture a firm’s exposure to climate risks. First, we examine
the list of most frequently discussed keywords in each of the measures and
find that the patterns are consistent with intuitions. Second, we examine the
time-series patterns as well as industry and firm-level variations in the climate
risk measures. While relative industry rankings vary across different types of
climate risks, they all exhibit significant variations that are consistent with
industry-level exposure to climate risks. Third, in our validation analysis using
various external benchmarks, we further demonstrate the validity of our climate
risk measures. Our analysis shows that the presence of natural disasters in a
local area is associated with a significant increase in both acute and chronic
climate risk measures for firms headquartered in that area over the subsequent
quarter.
Validating the transition risk measure, we examine its correlations with
two sets of existing external benchmarks: (1) firm-level MSCI Climate
Change Index (CCI) and (2) industry-level carbon dioxide (CO2 ) intensity
constructed by Shapiro (2021) and firm-level CO2 intensity based on the
U.S. Environmental Protection Agency’s (EPA) emissions data. First, we find
that our transition risk measure is positively and significantly correlated with
MSCI CCI. Second, we find a strong and positive correlation between the
average transition risk and CO2 intensity as measured by Shapiro (2021) at the
NAICS six-digit level for the manufacturing sector. Finally, analyzing firmlevel emissions data, we find that our transition risk measure—albeit only its
nonproactive component—is positively correlated with a firm’s CO2 intensity
in subsequent years. This relationship is significant in only one direction,
suggesting that firms that face higher transition risk but proactively respond
to such risks are indeed more active and effective in reducing their carbon
footprints.

The Review of Financial Studies / v 37 n 6 2024

4 For instance, in January 2010, the SEC issued its first interpretation of how existing disclosure requirements

apply to climate-related issues for public firms.

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While maintaining high correlation when overlapping, our newly developed
measures provide improved coverage and quantification of firm-level exposure
to climate risk compared to existing measures. Compared with ESG ratings, our
measures are available at the quarterly level for 4,719 public firms over a long
period of time, and are less prone to the selection bias that occurs commonly
with ESG data. Unlike the EPA’s plant-level CO2 emissions data, which are
limited only to firms that operate in the manufacturing, mining, and trade
sectors, our measures cover all sectors where earnings call data are available,
thus offering a comprehensive assessment of climate risk exposure across the
economy. Of all public firms with earnings call data available, about 61.8%
(2,918 firms) show at least one positive value in the transition risk measure,
which corresponds to 34.7% of the firm-years that have positive values in
transition risk. Even when considering the years when MSCI CCI data become
available, our measure, on average, provides coverage of transition risk to an
additional 952 firms with nonmissing values and 480 firms with positive values.
Furthermore, we show in a variance decomposition analysis that the majority of
variations in our three climate risk measures occur at the firm level, capturing
not only cross-firm but also within-firm variations in climate risk exposure.
Having established the validity of our measures, we next study one of
the most important issues in the climate finance literature—the extent to
which climate risk, especially transition risk, is priced in capital markets
(e.g., Bolton and Kacperczyk 2021a; Giglio, Kelly, and Stroebel 2021). We
first relate the firm-level transition risk measure to a firm’s market valuation
measured by Tobin’s q, and find that our transition risk measure is negatively
correlated with a firm’s Tobin’s q, suggesting that the firm’s transition risk
exposure is priced in equity markets. Second, we find that this relationship has
only become significant since 2010, likely because of rising aggregate investor
attention to climate risk (e.g., Choi, Gao, and Jiang 2020; Engle et al. 2020),
as well as climate-related initiatives and regulations implemented around
this time.4 Third, when analyzing the relative effects of the proactive and
nonproactive components of the transition risk measure, we find that only the
nonproactive component has a significantly negative relation with Tobin’s q,
suggesting that equity markets appear to discount only firms that do not actively
manage their transition risk, while not penalizing those that address risk
proactively. Importantly, these findings remain robust even after controlling
for firm fixed effects, providing additional support for the idea that changes in
climate risk discussion correlate with changes in Tobin’s q.
Further analysis shows that our measures capture unique information that
is useful in studying the pricing effects of climate risk based on horse-race
regressions with various alternative measures. In particular, we consider (1)
a transition climate risk measure constructed with the same dictionary but

Corporate Climate Risk: Measurements and Responses

1. Related Literature
Our paper contributes to the literature by constructing firm-level climate risk
measures. Properly measuring climate risk exposure across assets is critical
to any study of climate risk and its impact on the underlying assets. A
growing body of literature studies the effects of climate change on real estate
assets and housing markets using properties’ exposure to physical climate
risk factors, such as projected sea-level rise (SLR), flooding, and hurricanes
(e.g., Bernstein, Gustafson, and Lewis 2019; Baldauf, Garlappi, and Yannelis
2020; Goldsmith-Pinkham et al. 2023; Keys and Mulder 2020; Giglio et al.

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using textual information from firms’ 10-K/10-Q filings, (2) a transition risk
measure constructed based on climate-related company news from Dow Jones
Newswires, (3) MSCI CCI or ESG ratings, and (4) measures constructed by
Sautner et al. (2023) using different climate dictionaries and methods. In all of
these tests, the coefficients for our transition risk measure and its nonproactive
component remain negative and significant at the 1% level, confirming the
unique value added by both the earnings calls data and our construction
method. In summary, our transition risk measure generates new and valuable
information that is not already available in other public sources and also
provides comprehensive coverage over a large sample of public firms from
2002 onward.
In the last set of analysis, we explore how firms respond, in terms of
investments, innovation, and employment, to transition risk exposure. Our
results show that firms’ attitudes toward climate issues—their proactiveness—
matter significantly in how they respond to climate risk along these dimensions.
First, we find that, while there is no significant relation between transition
risk and investment as measured by total capital expenditures (CapEx) in
nonproactive firms, firms that proactively respond to climate risk tend to
increase their investment subsequently. Second, we find a negative relation
between transition risk and subsequent R&D expenditures, a finding that is
driven entirely by nonproactive firms. In contrast, proactive firms innovate
more actively by producing more green patents in subsequent years. Given
this relationship, we conduct further analysis to explore the attributes of
proactive firms and their potential differential impact on firm valuation. We
find some evidence that the equity markets tend to value proactive responses
to transition risk from green patenting firms more than nongreen proactive
responses. Finally, our employment analysis shows that firms that do not
proactively respond reduce employment following a rise in transition risk,
while the firms that proactively respond to transition risk do not reduce
employment subsequently. Taken together, our measures are useful not only
for understanding the pricing of transition risk in capital markets, but also for
predicting real outcomes as firms proactively respond to changes in climate
risk.

The Review of Financial Studies / v 37 n 6 2024

5 Relatedly, Engle et al. (2020) and Giglio et al. (2021) construct novel measures of market-level attention paid to

climate risk by analyzing textual descriptions of climate keywords in newspaper articles and property listings,
respectively.
6 Emissions data can be obtained from the EPA or the Carbon Disclosure Project (CDP). The former are mandatory,

as explained in Section 2.4, while the latter involve voluntary disclosure of emissions by firms. See, for example,
Bolton and Kacperczyk (2021a,b), Choi, Gao, and Jiang (2020), and Ramadorai and Zeni (2021).
7 For

studies of climate risk and fixed-income markets, see, among others, Painter (2020),
Goldsmith-Pinkham et al. (2023), and Huynh and Xia (2021). For studies of climate risk and real estate
markets, see, among others, Bakkensen and Barrage (2018), Bernstein, Gustafson, and Lewis (2019),
Baldauf, Garlappi, and Yannelis (2020), Murfin and Spiegel (2020), and Giglio et al. (2021).

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2021).5 With regard to equity assets, however, the literature still lacks a
set of measures with which to measure firms’ exposure to climate risks
systematically, and researchers must use alternative measures, for instance,
CO2 emissions data or ESG ratings (e.g., Engle et al. 2020)6 despite concerns
about their coverage and reliability (Stanny 2018; Berg, Koelbel, and Rigobon
2022). As a result, Giglio, Kelly, and Stroebel (2021) conclude in their
survey that there is “substantial scope for improvements of the measures of
climate risk exposure, in particular for equity assets.” Our paper represents
valuable progress toward developing new ways to quantify firms’ climate risk
exposure.
More broadly, our paper adds to the climate finance literature in several
ways. First, our measures can be used to study how capital markets price
climate risk. Several studies examine whether equity markets price risks
related to long-run temperature shifts, drought, sea-level rise, or carbon
emissions (e.g., Hong, Li, and Xu 2019; Bolton and Kacperczyk 2021a,b;
Hsu, Li, and Tsou 2023; Ilhan, Sautner, and Vilkov 2021). Other evidence
points to climate risks affecting fixed-income and real estate markets.7
Different from all these studies, we show, using our novel firm-level climate
risk measures, that climate risk is priced in equity markets, especially following
a rise in aggregate investor attention in recent years. We also document
that firms’ proactiveness attenuates the discounting of high climate risk in
equity markets. Second, our measures could help investors implement effective
hedging strategies, which is of great importance considering that many effects
of climate change will manifest far into the future and neither financial
derivatives nor insurance markets is available to directly hedge those longhorizon risks. Engle et al. (2020) propose an approach to dynamically hedging
climate risk using historical responses of individual stocks to their “Climate
News Index.” Our firm-level climate risk measures, along with their proactive
component, also can be used by investors to assess, construct, and hedge
portfolio exposure to aggregate climate risk in accordance with their risk
tolerance.
Our study is closely related to a contemporaneous paper by Sautner et al.
(2023). While both papers propose firm-level measures of climate exposure
using earnings call data, there are major differences in both the methodology
and the scope of the economic questions explored. Unlike Sautner et al.

Corporate Climate Risk: Measurements and Responses

2. Data
2.1 Earnings calls
To measure firm-level exposure to climate risk, we use as our primary
data source transcripts of earnings calls involving all U.S. public firms
obtained from Thomson Reuters’ StreetEvents database. These transcripts
record discussions between a public company’s management team, industry
analysts, investors, and the media regarding the company’s corporate strategy,
operating conditions, and financial performance for a given quarter. The same
data are used in several other papers, for example, Hassan et al. (2019), who
study corporate exposure to political risk, and Li et al. (2021), who create novel
measures of corporate culture. Firms typically hold one conference call in each
fiscal quarter following their earnings releases. Thus, we conduct most of our
analysis at the firm-quarter level. One important benefit, among others, of using
the earnings calls data is that, because the data are available for almost all public
firms, we can construct climate risk measures that place all public firms on a
level playing field, as opposed to using ESG scores only or other measures that
are available for only a small subset of firms that may be subject to selection
bias.8

8 We note that several caveats apply to the use of the earnings calls data. First, the data are available only for

public firms, thus missing a large number of private firms. This may introduce bias in estimating the effect of
high climate risk on firms’ responses if high-emitting firms choose to operate as private firms (Gilje and Taillard
2016). This factor should not, however, affect our estimates of the pricing effect of high climate risk because
Tobin’s q is a market valuation measure that is available only for public firms. Second, like any voluntary source
of disclosure data, earnings calls are not completely immune to how or when management chooses to discuss
climate-related topics. We believe that such strategic factors are less salient in earnings conference calls than
other disclosure data, as analysts could ask climate-related questions even if management chooses not to disclose
any information. More importantly, we carry out several additional analyses that we discuss in Section 7.5 to
alleviate the concern that our references will be materially changed by strategic disclosure.

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(2023), who use an ML algorithm, we construct climate-related dictionaries
manually through careful human supervision and iterative testing. Like that
of Loughran and McDonald (2011) and Baker, Bloom, and Davis (2016), our
approach is more transparent and less sensitive to initial inputs and parameter
choices than ML algorithms, providing us with what we consider as a necessary
and effective tool given the complexity of climate issues. More importantly,
the scope of the economic questions we explore in our study is quite different
from theirs. While they focus primarily on economic factors that correlate
with firms’ climate change exposure, we explore whether transition risk and,
especially, firms’ proactiveness in addressing it, are priced in equity markets as
well as how firms respond to transition risk. Our paper is unique as the first in
the literature to measure firms’ proactiveness in addressing climate issues. One
of our key contributions lies in documenting that proactive attitudes are priced
in equity markets and that proactive firms respond, in terms of investment,
green innovation, and employment, differently to rising transition risk.

The Review of Financial Studies / v 37 n 6 2024

2.2 Firm-level financial data
We obtain firms’ financial data from Compustat. We use Tobin’s q as the main
measure of a firm’s market valuation to examine whether the stock market has
priced the climate risks captured by our measures. To study a firm’s responses
to climate risk, we consider CapEx, R&D, and employment as outcomes. Other
firm-level attributes, such as total assets, property, plant, and equipment (PPE),
and the book leverage ratio, are used as control variables. All the firm-level
attributes are available at the quarterly level, except for employment data,
which are available only annually. Information about firms’ stocks is obtained
from the Center for Research in Security Prices (CRSP).
We match the earnings call data with other firm-level data using firm
identifiers and apply several filters. First, because many financial firms,
especially insurance companies, sell insurance products to others to hedge
climate- or disaster-related risks, we exclude financial firms (North American
Industry Classification System or NAICS 52) from our main analysis. Second,
we exclude firms whose headquarters are located outside the continental United
States. Our sample includes 4,719 unique firms and 139,959 firm–quarter
observations. Table 1 presents summary statistics for Tobin’s q, CapEx, R&D
expenditures, Property, Plant, and Equipment (PPE), book leverage, return on
assets (ROA), employment, and total assets. CapEx, R&D expenditures, and
PPE are all scaled by a firm’s total assets in the preceding quarter.9
2.3 Additional textual data
We also use textual information from firms’ regulatory filings, in particular
10-K and 10-Q filings, as alternative data sources to construct our climate risk
measures. We focus on the two most relevant sections in 10-K/10-Q filings: (1)
management discussion and analysis (MD&A) and (2) Item 1A “Risk Factors.”
MD&A section contains management discussions of firms’ performance, risks,
and future plans. The risk factors (RF) section provides information about the
risk factors a firm identifies that might influence the company or its equity
return. MD&A section is available for our entire sample period, from 2002
through 2018, while RF section is available only from 2006 onward following
the implementation of Regulation S-K Item 105.

9 Table A.1 in the appendix reports the descriptions and sources of the variables we use in our analysis.

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We use all earnings call data from January 2002 through the first half of
2018 in our analysis, and extract the texts of entire conference calls from the
raw XML transcript files using Python, which includes both presentations by
management and subsequent Q&A sessions. We also extract firm identifiers
(e.g., firm names, tickers, CUSIP numbers) and earnings call information (e.g.,
date and time) from the transcript files.

Corporate Climate Risk: Measurements and Responses

Table 1
Summary statistics
Variable

N

Mean

SD

Min

P25

P50

P75

Max

0.00
0.00
0.00
0.00
0.00
0.00
0.02

11.75
17.72
186.59
22.40
174.03
0.07
0.04

2.32
3.54
1.72
8.13
0.37
0.37
2.48
0.89
0.09
0.17
2.24

14.82
21.03
14.23
13.65
0.89
1.01
3.93
1.00
1.00
0.46
7.74

0.00
4.08
0.00
0.00
94.90
0.00
64.19

1.00
52.93
1.00
1.00
594.00
31.51
97.82

1.39
0.00
0.00

95.20
108.06
0.67

This table reports the summary statistics of all variables used in the regression analysis. All variables are at the
firm-quarter level, except that log(Employment), CO2 Intensity and green-patent-related variables are at the firmyear level. All the climate risk variables, including the acute, chronic, and transition climate risks are explained
in Section 2 and the statistics are summarized after winsorization, but before standardization. Table A.1 in the
appendix contains detailed definitions of all variables.

We use publicly available company news as another source of textual
data that we can use to construct firms’ climate risk measures. We obtain
such data from RavenPack, which provides a comprehensive sample of firmspecific news stories from Dow Jones Newswires.10 To identify news stories
about specific firms, we use relevance scores from RavenPack; these scores
range from 0 to 100, capturing how closely the underlying news is related
to a particular company. We identify relevant news stories for a given firm
by requiring the relevance score to be 75 or above, as recommended by
RavenPack.11 We also exclude repeated news using the event novelty score
provided by RavenPack so that our data capture only fresh news about a
10 News include The Wall Street Journal, Barron’s, MarketWatch, all major PR newswires and regulatory feeds.

This data have been frequently used in the literature (e.g., Kelley and Tetlock 2017; Jiang, Li, and Wang 2021).
11 We also experimented with a relevance score of 50 to retrieve RavenPack data, and our results are robust to this

variation.

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Firm-level measures constructed from earnings calls
Acute Climate Risk
139,959
0.06
0.61
0.00
0.00
0.00
Chronic Climate Risk
139,959
0.20
1.26
0.00
0.00
0.00
Transition Climate Risk
139,959
3.38
13.17
0.00
0.00
0.00
Transition Risk/Proactive
139,959
0.32
1.70
0.00
0.00
0.00
Transition Risk/Nonproactive
139,959
3.05
12.10
0.00
0.00
0.00
Energy Price Exposure
139,959
0.00
0.01
0.00
0.00
0.00
Action Index
139,959
0.02
0.01
0.01
0.02
0.02
Other firm-level data
Tobin’s q
130,450
2.03
1.50
0.46
1.16
1.56
CapEx
136,121
2.89
3.73
0.00
0.65
1.60
R&D
138,169
1.35
2.62
0.00
0.00
0.00
log(Asset)
138,208
6.84
1.92 −1.62
5.54
6.83
PPE
134,158
0.25
0.24
0.00
0.07
0.16
Book Leverage
130,244
0.24
0.23
0.00
0.03
0.21
log(No_Analysts)
139,959
1.83
0.89
0.00
1.39
1.95
Institution %
135,383
0.67
0.27
0.00
0.51
0.75
Institution HHI
134,985
0.10
0.13
0.01
0.04
0.05
ROA
136,881
0.06
0.23 −0.96
0.03
0.11
log(Employment) (annual)
38,917
1.45
1.29
0.00
0.34
1.12
External data
Disaster dummy
139,959
0.05
0.22
0.00
0.00
0.00
CO2 Intensity (annual)
2,774
4.12
7.97
0.00
0.23
0.97
I(Green patents) (annual)
39,505
0.08
0.27
0.00
0.00
0.00
Green patents ratio (annual)
12,664
0.04
0.14
0.00
0.00
0.00
MSCI CCI
17,304
56.44
66.62
0.00
0.00
33.00
RepRisk Environmental Score
40,925
2.15
4.89
0.00
0.00
0.00
Refinitiv Environmental Score
49,351
47.39
21.70
6.51
29.97
43.20
Firm-level measures constructed from alternative data
Transition Risk MDA
108,714
2.82
8.54
0.00
0.00
0.00
Transition Risk RF
89,999
2.16
8.96
0.00
0.00
0.00
Transition Risk News
139,959
0.01
0.06
0.00
0.00
0.00

The Review of Financial Studies / v 37 n 6 2024

company. Finally, we use the same transition risk dictionary to determine
whether a specific news story about a given firm is related to transition risk.

12 This data set is available at https://patents.darden.virginia.edu/. Bena et al. (2017) use the data to study the effects

of foreign institutional ownership on innovation output.

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2.4 Other external firm data
To analyze the firm-level response to climate risk through green innovation,
we obtain patent data from the Global Corporate Patent data set.12 We
follow Cohen, Gurun, and Nguyen (2020) and Haščič and Migotto (2015) and
classify green patents as those containing environment-related technologies,
such as emissions abatement technologies, renewable energy, and energy
storage. The patent data are available for U.S. firms from 2002 through 2017.
We calculate the number of green patents produced by each firm in a given
year and define two measures to capture the intensive and extensive margins
of firms’ green innovation activities: (1) an indicator that equals one if a firm
has been granted at least one green patent in a given year, and zero otherwise
and (2) the ratio of green patents to the total number of patents granted to the
firm in that year. The first measure is available for all public firms, while the
second measure is available only for firms that had at least one patent granted
in a given year.
We obtain several external data sets to validate the new climate risk
measures. The first data set contains natural disaster data from the Spatial
Hazard Events and Losses Database (SHELDUS) that has been used in
the economics literature (e.g., Barrot and Sauvagnat 2016) to examine the
effects of natural disasters. These data record the counties, beginning/end
dates, event names, main causes of damage (e.g., flooding, hurricanes), and
the estimated economic losses. We match these data with our sample using
firms’ headquarters locations, and we use the natural disasters as an external
benchmark for validating our physical risk measures.
Our second external benchmark comprises several external ESG index
or ratings. These scores measure how well a company manages ESG risks
and opportunities based on information published in news coverage and/or
corporate disclosures, such as sustainability reports and corporate websites,
surveys, and information provided by other stakeholders, such as regulatory agencies and industry associations (e.g., Berg, Koelbel, and Rigobon
2022; Christensen, Serafeim, and Sikochi 2021). We obtain ratings from
three sources (MSCI, RepRisk, and Refinitiv), and these ratings include
overall scores as well as three individual scores (environmental, social,
and governance) at the monthly or annual level. We use the MSCI CCI—
a climate change theme score that is directly comparable to our climate
risk exposure measures—as the main external benchmark. We note that the
environmental components of ESG ratings provided by rating agencies focus
on environmental risk that is entangled with, but different from, climate risk.

Corporate Climate Risk: Measurements and Responses

3. Measuring Climate Risk at the Firm Level
3.1 Constructing climate dictionaries
We follow the recent literature that exploits textual information in earnings
call data to identify risks (e.g., Hassan et al. 2019, 2023, 2020) to construct
our firm-level climate risk measures. We must overcome several challenges
in applying the textual analysis method to the construction of climate risk
measures.
First, as pointed out by Giglio, Kelly, and Stroebel (2021), when studying
climate risk and its impact on underlying assets, it is important to note the
several categories of climate risks and that these distinct risks often do not
materialize at the same time. Broadly speaking, climate-related risks can be
classified into two major categories: (1) physical risks, which are related to the
physical impacts of climate events, and are either acute (e.g., droughts, floods,
extreme precipitation and wildfires) or chronic (e.g., rising temperatures
and an accelerating loss of biodiversity), and (2) transition risks, which are
caused by not responding to climate change and improving how businesses
operate as society moves toward adopting sustainable practices (i.e., lowcarbon manufacturing). Transition risks are primarily influenced by policies
and regulations and by societal expectations and market pressure. Given the
multifaceted nature of climate risk, it is challenging to create a single measure
that captures all aspects of a firm’s climate risk exposure. Instead, using a
dictionary-based approach, we measure three climate-related risks separately:
(1) acute physical risk, (2) chronic physical risk, and (3) transition risk. Given
the complexity and multifaceted nature of climate issues and the importance of
generating replicable results, we believe, for several reasons, that the dictionary
approach is a better choice in this context than ML methods. First, ML methods

13 RepRisk, as one of the few ESG ratings not subject to green-washing bias, relies entirely on negative news

coverage by external sources (Berg, Koelbel, and Rigobon (2022)). It has been widely used in the literature
(e.g., Li and Wu 2020; Godfrey et al. 2020; Bansal, Wu, and Yaron 2021; Houston and Shan 2022).

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Nevertheless, we conduct supplemental validation exercises using the RepRisk
or Refinitiv Environmental Scores.13
Our third external benchmark consists of CO2 emissions data from the EPA’s
Greenhouse Gas Reporting Program (GHGRP) as an additional benchmark
for our transition risk measure. Since October 2009, the GHGRP program has
mandated that sources that emit 25,000 metric tons or more of CO2 greenhouse
gases per year must report their emissions, and the data are made publicly
available on an annual basis starting in 2010 at the plant level; and these data
include plant identity, geographic location, parent company, industry (NAICS),
and greenhouse gas emissions. Following Bartram, Hou, and Kim (2021), we
obtain plant-level emissions data from the EPA and match them with firm-level
data from Compustat based on the names of parent companies.

The Review of Financial Studies / v 37 n 6 2024

14 See, for example, studies based on the most advanced conversational AI algorithm, such as Google Meena

(Adiwardana et al. 2020) and Facebook BlenderBot (Roller et al. 2020; Xu, Szlam, and Weston 2021).
15 See https://en.wikipedia.org/wiki/List_of_severe_weather_phenomena.

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are not as transparent as the dictionary approach because many ML algorithms
function as black-box models. Second, ML methods are sensitive to initial
inputs and parameter choices. Third, the accuracy of ML predictions depends
heavily on constructing a large, representative training data set that is not
readily available in the context of complex and multifaceted climate issues.
Second, unlike using preexisting training libraries (as in, e.g., political
or accounting textbooks), developing climate-related keywords requires
considerable human effort. We detect two important issues once we apply
a set of commonly known weather or climate keywords to a large set of
transcripts. First, a significant number of false positive cases will arise in
which keywords are used to describe issues that are entirely unrelated to the
climate (e.g., “business climate,” “public cloud,” “economic storm”). A second
issue is that weather and climate irregularities are commonly expressed using
combinations of contrasting keywords (e.g., “warm winter,” “unseasonably
cold,” “cool summer”). If we rely on a dictionary that consists entirely of
unigrams, it is unlikely that we can include unigrams, such as “winter” or
“warm,” thus generating many false negatives. We address these issues by
manually constructing a hybrid dictionary consisting of both unigrams and
bigrams (adjacent two-word combinations) to reduce both false positives and
false negatives.
Specifically, our method builds on the premise that no algorithm understands
the context of a human conversation better than human beings do.14 We start our
dictionaries with a list of unigrams that we extract from the following sources:
(a) disaster “incident-type” indications in the Disaster Declarations Summary
of Federal Emergency Management Agency (FEMA), (b) Wikipedia’s list of
severe weather phenomena,15 and (c) additional seed words that we added
manually, namely, “temperature,” “cold,” “unseasonable,” and so on. We use
this list to obtain all bigrams that contain at least one of the unigrams from the
entire sample of earnings call transcripts. We then manually screen, for each
unigram, the top-500 associated bigrams. If the top-500 associated bigrams
are unambiguously used in the context of climate-related conversations, we
then include the corresponding unigrams in the unigram dictionary. If not, we
include the top-500 associated bigrams in the bigram library pending further
screening. To reduce the incidence of false negatives, we supplement the
bigram library with climate-related bigrams extracted from additional sources:
(a) white papers and reports on climate issues mentioned by Engle et al. (2020),
(b) news articles posted by The Weather Channel, and (c) an undergraduate
textbook on meteorology (Ahrens 2008). Lastly, we screen the library through
many iterations to eliminate false positives and include false negatives.

Corporate Climate Risk: Measurements and Responses

3.2 Measuring climate risk
Next, we construct our firm-level climate risk measures using these dictionaries. Specifically, we first decompose each of the earnings call transcripts
into a list of unigrams/bigrams. Because acute or chronic physical risks are
often brought up when short-term climate or weather events are reported in
news headlines (e.g., hurricane, wildfire, and warm winter), we require their
respective keywords to appear in the vicinity (±1 sentence) of at least one
risk synonym to ensure that firms are indeed exposed to climate risks (similar
to Hassan et al. 2019). Simply mentioning a well-publicized weather/climate
event without explicitly mapping to a firm’s risk profile could reflect a desire
for attention or shifting of blame, which does not contribute to our physical
climate risk measures. We divide the frequency of these occurrences by the
length of the transcript, and then multiply the quotient by 104 to reduce the
number of decimals. In essence, these measures capture the proportion of a
conversation in which acute or chronic weather/climate events as well as a
firm’s risk exposure are jointly discussed.
Transition risk differs from physical climate risk in that it relates to policies
and regulations, technological improvements, and evolving climate patterns.
Unlike physical risks, transition risk may not materialize in the short run
and thus does not pose immediate threats or introduce any uncertainty to a
firm’s business operations. As a result, we measure transition risk exposure
16 We exclude keywords such as “energy cost,” “energy costs,” “fuel bill,” “fuel cost,” “fuel costs,” “fuel expense,”

“fuel expenses,” “gas cost,” “gas costs,” “wind cost,” and “wind costs.”

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We distinguish between climate risk and other risks in building our
dictionaries. First, companies may discuss their climate topics that are related
to changes in energy prices, but the latter not exclusively related to climate
risk. To ensure that our climate risk measures are not driven by energy prices,
our climate dictionaries do not contain any keywords related to energy prices
or costs.16 Instead, we construct a firm-specific, time-varying energy-price
exposure index and include it as a control variable in our main analysis.
Furthermore, companies’ environmental responsibility and greenhouse gas
emissions efforts are likely correlated, but not equivalent. We thus remove
any keywords on general environmental risk (e.g., air pollution, environmental
issues, EPA, sulfur dioxide) from the climate dictionaries.
Our final dictionaries consist of 37 unigrams and 1,649 bigrams: the acute
physical risk dictionary contains 21 unigrams and 350 bigrams; the chronic
physical risk dictionary contains 16 unigrams and 977 bigrams; and the
transition risk dictionary includes 322 bigrams. The majority of the dictionaries
consist of bigrams, reflecting our deliberate effort to achieve accurate text
identification and quantification, as prior research shows that text classification
accuracy improves when applying bigrams of words as opposed to unigrams
(e.g., Tan, Wang, and Lee 2002; Bekkerman and Allan 2004).

The Review of Financial Studies / v 37 n 6 2024

4. Properties of Firm-Level Climate Risk Measures
In this section, we provide some preliminary validation using the underlying
keywords, present our climate risk measures, and examine their time-series and
cross-sectional properties.
4.1 Top keywords
In our first validation exercise, we examine the top keywords—unigrams or
bigrams—used to construct the climate risk measures, rank-ordered by the
frequency of mentions and frequency weight at the transcript level and report
the results in Table 2.18 The results, reported in columns 1–3, show that
hurricanes and hurricane are the most frequently mentioned acute climate
unigrams in the proximity of risk synonyms. The keywords storms, drought,
flooding, and wildfire(s) are also frequently discussed in earnings calls,
trending up in the later few years of our sample period. Columns 4–6 report
that weather is the single-most commonly discussed chronic climate keyword
appearing near risk synonyms. It is followed by words referencing specific
weather conditions, such as temperatures or snow. These keywords clearly
confirm that our measures accurately capture acute and chronic climate risks.

17 The complete list of the proactive verbs includes achieve, acquire, add, announce, build, change, create, develop,

enhance, evaluate, expand, generate, grow, hedge, help, improve, increase, initiate, integrate, invest, make,
prepare, produce, purchase, rebuild, reduce, replace, respond, restructure and spend.
18 The frequency weight of each bigram or unigram, denoted as fweight, is calculated by dividing the frequency of
its occurrences by the length of the transcript, multiplying the quotient by 104 to reduce the number of decimals,

and summing the values across all transcripts. The average length of earnings call transcripts in our sample is
approximately 4,200 words before cleaning and 2,440 words after cleaning, which is consistent with the literature
(e.g., Chen, Nagar, and Schoenfeld 2018).

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based on discussions of the keywords in our transition risk dictionary only,
without requiring these discussions to appear near a risk keyword. Moreover,
firms exhibit varying perceptions of and attitudes toward climate risk, with
some discussing and addressing transition risk more proactively than others.
With this in mind, we develop an additional measure that captures a firm’s
proactiveness when discussing transition risk. To achieve this, we analyze
verbs that appear near (within ±1 sentences of) discussions of transition risk
keywords in earnings calls, and manually identify a list of 30 verbs that suggest
more proactive attitudes when discussing climate issues.17 Using proactive
verbs, we separately identify our transition risk measures with and without
proactiveness.
Applying the above-mentioned procedures, we construct three separate
firm-level climate risk measures: (1) acute physical climate risk, (2) chronic
physical climate risk, and (3) transition risk. We decompose the transition risk
measure into proactive and nonproactive components. All are available at the
firm-quarter level.

1793

=

6371.9
2243.5
1622.7
1177.2
728.7
440.6
356.4
333.8
201.6
155.4
134.0
132.5
125.0
102.0
100.8
86.8
82.4
76.8
69.7
64.4
57.4
55.3
52.6
50.1
50.1
49.6
48.1
40.0
39.0
38.3

(3)

F reqb,P
× 104
BP

fweight

weather
temperatures
the snow
high water
heating season
precipitation
wind season
the ice
mild winter
snowfall
rainfall
degree days
normal winter
winter conditions
warm winter
rains
cold winter
hot summer
unseasonably warm
the fog
harsh winter
unseasonably cold
the clouds
the warmest
early winter
cool summer
cold season
the rain
wind hail
the winds

(4)

Unigram

Bigram/

Physical climate risk

6154
122
75
72
49
46
60
57
48
42
42
34
36
43
36
34
33
30
24
28
27
19
23
13
13
13
17
16
11
17

(5)

Freq

Chronic risk

=

26342.7
596.0
299.4
266.2
260.4
252.1
237.1
216.7
188.8
186.8
175.4
173.9
170.7
170.5
161.0
138.0
126.4
124.9
110.1
107.4
103.5
99.6
96.7
74.5
74.1
72.3
70.9
64.7
63.2
62.8

(6)

F reqb,P
× 104
BP

fweight

energy efficiency
renewable energy
the solar
clean energy
alternative energy
superior energy
higher energy
new energy
the renewable
the ecosystem
energy management
energy efficient
the carbon
green energy
wind energy
the climate
fuel efficiency
shale gas
lower energy
fuel efficient
energy technologies
solar power
alternative fuel
wind farm
fuel economy
the co2
solar cell
gas drilling
energy future
solar projects

(7)

Unigram

Bigram/

7738
6663
6623
5117
4160
3354
2806
2503
2389
2590
2156
2171
2243
2224
1893
1926
1874
1655
1553
1592
1643
1344
1301
1283
1586
1479
1170
1286
1214
1076

(8)

Freq

risk

Transition climate

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=

fweight

32512.0
29104.3
28819.0
21372.2
18367.0
12482.7
11273.8
10878.1
10564.8
10036.0
8861.2
8459.6
8414.0
8303.4
7817.5
7300.8
6730.5
6350.9
6290.3
5925.9
5883.5
5836.2
5776.1
5696.7
5487.9
5476.3
5457.9
4947.8
4715.9
4667.6

(9)

F reqb,P
× 104
BP

This table lists the top-30 unigrams or bigrams in each category of ClimateRiski,t measures, ranked by fweight. To calculate the fweight for acute and chronic climate risk measures, we
first identify the frequency of mentions of individual unigrams and bigram b in proximity to risk synonyms (F reqb,P ). We then divide this frequency by the length of the transcript P (BP ),
multiply the quotient by 104 , and sum the resultant values across all transcripts in our sample. The calculation of fweight in the case of transition climate risk is the same except that we do
not require the mention of the unigrams and bigrams to be in the proximity of risk synonyms, which leads to higher Freq and fweight for that specific category.

(2)

1560
552
409
294
185
108
110
75
54
30
33
31
28
24
25
21
22
22
14
10
14
13
13
12
14
11
11
10
11
11

(1)

Freq

hurricane
hurricanes
storms
drought
flooding
the flood
wildfire
windstorm
wildfires
storm losses
severe winter
storm related
wind storm
the floods
storm activity
storm costs
water flood
polar vortex
storm season
storm damage
droughts
tropical storm
snowstorms
snowstorm
winter storm
hailstorm
extreme cold
extremely cold
storm cost
the volcano

Unigram

Bigram/

Acute risk

Table 2
Top climate-related keywords
Corporate Climate Risk: Measurements and Responses

The Review of Financial Studies / v 37 n 6 2024

4.2 Summary statistics
The newly constructed climate risk measures are summarized in Table 1, in
which we cap them at the 99th percentile to limit outlier values. Among
all 4,719 firms in our sample, 18.0%, 27.2%, and 61.8% show at least
one quarter with a positive value for the acute, chronic, and transition
climate risk measures, respectively.19 When we divide these measures by
the respective standard deviations (SDs), the three standardized climate risk
measures have average values of 0.098, 0.159, and 0.256, respectively. The
correlation between the two physical risk measures is about 0.100, suggesting
that the two are somewhat related. In contrast, their correlations with the
transition risk measure are 0.021 and 0.033, respectively, clearly indicating the
distinction between physical and transition risk measures. Conditional only on
the presence of firms with at least one positive transition risk value, 23.9%
of the firm-quarters are identified as being associated with some proactive
keywords when transition risk is discussed.

19 Internet Appendix B provides more information on the frequency and distribution of climate risk discussions in

earnings calls, both on an absolute and relative scale. We focus on the transition risk measure, which is the main
focus of our paper. The 61.8% of sample firms (or 2,918) that have at least one quarter with a positive value of the
transition risk measure correspond to 20.4% of the firm-quarters and 34.7% of the firm-years that have positive
values in transition risk. These shares of positive values have increased over time, with 37% of the firm-years
having positive values in transition risk in 2017-2018. Figure IA.1 presents the distribution of the standardized
transition risk measure, either by firm-quarters in panels A and C or by firm-years in panels B and D. Panels A
and B are based on data in all years, and panels C and D are based on data in the most recent 2 years, 2017–2018,
in our sample.

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Unlike physical climate keywords, words that indicate transition risk are
more evenly distributed across many keywords. Among the most frequently
appearing are energy efficiency, renewable energy, solar, clean energy, and
alternative energy. In addition to these words, superior energy, higher energy,
new energy, the renewable, and the ecosystem are also discussed frequently.
Clearly, these keywords accurately signify discussions of transition climate
risk. The calculation of fweight in the case of transition climate risk is similar,
but we do not require the key unigrams and bigrams to appear in proximity
to risk synonyms, which leads to higher average frequencies and fweights.
Table IA.7 compares the frequency of climate-related bigrams and unigrams
with political-risk-related bigrams from a previous study Hassan et al. (2019)
and top climate keywords from another study Sautner et al. (2023). It includes
the number of earnings calls and the number of firms that mentioned each
of the climate-related words besides their frequency and fweight. Our results
show that the frequency of top climate-related bigrams is much higher (about
1,600 times) than that of the top political-risk-related bigrams (e.g., the
constitution) in Hassan et al. (2019), and similar to that of top climate keywords
in Sautner et al. (2023). Internet Appendix B provides further details.

Corporate Climate Risk: Measurements and Responses

4.4 Industry variations
Industries differ inherently in their exposure to climate risk, so we examine
industry variations in our climate risk measures. We regress different climate
risk measures on industry dummies, while controlling for time and state fixed
effects. Figure 2 plots the coefficients for the NAICS two-digit dummies. The
reference industry is other services (NAICS 81).
Panel A shows that utilities face the highest acute physical climate risk
among all industries, followed by agriculture, mining, transportation, and
construction. A significant portion of the business activities in these industries
take place outdoors and thus are subject to disruptions caused by natural
disasters. Panel B displays similar patterns, but with a few exceptions. While
utilities continue to exhibit high chronic physical climate risk (the secondhighest across industries), arts and recreation faces the highest chronic climate
risk with agriculture facing the third highest. The industry variations we
observe mostly conform to the industry-level exposure to both acute and
chronic climate risk.
Panel C shows even wider variations in transition risk than with the physical
climate risk measures. Utilities and transportation are subject to significantly
higher transition risk than other industries, while service industries face
significantly lower transition risk. Panel D displays the industry variations
in the proactive transition risk measures. Utilities firms are more likely than

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4.3 Time-series patterns
We now shift to examining the properties of the constructed measures to
provide face validation based on time-series and cross-sectional variations.
Figure 1 plots the averages of the climate risk measures over time. In panel
A, the acute risk series spikes six times over the past 17 years. We identify
the corresponding topics discussed in the conference calls that contribute to
the increases in climate risk and label each spike. For example, the spike that
occurs in 2005 reflects the catastrophic and long-lasting effect of Hurricane
Katrina, which flooded the New Orleans area. In contrast, the chronic risk
series has remained flat over the past two decades with spikes only between
2012 and 2014. The most commonly discussed keywords during the period
was abnormal weather.
Panel B plots the time series for the transition climate risk measure, which
shows a steady increase from the start of the sample period through 2008Q3
with a gradual retreat to its 2005 level since then. The downtrend in the recent
decade has matched well with that of U.S. greenhouse gas emissions. We
observe several local spikes, in 2006, 2008, 2011, and 2015, all of which
are driven by more frequent discussion of energy efficiency and renewable
energy. Panel C plots the average transition risk measures with and without
proactive keywords, divided by their corresponding SDs. The two time series
have diverged increasingly since 2008, with firms with proactive responses
displaying much lower transition risk than their 2008 levels.

