Climate Econometrics

Abstract

Identifying the effect of climate on societies is central to understanding historical economic development, designing modern policies that react to climatic events, and managing future global climate change. Here, I review, synthesize, and interpret recent advances in methods used to measure effects of climate on social and economic outcomes. Because weather variation plays a large role in recent progress, I formalize the relationship between climate and weather from an econometric perspective and discuss the use of these two factors as identifying variation, highlighting trade-offs between key assumptions in different research designs and deriving conditions when weather variation exactly identifies the effects of climate. I then describe recent advances, such as the parameterization of climate variables from a social perspective, use of nonlinear models with spatial and temporal displacement, characterization of uncertainty, measurement of adaptation, cross-study comparison, and use of empirical estimates to project the impact of future climate change. I conclude by discussing remaining methodological challenges. Expected final online publication date for the Annual Review of Resource Economics Volume 8 is October 05, 2016. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.

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RE08CH04-Hsiang ARI 2 September 2016 8:33
Climate Econometrics
Solomon Hsiang1,2
1Goldman School of Public Policy, University of California, Berkeley, California 94720;
email: shsiang@berkeley.edu
2National Bureau of Economic Research, Cambridge, Massachusetts 02138
Annu. Rev. Resour. Econ. 2016. 8:43–75
First published online as a Review in Advance on
August 8, 2016
The Annual Review of Resource Economics is online
at resource.annualreviews.org
This article’s doi:
10.1146/annurev-resource-100815-095343
Copyright c
⃝2016 by Annual Reviews.
All rights reserved
JEL codes: C33, H84, O13, Q54
Keywords
climate change, weather, disasters, causal inference
Abstract
Identifying the effect of climate on societies is central to understanding his-
torical economic development, designing modern policies that react to cli-
matic events, and managing future global climate change. Here, I review,
synthesize, and interpret recent advances in methods used to measure effects
of climate on social and economic outcomes. Because weather variation plays
a large role in recent progress, I formalize the relationship between climate
and weather from an econometric perspective and discuss the use of these two
factors as identifying variation, highlighting trade-offs between key assump-
tions in different research designs and deriving conditions when weather vari-
ation exactly identifies the effects of climate. I then describe recent advances,
such as the parameterization of climate variables from a social perspective,
use of nonlinear models with spatial and temporal displacement, character-
ization of uncertainty, measurement of adaptation, cross-study comparison,
and use of empirical estimates to project the impact of future climate change.
I conclude by discussing remaining methodological challenges.
43
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1. INTRODUCTION
How does the climate affect society and the economy? This question has challenged thinkers for
centuries, and the answer promises insight into why economies developed differently historically,
how modern society can best respond to current climatic events, and how future climate changes
may impact humanity. In recent years, numerous econometric analyses have emerged to address
this question by studying the effects of specific climatic conditions on different social and economic
outcomes. The recency of this research activity is explained primarily by methodological advances
that, combined with increasing access to computing power and climate data, catalyzed progress.
The goal of this review is to collect and synthesize these advances. In particular, I highlight core
innovations and explain linkages between different methods. I also attempt to tackle an issue that
has proved particularly thorny: the debate as to whether regressions on “weather” variables provide
meaningful insight into the effects of climate. By formalizing this question, I can derive conditions
under which the use of weather variables in regressions is justified and, perhaps surprisingly,
dominates traditionally preferred methods. In the latter portion of this review, I discuss how these
new econometric results are being used to understand other scientific or policy questions, such
as the optimal design of climate change policy. Throughout, I draw attention to methodological
challenges that remain unsolved.
This review focuses on methodology, so I will not describe data or results that are not examples
of methodological innovations. I encourage readers to consult Auffhammer et al. (2013) for a
discussion of climate data in general and other review articles surveying findings from this rapidly
growing field; for example, those regarding health impacts (Deschˆ
enes 2014), agricultural impacts
(Auffhammer & Schlenker 2014), energy impacts (Auffhammer & Mansur 2014), conflict impacts
(Burke et al. 2015b), climatic disaster impacts broadly speaking (Kousky 2014) and tropical cyclones
specifically (Camargo & Hsiang 2016), labor impacts (Heal & Park 2015), and a general summary
of findings from across the literature (Carleton & Hsiang 2016, Dell et al. 2014).
1.1. Defining Climate
Here I develop a formal definition for the climate that is flexible, general, and encompasses usages
throughout the literature.
For any position in space i, there exists a vector of random variables at each moment in time t
characterizing the conditions of the atmosphere and ocean that are relevant to economic conditions
at i. Heuristically, one could imagine this random vector as
vit =!temperatureit,precipitationit ,humidityit ,...
