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Leveraging the Disagreement on Climate
Change: Theory and Evidence

WP 23-01

Laura Bakkensen
University of Arizona
Toan Phan
Federal Reserve Bank of Richmond
Tsz-Nga Wong
Federal Reserve Bank of Richmond

Leveraging the Disagreement on Climate Change:
Theory and Evidence
Laura Bakkensen+

Toan Phan∗

Tsz-Nga Wong∗

December 30, 2022

Abstract
We theoretically and empirically investigate how climate risks affect collateralized debt markets. First, we develop a debt model where agents have different
beliefs over a long-run risk. In contrast with existing two-period competitiveequilibrium models, our infinite-horizon competitive-search model predicts more
pessimistic agents are more likely to make leveraged investments on risky collateral assets. They also tend to use longer maturity debt contracts, which are more
exposed to the long-run risk. Second, employing large data on real estate and
mortgage transactions, combined with high resolution sea-level-rise maps, we find
robust evidence for these findings. We also show how monetary and securitization
policies affect mortgage climate risk exposure. Our results highlight the importance of heterogeneous beliefs in understanding the effects of climate change on
the financial system.
Keywords: climate finance, sea level rise, heterogeneous beliefs, real estate,
mortgage, search and matching, monetary policy.
∗
The Federal Reserve Bank of Richmond; + University of Arizona.
Contacts: laurabakkensen@arizona.edu, toan.phan@rich.frb.org, and russell.wong@rich.frb.org. The views expressed
here are those of the authors and should not be interpreted as those of the Federal Reserve Bank of
Richmond or the Federal Reserve System. We are grateful for very helpful comments from our discussants Asaf Bernstein and Constantine Yannelis. We are also grateful for very helpful suggestions
from Mark Bils, Gadi Barlevy, Eduardo Dávila, Pablo Kurlat, Ryan Lewis, Miguel Molico, Ricardo
Reis, Guillaume Rocheteau, Esteban Rossi-Hansberg, Pierre-Daniel Sarte, and Felipe Schwartzman.
We also thank seminar and conference participants at the San Francisco Fed Virtual Seminar on Climate Economics, the PHBS Sargent Institute for Macro-Finance workshop, the Virtual East Asia
Macroeconomic Seminar series, the OCC Symposium on Climate Risk, the Society for Economic Dynamics meeting, Stanford Institute for Theoretical Economics workshop on New Frontiers in Asset
Pricing, Asia Meeting of the Econometric Society, the Richmond Fed, the Chicago Fed, the University
of Virginia–Richmond Fed–Duke University research workshop, the Chicago-area Housing and Macro
Conference, Notre Dame University, the University of Hong Kong, Jinan University, the University
of Arizona, the University of California Irvine, the Federal Housing Finance Agency, and the Bank
of Canada. We thank Rosemary Coskrey, Claire Conzelmann, and Elliot Tobin for excellent research
assistance. All errors are our own.

1

Introduction

Understanding how climate change may affect financial markets is a question of primary
importance to researchers, financial regulators, and policymakers around the world.1 A
rapidly growing “climate finance” literature is investigating the extent to which climate
risks affect asset markets, especially how sea level rise risks affect housing prices (Bernstein et al. 2019; Baldauf et al. 2020; Bakkensen and Barrage 2022). However, much less
is known about how climate risks affect debt markets, especially the mortgage market,
despite the critical role these markets play in the financial system and in past financial
crises (Phan 2021). This is likely because theoretically and empirically understanding
how credit markets allocate an emerging source of risk is nontrivial, in part due to
the agency problems that naturally arise in borrower-lender relationships (Tirole 1999;
Allen and Gale 2000). These complications compound when there is belief disagreement
across economic agents about future risks (Geanakoplos 2010; Simsek 2013), and belief
disagreement is especially pronounced for climate change (Howe et al. 2015; Ballew et al.
2019). A hypothesis common in policy discussions is that those who are less concerned
about climate risks (the “optimists”) are more likely to make leveraged investment on
assets exposed to climate risks – such as coastal real estate properties – relative to those
who are more concerned about climate risks (the “pessimists”) (e.g., Litterman et al.
2020; Brunetti et al. 2021). In fact, this hypothesis is consistent with the benchmark
prediction in standard models of leveraged investments under belief disagreement (e.g.,
Geanakoplos 2010; Simsek 2013; Fostel and Geanakoplos 2015).
In this paper, we provide novel theoretical predictions and empirical evidence on how
climate risks affect the mortgage market. We start by developing a parsimonious model
of a competitive collateralized credit market under belief disagreement, building upon
the literature that follows the pioneering work of Geanakoplos (2010). We introduce
two empirically-relevant elements: endogenous maturity choice and search frictions.
The maturity dimension is especially relevant for the context of climate change for two
reasons: (i) most of the damages from climate change will occur in the future, and
hence (ii) a contract with a longer maturity is naturally more exposed to climate risks
than a shorter contract. By allowing debt contracts to have different maturity lengths,
the model allows for a new channel where pessimistic borrowers can gain by trading
their exposure to the long-run risks with relatively more optimistic lenders.2 We show
that this new gain from trade can “overturn” the conventional prediction in standard
1

See, e.g., the recent reports on climate change and financial stability by the NGFS (Network for
Greening the Financial System 2019), by the Financial Stability Oversight Council (Council 2021),
by the U.S. Commodity Futures Trading Commission (Litterman et al. 2020), by the Federal Reserve
(Brunetti et al. 2021), and the Executive Order on Tackling the Climate Crisis by the White House.
2
We refer to this phenomenon as “leveraging the belief disagreement” in the title of the paper.

1

models of belief disagreement.
More specifically, we consider an infinite-horizon environment where the collateral
assets (e.g., coastal real estate properties) are exposed to a potentially damaging disaster risk in the long run (e.g., inundation due to sea level rise). We assume belief
heterogeneity in a simple way: borrowers (e.g., homebuyers) and lenders (e.g., banks
and buyers of mortgage-backed securities) disagree on the rate at which the disaster
arrives. More optimistic agents believe that the disaster will happen far into the future,
while more pessimistic ones believe that the it will happen sooner. Everyone’s belief is
common knowledge and agents agree to disagree.
A collateralized long-term loan (e.g., mortgage) is a contract where a lender loans
an amount to a borrower in exchange for a promise of a repayment stream by the
borrower until a maturity date. The borrower chooses the loan amount, repayment
stream, and the maturity of the contract. The borrower can always default before
the contract matures, but in doing so she will lose the collateral asset and face an
exogenous default cost. There is a competitive search process that matches the borrower
with a lender with an endogenous probability, which we call the leverage probability.
The equilibrium leverage probability depends on the loan amount, promised payment
stream, and maturity. This probability is a key moment from the model that maps to
the probability that a housing transaction is associated with a mortgage contract in the
data. Note that if the collateral asset is sufficiently exposed, then when the disaster
shock eventually hits, it will be optimal for the borrower to default and surrender the
damaged collateral to the lender. This linkage between the disaster risk and the default
risk will be important in determining equilibrium outcomes.
The model yields clear analytical results. If the underlying collateral asset is sufficiently exposed, then the equilibrium leverage probability and the equilibrium maturity are both increasing in the degree of borrower pessimism (relative to the beliefs of
lenders). At the extensive margin, purchases of exposed properties by pessimists are
more likely to be financed with debt. At the intensive margin, these debt contracts
tend to have longer maturity. These are two key implications of the model that we will
test in the data. Note that these predictions are in contrast to those of the standard
models of belief disagreement (e.g., Geanakoplos 2010; Simsek 2013), which assume exogenous debt maturity and predict that pessimists are less likely to leverage and have
no prediction on the maturity dimension.3
Figure 1 illustrates the intuition.4 In the absence of long-term insurance contracts,
a defaultable long-term debt contract provides implicit insurance against the long-run
3

Most existing models of credit markets with belief disagreement shut down the endogeneity of debt
maturity, either explicitly or implicitly, by assuming a two-period environment, where the maturity is
automatically fixed to be the duration between the two periods. See the related literature section.
4
We thank Asaf Bernstein for suggesting this illustration.

2

climate risk. And this insurance service is more valuable for more pessimistic agents.
Hence, there is a gain from trading a long-term debt contract, collateralized by the risky
asset, between a relatively optimistic lender and a relatively pessimistic borrower. The
pessimistic borrower believes that the disaster will happen soon, and when it does, she
knows that it will be optimal for her to default. All else equal, given that she expects
an early default, she would like to back-load the repayment promises. She could do so
by choosing a long-maturity debt contract, which stretches the payment stream over
a long horizon. On the other hand, the relatively more optimistic lender believes that
the disaster will happen later and thus does not assign a high default risk to the debt
contract. In sum, the belief disagreement gives rise to a gain from trading a defaultable
debt contract with long maturity.
Equilibrium maturity Tmature

Pessimistic borrower expects earlier disaster
(higher Pr[tdisaster < Tmature ])

Time t

Lender expects later disaster
(lower Pr[tdisaster < Tmature ])

Gain from trade

Figure 1: Illustration of the model’s main intuition.
We further show that the leveraging of the belief disagreement depends on macroeconomic factors that affect general credit conditions. One factor of particular relevance
is monetary policy. We provide an extension of the model where borrowers and lenders
have different funding costs, which depend on the interest rate sets by a monetary authority. We show that an expansionary monetary policy (e.g., a decrease in the Fed’s
interest rate) increases the equilibrium leverage probability by pessimists (effect at the
extensive margin). However, the policy does not affect the equilibrium maturity (no
effect at the intensive margin). These are two additional testable implications that we
can empirically evaluate.
Finally, we extend the model to endogenize the asset prices by allowing for a Nash
bargaining between buyers and a set of sellers. The extension implies rather intuitively
that, all else equal, the pricing of the long-run risk increases with the buyer’s pessimism.
This is another natural implication that we test in the data.
Next, we evaluate the testable implications of the model by analyzing the effects of
long-run sea level rise (SLR) risks on the mortgage market. We focus on SLR not only
because it is one of the most salient dimensions of climate change projected to affect
millions of households in the U.S.,5 but also because it is one type of climate risk that
5

For example, as highlighted in the Fourth National Climate Assessment (Fleming et al. 2018),

3

has been well documented with high-resolution spatial variation (see Figure 4 for an
illustration). We employ an extensive proprietary data set of real estate and mortgage
transactions provided by CoreLogic, a large data vendor, to examine the complete sales
history of single-family homes along the U.S. Atlantic Coast from 2001 to 2016.
We match each property’s coordinates with its projected exposure to permanent
coastal inundation under various long-run SLR scenarios, using the National Oceanic
and Atmospheric Administration’s (NOAA) state-of-the-art SLR mapping tool as well
as a series of additional control variables. Employing this large-scale yet highly granular data and additionally conditioning on a rich set of fixed effects, our identification
strategy is to compare the observable mortgage outcomes between the transactions
of properties that have different SLR risk exposure but are otherwise very similar in
other dimensions: having the same ZIP code, distance to coast, elevation, number of
bedrooms, year and month of sale, and mortgage lender.
To assign whether the buyer in a transaction is a (likely) pessimist or (likely) optimist regarding the underlying exposure of the house to future SLR risks, we follow the
most recent development in the climate finance literature (e.g., Bernstein et al. 2019
and Baldauf et al. 2020 – henceforth BGL and BGY, respectively) and rely on Yale
Climate Opinion Survey (Howe et al. 2015)’s national survey of public perception on
global warming. This database provides information on the fractions of adults in each
county who believe that global warming is happening, are worried about it, or believe
that it will harm them in the near future. For each property transaction, we match the
geographic location of where the buyer comes from to the respective county’s climate
belief measure. The key assumption in this matching is that a buyer who comes from a
county with a more pessimistic belief measure is more likely to have a pessimistic belief
herself.6
Our empirical results are as follows. First, in re-estimating the classic hedonic
housing price regression, after our rich set of fixed effects disentangles the SLR risk
capitalization from the effects of coastal amenity values, we find that at-risk properties
(those projected to be permanently inundated at six feet of SLR) sell at a 6% discount
on average, relative to similar but less-at-risk properties. The sign and magnitude of
our estimates align closely with the previous literature’s findings on the capitalization
of SLR risks in the coastal real estate market (e.g., BGL and BGY) and are robust to
various alternative measures of SLR risks and econometric specifications.
more than 40% of Americans live in coastal shoreline counties subject to SLR inundation risk.
6
In a related paper outside of the climate context, Meeuwis et al. (2021) exploit a large proprietary
household financial data set to evaluate the implications of the belief disagreement between (likely)
Republicans and (likely) Democrats for equity investment decisions after the 2016 presidential election.
Due to a data limitation similar to ours, the authors cannot observe households’ equity belief or political
affiliation. Instead, they devise ways to assign whether a household is a (likely) Democrat or (likely)
Republican.

4

Second, we find robust evidence for the model’s main implication on the relationship between risk exposure and the extensive margin of the leverage probability. The
transaction of an at-risk property has an approximately two percentage points higher
probability of being associated with a mortgage (relative to that of a similar but lessat-risk property), indicating higher leverage probabilities for riskier investments. The
magnitude is economically significant – two percentage points is about a half of the rise
in the share of property transactions that are leveraged in our data between 2001 (the
beginning of our sample) and 2007 (the peak of the housing boom before the Great
Recession).
Importantly, consistent with our theory, we find that belief disagreement is a key
moderator of the relationship between climate risk exposure and leverage at the extensive margin. Buyers who are more likely to be pessimists are more likely to use a
mortgage contract to finance the purchase of exposed properties. Among transactions
with such buyers, at-risk properties are about 3.4% more likely to be leveraged, while
the relationship between SLR risks and leverage is not statistically significant among
likely optimistic buyers.
Consistent with the theory, we also find that beliefs matter for the intensive margin
of maturity choice. Among transactions of at-risk properties, likely pessimistic buyers
are more likely to have a mortgage contract with a long maturity of thirty years. All
of the results above are robust to alternative specifications including fixed effects, SLR
risk definitions, operationalizations of climate beliefs, and a suite of additional control
variables. The findings affirm the novel implications of our theory – more pessimistic
buyers are more likely to shift their long-run risk exposure to lenders via long-term
defaultable debt contracts.
In response to potential concerns about our measurement of climate beliefs based
on the Yale survey, including the potential selection bias due to residential sorting over
climate risks (Bakkensen and Ma, 2020; Bakkensen and Barrage, 2022), we provide
several additional ways to measure homebuyers’ climate beliefs in Section 6.1. In one
approach, we obtain two decades of a nationally-representative proprietary survey data
set from Gallup to construct our own panel measure of climate beliefs that varies
at the county-by-year level. In another approach, instead of relying on surveys, we
develop a novel belief imputation strategy to estimate transaction-specific beliefs from
our micro data. Specifically, we recover individual homebuyer beliefs from the residuals
of a hedonic regression of the housing price on observable housing, neighborhood, and
buyer neighborhood characteristics. Intuitively, the extent to which a transaction price
capitalizes the SLR risk should reveal the extent to which the homebuyer is concerned
about the risk. We then use the transaction-level imputed beliefs in our mortgage
regressions. All our results are robust to these alternative measures of climate beliefs.
5

Diving deeper, we find evidence supporting the model’s two additional predictions
on the effects of monetary policies. A reduction in the interest rate – as measured by the
market yield on Treasury securities – increases the leverage probability (the extensive
margin) of purchases of at-risk properties by likely pessimistic buyers, but does not
affect the maturity of the associated mortgage contracts (the intensive margin).
A question may naturally arise as to why mortgage lenders are potentially (acting
as if they are) less pessimistic about climate risks than certain borrowers. Recent
papers in the literature have argued that mortgage lenders tend to shift climate risks to
government-sponsored enterprises (GSE) through the process of securitization and the
sale of mortgages below the conforming loan limits to such institutions. This is possible
since GSE securitization rules and fees tend to only reflect current official floodplain
maps and not necessarily future SLR risks (e.g., Liao and Mulder 2021; Ouazad and
Kahn 2022; Panjwani 2022). If this is indeed the case, then we should expect our
empirical results to hold more for the conforming loan segment than for the jumbo
segment. In fact, this is exactly what we find: our leverage and maturity results are
almost entirely driven by conforming loans as opposed to nonconforming loans.
Our findings have relevant policy implications. They highlight the nontrivial ways
that climate risk and climate beliefs affect the collateralized debt market, whose stability
is key for the stability of the financial system, as evidenced in past financial crises (e.g.,
Mian and Sufi 2015). The results also suggest the role of monetary and regulatory
policies in dampening or exacerbating the influence of climate risk in the financial
system. Because of the option to transfer climate risks via the debt market, adaptation
to climate change in the financial markets may have nuanced and nontrivial implications
for the distribution of climate risks across the financial system.
The rest of the paper is organized as follows. Section 2 discusses the related literature. Section 3 provides the theoretical model. Section 4 describes the data and
empirical framework. Section 5 describes our main empirical results. Section 6 provides a battery of robustness checks and our transaction-level belief imputation exercise.
Section 7 provides further evidence of the roles of securitization and monetary policies.
Section 8 concludes. The Appendix provides proofs and further details of the empirical
analysis.

2

Related literature

To the best of our knowledge, our paper is the first to investigate the effects of the
interaction between climate risks and heterogeneous climate beliefs on a collateralized
debt market. In doing so, it relates and contributes to several bodies of research.
The first is a rapidly growing (empirical) literature on climate finance, which studies
6

how climate risks interact with financial markets (for recent surveys of this literature
see Hong et al. 2020; Furukawa et al. 2020; Giglio et al. 2021). Our paper contributes
to the understanding of how SLR and increased flood risks affect the housing market
(BGL; BGY; Murfin and Spiegel 2020; Hino and Burke 2021; Keys and Mulder 2020;
Addoum et al. 2021; Bakkensen and Barrage 2022).7 Our paper also contributes to a
growing but important set of papers investigating how the interaction between climate
risks and existing government policies, including policies on securitization and insurance
subsidies, affects the mortgage market (Issler et al. 2020; Liao and Mulder 2021; Sastry
2021; Ouazad and Kahn 2022). Complementary to our paper, the evidence in Liao and
Mulder (2021) suggests that mortgage default could act as implicit insurance against
climate-related disaster risks. In investigating climate risks as a source of long-run risks
that could affect the prices of long-term financial assets/liabilities such as stocks and
long-term municipal or sovereign bonds, our analysis is related to those in Bansal et al.
(2021), Painter (2020), Goldsmith-Pinkham et al. (2021), and Barnett and Yannelis
(2021). In developing a method to infer investors’ climate beliefs from detailed financial
market data (residential housing transactions in our case), our paper is also related to
Alekseev et al. (2021) (changes in the portfolios of mutual funds) and Ouazad (2022)
(firm-level option prices).
On the theoretical side, our paper is related to the literature on modeling credit
markets with heterogeneous beliefs, as pioneered by Geanakoplos (1997, 2003, 2010).
To the best of our knowledge, ours is the first to apply such a theory to the context
of climate change. In doing so, we make two contributions. On the empirical side, we
are the first to exploit the well-documented heterogeneity in the beliefs about climate
change to evaluate theories of investment under belief disagreement.8 On the theoretical
side, we add a new insight on how the time dimension of endogenous maturity choice
can change the theoretical predictions. As mentioned previously, most existing models
– including those in Geanakoplos (2010), Simsek (2013), Fostel and Geanakoplos (2008,
2015), Geerolf (2015), Cao (2018), and Dong et al. (2022) – predict that optimists,
rather than pessimists, are more likely to make leveraged investments and thus cannot
explain the empirical finding that we document. In “overturning” this standard prediction, the closest paper to ours is Bailey et al. (2019), which develops a two-period model
of mortgage leverage choice with heterogeneous beliefs over future house prices, where
agents have an additional choice at the intensive margin to either purchase a cheaper
7
Also related is an empirical literature that uses hedonic empirical analyses to study how flood risk
affects property prices. See Hallstrom and Smith (2005), Bakkensen et al. (2019) and further references
in Daniel et al. (2009) and Bakkensen and Barrage (2022).
8
Also related is an empirical literature that studies the role of heterogeneous information (on
land/structure/neighborhood characteristics) in housing and mortgage markets. See Kurlat and
Stroebel (2015), Stroebel (2016), and references therein.