The Review of Financial Studies / v 37 n 6 2024

Physical risk measures

B

Transition risk measure

C

Proactive and nonproactive components of transition risk measure

Figure 1
Firm-level ClimateRiski,t
These panels report the average of firm-level ClimateRiski,t over time. Panels A and B show the timeseries average of firm-level acute risk, chronic risk, and transition risk (divided by its SD in the time series),
respectively. We label each spike with the corresponding topics discussed in the conference calls which contribute
to the increase in each type of climate risk. Panel C plots the time-series average of proactive and nonproactive
components of transition risk, divided by their corresponding SDs, based on a subsample of firms with positive
transition risk.

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A

Corporate Climate Risk: Measurements and Responses

Acute risk measure

B

Chronic risk measure

Figure 2
Industry variations in ClimateRiski,t
These panels plot the coefficients for industry (NAICS two-digit) fixed effects and their corresponding 95%
interval from regressions of acute climate risk (panel A), chronic climate risk (panel D), transition risk (panel
C), and the proactive transition risk (panel D). Time and state fixed effects are controlled in each regression. The
reference industry is other services (NAICS 81).

other firms to use proactive keywords when their management teams discuss
transition risk topics. In contrast, firms that operate in mining, information,
and real estate are less likely to use proactive keywords on such occasions.
The observed patterns match well with the broader industry-level exposure to
climate regulatory risk.

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A

The Review of Financial Studies / v 37 n 6 2024

Figure 2
(Continued)

Transition risk measure

D

Transition risk with proactive keywords

4.5 Firm-level variations
In Table 3, we report excerpts of the transcripts with the highest
ClimateRiski,t . The transcripts indicating the highest acute climate risk are
those of the two largest utility companies in California: Edison International
and PG&E Corporation, which have been linked to some of California’s
deadliest wildfires. Relatedly, the chronic risk measure captures discussions
of both abnormal weather and variability in weather conditions. The transcript

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C

Chronic risk

Chronic risk

Transition risk 298.2

Transition risk 267.5

Apr. 24, 2002

Oct. 30, 2013

Aug. 11, 2011

May. 4, 2018

May. 9, 2012

Aug. 12, 2009

Aug. 7, 2008

CH Energy Group
inc
Southern
Company Gas

CDTI Advanced
Materials Inc

New Jersey
Resources Corp
Magnetek Inc.

Lime Energy Co

Enel X North
America Inc

51.63

52.52

61.79

1799

Keywords

Clean Energy

Energy Efficiency

Renewable Energy

Clean Energy

Emission
Reductions

Weather;
Unpredictable

Weather; Risk

Weather;
Variability
Unseasonably
warm;
Uncertainty
Precipitation;
Chance

Storm; Risk

Hurricane; Unsure

Hurricane;
Unpredictable

Wildfire;
Uncertainty
Wildfire; Risks

Text surrounding the keywords

Looking at the domestic growth opportunities, we think that the economic recovery, although a little bumpy, is
spurring growth in our business and with our distributor network. Additionally, states such as California continue
to demonstrate their commitment for on-road diesel emission reductions through innovative programs to drive
early adoption by truck operators.
I talked about our strategy to provide our customers with reliable, affordable and clean energy services. To execute
that strategy, we remain focused on natural gas, energy efficiency, and clean energy investments.
Some of the growth we experienced in our served industrial markets was offset by lower sales in renewable energy,
namely, wind inverters, which declined by more than $3 million year over year to about $2.4 million in the
quarter.
This counterbalance truly reflects the underlying strength of our business model and supports our efforts to date in
the rapid deployment of tailored energy efficiency solutions to the public and utility marketplaces.
Various factors, ranging from unprecedented regulatory support for clean energy solutions, to rising fuel and
construction costs, have made the value proposition of our scalable solutions stronger and more important than
ever.

While the heating season presented some extreme weather variability, average temperatures across our service
territories were 8% cooler than the prior year.
Unseasonably warm and dry weather coming on top of a bad winter sports season last year, combined with our
customers’ general economic uncertainty along with our desire to be less promotional, all contributed to the
slight decrease in comparable store sales.
According to the National Oceanic Atmospheric Administration, in March through May, we are looking at about a
33% to 40% chance of above-normal precipitation in the southern portion of our service area and normal
precipitation levels in the northern portion.
A certain amount of variation from normal, either above or below normal degree days was a variation or risk that we
retained. Then there was a wider range where we would be compensated if weather were warmer than normal.
Given where you see the rates today, when you’re coming up for the 2014 expirations, do you expect – doesn’t
seem to have been much movement in the market. Is there anything out there that you think might have a
significant impact, other than unpredictable weather?

We also have the flexibility at these entities to obtain both short and long-term debt while we continue to evaluate
options as we work through uncertainty around the wildfire liability and cost recovery.
Our expanded Community Wildfire Safety Program was established after the 2017 wildfires to implement
additional precautionary measures intended to reduce or further reduce wildfire risks.
Hurricane Irma more directly impacted our operations as the state of Florida shut down for 2 or 3 days. This type of
business is generally less productive with long lines, unpredictable traffic patterns and other negative occurrences
leading to inefficient utilization of our equipment.
Heading into that markets’ high winter season we are unsure what the effects may be. The impact of hurricane
Matthew on our portfolio in early October was significant.
We’re also actively engaged in a program of accelerated idle well abandonment to mitigate the ongoing risk of
future storms.

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The table presents the excerpts in the earnings call transcripts with the highest acute, chronic and transition climate risks, respectively. The values of climate risk measures are ranked before
winsorization. For acute and chronic climate risks, we report the corresponding climate-related keywords and risk synonyms. For transition climate risk, we report only the climate-related
keywords.

Transition risk 256.7

Transition risk 267.2

Transition risk 464.9

Chronic risk

Feb. 18, 2016

Idacorp Inc

63.22

Chronic risk

Feb. 6, 2013

77.72

Chronic risk

29.00

Nov. 15, 2018

Acute risk

Nov. 5, 2008

32.40

35.63

39.85

40.00

Value

Suburban Propane
Partners
Sport Chalet Inc

Acute risk

Nov. 8, 2016

Sotherly Hotels
Inc
Talos Petroleum
LLC

Acute risk

Nov. 30, 2017

Patriot
Transportation

Acute risk

Nov. 5, 2018

Edison
International
PG&E Corp

Climate risk

Acute risk

Date

Oct. 30, 2018

Firm

Table 3
Excerpts in transcripts with highest climate risks
Corporate Climate Risk: Measurements and Responses

The Review of Financial Studies / v 37 n 6 2024

5. External Validation
In this section, we conduct a variety of validation tests using external
benchmarks to show that our climate risk measures indeed quantify firm-level
variations in exposure to climate risks.
5.1 Validating the physical risk measure
We first examine whether local natural disasters correlate with changes in
our two physical climate risk measures for the affected firms. Following the
literature, we match natural disaster data from SHELDUS with our firm-quarter
sample. We then relate local natural disaster events to firms’ physical climate
risk measures using the following specification:
ClimateRiski,t+1 =

3


βp ·Zc,t−p +γ ·Xi,t−1 +ζi,t +i,t ,

(1)

p=0

where Zc,t−p is a natural disaster event in the county where a firm’s
headquarters is located, and time p ranges from 0 to 3 across columns; Xi,t−1
represents firm-level attributes, such as total assets lagged by one quarter; ζi,t
refers industry-by-quarter fixed effects that we use to account for time-varying
heterogeneity across industries.20
Panel A of Table 4 reports the results. The results in columns 1 and 2 indicate
that natural disasters in quarter t motivate executives to discuss physical climate
risk in quarter t+1. The presence of local natural disasters is associated with a
significant 0.085-SD increase in the within-industry-time acute climate risk
measure in the subsequent quarter. The effect is statistically significant only
in quarter t, not in previous quarters. Similarly, columns 3 and 4 suggest
that natural disasters in the preceding quarter are associated with a 0.036SD increase in the within-industry-time chronic climate risk in the current

20 We exclude the firms in the energy industry in our regression, mainly due to the confounding impact of natural

disasters on energy usage.

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indicating the highest chronic climate risk comes from Suburban Propane
Partners, a utility company that offers propane primarily for heating.
The transcript indicating the highest transition climate risk is that of
CDTI Advanced Materials, a company that provides solutions to automotive
emissions control markets in the United States. On August 11, 2011,
the company discussed “states such as California continue to demonstrate
their commitment for on-road diesel emission reductions through innovative
programs to drive early adoption by truck operators.” The other transcripts
indicating the highest transition climate risk come from New Jersey Resources
Corp, Magnetek Inc., and Lime Energy Co, all of which provide clean or
renewable energy services.

Corporate Climate Risk: Measurements and Responses

Table 4
Validating firm’s climate risk measures
A. Correlations between physical risk measures and natural disaster data
Dep var

(3)

(4)

0.0849∗∗∗
(4.353)

0.0851∗∗∗
(4.374)
0.0041
(0.354)
−0.0145
(−1.326)
0.0045
(0.384)

0.0353∗∗∗
(2.754)

0.0363∗∗∗
(2.876)
−0.0038
(−0.287)
−0.0170
(−1.600)
0.0004
(0.028)

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

133,434
.020

133,434
.021

133,434
.043

133,434
.052

Natural Disasterc,t−1
Natural Disasterc,t−2
Natural Disasterc,t−3
Firm Attributesi,t−1
Industry × Time
N
Adj. R2

Chronic Riski,t+1
(2)

B. Correlations between transition risk measures and MSCI CCI
Dep Var

Transition Riski,t
All
(1)

Proactive
(2)

Nonproactive
(3)

0.0512∗∗∗
(3.461)

0.0446∗∗∗
(3.062)

0.0468∗∗∗
(3.154)

Firm Attributesi,t−1
Industry × Time

Yes
Yes

Yes
Yes

Yes
Yes

N
Adj. R2

15,747
.268

15,747
.142

15,747
.262

MSCI CCIi,t

C. Correlations between transition risk and CO2 intensity
Dep Var

CO2 Intensityi,t+h
h=1

h=2

h=3

h=4

h=5

0.4531**
(2.033)

0.5363**
(2.104)

Specification (1)
0.4671**
(2.639)

0.5420∗∗∗
(3.164)

0.6939∗∗∗
(3.416)

N
Adj. R2

2,529
.174

2,422
.245

2,312
.0944

2,202
.161

2,095
.178

Transition Risk/Nonproactivei,t

0.3061
(1.662)
0.1758
(1.497)

0.3579*
(1.852)
0.2188
(1.403)

Specification (2)
0.4082∗∗∗
(3.563)
0.0689
(0.431)

0.4449∗∗∗
(2.849)
0.1210
(0.667)

0.6449∗∗∗
(4.186)
0.0609
(0.393)

N
Adj. R2
F-test

2,529
.174
0.1303

2,422
.180
0.1457

2,312
.0939
0.3393∗

2,202
.0779
0.3239∗

2,095
.178
0.584∗∗∗

Firm Attributesi,t−1
Industry × Time

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Transition Riski,t

Transition Risk/Proactivei,t

This table reports the validation results of our firm-level climate risk measures. In panel A, we regress the acute and chronic climate
risk measures (standardized) on the occurrence of natural disasters in lagged periods. Natural disaster is a dummy variable that
equals one if there is a natural disaster in the county where a firm was headquartered in a given quarter, zero otherwise. Columns
1 and 2 use the acute climate risk as the dependent variable, and columns 3 and 4 use the chronic climate risk as the dependent
variable. Firm-level control variables (i.e., Firm attributes) include log(Asset), CapEx, PPE, Book Leverage, log(No_analysts),
Institution %, and Institution HHI, all lagged by one quarter. In panel B, we regress transition risk measures on MSCI CCI. Column
1 presents the results of the regressions using the overall transition risk as the dependent variable. Columns 2 and 3 report the
results using the proactive and nonproactive components of the transition risk measure as the dependent variable, respectively.
Firm attributes that are controlled in panel B include log(Asset), CapEx, PPE, Book leverage, and ROA (%). Panel C shows
the results of regressing CO2 intensity in different lead periods on different transition risk measures (standardized): transition
risk in Specification (1) and two decomposed transition risk measures in Specification (2). Lagged log(Asset) is controlled in all
columns of both specifications of panel C. Industry by time fixed effects are included in all three panels. Table A.1 in the appendix
defines all variables in detail. The standard errors are clustered at the firm level and t-statistics are shown in parentheses. *p < .1;
**p < .05; ***p < .01.

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Natural Disasterc,t

Acute Riski,t+1
(1)

The Review of Financial Studies / v 37 n 6 2024

quarter. Overall, our physical climate risk measures capture variations in a
firm’s exposure to local natural disasters, a key driver of physical climate risks.

21 Following Equation (1), we also run regressions of ClimateRisk on either RepRisk or Refinitiv environmental
i,t

scores as well their overall ESG scores. The results, untabulated in the version, show that our transition risk
measure is positively correlated with the environmental component of ESG scores, but not with their social and
governance components.

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5.2 Validating the transition risk measure
5.2.1 Correlations with ESG scores. We start our validation of the transition
risk measure with the MSCI CCI. We use MSCI rather than other ESG
databases for two reasons. First, it is arguably one of the best-accepted
ESG data vendors among practitioners and academia (e.g., Engle et al. 2020;
Serafeim and Yoon 2023). As the leading global provider of financial indexes,
MSCI has successfully incorporated its ESG ratings into a wide range of
investment products. Second, CCI is a climate change theme score, which is
more closely related to our transition climate risk exposure measures.21
To compare the two measures, we first compare the coverage of the
two measures. It’s worth noting that the CCI is only available after 2013
and maintains the same value if not updated, while our earnings-call based
measures have been available since 2002 and are only applied to the quarter of
earnings calls. Figure IA.2 in Internet Appendix B plots the number of unique
public firms for each year of our transition risk measure and the MSCI CCI
measure. We can see that even during the years when the two data sets overlap,
our measure adds substantial coverage beyond the MSCI data, as demonstrated
by the green bars. Specifically, for each year from 2013 to 2018, our measure
on average provides coverage of transition risk to an additional 952 firms with
nonmissing values and 480 firms with positive values. Over the same period,
on average, about 225 firms each year in the MSCI CCI data set do not have
earnings conference calls and are thus not covered in our sample.
We then match the CCI data with our sample, resulting in a small panel
of 15,995 firm-quarters. Panel A of Figure 3 displays the scatterplot between
our transition climate risk measure and the CCI, showing a positive and
significant correlation between the two series. We formalize the correlation
test by regressing ClimateRiski,t on the CCI following a specification that is
similar to Equation (1). We report the results in panel B of Table 4. The results
in column 1indicate a positive correlation between the two series, which is
significant at 1%, suggesting that a one-SD increase in the CCI is associated
with a 0.051-SD contemporaneous increase in the transition climate risk. In
columns 2 and 3, we document similar results using proactive and nonproactive
components of the transition risk measure as the dependent variables, with both
coefficients being statistically significant at the 1% level. This set of results
provides evidence that our transition risk measure is positively correlated with
the CCI within the same industry and time.

Corporate Climate Risk: Measurements and Responses

Transition climate risk and MSCI Climate Change index

B

Transition climate risk and CO 2 Intensity

Figure 3
Scatterplots of transition climate risk and external measures
The panels describe the correlation between the transition climate risk and two external measures. Panel A
presents the (binned) scatterplot between transition climate risk and MSCI CCI for firms that have both measures
available. Panel B illustrates the (binned) scatterplot of the average transition climate risk and the direct CO2
intensity at NAICS six-digit level for the manufacturing sector, sourced from Shapiro (2021).

Overall, we believe that our transition risk measure is highly complementary
to these ESG scores, with several additional benefits. First, our measure is
available for a large sample of public firms in the United States over a long
sample period starting in 2002, while ESG scores in the CCI are available after

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A

The Review of Financial Studies / v 37 n 6 2024

2012. Second, for the same reason, our measure is less subject to selection
bias. Third, our measure is more timely and thus can be better used to inform
real-time decisions.

Yi,t+k = β ·T ransitionRiski,t +γ ·Xi,t−1 +ζi,t +i,t ,

(2)

where Yi,t+k is the firm’s CO2 intensity in year t +k (k ranges from 1 to 5);
Xi,t−1 includes the firm’s total assets lagged by one year. We include industryby-year fixed effects in the analysis to account for time-varying heterogeneity
across industries. Our sample covers 762 firms for which both series are
available, mainly firms operating in the manufacturing, mining, energy, and
transportation sectors from 2010 to 2018.
We report the results in panel C of Table 4. In specification (1), we find
a positive and significant correlation between the transition risk measure and
the firm’s CO2 intensity from year t +1 onward, with the magnitude increasing
over time. A one-SD increase in the transition risk measure is associated with
an increase in CO2 intensity of 0.4531 basis points (which is significant at the
5% level) in year t +1 and of 0.6939 basis points (which is significant at the 1%
level) in year t +5. In Specification (2), where we separate the transition risk
measure into proactive and nonproactive components, we find a positive and
significant coefficient for the nonproactive component from year t +2 onward,
not on the proactive component, and the differences are significant at the 10%
or lower level. The contrast suggests that, while firms that face higher transition
risk and adopt nonproactive responses are associated with higher future CO2
emissions, those that face higher transition risk but adopt proactive responses

22 Direct CO intensity is measured as average emissions per $1 of output by each industry in 2007 by Shapiro
2

(2021).

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5.2.2 Transition risk and CO2 intensity. In our final validation, we examine
how well our transition risk measures correlate with a firm’s carbon intensity.
Recent studies use carbon intensity (carbon emissions scaled by total assets)
to estimate the effects of a firm’s exposure to climate risks, especially policy
and regulatory risks (e.g., Bolton and Kacperczyk 2021a,b). We also examine
whether and how firms that are identified with proactive keywords in earnings
calls manage their emissions in reality compared with how others do when
facing similar transition risks.
Panel B of Figure 3 presents a scatterplot of transition risk and direct CO2
intensity at the NAICS six-digit level for the manufacturing sector, sourced
from Shapiro (2021).22 We find a strong and positive correlation between the
two, with a correlation coefficient of 0.19, which is significant at the 1% level,
providing some validation that our transition risk measure captures variations in
carbon intensity. We then formalize the test by regressing a firm’s CO2 intensity
obtained from GHGRP on the transition risk measures as follows:

Corporate Climate Risk: Measurements and Responses

are not. In essence, our transition climate risk measures are predictive of the
firm’s future carbon emissions.23
6. Explaining Climate Risk Measures

6.1 Variance decomposition
We first conduct a variance decomposition analysis—calculating how much of
the variation in each of the three climate risk measures is accounted for by firmlevel characteristics and various sets of fixed effects. In panel A of Table 5,
we report R 2 values from a variety of specifications that explain the climate
risk measures. These results indicate that time + state + industries, together,
can explain only 2%, 3.4% and 12.4% of the variations in the acute, chronic,
and transition risk measures, respectively. Adding interactions between state,
industry, and time all help increase the explanatory power of the model, but
to a limited extent. Nevertheless, even with the strictest specification, where
we control for county-by-time and industry-by-time fixed effects, the model
explains less than 12.5% of the variations in any of the climate risk measures,
leaving more than 87% attributable to firm-level or other idiosyncratic factors.
This result suggests that, unlike natural disaster data or marketwide news about
long-run climate risk used by Engle et al. (2020), the majority of variations in
our three climate risk measures occur at the firm level.
When we add firm and time fixed effects, the model captures 9.7%, 20.9%,
and 65.7% of the variations in the three climate risk measures, respectively.
Further adding firm-level attributes and interaction between industry and time
or state and time offers some additional power in predicting the two physical
risk measures, but not the transition risk measure. This result suggests that
our climate risk measures capture both cross-firm differences and within-firm
variations in climate risk exposure. For example, the transition risk measure
for Sempra Texas Holdings increases to 184.97 in Q3 2013 from 11.10 in Q1
2006.
6.2 Correlations with firm characteristics
Panel B of Table 5 presents the results of regressions relating climate risk
measures to a list of important firm-level attributes, all lagged by one quarter, to

23 We also regress the transition climate risk measures on CO intensity in the contemporaneous and previous
2

quarters following the specification in Equation (1) to explore the two-way relationship in an exercise that is
similar to Granger Causality test. The results, reported in Table IA.1 in the Internet Appendix, suggest that the
relationship between our transition climate risk and CO2 intensity runs only one way, with transition climate
risk measures significantly predicting the firm’s CO2 emissions in the future, but not in the opposite direction.

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In this section, we analyze the relative contributions of aggregate, sectoral, and
firm-level variations as well as firm-level characteristics to the new climate risk
measures.

The Review of Financial Studies / v 37 n 6 2024

Table 5
Characteristics of climate risk measures
A. Variance decomposition
Dep Var
Chronic Riski,t

Transition Climate Riski,t

Adj. R 2



Adj. R 2



Adj. R 2



Time
Time + State
Time + County
Time + NAICS2
Time + NAICS3
Time + NAICS4
Time + State + NAICS2

.009
.015
.025
.016
.026
.028
.020

.015
.025
.016
.026
.028
.020

.001
.008
.040
.030
.043
.075
.034

.008
.040
.030
.043
.075
.034

.005
.018
.073
.118
.161
.199
.124

.018
.073
.118
.161
.199
.124

State + NAICS2 × Time
State × Time + NAICS2
State × Time + NAICS2 × Time
County × Time + NAICS2 × Time

.028
.037
.042
.063

.012
.021
.026
.047

.042
.037
.045
.064

.012
.007
.015
.034

.136
.118
.130
.121

.018
.000
.012
.003

Firm + Time
Firm + Time + Firm Attributes
Firm + Time + Firm Attributes
+ NAICS2 × Time
Firm + Time + Firm Attributes
+ State × Time

.080
.080

.064
.064

.200
.200

.170
.170

.655
.655

.537
.537

.088

.072

.209

.179

.673

.555

.097

.081

.209

.179

.657

.539

Residual

.903

Model specification

.791

.343

B. Firm characteristics of climate risk measures
Dep Var

log(Asset)i,t−1
CapExi,t−1
PPEi,t−1
Book Leveragei,t−1
log(No_Analysts)i,t−1
Institution%i,t−1
Institution HHIi,t−1

Physical Riski,t

Transition Riski,t

Acute
(1)

Chronic
(2)

All
(3)

Proactive
(4)

0.0074∗∗
(2.147)
−0.0011
(−0.845)
0.1204∗∗∗
(4.687)
−0.0095
(−0.463)
−0.0094
(−1.463)
0.0304∗
(1.680)
0.0133
(0.444)

0.0055
(0.992)
−0.0025
(−1.184)
0.1410∗∗∗
(2.907)
0.0194
(0.578)
−0.0455∗∗∗
(−3.414)
−0.0028
(−0.067)
−0.0724
(−1.240)

0.0138∗∗
(1.982)
−0.0008
(−0.314)
0.2768∗∗∗
(2.773)
−0.1163∗∗∗
(−3.318)
−0.0135
(−0.854)
−0.0767
(−1.132)
0.0413
(0.430)

0.0104∗∗∗
(2.989)
0.0007
(0.480)
0.0943∗∗
(1.976)
−0.0328∗
(−1.819)
−0.0218∗∗∗
(−3.190)
−0.0122
(−0.498)
0.0239
(0.553)
0.5858∗∗∗
(11.711)

Yes

Yes

Yes

Yes

124,682
.0243

124,682
.0419

124,682
.129

124,682
.386

Transition Riski,t
Industry × Time FE
N
Adj. R2

Panel A reports the results on the adjusted R 2 from a projection of ClimateRiski,t on various sets of fixed
effects. Column 1 reports the adjusted R 2 of the regressions with acute climate risk as the dependent variable
and different sets of fixed effects as the independent variables. In column 2, we report the change/improvement
in adjusted R 2 relative to a benchmark. The benchmark for regressions in the first block is zero (no fixed effects).
The benchmark for regressions in the second and third blocks is the fourth row in the first block (Time + NAICS2
fixed effects). We repeat the analysis in columns 3 and 4 with chronic climate risk as the dependent variable, and
in columns 5 and 6 with transition climate risk as the dependent variable. Panel B presents regressions of acute
risk, chronic risk, all transition risk, and proactive transition risk on a variety of lagged deterministic variables.
Industry by time fixed effects are included in all regressions in panel B. Standard errors are clustered at the firm
level. t-statistics are shown in parentheses. *p < .1; **p < .05; ***p < .01.

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Acute Riski,t

Corporate Climate Risk: Measurements and Responses

7. Do Capital Markets Price Climate Risks?
7.1 Baseline results
The pricing of climate risks in financial markets is a key issue in the climate
finance literature, as highlighted by recent studies (Giglio, Kelly, and Stroebel
2021; Stroebel and Wurgler 2021). In particular, regulatory risk associated with
transition risk is viewed as a top climate risk over the next 5–30 years. In
this section, we aim to investigate whether transition risk is priced in stock
24 They conclude that their results are consistent with the hypothesis that climate risk reduces leverage via larger

expected distress costs and higher operating costs.

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better understand what types of firms tend to have higher values in the climate
risk measures that we constructed. We control for industry-by-time fixed
effects to account for time-varying heterogeneity across industries. Among all
the variables, the first set is related to a firm’s physical exposure to climate risk.
We find an overall positive relationship between the firm’s physical assets and
the climate risk measures: the coefficients for PPE and total assets are positive
and significant in most regressions. The results suggest that firms that hold
more physical assets tend to face higher climate risk exposure.
A second set measures the firm’s financial leverage. We find it to be
negatively correlated with the transition risk, but not with the two physical
risk measures, suggesting that highly leveraged firms tend to be associated
with lower transition risk exposure. This evidence is consistent with the
evidence documented by Ginglinger and Moreau (2023), who find that firms
with greater climate risk have lower leverage even after controlling for firm
characteristics known to determine leverage.24
The final set of measures included in our regressions capture external
characteristics of firms, such as the number of analysts covering the firm
and institutional ownership. These measures could be correlated with how
climate issues are discussed in earnings calls. We find a negative relationship
between the number of analysts and our climate risk measures, with one
measure being statistically significant. This suggests that firms are less likely
to discuss climate-related topics during earnings conference calls when a large
number of analysts cover the firm. This could be because with higher analyst
coverage, ample information already may be available regarding the firm’s
climate exposure, leading to less need for discussion during earnings calls. We
do not find a significant correlation between institutional ownership and our
climate risk measures.
Lastly, we analyze the correlations between the proactive component of the
transition risk measure and firm-level attributes, controlling for transition risk
itself. Our results show that firms that carry low leverage, hold more physical
assets, and are followed by fewer analysts tend to respond more proactively to
rising climate risk.

The Review of Financial Studies / v 37 n 6 2024

T obin’s qi,t+k = β ·T ransitionRiski,t +γ ·Xi,t−1 +ζj,t +i,t ,

(3)

where the dependent variable is Tobin’s q in quarter t +k (k = 1,3,5);
T ransitionRiski,t is the main explanatory variable; Xi,t−1 includes the firm’s
assets, CapEx, PPE, book leverage, ROA, and energy price exposure that we
constructed using the earnings call data. We also include industry-by-quarter
fixed effects to account for both observable and unobservable time-varying
heterogeneity across industries.
In panel A of Table 6, we present the baseline results based on the
entire sample, where in each column we report the results of a regression
of Tobin’s q over various lead times k (1, 3 and 5). For columns 1–3 we
use T ransitionRiski,t as the main explanatory variable. All coefficients for
T ransitionRiski,t are negative and significant at the 1% level. For instance,
the results in column 1 suggest that a one-SD increase in the transition risk
measure is associated with about a 0.0389—1.9% of the mean—decrease in
Tobin’s q in the next quarter.25 Also, the magnitude of the coefficient increases
slightly when we use Tobin’s q as the dependent variable over a longer horizon
(k = 3,5), suggesting that there is no reversal in the estimated pricing effect.
Therefore, our results in this table suggest that transition risk has been priced
in equity markets.
For columns 4–6 we include proactive and nonproactive components of our
transition risk measures as the main explanatory variables. We also include
the firm-level Action I ndex as additional control, which captures the overall
proactiveness of firms that do not face high transition risk. This measure
is calculated as the total frequency of mentions of proactive verbs in an
entire transcript (except those that fall within ±1 sentences of climate-related
discussions), divided by the length of the transcript. Interestingly, we find that,
while the coefficient for nonproactive transition risk is negative and significant,
that on proactive measure is nonsignificant. The difference between the two

25 The estimate is comparable to those in several papers in the literature that estimate the pricing effect of carbon

emissions. For example, Matsumura, Prakash, and Vera-Munoz (2014) estimate that an increase of carbon
emissions from the 25th to 75th percentile is associated with 4.2% decrease in the market value of equity
(calculated as number of shares outstanding multiplied by year-end stock price). Both Bolton and Kacperczyk
(2021b) and Chava (2014) estimate a significant carbon premium, by 2.85% of stock returns per one-standarddeviation change in total emission levels in each country and 1.04% of expected cost of equity for U.S. firms
that have higher net environmental concerns, respectively.

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markets. To measure a firm’s valuation, we use Tobin’s q, which is the ratio of
a firm’s market value to the replacement value of its physical assets. Tobin’s
q has been widely used in the literature for this purpose, as it captures the
value of intangible assets in addition to physical capital. This measure is
high (low) when the firm has more (less) valuable intangible assets, which
makes it well-suited for our analysis of the predictable effects of a firm’s
transition risk on its value. Specifically, we estimate the following regression
specification:

Corporate Climate Risk: Measurements and Responses

Table 6
Pricing of climate risk
A. All years
Tobin’s qi,t+h
Dep Var

h=3
(2)

h=5
(3)

h=1
(4)

h=3
(5)

h=5
(6)

−0.0389∗∗∗
(−3.828)

−0.0404∗∗∗
(−3.978)

−0.0418∗∗∗
(−4.179)

−0.0416∗∗∗
(−4.764)
0.0047
(0.618)
−0.0601∗∗∗

−0.0407∗∗∗
(−4.466)
0.0005
(0.081)
−0.0545∗∗∗

−0.0405∗∗∗
(−4.719)
−0.0024
(−0.326)
−0.0517∗∗∗

−0.0634∗∗∗
(−5.814)

−0.0577∗∗∗
(−5.382)

−0.0547∗∗∗
(−5.059)

(−5.503)
−0.0583∗∗∗
(−4.458)

(−5.077)
−0.0520∗∗∗
(−3.941)

(−4.784)
−0.0462∗∗∗
(−3.455)

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

111,691
.182

104,442
.210

97,470
.171

111,691
.218
−0.0463∗∗∗

104,442
.211
−0.0412∗∗∗

97,470
.210
−0.0381∗∗∗

Transition risk/Nonproactivei,t
Transition risk/Proactivei,t
Energy Price Exposurei,t
Action Indexi,t
Firm attributesi,t−1
Industry × Time FE
N
Adj. R2
F-test

B. Transition risk by different periods
Dep var

Tobin’s qi,t+1

Sample

Year ≤ 2009
(1)

Year ≥ 2010
(2)

Transition Riski,t

−0.0041
(−0.305)

−0.0571∗∗∗
(−4.911)

Transition Risk/Nonproactivei,t
Transition Risk/Proactivei,t

Year ≤ 2009
(3)

Year ≥ 2010
(4)

−0.0151
(−1.412)
0.0174
(1.461)
−0.0527∗∗∗
(−3.546)
−0.0426∗∗∗

−0.0548∗∗∗
(−5.234)
−0.0045
(−0.537)
−0.0706∗∗∗
(−5.607)
−0.0702∗∗∗

−0.0554∗∗∗
(−3.729)

−0.0742∗∗∗
(−5.920)

(−3.013)

(−3.883)

Firm Attributesi,t−1
Industry × Time FE

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

N
Adj. R2

50,706
.180

60,985
.183

50,706
.181

60,985
.185

Energy Price Exposurei,t
Action Indexi,t

This table presents results from firm level regressions testing the relation between our transition climate risk
measures (standardized) and Tobin’s q. Panel A reports the results from regression analysis of firm’s Tobin’s q in
different lead time periods (t+1, t+3, and t+5) on the lagged transition climate risk (in quarter t). In columns 1–3,
the key explanatory variable is the overall transition risk measure. In columns 4–6, we decompose the transition
risk measure into proactive and nonproactive components and add Action Index as an additional control variable.
In panel B, we separately examine the relationship between Tobin’s q and lagged transition climate risk in two
subsample periods: 2002–2009 and 2010–2018. In both panels, all specifications include time-varying firm-level
control variables, including lagged (i.e., t-1) log(Asset), CapEx, PPE, Book Leverage, and ROA (%). Industry
(NAICS three-digit) by quarter fixed effects are also included in all tests. We exclude the firms in finance and
utility sectors in this analysis. Table A.1 in the appendix contains detailed definitions of all variables. Standard
errors are double clustered at the firm and quarter levels. t-statistics are shown in parentheses. *p < .1; **p < .05;
***p < .01.

coefficients is statistically different from zero at the 1% level. This result
suggests that equity markets appear to discount firms that do not actively
manage their transition risk, but not those that are proactive in addressing
the risk. This finding is also consistent with our earlier evidence that the

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Transition riski,t

h=1
(1)

The Review of Financial Studies / v 37 n 6 2024

nonproactive transition risk measure is associated with higher CO2 emissions
intensity, while the proactive transition risk measure is not.26

26 To address the potential concern that there are a large number of zero values in the climate risk measures, we

also conduct a set of zero-inflated regressions in which we control for a dummy variable that equals one if
the transition risk measure is positive and zero otherwise. The results in panel A of Table IA.2 in the Internet
Appendix show that the coefficients for the continuous transition climate measures are very similar in magnitude
and statistical significance to those in Table 6, while the coefficient for the dummy variable is not statistically
significant.
27 Further details on the SEC’s Interpretive Release can be found at https://www.sec.gov/news/press/2010/2010-

15.htm.
28 We acknowledge that it is difficult to identify the exact source of the change in the pricing effect of transition

risk. Several factors could be at play, such as shifts in investor attention and changes in climate-related policies
and regulations.

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7.2 Subsample analysis: Before and after 2010
In this section, we investigate whether there are any time-series variations in the
pricing effects of climate risk. The pricing of climate risks is likely to change
substantially over time, as noted by Giglio, Kelly, and Stroebel (2021), and the
rise in investor attention to climate risk is a relatively recent phenomenon.
Some global events play a crucial role in shaping societal expectations and
perceptions of climate change, as several studies have shown. For instance,
Engle et al. (2020) report that the intensity of climate news coverage peaked
in December 2009 when the UN Climate Change Conference in Copenhagen
announced a U.S.-backed climate deal with pledges to meet certain emissions
reduction targets. Moreover, in January 2010, the SEC issued its first guidance
to public firms on existing SEC disclosure requirements as they apply to
climate change issues.27 To examine how the pricing of climate risk evolves
over time, we conduct the analysis again after splitting the sample into
observations made before and after 2010.
In panel B of Table 6, we present the results of this analysis, in which we
focus on Tobin’s q in t +1 as the dependent variable. Based on the results
in column 1, the coefficient for T ransitionRiski,t is close to zero and not
significant in the early period (≤ 2009), but turns negative and significant
in the late period (≥ 2010) with a much larger magnitude, suggesting that
a firm’s climate risk is priced by the capital market with a significant
discount in recent years. The contrast between the results in columns 1 and
2 underscores the importance of rising investor attention as conjectured by
Giglio, Kelly, and Stroebel (2021) as well as various climate-related initiatives
and regulations that were implemented around that time.28 In columns 3 and
4, we report the results obtained when we decompose transition risk into
proactive and nonproactive components. We find that it is the nonproactive
component that primarily drives the negative relationship between transition
risk and market valuation in the late period. The coefficient for the proactive
transition climate risk measure is not statistically significant in the early or late
periods. Consistent with the evidence reported in panel A, there is a significant

Corporate Climate Risk: Measurements and Responses

difference in the pricing effects of proactive and nonproactive transition risk
components.

7.3.1 Transition risk measures constructed using SEC filings data. We
construct the first set of alternative measures using Management Discussion
and Analysis (MD&A) and Risk Factors (RF) sections in the 10-K/10-Q filings,
respectively. We apply the same climate dictionaries to the filings data to
construct T ransitionRiskMDAi,t and T ransitionRiskRFi,t . In panel A of
Table 7, we present the results of a horse-race analysis in which we regress
Tobin’s q, in t +1 or t +5, on both our transition risk measure and one of the two
alternative transition risk measures in each regression.29 The results in columns
1–4 show that the coefficients for our transition risk measure remain negative
and significant, while those on the alternative transition climate risk measures
are not statistically significantly different from zero except for in column 3,
where the coefficient for T ransitionriskRFi,t is less than half of that on
our transition risk measure. We note that, compared with the earnings call
data, one major drawback of using the Risk Factors section is that it contains
only information about the risk factors themselves, with no discussion of how
a company addresses or responds to those risks. In columns 5–8, we report
the results of an analysis where we decompose transition risk into proactive
and nonproactive components. We continue to find that the discount on our
transition risk measure is driven primarily by its nonproactive component,
which is also negative and significant at the 1% level in all columns, after
controlling for competing measures.
7.3.2 Transition risk measure constructed using firm-related news data.
The second alternative measure is constructed using firm-related news data.
T ransitionRisk N ewsi,t is the ratio between the number of news articles
related to a firm’s transition climate risk exposure and the number of all news
articles related to the company. We construct this measure by applying the same
transition risk dictionary to the firm-related news data. Panel B of Table 7

29 Table IA.3 in the Internet Appendix presents the correlation of these alternative measures.

1811

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7.3 Horse-race analysis
We perform additional analyses to assess the robustness of our results regarding
the pricing effects of climate risk. First, we carry out a horse-race analysis
between our transition risk measure and various alternative measures. These
competing measures include: (1) a transition risk measure constructed using
SEC filings data; (2) a transition risk measure constructed using firm-related
news data; (3) external ESG scores; and (4) climate exposure measures
from Sautner et al. (2023). In addition, we also perform sensitivity analysis
regarding regression specifications and strategic disclosure considerations.