".(1)
For an interval in time τ=[t,¯
t)ati, there exists a joint probability distribution ψ(Ciτ) from which
we imagine vit is drawn:
vit ∼ψ(Ciτ)∀t∈τ.(2)
Ciτis a vector of Krelevant parameters—ideally sufficient statistics—indexed by kthat character-
izes distributions in the ψ(.) family of distributions, such as location and shape parameters. Define
Ciτto be the climate at iduring τ, as it characterizes the distribution of possible realized states vit.
For each period τ, there is an empirical distribution ψ(ciτ) that characterizes the distribution
of states vi,t∈τthat are actually realized. In many contexts, some of the Kparameters in ciτhave
analogs to fitted values for a model where the distribution is constrained to the ψ(.) family, but
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RE08CH04-Hsiang ARI 2 September 2016 8:33
such an analogy is imperfect because ciτare actual measurements, not estimates.1Note that ciτ
and Ciτare vectors of the same length with analogous elements, but they are not the same. Ciτ
characterizes the expected distribution of vit, whereas ciτcharacterizes the realized distribution
of vi,t∈τ. Thus, we define ciτto be a description of the weather during τ.
Examples help clarify how these definitions of climate and weather differ. Consider that the
weather measures ciτmight contain the sample mean and sample standard deviation of daily
rainfall during a month, whereas the corresponding Ciτwould contain the true population mean
and true population standard deviation of rainfall that could occur during that period. In another
example, ciτcould contain the maximum sustained wind gust speed actually experienced during
a 24-h interval, whereas Ciτcontains the maximum of the true theoretical gust distribution for
that day. Finally, ciτcould contain the count of realized days with average temperatures below
freezing or above 30◦C in a year, whereas Ciτmight then contain the expected number of days in
these categories.
For notational simplicity, define c(C) as a realization of weather characteristics cconditional
on climate characteristics C.
Two questions immediately emerge for an applied econometrician. First, how should the
joint distribution ψ(C) for the high dimensional vector vbe summarized? Are we concerned
only with average values and variances or also with some other summary statistics, such as time
beyond a critical value (e.g., extreme heat days) or events that involve multiple dimensions of v
(e.g., wind and rain simultaneously)? Unfortunately, at present, no exhaustive list of summary
statistics or dimensions of vfully describes all socially and economically relevant parameters.
In practice, different researchers have explored whether and how different summary measures c
matter by examining one or a few at a time; for example, they examine average temperatures when
controlling for average rainfall, but these should be understood as rough characterizations of a
more highly structured multidimensional distribution. As current research progresses, the set of
known relevant summary parameters generally tends to grow.
Second, how long of a time interval τshould be considered? Historically, climate was sometimes
defined as an average over 30 years (Pachauri et al. 2014), but this definition is fairly arbitrary. In re-
ality, there exists a well-defined expected distribution of states that might occur even for very short
periods of time. For example, at every location there is an expected distribution of temperatures
that might occur for each 5-min interval on each day of the year. Furthermore, this distribution
might change between consecutive years, for example, due to the El Ni ˜
no-Southern Oscillation
(ENSO). This suggests that climate need not have a fundamental timescale and econometricians
may, in principle, study periods of varying lengths of time.
1.2. Influence of Climate Through Events and Information
The climate affects social outcomes in two ways. First, the climate during τinfluences what
realizations of weather cactually occur during that interval, which in turn affects a population
directly (e.g., a rainy climate generates rain, causing people to get wet); call this the direct effect of
1It is possible that some researchers may attempt to construct empirical estimates of ˆ
Ciτusing data that resemble or are
identical to measurements ciτ, but this need not always be the case. For example, an estimate for the population mean of
daily temperatures during a year, a climate parameter, happens to equal the sample mean of daily temperatures, a weather
parameter. But weather parameters need not always have the same form as estimators for climate parameters, and climate
parameters, describing an abstract population distribution that is never actually observed, need not depend on weather.
Weather parameters should always be interpreted as measurements associated with individual observations. In principle,
climate parameters could be formulated in the absence of real world measurements, for example, based on a theoretical or
numerical model of the climate.
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RE08CH04-Hsiang ARI 2 September 2016 8:33
climate. Second, individuals’ beliefs over the structure of Cmay affect their decisions and resulting
outcomes, regardless of what cis realized (e.g., if people believe their climate is rainy, some will
buy umbrellas); refer to this as the belief effect. Denote all actions resulting from beliefs as the
vector bof length N, indexed by n.Wecanthenwritethatanoutcomeisaffectedbytheclimate
because the climate affects what weather is realized and what actions individuals take based on
their beliefs about the climate:
Y(C)=Y[c(C),b(C)].(3)
Therefore, the total marginal effect of the climate on outcome Yis characterized by the K-element
vector of derivatives
dY(C)
dC=∇
cY(C)·dc
dC+∇
bY(C)·db
dC
=
K
#
k=1
∂Y(C)
∂ck
dck
dC
$%& '
direct effects
+
N
#
n=1
∂Y(C)
∂bn
dbn
dC
$%& '
belief effects
,(4)
where ∇cand ∇bare defined as gradients in the subspaces of cand b,respectively.