7

home or to rent, and evaluates the model’s predictions using Facebook data. Our
model provides a different yet complementary channel to that of Bailey et al. (2019):
the choice at the intensive margin of debt maturity. The endogenous maturity is key
in explaining the empirical patterns on the relationship we find between climate risks
and mortgage maturity. Our infinite-horizon long-run-risk model is also arguably more
appropriate to study the implications of future climate risks. Moreover, our model also
features search frictions, which allow us to endogenize and characterize the probability
of mortgage usage, which is a critical moment in mapping our model to data.
Our model also builds upon the housing market search literature (e.g., Ngai and
Tenreyro 2014; Head et al. 2014; Landvoigt et al. 2015; Garriga and Hedlund 2020)
and the credit market search literature (e.g., Bethune et al. 2022; Rocheteau et al.
2018). Our contribution to this literature is to incorporate long-run (climate) risks and
heterogeneous beliefs in a competitive search model, which generates a dispersion of
mortgage usage as well as prices and leverage as seen in the data.9 See Wright et al.
(2021) for a survey of competitive search models and their other applications. Our
model also relates to models of risk shifting in the markets for debt collateralized by
bubbly assets such as housing (Allen and Gale 2000; Barlevy 2014; Bengui and Phan
2018; Allen et al. 2022).
Finally, our paper adds to the growing literature on climate adaptation (e.g., Hsiang
and Narita 2012; Mendelsohn et al. 2012; Barreca et al. 2016; Desmet et al. 2021;
Alvarez and Rossi-Hansberg 2021; Fried 2021; Phan and Schwartzman 2021). While this
literature has mainly focused on physical adaptation (e.g., migration away from areas
exposed to SLR, building houses on stilts, adoption of air conditioning), we provide a
novel analysis of financial adaptation, in particular the leveraged investment strategies
we document.

3

Stylized model

3.1

Environment

Agents. Time is continuous and infinite. There is unit measure of atomistic buyers,
and there are competitive lenders with free entry. For simplicity, assume all agents are
9

Alternatively, Allen et al. (2014) and Allen et al. (2019) formulate a model of random search
and negotiation (à la English auction) with mortgage lenders. The key difference is that lenders in
their model compete for the borrower post-match a la English auction, while our competitive search
environment features the lenders’ pre-match competition in the loan approval probability (on top of the
terms like the loan amount and interest rate), which is particularly attractive to pessimistic borrowers
via the directed search and we find evidence of this mechanism.

8

risk neutral, discount future payoffs at a common rate r > 0, and have deep pockets.10
Assets. At the beginning of time, each buyer is matched exogenously with a seller of
an indivisible asset. If buyers desire to finance the asset purchase, buyers will search
for lenders for a loan contract in the competitive-search markets that we will describe
in details later. For now, we take the price P of the asset as given (we will endogenize
P in Section 3.3.3).
Disaster. Assets are exposed to a common disaster risk, which follows a Poisson
process. For analytical tractability, we assume that the disaster arrives only once at a
random period Td and causes a deterministic permanent damage to the asset’s returns.
The flow of returns of an asset is:

h
for t < Td
,
Ht =
h − d for t ≥ T
d

where d is the measure of risk exposure (which may vary across assets).
Beliefs. Buyers have different beliefs about the unobserved true Poisson arrival rate
of Td . Each buyer believes that the arrival rate is rλ, where the belief parameter λ is
distributed over a bounded support [λmin , λmax ] with a probability distribution ϕ. A
higher value of λ indicates more pessimism: the agent believes that the disaster will
arrive sooner. Similarly, a very low value of λ indicates optimism: the agent believes
that the shock will arrive very far into the future. For example, we can think of each
asset as a coastal property, and homebuyers disagree on how soon each house will be
permanently inundated due to sea level rise. We assume for simplicity that lenders
share a common belief, denoted by λ̄ ∈ [λmin , λmax ].11 Each agent’s belief is common
knowledge; agents agree to disagree with each other (and hence there is no learning or
signaling).
Loan contracts. Buyers/borrowers and lenders trade via loan contracts, collateralized by the assets. A contract specifies the amount L a lender loans to a buyer at t = 0,
10

The assumption of deep-pocketed buyers (whose budget constraints are nonbinding) is also arguably reasonable for our empirical context. As explained in Section 4.1, we will be focusing on
transactions of relatively expensive coastal properties, 40% of which are bought with cash.
11
This assumption is without loss of generality in our environment, where lenders have deep pockets.
¯ ]. Since lenders
Alternatively, suppose lenders’ beliefs about the arrival probability have a support [λ̄, λ̄
have deep pockets, in equilibrium, the supply of credit from the most optimistic lenders (those with
belief parameter λ̄) will crowd out that of other lenders. Hence, equilibrium outcomes are not affected
¯ ].
by the presence of other lenders in (λ̄, λ̄

9

and the amount M that the buyer promises to repay the lender continuously until the
loan matures at Tm (e.g., the monthly mortgage payment). As is usual in models of
long-term debt, we assume for convenience that the maturity date Tm is a random variable that arrives at a Poisson rate r( Γ1 − 1), where the discounted maturity parameter
Γ
,
Γ ∈ [Γ0 , 1] is an endogenous choice.12 The expected length of maturity is ETm = r(1−Γ)
and thus a higher Γ means a longer loan contract. The random maturity assumption
allows us to exploit the memory-less property of the Poisson process without keeping
track of the remaining loan balance. For example, the loan balance Bt at any period
t < Tm is always constant:
Z

Tm

re−r(τ −t) M dτ = ΓM.

Bt ≡ E
t

In sum, a loan contract is characterized by three attributes a ≡ (L, M, Γ), specifying
the loan amount, repayment flow, and discounted maturity, respectively.
Default option. Borrowers could default on their promise to repay at any time before
the contract matures. Defaulting, however, comes with a punishment: she will have
to surrender the collateral asset and will face an exogenous deterministic default cost
f ≥ 0 (e.g., legal costs and recourse due to foreclosure).
The period t = 0 expected utility for a buyer using the loan contract a = (L, M, Γ)
to finance the asset purchase and never defaulting (a risk-free leveraged buyer) is:
Tm

Z
−(P − L) + Eλ

re

−rt

Z

∞

(Ht − M )dt +

0

re

−rt


Ht dt ,

Tm

where the first term P − L is the down payment, and the second term is the total
expected utility from the asset return Ht , minus the debt repayment stream M until
the loan matures at Tm . Note that the entire term in the curly brackets can be rewritten
as vλ − ΓM , where the subjective value of the asset, vλ , is:
Z
vλ ≡ Eλ

∞

re−rt Ht dt = h −

0

λ
d.
1+λ

(1)

For unleveraged buyers (L = M = 0), their expected utility is simply −P + vλ . We
assume
P < vλ ,
(2)
so that buyers always want to purchase the asset.
The period t = 0 expected utility for a buyer choosing to default at some date
12

The lower bound Γ0 > 0 means that lenders cannot underwrite contracts that mature immediately.

10

Tf < Tm (a risky leveraged buyer) is instead given by:
Z

Tf

−(P − L) + Eλ

re

−rt

(Ht − M )dt + e

−rTf



max{pTf − BTf , 0} − f




,

0

where the last term in the square brackets indicates that the defaulting buyer will
surrender the collateral, walk away from any loan balance BTf in excess of liquidation
price of the asset pTf , and face the default cost f . Buyers and lenders take the liquidation
price pTf of the asset as given. Without loss of generality, we set the liquidation price
at pt = h − d if t ≥ Td (as all uncertainly will be resolved after the disaster date Td ). If
t < Td , we set pt = p̄λ , where p̄λ is an exogenous parameter that can depend on λ. For
tractability, we assume
p̄λ − f < vλ ,
(3)
so that defaulting before the disaster is never optimal.
Combining the above cases, a buyer’s optimal default time for a given loan contract
a, denoted by Tf (λ, a), solves:
 R min(Tm ,Tf )

re−rt (Ht − M )dt
 0
R ∞ −rt
Vλ (a) ≡ max Eλ
+1Tf ≥Tm Tm re Ht dt
Tf




+1Tf <Tm e−rTf max{pTf − BTf , 0} − f





.

(4)

Uλ ≡ max {αλ (a) [−(P − L) + Vλ (a)] + [1 − αλ (a)](−P + vλ )} ,

(5)




Finally, the buyer’s choice of the loan contract solves:

a∈Aλ

where Aλ is the menu of loan contracts and αλ (a) is the buyer’s probability of finding a
lender approving the loan contract a. Both Aλ and αλ will be specified in equilibrium.
Lender’s profit. Anticipating the buyer’s default strategy, a lender’s period t = 0
expected profit of offering loan contract a = (L, M, Γ) to a buyer of belief type λ is:
(6)

Πλ (a) ≡ −L + Rλ (a) − κ0 (Γ).

The term Rλ (a) is the lender’s expected present value of the loan repayment, given
lender belief λ̄ and the borrower’s optimal default time Tf = Tf (λ, a):
(Z
Rλ (a) ≡ Eλ̄

min{Tm ,Tf }

)
re−rt M dt + 1Tf <Tm e−rTf min{pTf , BTf }|Tf = Tf (λ, a) ,

0

(7)

11

Since a borrower can walk away from any loan balance in excess of the liquidation price
of the collateral asset, the lender collects min{pTf , BTf } at the default date Tf . Finally,
the term κ0 (Γ) in (6) is the operational cost of servicing a loan contract of maturity
Γ. We assume that longer maturity loans are costlier to service (κ′0 > 0) and that the
cost is convex (κ′′0 > 0), and we normalize κ0 (Γ0 ) = 0. This cost term will help yield an
interior solution to the optimal maturity choice.
Competitive search. Buyers search for lenders via a competitive search process.
We choose the search environment not only because we think it captures the essence of
credit search in practice (e.g., homebuyers searching for a mortgage lender), but more
importantly also because it will allow us to endogenize and characterize the probability
that an asset purchase is leveraged – a quantity at the extensive margin that is key in
our empirical analysis.13
As there are many types of borrowers, it will be convenient to define the concept of a
submarket. For each type-λ buyer/borrower and for each loan contract a, a submarket
consists of an (endogenous) measure nb of type-λ buyers for whom contract a solves their
optimization problem and an (endogenous) measure nl of lenders for whom approving
contract a to type-λ buyers satisfies their free-entry condition (to be described below).
Within each submarket, given the borrower mass nb and the lender mass nl , the
number of matches produced is given by N (nb , nl ), where N is a constant-returns-toscale matching technology function. A convenient implication of this specification is
that the implied probability that a borrower in the submarket finds a match – which
we will refer to as the leverage (or approval) probability – is given by:
αλ ≡

N (nb , nl )
= N (1, n),
nb

(8)

and the probability that a lender finds a match is:
ηλ ≡

N (nb , nl )
= N (1/n, 1),
nl

(9)

where n ≡ nl /nb is the loan market thickness. As usual, we assume that N (1, n) is
increasing and concave in n.
To pin down the equilibrium mass of lenders nl , we assume that lenders can freely
enter a submarket after paying a fixed entry cost ψ > 0. For each submarket, given the
probability ηλ (a) that a lender finds a type-λ borrower and given the expected profit
13

Without search frictions, our model would have a bang-bang solution: the leverage probability is
either zero or one, as in most existing models of belief disagreement (e.g., Geanakoplos 2010; Simsek
2013).

12

Πλ (a), the free-entry condition is given by:
ηλ (a)Πλ (a) − ψ ≤ 0, where strict inequality implies nl = 0.

(10)

In other words, competitive lenders in any active submarket (with nl > 0) must be
indifferent between entering or not. We can now define our equilibrium concept.
Definition 1. A competitive search equilibrium consists of, for each buyer’s type λ,
(i) a menu of all available loan contracts Aλ , (ii) measures (nb , nl ) of borrowers and
lenders, and (iii) their matching probabilities αλ and ηλ such that:
1. Given αλ (a) and Aλ , nb (λ, a) is the measure of type-λ borrowers choosing loan
contract a in their optimization problem (5);
2. Given ηλ (a), nl (λ, a) is the measure of lenders offering loan contract a to type-λ
borrowers to satisfy the free-entry condition (10);
3. Given nb (λ, a) and nl (λ, a), αλ (a) and ηλ (a) are given by the matching functions
(8) and (9);14 Aλ is the set of a such that (10) holds with equality;
4. The total measure of borrowers over submarkets clears the market:
Z
nb (λ, a)da = ϕ(λ),
a∈Aλ

where ϕ is the density function of the borrower’s type distribution.
Figure 2 summarizes the timeline of the model.
Loan market

Disaster
- Buyers/borrowers search for a loan contract (agents disagree over its timing)
(choose a submarket)
- Borrowers can default
(but surrender the asset
- Competitive search determines
and face default cost)
loan approval probability
Time t
Tc (random)

Figure 2: Illustration of the timing of events in the model.
14

For the submarkets with nb (λ, a) = nl (λ, a) = 0 (i.e., off-equilibrium contracts in Aλ not chosen
by any borrower nor lender), the market thickness n = nl /nb involves taking the limit of zero dividing
zero. We set ηλ (a) according to the free-entry condition (10) with equality and set αλ (a) by the
corresponding n according to (8) and (9).

13

Some brief remarks on our modeling choices are warranted. To focus on modeling
the choice of loan contract, we have assumed that agents do not resell the asset. Adding
other motivations to resell would significantly complicate the model. We could have
rewritten the model with a discrete deterministic maturity choice, but the continuoustime Poisson model is much more analytically tractable (e.g. we can compute ∂Tλ̄ /∂λ;
no need to keep track of remaining mortgage balances), while the implications are
qualitatively similar in both environments. Although agents are risk-neutral with deep
pockets, we can introduce concave consumption utility and convex cost of labor supply
in the search model a la Wong (2016) without changing much of the findings qualitatively. It is straightforward to extend the model to allow for richer specifications of
the disaster shock process (e.g., as in Barro 2009; Gourio 2012). However, the current
specification will give us very tractable solutions, including the solution to the default
decision, which we describe below. Finally, as in the belief disagreement literature, we
assume for clarity that the belief of a buyer is common knowledge; however, we can
extend our model to allow for the possibility that a buyer’s belief is private information
and the main results will be qualitatively similar.15

3.2

Equilibrium

We now characterize the equilibrium loan contracts and formalize the overall intuition
described in the introduction.
Step 1. We first solve the borrower’s optimal default problem given a contract:
Proposition 1. Given a loan contract a = (L, M, Γ), the optimal default time Tf that
solves problem (4) is:



0,
if B > brisky ;


Tf (λ, a) = Td , if B ∈ (bsafe , brisky
] and Td < Tm ;
λ



∞, otherwise,
15

Specifically, we can follow Guerrieri et al. (2010) to specify the menu A (without indexing on λ)
under private information. Here, we sketch the heuristic argument. Note that, from the perspective of
the revelation principle, pessimists always want to mimic the optimist to obtain a larger loan and then
default immediately. Thus, in the separating equilibrium, every buyer now is offered the same menu of
λmax in our benchmark economy. For the safe loans, buyers never default. For the risky loans under
the risky debt limit of type-λmax buyers, which is also the tightest, lenders always anticipate buyers to
default when the disaster hits, no matter the buyer’s belief. So the lender’s profit will not depend on
the type of buyer and the contract on the menu of λmax chosen. Thus, offering any buyers the menu
of λmax in our benchmark economy always satisfies the free-entry condition. We thank Pablo Kurlat
for raising this point to us.

14

,
where B = ΓM is again the loan balance, and the safe and risky debt limits, bsafe < brisky
λ
are given by:
λ
d + f.
(11)
bsafe ≡ h − d + f, brisky
≡ h − (1 − Γ)
λ
1+λ
Analyzing high-dimensional loan contracts and arbitrary price process may look
intractable, but our Poisson environment implies that the default problem of the buyer
, the
can be described by three regions of Proposition 1. In the first region B > brisky
λ
loan balances are so large that the buyer defaults immediately. In the second region
], the loan balances are between the safe debt limit and the risky debt
B ∈ (bsafe , brisky
λ
limit, and the buyer defaults only when the disaster hits. In the third remaining region,
the loan balances are less than the safe debt limit and the buyer never defaults. Since
rational lenders will not accept a loan contract with 100% default probability, any
equilibrium contract must satisfy B ≤ brisky
.
λ
Step 2. We now solve for the optimal loan contract. For any contract a in the menu
Aλ , the loan amount L must satisfy lenders’ free-entry condition (10):


ψ
L = Rλ (a) − κ0 (Γ) +
,
η(α)
|
{z
}

(12)

loan markup

where, by conveniently rewriting ηλ (a) as η(α), we have made use of the fact that (8)
and (9) implies η can be written as function of α. Borrowers pay a positive loan markup,
κ0 (Γ) + ψ/η(α), which is increasing in the discounted maturity Γ and the approval rate
α. The markup compensates the lenders for the fixed cost and service cost.
By substituting L from (12) into borrowers’ optimization problem (5), we get that
the optimal loan contract solves the following joint surplus maximization:16

ψ
,
Jλ ≡ max α max [Sλ (Γ) − κ0 (Γ)] −
α∈[0,1]
Γ∈[Γ0 ,1]
η(α)
|
{z
}


(13)

expected joint surplus (after deducting costs)

where
Sλ (Γ) ≡ max
M ≥0

[Vλ (a) − vλ + Rλ (a)]
|
{z
}

.

joint surplus (before deducting costs)

The term Vλ (a) − vλ captures the buyer’s surplus from using loan contract a (relative to
16

The fact that the equilibrium contract maximizes the joint surplus (rather than just the buyers’
surplus) is a typical property of the competitive search environment, where the First Welfare Theorem
holds (see, e.g., Wright et al. 2021). This is because the menu Aλ of all contracts satisfying the
lender’s free-entry condition (as specified in the equilibrium definition) is rich enough to include all
Pareto optimal contracts.