N
Adj. R2
F-test

Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

Transition Risk RFi,t

Transition Risk MDAi,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

Transition Riski,t

89,308
.186

Yes
Yes

(−5.494)

−0.0592∗∗∗

79,141
.176

Yes
Yes

(−4.661)

−0.0511∗∗∗

−0.0062
(−0.296)

−0.0425∗∗∗
(−4.141)

−0.0373∗∗∗
(−3.524)

−0.0102
(−0.491)

h=5
(2)

h=1
(1)

72,095
.188

Yes
Yes

−0.0161**
(−2.553)
−0.0582∗∗∗
(−5.030)

−0.0351∗∗∗
(−3.181)

h=1
(3)

62,792
.183

Yes
Yes

−0.0111
(−1.590)
−0.0494∗∗∗
(−4.236)

h=1
(5)

89,308
.187
−0.0403∗∗∗

Yes
Yes

(−5.185)
−0.0560∗∗∗
(−4.086)

−0.0559∗∗∗

−0.0384∗∗∗
(−4.126)
0.0019
(0.215)
−0.0122
(−0.585)

Tobin’s qi,t+h

−0.0422∗∗∗
(−4.035)

h=5
(4)

A. Alternative transition risk measures from SEC filings data

79,141
.177
−0.0351∗∗∗

Yes
Yes

(−4.402)
−0.0427∗∗∗
(−3.073)

−0.0483∗∗∗

−0.0398∗∗∗
(−4.414)
−0.0047
(−0.579)
−0.0076
(−0.366)

h=5
(6)

72,095
.190
−0.0403∗∗∗

Yes
Yes

−0.0157**
(−2.502)
−0.0549∗∗∗
(−4.729)
−0.0614∗∗∗
(−4.023)

−0.0370∗∗∗
(−3.828)
0.0033
(0.342)

h=1
(7)

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1812

Dep Var

Table 7
Alternative transition risk measures

(Continued)

62,792
.184
−0.0326∗∗∗

Yes
Yes

−0.0108
(−1.557)
−0.0462∗∗∗
(−3.956)
−0.0487∗∗∗
(−3.114)

−0.0388∗∗∗
(−4.221)
−0.0062
(−0.721)

h=5
(8)

The Review of Financial Studies / v 37 n 6 2024

N
Adj. R2
F-test

111,691
.182

Yes
Yes

−0.0051
(−0.514)
−0.0630∗∗∗
(−5.857)

97,470
.171

Yes
Yes

−0.0074
(−0.770)
−0.0540∗∗∗
(−5.056)

(−3.628)

−0.0389∗∗∗

(−3.403)

(2)

−0.0370∗∗∗

111,691
.183
−0.0444∗∗∗

Yes
Yes

−0.0398∗∗∗
(−4.163)
0.0046
(0.601)
−0.0047
(−0.481)
−0.0596∗∗∗
(−5.547)
−0.0583∗∗∗
(−4.458)

(3)

h=1

Relevance ≥ 75

h=5

(1)

h=1

97,470
.172
−0.0349∗∗∗

Yes
Yes

111,691
.182

Yes
Yes

0.0094
(0.814)
−0.0642∗∗∗
(−5.999)

(−3.937)

(5)

h=1

−0.0425∗∗∗

Tobin’s qi,t+h

−0.0375∗∗∗
(−4.040)
−0.0026
(−0.349)
−0.0074
(−0.776)
−0.0510∗∗∗
(−4.781)
−0.0462∗∗∗
(−3.455)

(4)

h=5

B. Alternative transition risk measures from news data

97,470
.171

Yes
Yes

0.0071
(0.641)
−0.0553∗∗∗
(−5.218)

(−4.201)

−0.0446∗∗∗

(6)

111,691
.183
−0.0499∗∗∗

Yes
Yes

−0.0452∗∗∗
(−4.772)
0.0047
(0.621)
0.0095
(0.819)
−0.0608∗∗∗
(−5.689)
−0.0583∗∗∗
(−4.454)

(7)

h=1

Relevance ≥ 50

h=5

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Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

Transition Risk Newsi,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

Transition Riski,t

Climate News Restriction

Dep Var

Table 7
(Continued)

(Continued)

97,470
.172
−0.0408∗∗∗

Yes
Yes

−0.0432∗∗∗
(−4.768)
−0.0024
(−0.328)
0.0069
(0.630)
−0.0523∗∗∗
(−4.944)
−0.0462∗∗∗
(−3.452)

(8)

h=5

Corporate Climate Risk: Measurements and Responses

1813

N
Adj. R2
F-test

Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

MSCI CCIi,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

13,564
.212

Yes
Yes

−0.1703∗∗∗
(−3.066)
−0.0564∗∗
(−2.182)

97,814
.182

Yes
Yes

−0.0601∗∗∗
(−5.535)

−0.0325∗∗∗
(−2.991)

−0.0567∗∗∗
(−3.501)

Transition Riski,t

87%
(2)

13%
(1)

Coverage

No

Yes

Sample

h=1

10,614
.203

Yes
Yes

−0.1706∗∗∗
(−3.015)
−0.0520∗
(−1.912)

−0.0445∗∗
(−2.680)

13%
(3)

Yes

h=5

87%
(4)

86,561
.172

Ye
Yes

−0.0516∗∗∗
(−4.866)

13,564
.213
−0.0769∗∗

Yes
Yes

−0.0618∗∗∗
(−3.773)
0.0151
(0.999)
−0.1661∗∗∗
(−3.031)
−0.0542∗∗
(−2.090)
−0.0453
(−1.171)

13%
(5)

Overlapped Sample
No
Yes

Tobin’s qi,t+h

−0.0377∗∗∗
(−3.642)

C. MSCI CCI

h=1

No

97,814
.183
−0.0377∗∗∗

Yes
Yes

−0.0570∗∗∗
(−5.233)
−0.0541∗∗∗
(−4.174)

−0.0346∗∗∗
(−3.919)
0.0031
(0.387)

87%
(6)

Yes

10,614
.203
−0.0301

Yes
Yes

−0.0401∗∗
(−2.463)
−0.0100
(−0.669)
−0.1685∗∗∗
(−2.995)
−0.0496∗
(−1.812)
−0.0264
(−0.689)

13%
(7)

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1814

Dep Var

Table 7
(Continued)

h=5

No

(Continued)

86,561
.172
−0.0345∗∗

Yes
Yes

−0.0489∗∗∗
(−4.607)
−0.0429∗∗∗
(−3.252)

−0.0366∗∗∗
(−4.312)
−0.0021
(−0.265)

87%
(8)

The Review of Financial Studies / v 37 n 6 2024

1815

124,444
.151

Yes
Yes

−0.1012∗∗∗
(−7.904)

0.0145
(0.749)

109,730
.149

Yes
Yes

−0.0888∗∗∗
(−7.028)

0.0026
(0.128)

(−3.363)

−0.0386∗∗∗

−0.0385∗∗∗

(−3.431)

(2)

h=5

(1)

h=1

All Years

124,444
.152
−0.0384∗∗

Yes
Yes

−0.0027
(−0.252)
0.0216
(1.574)
0.0075
(0.397)
−0.0979∗∗∗
(−7.680)
−0.0513∗∗∗
(−3.820)

−0.0413∗∗∗
(−3.838)
−0.0029
(−0.361)

(3)

h=1

109,730
.150
−0.0297∗

Yes
Yes

−0.0039
(−0.376)
0.0146
(1.094)
0.0041
(0.200)
−0.0857∗∗∗
(−6.844)
−0.0450∗∗∗
(−3.274)

−0.0391∗∗∗
(−3.677)
−0.0094
(−1.132)

(4)

h=5

Tobin’s qi,t+h

D. Measures from Sautner et al. (2023)

71,224
.159

Yes
Yes

−0.1159∗∗∗
(−7.534)

−0.0122
(−0.629)

(−3.854)

−0.0494∗∗∗

(5)

Year≥2010

h=1

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71,224
.161
−0.0400

Yes
Yes

0.0065
(0.422)
0.0055
(0.346)
−0.0216∗
(−1.690)
−0.1120∗∗∗
(−7.285)
−0.0595∗∗∗
(−3.352)

−0.0475∗∗∗
(−4.081)
−0.0075
(−0.822)

(6)

Year≥2010

This table presents the horse-race test results when we regress Tobin’s q in different lead time periods on both our transition risk measures using earnings call transcript data and other
transition risk measures constructed from alternative data source. In panel A, the alternative transition risk measures are the measure based on the MD&A section of SEC filings (columns
1–2, 5–6) and the measure based on the Risk Factors section of SEC filings (columns 3 and 4, 7 and 8), respectively. The alternative risk measures in Panel B are constructed from
company news data from RavenPack database. Transition risk news is equal to the number of news articles related to the firm’s transition climate risk exposure divided by the number
of all news articles related to the company. In column 1 to column 4, the news articles are filtered by relevance score higher than 75. According to RavenPack, Values above 75 are
considered significantly relevant. Column 5 to column 8 present the results when we change the relevance cutoff to 50. In Panel C, the alternative transition risk measure is the MSCI
CCI. Column 1, 3, 5, and 7 present the regression results on the overlapped sample (13% of our sample). Column 2, 4, 6, and 8 present the results on the other part of our sample (87%
of our sample) that is not covered in MSCI CCI. In panel D, we use the climate exposure measures from Sautner et al. (2023). Specifically, CCExposure is the relative frequency with
which bigrams related to climate change occur in the transcripts of earnings calls. CCExposureP hy is the relative frequency with which bigrams that capture physical shocks related
to climate change occur in the transcripts of earnings calls. CCExposureOpp is the relative frequency with which bigrams that capture opportunities related to climate change occur
in the transcripts of earnings calls. CCExposureReg is the relative frequency with which bigrams that capture regulatory shocks related to climate change occur in the transcripts of
earnings calls. Lagged firm attributes (log(Asset), CapEx, PPE, Book Leverage, and ROA (%)) and industry by quarter fixed effects are included in all tests of each panel. Table A.1 in
the appendix contains detailed definitions of all variables. Standard errors are double clustered at the firm and quarter levels. t-statistics are shown in parentheses. *p < .1; **p < .05; ***p < .01.

N
Adj. R2
F-test

Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

CCExposurei,t

Reg

Opp
CCExposurei,t

CCExposurei,t

P hy

CCExposurei,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

Transition Riski,t

Sample

Table 7
(Continued)

Corporate Climate Risk: Measurements and Responses

The Review of Financial Studies / v 37 n 6 2024

7.3.3 MSCI Climate Change index. The third alternative measure of
climate risk is MSCI’s CCI. In panel C of Table 7, we report the horse-race
results. In all specifications, the coefficients of our transition risk measure and
its nonproactive component are negative and significant at the 5% or lower
level, confirming that the estimated price discount indicated in Table 6 is robust
in the horse race against the CCI. The coefficient for the CCI measure is also
negative and significant at the 1% level, suggesting that firms with higher
climate change scores are also priced at a significant discount in the stock
market. The coexistence of the two competing measures also suggests that they
complement each other in capturing firms’ climate risk exposure.30

7.3.4 Climate risk measures from Sautner et al. (2023). Our final horserace test uses the climate change exposure measures developed by Sautner et al.
(2023) based on an ML approach as the competing measure. Panel D of
Table 7 reports the results. We find that the coefficients for our transition risk
measure and its nonproactive component are negative and significant at the
1% level, while those on their climate exposure measures are not statistically
significant from zero, as shown in columns 1–4. This pattern persists when we
focus on recent years (2010 or later), as Sautner et al. (2023) show a strong
correlation between their measures and Tobin’s q using only the data from
more recent years. There, we find the coefficient for their regulatory climate
exposure measure (CCExposureReg ) to be marginally significant and small
in magnitude compared with that on our transition climate risk measure.

30 In an additional analysis, we also consider the environmental components of the RepRisk and the Refinitiv ESG

scores in a similar horse-race specification. Panel A of Table IA.4 in the Internet Appendix reports the results.
We find that the coefficients for our transition risk measure and its nonproactive component remain negative and
significant at the 1% level after controlling for the environmental ratings of RepRisk and Refinitiv.

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reports the horse-race results. The results in columns 1 and 2 show that the
coefficient of our transition risk measure remains negative and significant at the
1% level in all specifications, while the coefficient for T ransitionrisknewsi,t
is not significant, suggesting that there is no relationship between the fraction
of firm-specific news that involves climate issues and Tobin’s q. The results
in columns 3 and 4 are very similar when we replace the transition risk
measure by its proactive and nonproactive components. The significant price
discount associated with transition risk is driven by firms that do not undertake
proactive responses, while the coefficient for T ransitionrisknewsi,t remains
nonsignificant. In columns 5–8, we repeat the above analysis using 50 as
the relevance score cutoff in RavenPack and find almost the same results.
This set of results suggests that our transition risk measure contains valuable
information not already available in other public sources.

Corporate Climate Risk: Measurements and Responses

7.5 Strategic disclosure in earnings calls
Like any other disclosure data, discussions during earnings calls are not
immune to selection bias introduced by strategic considerations. For instance,
executives may choose to speak about certain aspects of a firm’s climate
risk exposure while not necessarily answering certain questions brought
up by analysts. To address selection concerns regarding earnings calls, we
restrict the sample in two ways, such that the particular selection concern
is more constrained and repeat the pricing regression to see if our estimates
remain robust. In the first exercise, we filter out earnings calls where we
detect an extreme tone. The literature on qualitative disclosure has shown
that management can strategically determine the tone of textual disclosures
to achieve certain outcomes (e.g., Lang and Lundholm 2000; Feldman et al.
2010; Arslan-Ayaydin, Boudt, and Thewissen 2016). In the second exercise,
we exclude earnings calls which rank in the top quartile based on the
number of “nonanswers” from management during a call, measured using the

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7.4 Controlling for firm fixed effects
Our baseline regressions control for industry-by-time fixed effects, along with
firm-level attributes that vary over time. This specification allows us to compare
the differential outcomes, such as Tobin’s q, between firms that face high
and low climate risk within the same industry at a given time. However, it is
important to also consider within-firm variations over time to fully understand
the impact of climate risk on firms’ outcomes. To address this concern, we
have experimented with an alternative specification where we control for both
firm and industry-by-time fixed effects, which allows us to compare withinfirm changes in climate risk and firm outcomes while addressing potential
endogeneity issues. The results are reported in Table 8. Panel A uses the change
in Tobin’s q as the dependent variable and the change in T ransitionRiski,t as
the main explanatory variable. Our analysis shows that a higher increase in the
transition risk measure is associated with a larger decrease in Tobin’s q in the
future. The effect is statistically significant at the 10% level or lower after the
third quarter (including t +4, t +5, t +6,...), indicating that the stock markets
gradually price in the change in transition risk within a given firm.
Panel B focuses on changes in the proactive and nonproactive components
of our transition risk measures as the main explanatory variables. The results
indicate that only changes in transition risk with nonproactive responses are
significantly priced at a discount, while the coefficient for changes in transition
risk with proactive responses is negative, but not statistically significant. These
findings are consistent with our baseline results in Section 7.1, suggesting that
equity markets discount firms that do not actively manage their transition risk,
but not those that proactively address the risk.
Overall, our results remain robust after controlling for firm fixed effects and
further support the idea that changes in climate risk discussion correlate with
changes in Tobin’s q.

The Review of Financial Studies / v 37 n 6 2024

Table 8
Pricing of within-firm climate risk
A. Total transition risk
Dep Var

Energy Price Exposurei,t
Firm Attributesi,t−1 FE
Firm FE
Industry × Time FE
N
Adj. R2

h=2
(2)

h=3
(3)

h=4
(4)

h=5
(5)

h=6
(6)

−0.0003
(−0.164)
0.0008
(0.477)

−0.0025
(−1.023)
0.0032
(1.216)

−0.0030
(−1.177)
0.0037
(1.350)

−0.0053∗∗
(−2.066)
0.0030
(0.887)

−0.0034∗
(−1.824)
0.0041
(1.188)

−0.0046∗∗
(−2.127)
0.0041
(1.124)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

110,761
.103

106,830
.188

103,113
.311

99,421
.301

95,929
.392

92,554
.427

B. Proactive and nonproactive transition risk
Dep Var

Transition Risk/
Nonproactive i,t
Transition Risk/Proactive

Energy Price Exposurei,t
Action Indexi,t
Firm Attributesi,t−1
Firm FE
Industry × Time FE
N
Adj. R2

Tobin’s qi,t+h
h=1
(1)

h=2
(2)

h=3
(3)

h=4
(4)

h=5
(5)

h=6
(6)

−0.0009
(−0.454)
0.0010
(0.853)
0.0009
(0.531)
−0.0025
(−1.220)

−0.0026
(−1.222)
−0.0002
(−0.165)
0.0035
(1.333)
−0.0055∗
(−1.751)

−0.0035
(−1.571)
0.0006
(0.435)
0.0041
(1.501)
−0.0080∗∗
(−2.004)

−0.0046∗
(−1.944)
−0.0012
(−0.872)
0.0037
(1.104)
−0.0123∗∗
(−2.642)

−0.0033∗
(−1.857)
−0.0004
(−0.307)
0.0050
(1.443)
−0.0150∗∗∗
(−3.039)

−0.0050∗∗
(−2.137)
0.0004
(0.498)
0.0049
(1.351)
−0.0155∗∗∗
(−2.934)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

110,761
.103

106,830
.188

103,113
.312

99,421
.301

95,929
.392

92,554
.428

This table presents the results from firm level regressions testing the relation between the change in transition
climate risk measures (standardized) and the change in Tobin’s q while controlling for firm fixed effects. Panel
A reports the results from regression analysis of change in Tobin’s q in different lead time periods (t+1,t+2 t+3,
t+4, t+5 and t+6) on the lagged change in transition climate risk. The key explanatory variable is the change in
transition risk measure from t-1 to t. In panel B, we decompose the change in transition risk measure into the
change in proactive and nonproactive components and add Action Index as an additional control variable. In both
panels, all specifications include time-varying firm-level control variables, including lagged (i.e., t-1) Tobin’s q,
log(Asset), CapEx, PPE, Book Leverage, and ROA (%). Industry (NAICS three-digit) by quarter fixed effects
are also included in all tests. We exclude the firms in finance and insurance sector. Table A.1 in the appendix
contains detailed definitions of all variables. Standard errors are double clustered at the firm and quarter levels.
t-statistics are shown in parentheses. *p < .1; **p < .05; ***p < .01.

latest linguistic analysis method proposed by Gow, Larcker, and Zakolyukina
(2021).31 We report the results of this analysis in Table IA.5. We find that the

31 This measure is viewed in the literature as a proxy for strategic considerations or corporate disclosure policies.

Gow, Larcker, and Zakolyukina (2021) show that analyst questions that have a negative tone, greater uncertainty,
and greater complexity, or requests for greater detail are more likely to trigger nonanswers. Performance-related
questions tend to be associated with nonanswers, and this association is weaker when performance news is
favorable.

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Transition Riski,t

Tobin’s qi,t+h
h=1
(1)

Corporate Climate Risk: Measurements and Responses

price discount associated with high transition risk is still significant based on
the restricted samples. Our results suggest that the selection issue is not a major
concern for our analysis.

In this section, we investigate whether firm-level climate risk exposure
affects a firm’s real business activities. To do so, we estimate differences in
corporate responses associated with high climate risk by running regressions
specified in Equation (2), where the dependent variable includes CapEx, R&D
expenditures, the fraction of green patents, and employment over horizon t +k
(k > 0). The main explanatory variables are transition risk and its proactive
and nonproactive components in t. We control for a firm’s total assets as
well as industry-by-time fixed effects. In essence, we compare differences
in corporate responses between firms that face high and those that face low
transition climate risk, as well as between firms with and without proactive
responses to transition risk.

8.1 Investment
The theoretical literature has offered mixed predictions regarding
investment under uncertainty. While Bernanke (1983), Pindyck (1991),
Pindyck and Solimano (1993) and Dixit and Pindyck (1994) predict a decline
in investment in times of high uncertainty, other studies, such as Oi (1961),
Hartman (1972, 1976), Abel (1983), Roberts and Weitzman (1981), and
Bar-Ilan and Strange (1996), predict a positive relationship. Ultimately,
how firm-level investment varies with climate risk exposure is an empirical
question.
Table 9 presents the results of an analysis using CapEx scaled by total assets
as the dependent variable. The results in columns 1–3 indicate a positive,
but not significant, coefficient for ClimateRiski,t , suggesting that there is no
statistically significant difference in future investment between firms that face
high and those that face low transition risk. In columns 4–6, we investigate
differences between the responses of firms that do and those that do not respond
to climate risk proactively. To do so, we regress the same set of firm-level
outcomes on transition risk with and without proactive keywords. We see that
the coefficients for two of the transition risk measures are both positive, but
only the coefficient for proactive transition risk is statistically significant (at the
1% level), suggesting that firms that proactively respond tend to increase their
CapEx following an increase in transition risk. A one-SD increase in transition
risk with proactive keywords in t is associated with a 0.046-percentage-point
increase in CapEx in t +1 and about a 0.06-percentage-point increase in CapEx

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8. Firms’ Responses to Climate Risks

The Review of Financial Studies / v 37 n 6 2024

Table 9
Predicting the firm’s investment
CapExi,t+h
h=1
(1)

h=3
(2)

h=5
(3)

Transition Riski,t

0.0480
(1.460)

0.0498
(1.499)

0.0421
(1.256)

Transition Risk/Nonproactivei,t
Transition Risk/Proactivei,t
Energy Price Exposurei,t

N
Adj. R2
F-test

h=3
(5)

h=5
(6)

0.0236
(0.783)
0.0460∗∗∗
(2.951)
0.0867∗
(1.836)
0.0058
(0.274)

0.0158
(0.547)
0.0623∗∗∗
(3.455)
0.1030∗∗
(2.236)
0.0782∗∗∗
(3.442)

0.0074
(0.252)
0.0641∗∗∗
(3.287)
0.1136∗∗
(2.452)
0.0201
(0.909)

0.0896∗
(1.901)

0.1120∗∗
(2.435)

0.1186∗∗
(2.557)

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

Yes
Yes

126,099
.439

118,043
.437

110,313
.435

126,099
.439
−0.0224

118,043
.438
−0.0465

110,313
.435
−0.0567∗

Action Indexi,t
Firm Attributesi,t−1
Industry × Time FE

h=1
(4)

This table reports estimates of the regressions of capital expenditures (in different lead time periods) on transition
risk. Columns 1–3 shows the results using Transition risk as the key explanatory variable. In columns 4–6, we
replace transition risk measure with its two components: nonproactive and proactive transition risk, and we add
Action index as additional control variable. Lagged log(Asset) and industry by quarter fixed effects are included
in all tests. Table A.1 in the appendix defines all the variables. Standard errors are double clustered at the firm
and quarter levels. t-statistics are shown in parentheses. *p < .1; **p < .05; ***p < .01.

in t +3 and t +5.32 The estimates are economically meaningful, representing
approximately 1.6%–2.3% of the average investment level. In the bottom
row, we report the differences between the two coefficients along with their
significance levels based on F-tests, showing that the difference in CapEx
between proactive and nonproactive firms, when both face high climate risk, is
significant at the 10% level in t +5.
8.2 Innovation
To reach net-zero emissions or decarbonization, firms are inevitably required
to innovate or change the way they do business. Thus, innovation is a viable and
important response for firms facing high transition risk. We consider two measures of innovation: one is R&D expenditure, scaled by assets, the other is the
fraction of green patents. In panel A of Table 10, we report the results for R&D
expenditures. We find negative and significant coefficients for ClimateRiski,t
in columns 1–3, suggesting high transition risk is associated with lower R&D
expenditures. A one-SD increase in transition risk is associated with a 0.0529-

32 Although not fully reported in this table, our analysis reveals that the coefficients of the firm-level action

index (i.e., Action index ) are positive for the five consecutive quarters, with the magnitude varying over time.
Specifically, the coefficient is 0.0058 in t +1 and increases to 0.0782 in t +3 before decreasing to almost zero.
While the coefficient is not significant in t +1, it becomes statistically significant at the 1% level in t +2 and t +3,
before becoming insignificant thereafter. These results suggest that a higher level of action index, in general, is
associated with higher CapEx investments with a two-quarter lag, even for firms that do not face high climate
risk.

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Dep Var

1821

N
Adj. R2
F-test

h=1

32,713
.199

Yes
Yes

Yes
Yes

128,503
.388

0.0373∗∗∗
(4.930)

0.0115
(1.598)

(1)

−0.0529∗∗
(−2.269)

−0.0556∗∗
(−2.393)

32,713
.193

Yes
Yes

0.0352∗∗∗
(4.683)

0.0080
(1.276)

(2)

h=2
All Firms

32,713
.192
−0.0033

32,713
.193
−0.0089

Yes
Yes

(4.708)
0.0026
(0.745)

(4.903)
0.0063
(1.580)
Yes
Yes

0.0014
(0.200)
0.0103∗∗
(2.168)
0.0340∗∗∗

(4)

h=2

B. Green patents (annual)

111,971
.373

Yes
Yes

−0.1741∗∗∗
(−7.701)

(4)

h=1

9,372
.103

8,186
.110

Yes
Yes

0.0231∗∗
(2.367)

(6)
0.0331∗∗∗
(3.883)

Yes
Yes

h=1

9,372
.109
−0.0004

Yes
Yes

(2.339)
−0.0019
(−0.820)

0.0189∗∗
(2.252)
0.0193∗∗
(2.959)
0.0188∗∗

(7)

Firms with Patents Only
(5)

0.0207∗∗
(2.525)

119,997
.389
−0.0576∗∗

Yes
Yes

−0.0550∗∗
(−2.611)
0.0026
(0.179)
−0.1605∗∗∗
(−7.107)
−0.2463∗∗∗
(−10.685)

(5)

h=3

Green patents ratioi,t+h
h=2

0.0321∗∗∗
(3.914)

h=1

128,503
.398
−0.0515∗∗

Yes
Yes

−0.0548∗∗∗
(−2.697)
−0.0033
(−0.252)
−0.1603∗∗∗
(−7.174)
−0.2684∗∗∗
(−11.879)

R&D investmenti,t+h

−0.0565∗∗
(−2.391)

(3)

h=5

0.0057
(0.804)
0.0090∗∗
(2.396)
0.0359∗∗∗

(3)

h=1

I(Green patents)i,t+h

119,997
.381

Yes
Yes

−0.1782∗∗∗
(−7.756)

(2)

(1)

−0.1797∗∗∗
(−7.917)

h=3

h=1

A. R&D expenditures

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Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

Transition Riski,t

Sample

Dep Var

N
Adj. R2
F-test

Firm Attributesi,t−1
Industry × Time FE

Action Indexi,t

Energy Price Exposurei,t

Transition Risk/Proactivei,t

Transition Risk/Nonproactivei,t

Transition Riski,t

Dep Var

Table 10
Predicting the firm’s other responses

(Continued)

8,186
.122
−0.0086

Yes
Yes

(2.307)
−0.0018
(−0.908)

0.0165*
(1.836)
0.0251∗∗∗
(3.395)
0.0208∗∗

(8)

h=2

111,971
.382
−0.0532∗∗

Yes
Yes

−0.0557∗∗∗
(−2.675)
−0.0025
(−0.167)
−0.1561∗∗∗
(−7.015)
−0.2485∗∗∗
(−10.758)

(6)

h=5

Corporate Climate Risk: Measurements and Responses

32,165
.776

Yes
Yes

0.0032
(0.249)

30,533
.771

Yes
Yes

0.0007
(0.050)

32,165
.778
−0.0188

Yes
Yes

−0.0188∗
(−1.731)
−0.0000
(−0.003)
−0.0041
(−0.325)
0.0634∗∗∗
(6.647)

(3)

(2)
−0.0202∗∗
(−2.047)

(1)
-0.0195∗∗
(−2.050)

30,533
.773
−0.0199

Yes
Yes

−0.0197∗
(−1.692)
0.0002
(0.022)
−0.0067
(−0.508)
0.0624∗∗∗
(6.267)

(4)

h=2

In panel A, we regress R&D Investment (in t+1, t+3, t+5) on overall transition risk measure (in columns 1-3) and decomposed transition risk measures (in columns 4–6), respectively. In
columns 1–4 of panel B, the dependent variable is I(Green patents), a dummy variable equals one if a firm has at least one green patent, and zero otherwise. The sample includes all firms. In
columns 5–8 of panel B, the dependent variable is Green patents ratio, the number of green patents scaled by the total number of patents in the year. The sample is restricted to the firms with
patents. In panel C, the dependent variable is the natural logarithm of the firm’s employment level. All specifications include lagged (i.e., t-1) log(Asset) as the control variable. Industry by
quarter fixed effects are included in all tests. Table A.1 in the appendix defines all the variables. Standard errors are double clustered at the firm and quarter levels. t-statistics are shown in
parentheses. *p < .1; **p < .05; ***p < .01.

N
Adj. R2
F-test

Firm attributesi,t−1
Industry × Time FE

Action indexi,t

Energy price exposurei,t

Transition risk/proactivei,t

Transition risk/nonproactivei,t

Transition riski,t

h=1

log(Employment)i,t+h
h=2

h=1

C. Employment (annual)

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1822

Dep Var

Table 10
(Continued)

The Review of Financial Studies / v 37 n 6 2024

Corporate Climate Risk: Measurements and Responses

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to 0.0565-percentage-point decrease in future R&D expenditures. Again, the
coefficients are fairly stable over various horizons of R&D expenditures. The
results in columns 4–6 suggest that the negative relationship between transition
risk and a firm’s future R&D expenditures is significant only for the firms that
do not proactively respond, not for proactive firms.
In panel B of Table 10, we report the results of regressions using green patent
measures as the dependent variable. The results in columns 1–4 are based on all
firms and use an indicator of having at least one green patent as the dependent
variable. We find a positive, but not significant, coefficient for ClimateRiski,t
in columns 1 and 2, suggesting that there is no statistically significant difference
in future green patents between firms with high and low transition risk. For
columns 3 and 4, we investigate differences between the responses of firms
that do and those that do not respond to climate risk proactively. We see that
the coefficients for two of the transition risk measures are both positive, but
only the coefficient for proactive transition risk is statistically significant (at
the 5% level), suggesting that firms that proactively respond are more likely
to innovate via green patenting when facing high transition risk. A one-SD
increase in transition risk with proactive keywords in t is associated with a
0.01-percentage-point increase in the likelihood that a green patent is filed in t +
1 and 0.01-percentage-point increase in t +2. The estimates are economically
meaningful, representing approximately 12.5% of the average probability that
a green patent is filed.
The results in columns 5–8 are based on patenting firms only, using the
ratio of green patents to the total number of patents filed by a firm as the
dependent variable. We find positive and significant coefficients (at the 1%
level) on ClimateRiski,t as shown in columns 5 and 6, suggesting that firms
that face high transition risk are associated with a higher ratio of green patents.
A one-SD increase in transition risk with proactive keywords in t is associated
with a 0.0321-percentage-point increase in the ratio of green patents in t +1 and
a 0.0331-percentage-point increase in t +2. The results in columns 7 and 8 show
that the coefficients for two of the transition risk measures are both positive and
significant, but the coefficient for proactive transition risk is slightly higher and
more significant (at the 5% or lower level). A one-SD increase in transition
risk with proactive keywords in t is associated with a 0.0251-percentage-point
increase in the ratio of green patents in t +2.
Given the significant and positive relationship we find between a firm’s
greenness and their proactiveness in managing transition risk, we conduct
further analysis to explore the attributes of proactive firms and their potential
differential impact on firm valuation in Internet Appendix C. Starting with
firms that have patented green technologies and those that have not but are
proactive in their responses to transition risk, we find that green patenting firms
are more likely to be proactive in addressing transition risk, while nongreen
patenting firms do not show a significant difference in being proactive relative
to firms that do not patent. Panel A of Table IA.8 presents the results. Panel B of

The Review of Financial Studies / v 37 n 6 2024

8.3 Employment
Another strategy at a firm’s disposal for responding to rising climate risk is
adjusting employment (e.g., through plant closings, layoffs, or hiring freezes).
Layoffs and plant closings have been commonly adopted by executives at
public companies to increase productivity, address ongoing risks, and appeal
to capital markets. The results, reported in panel C of Table 10, indicate
that there is a negative and significant relationship (at the 5% level) between
transition risk and the logarithm of the employment level in the following 2
years. A one-SD increase in transition risk is associated with an approximately
0.02-percentage-point decrease in a firm’s employment stock. The negative
relationship is primarily driven by firms that do not proactively respond. The
relationship is not statistically significant for firms that proactively respond.
8.4 Summary
In summary, we find a significantly negative relationship between transition
risk and R&D expenditure as well as employment, driven primarily by firms
that face high transition risk but do not proactively respond. In contrast, firms
that proactively respond increase their total CapEx investment and file more
green patents following an increase in their transition risk.34 These findings,
while revealing divergent responses on the part of firms facing high transition
risk, may not suggest any causal relationships between the two, because

33 In an additional analysis, we also attempted to separate the proactive firms into two categories: (1) “fixer” firms,

which help address their customers’ climate risk (e.g., manufacturer of electric planes) and (2) nonfixer firms that
face high transition risk (e.g., airline company), using a more general approach that captures a set of keywords
in business descriptions. We observe a positive correlation between green patenting firms and fixer firms. Panel
C of Table IA.8 shows that fixer firms are more likely to be proactive in managing transition risk. However, after
controlling for other firm attributes, the relationship between fixer firms and proactive responses to transition
risk becomes statistically insignificant. Panel D of Table IA.8 shows that while both types of proactive firms are
not discounted by equity markets, the valuation is slightly larger for fixer proactive firms compared to nonfixer
proactive firms, but the difference is not statistically significant at the conventional level.
34 We conduct additional regressions to study the relationship between within-firm variations in climate risk and

firm-level outcomes (e.g., CapEx, the fraction of green patents, and employment). We report the results in panels
B–D of Table IA.6 in the Internet Appendix. We also show that firms that proactively respond to climate risk
increase total CapEx investment while controlling for firm and time fixed effects. The statistical and economic
significance of the coefficient for the proactive component of transition risk increase over time. Discussions of
proactive management of climate risks are associated with a significant increase in CapEx after quarter t +1
instead of immediately in quarter t +1, suggesting that these firms take time to put “words” into “actions.” We
do not, however, find a significant relationship between within-firm variation in transition risk and employment
in subsequent years. This is not surprising insofar as the employment variable is very sticky over time.

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that table shows that while both types of proactive firms are valued positively by
the equity markets, the difference between green proactive firms and those with
nonproactive responses is much larger than that between nongreen proactive
firms and those with nonproactive responses. Both differences are statistically
significant at the 1% level, indicating that the equity markets tend to value
green proactive responses to transition risk more than nongreen proactive
responses.33

Corporate Climate Risk: Measurements and Responses

our constructed measures simply capture transition risk discussions during
earnings calls. Instead, our evidence suggests that the new measures capture
new and valuable information about business conditions and can be highly
predictive of changes in these corporate outcomes.35

This paper quantifies the presence and materiality of firm-level climate risk
exposure. We develop a novel set of firm-level climate risk measures, covering
both physical and transition risks, by applying a modified textual analysis
method to earnings call transcript data. Most variations in physical climate risk
appear to be idiosyncratic factors that may be unrelated to firm-level attributes,
while most variations in transition risk can be explained by idiosyncratic
factors at the firm level. Using external benchmarks, we find that our three
risk measures capture changes in the respective types of climate risk a
company faces. As a unique innovation of our study, we also measure firms’
proactiveness in addressing climate issues. One key finding of our study is that
firms that face higher transition risk, especially those that do not proactively
respond, are valued at a discount in the equity market. Horse-race analyses
show that our measures offer unique value for studying how capital markets
price climate risk, particularly transition risk.
Using several corporate outcomes as dependent variables, we find that firms
that face high transition risk significantly decrease their R&D expenditures
and employment. This negative relation is primarily driven by firms that do
not proactively respond to rising climate risk. Firms that proactively respond
to this risk tend to significantly increase their total CapEx investment and file
more green patent applications. Thus, firms’ attitudes toward climate issues—
whether or not proactive— matter significantly in determining how firms
respond to rising climate risk.
Our key finding that firms that do not proactively respond to transition risk
are valued at a discount underscores the importance of disclosing climate risks
in a transparent and comprehensive manner to ensure that investors have access
to accurate information and can make informed investment decisions. Our
ability to identify variations in firm-level climate risk exposure and responses
suggests that when such information is available, investors find it relevant.
Indeed, regulators have begun to focus on how best to provide this information
to investors. In March 2021, the SEC created a Climate and ESG Task Force
to identify climate and ESG-related misconduct. In March 2022, the SEC
proposed new rules that require public companies to report climate-related risks
and emissions data in registration statements and annual reports.

35 In panels B–D of Table IA.2 in the Internet Appendix, we present the results from zero-inflated regressions of

CapEx, green patents, and employment, respectively. They show that coefficients for the continuous transition
risk measures and the dummy variable for nonzero values are both positive and significant.

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9. Conclusion

The Review of Financial Studies / v 37 n 6 2024

Appendix
Table A.1
Variable definitions
Description

Source

Acute climate risk

The frequency of mentions of the unigrams or bigrams
related to the acute climate discussion in the proximity
of risk synonyms, divided by the total length of the
transcript, and then multiplied by 104
The frequency of mentions of the unigrams or bigrams
related to the chronic climate discussion in the
proximity of risk synonyms, divided by the total length
of the transcript, and then multiplied by 104
The frequency of mentions of the unigrams or bigrams
related to the transition climate discussion, scaled by
the total length of the transcript, and then multiplied by
104
The frequency of mentions of the unigrams or bigrams
related to the transition climate discussion in the
proximity of proactive verbs, divided by the total
length of the transcript, and then multiplied by 104
The frequency of mentions of the unigrams or bigrams
related to the transition climate discussion which are
not in the proximity of proactive verbs, divided by the
total length of the transcript, and then multiplied by
104
The number of sentences that jointly mentions synonyms
of “energy” synonyms and “price” (two words not
necessarily synonyms for each other), divided by the
total number of sentences in the earnings call
transcript. Synonyms of “energy” include gas, fuel, oil,
and energy. Synonyms of “price” include cost,
expense, price, costs, expenses, and prices
The frequency of mentions of the “proactive” verbs in
the entire transcript (except those near, within ±1
sentences of, climate-related discussions), divided by
the length of the transcript
A dummy variable equal to one if there is a natural
disaster in the same county where a firm was
headquartered
Sum of CO2 emissions of all plants operated by the firm,
scaled by the total assets
(Total assets + Market value of equity - Book value of
equity) / Total assets
Capital expenditures, scaled by the total assets of the
previous quarter end
Research & Development expenditures, scaled by the
total assets of the previous quarter end
Natural logarithm of firm’s employment

StreetEvents

Chronic climate risk

Transition climate risk

Transition risk/proactive

Transition
risk/nonproactive

Energy price exposure

Action index

Disaster dummy

CO2 intensity
Tobin’s q
CapEx
R&D
log(Employment)
(annual)
I(Green patents)
(annual)

Green patent ratio
(annual)
log(Asset)
PPE
Book Leverage
log(No_Analysts)

A dummy variable that equals one if a firm has at least
one green patent in the year, and zero otherwise. Green
patents are identified following the OECD
classification
The number of green patents scaled by the total number
of patents in the year
Natural logarithm of firm’s total assets.
Property, Plant and Equipment, scaled by total assets of
the previous quarter end.
Total debt (= short-term debt + long-term debt), scaled
by the total assets.
The natural logarithm of number of analysts covering the
firm.