2Observe that
dc
dCand db
dCare K×Kand N×KJacobians.3
Note that all partial derivatives are evaluated “locally” at the current climate C. This localness
is important, as beliefs about the climate may alter ∂Y
∂ckif actions individuals take based on these
beliefs alter the direct effect of weather realizations cwhen they occur (e.g., individuals who
buy umbrellas because they believe they are in a rainy climate get less wet when it rains). Such
interactions between beliefs and direct impacts ( ∂2Y
∂bn∂ck) and belief effects themselves are together
often referred to as “adaptations” in the literature.
Researchers are generally interested in both pathways of influence, although credibly identi-
fying belief effects has proven challenging because beliefs are difficult to observe, and they tend
to be correlated with many other factors.
2. THE EMPIRICAL PROBLEM
We are interested in identifying the effect of the climate on a population or economy, holding all
other factors fixed. Denoting the vector of observable nonclimatic factors xthat affect outcome
Y,wecanexpresstheaveragetreatmenteffectβfor a change in climate %Ciτas
β=E[Yiτ|Ciτ+%Ciτ,xiτ]−E[Yiτ|Ciτ,xiτ].(5)
Inference is challenging because βcan never be observed directly, as the single population ican
never be exposed to both counterfactuals Cand C+%Cfor the exact same interval of time τ.
This is the Fundamental Problem of Causal Inference (Holland 1986).
In an ideal experiment aimed at recovering β,wewouldlocatetwosamplepopulations(iand
j) that are identical in every way and experimentally manipulate the climate of ito be Cand the
2Define ∇cY=[∂Y
∂c1,..., ∂Y
∂cK] and ∇bY=[∂Y
∂b1,..., ∂Y
∂bN],which can be concatenated to form the complete gradient vector
∇Y=[∇cY,∇bY].
3The Jacobian matrices are dc
dC=⎡
⎢
⎢
⎢
⎣
∂c1
∂C1··· ∂c1
∂CK
.
.
.....
.
.
∂cK
∂C1··· ∂cK
∂CK
⎤
⎥
⎥
⎥
⎦
and db
dC=⎡
⎢
⎢
⎢
⎣
∂b1
∂C1··· ∂b1
∂CK
.
.
.....
.
.
∂bN
∂C1··· ∂bN
∂CK
⎤
⎥
⎥
⎥
⎦
.
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RE08CH04-Hsiang ARI 2 September 2016 8:33
climate of jto be C+%C. We would then observe how these two treatments affect the outcome
Y. If they are identical, it must be true that
E[Yiτ|C,xiτ]=E[Yjτ|C,xjτ],(6)
the unit homogeneity assumption. Note that the right-hand term is not observed. We could then use
observations from our experiment to construct the unbiased estimator
ˆ
β=E[Yjτ|C+%C,xjτ]−E[Yiτ|C,xiτ]=E[Yiτ|C+%C,xiτ]
$%& '
never observed
−E[Yiτ|C,xiτ]=β.(7)
Unfortunately, such an experiment is usually impossible for most large-scale settings of interest,
although some laboratory experiments have applied a randomized version of this approach in psy-
chology (Mackworth 1946), ergonomics (Seppanen et al. 2006), sports medicine (Nybo & Secher
2004), and military research (Hocking et al. 2001). In these settings, where %Ccan be randomly
assigned and experimentally manipulated (e.g., warming a room), application of Equation 7 is suf-
ficient for inference. In all other cases, the econometrician requires a research design that delivers
an approximation of Equation 5.
2.1. Research Designs
There are essentially three research designs in use that approximate the average treatment effect
in Equation 5: cross-sectional approaches, use of time-series variation, and a hybrid known as long
differences. The conceptual trade-offs to these designs center around (a) whether it is reasonable
to assume that distinct populations are comparable units after the econometrician has conditioned
on observable characteristics, and (b) whether climatic events observed to affect a population are
sufficient to capture relevant direct effects and belief effects of climate.
2.1.1. Cross-sectional approaches. In cross-sectional research designs, different populations in
the same period τare compared to one another after conditioning on observables xiτ. The core
assumption needed for this approach is the unit homogeneity assumption as written in Equation 6.