15

not using any loan). In return, the buyer repays the lender Rλ (a), which is the lender’s
surplus. Thus, Vλ (a) − vλ + Rλ (a) is the joint surplus of the buyer and lender (before
deducting the service cost and fixed cost) from the loan contract a.
Using the optimal default time from Proposition 1, the joint surplus can be catego].17
rized in two regions: B ≤ bsafe and B ∈ (bsafe , brisky
λ
Safe loans. For loan contracts in the region B ≤ bsafe , the borrower never defaults.
In this case, we have shown that the buyer’s continuation value (4) is Vλ (a) = vλ − ΓM .
The lender’s present value of the loan repayment (7) is simply Rλ (a) = ΓM . Thus, the
joint surplus is zero. Intuitively, without default, the buyer and lender just exchange
cash flows without changing the present value of owning an asset. As borrowers and
lenders have the same preferences, a safe loan contract will not be used, given the
service and fixed costs.18
Risky loans. For loan contracts in the region B ∈ (bsafe , brisky
], the buyer defaults
λ
when the disaster hits before maturity, i.e., Tf = Td < Tm . Her continuation value (4)
can be written as:19
Vλ (a) = vλ − Qλ (h − d) − Tλ M − Qλ f,
and the lender’s present value of the loan repayment (7) can be written as:
Rλ (a) = Tλ̄ M + Qλ̄ (h − d).
Here, Tλ̄ and Tλ are the expected effective maturity, which take into account the expectation of the borrower’s optimal default time Tf = Td , under the respective beliefs of
the lender and borrower:
Z
Tx ≡ Ex

Tm ∧Tf

re−rt dt =

0

Γ
,
1 + xΓ

x ∈ {λ̄, λ}.

(14)

Similarly, Qλ̄ and Qλ are the discounted probability of default, defined as:

Qx ≡ Ex 1Tf <Tm e−rTf

=

xΓ
,
1 + xΓ

x ∈ {λ̄, λ}.

Recall that we can ignore the region B > brisky
, which will never occur in equilibrium.
λ
18
When lenders have a funding advantage compared to borrowers, safe loan contracts can be featured
in equilibrium – see the extension in Section 3.3.2.
19
We have made use of the fact that B > bsafe implies max {pTd − BTd , 0} = 0 following assumption
(3). Note that the liquidation price at the time of disaster is pTd = h − d.
17

16

Hence, unlike safe loans, the joint surplus of risky loans is non-zero and is given by:
Vλ (a) − vλ + Rλ (a) = (Tλ̄ − Tλ )M − (Qλ − Qλ̄ )(h − d) −
{z
}
|
{z
}
|
gain from maturity

loss of collateral

Qλ f
|{z}

.

(15)

default cost

Equation (15) highlights two opposite channels behind the potential gain from trading
a risky loan:
Maturity channel (new). The first term on the right-hand side of (15) captures
the gain from trading defaultable loans at long maturity. Tλ̄ M and Tλ M captures
the lender’s and borrower’s expected present values of the actual repayment stream,
under their respective beliefs about the timing of the climate shock. Since the borrower
defaults on the risky loan when the disaster hits before maturity (Proposition 1), a
borrower who is more pessimistic than the lender (λ > λ̄) believes that the default
time will arrive sooner and hence the expected actual repayment stream to be smaller
than what the lender believes. As a result, (Tλ̄ − Tλ )M > 0 when λ > λ̄. In other
words, there is a gain from trade when a relatively more pessimistic buyer borrows from
a relatively more optimistic lender.20 This maturity channel is missing from existing
static models of credit markets with heterogeneous beliefs.
Note that (Tλ̄ − Tλ )M is increasing in both the repayment flow M and the loan
maturity parameter Γ. Intuitively, a higher repayment promise or a longer maturity
increases the probability that the loan contract will end in default instead of maturing,
hence increasing the gain from disagreement.
Collateral channel (conventional). The second term of (15) captures the expected losses due to the surrender of the collateral from the borrower to the lender
after default. This term has the opposite sign compared to the previous gain-frommaturity term. A borrower who is more pessimistic than a lender (λ > λ̄) will have
a higher discounted probability of default (Qλ > Qλ̄ ), leading to an expected loss of
(Qλ − Qλ̄ )(h − d) > 0 from surrendering the collateral asset. This collateral channel
is standard in static models of heterogeneous beliefs (e.g., Geanakoplos 2010), where
optimistic buyers choose to borrow in equilibrium. The last term of (15) is the expected discounted default cost, which is also higher for a more pessimistic borrower
and strengthens the collateral channel.
20

This intuition was illustrated in Figure 1 in the introduction.

17

Step 3. Finally, we establish the existence and uniqueness of a competitive search
equilibrium. For convenience, we define the following functions:
k(x) ≡ κ′−1 (x), where κ(Tλ̄ ) ≡ κ0

1
Tλ̄

1
− λ̄

!
,

 

ψ
∂N (1, n)
−1
g (x) ≡ N 1, G
, where G (n) ≡
.
x
∂n
Note that g(x) = 0 for all x ≤ 0. Also, let T0 ≡ (λ̄ + Γ10 )−1 denote the minimum
expected effective maturity, and ∆λ denote the following belief disagreement term:
(16)

∆λ ≡ (1 + λ̄)(vλ̄ − vλ ) − λ̄f.
The following proposition characterizes the equilibrium in closed forms:

Proposition 2 (Equilibrium loan contracts). A competitive search equilibrium exists
and is unique. In equilibrium, there are two belief cutoff thresholds:

 λ̄(f +d) , if d > λ̄f
d−λ̄f
λa ≡
,
∞,
otherwise

λb ≡


 λ̄(f +d)+κ′ (T0 )

if d > λ̄f + κ′ (T0 )

∞,

otherwise

d−λ̄f −κ′ (T0 )

,

(17)

such that:
(i) Sufficiently optimistic buyers with λ ≤ λa choose not to borrow: α = L = M = 0.
(ii) Sufficiently pessimistic buyers with λ > λa search for a risky loan contract where
risky debt limit (11) binds at M = brisky
/Γ, the loan amount L is determined by
λ
lenders’ free-entry condition as in (12), and the parameter for the maturity rate
Tλ̄
, where the expected effective maturity Tλ̄ is given by:
is Γ = 1−λ̄T
λ̄


k(∆ ) > T
λ
0
Tλ̄ =
T
0

if λ > λb

.

if λ ∈ (λa , λb ]

(18)

The equilibrium probability of loan approval (or leverage probability) is:
α = g (∆λ Tλ̄ − κ(Tλ̄ )) .

(19)

Figure 3 illustrates the solutions over the regions of Proposition 2. The solid line
plots the equilibrium leverage probability α. The dashed line plots the equilibrium
expected effective maturity Tλ̄ . Since the payoff difference due to belief disagreement
∆λ is increasing in λ, both α and Tλ̄ are increasing in λ (and strictly increasing when
18

λ > λb ). In words, we find that the maturity channel dominates the collateral channel,
and, hence, both the extensive margin of the leverage probability and the intensive
margin of the maturity are increasing in the degree of the buyer’s pessimism. These
are two key implications of the model that we will test in the data.
Leveraged at long maturity
Maturity

Leveraged at short maturity

)
k (∆ λ
=
T λ̄

Tλ̄ = T0
Unleveraged

g
α=

α=0
Optimistic λ̄

λa

Leverage probability

)]
κ(T λ̄
−
T λ̄

[∆ λ

Asset buyer’s belief λ
Pessimistic

λb
Figure 3: Equilibrium loan contracts.

Note that an important condition for pessimists to leverage in equilibrium is that the
asset is sufficiently exposed to the disaster risk (i.e., the disaster damage d sufficiently
exceeds the default cost λ̄f : d > λ̄f + κ′ (T0 )). If instead the asset is not very exposed
(d ≤ λ̄f ), then Proposition 2 implies λa = λb = ∞. In that case, the gain from a risky
loan contract is not enough to justify the service and fixed costs. As a result, buyers
would not leverage and belief disagreement would not affect the equilibrium outcomes.
In summary, our model predicts that in a frictional market for defaultable loan
contracts, the interaction between the exposure to disaster (sufficiently high d) and
the belief disagreement (sufficiently high λ relative to λ̄) plays an important role in
determining the outcomes in the loan market. The model predicts that relatively more
pessimistic buyers are more likely to take out loans with longer maturity when purchasing an exposed asset. Table 1 summarizes the testable implications, which forms
the basis of our empirical investigation.

Leverage probability α
Maturity Tλ̄

Pessimistic buyers (λ > λb ) &
exposed asset (d > λ̄f + κ′ (T0 ))
high
long

Otherwise

Table 1: Main testable implications of the model.

19

low
short

3.3
3.3.1

Further results and extensions
Comparative statics

Given the tractability of the model, we could further characterize how equilibrium outcomes depend on the primitives. The following corollary summarizes the comparative
statics for the equilibrium maturity Tλ̄ , loan approval probability α, loan repayment
M , loan amount L, and implied loan rate rm , defined as 1 + rm ≡ R(a)/L.
Proposition 3. The comparative statics with respect to λ and d are given in Table 2.
climate belief
PessBuyer (λ > λb )
Somewhat PessBuyer (λ ∈ [λa , λb ])
Optimistic Buyer (λ < λa )

climate exposure

∂Tλ̄
∂λ

∂α
∂λ

M
∂λ

∂L
∂λ

∂rm
∂λ

∂Tλ̄
∂d

∂α
∂d

∂M
∂d

∂L
∂d

∂rm
∂d

+
0
0

+
+
0

−
−
0

?
−
0

?
+
0

+
0
0

+
+
0

−
−
0

?
−
0

?
+
0

Table 2: Comparative statics. Note: + means ≥ 0, − means ≤ 0, ? means ambiguous.

The comparative statics for the expected effective maturity Tλ̄ and the leverage probability α follow immediately from their closed-form solutions. The comparative statics
for the repayment flow M = brisky /Γ is also straightforward: it is weakly decreasing in
the buyer’s belief parameter λ and the disaster exposure parameter d.
However, the comparative statics for the loan amount L with respect to λ is ambiguous for a sufficient pessimistic buyer (λ > λb ), due to two opposite forces. On the
loan demand side, more pessimism (a higher λ relative to a fixed λ̄) implies more gain
from trade and hence more incentive for the buyer to borrow. On the loan supply side,
a higher λ implies a lower buyer’s valuation of the asset vλ , which in turn lowers her
willingness to repay and lenders’ willingness to lend. Similarly, a change in the disaster
exposure d would have two opposite effects on the loan amount. And finally, since the
implied loan rate rm is directly related to L, it follows that the comparative statics for
rm is ambiguous.
3.3.2

Extension: Monetary policy

Monetary policies are relevant in our context, as they are a powerful instrument affecting
the supply of credit in the market, and a large literature has studied their role in shaping
credit market outcomes (e.g., Bernanke et al. 1999; Khan et al. 2003; Bethune et al.
2022). We now extend the benchmark model to study the effects of monetary policies on
the loan market under belief disagreement. To do so, we introduce asymmetric costs of
20

funds. Specifically, we assume that at t = 0, buyers and lenders face exogenous funding
costs, denoted by ρ and ι respectively, so that the buyer’s problem (5) becomes:
Uλ ≡ max {α(a) [−(1 + ρ)(P − L) + Vλ (a)] + [1 − α(a)][−(1 + ρ)P + vλ ]} ,
a∈Aλ

(20)

and equation (6) for lenders’ expected profit from loan contract a becomes:
Πλ (a) ≡ −(1 + ι)L + Rλ (a) − κ0 (Γ).

(21)

We assume that ι < ρ. This is a natural assumption, given that banks have access to
cheaper wholesale funding (such as the Fed funds market or commercial papers), while
individual buyers (such as homebuyers) do not. This asymmetry implies two interacting
sources of potential gain from trade: belief disagreement and different funding costs.
To study policies, we assume that lenders’ funding cost ι depends on the policies
of a monetary authority. We will interpret an expansionary (contractionary) monetary
policy is a policy that reduces (increases) in ι. This captures the idea that a central
bank reduces the funding costs of banks to induce an expansion in the credit supply.
By substituting L into the buyer’s problem (20) using free-entry condition (10) and
the lender’s profit (21), the optimal loan contract still solves (13), but Sλ (the joint
surplus) becomes

1+ρ
Vλ (a) − vλ
+ Rλ (a) , where ω ≡
− 1.
Sλ (Γ) ≡ max
M
1+ω
1+ι


(22)

A larger parameter ω indicates a larger difference in funding costs.
The equilibrium still features three regions. As shown in Appendix A.1.4, the belief
threshold λb is the same, but λa now becomes:

λa =




ωf
λ̄(d+f )− (1+ω)T

0

d−λ̄f

, if d > λ̄f,

 ∞, otherwise.

(23)

The following proposition summarizes the equilibrium given a monetary policy.
Proposition 4 (Monetary policy). A competitive search equilibrium exists and is unique.
(i) In equilibrium, buyers with λ ≤ λa search for a safe loan, and buyers with λ > λa
search for a risky loan. The expected effective maturity is given by:

k(∆ ) > T , if λ > λ ,
λ
0
b
Tλ̄ =
T ,
if λ ≤ λb ,
0

21

where λa < λb ; the equilibrium probability of loan approval is given by:

α=


g[

ω
(v
1+ω λ

g[

ω
(h
1+ω

+ f ) + ∆λ Tλ̄ − κ(Tλ̄ )], if λ > λa ,

− d + f ) − κ(Tλ̄ )]

if λ ≤ λa .

(ii) An expansionary monetary policy (a reduction in ι) will increase the equilibrium
leverage probability α but does not affect the equilibrium maturity Tλ̄ .
Unlike part i of Proposition 2, part i of Proposition 4 states that optimistic buyers
with λ ≤ λa now choose safe loans at the minimum maturity (equivalently, Tλ̄ = T0 )
and never default. In the benchmark, these optimistic buyers prefer no borrowing at
all. The buyer’s contract choices in the other two regions are the same as Proposition
2. Given (23), it is immediate that an expansionary monetary policy that reduces ι will
also decrease λa .
Given the closed-form solution, it is straightforward to show that an expansionary
policy (lower ι) will increase the likelihood that a buyer takes out a loan (higher α), as
stated in part ii of Proposition 4.21 However, the policy has no effect on the equilibrium
maturity. This is intuitive, as a change in ι only changes the funding cost of lenders
in period 0 (and hence affects the extensive margin of the leverage probability), but
does not affect the incentives of borrowers once the funding costs have been paid (and
hence does not affect the intensive margin). The proposition thus generates two further
testable implications: changes in the short-term monetary policy rates will affect the
leverage probability (the extensive margin) but not the maturity (the intensive margin).
Altogether, an expansionary policy will induce more buyers to search for risky loans
(lower λa ), and each of them will have a higher chance of being approved (higher α).
Consequently, such a policy would increase the number of defaults after the disaster.
The result implies that changes in monetary policies can (unintentionally) induce buyers
to behave more like pessimists and increase the extent to which the “leveraging the belief
disagreement” takes place in the debt market.
3.3.3

Extension: Endogenous asset price

So far, we have taken the asset price P as given. We now extend the model to endogenize
P as an equilibrium object. Like in the literature of search models, assume that at t = 0
(before the loan market search takes place), a buyer is matched with a seller, and the
asset price is determined by Nash bargaining:
max Uλθ (P − vs )1−θ ,
P

21

It is straightforward to show that a reduction in ι will also raise the loan amount L.

22

(24)

where Uλ = vλ − (1 + ρ)P + (1 + ω)Jλ is the buyer’s utility as given by (22), θ ∈ (0, 1) is
her bargaining power, and vs is the seller’s value of the asset (which could be the same
as the buyer). The Nash bargaining problem solves the price that splits their surpluses
according to their bargaining powers. The bargaining solution is:
P =

1−θ
vλ + θvs
1+ρ
|
{z
}

standard “hedonic” term

+

1−θ
Jλ .
|1 +{zι }

(25)

loan term

Proposition 5. Suppose d > λ̄f +κ′ (T0 ). The asset price P is decreasing in the buyer’s
disaster belief λ, decreasing in the disaster exposure d, and decreasing in the policy rate
ι.
Proposition 5 states that, although pessimists have a higher loan surplus Jλ , the
effect of a lower subjective value vλ still dominates for asset pricing. Consequently, the
asset price decreases in the degree of pessimism and disaster exposure (and is consistent
with most of the existing literature’s empirical findings about how climate belief and
climate risk exposure affects housing prices). It is also intuitive that an expansionary
monetary policy that reduces lenders’ funding cost ι would also raise the loan’s joint
surplus and hence the asset price.
3.3.4

Comparison with the prediction in the literature

Our prediction that pessimists leverage more contrasts with the standard prediction in
the theoretical literature of heterogeneous beliefs, where optimists leverage more (Fostel
and Geanakoplos 2008, 2015; Geanakoplos 2010; Simsek 2013). Our key mechanism is
the maturity channel, which is absent in the standard two-period framework. To see
more clearly the role of the maturity channel, consider a modified case of our generalized
model in Section 3.3.2, where maturity is exogenously fixed at Tλ̄ = T0 and the minimum
maturity T0 is sufficiently short such that:
T0 <

ω
.
(1 + ω) 1 + λ̄

Buyers can still choose the loan amount L and repayment flow M . We focus on buyers
who are sufficiently pessimistic (λ > λa ) such that they choose a risky loan. There, the
equilibrium probability of loan approval is:



ω
α=g
(vλ + f ) + ∆λ T0 .
1+ω
A notable implication is that now the leverage probability is decreasing in λ, i.e.,
23

more pessimistic buyers are less likely to leverage.22 Intuitively, the gain from trading a
risky loan due to the belief disagreement is now weaker under a shorter loan such that
the collateral channel dominates the maturity channel. In summary, in this special
case without the possibility of choosing long-term loan contracts, our model would
imply that optimists would borrow more (both at the extensive and intensive margin),
consistent with the standard finding in the literature.

4

Data and methodology

Motivated by our theoretical insights, we now turn to an empirical analysis of how
climate risk and heterogeneous beliefs affect the mortgage market.

4.1

Data

We develop a new large-scale data set of coastal property sales along the U.S. Atlantic
Coast from 2001 to 2016, along with the associated mortgage information for each
transaction, and the exposure to sea level rise (SLR) risk for each property. We first
leverage an extensive proprietary set of real estate transactions data from CoreLogic,
a data vendor that compiles a thorough record of property tax roll information and
deed transactions. The tax roll information includes transaction prices and property
characteristics, including square feet of the lot, number of bedrooms, building age,
and address. The deeds data contain comprehensive information on any mortgage
contract associated with a transaction, including the mortgage origination amount and
maturity, the identity of the lender, and other characteristics. We use each property’s
coordinates to compute its distance to the nearest coast. Since this is a large data set
and the relevant variation comes from homes near the coast, we restrict our attention
to properties that lie within 1km of the coast. We focus on single-unit single-family
homes, and thus exclude condos and duplexes, which may have different exposure to
flood risks depending on the floors they are on. We also exclude outlier transactions with
sale prices under $50,000 or over $10,000,000, and exclude transactions with unavailable
property characteristics.
To exploit the spatial variation in exposure to SLR risk and define our key independent variable SLRi , we utilize state-of-the-art high-resolution maps from NOAA’s SLR
Viewer.23 These maps allow us to extract property-specific inundation readings across
various heights of SLR. NOAA utilizes a bathtub-style model to project future inundation based on local land elevation, local and regional tidal variability, topographical
22
23

Recall that g ′ (x) > 0 and vλ is decreasing in λ.
Publicly available at https://coast.noaa.gov/digitalcoast/tools/slr.html.