StreetEvents

StreetEvents

StreetEvents

StreetEvents

StreetEvents

StreetEvents

SHELDUS

EPA
Compustat
Compustat
Compustat
Compustat
Global Corporate Patent
data set

Global Corporate Patent
data set
Compustat
Compustat
Compustat
I/B/E/S
(Continued)

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Variable name

Corporate Climate Risk: Measurements and Responses

Table A.1
(Continued)
Description

Source

Institution %

The percentage of institutional ownership.

Institution HHI

The Herfindahl–Hirschman Index of institutional
ownership.
Operating Income Before Depreciation
(OIBDPQ), scaled by total assets of the
previous quarter end, multiply by 100.
The transition climate risk measure based on the
management discussion and analysis section of
SEC filings.
The transition climate risk measure based on the
risk factors section of SEC filings.
The number of news articles related to the firm’s
transition climate risk exposure divided by the
total number of news articles related to the firm.
The climate change materiality weight × the
climate change risk rating. The materiality
weight measures the importance of climate
change to a firm’s financial performance. The
climate change risk rating is calculated as (10 climate change theme score). Climate change
theme score is a continuous variable ranging
from 0 to 10, with higher value indicating better
performance (i.e., lower risk).
The environmental component of ESG rating
provided by RepRisk.
The environmental component of ESG score
provided by Refinitiv.

Thomson-Reuters Institutional
Holdings (13F)
Thomson-Reuters Institutional
Holdings (13F)
Compustat

ROA

Transition Risk MDA

Transition Risk RF
Transition Risk News

MSCI Climate Change
Index (CCI)

RepRisk Environmental
Score
Refinitiv Environmental
Score

10K/10Q

10K/10Q
RavenPack

MSCI

RepRisk
Refinitiv

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==> RFS11 - Climate Risk Disclosure and Institutional Investors.txt <==
Climate Risk Disclosure and Institutional
Investors
Emirhan Ilhan
National University of Singapore (NUS) Business School, Singapore

Zacharias Sautner
Frankfurt School of Finance & Management, Germany
Laura T. Starks
McCombs School of Business, University of Texas at Austin, USA
Through a survey and analyses of observational data, we provide systematic evidence
that institutional investors value and demand climate risk disclosures. The survey reveals
the investors have a strong demand for climate risk disclosures, and many actively
engage their portfolio firms for improvements. Empirical analyses of holdings data
corroborate this evidence by showing a significantly positive association between climateconscious institutional ownership and better firm-level climate risk disclosure. We establish
further evidence of institutional investors’ influence on firms’ climate risk disclosures by
examining a shock to the climate risk disclosure demand of French institutional investors
(French Article 173). (JEL G11, G3, Q54)
Received June 30, 2020; editorial decision November 24, 2022 by Editor Itay Goldstein.
Authors have furnished an Internet Appendix, which is available on the Oxford University
Press Web site next to the link to the final published paper online.

We thank Itay Goldstein (the Editor) and two anonymous referees for their very constructive comments. We thank
Edward Baker, Alexander Dyck, Miguel Ferreira, Henri Servaes, Harrison Hong, Andrew Karolyi, Michelle
Lowry, Pedro Matos, Jerry Parwada, and Jose Scheinkman and seminar participants at the PRI Academic
Conference 2019 in Paris, the Shenzhen Sustainable Finance Forum 2019, the European Commission Summer
School on Sustainable Finance in Ispra 2019, Stockholm School of Economics, Sveriges Riksbank, University
of Mannheim, University of St. Gallen, University of Groningen, Canadian Sustainable Finance Network,
the Sustainable Finance Conference 2021 at the University of Luxembourg, University of Duisburg-Essen,
University of Technology Sydney, Corporate Finance Webinar Seminar Series, ERIC 2021 Conference, the 2021
EFA Meetings, the 2022 University of Delaware Weinberg Center/ECGI Corporate Governance Symposium,
Cornell University, the AFA 2022 Meetings, the CEPR Paris Symposium 2022, and the Bank of England. Valentin
Jouvenot provided excellent research assistance. Krueger is Managing Partner of Greenium SARL, a firm that
provides consulting services in sustainable investment. He is also a member of the Board of Experts of Inrate
AG, a provider of sustainability ratings and a member of a Sustainable Investment Methodology Board at UBS
Switzerland AG. Sautner is a member of the Sustainability Council of Lampe Asset Management and a Regular
Research Visitor at the ECB. Starks was previously a board director for mutual funds and serves on unpaid
academic advisory committees for PRI and FTSE-Russell. Supplementary data can be found on The Review of
Financial Studies web site. Send correspondence to Zacharias Sautner, z.sautner@fs.de.
The Review of Financial Studies 36 (2023) 2617–2650
© The Author(s) 2023. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
https://doi.org/10.1093/rfs/hhad002
Advance Access publication January 9, 2023

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Philipp Krueger
University of Geneva and the Swiss Finance Institute, Switzerland

The Review of Financial Studies / v 36 n 7 2023

1 See Carney (2015), Davidson (2021), or European Central Bank and European Systemic Risk Board (2021).
2 Moreover, Bond and Goldstein (2015) show that if firm managers rely on market prices to learn, divulging too

much information can incur a cost that can affect the prices The authors’ setting is with governments as the
decision maker, but the authors point out that their results would also apply to firms. In a climate context, however,
given the uncertainties surrounding the effects of climate change and the governmental responses, managers may
rely more than in other circumstances on learning from prices.

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Financial market efficiency relies on timely and accurate information
regarding firms’ risk exposures, including an increasingly important and
pertinent risk, climate risk. High-quality information on firms’ climate
risk exposures is critical for informed investment decisions as well as the
appropriate pricing of these risks and their related opportunities (Litterman
2016; Krueger, Sautner, and Starks 2020). Moreover, with climate change
increasingly considered to be a danger to the financial system, sound disclosure
on climate risks can be essential for regulatory efforts to protect financial
stability, as pointed out by regulators in the United Kingdom, United States,
and European Union.1
However, many believe that investors lack sufficient information on
corporate climate risks. Because of the perceived shortcomings, initiatives have
been developed to encourage improved reporting on these risks. Examples
of such initiatives include the Task Force on Climate-related Financial
Disclosures (TCFD), the International Sustainability Standards Board (ISSB),
or letters by specific investor to CEOs (e.g., Blackrock 2021). In addition,
governments are increasingly mandating disclosures, particularly aligned with
the TCFD recommendations. Examples include the European Union, Japan,
New Zealand, Switzerland, and the United Kingdom. Countries that have
not yet moved on the regulatory front are evaluating the introduction of
mandatory climate risk disclosure (e.g., the United States; see SEC 2022).
Jointly, these initiatives reflect a belief that the provision of climate risk
information by publicly listed firms is valuable and necessary for investment
decision-making.
The fact that many firms do not provide the disclosures voluntarily suggests there exist counterbalancing considerations. As pointed out
in reviews by Goldstein and Yang (2017) for financial information, and
Christensen, Hail, and Leuz (2021) for nonfinancial information, although
disclosure may have benefits, for example, by increasing stock liquidity,
reducing a firm’s cost of capital, or making the pricing of risks more efficient,
disclosure may also impose unwarranted costs on a firm. For example, in
the climate context, disclosure on climate risks could reveal proprietary
information about a firm’s future strategy. Moreover, Goldstein et al. (2022)
show that mandated disclosure of nonpecuniary information may affect the
pricing of financial information.2
In this paper, we develop and test hypotheses regarding the preferences
of institutional investors with respect to climate risk disclosures. Preferences

Climate Risk Disclosure and Institutional Investors

3 The CDP is an international nonprofit organization that surveys firms (and other organizations, such as cities) to

obtain information on their environmental impacts

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for climate risk disclosures differ from preferences for traditional corporate
disclosure because of the multidimensionality of this type of disclosure,
combined with the properties of climate risk: Climate risk disclosure is difficult
to compare and standardize, it targets a wider audience, and it is argued to
have important externality benefits beyond a firm (Christensen, Hail, and Leuz
2021). Institutional investors have the potential to play a pivotal role for climate
risk disclosure given that their pressure is considered to be the most powerful
financial mechanism to reduce firms’ climate risk exposures according to a
survey by Stroebel and Wurgler (2021). This pressure is likely to also extend
to climate risk disclosure.
We provide evidence that institutional investors value and demand climate
risk disclosure. To establish these results, we employ firm-level climate risk
disclosure data from the CDP (formerly the Climate Disclosure Project) and
examine the relation between disclosure measures and holdings of institutional
investors.3 A shock to the institutions’ climate-related regulatory environments
allows us to identify disclosure-related influence effects of the institutional
investors. We preview our tests with insights from a survey of institutional
investors regarding their opinions about climate risk disclosure. The survey
also serves the purpose of validating key hypotheses tested in the data and of
adding insights difficult to research through archival methods.
The global respondent group of the survey consists of important decision
makers at some of the world’s largest investors: about one-third of the 439
respondents work at the executive level and 11% work for institutions with
more than $100 billion in assets under management. The respondents share a
strong belief that climate risk disclosure is important: 79% believe climate risk
reporting to be at least as important as financial reporting, with almost onethird considering it to be more important. At the same time, the respondents
state that the current disclosures are uninformative and imprecise. Investors that
incorporate climate risks into investment decisions because of legal obligations
or fiduciary duties, investors from countries with high environmental norms,
and very large (and arguably universal) investors attach a greater importance
to climate risk disclosure.
Constituting the core of our paper, we use equity holdings and climate risk
disclosure data to test hypotheses linking institutional ownership to climate
risk reporting in an international sample. Rather than considering broadly
defined institutional ownership, we focus on three specific types of institutional
owners who would be likely to have a stronger demand for meaningful climate
risk disclosure. We term these three groups “climate-conscious investors” and
predict effects for their holdings.
We define our first group of climate-conscious institutional investors as those
from countries where institutional investors are expected to follow stewardship

The Review of Financial Studies / v 36 n 7 2023

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codes designed to promote corporate sustainability. To follow these codes,
these institutions need more information from their portfolio firms and they
should in turn have a higher propensity to demand climate risk disclosure.
The second ownership group definition considers that the demand for climate
reporting depends, at least in part, on whether the investors are located
in countries where norms to be more climate-conscious exist (Dyck et al.
2019). Finally, the third group consists of universal owners, who by virtue of
their broad ownership across many firms face externalities in their holdings.
These investors would be expected to demand more climate risk disclosure
as they need the information to understand their externality exposures and to
potentially pressure firms to reduce carbon emissions, which would reduce
the externalities the investors face. We expect that higher ownership by the
three climate-conscious groups of investors should be associated with a greater
tendency for their portfolio firms to voluntarily disclose climate risks either
because of influence or because of selection effects.
We use three measures derived from CDP data to capture firms’ climate
risk disclosure choices. First, we identify whether firms disclose their Scope
1 carbon emissions to CDP. Scope 1 emissions derive from sources directly
owned or controlled by firms, and thus, serve as a proxy for regulatory
climate risks (Ilhan, Sautner, and Vilkov 2021; Bolton and Kacperczyk 2021a;
Seltzer, Starks, and Zhu 2022). Second, we use a measure of disclosure on
broadly defined climate risks developed by Flammer, Toffel, and Viswanathan
(2021) (FTV henceforth). This measure is based on whether firms identify
and disclose information on three climate-related risks to CDP: regulatory,
physical, and other risks. Finally, to capture the overall quality of a firm’s CDP
climate risk disclosures, we compute a score that measures the completeness
of a firm’s CDP survey responses.
Our analyses show that all of these CDP-based measures of climate risk
disclosure are positively and significantly associated with each of the climateconscious ownership groups. For example, a one-standard-deviation increase
in universal ownership implies an increase in the Scope 1 disclosure rate
by 6 percentage points (pp), or 23% of the variable’s mean. Similarly, a
one-standard-deviation increase in ownership from investors located in a highnorms country comes with an increase in the FTV disclosure measure of 0.07 or
14% of the variable’s mean. All estimations account for investor preferences for
overall voluntary disclosure by controlling for whether firms provide earnings
forecasts (e.g., Li and Yang 2016 or Tsang, Xie, and Xin 2019).
We complement these findings by providing suggestive evidence that
climate risk reporting depends on the costs and benefits of producing such
disclosures. While the disclosure costs should be considered by firms and
their investors, that is, in the supply and demand of the information, some
disclosure benefits are not fully internalized by firms and accrue only for
(some) investors. In particular, the relationship between climate-conscious
ownership and disclosure appears moderated for firms with high proprietary

Climate Risk Disclosure and Institutional Investors

4 See Leuz and Wysocki (2016), Goldstein and Yang (2017), and Christensen, Hail, and Leuz (2021) for reviews

of the disclosure literature.

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disclosure costs, but magnified for firms where the externality benefits of the
disclosure should be higher because they operate in high-emission industries.
We consider these tests to be informative, but not definitive since they are based
on rough proxies.
The estimated relationships we document between disclosure and climateconscious ownership could exist for two primary reasons. Climate-conscious
institutions may actively engage firms to demand that they voluntarily produce
such information (influence effect), or climate-conscious institutions could
have a propensity to invest in firms that already provide such disclosures
(selection effect). To show that institutional investors can actively influence
climate risk disclosure, we exploit a regulation adopted in France in 2015.
Article 173 of the Energy Transition for Green Growth Act requires French
institutional investors to disclose the climate risks of their portfolio assets.
As a result of the rule, firms owned by many French institutions experienced
a plausibly exogenous shock to the demand for climate risk disclosure.
Indeed, we demonstrate for firms owned by many French institutions that their
disclosures improve in response to Article 173. The Scope 1 disclosure rate,
for example, increases by 2 pp more at firms with high French institutional
ownership (above the median) when Article 173 takes effect compared to firms
with low French ownership, a large effect compared to the variable’s mean of
28% in the estimation period.
Additional tests support this influence channel interpretation, whereby
French institutions engage firms to improve their reporting after Article 173 (or
firms preempt this by disclosing more), rather than an interpretation whereby
French institutions increase holdings in firms with better disclosures. For
example, results are robust to using pre-reform French institutional ownership
in the estimation, instead of the more endogenous contemporaneous ownership.
We also try to isolate the influence channel by conditioning the estimation
on firm-level changes in French ownership around Article 173 and on preArticle 173 climate risk disclosure levels. Furthermore, we find no evidence
that French institutional ownership increases relatively more after Article
173 among firms with better pre-reform climate risk disclosure. Although
these tests provide support for the influence channel we propose, we do not
completely rule out the presence of some selection effects also existing around
the introduction of Article 173.
Our paper contributes novel findings to the literature on voluntary disclosure
(Bond and Goldstein 2015; Jayaraman and Wu 2019, 2020) and, specifically,
to the literature on nonfinancial reporting, of which climate risk disclosures
are arguably an important component.4 Most closely related to our paper is
the work by FTV who find that activism by long-term institutional investors
increases their portfolio firms’ climate risk disclosures to CDP. While our work

The Review of Financial Studies / v 36 n 7 2023

1. Conceptual Framework
Climate risk disclosure differs from financial disclosure as it often targets
a wider audience, is multidimensional, is difficult to measure in monetary
terms, is difficult to compare and standardize, and has externality benefits
beyond a firm (Christensen, Hail, and Leuz 2021). These aspects affect the
demand for climate risk information more for certain types of institutional
investors. Thus, we define three ownership groups of climate-conscious
investors, who plausibly exhibit a stronger demand for climate risk reporting
(Dasgupta, Fos, and Sautner [2021] highlight the importance of addressing
such heterogeneity).
The first group captures institutional ownership from countries with
stewardship codes that develop principles for institutional investors with regard

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is complementary to that of FTV, it is also fundamentally different given our
different focus in that we examine investor heterogeneity along the dimension
of investors’ climate-consciousness; we consider the role of influence effects
in a unique setting; we validate our insights with a survey instrument; and we
provide global evidence.
We also contribute to the broader literature on climate risk disclosure. Matsumura, Prakash, and Vera-Muñoz (2014) conclude that markets
discount firms that do not disclose emissions through CDP, although
Griffin, Lont, and Sun (2017) suggest that the differences may not arise
from CDP disclosure. Bolton and Kacperczyk (2021b) find that Scope
1 disclosures lead to lower returns and divestments by institutional
investors (because of exclusionary screening based on disclosed emissions).
Matsumura, Prakash, and Vera-Muñoz (2022) find that 10-K climate disclosure is associated with lower costs of equity, Kölbel et al. (2022) show that 10K climate disclosure affects CDS spreads, and Berkman, Jona, and Soderstrom
(2021) find that a 10-K measure of climate risk negatively correlates with firm
value. Solomon et al. (2011) interview investors revealing that they use private
channels of discourse with firms to compensate for the inadequacies of climate
reporting, and Ramadorai and Zeni (2021) and Bolton and Kacperczyk (2022)
use CDP data to infer emission abatement or net-zero commitments. Focusing
on the oil and gas industry, Eccles and Krzus (2019) examine the extent to
which firms disclose information in line with the TCFD recommendations.
Azar et al. (2021) find that institutional ownership by the Big 3 index investors
(Blackrock, Vanguard, and State Street) is associated with emission reductions,
and Kundu and Ruenzi (2021) show that firms that experience increases in
climate-conscious ownership reduce emissions in the longer run. We also
relate to Mésonnier and Nguyen (2022), who show that Article 173 reduced the
financing of fossil fuel firms by institutions subject to the new law. Our work
contributes unique insights regarding the relationship between institutional
investor ownership and firms’ climate risk disclosure.

Climate Risk Disclosure and Institutional Investors

5 While stewardship codes do not formally require compliance with their principles, institutions that do not comply

with them typically need to explain publicly why they did not follow a specific recommendation of the code.
Compliance is therefore usually high. Shiraishi et al. (2022) demonstrate that stewardship codes enhance the
monitoring activities of institutional investors. Bonacchi et al. (2022) show how compliance with the United
Kingdom’s stewardship code improves the ESG performance of portfolio firms.
6 As defined by Hawley and Williams (2000), a universal owner is a large institutional investor with three

attributes: owning a broad cross-section of the economy, holding shares for the long term, and not trading often,
making them exposed to firms’ externalities.

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to their portfolio firms. Stewardship codes relate to the oversight role of
institutions to create long-term value for their clients or beneficiaries, and
they aim to promote corporate sustainability. Investors subject to stewardship
codes should consequently have a higher propensity to demand climate risk
disclosure from portfolio firms.5
The second group definition reflects disclosure demand due to environmental norms in an institutional investor’s home country. In Williamson’s (2000)
framework for institutional influences on economic activity, the most fundamental are social norms and culture. Similarly, Guiso, Sapienza, and Zingales
(2006) discuss the link between economic and culture outcomes, which they
define as “those customary beliefs and values that ethnic, religious, and social
groups transmit fairly unchanged from generation to generation.” Further,
Dyck et al. (2019) show that investors from countries with high environmental
norms actively improve firms’ ESG policies. Thus, we expect that demand
for climate risk disclosure can originate from whether investors are based in
countries with more climate-conscious norms.
The third ownership group consists of universal owners, building on
the idea that these investors face externality risks and consequently they
demand more information and also could reap benefits from climate risk
disclosure.6 Specifically, climate risk disclosure can enhance the accountability
of firms, which in turn can cause the firms to reduce their emissions and the
corresponding negative externalities on other firms or society more generally
(Dasgupta, Fos, and Sautner 2021). These benefits likely matter most for
universal owners as they are long-term investors owning large parts of the
economy and thus subject to climate externalities. Consequently, firms with
greater ownership by universal owners would be expected to experience
stronger demand for climate risk disclosure.
As pointed out by Goldstein and Yang (2017) for disclosure in general,
and Christensen, Hail, and Leuz (2021) for CSR disclosure, the demand and
supply of climate risk disclosure should depend on the corresponding costs
and benefits. While the disclosure costs should be considered by firms and
their investors, that is, in their supply and demand of the information, since
the disclosure benefits are not fully internalized by firms, they would not be
equally rewarding to all investors. One potential cost arises because the climate
risk disclosure could reveal proprietary information about a firm’s strategy to
its competitors. For example, Google reportedly would not reveal its carbon

The Review of Financial Studies / v 36 n 7 2023

2. Climate Risk Disclosure and Institutional Investors: Survey Evidence
In this section, we provide insights from a survey that previews the main
analysis that uses climate risk disclosure and ownership data. The survey
analysis aims to corroborate our hypotheses and to provide results and insights
unobtainable from the observational data.
2.1 Data and survey design
The survey was developed through an iterative process and distributed through
four channels, yielding a total of 439 responses. Internet Appendix B1 provides
details on the design and delivery. Table 1, panel A, reports summary
statistics of the survey-based variables employed in our tests; Table A1 defines
the variables. Internet Appendix Table 1 documents that about one-third of
respondents hold executive-level positions in their institutions. Eleven percent
are employed by institutions with assets of more than $100 billion. We are
confident that in the vast majority of cases we have only one observation
per institution as for 87% of the observations, key identifying characteristics
do not coincide. Although our respondents are likely biased toward investors

7 Climate risk disclosure may have other more general costs (it may crowd out information acquisition, reduce risk

sharing, or increase return volatility) and benefits (it may improve liquidity, lower the costs of capital, improve
risk sharing, or facilitate monitoring).
8 Verrecchia (1990) shows that product market competition is pivotal for the magnitude of proprietary disclosure

costs, and that competition reduces the propensity to make proprietary disclosures. Internet Appendix A provides
anecdotal evidence on these costs.
9 Further evidence on the beneficial real effects of mandatory ESG disclosures comes from Christensen et al.

(2017), who consider effects of disclosure on mine safety records in financial reports, and from
Bonetti, Leuz, and Michelon (2022), who consider disclosure on hydraulic fracking fluids.

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footprint because of concerns regarding trade secrecy. Similarly, a group of
oil and gas firms maintain that practical or legal reasons could prohibit them
or limit their scope for revealing disaggregated information about climate
risks (WBCSD 2018).7 Griffin and Jaffe (2016) point out that these costs of
disclosure can be significant – that disclosing such confidential information,
which would be available to rivals, “could be particularly burdensome.”8 As
proprietary disclosure costs are likely to be higher for firms operating in
more competitive markets, we expect that the demand for such disclosure by
climate-conscious institutions is smaller when competitive pressures are larger.
A benefit of climate-specific disclosure for some investors is that the disclosure could increase pressure on firms to reduce the reported carbon emissions,
which has been shown to lead to a reduction in the negative externalities
generated on other firms and the environment more generally (Tomar 2022;
Downar et al. 2021; Jouvenot and Krueger 2021).9 This externality benefit
implies that the disclosure demand by climate-conscious institutions should
be larger for firms in high-emission industries.

Climate Risk Disclosure and Institutional Investors

Table 1
Summary statistics
A. Survey variables
Mean

SD

Median

N

Importance of climate risk disclosure
Demand more disclosure
Quant. information imprecise
Management discussions imprecise
TCFD engagement
Carbon footprint disclosure
Climate risk ranking
Climate risk materiality
Fiduciary duty institution
HQ country norms
Very large institution
ESG portfolio share
Medium-term horizon
Long-term horizon

3.12
0.28
0.19
0.21
0.78
0.72
2.95
3.73
0.27
0.61
0.11
0.41
0.77
0.18

0.94

3.00

1.64
0.82

3.00
3.67

0.06

0.57

0.32

0.30

416
413
413
413
304
327
386
393
415
425
430
415
432
432

1.08

0.00

32.82

0.00

0.17
0.11
0.14
0.22
0.24
0.14

0.07
0.05
0.09
0.06
0.09
0.08

B. Climate-related disclosure and investor holdings variables
Scope 1 disclosure
Climate risk disclosure
Regulatory risk disclosure
Physical risk disclosure
Other risk disclosure
Climate disclosure score
10-K Climate risk disclosure

0.26
0.50
0.19
0.18
0.17
16.47
0.70

Stewardship code IO
High-norms IO
Universal owner IO
Nonstewardship code IO
Low-norms IO
Nonuniversal owner IO

0.14
0.09
0.14
0.14
0.18
0.13

High-competition firm
High-emission industry

0.50
0.38

log(Assets)
Dividends/net income
Debt/assets
EBIT/assets
CapEx/assets
Book-to-market ratio
Forecast occurrence

15.03
0.38
0.45
0.07
0.04
0.72
0.72

43,221
25,932
25,932
23,892
23,892
25,934
3,962
43,221
43,221
37,740
43,221
43,221
37,740
4,739
43,221

2.05
0.69
0.20
0.10
0.05
0.57

15.00
0.27
0.45
0.06
0.03
0.58

1.12
0.0114

0.00
0.00

0.0208

0.001

43,221
42,867
36,164
42,317
42,967
43,174
43,221

C. French Article 173 variables
Scope 1 disclosure
Climate risk disclosure
 French IO pre- to post-Article 173
Post-Article 173
French IO
Forecast occurrence

0.28
0.54
−0.0001
0.40
0.007
0.73

21,606
17,284
19,229
21,606
21,606
21,606

This table provides summary statistics of the variables used in the survey (panel A) and in the climate disclosure
and investor holdings (panels B and C) analyses. Observations in panel A are at the respondent level. Observations
in panels B and C are at the firm-year level. The sample period in panel B is 2010 to 2019 and in panel C it is
2013 to 2017. Not all variables are available for all respondents and all firm-years. For dummy variables we
report only mean values and the number of observations. Table A1 defines all variables.

with a high ESG awareness (given the high median ESG share and that such
investors may be more disposed to participate in our survey), responses of such
investors are important, because they are more likely to shape future climate

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Variable

The Review of Financial Studies / v 36 n 7 2023

risk disclosure policies through engagement, industry initiatives, or lobbying.
Moreover, given that 27% of the investors manage more than $50 billion, they
have the clout to be effective in their efforts. Internet Appendix B2 discusses
concerns over nonresponse and acquiescence bias.
2.2 Investor views on climate risk disclosures
In light of the potential benefits and costs of climate risk reporting, the
importance that institutional investors attribute to this reporting is ambiguous.
To evaluate the ambiguity, we asked the survey participants to indicate how
important they consider the reporting on firms’ climate risks relative to the
reporting on financial information. Figure 1 shows that 79% of respondents
believe climate risk disclosure to be at least as important as financial disclosure,
with almost one-third considering it to be more important.
The fact that climate risk disclosures are considered important for the majority of the respondents raises the question of how they perceive the quality of the
current disclosure practices. According to Table 2, panel A, a widespread view
exists that current disclosures are uninformative. Many respondents believe
that management discussions on climate risks (68% agree/strongly agree)
and quantitative information on these risks (67% agree/strongly agree) are
imprecise. These responses suggest that the current largely voluntary reporting
regime does not enable fully informed climate-related investment decisions.
Further, these survey responses indirectly imply that many managers do not
consider the net benefits of climate risk reporting to be sufficiently high, as they
would otherwise reveal such information voluntarily and with better quality.

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Figure 1
Importance of climate risk disclosure
This figure illustrates how important investors consider reporting by portfolio firms on climate risks compared
to reporting on financial information (question B1 from the survey). Of the 439 individuals that participated in
our survey, 416 responded to this question. Internet Appendix B3 provides the actual survey question.

Climate Risk Disclosure and Institutional Investors

Table 2
Survey responses on climate risk disclosure
A. Respondents’ views on current climate risk disclosure practices
Strongly
Neither agree
Strongly
disagree Disagree nor disagree Agree
agree
(%)
(%)
(%)
(%)
(%)
1

9

22

47

21

1

7

24

48

19

2

5

20

46

27

2

7

16

48

27

3

12

24

40

21

3

6

28

46

18

2

6

18

46

28

No
(%)

Yes
(%)

Do not
know (%)

17

59

24

24

60

16

B. Respondents’ views on TCFD and carbon footprint disclosure

Do you engage (or plan to engage) portfolio
companies to report according to the
recommendations of the TCFD?
Do you disclose (or plan to disclose) the overall
carbon footprint of your portfolio?

Panel A displays survey responses to questions on different aspects of climate risk disclosure practices currently
in use (question B3). Respondents were asked to indicate their agreement with different statements. Panel B
reports survey responses to questions regarding whether the investors engage or plan to engage their portfolio
firms to report according to the recommendations of the Task Force on Climate-Related Financial Disclosures
(TCFD) (question E5) and whether the investors disclose or plan to disclose the carbon footprint of their own
portfolios (question B2). The actual survey questions are provided in Internet Appendix B3.

At the same time, many investors value such information, as indicated by their
responses, believing that the benefits outweigh the costs at a typical firm.
The diverging perspectives between firms and their investors raise the
question of whether mandatory and standardized reporting is needed. In
general, the rationale for mandatory disclosure regulation requires the
existence of externalities or market-wide cost savings that regulations can
mitigate (Shleifer 2005). A firm’s contribution to climate change is just such an
externality. Further, standardization would make it less costly for investors to
acquire and interpret information relevant to evaluating a firm’s climate risks.
Mandatory disclosure could also provide commitment and credibility for firms’
climate disclosures, especially if the standards are specific and well enforced
(Christensen, Hail, and Leuz 2021).
Indeed, Table 2, panel A, documents that many investors believe that
standardized and mandatory climate risk reporting is necessary (73%
agree/strongly agree). However, a significant challenge for changing the
current reporting environment seems to be that standardized disclosure tools
and guidelines are not yet widely available (61% agree/strongly agree), and that

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Management discussions on climate risk are not
sufficiently precise.
Firm-level quantitative information on climate risk is
not sufficiently precise.
Standardized and mandatory reporting on climate
risk is necessary.
There should be more standardization across markets
in climate-related financial disclosure.
Standardized disclosure tools and guidelines are
currently not available.
Mandatory disclosure forms are not sufficiently
informative regarding climate risk.
Investors should demand that portfolio firms disclose
their exposure to climate risk.

The Review of Financial Studies / v 36 n 7 2023

2.3 Explaining investor views on climate risk disclosures
As discussed earlier, we expect that views on climate risk disclosure are based
in part on whether investors are subject to stewardship codes, are located in
countries where norms make them more climate-conscious, or are universal
investors. In the survey analysis, we proxy for whether an institution is subject
to stewardship codes (or similar rules) based on a question in which the
respondents were asked whether their institutions have to incorporate climate
risks in the investment process because of legal obligations or fiduciary duties.
Fiduciary duty institution equals one if a respondent strongly agrees with
this statement, and zero otherwise. To quantify country norms, we follow
Dyck et al. (2019) and use Yale University’s Environmental Performance Index
(EPI) to measure environmental awareness. HQ country norms takes larger
values for investors from countries with a stronger common belief in the

10 The SEC proposal follows many of the TCFD recommendations (https://www.sec.gov/rules/proposed/2022/

33-11042.pdf).
11 Climate Action 100+ is an investor-led initiative launched in 2017 to engage the largest carbon emitters.

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those that exist are uninformative (64% agree/strongly agree). These views are
consistent with initiatives that provide explicit disclosure tools and guidelines.
Notably, part of the TCFD recommendations center on how climate risks
are reflected in metrics and targets. These recommendations are currently
voluntary in many jurisdictions, but some countries, such as the United States,
are considering to make them mandatory, and as such, they could eventually
constitute the basis for mandatory disclosures in many countries.10
As a result of current disclosure shortcomings, some investors have
developed engagement-focused initiatives beyond the TCFD to improve access
to climate risk data (e.g., Climate Action 100+).11 Consistent with such
initiatives, Table 2, panel A, shows that many respondents believe that
investors should put pressure on firms to disclose more on climate risks (74%
agree/strongly agree). In addition, in Table 2, panel B, 59% of investors
(plan to) engage firms to report according to the TCFD recommendations.
These responses indicate that many investors have a demand for climate risk
disclosure, as hypothesized in Section 1. In later tests we provide evidence that
this demand leads to more disclosure by firms.
Finally, we surveyed the investors’ opinions regarding the reporting on
climate risks in their own portfolios (as required by the French Article 173).
Our respondents indicate support for this approach with 60% stating that they
(plan to) disclose their portfolio carbon footprints (Table 2, panel B). Guided by
these responses and the resultant need for data, we test below whether Article
173 increased disclosures of firms owned by many French institutions.
Overall, the responses to our survey support key elements of our hypotheses
by indicating a strong demand for climate risk disclosure by institutional
investors, and by suggesting that many investors are willing to actively engage
firms to increase such disclosure.

Climate Risk Disclosure and Institutional Investors

Table 3
Explaining survey responses on climate risk disclosure
Importance of Management Quantitative
Carbon
climate risk discussions information Demand
TCFD
footprint
disclosure
imprecise
imprecise disclosure engagement disclosure
(2)

(3)

(4)

(5)

(6)

0.08
(0.05)
0.24
(0.37)
0.02
(0.04)
0.02∗
(0.01)
0.07∗∗
(0.03)
0.20∗∗∗
(0.07)
0.07
(0.08)
0.11
(0.10)

0.13∗
(0.06)
−0.15
(0.26)
0.11∗
(0.06)
0.01
(0.01)
0.04
(0.03)
0.14∗∗
(0.06)
0.01
(0.08)
0.06
(0.09)

0.16∗∗∗
(0.02)
0.07
(0.24)
−0.02
(0.04)
0.01
(0.01)
0.10∗∗∗
(0.03)
0.04
(0.12)
−0.06
(0.13)
−0.13
(0.12)

0.04
(0.05)
1.08∗∗∗
(0.18)
0.04
(0.10)
0.01
(0.01)
0.02
(0.02)
0.34∗∗
(0.13)
0.07
(0.09)
0.05
(0.07)

0.01
(0.06)
0.22
(0.34)
0.18∗∗∗
(0.06)
0.01
(0.01)
0.05∗∗
(0.02)
0.23∗∗∗
(0.07)
−0.02
(0.10)
−0.09
(0.10)

Respondent position fixed effects
Yes
Distribution channel fixed effects
Yes
Institutional investor type fixed effects Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

N
Adj. R 2

363
.099

363
.085

363
.135

277
.066

306
.025

HQ country norms
Very large institution
Climate risk ranking
Climate risk financial materiality
ESG portfolio share
Medium-term horizon
Long-term horizon

363
.207

This table reports OLS regressions at the respondent level explaining investors’ views on climate risk disclosure
where the dependent variables are as follows: (a) Importance of climate risk disclosure (as compared to reporting
on financial information) ranges between one and five, with one indicating that climate risk reporting is “much
less important” and five indicating that it is “much more important” (question B1); (b) Management discussions
imprecise equals one if a respondent indicates strong agreement that management discussions on climate risk
are not sufficiently precise, and zero otherwise (question B3); (c) Quantitative information imprecise equals one
if a respondent indicates strong agreement to the statement that firm-level quantitative information on climate
risk is not sufficiently precise, and zero otherwise (question B3); (d) Demand more disclosure equals one if a
respondent indicates strong agreement that investors should demand that portfolio firms disclose their exposure
to climate risk, and zero otherwise (question B3); (e) TCFD engagement equals one if a respondent engages
or plans to engage portfolio firms to report according to the recommendations of the TCFD (question E5), and
zero otherwise; and (f) Carbon footprint disclosure equals one if a respondent discloses or plans to disclose the
overall carbon footprint of their portfolio, and zero otherwise (question B2). We use the following independent
variables: Fiduciary duty institution; HQ country norms; Very large institution; Climate risk ranking (larger
numbers reflect that climate risk is ranked as relatively more important compared to other investment risks);
Climate risk financial materiality (larger numbers reflect greater perceived financial materiality); ESG portfolio
share; Medium-term horizon; Long-term horizon. Table A1 defines all variables. Standard errors (in parentheses)
are clustered at the respondent’s country level. *p < .1; **p < .05; ***p < .01.

importance of environmental issues. Finally, Very large institution equals one
for responses from an institution with more than $100 billion in assets under
management, and zero otherwise. Very large investors tend to be universal
owners whose broad-ranging ownership, as argued in Section 1, makes them
more susceptible to the externalities engendered by climate change. We thus
expect them to be more interested in climate risk disclosures and demand that
firms produce them.
Table 3 reports the analyses of the relations between these three ownership
variables and respondents’ views on climate risk disclosures. In column 1, more
importance is placed on climate risk reporting by all three identified ownership

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(1)
0.19∗
(0.10)
1.23∗∗
(0.52)
0.31∗∗
(0.11)
0.11∗∗∗
(0.02)
0.36∗∗∗
(0.04)
0.30
(0.29)
−0.05
(0.19)
−0.12
(0.26)

Fiduciary duty institution

The Review of Financial Studies / v 36 n 7 2023

3. Climate Risk Disclosure and Institutional Investors: Archival Evidence
In this section, we employ observational data to explore the relationship
between firms’ climate risk disclosures and institutional ownership. We
provide evidence from panel regressions and a regulatory disclosure reform
in France.
3.1 Data
3.1.1 Carbon-related disclosure data from CDP. Our disclosure data
derive from CDP, which conducts an annual survey of firms on behalf
of institutional investors and other stakeholders. CDP requests that firms
voluntarily produce the climate-related data. CDP does not reveal which firms
they contact, thus making it difficult to identify whether a missing observation
is due to a firm’s refusal to participate in the survey, or because a firm was not
requested to participate. To remedy this issue, we follow an approach inspired
by Krueger (2015), which builds on the idea that CDP typically requests
information from the largest listed firms in a country. Therefore, we create a
sample of firms that CDP likely contacted based on their size relative to other
firms in their countries. Internet Appendix Figure 1 in Internet Appendix D
shows the sample country distribution of our “universe” of firms.
We use three complementary measures of climate risk disclosure from the
CDP data over the 2010 to 2019 period: a measure of whether a firm discloses
its carbon emissions; a measure of the types of climate risks the firm discloses;
and a CDP-assigned score regarding the completeness of the firm’s disclosures.
Not all of these measures are available for every sample year because CDP
added or deleted some questions over time. CDP also modified the response

12 The estimates control for several variables. Climate risk ranking captures how the respondents rank climate

risks relative to traditional investment risks; Climate risk financial materiality reflects how financially material
the investor considers climate risks to be; and ESG portfolio share is the fraction of assets subject to ESG
principles. We control for investor horizon as longer-term investors may particularly value climate risk disclosure
(Starks, Venkat, and Zhu 2022; FTV), and for fixed effects for the respondents’ positions (e.g., CEO), the survey
distribution channels, and investor types.

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groups: the investors that incorporate climate risks in the investment process for
legal/fiduciary reasons, by investors from countries with higher environmental
norms, and by very large (potentially universal) investors. In the remaining
columns, the fiduciary duty investors also believe that current quantitative
information on climate risks is imprecise and that investors should demand
better disclosure. Further, investors from high-norms countries are more likely
to engage firms to demand reporting according to the TCFD recommendations,
and very large institutions are more likely to disclose their carbon footprints.
Overall, these estimates validate some key assumptions in the development of
our hypotheses.12

Climate Risk Disclosure and Institutional Investors

13 Between 2010 and 2015, CDP assigned a disclosure score (which we use in our analysis) and a letter rating that

measured the performance of a firm. From 2015, there is only one letter rating for each disclosure submission,
and the CDP describes its new methodology to “result in a score, which assesses the level of detail and
comprehensiveness of the content, as well as the company’s awareness of climate change issues, management
methods and progress toward action taken on climate change as reported in the response.”