Under this assumption, if different populations have the same climate, then their expected con-
ditional outcomes are assumed to be the same. This allows the econometrician to attribute all
differences in observed conditional outcomes to differences in climate, by estimating Equation 7
having assumed Equation 6. In a linear framework, this estimate is usually implemented via a
regression equation of the form
Yi=ˆ
α+Ciˆ
βCS +xiˆ
γ+ˆ
ϵi,(8)
where τsubscripts are omitted because all observations occur in the same period. Here, ˆ
αis a
constant, ˆ
γare effects of observables, and ˆ
ϵiare unexplained variations. The estimate of interest ˆ
βCS
is a column vector of coefficients describing marginal effects of terms in Ci, the set of parameters4
selected by the econometrician to characterize the probability distribution of vat each location i.
This design was used widely in early econometric analyses of the effect of the climate
(Fankhauser 1995, Tol 2009), gaining prominence in the seminal work by Mendelsohn et al.
(1994) who regressed farm prices across US counties on growing season temperatures and ob-
servable characteristics of farm properties. This implementation highlights a major strength of
this approach in the context of climatic effects: Because farmers who inhabit a location for a long
4Note that in practice, econometricians must estimate ˆ
Cfrom data, which is often implemented by estimating moments of
ψusing historical data describing v.Inprinciple,Cneed not be estimated from real world data; for example, it could be
constructed using a theoretical or numerical climate model.
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RE08CH04-Hsiang ARI 2 September 2016 8:33
period will have a strong grasp of Cat their location and will adjust farm investments and man-
agement to optimize based on these beliefs, farm prices can be assumed to reflect all direct effects
and all belief effects. An additional benefit of the cross-sectional research design is that it can be
enriched by imposing additional structure on the model and still remain tractable, as in work by
Costinot et al. (2016) and Desmet & Rossi-Hansberg (2015), who consider the effect of climate
on the spatial allocation of production, labor, and trade.
A weakness of the cross-sectional approach is its vulnerability to omitted variables bias. When
variables that affect Yiare not included in either Cior xibut are correlated with one of their
elements, the resulting estimates will be biased (Wooldridge 2002). The surmountability of this
problem may be limited because Equation 6 is untestable, i.e., there exists no systematic method
for determining whether any key variables are omitted from Equation 8. Thus, econometricians
can never be certain their model is unbiased.
One approach designed to address the concern of omitted variables bias is to saturate the model
with as many variables as possible. For example, Nordhaus (2006) developed a novel 1◦×1◦
gridded global data set of economic production and numerous geographic and climatic factors,
which was then applied to Equation 8 at the pixel level to estimate the effect of temperature on
economic productivity. Another approach to constrain the influence of omitted variables is to limit
the subsamples of observations for which Equation 6 is assumed by only comparing populations
that are thought to have similar unobservable characteristics. For example, Albouy et al. (2010)
estimate the effect of temperature on housing prices across the United States. They focus on
within-locality comparisons because many characteristics that distinguish localities are difficult to
parametrize for inclusion in Equation 8 but are likely correlated with climatic differences across
localities and would thus bias ˆ
βCS in a fully pooled regression.
It is not possible to determine if all important variables have been included in Equation 8,
although in some sectors where the data generating process is well known, such as maize yields
in the United States (Schlenker 2010), an accumulation of studies may provide us with modest
confidence that most important factors are accounted for. Yet in other cases, such as civil wars
(Burke et al. 2015b), it is generally assumed that a comprehensive suite of important nonclimatic
factors may never be known, imposing a ceiling on the assurance we can achieve when using the
cross-sectional research design for these outcomes.
2.1.2. Identification in time series. An alternative approach to approximating Equation 5,
instead of assuming that populations iand jare comparable, is to examine only population iacross
separate periods (indexed by τ) when different environmental conditions are realized at i. This
approach conditions outcomes on ciτ, where each observation summarizes a joint distribution
of many vectors vit observed during the period τ. An advantage of this approach is that it relies
on a plausibly weaker form of the unit homogeneity assumption because it only requires that an
individual population iis comparable to itself across moments in time. However, this approach
can only approximate Equation 5 by introducing a second assumption that I call the marginal
treatment comparability assumption:
E[Yi|cτ]−E[Yi|C1]=E[Yi|C1+(cτ−C1)
$%& '
%C
]−E[Yi|C1]=E[Yi|C2]−E[Yi|C1],(9)
where C2=C1+%C. This assumption states that the change in expected outcomes between a
period where cτis realized relative to outcomes conditioned on a benchmark climate C1is the
same as the change in expected outcomes if the distribution characterized by C1were distorted
by adjustments to climate parameters by %C(defined as the difference between the realized
measures cτand the climate values C1) to create a new distribution characterized by C2(Figure 1).