24

variation, and hydrological connectivity. Note that this SLR product is not based on
potentially endogenous factors such as land subsidence or future mitigation efforts that
could be impacted by local management decisions. Based on each property’s latitude
and longitude, we determine whether the property will be inundated with x feet of
SLR, where x ∈ {1, 2, . . . , 6}. We also use First Street Foundation’s data to obtain the
minimum bare-earth elevation of each property as a control variable.
To operationalize climate beliefs including the likely pessimistic buyers in our sample, we employ three approaches. First, we utilize data from the 2014 Yale Climate
Opinion Survey (Howe et al. 2015).24 This innovative data set, based on >13,000 individual responses to their national survey across multiple waves since 2008, provides
estimates of the average beliefs about climate change among the adult population in
each county. Given its novel scope and availability, the Yale Climate Opinion data
has been widely used in the climate finance literature to estimate climate beliefs (e.g.,
BGL, BGY, Keys and Mulder 2020; Goldsmith-Pinkham et al. 2021; Bakkensen and
Barrage 2022). Our benchmark proxy measure of the climate belief of a buyer in a
transaction is the percentage of people in the buyer’s county who answered “yes” to
whether they believe that climate change is happening. For robustness checks in Section 6.1.1, we will use two additional variables: the percentage of people who answered
“somewhat worried” or “very worried” to how worried they are about global warming,
and the percentage of people who answered “yes” to whether they believe that global
warming will start to harm people in the U.S. within 10 years. We refer to these three
measures as Belief: happening, Belief: worried, and Belief: timing in summary statistics Table 3. Second, we employ a proprietary data set containing almost two decades
of annual climate beliefs survey from the Gallup Environmental Poll, allowing us to
estimate a secondary proxy for climate beliefs that varies at the county-by-year level.
Finally, instead of relying on survey data, we develop a novel empirical approach to
recover homebuyer-specific climate beliefs from the capitalization of SLR risk in housing prices. We use this as a transaction-level proxy for climate beliefs at the time
of property purchase. See Section 6.1 for a complete explanation of the Gallup and
homebuyer-specific beliefs approaches.
Finally, we include a suite of county-by-year level socioeconomic and neighborhood
variables as additional controls. Our baseline specifications include controls for average
personal income and county population, using the data from the Bureau of Economic
Analysis’ (BEA) Regional Economic Accounts, which is available for all of the years in
our sample. In additional sensitivity analyses, we also gather data at the county-by-year
24
Publicly available at https://climatecommunication.yale.edu/visualizations-data/ycom/.
The Yale data set has more recent updates, but the 2014 vintage has the best overlap with our
CoreLogic sample period, which ends in 2016.

25

level on the demographic and ideological composition of the buyer’s county (gender, age,
race/ethnicity, voting behavior, and education) as well as local economic data from the
property’s location (unemployment rate, test scores, arrests, new building permits, and
previous flood events). Data for most of these additional control variables are available
since 2010. We use the annual county-level population files from the National Cancer
Institute’s Surveillance, Epidemiology, and End Results Program to calculate the share
of each county that is female, nonwhite, age 65 and older, and age 5 and younger. We
gather data from the MIT Election Lab on the percentage of Republican or Democratic
votes in the previous presidential election. As a proxy for education, we use annual test
scores data from the Stanford Education Data Archive (SEDA). SEDA provides average
academic achievement for grades 3-8 at the county level, as measured by standardized
tests in reading and math. We download annual county unemployment rates from the
Bureau of Labor Statistics. For data on the yearly total number of arrests at the county
level, we use the Uniform Crime Reporting (UCR) Program Data. We use the Building
Permits Survey from the Census Bureau to calculate the yearly number of new housing
units authorized by building permits in each county. Lastly, we use NOAA’s Storm
Events Database to calculate the number of flood events each year. We then lag this
measure by one year to control for the previous year’s flood events.
Mean
Sale Price
Leveraged (dummy)
Mortgage amount
Long Maturity (dummy)
Mortgage term (years)
Distance to coast (meters)
Elevation (meters)
Belief: happening (buyer county, %)
Belief: worried (buyer county, %)
Belief: timing (buyer county, %)
Inundated at 6ft SLR (dummy)
Moderate SLR Risk (dummy)
High SLR Risk (dummy)

Std

p10

p90

N

$419,337 $631,804 $95,000 $779,000 2,250,995
0.60
0.49
0
1 2,247,670
$300,517 $337,469 $90,000 $537,500 1,349,817
0.87
0.34
0
1 1,196,639
27.90
6.19
15
30 1,196,639
386.42
294.66
42.24
841.53 2,250,995
7.03
12.43
1.30
14.35
916,170
66.32
5.21
61
73 2,219,924
56.33
6.29
49
66 2,219,924
44.81
4.67
40
52 2,219,892
0.24
0.43
0
1 2,250,995
0.20
0.40
0
1 2,250,995
0.04
0.19
0
0 2,250,995

Table 3: Summary statistics of key variables. Leveraged is a dummy for whether
a transaction is associated with a mortgage or not. Long Maturity is a dummy for
whether the mortgage term is at least 30 years. Mortgage amount and term statistics
are reported conditional on having a mortgage. Inundated at 6ft of SLR is a dummy for
whether the property is predicted to be inundated at 6ft of SLR according to NOAA.
Moderate SLR Risk (High SLR Risk) indicates whether a property will be inundated
with >3 but ≤6 feet of SLR (≤3 feet of SLR). Main data sources: CoreLogic, NOAA
SLR Viewer, and Yale Climate Opinion Survey.

26

Table 3 provides the summary statistics of selected key variables. The final sample
in which main property and county control variables are available contains 1,582,525
transactions. It is worth noting that the houses in our sample are relatively expensive,
with an average sale price of $419,337, nearly 45% higher than the national average
over the same period ($288,742). Also nearly 40% of the transactions are purchased
without a mortgage (i.e., “bought with cash”). This is consistent with the well-known
stylized fact that buyers of coastal properties on average tend to come from the higher
end of the wealth distribution (Kahn and Smith 2017; Bakkensen and Ma 2020).

4.2

Econometric specifications

Housing price. To set the stage for our main empirical analysis, we begin by revisiting the literature’s previous findings regarding the effects of SLR risk on property
prices. Based on BGL (Bernstein et al. 2019), we adopt the following specification:
ln P riceit = βP SLRi + ϕ′P Xi + θP′ Zct + ΛPZDEBM + ϱP + ϵPit .

(P0)

Throughout, ln P riceit denotes the natural log of the transaction price of residential
property i sold in month-year t. SLRi denotes property i’s exposure to inundation risk
due to SLR. In our benchmark specification for housing price, we adopt the operationalization most often used in the existing literature (including BGL and BGY) and define
SLRi as equal to one if property i is predicted to be underwater if the sea level rises
by six feet and equal to zero otherwise. We explore more refined definitions of SLR
risk in various robustness exercises. Xi is a vector of property-level controls (age and
square footage), and Zct is a vector of controls at the county-by-year level of the buyer’s
previous residence (average income and population of the buyer’s county).25 Finally,
ϱP is a constant, and ϵPit is the error term, which we cluster at the ZIP code level.
Crucial for our identification, ΛPZDEBM denotes a rich set of fixed effects that allow
us to compare transactions within the same ZIP code (Z), distance to coast bin (D),
elevation bin (E), number of bedrooms (B), and time (year and month; M ) of sale.26
Our identification assumption is that with these controls, SLRi is uncorrelated with
ϵPit and therefore βP is a plausible estimate of the effects of SLR exposure on house
prices. Figure 4 provides an example the high-resolution spatial variation of exposure
to inundation risk under a scenario of six feet of SLR for Chesapeake, Virginia. We
compare the transaction outcomes of properties that are very similar but with one
25

In our sensitivity analysis in Section 6, we include the aforementioned host of additional control
variables, which are available for later years in our sample.
26
Following BGL, we use nonlinear bins for the distance from the East coast: 0 – .01 miles, .01 – .02
miles, .02 – .08 miles, .08 – .16 miles, and more than .16+ miles, and we use two-meter elevation bins.

27

more exposed to future climate-related risks than the other. In this illustration, all
five properties are within the same ZIP code, same distance bin to the coast, same
elevation bin, have the same number of bedrooms, and the same month and year of
transaction corresponding to the level of variation of our Z × D × E × B × M fixed
effects. However, the properties located at points B, C, and E (which lie inside the
predicted inundation area) are more exposed to future climate-related risks than the
properties located at points A and D.
In line with our model and the previous literature, we hypothesize that:
Hypothesis 1 (βP < 0). All else equal, properties with more exposure to SLR risks
sell at a discount relative to less exposed ones.
Going deeper, we re-investigate the literature’s findings on the effect of heterogeneous climate beliefs in the pricing of SLR risk. In the following specification, we
evaluate whether there is a larger SLR price discount in transactions with (likely) more
pessimistic buyers:
ln P riceit = βP SLRi + δP P essBuyerc + γP SLRi × P essBuyerc
+ ϕ′P Xi + θP′ Zct + ξP′ SLRi × Zct + ΛPZDEBM + ϱP + ϵPit .

(P1)

Here, P essBuyerc is an indicator variable equal to one if the average climate belief in
the county c = c(it) from which the buyer of property i at date t comes is above the
sample median and zero otherwise.27 We interpret P essBuyer = 1 as an indicator of
a likely more pessimistic homebuyer. Based on our model and the previous literature,
we further hypothesize that:
Hypothesis 2 (γP < 0). There is more discount of SLR risk in transactions with more
pessimistic homebuyers.
To control for potentially confounding factors that could correlate with climate beliefs, we include the interaction terms between SLR and the buyer county-by-year level
controls (the population and average income of the county where the buyer comes from),
as represented by the term SLRi × Zct . We provide a battery of robustness exercises
with alternative specifications of different cutoff thresholds and control variables, as
well as alternative proxies for climate belief in Section 6.
Leverage dummy (extensive margin). We now move to our main analysis of the
effects of SLR risks on mortgage outcomes. First, we evaluate whether SLR risk and
27

Specifically, in the benchmark spefication, we define P essBuyerc = 1 if > 65% of respondents in
county c state that they believe that global warming is happening, according to the Yale survey.

28

Figure 4: Illustration of our empirical identification strategy in Chesapeake, Virginia.
Five properties (points A through E) that are within the same ZIP code, same distance
bin to the coast, same elevation bin, having the same number of bedrooms, and having
the same month and year of transaction. Properties B, C, and E are expected to be
inundated under six feet of SLR rise whereas properties A and D are not. Light blue
shaded areas correspond to areas that are predicted to be inundated with six feet of
SLR. Dark blue shaded areas are currently inundated waterways. (Sources: authors’
calculations based on NOAA SLR Viewer and CoreLogic data; property locations are
adjusted for illustration purposes and do not reflect locations of actual observations).
climate beliefs affect the likelihood that transactions are leveraged:
Leveragedit = βL SLRi + δL P essBuyerc + γL SLRi × P essBuyerc
+ ρL ln P riceit + ϕ′L Xi + θL′ Zct + ξL′ SLRi × Zct + ΛLZDEBM + ϱL + ϵLit ,
(L1)
Here, Leveragedit is an indicator variable that is equal to one if the transaction on
property i at time t involves a mortgage and zero otherwise. As a benchmark, we
include housing price as a control variable, but our results are robust to omitting it (see

29

Section 6.2.4).28 The dummy P essBuyerc is defined as in price regression (P1). Based
on our model (recall Table 1), we hypothesize that:
Hypothesis 3 (γL > 0). In transactions of exposed properties, more pessimistic buyers
are more likely to take on a leveraged position.
Maturity (intensive margin). Next, we analyze the effects of SLR risks on the
maturity of mortgage contracts. For leveraged transactions (i.e., those associated with
a mortgage contract), we define LongM aturityit as an indicator equal to one if the
maturity of the mortgage contract for property i transacted at t is at least 30 years and
zero otherwise.29 We then run the following regression on the sub-sample of leveraged
transactions:
LongM aturityit = βM SLRi + δM P essBuyerc + γM SLRi × P essBuyerc
′
′
+ ρM ln P riceit + ϕ′M Xi + θM
Zct + ξM
SLRi × Zct
M
+ ΛM
ZDEBM + ΛL + ϱM + ϵit .

(M1)

Here, in addition to the set of fixed effects ΛZDEBM , we also include a lender fixed effect,
ΛL , to control for the possibility that different lenders may have varying tendencies to
issue different types of mortgage contracts.30 Based on our model, we hypothesize that:
Hypothesis 4 (γM > 0). When choosing a mortgage contract to finance the purchase
of an exposed property, more pessimistic buyers are more likely to pick a contract with
long maturity.
Specifications (L1) and (M1) are our main regression equations. We estimate them
using the ordinary least squares (OLS) estimator.31
28

The inclusion of the housing price is also consistent with our model, where buyers choose a debt
contract given the housing price.
29
The distribution of mortgage maturity is bimodal: most contracts either have a fifteen-year or a
thirty-year term. In the main specification for (M1), we exclude the small sub-sample of transactions
whose mortgages have maturity terms that are neither 15 nor 30 years (less than 4% of our sample),
which tend to be nonstandard mortgage contracts. Our results are robust to the inclusion of these
nonstandard observations.
30
For transactions with more than one mortgage, we use the lender fixed effect for the first mortgage.
In our sample, all mortgage contracts associated with the same contract have the same maturity, hence
our LongM aturity dummy is well defined for these observations. As a robustness check, we also exclude
transactions with more than one mortgage and the results are unaffected.
31
We utilize the OLS estimator given concerns over implementation and bias of fixed effects in
nonlinear models, including the probit and logit models (Greene et al., 2002).

30

5
5.1

Results
Setting the stage: Housing price

Table 4 reports the results for housing price regressions (P0) and (P1). To appreciate
the importance of controlling for amenity values, column 1 shows the estimates from a
naïve regression that does not include our rich set of fixed effects. It shows a positive
and significant correlation between SLR exposure and price. This is not surprising, as
properties exposed to SLR risk also tend to be close to the coast, and coastal properties
tend to have higher amenity values.
log(Housing Price)
SLR Risk

0.219***
(0.028)

-0.060***
(0.022)

-0.039*
(0.021)
-0.059***
(0.018)

Y

Y
Y

1,583,238
0.335

406,601
0.866

Y
Y
Y
406,601
0.867

SLR Risk × PessBuyer
Property & buyer county controls
Z × D × E × B × M fe
Buyer county controls × SLR
N
R2

Table 4: Effects of exposure to SLR risk and its interaction with climate belief on
housing prices. SLR Risk indicates whether a property’s location will be inundated
with six feet of SLR. PessBuyer indicates whether the buyer is from a county where the
fraction of respondents in Yale Climate Opinion Survey stating that they believe global
warming is happening is above the sample median. Z×D×E×B×M indicates ZIP code
× distance to coast bin × elevation bin × number of bedrooms × time (transaction
month-year) fixed effects. Property controls include age and square footage. Buyer
county controls include average county income and county population. Sample includes
all transactions of single-family homes that lie within 1km from the U.S. East Coast
between 2001 and 2016. See Section 4.1 for more data descriptions. Standard errors in
parentheses are clustered at the ZIP code level; * (p < 0.1), ** (p < 0.05), *** (p <
0.01).
Column 2, which corresponds to specification (P0), then includes our rich set of
fixed effects, and the sign of the estimated coefficient flips to be negative. It shows
that, all else equal, a property expected to be inundated with six feet of SLR is priced
about 6% lower than an otherwise equivalent but unexposed property. In other words,
the “SLR discount” is around 6%. The estimate is statistically significant (p < 0.01),
and the magnitude is very similar to the benchmark estimates of 5 to 6.6% in BGL.
Thus, column 2 replicates the recent finding in the climate finance literature that the
coastal property market is pricing in future SLR risks.
31

Furthermore, column 3, which corresponds to specification (P1), shows that the
extent of the pricing of SLR risk varies: much of the discounting of SLR risk is driven
by transactions with pessimistic homebuyers. The SLR discount is nearly 10% (≈
3.9 + 5.9) among transactions with likely pessimistic buyers, while the discount is only
3.9% among transactions with the other group of buyers. This result of the variation in
the pricing of SLR risk based on buyers’ climate beliefs is consistent with that in BGY.
Having replicated the literature’s findings on the SLR discount in housing prices,
providing reassuring evidence on the validity of our data set and identification strategy,
we now move on to our main results on mortgage outcomes.

5.2

Extensive margin: Leverage probability
Leveraged

SLR Risk
SLR Risk × PessBuyer
Moderate SLR Risk

-0.093*** 0.021*** -0.004
-0.003
(0.008)
(0.007)
(0.007)
(0.014)
0.047*** 0.034***
(0.009)
(0.011)

High SLR Risk
Moderate SLR × PessBuyer
High SLR × PessBuyer
Log Housing Price

0.064***
(0.006)

Property & buyer county controls Y
Z × D × E × B × M fe
Buyer county controls × SLR
N
1,580,756
R2
0.019

0.003
(0.014)
-0.035
(0.031)
0.026**
(0.011)
0.083***
(0.023)
0.161*** 0.161*** 0.161*** 0.162***
(0.010)
(0.010)
(0.010)
(0.010)
Y
Y

Y
Y

405,893
0.473

405,893
0.473

Y
Y
Y
405,893
0.473

Y
Y
Y
405,893
0.473

Table 5: Effects of exposure to SLR risk and its interaction with climate belief on
Leveraged, an indicator for whether the transaction is associated with a mortgage.
Moderate SLR Risk (High SLR Risk ) indicates whether a property’s location will be
inundated with > 3 to ≤ 6 feet of SLR (≤ 3 feet of SLR). See Table 4 for the definitions
of the remaining variables.
Moving to the main results, Table 5 reports estimates from regressions where the
dependent variable is Leveraged – the indicator variable equal to 1 if a transaction is
financed with a mortgage contract and 0 otherwise. Again, column 1 shows a naïve
regression that excludes the set of fixed effects. The result shows a negative correla32

tion between SLR risk exposure and leverage, suggesting that transactions of exposed
properties on average are less likely to be financed with debt, consistent with existing
conventional views (e.g., Litterman et al. 2020; Brunetti et al. 2021).
However, the result reverses in column 2, where we include the rich set of fixed
effects. The estimate in column 2 shows that, in contrast to conventional wisdom,
transactions of properties exposed to SLR risk are about two percentage points more
likely to be leveraged. The estimate is not only statistically significant (p < 0.01) but
also economically meaningful. To get a sense of relative magnitude, note that the rise
of leveraged transactions – measured by the fraction of property transactions associated
with mortgages in our data – from 2001 (the beginning of our sample) to 2007 (the peak
of the housing boom before the 2008 financial crisis) is about four percentage points,
or twice our estimated coefficient.
Crucially, column 3, which corresponds to specification (L1), shows that the SLRleverage association is driven by transactions with pessimistic homebuyers. The estimate
for the interaction term indicates that, among transactions with likely pessimistic buyers, properties exposed to SLR risk are about 4.7% more likely to be leveraged. The
estimate for the uninteracted SLR Risk term indicates that the association between
SLR risk and the leveraged dummy is negative but not statistically significant for the
other group of homebuyers.
A potential concern for the specification in column 3 is that climate beliefs are
correlated with other factors that predict leverage outcomes.32 Column 4 repeats the
benchmark regression in column 3 but includes the interaction terms between SLR
and buyer county controls, namely the population and average income of the county
where the buyer comes from. The estimate of SLR Risk ×PessBuyer remains strongly
statistically significant. The magnitude of the coefficient reduces slightly to about 3.4%,
but is not statically different from before. In Section 6, we show that the results are also
robust to the inclusion of a wider variety of county-level socioeconomic variables that
become available for later years in our sample, including political ideology, education,
race and ethnicity, age, and gender as well as unemployment, new building permits,
crime statistics, and flood events from the property’s neighborhood.
Another potential concern is that the measure of SLR exposure is too coarse. In
particular, despite being a commonly used benchmark definition in the empirical climate
literature, it is very unlikely that the sea level will rise by six feet in the next thirty
years.33 Column 5 aims to address this concern. It repeats the exercises in column 4
32

Ideally, we would like to control for buyer-specific characteristics such as income, wealth, or credit
score. However, as described in Section 4.1, the only individual-level information we observe is the
location that buyers comes from. Thus, we also include aggregated statistics from the buyer’s origin.
33
However, it is plausible that properties inundated with six feet of SLR face higher climate-related
risks that will likely realize in thirty years, e.g., increased flooding from storm surges (Zhang et al.