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categories for some questions, making a reliable comparison across years
difficult. We indicate for which years the respective variables are available.
The first variable, Scope 1 disclosure, equals one if a firm discloses Scope 1
carbon emissions to CDP in a year, and zero otherwise. Scope 1 emissions are
direct emissions from owned or controlled sources of the disclosing firm, and
the variable is available for all sample years. Scope 1 emissions are disclosed
in 26% of sample firm-years (Table 1, panel B).
Next, to capture disclosure on climate risks more broadly, we adopt a
variable used by FTV which leverages the fact that CDP asks firms to disclose
information on regulatory, physical, and other climate risks. Climate risk
disclosure can take four values: zero if no information on the risks is disclosed;
one if information on one risk type is disclosed; two if information on two risk
types is disclosed; and three if information on all three risk types is disclosed.
We construct the measure from 2010 to 2016 (from 2017 onward, the structure
of the question changed). Climate risk disclosure has a mean of 0.5, and the
correlation with Scope 1 disclosure is 78% (Internet Appendix Table 2, panel
A). We provide complementary tests for Regulatory, Physical, and Other risk
disclosure (each variable equals one if information on the respective risk is
disclosed, and zero otherwise); these three risks are disclosed in 17% to 19%
of the firm-years.
Finally, to capture the overall quality of climate risk disclosures, we use
a score computed by CDP to measure the completeness of a firm’s survey
responses. CDP allocates points to each survey question depending on the
amount of data requested, and the Climate disclosure score reflects the fraction
of the answered questions (the score is multiplied by 100 and ranges from 0
to 100). The score is available from 2010 to 2015 as the CDP introduced a
new methodology from 2015 onward.13 The average score across all firm-years
is 16.
Throughout our analysis, we focus on understanding institutional investors’
preferences toward voluntary climate risk disclosure. To disentangle the
preference for such disclosure from a preference for overall voluntary
disclosure, we employ a measure from the accounting literature that proxies
for firms’ voluntary disclosure practices. We follow Li and Yang (2016) and
Tsang, Xie, and Xin (2019) and create Forecast occurrence, which equals one
if a firm issues at least one voluntary earnings forecast in a year, and zero
otherwise. Results are unaffected if we use the logarithm of the number
of voluntary earnings forecasts. Internet Appendix E contains details on the
variable construction.

The Review of Financial Studies / v 36 n 7 2023

3.2 Climate risk disclosure and institutional investors: Evidence from
panel data
3.2.1 Climate risk disclosure and climate-conscious institutions. We
analyze the CDP data by relating climate risk disclosure to climate-conscious
institutional ownership. For firm f in country c and year t, the model is as
follows:
Climate disclosuref,c,t = α +βIOf,c,t +δXf,c,t +Fixed effects+εf,c,t ,

(1)

where Climate disclosuref,c,t represents Scope 1 disclosure, Climate risk
disclosure, or log(1 + Climate disclosure score); IOf,c,t denotes Stewardship
code IO, High-norms IO, or Universal owner IO; and Xf,c,t contains the control
variables. The control variables include the residual ownership measures,
financial characteristics, and the proxy for overall voluntary disclosures. As
climate risks vary across sectors and time, we include industry fixed effects
interacted with year fixed effects. Unless indicated differently, we also include
country fixed effects to account for cross-country differences. Standard errors
are clustered at the country level (unless indicated differently).
Table 4 reports the results in columns 1 to 3 for Scope 1 disclosure, in
columns 4 to 6 for Climate risk disclosure, and in columns 7 to 9 for log(1
+ Climate disclosure score). As explained earlier, the number of observations
differ across regressions as the three variables are available for different years.
We indicate the sample periods in the table.

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3.1.2 Institutional ownership data. Consistent with the conceptual framework in Section 1, we use FactSet data to create three institutional ownership
variables. Stewardship code IO is the fraction of a firm owned by institutional
investors from countries with stewardship codes. To determine whether an
institution’s home country has a stewardship code in place, we use data from
Katelouzou and Siems (2021), who document the staggered introduction of
these codes across countries. High-norms IO captures the fraction of ownership
by institutions from countries with high environmental norms as suggested by
Dyck et al. (2019). We again use the data from EPI and the same procedure as in
Section 2.3. Universal owner IO reflects the fractional ownership by universal
owners. To identify such owners, we use FactSet to rank institutions based on
the number of firms they own in a year, and classify investors as universal
owners if they rank in the top 1%. Beyond the three largest index fund providers
(Blackrock, Vanguard, and State Street), the universal owners include a number
of institutions that are not primarily passive investors.
Table 1, panel B, shows that the three ownership variables vary between 9%
and 14%, with considerable cross-sectional heterogeneity. Internet Appendix
Table 2, panel B, demonstrates that the measures, as would be expected,
correlate positively, but the fact that correlations are between 34% and 58%
reflects that they capture different aspects. We create and control for three
measures of the residual ownership by “non-climate-conscious” institutions.

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35,350
.291

Yes
Yes

0.13∗∗∗
(0.01)
0.02∗∗∗
(0.00)
−0.03
(0.03)
0.01
(0.05)
0.05
(0.14)
−0.08∗∗∗
(0.01)
0.06∗∗∗
(0.02)

35,350
.291

Yes
Yes

All firms
2010–2019

0.13∗∗∗
(0.01)
0.02∗∗∗
(0.00)
−0.03
(0.03)
0.01
(0.05)
0.05
(0.14)
−0.08∗∗∗
(0.01)
0.06∗∗∗
(0.02)

0.01
(0.11)

0.30∗∗
(0.13)

31,059
.290

Yes
Yes

−0.15
(0.10)
0.13∗∗∗
(0.01)
0.02∗∗∗
(0.00)
−0.03
(0.03)
0.02
(0.05)
0.05
(0.14)
−0.08∗∗∗
(0.01)
0.06∗∗∗
(0.02)

0.41∗∗∗
(0.08)

(3)

21,312
.252

Yes
Yes

0.30∗∗∗
(0.03)
0.05∗∗∗
(0.01)
−0.23∗∗∗
(0.07)
−0.12
(0.12)
0.14
(0.33)
−0.19∗∗∗
(0.03)
0.12∗
(0.06)

−0.21
(0.30)

0.64∗∗
(0.28)

(4)

21,312
.251

Yes
Yes

All firms
2011–2016

0.30∗∗∗
(0.03)
0.05∗∗∗
(0.01)
−0.22∗∗∗
(0.07)
−0.12
(0.12)
0.15
(0.33)
−0.19∗∗∗
(0.03)
0.12∗
(0.06)

−0.10
(0.35)

0.63∗∗
(0.29)

(5)

Climate risk disclosure

20,716
.249

Yes
Yes

−0.27
(0.31)
0.29∗∗∗
(0.03)
0.06∗∗∗
(0.01)
−0.20∗∗∗
(0.07)
−0.08
(0.12)
0.24
(0.33)
−0.18∗∗∗
(0.04)
0.13∗
(0.07)

0.67∗∗∗
(0.20)

(6)

21,168
.304

Yes
Yes

0.57∗∗∗
(0.04)
0.08∗∗∗
(0.02)
−0.47∗∗∗
(0.10)
0.02
(0.19)
−0.24
(0.48)
−0.39∗∗∗
(0.05)
0.12∗∗
(0.06)

−0.38
(0.44)

1.17∗∗
(0.51)

21,168
.303

Yes
Yes

All firms
2010–2015

0.57∗∗∗
(0.04)
0.08∗∗∗
(0.02)
−0.46∗∗∗
(0.10)
0.02
(0.19)
−0.20
(0.48)
−0.39∗∗∗
(0.05)
0.13∗∗
(0.06)

−0.18
(0.51)

1.00∗∗
(0.45)

(8)

20,584
.301

Yes
Yes

−0.62
(0.50)
0.56∗∗∗
(0.04)
0.09∗∗∗
(0.02)
−0.42∗∗∗
(0.10)
0.09
(0.19)
−0.12
(0.47)
−0.38∗∗∗
(0.06)
0.14∗∗
(0.06)

1.28∗∗∗
(0.26)

(9)

log(1+ Climate disclosure score)
(7)

This table reports regressions at the firm-year level explaining firms’ climate risk disclosures. The dependent variables are as follows: Scope 1 disclosure equals one if a firm discloses Scope
1 carbon emissions to CDP in a year, and zero otherwise. Climate risk disclosure captures disclosure to CDP on up to three types of climate risks (regulatory, physical, or other climate risks)
in a year. It takes the value of zero if a firm does not disclose climate risks to CDP in the year, one if it discloses information on one type of climate risk, two if it discloses information on two
types of climate risk, and three if it discloses information on all three types of climate risk. Climate disclosure score measures how comprehensive a firm’s climate risk disclosure is to CDP
by counting the fraction of questions that were answered in the CDP survey in a year. The measure varies between 0 and 100, and higher numbers indicate better climate disclosure. We use
the following key independent variables: (a) Stewardship code IO is the fraction of outstanding shares owned by institutional investors subject to stewardship codes in their home countries
in a year; (b) High-norms IO is the fraction of outstanding shares owned by institutional investors from high social norms countries in a year; and (c) Universal owner IO is the fraction of
outstanding shares owned by institutional investors classified as universal owners in a year. Table A1 defines all variables. Standard errors (in parentheses) are clustered at the country level.
*p < .1; **p < .05; ***p < .01.

N
Adj. R 2

Industry × year fixed effects
Country fixed effects

Sample
Years

Forecast occurrence

Book-to-market ratio

CapEx/assets

EBIT/assets

Debt/assets

Dividends/net income

log(Assets)

Nonuniversal owner IO

0.04
(0.08)

0.17∗∗
(0.08)

(2)

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Low-norms IO

Nonstewardship code IO

Universal owner IO

High-norms IO

Stewardship code IO

(1)

Table 4
Climate risk disclosure and institutional investors
Scope 1 disclosure
Climate Risk Disclosure and Institutional Investors

The Review of Financial Studies / v 36 n 7 2023

14 Internet Appendix Table 3 shows that it is important to control for voluntary disclosure, with High-norm IO being

positively and significantly related to Forecast occurrence. (These results are unaffected if we use the logarithm of
the number of voluntary earnings forecasts). Hence, some evidence indicates that climate-conscious institutions
have a preference for voluntary disclosure more generally.
15 In Internet Appendix Table 6, climate-conscious ownership positively and significantly relates to CDP-based

disclosures among US firms.

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In columns 1 to 3, we find strong and consistent evidence that climateconscious ownership positively relates to the decision to disclose Scope 1
emissions. In column 1, a one-standard-deviation increase in Stewardship code
IO is associated with a 3-pp increase in the propensity to disclose emissions,
or 12% of the variable’s mean. Effects are strongest in column 3, with a
one-standard-deviation shock to Universal owner IO increasing the Scope
1 disclosure rate by 6 pp, or 23% of the variable’s mean. We again find
strong and significant effects in columns 4 to 6 where we use Climate risk
disclosure as the dependent variable. For example, in column 5, a one-standarddeviation increase in ownership from high-norms country investors comes
with an increase in the disclosure measure by FTV of 0.07 or 14% of the
variable’s mean. Finally, in columns 7 to 9, for our third measure, the climate
risk disclosure score, we continue to find positive and significant effects for all
three climate-conscious ownership variables when we explain the climate risk
disclosure score.
The table also reports interesting results for the firm characteristics. Across
all specifications, large firms, firms with higher dividend payouts, growth firms
disclose more and firms that voluntarily provide earnings forecasts disclose
more regarding their climate risks.14
We provide additional tests in the Internet Appendix. In Internet Appendix
Table 4, we examine the disclosure of the three components of climate
risk separately. Climate-conscious ownership positively relates to regulatory,
physical, and other climate risk disclosures.
In Internet Appendix Table 5, for comparison purposes, we provide complementary tests using a text-based measures of climate risk disclosure in the
10-Ks of U.S. sample firms defined by Matsumura, Prakash, and Vera-Muñoz
(2022). In these tests the dependent variable equals one if at least one of
eight climate-related keywords occurs in a 10-K, and zero otherwise (Internet
Appendix F contains details). We find no relationship between this variable and
climate-conscious ownership. The lack of an effect may be explained by the
less-structured and less-standardized climate disclosures currently available
in 10-Ks. (The 10-K-based measure correlates only weakly with the CDP
measures, see Internet Appendix Table 2, panel A.) Investors may in turn
prefer the structured and standardized CDP disclosures.15 This interpretation
is consistent with our survey results in which the investors emphasized a lack
of standardization and uninformative disclosures as problems of mandatory
disclosure, such as 10-Ks.

Climate Risk Disclosure and Institutional Investors

3.2.2 Climate risk disclosure: Role of disclosure costs and benefits.
We next consider that the demand for climate risk disclosure by climateconscious institutions should depend on the costs and benefits of making these disclosures. For this purpose, we amend Equation (1) and
allow the effects of IOf,c,t , to vary across firms depending on costs or
benefits:
Climate disclosuref,c,t = α +β1 IOf,c,t ×Zf,c,t +β2 IOf,c,t +β3 Zf,c,t +δXf,c,t
(2)

where Climate disclosuref,c,t , and IOf,c,t are defined as above, and Zf,c,t is
a proxy for a cost or benefit of climate risk disclosure. To test for the role of
proprietary disclosure costs, we use the Hoberg and Phillips (2016) text-based
HHI measure for whether a firm operates in a competitive environment. Highcompetition firmf,c,t , is one if a firm operates in a competitive environment
where the HHI is below the median in a year (this measure is only available
for U.S. firms). Since proprietary disclosure costs are expected to be higher for
firms in more competitive markets, the demand for climate risk disclosure by
climate-conscious institutions should be smaller among such firms; this implies
a negative estimate for β1 .
Further, the demand for climate risk disclosure by climate-conscious
investors should be greater for firms in high-emitting industries, mainly
because of the potential disclosure externality benefits in such sectors. We test
this effect by interacting IOf,c,t with High-emission industryf , which equals
one if a firm operates in 1 of the 20 SIC2 industries with the highest Scope 1
emissions. In these regressions, we expect that β1 is positive.
Table 5 reports the results. In panel A, proprietary costs affect the disclosure
demand as the β1 coefficients are negative across all disclosure variables
and for all climate-conscious ownership variables. Panel B also suggests a
stronger disclosure demand for firms in high-emitting industries, with six
of the nine specifications providing positive and significant β1 estimates.
Surprisingly, the disclosure demand by Universal owner IO for firms in highemitting industries is only significant for Climate risk disclosure. Overall,
Table 5 provides descriptive evidence that the climate risk disclosure demand
by climate-conscious institutions depends on the costs and benefits of the
reporting.
3.3 Climate risk disclosure and institutional investors: Evidence from
French Article 173
3.3.1 Institutional setting and estimation. The positive relationship
between climate-conscious ownership and climate risk disclosure in
Section 3.2.1 could exist for two reasons. One explanation is that climateconscious institutions actively engage firms and demand that they voluntarily
produce climate risk information as suggested by our survey results. Such an

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+Fixed effects+εf,c,t ,

Yes
Yes
3,967
.235

N
Adj. R 2

(0.14)

0.53∗∗∗

3,967
.240

Yes
Yes

U.S. firms
2010–2019

1.71∗∗∗
(0.30)

−1.09∗∗∗
(0.39)

0.17∗∗
(0.09)

0.16∗
(0.09)
−0.29∗∗
(0.11)

Controls
Year fixed effects

Sample
Years

Universal owner IO

High-norms IO

Stewardship code IO

High competition firm × Universal owner IO

High-competition firm × High-norms IO

High-competition firm × Stewardship code IO

High-competition firm

(2)

Scope 1 disclosure
(1)

3,575
.254

Yes
Yes

0.76∗∗∗
(0.12)

−0.48∗∗∗
(0.16)

0.17∗
(0.09)

(3)

2,387
.193

Yes
Yes

(1.05)

5.98∗∗∗

2,387
.184

Yes
Yes

U.S. firms
2011–2016

4.67∗∗∗
(1.12)

−3.44∗∗
(1.46)

0.65∗∗
(0.33)

(5)

(6)

2,387
.179

Yes
Yes

0.85∗
(0.46)

−1.02∗
(0.57)

0.62∗
(0.34)

Climate risk disclosure
0.71∗∗
(0.32)
−5.47∗∗∗
(1.27)

(4)

2,372
.279

Yes
Yes

(1.84)

8.48∗∗∗

0.37
(0.48)
−5.59∗∗
(2.30)

2,372
.274

Yes
Yes

U.S. firms
2010–2015

7.12∗∗∗
(1.81)

−6.09∗∗
(2.43)

0.33
(0.48)

(8)

(Continued)

2,372
.280

Yes
Yes

2.80∗∗∗
(0.65)

−1.67∗
(0.86)

0.28
(0.50)

(9)

log(1 + Climate disclosure score)
(7)

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A. Proprietary disclosure costs

Table 5
Climate risk disclosure and institutional investors: Costs and benefits of disclosure

The Review of Financial Studies / v 36 n 7 2023

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35,350
.292

Yes
Yes
Yes

0.11
(0.07)

35,350
.293

Yes
Yes
Yes

All firms
2010–2019

(0.11)

0.22∗

0.21∗∗∗
(0.06)

(2)

Scope 1 disclosure

31,059
.291

Yes
Yes
Yes

(0.08)

0.35∗∗∗

0.12
(0.11)

(3)

21,312
.254

Yes
Yes
Yes

(0.22)

0.46∗∗

0.39∗
(0.19)

(4)

21,312
.253

Yes
Yes
Yes

All firms
2011–2016

(0.20)

0.41∗∗

0.53
(0.33)

(5)

(6)

20,716
.251

Yes
Yes
Yes

(0.17)

0.40∗∗

0.60∗∗∗
(0.21)

Climate risk disclosure

21,168
.306

Yes
Yes
Yes

0.81
(0.49)

0.83∗∗∗
(0.21)

21,168
.304

Yes
Yes
Yes

All firms
2010–2015

0.60
(0.39)

1.03∗∗∗
(0.29)

(8)

20,584
.303

Yes
Yes
Yes

1.02∗∗∗
(0.32)

0.47
(0.41)

(9)

log(1+ Climate disclosure score)
(7)

This table reports regressions at the firm-year level explaining how firms’ climate risk disclosures vary with proxies of the costs and benefits of climate-related disclosure. The dependent
variables are as follows: Scope 1 disclosure equals one if a firm discloses Scope 1 carbon emissions to CDP in a year, and zero otherwise. Climate risk disclosure captures disclosure to
CDP on up to three types of climate risks (regulatory, physical, or other climate risks) in a year. It takes the value of zero if a firm does not disclose climate risks to CDP in a year, one if it
discloses information on one type of climate risks, two if it discloses information on two types of climate risks, and three if it discloses information on all three types of climate risks. Climate
disclosure score measures how comprehensive a firm’s climate risk disclosure is to CDP by counting the fraction of questions that were answered in the CDP survey in a year. The measure
varies between 0 and 100, and higher numbers indicate better climate disclosure. We use the following key independent variables: (a) Stewardship code IO is the fraction of outstanding
shares owned by institutional investors subject to stewardship codes in their home countries in a year; (b) High-norms IO is the fraction of outstanding shares owned by institutional investors
from high social norm countries in a year; and (c) Universal owner IO is the fraction of outstanding shares owned by institutional investors classified as universal owners in a year. In panel A,
High-competition firm equals one if a firm operates in a very competitive industry based on the text-based HHI measure by Hoberg and Phillips (2016), and zero otherwise. A firm operates
in a very competitive industry if its HHI is below the sample median in a year. In panel B, High-emission industry equals one if a firm operates in an SIC2 industry that is in the top-20 across
SIC2 industries based on Scope 1 emissions, and zero otherwise. Panel A contains only U.S. firms as the competition measure is only available for such firms. High-emission industry in
panel B is absorbed by the fixed effects. Table A1 defines all variables. In panel A, standard errors (in parentheses) are clustered at the industry-by-year level. In panel B, standard errors (in
parentheses) are clustered at the country level. *p < .1; **p < .05; ***p < .01.

N
Adj. R 2

Controls
Industry × year fixed effects
Country fixed effects

Sample
Years

Universal owner IO

High-norms IO

Stewardship code IO

0.13∗∗∗
(0.04)

(1)

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High-emission industry × Universal owner IO

High-emission industry × High-norms IO

High-emission industry × Stewardship code IO

B. Disclosure externality benefits

Table 5
(Continued)

Climate Risk Disclosure and Institutional Investors

The Review of Financial Studies / v 36 n 7 2023

Climate disclosuref,c,t = α +β1 Post-Article 173t ×High French IOf,c,t
+β2 High French IOf,c,t +δXf,c,t +Fixed effects+εf,c,t ,
(3)

16 Though, formally, the regulation is on a “comply or explain” basis, compliance among French institutions is high

(86% in the years 2017 and 2018, according to Novethic 2018).
17 Our choice of event window tries to be sufficiently narrow to isolate the effects of Article 173, without being too

wide to be affected by disclosure spillover effects or unrelated market and disclosure developments.

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influence effect may arise, for example, through (behind the scenes) dialogue
between investors and a firm’s management or the submission of shareholder
proposals calling for firms to share more information on their exposure to
climate risks. Engagement by institutional investors to demand disclosure
can originate from several potential sources: the investors’ beliefs that the
disclosure will inform their investment decisions, including the possibility that
disclosure will reduce climate risks in their portfolios; the investors’ needs
to publish climate-related data in their own regulatory filings; or demands
from the investors’ clients or beneficiaries. An alternative but nonmutually
exclusive explanation is related to selection effects, that is, climate-conscious
institutions may invest more in firms that provide better disclosures because
they believe such firms are less risky or because their clients and beneficiaries
impose such a constraint.
To test for the presence of influence effects, we exploit a regulatory shock to
the demand for climate risk information. On August 17, 2015, shortly before
the Paris Agreement, France passed the Energy Transition for Green Growth
Act. As part of this law, Article 173 requires French institutional investors to
disclose their climate risk exposures.16 To comply with Article 173, French
institutional investors would need climate risk information on their portfolio
holdings, increasing their demand for climate risk disclosures. Consequently,
we hypothesize that firms held by many French institutions increased their
climate risk disclosures after Article 173 went into effect in January 2016,
either because French institutions actively engaged these firms or because these
firms wanted to preempt such engagement (the latter effect also would be
consistent with an influence channel). French institutions may engage firms
on their own or as lead investors in investor coalitions, as documented for
PRI, the Principles for Responsible Investment, in Dimson, Karakaş, and Li
(2021). The latter channel leverages the equity stakes of other investors and is,
for example, used by Amundi, France’s largest institutional investor (Amundi
2020).
To test for our prediction of influence effects as a result of Article 173, we
estimate for firm f in country c and year t variants of the following regression
model for the narrow [−2; +2]-year event window around the passage of Article
173 in 2015:17

Climate Risk Disclosure and Institutional Investors

3.3.2 Baseline regression results. Table 6 provides the baseline estimations
of Equation (3). In this and the following tables, we focus primarily on Scope
1 disclosure (columns 1 to 4), as observations on Climate risk disclosure
(column 5) are only available for one year after the passage of Article 173.
In column 1, firms with high French institutional ownership (High French IO)
have a significantly higher propensity of disclosing their Scope 1 emissions
after Article 173 becomes effective, compared to firms with lower French
ownership. The magnitudes are meaningful: after Article 173 takes effect,
Scope 1 disclosure increases by 2 pp more at firms with high French ownership
compared to firms with low French ownership, a large effect compared to the
variable’s mean of 28% during the estimation period.
In column 2, we exclude French firms from the estimation for two
reasons. First, French investors would presumably exercise more pressure on local firms, possibly because of domestic reputational concerns
(Krueger, Sautner, and Starks 2020) or privileged access to the French firms’
executives, perhaps because of shared educational background. Second, Article
173 also mandates that French-listed firms disclose their climate risks, which
implies a potentially confounding shock to the supply of climate risk reporting
for French firms. When adding the sample restriction in column 2, we continue
to find a positive and significant effect of High French IO among the large
set of non-French firms. The magnitude of the effect is unchanged relative
to column 1. In column 3, we replace the industry-by-year fixed effects with
firm fixed effects (and year fixed effects) to identify the changes in Scope
1 disclosure around the passage of Article 173 from within-firm variation
(we use a balanced panel for these within-firm regressions). The estimated
effects of Article 173 are about 50% larger compared to those obtained in
columns 1 and 2. In column 4, we replace High French IO with French
IO, a continuous measure of French institutional ownership, and additionally
require that French ownership is at least 3% to ensure that results are present
among the subsample of firms where very large French institutional ownership

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where Climate disclosuref,c,t is Scope 1 disclosuref,c,t or Climate risk
disclosuref,c,t (our third variable, Climate disclosure scoref,c,t , is unavailable
after Article 173, which is why we do not use it in this setting). Post-Article
173t reflects that the regulation became effective in 2016 and in turn equals one
in the years 2016 and 2017, and zero in the years before. (The noninteracted
effect of Post-Article 173t is absorbed by the fixed effects.) High French IOf,c,t
equals one if French institutional ownership is above the median in a year. The
coefficient of interest is β1, which captures how the disclosure of firms with
high French institutional ownership changes from before to after Article 173,
relative to firms with low French ownership. Our main specifications include
industry fixed effects interacted with year fixed effects as well as country fixed
effects. Some regressions also estimate firm fixed effects. Table 1, panel C,
reports the summary statistics for the key variables used in this analysis.

The Review of Financial Studies / v 36 n 7 2023

Table 6
Climate risk disclosure and institutional investors: Baseline effects of French Article 173
Climate risk
disclosure

Scope 1 disclosure

Post-Article 173 × High French IO

(2)

(3)

0.020∗∗

0.021∗∗

0.032∗∗

(0.009)

(0.010)

(0.014)

0.059∗∗∗
(0.012)

0.059∗∗∗
(0.012)

−0.007
(0.012)

0.13∗∗∗

0.13∗∗∗

(0.01)
0.03∗∗∗
(0.01)
−0.02
(0.03)
−0.03
(0.05)
0.05
(0.17)
−0.08∗∗∗
(0.01)
0.07∗∗∗
(0.02)

(0.01)
0.03∗∗∗
(0.01)
−0.02
(0.03)
−0.01
(0.06)
0.09
(0.17)
−0.07∗∗∗
(0.01)
0.07∗∗∗
(0.02)

Post-Article 173 × French IO
High French IO
French IO
log(Assets)
Dividends/net income
Debt/assets
EBIT/assets
CapEx/assets
Book-to-market ratio
Forecast occurrence

Sample
Years

0.00
(0.02)
0.01
(0.00)
0.08
(0.06)
0.10∗∗
(0.04)
−0.14∗
(0.07)
−0.02
(0.01)
0.02
(0.02)

(4)

1.379∗∗
(0.540)

(5)
0.078∗∗
(0.037)

0.074
(0.052)
0.621
(0.445)
0.18∗∗∗
(0.01)
0.02
(0.03)
−0.06
(0.15)
0.00
(0.23)
−1.22∗∗∗
(0.22)
−0.11∗∗∗
(0.03)
−0.06∗
(0.03)

All
All firms,
All firms
All
non-French balanced with French IO
firms
firms
panel
>3%
2013–2017 2013–2017 2013–2017
2013–2017

0.30∗∗∗
(0.03)
0.06∗∗∗
(0.01)
−0.20∗∗
(0.08)
−0.12
(0.14)
0.06
(0.34)
−0.18∗∗∗
(0.03)
0.15∗∗
(0.06)

All
firms
2013–2016

Industry × year fixed effects
Country fixed effects
Year fixed effects
Firm fixed effects

Yes
Yes
No
No

Yes
Yes
No
No

No
No
Yes
Yes

Yes
Yes
No
No

Yes
Yes
No
No

N
Adj. R 2

17,878
.302

16,835
.295

13,126
.784

1,113
.485

14,294
.257

This table reports regressions at the firm-year level explaining how firms’ climate risk disclosures change around
the passage of Article 173 in France in 2015. The dependent variables are as follows: Scope 1 disclosure equals
one if a firm discloses Scope 1 carbon emissions to CDP in a year, and zero otherwise. Climate risk disclosure
captures disclosure to CDP on up to three types of climate risks (regulatory, physical, or other climate risks) in
a year. It takes the value of zero if a firm does not disclose climate risks to CDP in a year, one if it discloses
information on one type of climate risks, two if it discloses information on two types of climate risks, and three
if it discloses information on all three types of climate risks. We use the following key independent variables:
Post-Article 173 equals one for the years of 2016 and afterward, and zero otherwise; High French IO equals one
if the fraction of outstanding shares owned by French institutional investors is above the median of a given year,
and zero otherwise; and French IO is a continuous measure of institutional ownership by French institutions.
Table A1 defines all variables. Standard errors (in parentheses) are clustered at the country level. *p < .1; **p <
.05; ***p < .01.

most plausibly predicts improved disclosures. We continue to find a positive
and significant effect of French institutional ownership. Finally, in column 5,
Climate risk disclosure also increases more strongly after Article 173 came
into force at firms with high French institutional ownership.
3.3.3 Alternative explanations and robustness. The estimates in Table 6
are consistent with an influence effect interpretation, whereby the shock to the

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(1)

Climate Risk Disclosure and Institutional Investors

Table 7
Climate risk disclosure and institutional investors: Robustness of French Article 173 effects
A. Addressing selection effects
Scope 1 disclosure
(1)
Post-Article 173 × High French IO

0.022∗∗
(0.010)

Post-Article 173 × High French
IO pre-Article 173
2017 × High French IO

(2)

0.024∗∗
(0.011)

(3)

B. Alternative specifications
Scope 1 disclosure
(4)

0.025∗∗∗ 0.032∗∗∗
(0.008)
(0.011)

(5)

2013 × High French IO

 French IO pre- to postArticle 173

(0.565)
High French IO preArticle 173

0.683
(0.615)
0.056∗∗
(0.024)

Scope 1 disclosure preArticle 173

0.009
(0.005)
0.179

−0.007
(0.010)

−0.017
(0.013)

(0.178)

(0.011)
0.002
(0.013)
0.005
(0.015)
0.050∗∗∗
(0.013)
0.467

0.046∗∗
(0.023)

(0.564)

0.954∗∗∗
(0.013)

0.012∗
(0.007)

Post-Article 173

All firms
2013–2017

All firms
2013–2017

All firms
2013–2017

All firms,
balanced
panel, SE
clustered
by firm
2013–2017

Controls
Industry × year fixed effects
Country fixed effects
Year fixed effects
Firm fixed effects

Yes
Yes
Yes
No
No

Yes
Yes
Yes
No
No

Yes
Yes
Yes
No
No

Yes
No
No
Yes
Yes

Yes
No
No
No
Yes

Yes
Yes
Yes
No
No

Yes
Yes
Yes
No
No

N

15,907

15,907

15,907

13,126

6,786

15,907

17,878

Adjusted R 2

.296

.296

.730

.784

.818

.296

.221

Sample
Years

All firms,
firm-years
collapsed in
pre/post
years
2013–2017

All firms
2013–2017

All firms
2013–2017

This table reports regressions at the firm-year level (except in column 5) explaining how firms’ climate risk
disclosures change around the passage of Article 173 in France in 2015. The dependent variables are as follows:
Scope 1 disclosure equals one if a firm discloses Scope 1 carbon emissions to CDP in a year, and zero otherwise.
Forecast occurrence equals one if a firm issues at least one voluntary earnings forecast in a given year, and zero
otherwise. We use the following key independent variables: Post-Article 173 equals one for the years of 2016 and
afterward, and zero otherwise; High French IO equals one if the fraction of outstanding shares owned by French
institutional investors is above the median of a given year, and zero otherwise;  French IO pre- to post-Article
173 is the average value of the fraction of outstanding shares owned by French institutional investors for the
years 2016 and afterward minus the same average value for the years before 2016; High French IO pre-Article
173 equals one if the average fraction of outstanding shares owned by French institutional investors in the years
before 2016 is above the median, and zero otherwise, and Scope 1 disclosure pre-Article 173 is the average value
of Scope 1 disclosure for the years before 2016. Table A1 defines all variables. Standard errors (in parentheses)
are clustered at the country level, except in columns 4 and 5 (clustered by firm). *p < .1; **p < .05; ***p < .01.

demand for climate risk disclosure by French institutions due to Article 173
leads to improved firm-level disclosures. To bolster this interpretation, Table 7
provides a series of tests that address different concerns with the analysis
in Table 6.
Table 7, panel A, addresses the concern that the estimates may in part reflect
selection effects. Specifically, as French institutional investors are required to

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2014 × High French IO

0.053∗∗∗
(0.014)
0.467

(7)

0.006
(0.008)
0.027∗∗∗
(0.010)
0.022∗

2016 × High French IO

High French IO

(6)

0.030∗∗∗
(0.010)

C. Placebo test
Forecast occurrence

The Review of Financial Studies / v 36 n 7 2023

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disclose their climate risk exposures, they may select to increase (decrease)
holdings in firms with better (worse) climate risk disclosures. We estimate
different variations of Equation (3) to gauge the importance of this alternative
channel. The objective of these tests is to isolate – as much as possible – the
influence channel of French institutions.
In column 1, we control for changes in French institutional ownership around
Article 173’s passage, measured as the change in the firm-level average of
French IO from before to after the reform. We continue to find a positive
and significant effect of Post-Article 173×High French IO. Importantly, the
magnitude of the effect is almost identical to the baseline estimate in Table 6,
column 1. Unobserved variables correlated with French ownership changes
around the introduction of Article 173 should thus not unduly bias our
estimation.
In column 2, we replace High French IO with High French IO pre-Article
173, which captures whether French ownership is large in the years prior to
Article 173’s effective date. The benefit of using past values in the estimation
is that it reduces concerns about the treatment status (high French institutional
ownership) being endogenously affected by a selection channel. Column 2
confirms the results obtained in the prior column.
Finally, in column 3, we control for a firm’s Scope 1 disclosures in the
years before Article 173 comes into force, as the selection channel is plausibly
strongest among those firms that already provided climate-related disclosures
prior to the reform – these firms may see the strongest increase in French
holdings. Again, results are unaffected and, if anything, become stronger in
terms of economic magnitude and statistical significance.
Table 7, panel B, addresses different concerns about the empirical
specification used to estimate Equation (3). One concern is that our results are
affected by serial correlation in the error term. Following the guidance provided
by Bertrand, Duflo, and Mullainathan (2004), in the specification reported
in column 4, we cluster standard errors at the firm level after estimating
regressions on a balanced panel with firm fixed effects. Next, in the column
5 specification we estimate a firm-level regression model using data that are
collapsed in the pre- and post-Article 173 period (2013–2015 vs. 2016–2017),
after including again firm fixed effects. The estimates in both columns are in
line with our previous results.
In column 6, we consider the role of pre-trends by estimating a version
of Equation (3) that includes dynamic treatment effects for the individual
years around the passage of Article 173 in 2015 (the year 2015 constitutes
the baseline year). We observe no significant effects of High French IO
for the years prior to the passage of Article 173 (2013 and 2014), but
positive and significant effects for 2016 and 2017. The effect size for 2016
is about ten times larger than that for 2014, and the effect increases further
in 2017.

Climate Risk Disclosure and Institutional Investors

Table 8
Changes in French institutional ownership around Article 173
French IO (×100)
(1)
Post-Article 173 × Scope 1 disclosure pre-Article 173
Post-Article 173 × Climate risk disclosure pre-Article 173
Scope 1 disclosure pre-Article 173

0.214∗∗
(0.100)

Climate risk disclosure pre-Article 173

−0.028
(0.026)
0.091∗∗
(0.039)

All firms
2013–2017

All firms
2013–2017

Controls
Industry × year fixed effects
Country fixed effects

Yes
Yes
Yes

Yes
Yes
Yes

N
Adj. R 2

17,178
.513

17,159
.513

This table reports regressions at the firm-year level explaining institutional ownership by French institutions.
The dependent variable is as follows: French IO is a continuous measure of the fraction of outstanding shares
owned by French institutional investors (multiplied by 100). We use the following key independent variables:
Post-Article 173 equals one for the years of 2016 and afterward, and zero otherwise; Scope 1 disclosure preArticle 173 is the average value of Scope 1 disclosure for the years before 2016; and Climate risk disclosure
Pre-Article 173 is the average value of Climate risk disclosure for the years before 2016. Table A1 defines all
variables. Standard errors (in parentheses) are clustered at the country level. *p < .1; **p < .05; ***p < .01.

Table 7, panel C, provides a placebo test to corroborate that our results are
not due to unobservable differences in general voluntary disclosure practices
between firms with high- and low French institutional ownership that coincided
with Article 173. To this end, we reestimate Equation (3) but replace climate
risk disclosure with Forecast occurrence, the proxy for general voluntary
disclosure. As is evident from column 7, in this falsification test Post-Article
173 × High French IO is not significantly different from zero.
3.3.4 Changes in French institutional ownership. In Table 8, we take
further steps to mitigate concerns about selection effects. Specifically, we
examine whether changes in French IO around Article 173 depend on the
practices of firm-level climate risk disclosure in years before the reform. For
this purpose, we estimate for firm f in country c and year t the dynamics of
French institutional ownership around Article 173:
French IOf,c,t = α+β1 Post-Article173t ×Climate disclosure pre-Article 173f,c,t
+ β2 Climate disclosure pre-Article 173f,c,t +δXf,c,t
+ Fixed effects+εf,c,t ,

(4)

where French IOf,c,t is French institutional ownership, and Climate disclosure
pre-Article 173f,c,t is Scope 1 disclosure or Climate risk disclosure in the years
before Article 173 became effective. We measure pre-reform disclosure using

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Sample
Years

(2)

−0.092
(0.065)

The Review of Financial Studies / v 36 n 7 2023

4. Conclusion
High-quality information on firms’ climate risks is a necessary component
of informed investment decisions and of the correct market pricing of
climate-related risks and opportunities. In this paper, we provide systematic
international evidence from survey and equity portfolio holdings data on the
preferences of institutional investors with respect to climate risk disclosures.
We advance the literature by making two primary contributions.
First, we illustrate that institutional investors value and demand climate risk
disclosures. In our survey, the respondents share a strong belief that climate risk
disclosure is important, that their institutions have a strong investor demand
for such disclosures, and that they actively engage portfolio firms to improve
them. We corroborate these conclusions in our empirical tests using investor
holdings, showing that ownership by institutions with a plausibly higher
disclosure demand (“climate-conscious institutions”) is positively associated
with CDP-based measures of climate risk disclosure.
Second, we demonstrate that climate risk disclosure of firms owned by many
French institutions improves in response to Article 173, which provides a
shock to the disclosure demand of French institutional investors. The results
support an interpretation whereby institutions influence firms to improve their
reporting.
Overall, our results show the importance of institutional investors in
demanding informative, high-quality disclosures from firms, in this case for
climate-related risk disclosures.

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the firm-level averages of the disclosure measures for the years before 2016. As
before, Post-Article 173t equals one for 2016 and afterward, and zero before,
and we use again the same two-sided 2-year time window around the passage
of the reform in 2015. (The noninteracted effect of Post-Article 173t is again
absorbed by the fixed effects.)
In columns 1 and 2, we are unable to detect that French IO increases more
strongly among firms with relatively high pre-Article 173 disclosure levels. The
absence of a significant effect further mitigates the concern that our results in
Table 6 are driven by selection effects. The regressions also show that French
institutional ownership is generally larger when firms disclose more on climate
risks prior to Article 173. A natural caveat of this test is that, by conditioning
on pre-Article 173 disclosure, we cannot eliminate any role of expected future
disclosure after the reform, which may theoretically still explain some of the
Table 6 effects. Overall, we believe that the set of results on Article 173 are
more consistent with an influence channel. However, we do not want to rule
out that some selection effects around the introduction of Article 173 might
also have been at play.