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RE08CH04-Hsiang ARI 2 September 2016 8:33
–15 –10 –5 0 5 10 15 20 25 >30
Daily temperatures (˚C)
aIdentifying variation
from a small change
in daily temperature
distribution during τ
C1
C1
cτ
cτ – C1
C2 – C1
b
d
c
–15 –10 –5 0 5 10 15 20 25 >30
Daily temperatures (˚C)
Figure 1
Illustration of the marginal treatment comparability assumption, adapted from Deryugina & Hsiang (2014). (a) Expected annual
distribution of daily temperatures for Middlesex County, Massachusetts, a characterization of the climate C1.(b)Black-outlinedbars
are an example weather summary cτof temperature realizations during period τ, in the form of a distribution, overlaid on C1.
(c)DifferencebetweenaclimateC2, with structure identical to the realized distribution of weather cτin panel b,andtheinitialclimate
C1in panel a.(d) The difference between the realized distribution of weather and the climate, cτ−C1. The marginal treatment
comparability assumption states that the effect of the change in the weather distribution in panel dis the same as the effect of the change
in the climate distribution in panel c.
In other words, marginal treatment comparability assumes that the effect of a marginal change
in the distribution of weather (relative to expectation) is the same as the effect of an analogous
marginal change in the climate. Because this assumption has been widely debated, in the following
subsections I propose a partial test of this assumption and derive some conditions under which it
holds exactly.
In a linear framework, this approach is usually implemented using either time-series or panel
data via a regression equation of the form
Yiτ=ˆ
αi+ciτˆ
βTS +xiτˆ
γ+ˆ
θ(i)(τ)+ˆ
ϵi,(10)
where ˆ
αiare unit-specific fixed effects that absorb the effect of all time-invariant factors that differ
between units, including unobservables that could not be accounted for in the cross-sectional
research design. ˆ
θ(i)(τ) are trends in the outcome data, often accounted for using period fixed
effects and/or linear or polynomial time trends, which may be region or unit specific.
This approach was probably first proposed by Huntington (1922, p. 14) who argued, “The ideal
way to determine the effect of climate would be to take a given group of people and measure their
activity daily for a long period, first in one climate, and then in another,” and implemented analogs
to Equation 10 using factory worker data. This approach gained prominence in modern economic
analysis when used by Deschˆ
enes & Greenstone (2007), who analyzed whether agricultural profits
in US counties responded to “random fluctuations in weather.”
The core benefit of this approach is that it accounts for unobservable differences between
units, eliminating a potential source of omitted variables bias. However, this approach still remains
vulnerable to omitted variables bias if there are important time-varying factors that influence the
outcome and are correlated over time with ciτor xiτafter conditioning on trends θ(i)(τ). It is usually
assumed that variations in ciτover time are exogenous to changes in social and economic changes
because they are driven by stochastic geophysical processes. However, Hsiang (2010) points out
that many dimensions of ciτare correlated over time because they are partially driven by the same
processes—e.g., temperature, rainfall, and hurricanes are all modulated by ENSO—so ˆ
βTS may be
biased if important climatic variables are omitted. A separate concern raised by Auffhammer et al.
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RE08CH04-Hsiang ARI 2 September 2016 8:33
(2013) and Hsiang et al. (2015) is that weather data might not be orthogonal to socioeconomic
conditions because weather reporting is endogenous. The extent to which these two issues affect
the literature as a whole remains unknown.
Some authors introduce time-varying nonclimatic factors as controls in Equation 10, such as
crop prices or avoidance behavior. However, Hsiang et al. (2013) caution that this may introduce
new biases if these factors are endogenous and affected by climatic events, a situation known as
bad control (Angrist & Pischke 2008).
A special case of the time-series research design are cohort analyses, such as those conducted
by Maccini & Yang (2009) who examined the long-term effects of rainfall during childhood
among girls in Indonesia. In these implementations, sequential cohorts within a location iare
assumed to be comparable to one another conditional on xiτ, differing only in their exposure to
sequential realizations of ciτ. This represents a strengthening of the unit homogeneity assumption,
as sequential cohorts within iare different populations that are assumed to be comparable.