33

but replaces the benchmark SLR Risk indicator with a more refined measure of risk
exposure: Moderate SLR Risk indicates whether a property will be inundated with > 3
but ≤ 6 feet of SLR. Similarly, High SLR Risk indicates whether a property will be
inundated with ≤ 3 feet of SLR. The comparison group is Low SLR Risk, indicating
properties that will not be inundated even with six feet of SLR.
Using the same base specification as columns 3 and 4, column 5 shows that the
estimates for the interaction between the SLR terms and the pessimistic buyer dummy
are both positive and statistically significant, while the estimates for the uninteracted
SLR terms are not significant, highlighting the importance of climate beliefs in this setting. Furthermore, the estimate of 8.3% for High SLR Risk × P essBuyer is larger and
statistically different than the estimate of 2.6% for Moderate SLR Risk × P essBuyer.
This monotonic ordering is consistent with our model’s prediction: the more exposed a
property is, the higher the likelihood that its transaction with a buyer from a county
with strong climate belief is going to be leveraged. See section Section 6.2 for additional
robustness surrounding our SLR risk measure. Overall, our findings on the relationship
between SLR exposure and leverage are consistent with our theoretical model’s prediction on the extensive margin of leverage: in purchases of properties exposed to climate
risks, buyers with more pessimistic climate beliefs are more likely to make a leveraged
investment.

5.3

Intensive margin: Maturity

With a similar structure to Table 5, Table 6 reports the estimates for regressions of
the long maturity dummy. Recall that these are results at the intensive margin of the
mortgage choice, as the dependent variable LongM aturity is only defined for transactions that have an associated mortgage contract. As in previous tables, the first column
shows a naïve regression that excludes the set of fixed effects. There, the coefficient of
SLR risk is negative and significant. However, once the fixed effects are introduced in
column 2, the sign of the estimated coefficient changes sign and becomes statistically
insignificant. Column 2 thus indicates that, on average, there does not seem to be a
significant relationship between SLR risk exposure and maturity.
A pattern emerges when we examine this relationship by category of buyers. Column
3, consistent with empirical model (M1), shows that among leveraged transactions
with likely pessimistic buyers, properties exposed to SLR risk are about 1.8 percentage
points more likely to be associated with long maturity mortgage contracts (relative to
leveraged transactions with likely optimistic buyers). Column 4 repeats the exercise in
column 3 but includes the interaction terms between SLR and buyer county controls.
2013).

34

Long Maturity
SLR Risk
SLR Risk × PessBuyer

-0.019*** 0.005
(0.002)
(0.005)

Moderate SLR Risk

-0.004
0.002
(0.007)
(0.014)
0.018*** 0.024***
(0.007)
(0.007)

Log Housing Price

0.001
(0.001)

-0.003
(0.004)

-0.003
(0.004)

-0.003
(0.004)

0.006
(0.014)
-0.028
(0.024)
0.023***
(0.008)
0.031*
(0.019)
-0.003
(0.004)

Property & buyer county controls
Z × D × E × B × M fe
Lender fe
Buyer county controls × SLR
N
R2

Y

Y
Y
Y

Y
Y
Y

822,890
0.002

150,746 150,746
0.441
0.441

Y
Y
Y
Y
150,746
0.441

Y
Y
Y
Y
150,746
0.441

High SLR Risk
Moderate SLR × PessBuyer
High SLR × PessBuyer

Table 6: Effects of exposure to SLR risk and its interaction with climate belief on Long
Maturity, an indicator for whether the mortgage term is 30 years (as opposed to 15
years). Lender fe indicates lender fixed effects. Sample excludes transactions that do
not have an associated mortgage contract (for which the dependent variable is not well
defined) and excludes nonstandard mortgage observations where term is not 15 nor 30
years. The rest is the same as in Table 5.
The estimate for the interaction term remains highly statistically significant, and the
magnitude increases slightly to 2.4%.
Finally, column 5 repeats the exercise in column 4 but replaces the benchmark SLR
Risk indicator with the Moderate SLR Risk and High SLR Risk indicators. The pattern
in columns 3 and 4 continues to hold with the more refined measure of SLR risk. The
relationship between SLR exposure and the long maturity dummy is not statistically
significant. However, the relationship becomes statistically significant when the SLR
exposure is interacted with beliefs. Among leveraged transactions with pessimistic
buyers, mortgage contracts of properties with moderate SLR risk are 2.3% more likely
to have long maturity (p < 0.01), and those with high SLR risk are 3.1% more likely
(p < 0.1), relative to similar transactions optimistic buyers.
Overall, our findings are consistent with the model’s predictions: in purchases of
properties exposed to climate risks, buyers with more pessimistic climate beliefs are
more likely to leverage and use debt contracts with longer maturities.
35

6

Robustness and sensitivity

6.1

Climate beliefs

A classic concern for empirical analyses are unobservable confounders. In this case,
a concern can arise from potential sorting across SLR risk based on climate beliefs,
which has been documented in the coastal housing literature (Bakkensen and Barrage,
2022). If climate optimists are more likely to move into coastal properties, then our
county-level beliefs measure could be a biased proxy for individual-level buyer beliefs,
as the county-level measure would overestimate the level of climate pessimism in our
coastal buyers.
While we cannot definitively rule out sorting over climate beliefs in this setting, to
the extent that it may be occurring, we do not believe it to be a large biasing force
on our lending results. First, Bakkensen and Barrage (2022) find that the county-level
Yale Climate Opinion data are strongly correlated (R̄2 = .999) with individual-level
beliefs data collected through door-to-door surveys in coastal Rhode Island.34 Second,
if sorting was strong enough to confound our results, we should find the SLR coefficient
in our house sales price regressions to be attenuated towards zero, given that climate
optimists would pay more for a home at high SLR risk relative to its value based on
market fundamentals. Recall from Table 4 that we find a strong and robust negative
capitalization of SLR risk into home prices, in line with, e.g., BGL. Third, if sorting
was dominant in our data, then we would expect to find a strong negative correlation
between the frequency of coastal buyers in a county and the county’s beliefs. In other
words, we might expect fewer buyers of coastal homes coming from pessimistic counties.
However, as shown in Appendix Table A1, when controlling for income, population,
education, age, and racial composition of the buyer’s county, the fraction of buyers
from a county choosing a coastal home is actually positively related to county beliefs
(p < 0.1).35
Nonetheless, since climate beliefs play a central role in our analysis, in this subsection, we evaluate how robust our results are to alternative definitions of the pessimistic
buyer variable. In particular, while Sections 6.1.1 and 6.1.2 provide sensitivity analyses surrounding the cross-sectional Yale Climate Opinion data commonly utilized by
the climate finance literature, Sections 6.1.3 and 6.1.4 provide two additional (novel)
estimates of climate beliefs. Reassuringly, our results persist across the different operationalizations of climate beliefs. All together, these additional results reassure us to
34

This is from a small sample of 187 individual-level respondents across three counties.
This correlation may not occur if the supply of coastal homes is so small relative to the housing
market that no climate optimists buy along the coast. However, Bakkensen and Barrage (2022)
estimate that even in the highly optimistic settings across the U.S. coast that they consider, optimists
do not exceed 48% of the share of coastal residents.
35

36

the persistence of our main findings across a variety of belief specifications and operationalizations.
6.1.1

Alternative specifications using Yale Climate Opinion data

Table A2 provides a series of robustness checks for our benchmark regressions (L1)
and (M1) with alternative specifications for the buyer county climate belief variable
from the Yale Climate Opinion data. For brevity, we only report the estimates for the
relevant coefficients of the interaction term between SLR Risk and the corresponding
belief variable. However, the set of controls and fixed effects remain as in the benchmark
regressions and are reported at the bottom of the table. Columns 1 and 4 (Happening)
use the benchmark (cross-sectional) 2014 Yale Climate Opinion survey data for the
percentage of people in each county who say they believe climate change is happening.
Columns 2 and 5 (Worried ) instead use the percentage who say they are worried about
climate change. Similarly, columns 3 and 6 (Timing) use the percentage who think
global warming will start to harm people in the U.S. within 10 years.
Row 1 uses the PessBuyer variable for whether the buyer is from a county where the
corresponding climate belief variable is above the sample median, thus repeating our
benchmark specification. Rows 2 to 4 rank counties into quartiles of the climate belief
variable, and nth Quartile Belief is equal to one if the buyer is from a county in that nth
quartile of belief and zero otherwise. Here, the comparison group is the first quartile,
namely those with the most optimistic beliefs. Finally, row 5 uses the continuous
measures of the belief variables: the fractions of the buyer’s county saying that they
believe climate change is happening, that they are worried about climate change, or
that they think that global warming will harm the U.S. within 10 years. Overall, we
find our main results to be consistent across this variety of climate beliefs specifications
and operationalizations, and as motivated by our theory, our results generally increase
monotonically in magnitude with the level of climate pessimism.
6.1.2

Omitted belief covariates

A related concern about climate beliefs is that this beliefs variable could be correlated
with other individual-level unobservable characteristics that could confound the analysis. Hornsey et al. (2016) perform a meta-analysis on the determinants of climate
beliefs, finding political affiliation to be most strongly related to climate beliefs relative
other sociodemographic variables such as education, gender, and income. To address
these concerns, we include a variety of additional control variables in our main specifications. In Table A3, in addition to income and population, we also include an expanded
suite of county-level control variables including data at the county-by-year level on the
37

demographic composition of the buyer’s county (gender, age, race/ethnicity, and education) as well as local economic data from the property’s location (unemployment rate,
test scores, arrests, new building permits, and the count of previous flood events).36 In
Table A4, in addition to income and population, we include data on political affiliation
(percent of Republican or Democrat vote shares in the previous presidential election at
the county level). As shown in both tables, our main results are robust.
6.1.3

Beliefs using Gallup data

While the Yale Climate Opinions survey remains a frontier data source for climate belief
surveys across the U.S., a limitation is that it is a cross-sectional estimate at the county
level.37 As additional robustness, we replicate the Yale Climate Opinions estimation
approach using survey data from Gallup’s annual Environment poll to estimate a panel
of climate opinions at the county-by-year level. In particular, we utilize annual waves
of Gallup survey data from 2000 to 2020, totalling 10,339 observations where climate
beliefs are elicited.38 In parallel with the Yale climate beliefs estimation methodology
described in Howe et al. (2015), we model beliefs based on respondent age (<30, 30-49,
50-64, >64), race and ethnicity (White, Black, Hispanic, Asian, Other), education (no
college, some college, college graduate only, post-graduate), gender (male, female), as
well as location (state) and time (year) fixed effects. We then use the model results to
predict climate beliefs at the county-by-year level utilizing data on age, race/ethnicity,
and gender from the National Cancer Institute’s Surveillance, Epidemiology, and End
Results Program’s U.S. County Population Data. We use county by 5 year average estimates for educational attainment from the U.S. Census’ American Community Survey.
Finally, we define P essBuyer to be equal to one if the buyer in a transaction i in
year y is from a county where the predicted belief is greater than or equal to the median
sample belief level in that year y, and zero otherwise. Table 7 displays the Gallup beliefs
model replicating our leverage and maturity results, which remaining strikingly similar
to our main results.
36

Since test score data and other data are only available for a subset of years, our sample for this
robustness check covers years 2009 to 2016.
37
Cross-sectional county-level estimates from the Yale Climate Opinions survey have been released
across several years, but the Yale data set is not designed to be used as a panel, due to changes in the
survey methodologies over time (Howe et al. 2015; Ballew et al. 2019).
38
We utilize the question on the timing of climate beliefs that asks "Which of the following statements
reflects your view of when the effects of global warming will begin to happen: they have already begun
to happen, they will start happening within a few years, they will start happening within your lifetime,
they will not happen within your lifetime, but they will affect future generations, (or) they will never
happen]?" For an additional sensitivity check, we also estimate beliefs based on how worried the
respondent is regarding climate change.

38

SLR Risk
SLR Risk × PessBuyer
Z × D × E × B × M fe
Property & buyer county controls
Buyer county controls x SLR
Lender fe
N
R2

Leveraged

Long Maturity

-0.031
(0.021)
0.033**
(0.015)
Y
Y
Y

0.007
(0.021)
0.026*
(0.015)
Y
Y
Y
Y
62,926
0.442

210,764
0.439

Table 7: Robustness with P essBuyer derived from county-by-year climate beliefs interpolated from Gallup survey data according to the procedure in Section 6.1.3. Column 1
reports results for leveraged regression (L1) and column 2 for long maturity regression
(M1). The rest is the same as in Tables 5 and 6.
6.1.4

Inferring individual-level climate beliefs from home prices

Finally, rather than relying on county-level averages based on survey data, we present
a novel method to impute the climate beliefs of the homebuyer in each transaction.
The underlying idea is that the housing price should reflect the homebuyer’s climate
belief (recall the theoretical model in Section 3.3.3). Hence, the extent to which the
housing price capitalizes the SLR risk should reveal the extent to which the homebuyer
is concerned about the future climate risk.
For a transaction of property i at time t, we impute the homebuyer’s relative degree
of climate pessimism λit as follows. Suppose that there is a true but unobserved distribution of climate beliefs in the population of homebuyers in our transaction data. Let
λit denote the (unobserved) climate belief of the homebuyer in transaction it, where a
higher value of λit represents a higher level of climate pessimism. Based on specification
(P1) in Section 4.2, suppose that housing price is given by:
ln P riceit = βP SLRi + γP SLRi × λit + δP λit + controlsit + ϵλit

(26)

where the impact of the SLR risk on the house price contains the general SLR discount
βP (< 0), as well as the belief-moderated discount γP (< 0) for the interaction between
the SLR risk and the (unobserved) transaction-specific buyer belief term λit . The set
of control variables are the same as in (P1).39
39

In particular, controlsit = ϕ′P Xi + θP′ Zct + ξP′ SLRi × Zct + ΛP
ZDEBM + ϱP .

39

To impute the unobserved λit , we first estimate the housing price without beliefs:
ln P riceit = βP SLRi + controlsit + ζit .

(27)

We then predict the residual from equation (27) as ζ̂it . Note that moments of ζit are
informative about the unobserved belief λit , because ζit = γP SLRi × λit + δP λit + ϵλit
according to equation (26).40 Intuitively, if we observe a buyer paying a lower price for
an identical property in a location exposed to SLR risk, ceteris paribus, then she must
be more SLR-pessimistic. Define our imputed (cardinal) climate belief parameter as:
λ̂it ≡ −ζ̂it .

(28)

Under the assumptions above, the imputed λ̂it is positively correlated with the unobserved climate pessimism λit of the homebuyer in each transaction it. Finally, to incorporate the imputed beliefs into mortgage regressions, we define the (ordinal) dummy
\ it to be equal to one if λ̂it is above the median predicted sample value and
P essBuyer
SLRi = 1, and equal to zero otherwise.41
Appendix tables A5 and A6 provide the pairwise correlation between the continuous
and binary versions of our imputed λ̂it beliefs data and other beliefs operationalizations
in this paper. Despite the large differences in how λ̂it is imputed from real estate transactions relative to how the Yale and Gallup beliefs are constructed from surveys, the
pairwise correlations are significantly and positively correlated (p<0.000) with almost
all other beliefs operationalizations.
\ it , we
Replacing the county-level P essBuyerc with the transaction-level P essBuyer
re-estimate the main mortgage regressions in (L1) and (M1). As reported in Table 8,
our result for the leveraged regression continues to hold: largely consistent with our
previous estimates in Table 5, pessimistic buyers are 3.8% more likely to take out a
mortgage (p < 0.01). Our long maturity result also holds, with pessimistic buyers
1.3% more likely to have a 30 year mortgage (p < 0.1). Overall, our main results are
robust to using imputed climate beliefs at the transaction level. This gives us additional
confidence that our main empirical findings are not purely driven by the selection bias
due to residential sorting.
40

Note that SLRi is a binary variable and γP and δP are scalar transformations of λit . Following
previous literature and our own empirical findings in Section 5.1, we assume that climate pessimists
will pay less for a property relative to climate optimists (γp + δp < 0). Assuming E(λit ϵλit ) = 0, then
ζ̂it can recovery individual climate beliefs.
41
Note that for transactions of properties with SLRi = 0, the interaction of SLRi with individuallevel belief λit does not matter for the choice of leverage and maturity, so without loss of generality
\ it = 0.
we can assign P essBuyer

40

SLR Risk
\
SLR Risk ×P essBuyer

Leveraged

Long maturity

-0.031
(0.044)
0.038***
(0.009)

0.130**
(0.059)
0.013*
(0.008)

Z x D x E x B x T fe
Y
Property & buyer county controls Y
Buyer county controls × SLR
Y
Lender fe
N
210,764
2
R
0.440

Y
Y
Y
Y
62,926
0.442

Table 8: Robustness with alternative specifications for the belief measure using
transaction-level imputed beliefs. Beliefs are imputed following the procedure in Section 6.1.4. Column 1 reports results for leveraged regression (L1) and column 2 for long
maturity regression (M1). The rest of the table is the same as in Tables 5 and 6.