Climate Risk Disclosure and Institutional Investors

Appendix
Table A1
Variable definitions
A. Survey analysis
Variable

Definition

Survey
question

(Continued)

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Measures how important investors consider reporting by portfolio firms Question B1
on climate risks compared to reporting on financial information. The
variable ranges between one and five, with one indicating that
climate risk reporting is “much less importance” and five indicating
that it is “much more important”
Question B3
Demand more
Equals one if a respondent “strongly agrees” that investors should
disclosure
demand that portfolio firms disclose their exposure to climate risk,
and zero otherwise. In the underlying questions, respondents were
asked to indicate their agreement with the statements on a scale of
one (“strongly disagree”) through five (“strongly agree”)
Quant. information Equals one if a respondent “strongly agrees” that firm-level quantitative Question B3
imprecise
information on climate risk is not sufficiently precise, and zero
otherwise. In the underlying questions, respondents were asked to
indicate their agreement with the statements on a scale of one
(“strongly disagree”) through five (“strongly agree”)
Question B3
Management
Equals one if a respondent “strongly agrees” that management
discussions
discussions on climate risk are not sufficiently precise, and zero
imprecise
otherwise. In the underlying questions, respondents were asked to
indicate their agreement with the statements on a scale of one
(“strongly disagree”) through five (“strongly agree”)
TCFD engagement Equals one if a respondent engages or plans to engage portfolio
Question E5
companies to report according to the recommendations of the Task
Force on Climate-related Financial Disclosures, and zero otherwise
Carbon footprint
Equals one if a respondent discloses or plans to disclose the overall
Question B2
disclosure
carbon footprint of the portfolio, and zero otherwise
Climate risk ranking Outcome of a ranking of the importance of climate risks relative to
Question A1
other investment risks. The variable ranges from one (if they are
considered the least important risk) to six (if climate risks are
considered the most important risk)
Question A2
Climate risk
Averages the responses to three questions about the financial
financial
materiality of regulatory, physical, and technological climate risk.
materiality
Each of these three variables can range between one (not at all
important) and five (very important)
Question A4
Fiduciary duty
Equals one if a respondent strongly agrees to the statement that
institution
incorporating climate risks in the investment process “is a legal
obligation/fiduciary duty that we have to consider,” and zero
otherwise
Question G7
HQ country norms
Captures the importance of environmental issues in the country in
which an institutional investor is headquartered. The data are from
Dyck et al. (2019), who construct the variable based on the
Environmental Performance Index obtained from the Yale Center for
Environmental Law (Yale University) and the Center for
International Earth Science Information Network (Columbia
University) for 2004. Larger numbers reflect a stronger common
belief in the importance of environmental issues
Very large institution Equals one if the size of an institutional investor is more than $100
Question G6
billion, and zero otherwise
ESG portfolio share Percentage of the institution’s portfolio that incorporates ESG issues
Question G5
Medium-term
Equals one if the indicated typical holding period of an institutional
Question G2
horizon
investor is between 6 months and 2 years, and zero otherwise
Long-term horizon Equals one if the indicated holding period of an institutional investor is Question G2
above 2 years, and zero otherwise
Importance of
climate risk
disclosure

The Review of Financial Studies / v 36 n 7 2023

Table A1
(Continued)
B. Holdings and disclosure data analysis
Variable

Definition

Source, sample years

Scope 1
disclosure
Climate risk
disclosure

Equals one if a firm discloses Scope 1 carbon emissions to
CDP in a year, and zero otherwise
Follows the definition in Flammer, Toffel, and Viswanathan
(2021) and captures disclosure to CDP on up to three types
of climate risks (regulatory, physical, or other climate risks)
in a year. It takes the value of zero if a firm does not disclose
climate risks to CDP in year, one if it discloses information
on one type of climate risks, two if it discloses information
on two types of climate risks, and three if it discloses
information on all three types of climate risks. This variable
is available for the years 2011 to 2016 as CDP did not
include this question in 2010 and changed the question
design from 2017 onward such that the responses are not
comparable anymore for these years
Measures how comprehensive a firm’s climate risk disclosure
is to CDP by counting the fraction of questions that were
answered in the CDP survey in a year. This variable is only
available between 2010 and 2015 as the score replaced by
CDP in 2016 with an alternative measure that mixes
disclosure and climate performance. The measures varies
between 0 and 100 and higher numbers indicate better
climate risk disclosure
Follows Matsumura, Prakash, and Vera-Muñoz (2022) and
equals one if a 10-K contains the climate change words
“carbon,” “climate change,” “emissions,” “greenhouse,”
“GHG,” “hurricanes,” “renewable energy,” and “extreme
weather” in a year, and zero otherwise. Only available for
U.S. firms
Fraction of outstanding shares owned by institutional investors
that are subject to stewardship codes in their home countries
in a year. Winsorized at 1%
Fraction of outstanding shares owned by institutional investors
from high-norms countries (as defined by Dyck et al. 2019)
in a year. An institutional investor’s country is in the
high-norms group if its Environmental Performance Index
(EPI) is higher than the median in a year. Winsorized at 1%
Fraction of outstanding shares owned by institutional investors
that are classified as universal owners in a year. We classify
as universal owners those institutional investors whose
number of stocks in the portfolios is ranked in the top 1%
across all institutions in a year (calculated at the parent
level). The number of observations for this variable is lower
than that for the other two ownership measures as we miss
parent data for the last sample year. Winsorized at 1%
Fraction of outstanding shares owned by institutional investors
that are not subject to stewardship codes in their home
countries in a year. Winsorized at 1%
Fraction of outstanding shares owned by institutional investors
from low-norms countries (as defined by Dyck et al. 2019)
in a year. An institutional investor’s country is in the
low-norms group if its Environmental Performance Index
(EPI) is lower than the median in a year. Winsorized at 1%
Fraction of outstanding shares owned by institutional investors
that are not classified as universal owners in a year.
Winsorized at 1%
Equals one if a firm operates in a very competitive industry
based on the text-based HHI measure developed by
Hoberg and Phillips (2016), and zero otherwise. A firm
operates in a very competitive industry if its HHI is below
the sample median in a year. Only available for U.S. firms
Equals one if a firm operates in an SIC2 industry that is in the
top-20 across SIC2 industries based on Scope 1 emissions,
and zero otherwise

CDP, 2010–2019

10-K Climate risk
disclosure

Stewardship code
IO
High-norms IO

Universal owner
IO

Nonstewardship
code IO
Low-norms IO

Nonuniversal
owner IO
High-competition
firm

High-emission
industry

CDP, 2010–2015

SEC EDGAR,
2010–2019, U.S. firms

FactSet,
Katelouzou and Siems
2021, 2010–2019
FactSet, 2010–2019

FactSet, 2010–2018

FactSet,
Katelouzou and Siems
2021, 2010–2019
FactSet, 2010–2019

FactSet, 2010–2018

Hoberg and Phillips
2016, 2010–2016,
U.S. firms
Ilhan, Sautner, and Vilkov
2021, 2010–2019
(Continued)

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Climate
disclosure
score

CDP, 2011–2016

Climate Risk Disclosure and Institutional Investors

Table A1
(Continued)
Variable

Definition

Source, sample
years

Assets

C. French Article 173 Analysis
Post-Article 173

Equals one for the years of 2016 and afterward, and zero otherwise

Selfconstructed,

High French IO

Equals one if the fraction of outstanding shares owned by French
institutional investors is above the median of a year, and zero
otherwise
Continuous measure of institutional ownership by French institutions

FactSet,
2010–2019

French IO
High French IO
pre-Article 173

Equals one if the average fraction of outstanding shares owned by
French institutional investors in the years before 2016 is above the
median, and zero otherwise
 French IO pre- to Average value of the fraction of outstanding shares owned by French
post-Article 173
institutional investors for the years 2016 and afterward minus the
same average value for the years before 2016
Scope 1 disclosure
Average value of Scope 1 disclosure for the years before 2016
pre-Article 173
Climate risk
Average value of Climate risk disclosure for the years before 2016
disclosure
pre-Article 173
French firm
Equals one if a firm is from France, and zero otherwise

FactSet,
2010–2019
FactSet,
2010–2019
FactSet,
2010–2019
CDP,
2010–2019
CDP,
2011–2016
FactSet,
2010–2019

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==> RFS13 - Corporate ESG Profiles and Banking Relationships.txt <==
Corporate ESG Profiles and Banking
Relationships
Joel F. Houston
University of Florida

We show that banking relationships promote corporate environmental, social, and
governance (ESG) policies. Specifically, banks are more likely to grant loans to borrowers
with ESG profiles similar to their own and positively influence the borrower’s subsequent
ESG performance. Their influence is more pronounced when (1) banks have significantly
better ESG ratings than borrowers and (2) borrowers are bank dependent. We exploit M&A
among lenders as a source of quasi-exogenous variation in the lender’s ESG standard to
alleviate endogeneity concerns. Overall, our study presents the first evidence on the interplay
between responsible bank lending and borrowers’ ESG behavior. (JEL G21, G28, G38)
Received April 30, 2020; editorial decision July 12, 2021 by Editor Philip Strahan.

Beyond meeting their financial objectives, firms often strive to integrate a wide
variety of environmental, social, and governance (ESG) goals into their business
models (Bénabou and Tirole 2010; Hart and Zingales 2017). Coincident with
these efforts, firms face growing internal and external pressures to improve their
performance along various nonfinancial dimensions, including environmental
impacts, social welfare, and fair labor practices. While these pressures apply
to a wide range of firms, banks in recent years have particularly faced
increased pressure to be more accountable to their customers and to make more
socially responsible lending decisions.1 Relatedly, in April 2019, a group of

We appreciate the helpful comments from editor Philip Strahan and two anonymous referees. We thank Nemmara
Chidambaran, Chitru Fernando, Iftekhar Hasan, Christopher James, Sehoon Kim, Hao Liang, Peter MacKay,
William Megginson, Jay Ritter, Gregory Udell, Guner Velioglu, An Yan, and Xinyan Yan and conference
participants at the University of Oklahoma - Review of Financial Studies Energy and Commodities Finance
Research Conference and the Fixed Income and Financial Institutions Conference for comments and suggestions.
Hongyu acknowledges financial support from Fordham Social Innovation Fellowship. All remaining errors are
our own. Send correspondence to Hongyu Shan, hshan6@fordham.edu.
1 We find that banks are more actively discussing how ESG fits into their business models. The total frequency

of mentions of the keyword “ESG” in Bank of America, JPMorgan Chase, and Wells Fargo’s proxy statements
increased from 2 in 2015 to 81 in 2019.
The Review of Financial Studies 35 (2022) 3373–3417
© The Author(s) 2021. Published by Oxford University Press on behalf of The Society for Financial Studies.
All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
doi: 10.1093/rfs/hhab125
Advance Access publication November 23, 2021

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Hongyu Shan
Fordham University

The Review of Financial Studies / v 35 n 7 2022

2 For details on these two examples, see Hsu (2019) and Lim (2021).
3 The literature on the causes and effects of firm ESG policies is long-standing. Earlier studies largely focused

on the determinants motivating the cross-sectional differences in the observed levels of ESG ratings, as well as
the wealth effects of these policies, with a particular emphasis on the positive impact of institutional investors
(Starks, Venkat, and Zhu 2020; Cao et al. 2020; He, Kahraman, and Lowry 2020; Dimson, Karakaş, and Li 2015,
among others). Given this focus, most studies have concentrated on public firms. Nevertheless, the data from
RepRisk, a Zurich-based data science company that scans negative ESG news incidents, reveal that the number
of private firms involved in ESG incidents was six times higher than that of public firms between 2007 and 2018.
In fact, the majority of firms that pose ESG risks to society are small, private firms that receive a minimal level of
public scrutiny from the equity market. In light of these facts, the roles played by critical stakeholders in shaping
corporate ESG practice remain underexplored.
4 Extensive discussions have ensued on how ESG engagements help improve long-term firm performance by, for

example, (1) avoiding myopic managerial decisions (Bénabou and Tirole 2010), (2) attracting customers who
will pay more for environmentally and socially responsible products (Baron 2009), and (3) reducing litigation
risks (Eccles, Ioannou, and Serafeim 2014), among others.

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stakeholders promoting gun control released a well-publicized report card
ranking banks on their ties to firearm manufacturers and firearm organizations,
such as the National Rifle Association (NRA). Growing evidence indicates
that pressure from stakeholders is being indirectly passed along to borrowers
through the concrete steps taken by their lenders. As an interesting example, a
recent Wall Street Journal article describes how a group of lenders structured a
deal with BlackRock where the stability of lending relationship was explicitly
tied to BlackRock’s ability to meet certain goals related to diversity hiring and
increasing assets in ESG-related funds.2 Despite the observed actions taken by
banks and the heightened public interest in the social economic impact of bank
lending practices, there is no apparent consensus in the literature on whether
banks can and should effectively shape borrowers’ ESG activities.3
In this paper, we propose a novel economic mechanism to explain the
propagation of ESG policies through lending relationships. Despite the
considerable evidence that bankers may affect their borrowers’ policies and
investments (Shleifer and Vishny 1997; Chava and Roberts 2008; Nini, Smith,
and Sufi 2012), whether lenders use this leverage to specifically influence
borrowers’ ESG policies remains an open question. One view is that lenders
primarily focus on borrowers’ financial performance, and consequently resist
costly investments that chiefly benefit other nonbank stakeholders. This view
is consistent with the classic argument made by Friedman (1970) that the
firm’s only responsibility is to increase its profit. Brammer and Millington
(2008) present evidence in support of this argument showing that high social
responsibility firms score the lowest in short-term financial performance.4
However, beyond this narrow view, we hypothesize two further avenues
by which banks are concerned about the ESG performance of their potential
borrowers. The first avenue is that poor ESG performance may ultimately
translate into greater credit risk. Arguably, firms with poorer ESG performance
are more likely to face costly backlash from various stakeholders. Stakeholder
backlash may draw negative publicity, as well as induce consumer boycotts,
employer backlash, and increased regulation and litigation. Ultimately, we

Corporate ESG Profiles and Banking Relationships

5 We show that the level of bank reputational risk exposure is positively related to risk-adjusted capital ratios. See

Appendix A.2 for details.

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would expect these risks to affect the likelihood of debt repayment and that
bankers would incorporate these factors into the structure and pricing of
loan agreements. Consistent with this financial motivation, recent research
has shown that promoting engagements in ESG issues can reduce firms’
downside risk (Hoepner et al. 2018), and has documented an association
between measures of ESG ratings and loan pricing (Sharfman and Fernando
2008; Goss and Roberts 2011; Chava 2014; Hasan et al. 2017; Hauptmann
2017).
The second possible avenue is that bankers are concerned about their own
reputation and social capital, and fear that the value of this capital may be
diminished by doing business with poor ESG-rated borrowers. Banks that suffer
a hit to their reputation because of their dealings with poor-ESG borrowers may
particularly find it difficult to engage future business in other areas (Homanen
2018). Banks may also face considerable negative media coverage and increased
regulatory scrutiny. Given that they are heavily regulated and are often the
focus of public condemnation, they have a strong incentive to reduce negative
reputational incidents (both their own and that of their borrowers). For example,
after the high school mass shooting in Parkland, Florida, that claimed 17
deaths and left 17 injured, Bank of America announced it would stop lending
money to gun manufacturers that choose to continue the production of militaryinspired firearms for civilian use. Note that the bank’s decision is unlikely
based on considerations of the default and lender liability risks, given the
lucrative nature and liquidity of its clients. This event is hardly an isolated
occurrence. In another example, Morgan Stanley and Wells Fargo stopped
lending to firms that extract coal using methods that, while legal and lucrative,
are often very harmful to the environment (Nussbaum 2015). This anecdotal
evidence collectively demonstrates that banks’ ESG-related concerns extend
beyond a simple consideration of credit and liability risk.5
Altogether, these arguments suggest that banks have financial and
reputational motivations for focusing on a borrower’s ESG performance. We
further hypothesize that banks are differentially concerned about the ESG
performance of their potential borrowers, and that a bank’s degree of concern
is partially captured by its own ESG rating. In one respect, the bank’s own ESG
rating may provide a strong signal of its views on ESG-related issues. If so, we
would expect banks with strong ESG performance to tilt toward borrowers with
strong ESG ratings. Alternatively, banks with poor ESG performance may be
more interested in repairing their social capital and therefore may subsequently
tilt toward borrowers with strong ESG ratings in an attempt to enhance their
image. Consequently, the connection between a lender’s ESG performance and
that of its potential borrowers remains an empirical question.

The Review of Financial Studies / v 35 n 7 2022

6 To the best of our knowledge, other ESG databases such as KLD and Asset4 focus on large, public firms. The

limited coverage inevitably introduces selection and reverse causality problems that confound our understanding
of the interactions between lenders and borrowers in the corporate loan market.
7 An increasing number of studies in ESG focus on the real outcomes, instead of discretionary disclosures, which

are often subject to greenwashing bias, for example, legal and litigation risks (Schiller 2018 and toxic and/or
carbon emissions (Bartram, Hou, and Kim 2021; Shive and Forster 2020; Xu and Kim 2021, among others). In the
same spirit, RepRisk focuses on real outcomes (externally reported ESG related incidents), which incorporate
a broad range of ESG accidents that span across 28 issues. Notably, the rating system incorporates not only
the number of incidents but also the severity, reach, and novelty of the events to evaluate the firm’s reputation
exposure to ESG and business conduct risks. See WRDS RepRisk data manual for details.

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To explore these issues, we conduct a series of tests using the RepRisk
database to obtain the negative news coverage and ESG ratings of both
borrowers and lenders. The database is uniquely suited for our study because
its coverage includes a wide range of private borrowers and because of its
outcome-driven approach. The coverage on private firms is critical when we
explore the corporate loan market, where the majority of borrowers are private
firms that often receive a minimal level of scrutiny from the equity market.6
RepRisk also focuses on ESG-related events that are actually reported. By
contrast, many other databases primarily assign ESG ratings based on whether
the firm “claims” to enact certain policies that are more discretionary and subject
to greenwashing bias.7
To the extent that banks are concerned about their borrowers’ ESG
performance, they can express these concerns in multiple ways, each of
which can be linked to the literature that highlight how principals may use
a combination of voice or exit to influence an agent’s behavior. The first way
that a bank may influence borrower ESG-related behavior is through the initial
decision whether or not to lend. To the extent that a bank tilts away or completely
avoids lending to certain types of borrowers, this becomes a form of exit that
imposes costs on borrowers with poor ESG ratings. Thus, in our first set of
“matching” tests, we show that lenders tend to match with borrowers who have
similar ESG profiles. Specifically, we first remove the firm-level time-series
mean from both the lender and borrower’s ESG ratings. Then for each given
year, we equal-weight and value-weight (by loan amount) the ESG ratings of
the borrowers who initiated loans from the same lender. We scatter plot the
equal-weighted and value-weighted ESG ratings of the borrowers in the loan
portfolio against the ESG rating of the lender for each observed lender-year.
The fitted linear relationship and the corresponding 95% confidence interval
point to a significant and positive cross-sectional correlation between the loan
portfolio’s average ESG rating and the lender’s own ESG rating. Note that we
only consider lenders and borrowers without prior lending relationships, to rule
out the possibility that the observed ESG ratings are the reverse outcome of a
prior lending relationship, rather than the determinant of the establishment of
new relationship.
While these results strongly demonstrate that ESG factors are an important
determinant of whether a particular lender matches with a particular borrower,

Corporate ESG Profiles and Banking Relationships

8 The flip side of the selection problem is that the more effective a bank is at improving a borrower’s ESG

performance ex post, the more willing it might be to accept ESG risk ex ante.
9 We believe that the timing and the decision of bank M&A activities are arguably exogenous to the borrowers’

firm-level unobservable characteristics that determine ESG ratings. As noted by prior studies, the bank merger
waves were largely driven by regulatory, technological, and competitive changes (Pilloff 2004).

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we fully recognize that these factors are not the only factor influencing lending
decisions. Consequently, it remains likely that individual borrowers may align
with lenders with different levels of ESG performance. Given this last point,
our second set of tests ask whether these differences persist, and if lenders
systematically influence borrower ESG performance over time. More directly,
do borrowers’ ESG levels evolve in ways that are consistent with the lender’s
views about ESG issues? If so, this suggests a second way in which bankers
may influence a borrower’s ESG policy through a “dynamic” channel.
In these tests, we provide evidence that lenders significantly influence the
evolution of their borrowers’ ESG profile. Here, we find that a one-standarddeviation increase in the difference between the borrower and lender’s ESG
ratings is associated with a 0.66 increase in the borrower’s RepRisk rating over
a 2-year window centered on the package initiation date, which is equivalent to
6% of the standard deviation of the changes in borrowers’ ESG ratings during
the same 2-year window. These results confirm that banks, as a unique and novel
source of influence, can affect borrowers’ ESG performance in a significant and
dynamic manner.
While the demonstrated associations appear to be economically significant
and robust to a variety of specifications, establishing direct causation
is notoriously challenging. The biggest identification concern relates to
disentangling treatment from selection effects. While we believe that banks
have a positive impact on the evolution of borrowers’ ESG performance
(treatment), a reasonable alternative explanation is that borrowers who expect
to improve their ESG standard choose to borrow money from ESG focused
banks (selection).8 To alleviate these concerns, we exploit M&A in the banking
industry as a source of quasi-exogenous variations of the lender’s ESG standard
(Asker and Ljungqvist 2010; Hong and Kacperczyk 2010; Chen, Harford, and
Lin 2015).9 In a difference-in-differences setting, we examine whether the
variation in lenders’ ESG standard transmits through the established lending
relationship to affect the evolution of borrowers’ ESG ratings following the
M&A. We apply a wide range of fixed effects on the (1) borrower, (2)
industry, and (3) year levels to absorb the remaining unobservable timeinvariant heterogeneities across borrowers and industries, and to preclude
the effects of common time trends. This test helps us identify the dynamic
component of bank impact on borrower ESG performance, in a setting that is
not confounded by borrower-lender matchings or other selection issues.
We further explore banks’ incentives to shape borrowers’ ESG activities. If
both financial and reputational channels are driving banks’ actions, we suspect

The Review of Financial Studies / v 35 n 7 2022

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that banks are particularly concerned with (1) borrowers’ ESG practices that
could potentially expose lenders to liability risk and (2) controversial social
and/or environmental issues that would cast lenders in the spotlight of media
coverage. In support of this financial channel, we show that the bank’s influence
is stronger among secured loans where the liability risk exposures dramatically
increase if there is an adverse shock. To better understand the areas that banks
care most about when assessing borrower exposure, we examine the 28 news
topics tracked by RepRisk. Consistent with the reputational channel, we find
that banks are most likely to discipline borrowers in cases of (1) human rights
abuse, (2) social discrimination, and (3) climate change. In contrast, their impact
on other issues such as executive compensation is negligible. We interpret the
results as evidence showing that banks have incentives to minimize negative
exposures in catastrophic social and environmental scandals in order to preserve
future business opportunities.
While we find evidence supporting both the financial and reputational
motivations, we acknowledge the difficulty in completely isolating them, as
these two incentives are by no means mutually exclusive.
Moreover, while these results show that banks have strong incentives to
discipline and shape borrower ESG activities, the exact mechanisms in which
lenders influence borrower ESG performance over time are not immediately
clear. We can think of at least three reasons we observe these findings. First,
“when in Rome, do as the Romans do”; this argument suggests that agents may
tend to adopt the behavior of those they contract with over time. While certainly
plausible, directly testing this possible mechanism seems quite challenging.
Another possibility is that high-quality lenders directly force or nudge
borrowers to improve their ESG performance. One important limitation is that
lender liability concerns may strongly constrain the lender’s ability to directly
impose specific constraints on borrowers’ decision-making. For these same
reasons, it may be difficult to observe actual cases in which banks are explicitly
directing borrowers to take certain actions.
Nevertheless, bankers may be able to impose indirect pressure on their
borrowers to improve their ESG performance. Ultimately, the third and key
element that may facilitate these improvements is the subsequent decision
whether to renew the loan. In the process of lending to a firm, a bank
acquires proprietary firm-specific information that is unavailable to nonlenders
(Schenone 2009). Switching lenders is costly for borrowers and is often
accompanied by reduction in the availability of credit (Petersen and Rajan
1994). In the context of the exit/voice dichotomy, banks may be able to
imperfectly use their “voice” to influence borrower behavior, but the ultimate
hammer may be the fear of subsequent exit. This possible mechanism provides
a third way in which banks may influence borrower ESG behavior.
In our final set of tests, we present evidence supporting this novel disciplinary
mechanism. We find that borrowers are significantly more likely to observe a
shift in lead lender(s) following negative shocks to their ESG-related reputation.

Corporate ESG Profiles and Banking Relationships

10 Instead of examining the impact of bank lending on borrower ESG activities, Flammer (2021) and Tang and Zhang

(2020) examine through the lens of announcement returns, operating performance, and/or green innovations
whether the issuance of “green” bonds is beneficial to the firm and shareholders. Also, a recent study by Kim
et al. (2021) examines the factors determining the emergence of ESG lending and green bonds in the global
market.

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More specifically, conditional on obtaining new loan financing within a 2-year
period centered on the end date of the original loan, we find that borrowers
are 3% less likely to renew loans with the same lead lender(s) if there was
a negative ESG-related reputational shock. Furthermore, we find that these
borrowers exposed to negative ESG-related news are more likely to shift to
lenders with worse RepRisk ratings. We control for both (1) the level and
(2) the change in the borrower’s financials, including ROA, assets, leverage, and
Tobin’s q, to make sure that the switch in lending relationship is not driven by
fundamental changes in credit and liability risk. To further alleviate concerns of
omitted variable bias, we utilize negative news coverage initiated by outsiders,
whose timing relative to the loan expiration date is arguably quasi-exogenous
and out of the control of corporate insiders.
This “fear of subsequent exit” should also vary across borrowers. It is
intensified among bank-dependent borrowers and borrowers with relatively
poor ex ante ESG ratings. We find that lenders have a more profound influence if
the borrower is bank dependent. We also document important asymmetry: banks
that have better ESG-related ratings relative to the borrower are more likely to
induce borrowers to improve their ESG performance over time. On the other
hand, the lender’s impact on the borrower’s ESG evolution is indistinguishable
from zero if the lender’s ESG rating is worse relative to that of the borrower.
On balance, our findings clearly demonstrate that the banking system has
an important systematic effect on corporate ESG policies. In this regard, we
believe our findings make an important contribution to the growing literature
on the role of key stakeholders in shaping corporate ESG policies (Shive and
Forster 2020; Lins, Servaes, and Tamayo 2017; Starks, Venkat, and Zhu 2020;
Chava 2014; Dimson, Karakaş, and Li 2015; Bartram, Hou, and Kim 2021;
Gillan, Koch, and Starks 2021; Avenancio-León and Shen 2021). Most notably,
recent papers by Schiller (2018) and Dai, Liang, and Ng (2020) document that
socially conscious customers have taken steps to induce their key suppliers to
become more socially responsible. Given the importance of a sound evaluation
of efficacy and real effects of bank lending, it is surprising how little empirical
work has been done on this front. Our work presents the first evidence on the
interplay between responsible bank lending and borrower ESG behavior to fill
this gap.10
At the same time, our paper contributes to the vast literature on banking
relationships, by highlighting another important factor that influences the
choice of lender and the role that lenders play in influencing firm performance
and investment decisions (Shleifer and Vishny 1997; Chava and Roberts 2008;
Nini, Smith, and Sufi 2012; Schwert 2018, among others). In this vein, our

The Review of Financial Studies / v 35 n 7 2022

work is related to the long-standing theories of relationship lending (Sharpe
1990; Berger and Udell 1995, among others) and bank monitoring (Holmstrom
and Tirole 1997; Diamond 1991, among others).
1. Data

11 RepRisk does not cover positive ESG events. Part of the reason can be attributed to the fact that positive news is

more likely to be self-reported for branding and marketing purposes and is subject to greenwashing biases. To
the best of our knowledge, we are not aware of the existence of any positive ESG news database. See Li and Wu
(2020) for an extended discussion of the collection of positive news.
12 The RRI is constructed as a function of negative news coverage that may be correlated with firm financials, such

as firm size and growth opportunities. Larger firms and firms with higher growth opportunities may be cast in the
spotlight and attract greater media attention. In our regressions, we control for a variety of variables, such as log
assets, Book leverage, Return on assets, and Tobin’s q, to mitigate the confounding impacts of firm financials.

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1.1 ESG data
This study employs an event-based outcome measure of firm-level environmental, social, and governance (ESG) profile for both public and private firms
using data from RepRisk. The RepRisk data provide a monthly unbroken timeseries ESG rating and coverage on negative ESG news incidents from January
2007 to June 2017.11 A dedicated team of analysts leverage a combination of
artificial intelligence and curated human analysis to track a universe of over
95,000 firms globally, among which 82,000 are private firms with no selfreported ESG compliance information. On a daily basis, over 80,000 public
sources and stakeholders in 20 languages are screened. Once an incident is
identified, analysts conduct additional analysis to (1) confirm that the incident
is indeed ESG-related, (2) remove possible duplicate media coverage on the
same incident to make sure each risk event only enters once into the RepRisk
Platform, and (3) identify the specific nature of the incident, by mapping it to
28 ESG Issues and 45 ESG topics. Each incident is assigned three proprietary
scores based on severity (harshness), reach (influence), and novelty (newness).
Finally, the RepRisk index (RRI hereafter) is updated, reflecting the ensuing
impact of the news incident.12 A higher level of RRI indicates a greater history
of negative events (i.e., worse ESG performance).
Compared with the widely used annual KLD database (now MSCI
ESGSTATS), the RepRisk data are uniquely suited for our study for three
reasons. First, the event-based data evaluate the outcome of ESG activities,
which can be directly linked to the societal impact of ESG compliance. The
KLD data instead rely on the firm’s self-reported information, which varies
largely with the firm’s discretionary disclosures related to ESG compliance.
RepRisk arguably provides a more objective assessment of the societal impact
of each firm over time, because it is more difficult for firms to endogenously
manipulate media attention/negative news detection, than to manipulate selfdisclosed policy adoptions. Second, the KLD data do not cover private firms,
which are predominant in the corporate loan market. Third, RepRisk has

Corporate ESG Profiles and Banking Relationships

13 The RepRisk database is not perfect. We cannot fully separate the attention effects of news media from the

deterioration of the borrower’s ESG activities. RepRisk does not provide news content, and, thus, we are not
able to evaluate whether changes in ESG ratings are triggered by news reporters’ shifting attention. In fact, any
judgment of reporters’ motivation would be subjective, even if the content of the news coverage can be properly
obtained.
14 According to the RepRisk data manual (December 2020) obtained from Wharton Research Data Services

(WRDS), for any given month, two events drive the change in RRI: (1) New risk incidents for a company
or project, in which case the RRI is recalculated. The magnitude of the increase depends on the severity, reach,
and novelty of the incident. Or (2) there is no new risk exposure, in which case the RRI decays. The RRI decays
over time as follows: for the first 14 days after a significant risk incident, the RRI remains at the same value. If
no new exposure is captured, the RRI then decays to zero over a maximum period of two years. The decaying
speed occurs at a rate of 25 every 2 months until it reaches 25, then a rate of 25 every 18 months until it reaches
zero.

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unparalleled granularity. It employs a monthly, continuous ESG rating ranging
from 0 to 100, while most of the KLD ratings are structured as an annual,
indicator variable that equals 0 or 1.13
Figure 1 presents the cross-sectional distribution of the RepRisk ratings. We
first calculate the average RepRisk index of all firms covered by the database
(9,500 + firms as of 2018) and plot the distribution in Figure 1, panel A. We
also calculate the average RepRisk index of the borrowers in our sample, and
plot the distribution in Figure 1, panel B. The cross-sectional distributions in
both figures are positively skewed, with medians at 2.02 (all RepRisk firms) and
3.87 (borrowers in our sample), and standard deviations at 3.32 (all RepRisk
firms) and 6.90 (borrowers in our sample). Notably, the number of firms that
are involved with severe ESG incidents is much smaller than the number of
firms that do not receive any negative ESG-related news coverage. We suspect
that the skewness arises from the underlying skewed nature of news reporting
(a few high-profile events attract large attention) and the large sample of firms
tracked by the database.
The evolution of a firm’s RRI is notably path dependent. That is, the change
in a firm’s RRI from year t to t+1 is correlated with the level of firm’s RRI in
year t. We highlight two reasons underlying the observed time-series pattern.
First, borrowers who are exposed in negative ESG-related news are more likely
to proactively manage the crisis. The chance of showing up in the headlines
of negative news for consecutive months is low. Second, according to the data
manual of RepRisk, the ESG rating of any firm decays over time, and the speed
of decay depends only on the current level of RRI.14 The decay assumes that
the perceived ESG risk decreases over time. In other words, a borrower who has
not been involved in any ESG-related scandals for 2 years is considered to have
a lower risk than the same borrower who is scandal-free for only one year. In
our empirical analysis, we regress the evolution of the borrower’s ESG ratings
as a function of the difference between the lender and borrower’s ESG ratings
observed one year before the loan initiation. Given the documented time-series
patterns above, we conclude that it is necessary to control for the ex ante level
of the borrower’s RRI when we study the lender’s impact on the evolution of
the borrower’s ESG performance.

The Review of Financial Studies / v 35 n 7 2022

A

Distribution of the average RepRisk index, borrowers
Figure 1
Cross-sectional distribution of the RepRisk index
Panel A reports the cross-sectional distribution of the average RepRisk index (RRI) of all firms covered by
RepRisk. We also calculate the average RepRisk index of the borrowers in our sample and plot the distribution
in panel B. The average RepRisk index of each firm is calculated as the time-series mean of the firm’s monthly
RRIs observed during our sample period.

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Distribution of the average RepRisk index, all RepRisk firms

B

Corporate ESG Profiles and Banking Relationships

1.3 M&A data
From the SDC M&A database, we extract the set of completed merger and
acquisitions in the financial industry from 2007 through 2017. The following
filters are applied: (1) both the acquirer and the target have SIC codes between
6000 and 6999, (2) the acquirer owned less than 50% of the target bank’s
shares 6 months before the transaction and more than 50% of the shares after
the transaction, and (3) we exclude deals with missing transaction values. The
output sample is merged with both the RepRisk and Compustat Bank databases
to obtain the acquirer and target’s RRI and total assets. This step leaves us with
28 M&As with nonmissing RepRisk profiles and bank financial data.
We subsequently match the acquirer and the target’s names to the lender’s
names in the DealScan database. We exploit the merger as a quasi-exogenous
shock to the ESG-related performance of the borrowers who have an established
lending relationship with the lender involved in the M&A. This setup enables

15 Alternatively, as a robustness test, we select a unique lead lender for each loan following Ivashina and Kovner

(2011). This procedure considers the past borrowing history between lenders and firms and selects the lead lender
that the firm has the strongest relationship with. We present our findings under this alternative approach in Section
4.2.

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1.2 Banking data
We obtain loan pricing and contract information from Loan Pricing
Corporation’s (LPC) DealScan database, for the sample period from 2007 to
2017. We focus on the loans granted to U.S.-incorporated firms. DealScan
provides characteristics information for each loan such as size, maturity, type,
and purpose, as well as information about the outstanding financial covenants
and other terms. We hand-match the DealScan loan data to RepRisk ESG ratings
using company names. We use S&P Capital IQ as well as Google search to track
the historical names of each company to verify the accuracy of matches.
One concern is that the borrower ESG profile, which we use to construct
the main independent variable of interest, is the same across facilities within
the same package, which inevitably inflates the statistical significance of the
coefficient estimates. Consequently, we study the evolution of borrower ESG
ratings over time at the package level, instead of the facility level. Specifically,
we consider each package as a relationship between a borrower and a lead
lender that finances the package. Following Bharath et al. (2009), we classify a
lender as lead lender if the “LeadArrangerCredit” field indicates “Yes” or if the
“LenderRole” field indicates one of the following: administrative agent, agent,
arranger, lead arranger, lead bank. For some packages in our sample, we have
multiple lead lenders in the syndicate. In these cases, we calculate the equally
weighted average of ESG ratings of lead-lenders in the syndicate.15 Finally,
we drop a small part of our sample, specifically 3.6% of the total number of
packages, where different facilities within the same package have different lead
lenders.

The Review of Financial Studies / v 35 n 7 2022

1.4 Financials
After constructing the sample of packages with corresponding deal
characteristics as well as borrower and lender ESG ratings, we also incorporate
a broad range of firm-level control variables in the subsample analysis that
consists of only public borrowers. Specifically, we collect firms’ financial
information from Compustat for the most recent fiscal year ending within a
1-year window prior to the package start date (i.e., lagged). We use the
Chava and Roberts (2008) linking file to link loans from DealScan to firms
in Compustat. We then supplement the firm controls with S&P credit ratings.
An important dimension of our study is its inclusion of both public and private
borrowers. We classify a borrower as a public borrower if we can find a stock
price available from the Center for Research in Security Prices (CRSP) for the
same fiscal year and as a private borrower otherwise. Appendix A.1 lists and
defines required firm- and package-level variables in detail.
1.5 Summary statistics
Table 1 presents the summary statistics for our sample of packages and the
corresponding borrowers. In our sample, we have 8,128 packages, taken out by
2,407 borrowers and granted by 116 lenders from 2007 to 2017. The median
borrower has an ESG rating of zero, which suggests that median firm has no
publicly known issues (the lower the ESG rating, the better). The median lender
on the other hand has an ESG rating of 18, which indicates that it has some
known issues. Two factors could explain these differences: (1) the median bank
in our sample is larger than the median borrower, and larger firms are more likely
to receive publicity; (2) financial industry firms often receive more attention
and greater scrutiny, especially during our sample period, which corresponds
to the financial crisis and postcrisis periods. Overall, our interest is the relative
standing of each borrower and lender within its own industry, as well as the
difference in their ESG ratings.
To account for the size and credit risk of the borrower, we include firm-level
controls. About 62% of the packages are granted to rated borrowers, and 34%
of all packages are granted to investment-grade firms. Similarly, we find that
64% of the packages are granted to public firms. These statistics suggest that a

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us to determine whether borrower ESG performance evolve differently if their
lender(s) undergo a shift in their ESG standard. The magnitude of the shock
depends on the relative size of the acquirer and target (see detailed discussion
in section 3). Our final merged sample consists of 423 treated loans initiated
from 2007 to 2017. These 423 treated loans are linked to 266 unique packages,
associated with 17 out of the 28 M&As. Among the treated loans, the ESG
shock variable (i.e., ESG_shock) has a mean of -3.28 and a standard deviation
of 6.52. Eighty-five percent of the treated loans have a negative ESG_Shock,
suggesting that their old lender was acquired by another firm with a better ESG
profile.