2.1.3. A hybrid approach: long differences. An approach that aims to compromise between
the strengths and weaknesses of cross-sectional analysis and time-series identification is the long-
differences strategy, in which changes for both the outcome and the climate within locations
are correlated across locations. The long-differences strategy is a cross-sectional comparison of
changes over time, which for two periods of observation {τ1,τ
2}is implemented with the regression
Yiτ2−Yiτ1=ˆ
α+(ciτ2−ciτ1)ˆ
βLD +(xiτ2−xiτ1)ˆ
γ+ˆ
ϵi,(11)
where ˆ
αrepresents the secular change in Yover time, and ˆ
βLD represents the extent to which
trends in climate are correlated across space with trends in Y.Thisapproachisknownas“long”
differences because it is primarily used to test whether gradual changes in cinduce gradual changes
in Y,soτ1and τ2are usually chosen to be two periods far apart in time. When long differences
has been implemented to measure the effects of climate on growth (Dell et al. 2012), crop yields
(Burke & Emerick 2016, Lobell & Asner 2003), and conflict (Burke et al. 2015b), authors have
found that βLD is almost identical to βTS, leading them to conclude that gradual changes in clikely
induce similar effects to more rapid changes in c.
The benefit of using long differences, relative to time-series analyses that use short differences,
is that the marginal treatment comparability assumption in Equation 9 might be more plausibly
satisfied because changes in care gradual—although a weakness of this approach relative to pure
cross section is that some form of this assumption is still required. The benefit of this approach
relative to pure cross-sectional analyses is that it requires a weaker form of the unit homogeneity
assumption, where only changes in Yare assumed to be comparable across units rather than
requiring levels of Yto be comparable. But this assumption remains stronger than the weak
within-unit homogeneity assumption required for time-series identification. This tension between
the marginal treatment comparability assumption and the unit homogeneity assumption is an
overarching challenge to research design in this literature, as discussed below.
2.2. The Trade-Off Between Low-Frequency Variations
and Credible Identification
The extent to which Equation 10 identifies direct effects and belief effects of the climate is often
thought to depend on the lengths of periods over which the distribution ψ(ciτ) is summarized,
that is ¯
t−t. Because belief effects are caused by agents responding to the belief that they face
a probability distribution of outcomes described by Ciτ, the extent to which these effects are
captured by Equation 10 likely depends on an agent’s belief that changes in the distribution of
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RE08CH04-Hsiang ARI 2 September 2016 8:33
realized measures ciτreflect changes in the prior probability of those events occurring. It is widely
assumed that agents facing events vit for long τwill update their beliefs over Ciτ,whereasagents
experiencing events during a short period—perhaps only for a 5-min period—will not alter their
beliefs over Ciτfor that interval. Thus, individuals might experience the direct effects of climatic
events during short τ, but they may be unlikely to alter their beliefs about the climate they face
because of a short-lived event.
Because of this logic, it is widely thought that low-frequency data (long %τ =τ2−τ1=¯
t−t
for regularly spaced data) are required to measure belief effects when using time-series variation,
as populations only adjust their beliefs if environmental changes are persistent. In the limit that
frequencies of ciτexploited by the econometrician approach zero (i.e., the length of %τ approaches
infinity), the research design actually approaches the pure cross-sectional analysis in Equation 8.
Thus, the motivation to exploit low-frequency data in time-series designs mirrors the motivation of
cross-sectional analysis, as those data are thought to capture both the direct effects and belief effects
of climate changes. Early examples of this approach are Zhang et al. (2007) and Tol & Wagner
(2010), both of whom apply a low-pass filter to climatic variables before estimating Equation 10.
A related alternative approach is to use climate data sampled at a low frequency, as implemented
by Bai & Kung (2011), who count droughts over each decade to form each observation in a
millennial-scale time series.
Although exploiting low-frequency variations in cis appealing because such an approach might
capture both direct and belief effects, it comes at the cost of less credible identification, an issue
highlighted by Hsiang & Burke (2014, p. 2) as the “frequency-identification trade-off.” The unit
homogeneity assumption for time series identification is
E[Yiτ|C,xiτ]=E[Yi,τ+%τ |C,xi,τ+%τ ],(12)
where units of observation are assumed to be comparable across periods of observation. How-
ever, as the frequency (1/%τ ) of observation becomes lower, the assumption that Yiτand Yi,τ+%τ
are comparable becomes increasingly difficult to justify. For example, populations separated by
multiple centuries might not be comparable units.
The tension between credible identification and use of low-frequency climate variation is not
easily resolved if populations do not update their beliefs about the climate more quickly than
these populations naturally change in other fundamental ways. For cases in which belief effects are
large relative to direct effects, then the frequency-identification trade-off may represent a major
challenge to credible identification of the total effect of the climate. Importantly, however, if the
primary way in which belief effects manifest is to alter the direct effects of the climate—i.e., belief
effects are mostly adaptations designed to cope with direct effects—then the total effects of climate
still may be nearly identified with high-frequency time series. Even when this condition is not
satisfied, exact identification may still be possible, as shown in Section 2.4.