6.2
6.2.1

Additional robustness
SLR measures

We further examine the sensitivity of our results to alternative operationalizations of
SLR risk measurement. To provide a more nuanced measure of SLR exposure, we
define a monotonically increasing exposure variable SLR Risk, which is equal to zero if
a property is not expected to be inundated with six feet of SLR, one if it is expected
to be inundated with six feet, two if inundated with five feet, three if inundated with
four feet, and four if inundated with three or fewer feet. Thus, the higher the value,
the higher the exposure to inundation risk.
Table A7 repeats the benchmark mortgage regressions (L1) and (M1) using this
more nuanced measure of SLR. The table shows that our results continue to hold
with this more refined measure of exposure. The estimates for the interaction terms
between SLR Risk and PessBuyer are positive and significant for higher values of the
SLR Risk variables. Also, generally, the higher the exposure value, the larger the
estimated coefficients – though the differences are not always statistically significant
from each other – highlighting that our results are robust to different SLR definitions
and individuals are attentive to the magnitude of SLR inundation risk consistent with
our theory.
6.2.2

Fixed effect specifications

Recall that our main results include ZIP code × distance to coast bin × elevation bin ×
number of bedrooms × time (transaction month-year) fixed effects (Z×D×E×B×M),
41

in addition to lender fixed effects in our long maturity results. Table A8 tests whether
our main results are robust to alternative fixed effects specifications. The top panel
reports results for the leveraged regression (L1) and the bottom panel reports those for
long maturity regression (M1).
Column 1 uses a more flexible fixed effect specification relative to the benchmark
specification by dropping the time dimension: ZIP code × distance to coast bin ×
elevation bin × number of bedrooms (Z×D×E×B). The estimate for the coefficient of
the interaction term between SLR risk and PessBuyer remains positive and significant
for the leveraged regression. It remains positive but is no longer significant for the
maturity regression. Column 2 reintroduces a time dimension to the fixed effects by
incorporating the quarter and year of the transaction (Z×D×E×B×Q). The estimate
for the interaction term between SLR risk and PessBuyer is now both positive and
statistically significant, in line with our benchmark specification.
6.2.3

Owner occupied vs. non-owner occupied

A potential concern for our benchmark regressions (L1) and (M1) is that they pool
together owner-occupied (OO) transactions and non-owner-occupied (NOO) ones. It is
possible that NOO buyers have different incentives or constraints compared to OO buyers, as the former could be using their property as an investment vehicle and therefore
could be more “sophisticated” in processing future SLR risk (see BGL) or more “deeppocketed.” For this reason, column 3 of Table A8 augments the specification in column
2 with a dummy O, which is equal to one if the transaction is OO and zero otherwise,
leading to a specification denoted by Z×D×E×B×Q×O. Hence, we are comparing two
transactions that are not only in the same ZIP code, distance to coast bin, elevation
bin, having the same number of bedrooms, the same quarter and year of transaction,
but also having the same owner occupied status (i.e., both OO or both NOO). Our
main results hold: the coefficient for the interaction term is positive and significant in
both the leveraged and in the long maturity regression. Column 4 repeats the exercise
in column 3, but replaces the quarter-year variable for the transaction time Q with the
benchmark month-year variable M . Again, our main results hold. Thus, we find that
our main results are robust to a variety of alternative fixed effect specifications.
In addition to the inclusion of a fixed effect for OO interacted with our other fixed
effects, we also directly examine how the main results differ for OO versus NOO buyers.
In particular, we re-estimate the main house price regression results from BGL using
our data. We replicate their findings that NOO buyers are more attentive to SLR and,
on average, pay a lower price for a home exposed to SLR relative to one not exposed.
However, when we re-estimate our main mortgage regressions instead interacting SLR
42

exposure with a variable for NOO buyer, we find that NOO buyers are not more strategic
or sophisticated in the probability that they take out a mortgage or the terms of a
mortgage, relative to OO buyers of high SLR risk properties.
6.2.4

Bad controls

In examining the effects of climate beliefs on mortgage decisions, and as highlighted
in our theoretical model, we note that multiple mortgage characteristics (e.g., lending
decision, maturity length, interest rate, loan amount) are endogenously co-determined
in the lending process. Since these endogenous mortgage characteristics are outcomes,
themselves, we do not include them in our main specifications, as we consider them
to be “bad controls.” Conditioning on them would change the characteristics of our
treatment and control comparisons, leading to results that do not represent the average
effect on our sample as a whole (Angrist and Pischke, 2008). However, as a robustness
check, we also include the interest rate as a control variable in the analysis and find the
results to be robust.42
We note that we include house price as a control variable in our main regression
results. However, while less directly negotiated in the lending decision, house price may
also arguably be a bad control if buyers include expectations about mortgage lending
in their purchase offers. Thus, Table A9 performs a further robustness check where
we repeat the leverage and maturity regressions (L1) and (M1) but omit the housing
price as a control variable. As the table shows, our results are qualitatively unaffected:
the interaction term between SLR and climate belief is positive and significant in both
columns.
6.2.5

Floods, insurance, and other natural disasters

Another potential concern is the role of flood events, current flood risk, and flood
insurance in this setting. To examine, first recall that in Table A3, we include the
count of flood events in the previous year in the property’s county, finding that its
inclusion does not alter the main results. In addition, we matched each property with
its flood risk zone using National Flood Insurance Program (NFIP) Flood Insurance
Rate Maps, which provide digitized maps for flood risk zones across the U.S. The NFIP
defines high flood risk as a probability of >1 in 100 of inundation by flooding in a
given year. Thus, we define the variable FEMA Zone equal to one if a property is
in a high risk flood zone and zero otherwise.43 In Table A10, we include this as an
42

The interest rate is only available for ≈30,000 observations in our sample. Results available by
request.
43
Specifically, FEMA Zone is equal to one if the property is in an A- or V-type zone, which comprise
the Special Flood Hazard Area. Note that location in an NFIP high risk flood zone implies both high

43

additional variable in our main regressions and also interact the variable FEMA Zone
with our climate beliefs variable. Our main results remain robust in sign, magnitude,
and significance. Interestingly, the interaction between climate beliefs and FEMA flood
zone does not significantly impact the leverage decision, further reassuring us that our
results are being driven by beliefs over SLR and not current flood risk or insurance.
This finding is logical when considering that NFIP insurance contracts are only written
for one year without the possibility of multi-year or longer-term contracts. Thus, there
are missing markets for longer-term coverage as the long-run risk cannot be hedged
through insurance.44 Defaultable long-term debt contracts could plausibly fill this gap
orthogonal to short term insurance.
When examining flood risk separate from SLR, a natural question arises regarding
other types of natural disasters as potential confounders of the analysis. Given our use
of high-dimension fixed effects (ZIP code × distance to coast × elevation × number of
bedrooms × transaction month-year), confounding variation in underlying disaster risk
would need to vary across properties at this fine of a spatial scale and be correlated
with SLR risk. Many types of disaster risk are arguably constant across this fine of
a spatial scale, including risk from earthquakes, hurricane winds, wildfires, tornadoes,
extreme precipitation, and heat. Outside of current flood risk, which we do not find to
be confounding our regressions, storm surge is a potential candidate. While we do not
have data on future storm surge estimates, we are less concerned about the potential
for this confounding our results for several reasons. First, while it is well agreed that
a changing climate will increase storm surge risk for coastal communities in the U.S.
(Wuebbles et al., 2017), the impacts of climate change on storm surge is a frontier of
climate science. Unlike for SLR, where data products such as the NOAA projections are
readily available, there is a dearth of high-resolution, national-scale estimates of storm
surge under a changing climate. Thus, unlike for SLR, there is no easily available viewer
for the public to find the specific risk of their properties or communities, casting doubt
on the public’s ability to find their future storm surge risk.45 Second, NOAA does not
include storm surge risk in their SLR model, which is based on a calm-water bathtubstyle inundation model. Thus, to the extent that storm surge matters, it is separate
from our SLR definition. Since FEMA’s flood risk maps are created to include the
flood risk and the mandate to hold flood insurance, although uptake of flood insurance remains low
even in high risk zones (Kousky and Michel-Kerjan, 2017; Kousky et al., 2017).
44
Most flood insurance contracts in the U.S. have a one-year maturity, and the maximum maturity
is three years. However, immediately following a disaster, some households are eligible to buy Group
Flood Insurance for a three-year policy period, but this temporary insurance is not renewable and thus
would not cover longer-run risk.
45
Property-specific SLR risk can easily be found through NOAA’s SLR Viewer site:
https://coast.noaa.gov/slr/ .

44

impacts of current storm surge,46 it is also reassuring that our results are robust to the
inclusion of flood risk information. Further, as discussed above, climate beliefs do not
significantly modify the mortgage decision of buyers in high-flood-risk zones relative to
low-risk zones. While we leave to future work the interesting question of the impact of
climate beliefs on mortgage decisions in other types of natural disaster risk zones, we
are reassured that our results are likely not confounded by them.

7

Diving deeper

7.1

Securitization

Thus far we have focused on testing the main implication of the model regarding the
belief heterogeneity across homebuyers (the λ’s in our model). However, the main
driving force in the model is the disagreement between lenders and borrowers (the
difference between λ̄ and λ captured by ∆λ ). To further check this mechanism, we
consider an important institutional detail that could lead banks to behave as if they
are more optimistic about future climate risks. In particular, Ouazad and Kahn (2022)
have highlighted a mechanism through which mortgage lenders can potentially shift
climate risks to government-sponsored enterprises (GSEs): by approving and securitizing mortgages that are below the conforming loan limit, which are eligible to be sold
to the GSEs. Doing so would be profitable to mortgage lenders if mortgage securities
exposed to the SLR risks are mispriced, as the GSEs’ rules and fees tend to only reflect
current official flood-plain maps and do not necessarily reflect future SLR risks.47 Via
this mechanism, mortgage lenders are more SLR-optimistic because they can shift the
SLR risks favorably to the GSEs.
This securitization mechanism is potentially relevant and complementary to our theoretical and empirical findings. Suppose it is true that mortgage lenders can securitize
and sell conforming mortgage contracts to the GSEs. Then we may expect that the
effects of SLR exposure interacted with the climate belief of buyers on leverage and
maturity outcomes to strengthen in the segment of conforming loans. Based on this
mechanism, we hypothesize that:
Hypothesis 5. The leverage and maturity channels should be stronger in the sample
of conforming loans than the non-conforming loans (γLconforming loans > γLnonconforming loans ,
conforming loans
nonconforming loans
γM
> γM
).
46

FEMA Zone V, a type of high risk flood zone, designates locations at risk from high coastal velocity
flooding.
47
It has been argued that GSE policies generally tend to be rigid and do not reflect relevant spatial
variations, including predictable regional variations in default risks (Hurst et al. 2016).

45

We investigate this securitization mechanism in Table 9. We collect data on Fannie
Mae and Freddie Mac conforming loan limits for single-unit single family homes across
our data sample from 2001 to 2016.48 Between 2001 and 2007, when the conforming loan
limit was constant across our data sample each year, we collect loan limit information
from data replication files from LaCour-Little et al. (2022). From 2008 onward, we
collect county-by-year loan limit information from the Federal Housing Finance Agency
(FHFA).49 We then match each property with the conforming loan limit in the county
and year of purchase. In column 1, we repeat our main empirical leverage regression
(L1), but replace the dependent variable with a dummy for whether a transaction is
leveraged and the mortgage is conforming. In column 2, we do the same thing as in
column 1, but replace conforming with nonconforming. Confirming our intuition above,
the estimates for SLR × P essBuyer is positive and significant for the conforming
leveraged dummy (column 1). It is negative but not statistically significant for the
nonconforming leveraged dummy (column 2).
Similarly, we repeat the long maturity regression (M1) but replace the dependent
variable with a dummy for whether the leveraged transaction is associated with a longmaturity mortgage and the mortgage is conforming (nonconforming) in column 3 (column 4). Again, the estimates for SLR × P essBuyer is positive and significant for the
conforming long-maturity outcome (column 3), but is negative and significant for the
nonconforming long-maturity outcome (column 4).
Overall, the results in Table 9 confirm our hypothesis: the effects of SLR exposure
interacted with climate belief are stronger for the conforming loan segment – which
banks can securitize loans and sell to the GSEs – than for the nonconforming loan
segment.50
48

Recall that we keep only single-unit single family homes and exclude duplexes, triplexes, and
quadruplexes.
49
Available
online
at
https://www.fhfa.gov/DataTools/Downloads/Pages/
Conforming-Loan-Limit.aspx
50
We note three potential concerns about the conforming loan results. First, prior work has highlighted concerns about mismeasurement of the conforming loan limit in empirical analyses (LaCourLittle et al., 2022). In particular, the conforming loan limit could be misassigned if using the national
annual average loan limit or using loan values rounded to the nearest $1,000. We note that we utilize
county-by-year specific conforming loan limits from the FHFA, and our data on the mortgage loan
amount at origination from CoreLogic are not rounded, therefore alleviating these concerns. Second,
there is a potential concern that since conforming loan limits are based on average housing prices
within a county, the loan limit could be endogenous to the underlying SLR risk. We note that in our
sample from 2001 to 2007, this would not be a concern since the FHFA sets uniform limits across our
data sample during this time period. In addition, our rich set of fixed effects will compare the leverage
behavior of similar houses within the same zip code, which should control for this concern. A final
concern is that conformity is defined by the origination loan amount relative to the loan limit at the
year of acquisition by the GSE, not the limit in the year of the mortgage origination, which we observe
in our data. As additional robustness, we re-estimate our conforming loan results using only years 2009
to 2016, when the conforming loan limits remained unchanged for nearly all counties in the U.S., and
therefore should be immune to measurement concerns regarding origination versus acquisition year.

46

SLR Risk
SLR Risk × PessBuyer
Property & buyer county controls
Buyer county controls × SLR
Z × D × E × B × M fe
Lender fe
N
R2

Leveraged &
Conforming Nonconform

Long Maturity &
Conforming Nonconform

-0.016
(0.015)
0.033***
(0.012)

0.013*
(0.007)
-0.001
(0.004)

-0.009
(0.021)
0.033***
(0.012)

0.007
(0.013)
-0.015**
(0.007)

Y
Y
Y

Y
Y
Y

406,601
0.478

406,601
0.566

Y
Y
Y
Y
182,771
0.569

Y
Y
Y
Y
182,771
0.669

Table 9: Role of conforming loans. Column 1: dependent variable is whether a transaction is leveraged and the mortgage is conforming. Column 3: restricting to leveraged
sample, dependent variable is whether the mortgage has long maturity (≥30 years)
and is conforming. Column 2 and 4 repeat columns 1 and 3, respectively, but replace
conforming with nonconforming. For brevity, only estimates of the coefficients of SLR
Risk and the interaction term SLR Risk × Pessimistic Buyer are reported. The rest is
the same as in Tables 5 and 6.

7.2

Monetary policy implications

We now test the model’s monetary policy implications. We augment specification (L1)
by including a triple interaction of our SLR and beliefs variables with the policy interest
rate ιt :
Leveragedit = βL SLRi + γL SLRi × P essBuyerc + ζL SLRi × P essBuyerc × ιt
+ ϖL0 ιt + ϖL1 SLRi × ιt + ϖL2 P essBuyerc × ιt + δL P essBuyerc
+ ρL ln P riceit + ϕ′L Xi + θL′ Zct + ξL′ SLRi × Zct + ΛLZDEBM + ϵLit .

(L2)

The key coefficient of interest is ζL . For an empirical measure of ιt , we use the market
yield on Treasury securities at two-year maturity, a standard proxy for lenders’ funding
cost affected by the nominal interest rate set by the monetary authority in the U.S.51
Similarly, we set up a maturity regression (M2) with all the interaction terms with ιt .
Based on Proposition 4, we hypothesize that:
Hypothesis 6. In transactions of properties exposed to SLR risk, a decrease (increase)
in the interest rate ι increases (decreases) the probability that a purchase of an exposed
property by a pessimist is leveraged, but it does not impact the maturity choice (ζL >
Table A11 presents the results. Our leverage results remain robust. Our long maturity results on the
interaction term remain robust in magnitude although lose significant under the reduced sample size.
51
Retrieved from https://fred.stlouisfed.org/series/DGS2.

47

0, ζM = 0).

SLR Risk
SLR Risk × PessBuyer
SLR Risk × PessBuyer × Policy Rate
Property & buyer county controls
Buyer county controls × SLR
Z × D × E × B × M fe
Lender fe
N
R2

Leveraged

Long Maturity

-0.022
(0.017)
0.049***
(0.015)
-0.009**
(0.005)

0.003
(0.016)
0.035***
(0.012)
-0.005
(0.004)

Y
Y
Y

Y
Y
Y
Y
150,746
0.441

405,893
0.473

Table 10: Effects of monetary policy. Dependent variable in Column 1 is Leveraged
(whether the transaction is associated with a mortgage) and in Column 2 is Long
Maturity (whether the mortgage term is 30 years; sample restricted to transactions with
an associated mortgage contract). Policy Rate denotes the market yield on Treasury
securities at two-year maturity. For brevity, only estimates of the coefficients of SLR
Risk and its interaction terms are reported. The rest is the same as in Tables 5 and 6.
Column 1 of Table 10 reports the estimates for βL , γL and ζL from equation (L2).
As before, the coefficient γL for the double interaction term between SLR risk and High
Buyer Belief remains significant and positive. However, as the model predicted, the
estimate for the coefficient ζL for the triple interaction term is negative and statistically
significant. Column 2 repeats the exercise but replaces the left-hand-side variable with
the Long Maturity dummy. There, the triple interaction term is not significant. This
is consistent with the model’s prediction that the interest rate ιt does not have any
significant effect on maturity choice. Overall, our empirical results suggest support for
the model’s implication on the effect of monetary policies on the leverage probability of
property transactions that are subject to SLR risk. The results highlight the potential
impact of monetary policies on climate risk in the financial system.

7.3

Results over time

Since both the attention to global warming and the disagreement in public opinion
about climate change have become more salient in the past decade (Engle et al. 2020;
Bernstein et al. 2022), it is natural to ask whether our results change over time. Table
A12 investigates this question. Columns 1, 3, and 5 repeat regressions (P1), (L1), and
(M1), respectively, for the subsample of transactions that took place before 2010, while
columns 2, 4, and 6 repeat them for transactions during or after 2010.
48

Consistent with the earlier literature (e.g., BGL and Goldsmith-Pinkham et al.
2021), columns 1 and 2 show that the pricing of SLR risk is more pronounced after 2010,
as the estimates for the SLR variable are more significant and negative in the recent
sample. More importantly, the estimates of the interaction terms SLR Risk × PessBuyer
in columns 3 to 6 show that our main results on the effects of SLR and climate beliefs
on mortgage outcomes are more significant (statistically and economically) in the more
recent sample. Thus, these results are consistent with climate risk in financial systems
becoming more pronounced over time as heterogeneous climate beliefs, and climate risk
salience among pessimists, has increased.

7.4

Other intensive margins

A natural question arises as to how climate beliefs affect other intensive margin outcomes such as the loan amount and interest rate mortgage characteristics.52 Thus, we
re-estimate our main regression specifications using the loan amount and interest rates
as outcome variables. Table A13 reports these results. Consistent with our theoretical
model, which produce ambiguous comparative statics with respect to the equilibrium
loan amount B, column 1 shows that the interaction between the SLR risk and the
pessimistic buyer dummy does not have a significant impact on the mortgage amount:
the estimated coefficient is positive but not statistically significant. Similarly, in column 2, where the dependent variable is the mortgage interest rate, the estimate of the
interaction term is positive but not statistically significant.53

8

Conclusion

What makes climate risks special? Three outstanding characteristics are that (i) climate risks could have potentially large damages, (ii) the risks are back-loaded (i.e.,
most damages are expected to occur in the future), and (iii) there is substantial belief disagreement over climate risks, especially in the U.S. Our paper theoretically and
empirically argues that the combination of these features is key in understanding the effects of climate risks on the financial market. In particular, we find that despite paying
less for an at-risk property, climate pessimists are more likely to take out a mortgage
and for a longer maturity relative to climate optimists.
52
Recall from Section 6.2.4 that we do not include these in endogenous mortgage characteristics in
our main regression models as they are bad controls.
53
Note that in column 2, we also include a fixed effect for whether a mortgage has a 30-year maturity,
so that we are only comparing the mortgage interest rates of loans that have similar maturity. Also
note that the sample size shrinks to approximately 30,000 observations in this exercise. It is possible
that the interaction term becomes statistically significant if we had a larger sample.