Corporate ESG Profiles and Banking Relationships

Table 1
Descriptive statistics
Variable

Mean

SD

P10

P50

P90

8,128
8,128
8,128
8,128
8,128
8,128
8,128
8,128
8,128
8,128

1.83
7.86
19.12
11.26
16.37
20.04
1.41
0.62
0.34
0.64

11.38
11.73
21.15
22.97
18.42
1.23
0.84
0.49
0.48
0.48

−12.00
0.00
0.00
−16.00
−3.50
18.42
1.00
0.00
0.00
0.00

0.00
0.00
18.00
1.50
15.00
20.03
1.00
1.00
0.00
1.00

18.00
24.00
61.00
45.00
41.00
21.54
2.00
1.00
1.00
1.00

Avail for public borrowers
log assets
Book leverage
Return on assets
Tobin’s q

5,855
5,855
5,753
5,121

8.55
0.32
0.04
1.73

1.62
0.23
0.11
0.98

6.53
0.06
−0.03
0.99

8.50
0.29
0.04
1.46

10.62
0.59
0.12
2.68

Avail for switching tests
Same
Same res
Num rep event
Original package length

2,662
2,662
2,662
2,662

0.56
0.51
2.43
3.15

0.50
0.50
3.01
1.75

0.00
0.00
0.00
1.00

1.00
1.00
1.00
3.00

1.00
1.00
7.00
5.00

This table summarizes sample statistics. All variables are constructed on the loan package level. Rated, Investment
grade, Public, Same, and Same res are dummy variables. log assets, Book leverage, Return on assets, and Tobin’s
q are only available for public firms and select private firms through Capital IQ. Same, Same res, Num rep event,
and Original package length are the main variables of interest in the switching (loan renewal) tests. Appendix
A.1 defines the variables in detail.

significant portion of our sample has limited access to public debt and equity
markets. An important dimension of our analysis considers cases where the
lender has stronger influence over its borrower. Arguably, these cases arise
more frequently in the roughly 40% of packages where the borrower does
not have access to public markets. Consequently, even though we do not have
accounting information for these private firms, we still include these packages
in our baseline tests to determine the importance of creditor control in shaping
the ESG policies of bank-dependent borrowers. In subsample regressions in
which we consider only the public borrowers, we include controls, such as log
assets, book leverage, return on assets, and Tobin’s q. Our results are robust to
these additional considerations.
One of the empirical challenges in ESG studies is the limited comparability
of scores and ratings across industries and years. In Figure 2, we calculate the
mean level of RRI of all borrowers and lenders in our sample. Figure 2, panel
A, documents a rising level of RRI over time, partly driven by an increasing
number of ESG related news coverage in recent years. Figure 2, panel B, shows
that the level of ESG exposures vary by industry. Borrowers in Utilities, Energy,
and Chemicals on average have a higher level of RRI. Figure 2, panel C, presents
a similar rising level of RRI of lenders over time. We address the comparability
across industries and time by subtracting the sector-month average RRI from

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N

ESG_chg
ESG_borrower
ESG_lender
Unadjusted ESG_diff
ESG_diff
log package amt
Num of facilities
Rated
Investment grade
Public

The Review of Financial Studies / v 35 n 7 2022

A

Avg RRI of borrowers by industry

C

Avg RRI of lenders
Figure 2
RepRisk index by year and industry
The panels show the mean level of an unadjusted borrower’s RepRisk index (RRI) by year-month (Figure 2,
panel A), the mean level of an unadjusted borrower’s RRI by industry (Figure 2, panel B), and the mean level of
an unadjusted lender’s RRI by year-month (Figure 2, panel C). The sample includes 126 monthly RRI for each
borrower in our sample (from January 2007 to June 2017). Industry classifications are based on the Fama-French
12 industry classifications.

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Avg RRI of borrowers

B

Corporate ESG Profiles and Banking Relationships

the borrower and lender’s raw RRIs to obtain the sector-month-adjusted RRIs,
which we use to construct the independent variables.16
2. Main Results

16 We obtain the sector-month average from RepRisk. The variable name is “Country_sector_average.” Since we

focus on packages granted to U.S.-incorporated firms, there is no variation at the country level. In the robustness
test section (Table 10), we show that our baseline results are robust if we use the unadjusted RRI as independent
variables.

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2.1 ESG ratings and the matching of borrowers and lenders
We first consider whether lenders are more likely to grant loans to borrowers
with similar ESG profiles. One might expect that a lender’s attitude regarding
the desirability of a borrower’s ESG performance to be related to its own views
regarding ESG-related policies, which are reflected in the bank’s own ESG
rating. Alternatively, lenders may view the borrower’s ESG rating as largely
immaterial when making lending decisions. Finally, there may be cases where
banks with poor ESG ratings tilt toward lending to high ESG-rated borrowers,
perhaps as a means of indirectly improving the bank’s image. To explore these
alternative hypotheses, we present the cross-sectional correlation between the
borrower’s and the lender’s ESG ratings using scatter plots.
Specifically, we first remove the firm-level time-series mean from the lender
and borrower’s RepRisk index (RRI). In Figure 3, panels A and B, we
only consider the matching of borrowers and lenders with no prior lending
relationships. In Figure 3, panel A, we equally weight the RRIs of the borrowers
who obtained loan financing from the same lead lender in the same year and
generate an aggregate lender-year-level RRI of the loan portfolio. We plot the
lender’s RRI (x-axis) and that of the loan portfolio (y-axis) for each year during
our sample period. The fitted linear relationship and the corresponding 95%
confidence interval point to a significant and positive cross-sectional correlation
between the loan portfolio’s average ESG ratings and the lender’s own ESG
ratings.
In Figure 3, panel B, we further confirm the robustness of the cross-sectional
correlation. For the loans initiated in the same year by the same lead lender,
we weight every borrower’s RRI by the total loan amount between the lender
and borrower in a given year, and generate an aggregate lender-year-level RRI
of the loan portfolio. We choose to weight the borrower’s ESG rating by the
total loan amount, instead of equally weighting, based on the assumption that
the lender’s exposure to a borrower’s ESG misconduct increases with the loan
amount. Using this new weighting method, we plot the lender’s RRI (x-axis)
and that of the loan portfolio (y-axis) for each year during our sample period.
The fitted linear relationship once again confirms the significant and positive
correlation between the loan portfolio’s average ESG ratings and the lender’s
own ESG ratings.

The Review of Financial Studies / v 35 n 7 2022

A

Weight borrowers’ RRIs by loan amount
Figure 3
Distribution of the Lender and its Loan Portfolio’s RepRisk index (RRI)
The figures present the scatterplots of the lender and its loan portfolio’s RRIs. Lenders and borrowers’ RRIs
are adjusted by the time-series means, by subtracting the firm-level average RRI observed during our sample
period. The sample only includes lenders and borrowers without prior lending relationship and matched for the
first time. In each year, we weight the RRIs of the borrowers who obtained loan financing from the lender, and
obtain an aggregate lender-year-level RRI for the lender’s loan portfolio. In Figure 3, panel A, borrowers’ RRIs
are equally weighted. In Figure 3, panel B, borrowers’ RRIs are weighted by loan amount. In both panels, we
report the RRI of the loan portfolio on the y-axis, and the lender’s RRI on the x-axis. The fitted linear relationship
is represented by a solid line, and the corresponding 95% confidence interval is represented by a dashed line.

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Equally weight borrowers’ RRI

B

Corporate ESG Profiles and Banking Relationships

2.2 Evolution of borrowers’ ESG performance
This section explores how corporate ESG policies propagate through lending
relationships. We examine the direct impact of banks on the evolution of the
borrowers’ ESG performance using package-level data. The empirical analysis
is based on the following ordinary least squares (OLS) specification:
ESG_Chgi,t−1,t+1 = α +βESG_Diff i,j,t−1 +λLender_Chgj,t−1,t+1
(1)

+θ ESG_Borrower i,t−1 +γ Xi,t−1 +Iffindustry
+δt +ξi,j,t ,

where i indexes borrower, j indexes lender, t indexes the package initiation year.
For each package, the change in the borrower’s ESG profile (ESG_Chgi,t−1,t+1 )
is defined as the change in the borrower’s RRI over a 2-year window, from one
year before (t-1) to one year after the package initiation date (t+1). The ex ante
difference between the lender and borrower’s ESG ratings (ESG_Diff i,j,t−1 ) is
defined as the difference between the lender and borrower’s RepRisk ESG rating

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Overall, we show consistent evidence that banks tend to match with
borrowers with similar ESG levels. These results may be driven by two possible
channels. One is that banks with higher RRI (i.e., worse ESG performance) have
demonstrated that they are less concerned with ESG policies. Consequently,
these banks are less likely to reward low RRI borrowers with lower lending
rates and/or to penalize high RRI borrowers with higher lender rates. In this
case, the likely equilibrium outcome is that borrowers and lenders with similar
ESG levels are more likely to gravitate together. A second possible channel is
that ESG policy is part of a two-sided matching problem similar to the market
for underwriters described by Fernando, Gatchev, and Spindt (2005). In this
scenario, loans with similar risk are priced similarly by all lenders, but the
allocation of lenders and borrowers are driven by nonprice factors such as the
perceived reputation related to ESG issues.
These two channels are by no means mutually exclusive, and it is difficult
to completely isolate the motivation for the observed matching. We partially
disentangle these effects by looking at the connection between loan pricing and
the ESG ratings of the borrower and lender. We show related results in Appendix
A.3. Interestingly, we find some (but fairly weak) evidence suggesting that, all
else equal, banks with worse ESG ratings offer slightly lower loan spreads.
Moreover, after controlling for the lender’s RRI, we find no significant link
between the borrower’s ESG rating and loan pricing. Put more directly, banks
price loans largely based on the traditional borrower and loan characteristics,
but are more likely to ultimately match with borrowers on nonprice factors,
such as perceived reputation on ESG issues. On balance, these results seem to
suggest an equilibrium similar to the matching of underwriters described by
Fernando, Gatchev, and Spindt (2005).

The Review of Financial Studies / v 35 n 7 2022

17 The size of the randomly generated sample is larger than the size of the sample in Table 2. The fact that the

coefficient estimate is insignificant in the placebo test is unlikely explained by the difference in the power of the
tests.

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measured one year before the package initiation date. To alleviate potential
concerns about the comparability of ESG scores across industries and years,
we adjust both the lender and the borrower’s RRI by the sector-month mean.
Lender_Chgj,t−1,t+1 controls for the evolution in the lender’s ESG rating over
the same 2-year window.
We realize that the evolution of the borrower’s ESG rating may be both path
dependent and mean-reverting. That is, borrowers with ex ante poor ESG rating
are more likely to improve over time (i.e., converge to the mean level), compared
to borrowers with an ex ante pristine ESG rating. By including the control
variable ESG_Borroweri,t−1 , we effectively compare the ESG evolution
among borrowers with similar ex ante ESG ratings to alleviate concerns of pathdependency. Other control variables include the Num of facilities in the package,
log package amt, country of syndication - USA, and the borrower’s Public status.
IF F industry and δt denote the dummies for the Fama-French 12 industry and year
fixed effects. We cluster the standard errors at the borrower level.
Table 2 presents these results. In columns 1, 2, and 3, we run the regressions
with only basic control variables related to the borrower and lender’s ESG
ratings; in column 4, we include the control variables that are available for both
public and private borrowers including the Num of facilities in the package, log
package amt, country of syndication - USA, and the borrower’s Public status;
and in column 5, we further restrict our analysis to a subsample consisting of
public firms with additional publicly available control variables including size
(log assets), Book leverage, Return on assets, and Tobin’s q.
The key coefficient of interest, the difference between lender and borrower
ESG ratings (i.e. ESG_diff ), is statistically significant at the 1% level in the
first four columns, and at the 5% level in column 5. The economic magnitude
is also sizable. Take column 4, for example, which uses the full sample whose
summary of statistics are reported in Table 1, a standard deviation increase in
ESG_Diff is associated with a 0.66 (18.42 × 0.036) increase in the borrower’s
RRI over time, which is equivalent to 6% (0.66/11.38) of the standard deviation
of ESG_Chg.
Given the cross-sectional and time-series characteristics of the RRI
documented in Section 1.1, a reasonable concern is that our empirical
specification only picks up mechanic/spurious correlation hardwired in the
data, instead of identifying the economic relationship.
We rule out this possibility with two additional tests. In the first test,
we generate 10,000 randomized borrower-lender pairs. For 10,000 times,
we randomly draw from the pool of unique borrowers who initiated loans
during our sample period, and pair it with a random lender from the
pool of unique lenders.17 We then generate a random year-month as the

Corporate ESG Profiles and Banking Relationships

Table 2
Evolution in corporate ESG profile and bank lending

ESG_diff
Lender_chg
ESG_borrower

(2)
ESG_chg
All

(3)
ESG_chg
All

(4)
ESG_chg
All

(5)
ESG_chg
Public

0.0718∗∗∗
(10.03)
0.0617∗∗∗
(5.85)
−0.396∗∗∗
(−37.23)

0.0718∗∗∗
(8.69)
0.0617∗∗∗
(5.03)
−0.396∗∗∗
(−17.51)

0.0616∗∗∗
(6.64)
0.0465∗∗∗
(3.68)
−0.409∗∗∗
(−15.99)

0.0357∗∗∗
(4.05)
0.0208∗
(1.70)
−0.517∗∗∗
(−22.09)
−0.784∗∗∗
(−4.23)
1.905∗∗∗
(13.18)
−2.844∗∗
(−1.99)
1.246∗∗∗
(4.10)

0.0295∗∗
(2.57)
0.0299∗∗
(1.99)
−0.603∗∗∗
(−22.73)
0.0139
(0.07)
0.503∗∗
(2.37)
−0.118
(−0.07)

Yes
Yes
Yes
8,104
.264

Yes
Yes
Yes
5,120
.320

Num of facilities
log package amt
USA
Public
log assets
Book leverage
Return on assets
Tobin’s q
Ind FE
Year FE
Cluster
N
Adj. R2

No
No
No
8,128
.220

No
No
Yes
8,128
.220

Yes
Yes
Yes
8,104
.227

2.371∗∗∗
(12.87)
−2.342∗∗∗
(−2.90)
−1.655
(−1.30)
0.765∗∗∗
(3.72)

This table reports the OLS regression of the change in the borrower’s ESG profile on the ex ante difference
between the bank and borrower’s ESG ratings. The change in the borrower’s ESG profile (ESG_chg) is defined
as the difference between the borrower’s RepRisk indexes over a 2-year window, from one year before to one
year after the package initiation date. The ex ante difference between the bank and borrower’s ESG ratings
(ESG_diff ) is defined as the difference between the bank and borrower’s RepRisk indexes measured one year
before the package initiation date. Lender_chg controls for the evolution in the lender’s ESG indexes over the
same 2-year window. ESG_borrower controls for the potential path dependency problem and is defined as the
borrower’s RepRisk index one year before the package initiation date. In column 1, we report the basic regression
without fixed effects and clustering of standard errors. Column 2 clusters the standard errors at the borrower
level. Column 3 adds industry and year fixed effects. In column 4, we also include the Num of facilities in the
package, log package amt, country of syndication - USA, and the borrower’s Public status as control variables.
In column 5, we show that our results are robust in the subsample of public firms only, and we further control for
borrowers’ financials, including log assets, Book leverage, Return on assets, and Tobin’s q. Industry FE is based
on the Fama-French 12 industry classification. Standard errors are clustered at the borrower level. t-statistics are
reported in parentheses. *p <.1; **p <.05; ***p <.01.

“package initiation date,” assuming the likelihood of initiating the loan is equal
at any time during our sample period. Note that the random pairing and
assignment of package initiation date do not alter the cross-sectional and timeseries characteristics in ESG ratings. If our model is picking up the spurious
correlation hardwired in the data, we should observe a significant coefficient
estimate in this placebo test. Column 1 of Appendix A.4 reports the results. The
relationship between the change in borrowers’ RRI and the difference between
the lender and borrower’s ESG ratings is not significant, thereby alleviating
concerns.

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(1)
ESG_chg
All

The Review of Financial Studies / v 35 n 7 2022

2.3 Asymmetric bank influence
Our baseline results demonstrate that the gap between the lender and borrower’s
ESG ratings is significantly related to the evolution of a borrower’s rating over
time. A natural question arises whether the results are symmetric depending on
whether the borrower has a higher or lower rating than its lender. One scenario
explaining the observed results is that banks with an ESG rating that is relatively
stronger than that of the borrowing firm take implicit and explicit steps to force
the borrower to improve their ratings. Another explanation is that when a bank
has a relatively weaker ESG rating than its borrower, its failure to nudge the
borrowing firm creates an environment where the borrower may feel freer to
take actions that ultimately weaken its ESG rating. If the effects are symmetric,
18 Our original sample contains 8,128 packages. We are only able to find matched potential borrowers for 6,946

(or 85.5%) of them after applying the matching criteria discussed above.

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In the second test, we construct the group of “potential borrowers” under
a more restrictive assumption: for each “realized” borrower-lender pair in our
current sample, a “pseudo”-potential borrower is defined as a company (1) with
the same public/private status, (2) in the same SICH industry, and (3) operating
within a 50 miles radius of the borrower who successfully secured the package.
We implicitly assume that companies (1) with similar access to public market,
(2) in the same industry, and (3) clustered in the same neighborhood are likely
to act together (in time) to search for corporate loan financing, and the group of
lenders they approach are likely to be the same. If there are multiple matched
“pseudo”-potential borrowers, we keep the one with closest ex ante RRI to the
“realized” borrower as measured at one year before the package initiation date.
In this way, we replace the “realized” borrower with the “pseudo”-borrower oneto-one, and construct a sample consisting of the “pseudo”-potential borrowerlender pairs.18 We rerun the evolution regression to examine whether the bank’s
impact on the group of potential borrowers is persistent.
Columns 2 and 3 in Appendix A.4 report the results. We use the same
specification employed in Table 2 but exclude the package-level control
variables: the Num of facilities in the package, log package amt, and the
country of syndication - USA. This is because the matching between potential
borrower and lender is based on a “virtual loan package” that never existed.
Borrower-level control variables are included in column 3.
The coefficient estimates of ESG_Diff, which is defined as the difference
between the lender’s and the potential borrower’s RRIs, are neither statistically
nor economically significant. However, if we look at the coefficients of the
control variables in columns 2 and 3, we see that the directions of association
and the levels of statistical significance are consistent with those in Table 2, as
they should be. Overall, the results from the two placebo tests confirm that our
results are unlikely driven by spurious correlations that may be hardwired in
the data and model specification.

Corporate ESG Profiles and Banking Relationships

Table 3
Asymmetric bank impact
A

(1)

(2)

(3)

Better bank = 1

ESG_diff
Lender_chg
ESG_borrower

log package amt
USA
Public

ESG_Chg

ESG_Chg

0.066∗∗
(2.39)
0.045
(1.32)
−0.488∗∗∗
(−10.38)
−0.677∗
(−1.83)
4.152∗∗∗
(12.69)
−10.367∗∗∗
(−3.60)
1.809∗∗
(2.05)

0.072∗∗
(2.46)
0.040
(1.02)
−0.624∗∗∗
(−12.53)
0.312
(0.81)
1.508∗∗∗
(2.94)
−3.714
(−1.27)

Yes
Yes
Yes
1,539
.328

Yes
Yes
Yes
1,154
.415

log assets
Book leverage
Return on assets
Tobin’s q
Ind FE
Year FE
Cluster
N
Adj. R2

3.485∗∗∗
(8.33)
−2.037
(−1.00)
3.373
(0.76)
1.089∗∗
(2.39)

ESG_Chg

ESG_chg

0.013
(1.11)
−0.017
(−0.94)
−0.584∗∗∗
(−20.48)
−0.889∗∗∗
(−3.48)
1.562∗∗∗
(8.35)
−0.255
(−0.16)
1.103∗∗∗
(2.80)

0.013
(0.83)
−0.002
(−0.08)
−0.629∗∗∗
(−17.86)
−0.136
(−0.52)
0.456∗
(1.65)
1.378
(0.76)

Yes
Yes
Yes
4,132
.240

Yes
Yes
Yes
2,447
.273

2.101∗∗∗
(8.74)
−2.431∗∗
(−2.43)
−3.345∗
(−1.93)
0.706∗∗∗
(2.67)

(Continued)

both explanations may be equally relevant. Alternatively, the effects may be
asymmetric, in which case the results are driven primarily by one of these two
scenarios.
To empirically address this issue, we start by sorting the packages into groups
where the lender has a better (i.e., smaller (<)) ESG rating than the borrower
(“Better bank = 1”), and into groups where the lender has a worse (i.e., greater
(>)) ESG rating than the borrower (“Better bank = 0”). Table 3, panel A, presents
the results. In columns 1 and 2, we regress the borrower ESG changes for the
subsample of packages where the lenders have a better ESG rating. We find
that the economic effect of the ESG difference is even greater when the lender
has a better ESG rating. This suggests that lenders have a disciplining influence
over the borrowers when they have relatively better ESG ratings.
In columns 3 and 4 of panel A, we run the test for the subsample of packages
where the lenders have worse ESG ratings than their borrowers. In these
circumstances, we find no evidence of lenders influencing the evolution of
their borrowers’ ESG ratings. Overall, our findings suggest that while “good”
lenders from an ESG perspective may encourage their borrowers to become

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Num of facilities

(4)
Better bank = 0

The Review of Financial Studies / v 35 n 7 2022

Table 3
(Continued)
B

ESG_diff
Lender_chg
ESG_borrower

log package amt
USA
Public

ESG_chg

ESG_chg

ESG_chg

0.212∗∗∗
(3.76)
0.058∗∗
(2.16)
−0.447∗∗∗
(−10.31)
−0.544
(−0.97)
2.552∗∗∗
(8.72)
−7.324
(−1.59)
1.615∗∗
(2.33)

0.256∗∗∗
(4.52)
0.061∗
(1.72)
−0.553∗∗∗
(−10.86)
−0.067
(−0.08)
1.107∗∗
(2.52)
−1.234
(−0.33)

0.025∗∗
(2.49)
0.021
(1.44)
−0.526∗∗∗
(−20.88)
−0.793∗∗∗
(−4.13)
1.676∗∗∗
(10.64)
−2.041
(−1.49)
1.046∗∗∗
(3.24)

Yes
Yes
Yes
1,384
.368

Yes
Yes
Yes
899
.439

log assets
Book leverage
Return on assets
Tobin’s q
Ind FE
Year FE
Cluster
N
Adj. R2

(3)
(4)
Better bank (adj) = 0

2.527∗∗∗
(7.00)
−1.132
(−0.57)
0.181
(0.06)
1.046∗∗
(2.29)

Yes
Yes
Yes
6,482
.211

ESG_chg
0.020
(1.51)
0.030∗
(1.69)
−0.593∗∗∗
(−20.96)
0.054
(0.29)
0.318
(1.38)
0.044
(0.03)
2.290∗∗∗
(11.55)
−2.535∗∗∗
(−2.83)
−2.548∗
(−1.80)
0.831∗∗∗
(3.74)

Yes
Yes
Yes
4,079
.262

This table reports the OLS regression of the change in the borrower’s ESG profile on the ex ante difference
between the bank and borrower’s ESG ratings. The change in the borrower’s ESG profile (ESG_chg) is defined
as the difference between the borrower’s RepRisk indexes one year after and one year before the package
initiation date. The ex ante difference between the bank and borrower’s ESG ratings (ESG_diff ) is defined as the
difference between the bank and borrower’s RepRisk indexes measured one year before the package initiation
date. ESG_borrower controls for the potential path dependency problem and is defined as the borrower’s RepRisk
index one year before the package initiation date. Panel A presents the results for the subsamples where lender
has a better or worse unadjusted ESG rating than the borrower. Samples in columns 1 and 2 include only loans
where the bank’s unadjusted RRI is smaller (<) than the borrower’s unadjusted RRI. Samples in columns 3 and 4
include those where the bank’s unadjusted RRI is larger (>) than the borrower’s. Panel B presents the results for
the subsamples where lender has a better or worse sector-month-adjusted ESG rating than the borrower. We also
include the Num of Facilities in the package, log package amt, country of syndication - USA, and the borrower’s
Public status as control variables. Industry FE is based on the Fama-French 12 industry classification. Standard
errors are clustered at the borrower level. t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

more socially responsible, “bad” lenders do not induce their borrowers to
become less responsible.
Panel B of Table 3 repeats the analysis using alternative definitions of “better
bank.” In columns 1 and 2, we consider the subsample of packages where the
lender’s sector-month-adjusted RRI is smaller (<) than the borrower’s sectormonth-adjusted RRI (better bank (adj) =1). In those cases, we find a significant
improvement in borrowers’ ESG ratings. With similar intuition, we consider
the subsamples in columns 3 and 4, where the lender’s sector-month-adjusted
RRI is greater (>) than the borrower’s sector-month-adjusted RRI (better bank
(adj) =0). While the coefficient estimate of ESG_Diff in column 3 of panel B

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Num of facilities

(1)
(2)
Better bank (adj) = 1

Corporate ESG Profiles and Banking Relationships

2.4 Cross-sectional variation in bank dependency and liability risk
In Table 4, we focus on those cases in which we expect the lender to have a
particularly strong influence on its borrowers. We posit that bank dependent
borrowers have stronger incentives to preserve the existing lending relationship,
and are thus more likely to discipline themselves when lenders hold a high ESG
lending standard. We test our hypothesis using the following specification:
ESG_Chgi,t−1,t+1 =α +βESG_Diff i,j,t−1 ×Idependency,t−1
+ςESG_Diff i,j,t−1 +τ Idependency,t−1

(2)

+λLender_Chgj,t−1,t+1 +θESG_Borroweri,t−1
+γ Xi,t−1 +Iff industry +δt +ξi,j,t ,
where i indexes borrower, j indexes lender, t indexes the package initiation
year. ESG_Diff i,j,t−1 ×Idependency is an interaction term between the lender
and borrower ESG difference and our proxies for bank dependency. These
proxies include indicators for credit rating (Rated) and investment-grade status
(Investment grade). We include the same set of control variables (X) as specified
in Equation (1), including the Num of facilities in the package, log package amt,
country of syndication - USA, and the borrower’s Public status.
We first consider whether bankers are more able to influence unrated
borrowers. Unrated borrowers typically have less access to public financing,
which arguably makes them more bank-dependent and more sensitive to holdup
problems. In column 1 of Table 4, we find that lenders have greater influence
on borrowers’ ESG policies if the borrower is unrated. We repeat this test with
investment-grade versus non-investment-grade firms in column 2 of Table 4. We

19 Note that in both panels A and B, we drop the packages where the lender’s RRI it equal to the borrower’s RRI

(adjusted RRI in panel B). The sample size in panel A is smaller than that in panel B because of the clustering
of unadjusted RRIs at zero, in which case packages are dropped from the (combined) better and worse lender
subsamples.

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is statistically significant, the economic magnitude is about one-ninth of that in
column 1 of panel B. Overall, we find little evidence of the lenders’ influence
over the borrowers for these subsamples.19 Lastly, we compute the Wald chisquare statistics using the post-estimation command suest, and confirm that we
can reject the equality of the coefficients (ESG_Diff ) across pairwise regression
samples (panel A, column 1 vs. 3; panel A, column 2 vs. 4) at the 10% level,
and across the pairwise regression samples (panel B, column 1 vs. 3; panel B,
column 2 vs. 4) at the 1% level.
Overall, our findings suggest that the lenders’ influence over borrowers’ ESG
ratings is asymmetric. In particular, the magnitude as well as the sign of the
distance (ESG_Diff ) are strong determinants of the evolution of borrowers’
ESG performance.

The Review of Financial Studies / v 35 n 7 2022

Table 4
Bank dependency, secured loans, and bank lending

ESG_diff
Rated
ESG_diff × Rated

(1)
ESG_chg

(2)
ESG_chg

(3)
ESG_chg

0.060∗∗∗
(5.12)
1.820∗∗∗
(4.11)
−0.046∗∗∗
(−3.17)

0.055∗∗∗
(5.62)

0.023∗∗
(2.22)

Investment grade

0.019
(1.59)
−0.528∗∗∗
(−22.13)
−0.732∗∗∗
(−3.99)
1.762∗∗∗
(11.39)
−2.823∗∗
(−2.03)
0.943∗∗∗
(2.92)

0.018
(1.52)
−0.549∗∗∗
(−23.87)
−0.559∗∗∗
(−3.32)
1.604∗∗∗
(11.09)
−2.624∗∗
(−1.98)
0.836∗∗∗
(2.70)

−2.313∗∗∗
(−6.27)
0.033∗∗
(2.40)
0.020
(1.64)
−0.529∗∗∗
(−23.08)
−0.661∗∗∗
(−3.77)
1.852∗∗∗
(13.06)
−2.710∗
(−1.91)
1.294∗∗∗
(4.30)

Yes
Yes
Yes
8,104
.267

Yes
Yes
Yes
8,104
.276

Yes
Yes
Yes
8,104
.270

Secure
ESG_diff × Secure
Lender_chg
ESG_borrower
Num of facilities
log package amt
USA
Public
Ind FE
Year FE
Cluster
N
Adj. R2

This table reports the OLS regression of the change in the borrower’s ESG profile on the ex ante difference
between the bank and borrower’s ESG ratings. The change in the borrower’s ESG profile (ESG_Chg) is defined
as the difference between the borrower’s RepRisk indexes one year after and one year before the package
initiation date. The ex ante difference between the bank and borrower’s ESG ratings (ESG_diff ) is defined as the
difference between the bank and borrower’s RepRisk indexes measured one year before the package initiation
date. Interaction terms of ESG_diff and proxies of bank dependency are included. Proxies of bank dependency
include the Rated dummy and Investment-grade dummy. Secure is the dummy variable that turns on if the loan is a
secured loan. ESG_borrower controls for the potential path dependency problem and is defined as the borrower’s
RepRisk index one year before the package initiation date. We also include the Num of facilities in the package,
log package amt, country of syndication - USA, and the borrower’s Public status as control variables. Industry
FE is based on the Fama-French 12 industry classification. Standard errors are clustered at the borrower level.
t-statistics for the regressions are reported in parentheses. *p <.1; **p <.05; ***p <.01.

similarly find that lenders have greater influence over the non-investment-grade
borrowers’ ESG policies.
Lastly, we posit that the bank’s impact is stronger among secured packages,
where a negative shock to the borrower could significantly increase the lender’s
liability risk. Strahan (1999) shows that loans to smaller borrowers, borrowers
with less cash, and borrowers who are difficult to value by outside investors are
more likely to be secured by collateral. Column 3 of Table 4 presents results
consistent with our hypothesis.

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ESG_diff × Investment grade

3.924∗∗∗
(8.18)
−0.077∗∗∗
(−4.74)

Corporate ESG Profiles and Banking Relationships

Chg_RRI j,t−1,t+1 = (RRI t+1 −RRI t−1 )×
(# of News Associated with I ssue j f rom t −1 to t +1)/

(3)

(T otal # of News Associated with All I ssues f rom t −1 to t +1),
where Chg_RRI j,t−1,t+1 is the change in borrowers’ RRIs attributable to issue
j from years t −1 to t +1. RRI t+1 and RRI t−1 are borrowers’ RRIs measured at
years t +1 and t −1, respectively.
Table 5 reports the regression results. We find that banks are more likely
to discipline borrowers along (1) climate change, (2) human rights abuse, and
(3) social discrimination. In contrast, their impact on other issues, including
executive compensation, is negligible. Note that the borrowers in our sample
are not in the news related to 3 of the 28 issues, where we mark the
regression results as n/a. Overall, other than the regression related to the issue
of animal mistreatment (am), our results confirm that banks have stronger
incentives to minimize negative exposures in borrowers’ catastrophic social
and environmental scandals in order to engage in future business.
2.6 Negative reputational news events and changes in banking
relationship
So far, we have demonstrated circumstances in which banks with high ESG
ratings have a positive influence on the evolution of their borrowers’ ESG ratings
over time. A natural question arises concerning what drives the mechanism of
this evolution? We can think of three possible mechanism in which banks may
influence their borrowers to improve their ESG performance over time. One
possibility is an “association” effect, in which borrowers tend to gradually
incorporate the viewpoints and policies of the parties they contract with
(including their bankers). A second scenario is that the bankers may take
active steps to encourage their borrowers to improve their ESG ratings over
time. While it is difficult for banks to explicitly and overtly mandate such
actions (in part because of lender liability concerns), they may take subtle
steps to use their “voice” to “nudge” borrowers to improve their ESG rating.

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2.5 Propagation of bank influence along E, S, and G
Arguably, creditors may react differently to certain borrower ESG-related
behaviors (Dimson, Karakaş, and Li 2015). We suspect that banks are
particularly concerned with controversial social and/or environmental issues
that would focus the spotlight on their lenders, thereby harming their reputation,
reducing their social capital, and ultimately diminishing the opportunities to
engage future business.
To further explore these issues, we analyze the lender’s impact across a
variety of ESG issues. RepRisk database tracks company negative news related
to 28 different issues spanning across E, S, and G dimensions. However, it does
not provide a “by issue” RRI. We construct a proxy of the borrower’s evolution
along the specific issues using the following method:

The Review of Financial Studies / v 35 n 7 2022

Table 5
ESG Issues and Bank Impact
Environmental issues

(1)
chg_rri_cc

(2)
chg_rri_lp

(3)
chg_rri_iol

(4)
chg_rri_oaw

(5)
chg_rri_wi

(6)
chg_rri_am

ESG_diff

0.0007∗∗
(1.975)

0.0001
(0.055)

0.0005
(0.550)

0.0000
(0.137)

−0.0004
(−0.730)

−0.0007∗
(−1.866)

Community issues

(1)
chg_rri_hra

(2)
chg_rri_ioc

(3)
chg_rri_lpi

(4)
chg_rri_sd

ESG_diff

0.0029∗∗
(1.977)

0.0016
(1.178)

0.0004∗∗
(2.138)

0.0009∗
(1.822)

(1)
chg_rri_fl

(2)
chg_rri_cl

(3)
chg_rri_foa

(4)
chg_rri_die

(5)
chg_rri_oh

(6)
chg_rri_pec

ESG_diff

0.0000
(0.117)

0.0002
(1.431)

0.0010
(1.135)

−0.0001
(−0.165)

0.0022
(1.393)

−0.0014
(−1.499)

Governance issues
ESG_diff

(1)
(2)
(3)
(4)
(5)
(6)
(7)
chg_rri_cbe chg_rri_ec chg_rri_mc chg_rri_fd chg_rri_te chg_rri_to chg_rri_ap
−0.0001
(−0.075)

0.0005
(0.782)

−0.0000
(−0.040)

−0.0012
(−0.594)

0.0000
(0.038)

0.0006
(0.977)

Cross-cutting Issues

(1)
chg_rri_cp

(2)
chg_rri_phe

(3)
chg_rri_voi

(4)
chg_rri_von

ESG_diff

0.0009
(1.509)

n/a
n/a

n/a
n/a

n/a
n/a

0.0007
(0.854)

(5)
chg_rri_sci
−0.0002
(−0.288)

This table reports the OLS regression of the change in the borrower’s RRI related to 28 issues. The abbreviation
of the specific issues are cc: Climate change, lp: Local pollution, iol: Impacts on landscapes, oaw: Overuse and
wasting, wi: Waste issues, am: Animal mistreatment, hra: Human rights abuses, ioc: Impacts on communities,
lpi: Local participation, sd: Social discrimination, fl: Forced labor, cl: Child labor, foa: Freedom of association,
die: Discrimination in employment, oh: Occupational health and safety, pec: Poor employment conditions, cbe:
Corruption, ec: Executive compensation, mc: Misleading communication, fd: Fraud, te: Tax evasion, to: Tax
optimization, ap: Anticompetitive, cp: Controversial products, phe: Health and environmental, voi: Violation of
international standards, von: National legislation, and sci: Supply chain. The ex ante difference between the bank
and borrower’s ESG ratings (ESG_Diff ) is defined as the difference between the bank and borrower’s RepRisk
indexes measured one year before the package initiation date. We compressed the coefficients of Lender_chg,
ESG_borrower, the Num of Facilities, log package amt, USA, and the borrower’s Public status. Year and industry
FEs are included. Industry classifications are based on the Fama-French 12 industry classification.
Standard errors are clustered at the borrower level. t-statistics are reported in parentheses.
*p <.1; **p <.05; ***p <.01.

A third possibility is that borrowers take steps to improve their ESG because
they want to ensure that the bank renews their loan and/or provides them
with additional financing over time. These “exit” concerns may be particularly
relevant for bank dependent borrowers who fear the disruption of their lending
relationship.
While they may be relevant, it is difficult to envision a series of empirical
tests that will convincingly support the first two possible mechanism. However,
it is possible to shed light onto the relevance of the third mechanism. In
this section, we answer this important second-stage question by examining
the relationship between the damages to the borrower’s reputation, and the
likelihood of initiating new loan(s) with the same lead lender within a 2-year
period centered on the original package’s end date. In this test, we define “a
hit to the borrower’s reputation” as one borrower-month where the borrower is

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Employee issues

Corporate ESG Profiles and Banking Relationships

covered in negative ESG-related news.20 We use “month” as the unit or window
of observation, rather than focusing on individual daily news stories because
many news stories originate from the same public-image fiasco, where a single
accident could lead to an ongoing saga that dribbles out over weeks. In this
study, we collectively refer to all news reports (if any) covered within the same
month as one negative reputational shock.
P r(Samei,j,te = 1) =φ(α +βN um Rep Eventi,ts,te +γ Xi,te−1 +Si,j
(4)
In the probit model, φ(.) denotes the cumulative distribution function (CDF)
of the standard normal distribution. samei,j,te is a dummy variable that equals
one if at least one of the lead lenders (j) in the original package extends a
new package to the borrower i within a 2-year period centered on the original
package’s end date, te. N um Rep Eventi,ts,te is the main explanatory variable
that measures the number of months with negative news coverage on the
borrower i from the start (ts) to the end (te) dates of the original package. Xi,te−1
is the vector of borrowers’ characteristics that we use as control variables. These
variables include the (1) ex ante level and (2) change in Book Leverage, size (log
assets), return on assets (Return on Assets), and Tobin’s q. Si,j denote additional
control variables that include the Original Package Length (in years), and the
Investment-grade dummy. IF F industry and δt , respectively, denote dummies for
Fama-French 12 industry, and year fixed effects. Finally, standard errors are
clustered at the borrower level.
Note that we restrict the regression sample to borrowers who received
at least one package financing within the 2-year period centered on the
original package’s end date. This mitigates concerns related to demand side
heterogeneities, because we are only looking at borrowers actively seeking
new loan financing. Table 1 reports the summary of statistics of key variables
in the test. Conditional on initiating new packages around the expiration of the
original package, 51% obtain it from exactly the same group of lead lenders,
56% are able to retain at least one of the lead lenders. The median length of the
original package is 3 years, and the median borrower experiences at least one
negative ESG-related reputational shock during this period.
Columns 1 and 2 of Table 6 report the results. The coefficient estimate of
Num rep event in column 1 is statistically significant, and negatively related
to the likelihood of retaining the same lead lender. It indicates that borrowers
with greater negative news coverage are more likely to switch lead lender(s)
after the end date of the original package, controlling for the length of the
original package. The coefficient in column 2 is significant at the 10% level,

20 RepRisk tracks firm-level negative news in its News database. Each piece of news coverage is recorded with a

specific news date and is mapped to a related ESG issue and/or topic. For details, please refer to the WRDS
RepRisk Data Manual.