2.3. A Partial Test of Marginal Treatment Comparability
Unit homogeneity assumptions can be weakened but never tested or eliminated entirely, a funda-
mental limitation in causal inference generally. However, it may be possible to implement a partial
test of the marginal treatment comparability assumption by comparing whether estimated effects
are similar when using approaches that exploit climatic variations at different temporal frequencies.
If ˆ
βCS =ˆ
βLD =ˆ
βTS, i.e., if the effects of high-frequency changes equal the effects estimated with
long differences and in cross section, then one possible explanation is that the marginal treatment
comparability assumption is valid, and temporary changes in realizations of chave similar effects to
analogous changes in C. This could be true if the sum of all belief effects is small on net. Versions
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of these different comparisons were implemented and discussed in Burke & Emerick (2016), Burke
et al. (2015b), Dell et al. (2009), Hsiang & Jina (2015), Lobell & Asner (2003), and Schlenker &
Roberts (2009), in which any differences in estimated effects were attributed to adaptations to
climate, i.e., belief effects that interact with direct effects. However, a known difficulty is that the
strength of this test relies directly on the validity of the different unit homogeneity assumptions
used in each of the models compared. It is theoretically possible to obtain ˆ
βCS =ˆ
βLD =ˆ
βTS by
chance even if all key assumptions are violated, so long as biases have countervailing effects.
Building on these earlier partial tests, I propose that the credibility of this approach can be
further strengthened by estimating climate effects using a spectrum of data that has been filtered at
all different temporal frequencies. If the estimated effect of changes in cis stable across all temporal
frequencies spanning from unfiltered time-series data to long differences and the zero-frequency
cross section, then it seems less plausible that omitted variables biases at different frequencies
are exactly offsetting belief effects and more plausible that the marginal treatment comparability
assumption is valid. The idea for this test comes from the observation that a time series of the kth
element of the vector ccan be decomposed into the Fourier series
ckτ=ak
0+
∞
#
ω=1!ak
ωsin(ωτ)+bk
ωcos(ωτ)",(13)
where ak
ωand bk
ωare constants representing projections onto the basis functions sine and cosine
at varying frequencies ω,andak
0is a constant, analogous to a long-run average (i.e., ω=0).
Outcome data Ycan be similarly decomposed. If we can find appropriate filters that allow us to
isolate only certain frequency bands [ω,¯
ω], then we can estimate Equation 10 using these filtered
data and obtain ˆ
β[ω,¯
ω]
TS , the estimated relationship between climate variables and an outcome at
each timescale. As timescales become longer (and frequencies become lower), this estimate should
continuously approach the long-differences estimate and eventually the cross-sectional estimate
if the marginal treatment comparability assumption is valid and these estimates are unbiased.
To demonstrate this test, I obtained panel data on annual county-level maize yield, temperature,
and rainfall used in Schlenker & Roberts (2009), updated to the year 2014 and restricted to the 730
counties east of the 100th meridian that had no missing observations. I then applied a Baxter-King
approximate band-pass filter (Baxter & King 1999) to all three variables for various frequencies and
estimated Equation 10 with each set of filtered data. Figure 2 shows the effect of temperature on
yields at these various timescales overlaid with estimates of ˆ
βTS as in Schlenker & Roberts (2009),
ˆ
βLD as in Burke & Emerick (2016), and ˆ
βCS as in Schlenker et al. (2006). In all cases, except the cross
section, these estimated effects are near one another and not statistically different, suggesting that
variations in temperature over time have similar effects on maize yields in this context, regardless of
the timescale of these variations. The uniqueness of the cross-sectional estimate could be explained
either by belief effects that emerge only at timescales longer than 33 years (the longest timescale
of the filtered data) or omitted variables bias—although the fact that ˆ
βCS changes substantially
(to more closely resemble time-series estimates) when rainfall terms are omitted highlights the
vulnerability of the cross-sectional approach to misspecification. Nonetheless, these results overall
appear consistent with an assumption of marginal treatment comparability in this context, at least
for timescales shorter than 33 years.