49

We believe that the exploration of the implications of climate risks for debt markets
is an exciting area for future research, both theoretically and empirically. For instance,
our analysis implies that adaptation strategies in financial markets, which are known
to be subject to agency problems, may have nontrivial implications, specifically due
to the strategic transfers of climate risks. Whether this could lead to concentration
of climate risks among a small set of systemically important financial institutions and
whether it could affect financial stability or general welfare remain open questions (Phan
2021, 2022). While we have focused entirely on a positive analysis, future work could
explore a normative analysis of prudential policies vis-a-vis the strategic transferring of
climate risks we documented. For example, it could be interesting to introduce belief
heterogeneity into a quantitative macro model with climate risk (e.g., à la Panjwani
2022) and study optimal prudential policies (e.g., à la Bianchi and Mendoza 2018).
Moreover, future research on the potential effects of climate change on financial stability
(such as climate stress testing exercises à la Jung et al. 2021) should take the strategic
transferring of climate-related risks into account.
Finally, future work could explore the roles of several important margins we have
not considered in this paper. For instance, one could extend our theoretical model to
allow agents to resell the house, and one could expand our empirical analysis to study
whether climate risks and climate beliefs affect how resalable a property is. One could
extend our analysis to theoretically and empirically study potential interactions between
mortgage choice and residential sorting (à la Bakkensen and Ma 2020; Bakkensen and
Barrage 2022). These are some open questions that are exciting for future research.

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A
A.1
A.1.1

Appendix
Omitted proofs
Proof of Proposition 1

Given the Poisson nature of the disaster and loan maturity, there is no new information
nor change in the individual state before the arrival of the disaster or loan maturity.
Thus, the optimal default time is time-independent and will take the following form,
which is contingent on the timing of the disaster and loan maturity:



τ

 0
Tf = Td + τd



∞

before the disaster and loan maturity
after the disaster but before loan maturity .
after loan maturity

We solve the buyer’s default decision using backward induction. Consider the subgame after the disaster has happened at t = Td but before the loan maturity. Denote
Tm = Td + τm as the loan maturity date, where τm follows an exponential distribution
with parameter rµ, where
µ=

1
1
− 1 ≤ µ0 =
− 1.
Γ
Γ0

The buyer’s continuation value at t = Td of defaulting at Tf = Td + τd is given by:
Z
W (τd ) ≡

 R min(τm ,τd )

re−rt (h − d − M ) dt
 0


rµe−rµτm
+e−rτd 1τd ≤τm −f + {h − d − B}+


+e−rτm 1τd >τm (h − d)





dτm




where we have made use of the fact that pt = h − d and Bt = B = ΓM . Note that the
value function satisfies the following Hamilton–Jacobi–Bellman (HJB) equation:
d
W (τ ) = r (h − d − M ) + rµ [h − d − W (τ )] − rW (τ ) .
dτ

(29)

The HJB states that the marginal value of postponing default (the left-hand side) is
equal to the sum of the flow of asset return (post-disaster) net of the loan repayment,
57

r (h − d − M ), and the expected gain of paying off the loan, rµ [h − d − W (τ )], minus
the cost of discounting, rW (τ ). The case τ = 0 represents that the buyer defaults
immediately, which gives the following boundary condition to (29):
W (0) = −f + {h − d − B}+ .
Using the boundary condition, the HJB equation has the following solution:




W (τ ) = 1 − e−r(1+µ)τ (h − d − B) + e−r(1+µ)τ −f + {h − d − B}+ .

(30)

The first term is the present value of never default, and the second term is the value
of immediate default. Thus, W (τ ) is the average weighing the latter by the factor
exp [−r (1 + µ) τ ]. The optimal stopping time to default is τd = ∞ if the first term is
weakly larger and τd = 0 if the second term is strictly larger, imposing a tie-breaking
rule that a borrower chooses to never default when he is indifferent. The first term is
a downward-sloping curve in B; the second term is downward-sloping curve in B with
the same slope for all B < h − d but then flat at −f for all B ≥ h − d. Thus, the first
term cuts the second term from above in the flat region of the second term at the single
crossing point B = bsafe , where
bsafe = h − d + f .

(31)

Denote W ∗ (b) ≡ maxτ W (τ ) as the continuation value under the optimal stopping
time of default τd , which is given by:
(
W ∗ (B) ≡ W (τd ) =

h − d − B, if B ≤ bsafe
−f , if B > bsafe

(32)

which is given by:
(
τd ≡ arg max W (τ ) =
τ

∞, if B ≤ bsafe
.
0, if B > bsafe

(33)

Now, consider the subgame at t = 0 before the disaster and loan maturity. Denote
Tm as the loan maturity date in this case, where Tm follows an exponential distribution
with parameter rµ. Recall the disaster arrives at Td , which follows the Poisson rate rλ.

58

At t = 0, the buyer’s continuation value of defaulting at τ0 , where τ0 ≤ Td , is given by:
 R
min(Tm ,τ0 ,Td )

re−rt (h − M ) dt

0


Z
Z
 +e−rTd 1
∗
Td ≤min(Tm ,τ0 ) W (BTd )
−rλTd
−rµTm


V (τ0 ) ≡ rλe
rµe
−rτ0

+e
1
−f
+
{p̄
−
B
}
λ
τ
τ
≤T
,τ
<T

m
0
0
0
d
+


 +e−rT 1
Tm <τ0 ,Tm <Td vλ








dTm dTd






(34)

Note that the value function satisfies the following HJB equation:
d
V (τ ) = r (h − M ) + rµ [vλ − V (τ )] − rλ [V (τ ) − W ∗ (B)] − rV (τ ) .
dτ

(35)

The HJB states that the marginal value of postponing default is equal to the sum of
the flow of asset return (pre-disaster) net of the loan repayment, r (h − M ), and the
expected gain of paying off the loan, rµ [vλ − V (τ )], minus the expected loss from the
exposure to the disaster, rλ [V (τ ) − W ∗ (B)], and the cost of discounting, rV (τ ). At
τ = 0, the buyer defaults immediately, which gives the boundary condition to (35):
V (0) = −f + {p̄λ − B}+ .
Using the boundary condition, the HJB equation has the following solution:
V (τ ) =


 h − (1 + µ) B + λW ∗ (B) + µvλ
1 − e−r(1+λ+µ)τ
1+λ+µ
|
{z
}
V1 (B)

−r(1+λ+µ)τ

+e



−f + {p̄λ − B}+ .
|
{z
}

(36)

V2 (B)

The first term is the present value of never default before the disaster, and the second
term is the value of immediate default. Define the first term as V1 (B) and the second
term as V2 (B). Thus, we have τ0 = 0 if V1 (B) < V2 (B) and τ0 = ∞ if V1 (B) ≥
V2 (B), imposing a tie-breaking rule that a borrower chooses to never default when he
is indifferent. We want to solve the region of B such that V1 (B) < V2 (B).
Using W ∗ (B) from (32), V1 (B) is given by:
(
V1 (B) =

vλ − B, if B ≤ bsafe
.
h−λf +µvλ
1+µ
safe
−
B,
if
B
>
b
1+λ+µ
1+λ+µ

V1 (B) features the values for two default strategies: in the first region B ≤ bsafe , the
buyer never defaults; in the second region B > bsafe , the buyer defaults immediately
after the disaster (which is also optimal in that subgame, shown above) but does not
59

default beforehand. Thus, V1 (B) is descreasing in B with slope equal to −1 in the first
1+µ
∈ (−1, 0) in the second region.
region and with slope equal to − 1+1+λ+µ
On the other hand, V2 (B) is decreasing in B, with the slope equal to −1 when B ≤
p̄λ ; otherwise the slope equals 0. Also, notice that we have V1 (0) = vλ > p̄λ −f = V2 (0)
following the assumption (3). Thus, we must have V2 (B) intersecting V1 (B) from below
at the flat region of V2 (B) – see the
in Figure A1. Denote the intersection

 illustration
risky
risky
risky
and
= −f , where V1 (b) > V2 (b) if B < brisky
= V2 bλ
as B = bλ , i.e., V1 bλ
 λ


, we must
vice versa. Notice that since V1 bsafe = vλ − (h − d + f ) > −f = V1 brisky
λ


risky
risky
risky
safe
to
have bλ > b . In sum, bλ is given by setting the second region of V1 bλ
−f :
λ
= h − (1 − Γ)
brisky
d + f.
(37)
λ
1+λ
V
vλ
V1 (B)
p̄λ − f
V2 (B)
d
1+λ

−f

−f

bsafe

brisky
λ

p̄λ

B

Figure A1: Illustration of value functions V1 (B) and V2 (B) from equation (36) and the
determination of the risky debt limit brisky
in (37).
λ
Summarizing the above cases, the optimal stopping time of default before the disaster is given as:



∞ if B ≤ bsafe ,


Tf = Td if B ∈ (bsafe , brisky
] and Td < Tm , .
λ



0 otherwise.
QED

60

A.1.2

Proof of Proposition 2

In this section, we solve for the optimal contract a = (L, M, Γ) in the general case with
the difference in funding costs ω ≥ 0 (as described in Section 3.3.2); Proposition 2 is
the special case with ω = 0. Using Proposition 1, the borrower’s surplus of buying an
asset with the loan contract a is given by:



−B
if B ≤ bsafe ,


Vλ (a) = vλ + −Tλ M − Qλ (h − d + f ) if B ∈ (bsafe , brisky
],
λ



−v − f
otherwise
λ

(38)

where
Z

Tm ∧Tf (λ,a)

Tλ ≡ Eλ

re−rt dt =

0

Qλ ≡ Eλ 1Tf (λ,a)<Tm e−rTf (λ,a)


1
,
1+λ+µ
λ
.
=
1+λ+µ

Given the buyer’s default strategy Tf (λ, a) from Proposition 1, the expected present
value of the loan repayments before the disaster is



B
if B ≤ bsafe


Rλ (a) = Tλ̄ M + Qλ̄ (h − d) if B ∈ (bsafe , brisky
],
λ



p̄
otherwise
λ

(39)

where
Z

Tm ∧Tf (λ,a)

Tλ̄ ≡ Eλ̄

re−rt dt =

0

Qλ̄ ≡ Eλ̄ 1Tf (λ,a)<Tm e−rTf (λ,a)


Γ =

1
,
1 + λ̄ + µ
λ̄
= λ̄Tλ̄ ,
=
1 + λ̄ + µ

Tλ̄
.
1 − λ̄Tλ̄

The joint surplus is thus given by

ω


B

1+ω

B
Vλ (a) − vλ
Tλ
+Rλ (a) =
Tλ̄ − 1+ω
+ Qλ̄ −
Γ

1+ω


p̄ − vλ +f
λ

1+ω

if B ≤ bsafe
Qλ
1+ω



(h − d) − Qλ f

if B ∈ (bsafe , brisky
].
λ
otherwise
(40)

61

The equilibrium contract solves

max
a


V (a) − vλ
+ Rλ (a) − κ0 (Γ) = max {Sλ (Tλ̄ ) − κ (Tλ̄ )} ,
Tλ̄ ≥T0
1+ω

with

o
n
Sλ (Tλ̄ ) = max S safe , Sλrisky (Tλ̄ ) , Sλ0 ,

where the optimal joint surpluses in three regions are given by:
ω safe
b ,
1+ω





Tλ
Qλ
B
risky
max
Tλ̄ −
Sλ (Tλ̄ ) ≡
+ Qλ̄ −
(h − d) − Qλ f ,
1+ω Γ
1+ω
B∈(bsafe ,brisky ]
vλ + f
.
Sλ0 ≡ p̄λ −
1+ω
S safe ≡

Assume that ω is sufficiently small such that

vλ + f − p̄λ > ω p̄λ − bsafe for all λ.

(41)

Thus, we have S safe > Sλ0 . In other words, the borrower prefers never default over
immediate default. That is, the optimal S in the first region of (40) always dominates
any S in the third region, and so we can ignore the third region. The condition is
automatically satisfied when ω = 0.
Notice that the optimal B for Sλrisky is given by
(
B=


brisky
, if λ − λ̄ Tλ̄ ≥
λ
bsafe , otherwise,

−ω
,
1+ω


Tλ
where we have made use of the fact that Tλ̄ − 1+ω
≥ 0 is equivalent to λ − λ̄ Tλ̄ ≥
Substituting the optimal B, we have
(
Sλrisky

(Tλ̄ ) ≡


+ f ) + ∆λ Tλ̄ , if λ − λ̄ Tλ̄ ≥
− λ̄f Tλ̄ , otherwise.

ω
(vλ
1+ω
safe

S

−ω
.
1+ω

−ω
,
1+ω

We define the following constants (the version in Proposition 2 is the special case

62

ω = 0):

λa ≡

λb ≡




ωd
λ̄(f +d)− (1+ω)T

, if d > λ̄f,
,
 ∞, otherwise,
( λ̄(f +d)+κ′ (T )
0
, if d > λ̄f + κ′ (T0 ) ,
d−λ̄f −κ′ (T0 )
0

d−λ̄f

∞, otherwise,

We note the following results. First,
Tλ̄ > T0 ⇔ Sλrisky′ (T0 ) > κ′ (T0 ) ⇔ λ > λb .

(42)

Second, the condition that a binding risky loan with B = brisky
and Tλ̄ = T0 dominates
λ
safe
a binding safe loan B = b
and Tλ̄ = T0 is given by
Sλrisky (T0 ) > S safe ⇔ λ > λa .

(43)

Third, rearranging terms, we have that

−ω
.
λ > λa ⇒ λ − λ̄ Tλ̄ >
1+ω

(44)

We want to verify the three cases in Proposition 2. First, if λ > λb , then the
equilibrium contract is the risky loans with B = brisky
and Tλ̄ > T0 . Second, if λ ∈
λ
(λa , λb ], then the equilibrium contract is also the risky loans with B = brisky
but Tλ̄ = T0 .
λ
Third, if λ ≤ λa , then the equilibrium contract is in the safe loans with B = bsafe and
Tλ̄ = T0 if ω > 0, and no borrowing at all if ω = 0. Notice that λb > λa , so these
regions are well-defined.
Consider the case λ > λb . Notice that Sλrisky (Tλ̄ ) ≥ Sλrisky (T0 ) and λb > λa , so the
buyer always searches for a risky loan with Tλ̄ , following (43). Following λ > λb , we
have Tλ̄ > T0 from (42). The first-order condition of Tλ̄ is
κ′ (Tλ̄ ) = Sλrisky′ (Tλ̄ ) = ∆λ ,
and hence we have Tλ̄ = k (∆λ ) stated in Proposition 2. Using the fact that λ > λb > λa ,

−ω
from (44), so the optimal risky loan features B = brisky
.
we have λ − λ̄ Tλ̄ > 1+ω
λ
Consider the case λ ∈ (λa , λb ]. Notice that λ > λa , so the buyer always searches
for a risky loan with Tλ̄ , following (43). Since λ ≤ λb , we have Tλ̄ = T0 from (42),

−ω
Since λ > λa , we have λ − λ̄ Tλ̄ > 1+ω
from (44), so the optimal risky loan features
risky
B = bλ .
Consider the case λ ≤ λa . Notice that λ ≤ λa , so the buyer does not search for
63

a risky loan, following (43). She searches for a safe loan with B = bsafe and Tλ̄ = T0
if S safe > 0, which is equivalent to ω > 0. Otherwise, if ω = 0, then she prefers
not searching for any loan at all. In sum, we have established the three regions of
Proposition 2.
Finally, given the optimal loan contract a, the buyer’s problem w.r.t. α is



ψ
Jλ = max α max {Sλ (Tλ̄ ) − κ (Tλ̄ )} −
= max N (1, n) max {Sλ (Tλ̄ ) − κ (Tλ̄ )} − ψn ,
n≥0
Tλ̄ ≥T0
Tλ̄ ≥T0
α∈[0,1]
η (α)


where we have made use of the matching function identities from (8) and (9) that
α = N (1, n) and α/η (α) = n. The first-order conditions with respect to n is
ψ≥

∂
N (1, n) max {Sλ (Tλ̄ ) − κ (Tλ̄ )} ,
Tλ̄ ≥T0
∂n

(45)

with equality if α > 0 and otherwise α = 0 if Sλ (Tλ̄ ) − κ (Tλ̄ ) ≤ 0. Substituting the
functional form of g (x), we have the formula of α stated in Proposition 2.
The competitive-search equilibrium exists and is uniquely constructed by setting
(
Aλ =
ηλ (a) =
αλ (a) =

a

)

ψ
Vλ (a)−vλ
1+ω

+ Rλ (a) − κ0 (Γ)
ψ
;
+ Rλ (a) − κ0 (Γ)

∈ [0, 1]

;

Vλ (a)−vλ
1+ω
−1
η [ηλ (a)] ;

(
nb (λ, a) =

ϕ (λ) if type-λ buyers choose a,
0 otherwise,

nl (λ, a) = nb (λ, a)

αλ (a)
.
ηλ (a)
QED

A.1.3

Proof of Proposition 3

Notice that
κ′ (Tλ̄ ) = κ′0
κ′′ (Tλ̄ ) = κ′′0

1
Tλ̄

1
Tλ̄

1
− λ̄

!

1
− λ̄

!

1
1 − λ̄Tλ̄
1
1 − λ̄Tλ̄

2 > 0,
′
4 + κ0

64

1
Tλ̄

1
− λ̄

!

2λ̄
1 − λ̄Tλ̄

3 > 0,

Thus, k (x) is increasing in x as we have k ′ (x) = 1/κ′′ (Tλ̄ ) > 0. Similarly, notice that
G (n) ≡ ∂N (1, n) /∂n is decreasing in n following the concavity of N (1, n) and hence
g (x) ≡ N [1, G−1 (ψ/x)] is increasing in x. Using these results, the comparative statics
of Tλ̄ and α are straightforward following the closed forms provided in Proposition 2.
We will focus on the comparative statics of m, B and rm .
Using Proposition 2, for any λ > λa , M is given by


brisky
µ
λµ
λ
M=
= (1 + µ) (h − d + f ) + 1 +
d = (1 + µ) (h + f ) −
d (46)
Γ
1+λ
1+λ

Recall that Tλ̄ = 1/ 1 + λ̄ + µ . Since ∂µ/∂λ < 0 for any λ > λa following ∂Tλ̄ /∂λ > 0,
differentiating the sides of the first equality above, we have ∂M/∂λ < 0. Similarly, since
∂µ/∂d < 0 for any λ > λa following ∂Tλ̄ /∂d > 0, differentiating the sides of the second
equality above, ∂M/∂d < 0 as stated in Proposition 3.
For the comparative statics of B, notice that the free-entry condition implies that
L=

M
λ̄
k
+
(h − d) − κ (Tλ̄ ) −
.
η (α)
1 + µ + λ̄ 1 + µ + λ̄

(47)

Since µ is constant in the region of λ ∈ (λa , λb ], using the above result that ∂M/∂λ < 0
and ∂α/∂λ > 0 (hence −ψ/η (α) is decreasing in λ), we have ∂L/∂λ < 0 in the region
of λ ∈ (λa , λb ]. Similarly, we can show ∂L/∂d < 0. In region of λ > λb , we have
∂µ/∂λ < 0 so, via µ, λ additionally increases the first two terms of (47) but decreases
the third term. The overall sign of ∂L/dλ becomes ambiguous for λ > λb . The same is
true for ∂L/∂d for λ > λb .
For the comparative statics of rm , notice that rm is defined as the lender’s yield of
mortgage payments such that:
κ (Tλ̄ ) +
Rλ (a)
−1=
r ≡
L
L
m

ψ
η(α)

.