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+Iff industry +δt +ξi,j,t )

The Review of Financial Studies / v 35 n 7 2022

Table 6
Negative reputational news incidents and switch in lending relationship
(1)
Same
All

(2)
Same
Public

Ind FE
Year FE
Cluster
N
Pseudo-R2

Yes
Yes
Yes
2,880
.035

Yes
Yes
Yes
1,903
.065

(4)
Same res
Public

−0.0546∗∗∗ −0.0278∗∗
(−5.60)
(−1.99)
0.0117∗∗∗
0.00245
(4.55)
(0.77)
−0.102
(−1.45)
−0.0387
(−0.19)
−0.0902
(−1.54)
0.595
(1.25)
−0.0415
(−1.25)
0.114
(0.42)
−0.0378
(−0.63)
0.603∗
(1.88)
−0.0907
(−1.16)
−0.125∗∗∗
(−4.78)
0.213∗∗
(2.41)

Yes
Yes
Yes
2,880
.027

Yes
Yes
Yes
1,903
.056

(5)
Same sgl
All

(6)
Same sgl
Public

−0.0704∗∗∗ −0.0624∗∗
(−3.01)
(−1.97)
0.0191∗∗∗
0.00843
(3.53)
(1.14)
−0.303∗∗
(−2.14)
0.128
(0.36)
−0.223∗∗
(−2.08)
1.951∗∗
(2.19)
0.0718
(1.15)
−0.0249
(−0.05)
−0.0484
(−0.44)
1.921∗∗∗
(2.83)
0.0394
(0.26)
−0.0598
(−1.22)
−0.0314
(−0.18)

Yes
Yes
Yes
950
.038

Yes
Yes
Yes
543
.079

This table reports the probit regression of the number of the borrower’s negative reputational news on the
likelihood of initiating new loan package(s) with the same lead lender from 12 months before, to 12 months
after the original package’s maturity date. Num Rep Event is the number of borrower-months with negative news
coverage from the start to the end dates of the original package. Same is the dummy variable that turns on if the
borrower initiates new package(s) with at least one of the same lead lenders from 12 months before, to 12 months
after the original package’s maturity date. Same res is defined more restrictively, as the dummy variable that turns
on if the borrower initiates new package(s) with exactly same group of lead lenders. Same sgl is defined most
restrictively, as the dummy variable that turns on if the original loan has a single lead lender, and the borrower
initiates new package(s) with the same lender. Note that we construct the sample to include only borrowers who
need new financing to minimize the demand side heterogeneity. ESG_borrower_start is the borrower’s adjusted
RepRisk index measured at the start date of the original package. Original package length refers to the number
of years between the start and end dates of the original package. Controls include the borrower’s ex ante level
and change (during the original loan window) in log assets, Book Leverage, Return on Assets, and Tobin’s q.
Industry FE is based on the Fama-French 12 industry classification. Year FE is based on the end year of the
original package. Standard errors are clustered at the borrower level. z-statistics are reported in parentheses. *p
<.1; **p <.05; ***p <.01.

after including all of the control variables and focusing on the public borrowers.
In column 3 and 4, we define the dependent variable more restrictively. Same
res (restrictive) is the dummy variable that turns on if the borrower initiates
new package(s) with exactly the same group of lead lenders within the 2-year
period centered on the original package’s end date. Our main results remain
statistically and economically robust to this variation. Finally, in columns 5

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−0.0489∗∗∗ −0.0242∗
(−4.99)
(−1.75)
ESG_borrower_start
0.0147∗∗∗
0.00401
(5.54)
(1.23)
Num of facilities
−0.107
(−1.58)
Book leverage
0.0762
(0.39)
Tobin’s q
−0.0432
(−0.75)
Return on assets
0.654
(1.48)
log assets
0.0273
(0.81)
Chg in book leverage
0.0705
(0.26)
Chg in Tobin’s q
0.00496
(0.08)
Chg in return on assets
0.562∗∗
(2.03)
Chg in log assets
−0.0531
(−0.68)
Original package length
−0.143∗∗∗
(−5.57)
Investment grade
0.0181
(0.20)

Num rep event

(3)
Same res
All

Corporate ESG Profiles and Banking Relationships

Lender_Diff =α +βN um Rep Eventi,ts,te +σ Samei,j,te
(5)
+γ Xi,te−1 +Si,j +Iff industry +δt +ξi,j,t .
Here, Lender_Diff is defined as the ESG rating of the lender(s) of the new
package minus the ESG rating of the lender(s) of the original package.
N um Rep Eventi,ts,te is the main explanatory variable that measures the
number of months with negative news coverage on the borrower i from the
start (ts) to the end (te) dates of the original package. Samei,j,te is a dummy
variable that equals one if at least one of the lead lenders (j) in the original
package extends a new package to the borrower i within a 2-year period centered
on the original package’s end date, te. Xi,te−1 is the vector of borrowers’
characteristics that we use as control variables. These variables include the
(1) ex ante level and (2) change in Book leverage, size (log assets), Return
on assets (ROA), and Tobin’s q. Si,j denote additional control variables that
include the Original package length (in years), and the Investment-grade
dummy. IF F industry and δt , respectively, denote dummies for Fama-French 12
industry, and year fixed effects. Finally, standard errors are clustered at the
borrower level.
Table 7 presents the corresponding results. The coefficients of
N um rep eventi,ts,te are positive and statistically significant in all of the
columns. It confirms that borrowers who are exposed in greater number of
reputational events obtain loan financing from lenders with much worse ESG
ratings at the expiration date of the original loan package. The coefficients
of the Samei,j,te are negative, and statistically significant in columns 1 and
2. We interpret the results as evidence that borrowers who switch lenders

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and 6, we define same sgl (single lead lender) most restrictively, as the dummy
variable that turns on if the original package has a single lead lender, and
the borrower initiates new package(s) with the same single lead lender within
the 2-year period centered on the original package’s end date. The economic
magnitudes in all regressions are sizable. Taking column 6, for example, which
has the most restrictive specification and richest set of controls, a marginal unit
increase in Num rep event is associated with a 0.03 decrease in the likelihood
of retaining the same lead lender(s). Here, the marginal effects of the probit
model (0.03) are estimated at the sample means.
Lastly, we examine the ESG profile of the new lead lender(s) as a function
of the number of borrowers’ reputational incidents during the original package
period. We posit that borrowers with deteriorating ESG profile are matched
to lenders with worse ESG ratings at the expiration of the original package.
Specifically, we look at the same sample of borrowers who received at least
one loan financing within the 2-year period centered on the original package’s
end date. Then we calculate the difference between the lender ESG rating of the
new package and the lender ESG rating of the original package, which we use
as the dependent variable. We perform an OLS regression using the following
specification:

The Review of Financial Studies / v 35 n 7 2022

Table 7
Negative reputational news incidents and change in lenders’ ESG profile

Num rep event
ESG_borrower_start
Same

(2)
Lender_diff
Public

(3)
Lender_diff
Public

(4)
Lender_diff
Public

0.912∗∗∗
(6.79)
−0.233∗∗∗
(−7.62)
−2.335∗∗∗
(−2.85)

1.258∗∗∗
(7.81)
−0.195∗∗∗
(−5.21)
−1.670∗
(−1.79)
0.877
(1.49)
1.238
(0.57)
−0.729
(−1.31)
5.224
(1.02)
−1.137∗∗∗
(−3.18)

1.235∗∗∗
(7.49)
−0.199∗∗∗
(−5.35)
−1.339
(−1.44)
1.120∗
(1.83)
−0.848
(−0.32)
−0.323
(−0.48)
1.226
(0.18)
−0.879∗∗
(−2.43)
−3.933
(−0.96)
0.908
(1.12)
−5.223
(−0.98)
2.581∗∗
(2.16)

0.510∗∗∗
(2.67)
−0.0836∗∗
(−2.22)
−0.195
(−0.21)
0.519
(0.82)
−0.415
(−0.16)
−0.125
(−0.19)
−1.090
(−0.16)
−0.0847
(−0.22)
−4.640
(−1.17)
0.586
(0.72)
−5.177
(−1.01)
1.666
(1.44)
3.041∗∗∗
(9.86)
0.502
(0.47)

Yes
Yes
Yes
2,698
.102

Yes
Yes
Yes
1,908
.113

Yes
Yes
Yes
1,796
.121

Yes
Yes
Yes
1,796
.163

Num of facilities
Book leverage
Tobin’s q
Return on assets
log assets
Chg in book leverage
Chg in Tobin’s q
Chg in return on assets
Chg in log assets
Original package length
Investment grade
Ind FE
Year FE
Cluster
N
Adj. R2

This table reports the OLS regression of the number of borrower-months with negative news coverage on the
changes in the lead lenders’ ESG ratings (average ESG ratings of the new lead lenders minus the average ESG
ratings of the lead lenders of the original package). The new group of lenders are the banks that lend money
to the borrower within 12 months of the original package’s expiration date. Num rep event is the number of
borrower-months with negative news coverage from the start to the end dates of the original package. Note that
we construct the sample to include only borrowers who successfully find new financing to minimize the demand
side heterogeneity. ESG_borrower_start is the borrower’s adjusted RepRisk index measured at the start date of
the original package. Same is the dummy variable that turns on if the borrower initiates new package(s) with at
least one of the same lead lenders from 12 months before, to 12 months after the original package’s maturity date.
Original package length refers to the number of years between the start and end dates of the original package.
Controls include the borrower’s ex ante level and change (during the original loan window) in log assets, Book
leverage, Return on assets, and Tobin’s q. Industry FE is based on the Fama-French 12 industry classification.
Year FE is based on the end year of the original package. Standard errors are clustered at the borrower level.
t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

generally engage lenders with worse ESG profiles, instead of pairing with
lenders with higher ESG standard. Taken together, we show that borrowers
with higher number of reputational events are more likely to switch lenders,
and also more likely to engage lenders with worse ESG ratings at loan
renewal.

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(1)
Lender_diff
All

Corporate ESG Profiles and Banking Relationships

3. Source of Endogeneity and Identification

3.2 Difference-in-differences analysis using bank mergers
Following Asker and Ljungqvist (2010), Hong and Kacperczyk (2010),
Ergungor et al. (2015), and Chen and Vashishtha (2017), our identification
strategy leverages the quasi-exogenous shocks to the bank’s ESG standard
arising from bank mergers. Specifically, we examine how borrowers react to
exogenous variations in the lead lender’s ESG standard. This DiD strategy is
best suited to our study for two reasons. First, it helps disentangle the selection
and treatment effects, by looking at shocks to lenders in the existing lending
relationships. In other words, the shocks take place after the borrower-lender
matching is completed. Second, the timing and the decision of bank M&A
activities are arguably exogenous to the borrowers’ firm-level unobservable
characteristics. As noted by prior studies, the bank merger waves were largely
driven by regulatory, technological, and competitive changes (Pilloff 2004).
We quantify the magnitude of the shock to the lender’s ESG standard by
incorporating the size effect. If the lender is the acquirer in the M&A, and the
target is extremely small relative to the acquirer, we assume that the shock to the
acquirer’s ESG standard post-M&A is virtually zero. Empirically, we calculate

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3.1 Source of endogeneity
We document that lenders have a direct and positive impact on the evolution
of borrowers’ ESG profile. However, interpreting the result as causal evidence
can be confounded by endogeneity concerns.
First, two types of selection problems are embedded in our current
framework. One concern is that borrowers with a certain level of ex ante ESG
rating (ESG_borroweri,t−1 ) may self-select to borrow from high ESG standard
banks. We alleviate this concern by controlling for the borrower’s ex ante ESG
rating. By holding the borrower’s ex ante ESG standard constant, we explore
how the difference in the bank’s ESG standard affect the borrower’s subsequent
improvement in ESG performance. The second type of selection bias is that
borrowers who expect to improve their ESG performance (ESG_chgi,t−1,t+1 )
may self-select to borrow from banks with high ESG standards. If this is the
case, the borrower’s ex post ESG change reversely leads to the establishment
of a lending relationship with a bank with high ESG standards.
Furthermore, there may be other omitted variables. A notable one is
the CEO’s awareness of/concern about ESG issues. Borghesi, Houston, and
Naranjo (2007) document various factors that motivate managers to make
socially responsible investments. In particular, borrowers with CEOs who are
attuned to ESG issues are more likely to improve their ESG performance over
time; at the same time, they are more likely to borrow from high-quality and
high ESG standard banks. This behavior simultaneously causes variations in
both the dependent and independent sides of the regression, which contaminates
the causal interpretation of the main results.

The Review of Financial Studies / v 35 n 7 2022

Table 8
Balancing table
Treatment

Control

Name

Mean

SD

Min

Max

Mean

SD

Min

Max

Package date
(initiation year-month)
RepRisk index
(ex ante)
Public (Y/N)
log assets

n/a

n/a

n/a

n/a

n/a

n/a

n/a

n/a

0.00

(0.00)

5.67 11.49

0

62

7.40

10.31

0

39

−1.73

(−1.48)

0.49
0
1
1.96 2.37 13.93

0.69
8.50

0.47
0
1
1.68 3.76 13.34

−0.08
−0.01

(−1.60)
(−0.06)

0.61
8.49

Diff-in-mean t-statistic

ESG_Shock j for the treatment group using the following specification, and
assign zero to all control units:
ESG_Shock j = (RRI a −RRI t )×Sizea /(Sizea +Sizet ),
if the lender j is the target
ESG_Shock j = −(RRI a −RRI t )×Sizet /(Sizea +Sizet ),

(6)

if the lender j is the acquirer.
We pair each treated loan one-to-one with a control unit using a method
similar to that used in Barko, Cremers, and Renneboog (2021). We first require
the control unit to be initiated in the same year-month as the treated loan.
This guarantees that the DiD inferences are not being driven by time-series
dynamics in the syndicated loan market. The second binding requirement is
that the borrower and the lender in the control unit must be different from the
borrower and the lender in the treated loan. Third, the borrower in the control
group is selected as the one with closest ex ante RRI (measured at the time
of package initiation) to that of the borrower in the treated group. This setup
ensures that the assignment of the treatment versus the control is orthogonal
to the main endogenous variable of interest, that is, borrowers’ historical RRI.
Finally, if multiple potential control units have the same ex ante borrower’s
RRI, we compare and pick the (control) borrower whose lender has the closest
ex ante RRI to that of the (treatment) borrower’s lender.
Table 8 reports on the balancing test between the ex ante characteristics of
borrowers in the treatment and control groups. Package date is the package
initiation date. RepRisk index is measured ex ante at the package start date,
rather than at the merger and acquisition date. Public refers to the public status
of the borrowers. log assets (if publicly available) compares the size of the
borrowers between the treatment and control group. The t-statistics of two-sided
difference tests are reported in parentheses. None of the reported characteristics
are statistically different across groups. Finally, we apply borrower fixed effects

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The following table reports the balancing test between the ex ante profiles of borrowers in the treatment and
control groups. Package date is the package initiation date. We construct the control group by selecting packages
initiated in the same year-month as the treated packages. RepRisk index is measured ex ante at the package
start date, rather than at the merger and acquisition date. Public refers to the public status of the borrowers. log
assets (if publicly available) compares the size of the borrowers between the treatment and control group. The
t-statistics of two-sided difference tests are reported in parentheses. *p <.1; **p <.05; ***p <.01.

Corporate ESG Profiles and Banking Relationships

in columns 3 and 4 of the DiD analysis (Table 9) to absorb any remaining
unobservable heterogeneity between the borrowers in the control and treatment
groups.
We present the DiD analysis in Table 9. To be consistent with the level of
observation in the earlier regressions, we conduct the analysis at the package
level, where we collapse facilities within the same package into one single
treatment or control observation. In columns 1 and 2, we employ the following
specification:
(7)

+γ Xi,j +Iffindustry +ξi,j,t ,
where i indexes borrower, j indexes lender, and t indexes the year of observation.
This specification represents a panel DiD regression of the borrower’s yearly
average RepRisk indexes (RRI i,t ) over a 4-year window around the M&A event.
The treatment group consists of all loans where the lender is involved in an
M&A event within a 5-year window after the package initiation date. We obtain
the yearly average RRI (if available) from 2 years before to 2 years after the
M&A date. ESG_Shock j is the quasi-exogenous variation to the lender’s ESG
standard in the merger and acquisition. P ostt dummy equals one if the year
of observation is after the M&A event date. We also include the log package
amt, country of syndication USA, the borrower’s Public status, and the Num of
Facilities in the package as control variables. Iff industry denote the dummies
for Fama-French 12 industry fixed effects. Finally, standard errors are clustered
at the borrower level.
Table 9 reports the main results from the DiD analysis. The key coefficient
estimates of the interaction term, ESG_Shock j ×P ostt , are positive and
statistically significant at the 1% level in columns 1 and 2. It indicates that
shocks to the lender’s ESG standard propagates through the lending relationship
post-M&A, causing a change in the borrower’s ESG performance in the same
direction, and in proportion to the magnitude of the quasi-exogenous shock to
the lender’s ESG rating. The significant coefficient related to Post captures an
upward trend in the RRI over time. In columns 3 and 4, we repeat the analysis
in columns 1 and 2 but replace the Post dummy with year FEs, and replace
the industry FEs with the borrower FEs. As expected, we observe a significant
reduction in the explanatory power of the control variables (absorbed by the
borrower FEs). The coefficient of the interaction term remains positive and
statistically significant at the 5% level, and our DiD inference is robust to
variations in specifications.
Admittedly, the limited sample of packages in the DiD analysis is drastically
different from the sample that we use in the rest of the study. The number
of borrowers whose lenders are involved in a M&A is very small. To make a
transparent comparison across different empirical specifications, we run an OLS
regression using the same specification in Table 2, but based on the DiD sample.
Each package only enters the regression once (instead of four times involving

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RRI i,t = α +βESG_Shock j ×Post t +ς ESG_Shock j +τ Post t

The Review of Financial Studies / v 35 n 7 2022

Table 9
Diff-in-diff analysis using bank mergers

ESG_shock × Post
ESG_shock
Post

(2)
ESG

(3)
ESG

(4)
ESG

0.186∗∗∗
(3.57)
0.130∗∗
(2.59)
2.212∗∗∗
(4.91)

0.180∗∗∗
(3.42)
−0.029
(−0.57)
2.122∗∗∗
(4.85)

0.143∗∗
(2.41)
−0.040
(−0.35)

0.147∗∗
(2.46)
−0.043
(−0.38)

0.265∗∗∗
(3.05)

0.026
(0.71)
−0.340
(−1.20)
1.066
(0.91)
3.872∗∗
(2.19)

−0.701∗∗∗
(−12.14)
−0.368∗
(−1.83)
1.396∗∗∗
(3.59)
−8.335∗
(−1.77)
1.284
(1.21)

No
Yes
Yes
Yes
1,879
.703

Yes
No
Yes
Yes
455
.398

ESG_borrower
−0.213∗∗∗
(−7.44)
2.546∗∗∗
(7.72)
−8.809∗∗∗
(−5.22)
4.031∗∗∗
(5.56)

Num of facilities
log package amt
USA
Public
Ind FE
Borrower FE
Year FE
Cluster
N
Adj. R2

Yes
No
No
Yes
1,851
.059

Yes
No
No
Yes
1,851
.235

No
Yes
Yes
Yes
1,879
.703

(5)
ESG_chg

This table reports the OLS regression of the borrower’s yearly average RepRisk indexes (ESG) over a 4-year
window around the M&A event. The sample consists of all packages where the lender is involved in a M&A event
within a 5-year window after the package initiation date, and the matched loan packages in the control group.
We obtain the yearly average RepRisk index (if available) from 2 years before to 2 years after the M&A date.
ESG_Shock is the exogenous variation to the lender’s ESG profile in the merger and acquisition. Post dummy
equals one if the year of the RepRisk index is after the M&A event date. In columns 3 and 4, we replace the
industry FEs and the Post dummy employed in columns 1 and 2 with the borrower and year FEs. We also include
the Num of facilities in the package, log package amt, country of syndication - USA, and the borrower’s Public
status as control variables. Industry FE is based on the Fama-French 12 industry classification. Standard errors
are clustered at the borrower level. t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

two yearly observations before and after the “shock”), and dependent variable
(ESG_Chg) is the evolution of the borrower’s RRI from before to after the
M&A. We present the results from the OLS regression in column 5 of Table 9.
The economic magnitudes are different but comparable: a unit increase in the
merged lender’s RRI is associated with a change of 0.14–0.19 in the borrower’s
RRI (columns 1–4), compared with a change of 0.27 in the borrower’s RRI if
we use the OLS specification.

4. Robustness Tests
In this section, we conduct several robustness tests to confirm our baseline
results related to borrower ESG rating evolution. Section 4.1 calculates the main
explanatory variable using the raw, instead of sector-month-adjusted RRIs.
Section 4.2 considers an alternative method of defining lead lender(s). Section
4.3 examines alternative sampling criteria. Section 4.4 analyzes alternative
specifications.

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(1)
ESG

Corporate ESG Profiles and Banking Relationships

Table 10
Robustness tests
(1)
ESG_chg
Unadjusted_ESG_diff

(3)
ESG_chg

(4)
ESG_chg

0.013
(1.05)
−0.526∗∗∗
(−23.46)
−0.744∗∗∗
(−4.07)
1.939∗∗∗
(13.28)
−2.896∗∗
(−2.04)
1.203∗∗∗
(3.96)

0.031∗∗
(2.34)
0.001
(0.04)
−0.559∗∗∗
(−14.33)
−0.426
(−1.27)
1.157∗∗∗
(4.88)
−6.239∗∗∗
(−2.79)
1.369∗∗∗
(2.84)

0.030∗∗∗
(3.68)
0.028∗∗
(2.33)
−0.522∗∗∗
(−21.42)
−0.766∗∗∗
(−3.77)
1.881∗∗∗
(12.19)
−2.218
(−1.42)
1.039∗∗∗
(3.07)

0.037∗∗∗
(3.67)
0.018
(1.36)
−0.511∗∗∗
(−18.97)
−0.727∗∗∗
(−3.39)
2.126∗∗∗
(12.87)
−1.165
(−0.67)
0.792∗∗
(2.24)

Yes
Yes
Yes
8,104
.262

Yes
Yes
Yes
2,137
.238

Yes
Yes
Yes
6,864
.265

Yes
Yes
Yes
6,090
.265

0.022∗∗∗
(2.88)

ESG_diff
Lender_chg
ESG_borrower
Num of facilities
log package amt
USA
Public
Ind FE
Year FE
Cluster
N
Adj. R2

This table reports on four robustness tests for the baseline result of ESG evolution. Column 1 presents the results
if ESG_Diff variable is calculated without sector-month adjustments. Sample in column 2 include only packages
with a unique lead arranger in the syndicate. In column 3, we repeat the baseline estimation based on the ESG
rating of the lead lender with the strongest relationship with the borrower, instead of averaging the ESG ratings
of the lead arrangers in the syndicate. Finally, column 4 presents the results under alternative sample selection
criteria: USD-denominated packages of nonfinancial and nonutility U.S. firms. The change in the borrower’s
ESG profile (ESG_Chg) is defined as the difference between the borrower’s RepRisk indexes one year after and
one year before the package initiation date. The ex ante difference between the bank and borrower’s ESG ratings
(ESG_Diff ) is defined as the difference between the bank and borrower’s RepRisk indexes measured one year
before the package initiation date. ESG_Borrower controls for the potential path dependency problem and is
defined as the borrower’s RepRisk index one year before the package initiation date. We also include the Num
of Facilities in the package, log package amt, country of syndication - USA, and the borrower’s Public status
as control variables. Industry FE is based on the Fama-French 12 industry classification. Standard errors are
clustered at the borrower level. T-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

4.1 Measuring ESG rating differences between borrowers and lenders
In our main specifications, we adjust both the borrower and lender ESG ratings
by the sector-month averages. This alleviates the potential concerns about the
comparability of ESG ratings across industries and years.
We now investigate whether our results are sensitive to using raw ESG ratings
of lenders and borrowers when comparing their relative standing. Table 10,
column 1, presents the results. We find that the direction of impact does not
change, and the level of statistical significance remain at the 1% level.
4.2 Lender profiles, single lead loans, and strongest relationship lead
lenders
In our main specifications, when there are multiple lead lenders in the package
syndicate, we calculate the lead lenders’ ESG rating by taking the average
lender ESG rating for each package. Which lender dictates the relationship
and influences the borrower is unclear; therefore, we follow this conservative

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(2)
ESG_chg

The Review of Financial Studies / v 35 n 7 2022

4.3 Sample selection criteria
A third robustness check is related to sample selection criteria. In our main
regressions, we aim to censor as few observations as possible from the DealScan
database, if we are not clearly guided, theoretically and empirically, by earlier
works to do so. In this section, we test our findings to the usage of a few
additional sample selection criteria. Specifically, we require the packages to be
USD denominated, and issued by nonfinancial, nonutility borrowers. Column
4 of Table 10 presents our findings under these criteria. We find that our results
are robust under this approach. Overall, the robustness tests confirm our finding
that high ESG rating lenders influence their borrowers in their ESG policies.
4.4 Alternative specification
In our main analysis, we regress the improvement in the borrower’s ESG over
time, on the ex ante difference between the lender and borrower’s ESG ratings,
while controlling for the borrower’s ex ante ESG standard. This empirical
specification views each package initiation as an “event” and makes sure each
package enters only once into the analysis. The empirical design alleviates
concerns on the stacking of sticky ESG scores/ratings in the panel regression.
In this section, we repeat our baseline analysis in Table 2 using levels, rather
than changes, as the main variables of interest. Our regressions follow the
specification below:
RRI_Borrower t+1 = α +βRRI_Lender t−1 +ς RRI_Borrower t−1
+τ Lender_Chgj +γ Xi,t−1 +Iffindustry

(8)

+δt +ξi,j,t .

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approach. However, would the results change if we were to instead choose one
of the lead lenders randomly, or if we have followed an alternative approach?
We empirically address this robustness concern in this section.
We first start with a conservative, simplistic approach, in which we run the
baseline estimation for the subsample of packages where a single unique lead
lender is in the syndicate. Column 2 of Table 10 presents the results. We find
that our results are unchanged for the subsample of packages where we have a
single lender.
Other alternative approaches to choosing lead lenders include choosing the
lead lender with the strongest historical relationship with the borrower or
randomly choosing one of the lead lenders as the lead for the package. We
test the former approach as it is more intuitive (Ivashina and Kovner 2011).
We classify the “strongest relationship” lead-lender as the lead lender who
financed the greatest fraction of loan amount in the past 5 years before the
current package. Column 3 shows our results under this alternative approach.
We again find that if the lender has a better ESG rating, the borrower’s ESG
rating is more likely to improve.

Corporate ESG Profiles and Banking Relationships

5. Conclusion
Our study demonstrates that banks profoundly influence firms’ ESG policies.
We find that banks are significantly more likely to partner with borrowers who
have similar ESG ratings. This result suggests that ESG policies influence
the construction of bank lending relationships and that different banks have
different attitudes toward borrower ESG policies. Our findings echo the
mounting anecdotal evidence where banks have announced that they are cutting
off lending in response to a borrower’s reputational shock related to ESG issues.
We also find that banks have a dynamic influence on their borrowers’
subsequent ESG performance. Notably, firms that borrow from banks with
relatively better ESG profiles are more likely to improve their own ESG
performance over time. By examining the decisions on loan renewal, we show
that borrowers who continue to engage in risky ESG practice are subject
to costly disruptions in lending relationships. We also find that banks are
more likely to influence bank-dependent borrowers, and that their influence is
predominantly concentrated among environmental and social issues that likely
focus the spotlight on the lenders, leading to severe reputational and financial
consequences. Overall, our work demonstrates a novel channel by which a key
stakeholder can profoundly promote socially responsible decision-making.

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RRI_Borrower t+1 is defined as the level of borrowers’ RepRisk indexes (rather
than the change) one year after the package initiation date. RRI_Lender t−1 is
defined as the level of lenders’ RepRisk indexes one year before the package
initiation date. RRI_Borrower t−1 is defined as the level of borrowers’ RepRisk
indexes one year before the package initiation date. We also include the
log package amt, country of syndication USA, the borrower’s Public status,
and the Num of Facilities in the package as control variables. In column 5,
we perform a subsample analysis in the public space only, and control for
borrowers’ financials, including log assets, Book leverage, Return on assets, and
Tobin’s q. Note that the level of observation in this case are at the package level.
Each package only enters once into the regression, and the year t is defined as
the year of package initiation.
Appendix A.5 reports the results. In columns 1, 2, 3, and 4, the coefficients
are statistically significant and economically sizable. Column 5 presents the
subsample analysis focusing on public borrowers only. The t-statistic is not
significant at the 10% level, but the economic magnitude remains comparable
to estimates in earlier columns.

The Review of Financial Studies / v 35 n 7 2022

Table A.1
Variable Definitions
Variable name
ESG_chg
ESG_borrower
Lender_chg

ESG_diff

Secure
log package amt
Public
log assets
Book leverage
Return on assets
Tobin’s q
Size of target
Size of acquirer
ESG_diff_MA
ESG_shock

Source

The change in the borrower’s RepRisk index from one year before, to
one year after the package initiation date
The RepRisk index of the borrower measured one year before the
package initiation date
The change in the lead lender’s RepRisk index from one year before, to
one year after the package initiation date. If there is more than one
lead lender, use the average of the changes
The difference between the lead lender and borrower’s
sector-month-adjusted RepRisk indexes measured one year before
the package initiation date. If there is more than one lead lender, use
the average of the differences
Number of facilities in the package
An indicator that equals one if the borrower is rated, and zero otherwise
An indicator that equals one if the borrower is investment grade, and
zero otherwise
An indicator that equals one if the loan is secured, and zero otherwise
The natural logarithm of the size of the syndicated package
An indicator that equals one if the borrower firm’s equity is publicly
traded, and zero otherwise
The natural logarithm of the borrower’s total assets (in millions) at the
latest fiscal period that ended prior to package start date
The ratio of total book debt to total assets
The ratio of net income to total assets
The ratio of market value of total assets to the book value of total assets
The M&A transaction value divided by the percentage of target
acquired (in millions)
Value of the acquirer’s asset LTM (in millions)
The difference between the acquirer and target’s RepRisk indexes at the
time of the M&A
The shock to the ESG standard of the lender introduced by the M&A
transaction, adjusted by the relative sizes of both parties involved in
the transaction

RepRisk
RepRisk
RepRisk

RepRisk

DealScan
Compustat
Compustat
DealScan
DealScan
CRSP
Compustat
Compustat
Compustat
Compustat
SDC
SDC
RepRisk, SDC
RepRisk, SDC

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Num of facilities
Rated
Investment grade

Description

Corporate ESG Profiles and Banking Relationships

Table A.2
Reputational risk exposure and risk-adjusted capital ratios
(1)
Tier 1
ESG_lag

0.0194∗∗
(2.61)

Num_news

(2)
Tier 1

0.00911∗∗∗
(2.90)

Num_news_H

(3)
Tier 1

0.0132∗∗∗
(3.14)

(5)
Tier 1

(6)
Tier 1

0.0241∗∗
(2.46)

Num_news_env

0.0429
(1.37)

Num_news_soc

0.0267∗∗∗
(2.84)

Num_news_emp
Bank FE
Month FE
Cluster by bank
N
Adj. R2

Yes
Yes
Yes
1,340
.607

Yes
Yes
Yes
1,340
.616

Yes
Yes
Yes
1,340
.616

(7)
Tier 1

Yes
Yes
Yes
1,340
.609

Yes
Yes
Yes
1,340
.606

Yes
Yes
Yes
1,340
.606

0.0806∗∗
(2.41)

Yes
Yes
Yes
1,340
.609

This table reports the OLS regression of the bank’s ESG and business conduct risk on the level of risk-adjusted
Tier 1 capital ratio. The level of observation is on the bank-quarter level. ESG_lag is the RepRisk index of
the bank at t-1 (lagged quarter). Num_news is the number of negative news coverage from t-5 to t-1 (in
quarters). Num_news_H and Num_news_VH count the number of high impact and very high impact negative
news coverage during the same window. Num_news_env, Num_news_soc, and Num_news_emp count the number
of negative news coverage related to environmental, social, and employee issues during the same window. Bank
and month fixed effects are included to place the focus on within-bank variations and to preclude the impact
of common time trends. Standard errors are clustered at the bank level. t-statistics are reported in parentheses.
*p <.1; **p <.05; ***p <.01.

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Num_news_VH

(4)
Tier 1

The Review of Financial Studies / v 35 n 7 2022

Table A.3
Loan pricing and RRI

log borrower RRI
log lender RRI

(2)
log spread

(3)
log spread

−0.002
(−0.42)
−0.007∗
(−1.76)

−0.005
(−1.05)
−0.007∗
(−1.72)

−0.021∗∗∗
(−3.85)
−0.049∗∗∗
(−9.00)

−0.032∗∗∗
(−4.56)
−0.032∗∗∗
(−5.45)
−0.034∗
(−1.69)
0.013
(0.31)
−0.053∗∗∗
(−6.64)
0.006
(1.16)
−0.283∗∗∗
(−2.94)
−0.066∗∗∗
(−7.65)
4.025∗∗∗
(8.29)
0.002∗∗∗
(6.75)
0.019∗∗∗
(6.30)
0.246∗∗∗
(16.26)
−0.060∗∗∗
(−4.47)
−0.020
(−1.47)
0.223∗∗
(2.21)

−0.008
(−1.04)
−0.008∗
(−1.70)
0.001
(0.52)
−0.032∗∗∗
(−4.56)
−0.032∗∗∗
(−5.44)
−0.034∗
(−1.70)
0.013
(0.32)
−0.053∗∗∗
(−6.64)
0.006
(1.17)
−0.284∗∗∗
(−2.95)
−0.065∗∗∗
(−7.63)
4.017∗∗∗
(8.27)
0.002∗∗∗
(6.75)
0.019∗∗∗
(6.28)
0.245∗∗∗
(16.23)
−0.060∗∗∗
(−4.47)
−0.020
(−1.46)
0.223∗∗
(2.21)

log borrower RRI × log lender RRI
log assets
log amount
Commercial paper rating
Book leverage
Tobin’s q
Current ratio
Return on assets
log interest coverage
Stock volatility
Maturity
Num leads
Secured dummy
Covenant dummy
Performance pricing
Prime base rate
FEs
N
Adj. R2

6,582
.550

ratings score, revolver dummy, industry, year
4,914
4,914
.615
.615

This table examines the relationship between loan spread and both the borrower and lender’s RRI at the facility
level. Control variables include the log assets, log loan amount, commercial paper rating, book leverage, Tobin’s
q, return on assets, current ratio, log interest coverage, stock volatility, loan maturity, number of lead lenders,
secure (dummy), covenant (dummy), performance pricing, and prime base rate. We include ratings score, revolver
dummy, industry, and year FEs. t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

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(1)
log spread

Corporate ESG Profiles and Banking Relationships

Table A.4
Evolution in corporate ESG profile and bank lending: Placebo tests on empirical model
(1)
Randomized

ESG_diff
Lender_chg
ESG_borrower

(2)
(3)
One-to-one replacement
ESG_chg

ESG_chg

−0.004
(−0.59)
0.008
(0.99)
−0.599∗∗∗
(−39.94)

−0.00228
(−0.27)
−0.00351
(−0.26)
−0.491∗∗∗
(−26.24)
1.629∗∗∗
(4.25)

−0.0102
(−1.02)
−0.0118
(−0.79)
−0.652∗∗∗
(−33.02)

Yes
Yes
Yes
6,946
.238

Yes
Yes
Yes
4,941
.340

Public
log assets
Book leverage
Return on assets
Tobin’s q
Ind FE
Year FE
Cluster
N
Adj. R2

Yes
Yes
Yes
10,000
.270

2.176∗∗∗
(22.00)
−1.599∗∗∗
(−3.26)
−0.786∗∗
(−1.99)
0.191∗∗
(2.08)

The following table reports the OLS regression of the evolution in the borrower’s ESG profile on the ex ante
difference between the bank and borrower’s ESG ratings. The change in the borrower’s ESG profile (ESG_Chg)
is defined as the difference between the borrower’s RepRisk indexes over a 2-year window, from one year before
to one year after the package initiation date. The ex ante difference between the bank and borrower’s ESG ratings
(ESG_Diff ) is defined as the difference between the bank and borrower’s RepRisk indexes measured one year
before the package initiation date. Lender_Chg controls for the evolution in the lender’s ESG indexes over the
same 2-year window. ESG_Borrower controls for the potential path dependency problem and is defined as the
borrower’s RepRisk index one year before the package initiation date. In column 1, we use the sample consisting
of 10,000 randomly constructed borrower-lender pairs with randomized package initiation dates. In columns 2
and 3, we replace the borrower in Table 2 “one-to-one” using propensity score matching. Appendix A.1 defines
the variables in detail. Industry FE is based on the Fama-French 12 industry classification. Standard errors are
clustered at the borrower level. t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

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ESG_chg

The Review of Financial Studies / v 35 n 7 2022

Table A.5
Alternative specification
(2)
RRI_borrowert+1
All

(3)
RRI_borrowert+1
All

(4)
RRI_borrowert+1
All

(5)
RRI_borrowert+1
Public

0.0217∗∗∗
(3.81)
0.554∗∗∗
(57.49)
0.0322∗∗∗
(3.11)

0.0217∗∗∗
(3.36)
0.554∗∗∗
(25.62)
0.0322∗∗∗
(2.82)

0.0140∗∗
(2.03)
0.544∗∗∗
(23.45)
0.0229∗
(1.91)

0.0130∗
(1.95)
0.453∗∗∗
(21.70)
0.00890
(0.76)
−0.794∗∗∗
(−4.25)
1.992∗∗∗
(13.59)
−2.906∗∗
(−2.02)
1.228∗∗∗
(4.04)

0.00906
(1.06)
0.372∗∗∗
(16.28)
0.0196
(1.36)
0.00739
(0.04)
0.554∗∗∗
(2.59)
−0.196
(−0.12)

RRI_lendert−1
RRI_borrowert−1
Lender_chg
Num of facilities
log package amt
USA
Public

2.396∗∗∗
(12.95)
−2.272∗∗∗
(−2.83)
−1.682
(−1.32)
0.771∗∗∗
(3.75)

log assets
Book leverage
Return on assets
Tobin’s q
Industry FE
Year FE
Cluster
N
Adj. R2

No
No
No
8,128
.295

No
No
Yes
8,128
.295

Yes
Yes
Yes
8,104
.303

Yes
Yes
Yes
8,104
.340

Yes
Yes
Yes
5,120
.402

This table replicates the analysis in Table 2 using a different specification. RRI _Borrower t+1 is defined as the
level of borrowers’ RepRisk indexes one year after the package initiation date. RRI _Lender t−1 is defined as the
level of lenders’ RepRisk indexes one year before the package initiation date. RRI _Borrower t−1 is defined as
the level of borrowers’ RepRisk indexes one year before the package initiation date. We also include the Num
of facilities in the package, log package amt, country of syndication - USA, and the borrower’s Public status
as control variables. In column 5, we perform a subsample analysis in the public space only, and control for
borrowers’ financials, including log assets, Book leverage, Return on assets, and Tobin’s q. Appendix A.1 defines
the variables in detail. Industry FE is based on the Fama-French 12 industry classification. Standard errors are
clustered at the borrower level. t-statistics are reported in parentheses. *p <.1; **p <.05; ***p <.01.

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(1)
RRI_borrowert+1
All

Corporate ESG Profiles and Banking Relationships

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