(48)

In the region of λ ∈ (λa , λb ], since Tλ̄ is constant, using the result that ∂L/∂λ < 0
and ∂α/∂λ > 0 (hence ψ/η (α) is increasing in λ), we have ∂rm /∂λ > 0 in the region
of λ ∈ (λa , λb ]. Similarly, we can show ∂rm /∂d < 0. In region of λ > λb , we have
∂Tλ̄ /∂λ > 0 so, via Tλ̄ , λ additionally increases the term κ (Tλ̄ ) of (48), but the sign of
∂L/∂λ is ambiguous. The overall sign of ∂rm /∂λ becomes ambiguous for λ > λb . The
same is true for ∂rm /∂d for λ > λb .
QED

65

A.1.4

Proof of Proposition 4

The first part was already proved in Section A.1.2. For the second part, note that an
expansionary monetary policy means a higher ω. The comparative statics of Tλ̄ with
respect to ω is straightforward, so we focus on α. The derivative of (45) is
∂λ
d
−G′ (n)
∂n =
max {Sλ (Tλ̄ ) − κ (Tλ̄ )}
,
G (n)
dω Tλ̄ ≥T0
maxTλ̄ ≥T0 {Sλ (Tλ̄ ) − κ (Tλ̄ )}
where the envelope theorem implies that
1
d
max {Sλ (Tλ̄ ) − κ (Tλ̄ )} =
dω Tλ̄ ≥T0
(1 + ω)2

(

bsafe , if λ ≤ λa ;
>0
vλ + f , if λ > λa .

(49)

Notice that ∂α = G (n) ∂n and G′ (n) < 0, so combining the above we have ∂α/∂ω > 0.
QED
A.1.5

Proof of Proposition 5

Notice that

ψ
,
= max α max {Sλ (Tλ̄ ) − κ (Tλ̄ )} −
Tλ̄ ≥T0
α∈[0,1]
η (α)






ψ
ω (vλ + f ) 
= max α max
+ 1 + λ̄ (vλ̄ − vλ ) + λ̄f Tλ̄ − κ (Tλ̄ ) −
.
Tλ̄ ≥T0
α∈[0,1]
1+ω
η (α)


Jλ

The envelope theorem implies that
∂Jλ
=α
∂λ



ω
1 + λ̄
−
1 + ω 1 + µ + λ̄



∂vλ
∂λ

Recall that the bargaining solution of the house price is
P =

1−θ
[vλ + (1 + ω) Jλ ] + θvλs ,
1+ρ

Thus we have
∂P
∂λ






1 − θ ∂vλ
∂Jλ
1−θ
1 + λ̄
∂vλ
=
+ (1 + ω)
=
1+α ω−
(1 + ω)
1 + ρ ∂λ
∂λ
1+ρ
∂λ
1 + µ + λ̄


<1
z
}|
{

1 + λ̄
1 − θ
αωµ 
 ∂vλ < 0.
=
1
−
α
+

1+ρ
∂λ
1 + µ + λ̄ 1 + µ + λ̄ |{z}
<0

|

{z

}

>0

66

Similarly, we have
∂Jλ
=α
∂d

1 − λλ̄
ω
−
1 + ω 1 + µ + λ̄

!

∂vλ
,
∂d

where we have made use of the fact that
 ∂vλ̄
λ̄ ∂vλ
1 + λ̄
= (1 + λ)
.
∂d
λ ∂d
Thus we have
 

λ̄
(1
+
ω)
1
−
λ
1−θ 
 ∂vλ
=
1 + α ω −
1+ρ
∂d
1 + µ + λ̄


<1
z  }| {



λ̄ 
λ̄


αω
µ
+
λ̄
+
α
1
−
λ
λ  ∂vλ
1 − θ
< 0.
+
=
1 −

1 + ρ
∂d
1 + µ + λ̄
1 + µ + λ̄ |{z}




∂P
∂d



<0

|

{z

}

>0

Finally, we have




Jλ
∂ω ∂Jλ 
∂P

= (1 − θ) −
 < 0.
2 +
∂ι
∂ι |{z}
∂ω
(1 + ι)
|{z}
<0

>0

QED

67

A.2

Omitted tables
Fraction of buyers from county
choosing a coastal home
Buyer county belief
Buyer county
Buyer county
Buyer county
Buyer county
Buyer county

0.001*
(0.001)
income
0.003***
(0.000)
population
-0.000***
(0.000)
share with bachelor’s degree -0.006
(0.072)
share 18-29 age
-0.089
(0.056)
share of white
-0.067***
(0.019)

Time F.E.
State F.E.
N
R2

Y
Y
14921
0.174

Table A1: Coastal buyers and buyer beliefs. This figure models the fraction of buyers
in a county that select a coastal home. If sorting were a concern, one would expect
a negative correlation between the fraction of buyers purchasing a coastal home and
the climate beliefs of where the buyer is from (a proxy for the buyer’s climate belief).
Instead, after controlling for sociodemographic factors from the buyer’s county of origin
as well as time and state fixed effects, we find a positive correlation between the buyer’s
county beliefs and the fraction of buyers purchasing a coastal home.

68

Happening

Leveraged
Worried

Timing

Long Maturity
Happening Worried Timing

SLR Risk × Pess Buyer (above median)

0.034***
(0.011)

0.046***
(0.012)

0.031**
(0.013)

0.024***
(0.007)

0.027***
(0.007)

0.023***
(0.007)

SLR × 2nd Quartile Belief

0.023**
(0.011)
0.010
(0.017)
0.046**
(0.018)

0.006
(0.012)
0.058***
(0.013)
0.047*
(0.027)

0.002
0.030***
(0.011)
(0.008)
0.021
0.034***
(0.015)
(0.011)
0.051*** 0.035***
(0.015)
(0.010)

0.008
(0.010)
0.033***
(0.009)
0.023
(0.017)

0.025**
(0.010)
0.016
(0.010)
0.038***
(0.010)

SLR Risk × Belief (continuous)

0.002
(0.001)

0.003*** 0.003**
(0.001)
(0.001)

0.002**
(0.001)

0.002**
(0.001)

0.003***
(0.001)

Z × D × E × B × M fe
Property & buyer county controls
Buyer county controls × SLR
Lender fe

Y
Y
Y

Y
Y
Y

Y
Y
Y
Y

Y
Y
Y
Y

Y
Y
Y
Y

SLR × 3rd Quartile Belief
SLR × 4th Quartile (highest) Belief

Y
Y
Y

Table A2: Robustness with alternative specifications for the buyer county belief measure. Columns 1-3 report results for variations of leveraged regression (L1) and columns
4-6 for long maturity regressions (M1). Columns 1 and 4 (Happening) use 2014 Yale
Climate Opinion survey data for the percentage of people in each county who say they
believe climate change is happening; Columns 2 and 5 (Worried ) – the percentage who
say they are worried about climate change; Columns 3 and 6 (Timing) – the percentage who think global warming will start to harm people in the U.S. within 10 years.
PessBuyer in row 1 indicates whether the buyer is from a county where the climate
belief variable is above the sample median. Rows 2-4 rank counties into quartiles of the
climate belief variable, and nth Quartile Belief is one if the buyer is from a county in
that nth quartile of belief and zero otherwise. Row 5 uses the continuous measure of
the belief variable (i.e., respectively, the fraction of the buyer’s county saying that they
belief climate change is happening, or that they are worried about climate change, or
that they think that global warming will harm the U.S. within 10 years). For brevity,
only estimates of the coefficients of the interaction term SLR Risk × belief are reported.
The rest is the same as in Tables 5 and 6.

69

SLR
SLR × PessBuyer

Leveraged

Long Maturity

0.425
(0.347)
0.036**
(0.014)

0.514**
(0.249)
0.033**
(0.014)

Additional Controls
Y
Property & Buyer County Controls Y
Z × D × E × B × M fe
Y
Buyer County Controls × SLR
Y
Lender fe
N
222,920
R2
0.444

Y
Y
Y
Y
Y
67,299
0.447

Table A3: Robustness to the inclusion of a variety of additional control variables,
including buyer’s county average test scores, race, age, and gender as well as crime,
unemployment, new building permits and previous flood events from the property’s
county. The sample is 2010 to 2016. The rest is the same as in Tables 5 and 6.

SLR
SLR × PessBuyer

Leveraged

Long Maturity Leveraged

Long Maturity

-0.013
(0.04)
0.036***
(0.013)

0.016
(0.025)
0.022***
(0.008)

0.005
(0.023)
0.025***
(0.009)

Political Control
Repub. share Repub. share
Z × D × E × B × M fe
Y
Y
Buyer county controls × SLR Y
Y
Lender fe
Y
N
405,893
150,746
R2
0.473
0.441

0.006
(.025)
0.036***
(0.014)

Dem. share Dem. share
Y
Y
Y
Y
Y
405,825
150,734
0.473
0.441

Table A4: Robustness to the inclusion of political affiliation data (percent of Republican
or Democrat vote shares in the previous presidential election at the county level). The
rest is the same as in Tables 5 and 6.

70

Continuous

Yale
happening
1
(0.0000)
Yale worried
0.9020***
(0.0000)
0.8526***
Yale timing
(0.0000)
Gallup when
0.5685***
(0.0000)
Gallup worried 0.6759***
(0.0000)
Individual λ̂
0.0046**
(0.0339)
County mean λ̂ 0.1391***
(0.0000)

Yale
worried

Yale
timing

Gallup
when

Gallup
worry

Individual
b
λ

1
(0.0000)
0.9187***
(0.0000)
0.6414***
(0.0000)
0.7742***
(0.0000)
0.0021
(0.346)
0.1267***
(0.0000)

1
(0.0000)
0.5133***
(0.0000)
0.6843***
(0.0000)
0.0005
(0.8041)
0.1216***
(0.0000)

1
(0.0000)
0.8083*** 1
(0.0000)
(0.0000)
0.0029
0.0001
1
(0.1777)
(0.9465)
(0.0000)
0.0627*** 0.0919*** 0.1165***
(0.0000)
(0.0000)
(0.0000)

County average
b
λ

1
(0.0000)

Table A5: Pairwise correlation of continuous belief variables. Yale beliefs data are from
the Yale Climate Opinions survey operationalized as the average county-level climate
belief. Beliefs from the Gallup data are imputed by the authors as described in the main
b is the transaction-level beliefs imputed
text at the county-by-year level. Individual λ
b represents a countyby the authors as described in the main text. County mean λ
b
level mean value of the continuous λ variable averaged across buyers from that county.
Pairwise correlation p-values are shown in parentheses.

Above median

Yale
happening
Yale happening
1
(0.0000)
Yale worried
0.6458***
(0.0000)
Yale timing
0.5898***
(0.0000)
Gallup when
0.4631***
(0.0000)
Gallup worried
0.4697***
(0.0000)
\
P essBuyer
0.0464***
(0.0000)
County above med. λ̂ 0.0909***
(0.0000)

Yale
worried

Yale
timing

Gallup
when

Gallup
worry

Individual County average
b
b
λ
λ

1
(0.0000)
0.6868***
(0.0000)
0.6794***
(0.0000)
0.7178***
(0.0000)
0.0299***
(0.0000)
0.0493***
(0.0000)

1
(0.0000)
0.4574***
(0.0000)
0.5075***
(0.0000)
0.0302***
(0.0000)
0.1106***
(0.0000)

1
(0.0000)
0.7425***
(0.0000)
0.0058***
(0.0000)
-0.0382***
(0.0000)

1
(0.0000)
0.0419***
(0.0000)
0.0166***
(0.0000)

1
(0.0000)
0.0491***
(0.0000)

1
(0.0000)

Table A6: Pairwise correlation of dichotomous (above median) belief variables, which
are defined to be one if the corresponding belief variable from Table A5 is above the
sample median and zero otherwise.

71

1.SLR (6ft)
2.SLR (5ft)
3.SLR (4ft)
4.SLR (≤3ft)
1.SLR × PessBuyer
2.SLR × PessBuyer
3.SLR × PessBuyer
4.SLR × PessBuyer
Property & buyer county controls
Buyer county controls x SLR
Z × D × E × B × M fe
Lender fe
N
R2

Leveraged

Long Maturity

0.0180
(0.014)
0.0140
(0.020)
-0.0343
(0.027)
-0.0362
(0.031)
0.0154
(0.012)
0.0246*
(0.015)
0.0455**
(0.018)
0.0856***
(0.023)

0.0169
(0.017)
-0.0042
(0.026)
-0.0038
(0.020)
-0.0305
(0.024)
0.0140
(0.009)
0.0321**
(0.014)
0.0323**
(0.014)
0.0322*
(0.018)

Y
Y
Y

Y
Y
Y
Y
150,746
0.441

405,893
0.473

Table A7: Robustness with more refined measure of SLR risk. i.SLR Risk where
i ∈ {1, . . . , 4} indicates whether a property will be inundated with 6, 5, 4, or less than
or equal to 3 feet of SLR, respectively. Comparison group: properties that will not be
inundated even with six feet of SLR. The rest is the same as in Tables 5 and 6.

72

Leveraged
SLR Risk
SLR Risk × PessBuyer

0.007
(0.016)
0.032***
(0.010)

-0.005
(0.012)
0.031***
(0.011)

0.010
(0.010)
0.019**
(0.008)

0.012
(0.013)
0.021**
(0.010)

Fixed effects
Z×D×E×B Z×D×E×B×Q Z×D×E×B×Q×O Z×D×E×B×M×O
Property & buyer county controls Y
Y
Y
Y
Buyer county controls × SLR
Y
Y
Y
Y
N
852,817
568,636
490,546
322,484
R2
0.188
0.404
0.461
0.526
Long Maturity
SLR Risk
SLR Risk × PessBuyer

-0.011*
(0.006)
0.007
(0.005)

-0.003
(0.011)
0.017***
(0.006)

-0.005
(0.012)
0.012*
(0.007)

-0.010
(0.019)
0.022**
(0.009)

Fixed effects
Z×D×E×B Z×D×E×B×Q Z×D×E×B×Q×O Z×D×E×B×M×O
Property & buyer county controls Y
Y
Y
Y
Buyer county controls × SLR
Y
Y
Y
Y
Lender fe
Y
Y
Y
Y
N
852,817
568,636
490,546
322,484
R2
0.188
0.404
0.461
0.526

Table A8: Robustness with alternative fixed effects. Top table: dependent variable in
Column 1 is Leveraged (whether the transaction is associated with a mortgage). Bottom
table: dependent variable is Long Maturity (whether the mortgage term is 30 years).
Fixed effect abbreviations: Z – ZIP code, D – distance to coast bin, E – elevation bin,
B – number of bedrooms, Q – quarter and year of transaction, M – month and year of
transaction, O – owner-occupied status. The rest is the same as in Tables 5 and 6.

SLR Risk
SLR Risk × PessBuyer
Log Housing Price

Leveraged

Long Maturity

-0.009
(0.014)
0.025**
(0.010)
−

0.002
(0.014)
0.024***
(0.007)
−

Property & buyer county controls Y
Z × D × E × B × M fe
Y
Buyer county controls × SLR
Y
Lender fe
N
405,893
R2
0.465

Y
Y
Y
Y
150,746
0.441

Table A9: Robustness where housing price is not included as a control variable. The
rest is the same as in Tables 5 and 6.

73

SLR
SLR × PessBuyer
FEMA Zone
FEMA Zone × PessBuyer
Z × D × E × B × M fe
Buyer county controls × SLR
Lender FE
N
R2

Leveraged

Long Maturity

0.006
(0.014)
0.026**
(0.011)
-0.024***
(0.008)
0.014
(0.011)

0.002
(0.014)
0.024***
(0.008)
-0.002
(0.004)
0.000
(0.007)

Y
Y

Y
Y
Y
150,746
0.441

405,893
0.473

Table A10: The main results are robust to the inclusion of current National Flood
Insurance Program flood zone information. The rest is the same as in Tables 5 and 6.

SLR Risk
SLR Risk × PessBuyer
Property & buyer county controls
Buyer county controls × SLR
Z × D × E × B × M fe
Lender fe
N
R2

Leveraged &
Conforming Nonconform

Long Maturity &
Conforming Nonconform

-0.058***
(0.019)
0.030**
(0.015)

0.024***
(0.008)
0.006
(0.005)

0.005
(0.027)
0.027
(0.016)

0.003
(0.018)
-0.001
(0.011)

Y
Y
Y

Y
Y
Y

229,294
0.437

229,294
0.540

Y
Y
Y
Y
87,623
0.539

Y
Y
Y
Y
87,623
0.652

Table A11: Role of conforming loans in years ≥ 2009. Column 1: dependent variable
is whether a transaction is leveraged and the mortgage is conforming. Column 3:
restricting to leveraged sample, dependent variable is whether the mortgage has long
maturity (≥30 years) and is conforming. Column 2 and 4 repeat columns 1 and 3,
respectively, but replace conforming with nonconforming. Only mortgages from 2009
to 2016 are included in these results. For brevity, only estimates of the coefficients of
SLR Risk and the interaction term SLR Risk × Pessimistic Buyer are reported. The
rest is the same as in Tables 5 and 6.

74

log(Housing Price)
<2010
≥2010
SLR
SLR x PessBuyer

Leveraged
<2010 ≥2010

-0.018
-0.060** 0.022
(0.023)
(0.027)
(0.016)
-0.056*** -0.066*** 0.025*
(0.018)
(0.022)
(0.013)

Property & buyer county controls Y
Buyer county controls × SLR
Y
Z × D × E × B × M fe
Y
Lender fe
N
195,521
R2
0.883

Y
Y
Y

Y
Y
Y

211,080
0.854

195,096
0.474

-0.033
(0.021)
0.037**
(0.014)
Y
Y
Y

Long Maturity
<2010 ≥2010
0.002
0.009
(0.017) (0.020)
0.015* 0.038**
(0.009) (0.015)

Y
Y
Y
Y
210,797 86,992
0.439
0.448

Y
Y
Y
Y
62,927
0.442

Table A12: Results over time. Columns 1, 3, and 5 use only the sample of property
transactions that take place up to December 2009. Columns 2, 4, and 6 use only those
that take place from January 2010 onward. The rest is the same as in Tables 4, 5, and
6.

SLR Risk
SLR Risk × PessBuyer
Property & buyer county controls
Buyer county controls × SLR
Z × D × E × B × M fe
Lender fe
30 year f.e.
N
R2

log(Loan amount)

Mortgage interest rate

0.001
(0.011)
0.008
(0.009)

-0.095
(0.160)
0.037
(0.088)

Y
Y
Y
Y

Y
Y
Y
Y
Y
28,873
0.725

168,409
0.920

Table A13: Other intensive margins: Effects of exposure to SLR risk and its interaction
with climate belief on mortgage loan amount (column 1) and mortgage interest rate
(column 2). Sample restricted to transactions associated with a mortgage contract. In
order to compare the mortgage interest rates across only loans with similar maturity,
column 2 also includes a fixed effect equal to one if a mortgage has a 30-year maturity
(and zero if it has a 15-year maturity). The rest is the same as in Tables 5 and 6.

75