2.4. Exact Identification of Climate Effects Using Weather Variation
Why should low- and high-frequency variations in climatic variables ever provide comparable
treatments? It is possible that cross-section, time-series, long-difference, and filtered data all
provide similar parameter estimates for βby chance, such that the above test of marginal
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RE08CH04-Hsiang ARI 2 September 2016 8:33
0 10 20 30 40
10
1950 1962 2002 2014
Year
10
1
1
1950 1962 2002 2014
Year
2–5
6–9
10–13
14–17
18–33
Raw annual data
bd
Change in log annual yields
Temperature during additional 24 h (˚C)
–0.08
–0.04
[9]
[8]
[7]
[6]
[1,2,5]
[3,10]
[4]
0
Filtered data by periodicity (years)
ac e
Raw annual (1950–2014) [1] (Schlenker & Roberts 2009)
Raw annual (1962–2002) [2]
2–5 year period [3]
6–9 year period [4]
10–13 year period [5]
14–17 year period [6]
18–33 year period [7]
Long dierence (1980–2000) [8] (Burke & Emerick 2016)
Cross section (1950–2014) [9] (Schlenker et al. 2006)
Cross section without rainfall (1950–2014) [10]
BK ltered data (1962–2002)
–0.12
Degree days above 29˚C
(Grand Traverse, MI) Corn yields (bushels/acre)
(Grand Traverse, MI) Change in log annual yields
Figure 2
(a–d) Example outcome and climate time series data from Grand Traverse, Michigan, filtered at different frequencies. (a)Rawannual
degree-days data (black)anda30-year-longdifference(maroon) following Burke & Emerick (2016). (b) The same data decomposed into
time series at different frequencies, where a Baxter-King band-pass filter has been applied for different periodicities. Filtering causes
loss of data at the start and end of the time series. (c) Illustrates analogous data as in panel abut for corn yields. (d) Illustrates analogous
data as in panel bbut for corn yields. (e) Comparison of the estimated effect of daily temperature using raw panel data sets, filtered data
sets, long differences, and cross-sectional approaches. Sample and estimation indicated by both line and bracketed numbers.
treatment comparability paints a misleadingly consistent picture of climate effects and weather
effects that are not related. Such critiques, relying on heuristic arguments, are common in
the literature. Nonetheless, there is actual theoretical justification for the marginal treatment
comparability assumption. In this section I provide a new derivation demonstrating how, under
certain conditions, the total effect of climate can be exactly recovered using ˆ
βTS derived from
weather variation. In essence, this result is a combined application of two well-known results, the
Envelope Theorem and the Gradient Theorem.
The intuition of the result is as follows. Imagine there are two otherwise identical households
that are next-door neighbors on a street that runs north–south. The more northern household
faces a very slightly different climate because it is very slightly further north. The difference in
climate faced by the two households is vanishingly small, but nonzero. These two households
have the ability to adapt many dimensions of their daily life to their beliefs about their respective
climates, and they will adopt slightly different behaviors and investments that maximize various
outcomes, generating belief effects. However, if we focus on outcomes that are maximized by the
households, then the overall net effect caused by these slightly different adaptation decisions is zero
because any marginal benefits that the northern household reaps are exactly offset by additional
marginal costs (which is known because the household is at a maximum). Therefore, any difference
in the optimized outcome between the two households must come from the direct effects of the
slightly different climate, and the influence of slightly different beliefs and adaptations between the
two households can be ignored. If a weather realization occurs such that the southern household
experiences conditions that are slightly different from what they expect, and its distribution of
weather actually matches the climate of the northern household, then this weather effect on the
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RE08CH04-Hsiang ARI 2 September 2016 8:33
optimized outcome of the southern household must be exactly the same as the cross-sectional dif-
ference across the two households in a year when their weather realizations match their respective
climates perfectly. This is because in both cases, there is no influence of changing beliefs on the
optimized outcome. Stated simply, the marginal effect of the climate on an optimized outcome is
exactly the same as the marginal effect of the weather.
Based on this insight, we can trace out a curve describing climate effects between sequential
neighbors by watching how optimized outcomes in each household change when that household
is confronted by a weather distribution that matches the climate of their immediate next-door
neighbor. The integral of these marginal differences between sequential neighbors must then
describe how the climate generates larger differences between households that are not adjacent
neighbors and how they experience climates that differ by a nonmarginal amount. Importantly,
this integration procedure does not assume that individuals do not adjust their beliefs and adapt
to their climate. Rather, the marginal effect of such adjustments for marginal climate changes
is zero on an optimized outcome, so marginal effects of weather—which do not cause beliefs to
change—can be used as a substitute for marginal climate changes in the integration, despite the
presence of changing beliefs and adaptations.
To see this result formally, consider an outcome of interest Ythat may be affected by the
climate Cthrough its effect on weather realizations cand actions band which is optimized so it
can be written as a value function, i.e., the solution to a maximization problem over an outcome-
generating function z(b,c). If we assume zis differentiable and concave in b, there will be a unique
optimum b∗(C) for each climate:
Y(C)=Y[b∗(C),c(C)] =max
b∈RNz[b,c(C)].(14)
Recall that the notation c(C) means weather realization cgenerated from climate C. Note that
maximization of zis allowed to occur through some indirect process, such as efficient market al-
locations, and need not result from explicit maximization by agents. Figure 3aplots the outcome
surface zfor an example case in which C,c,andbeach have only one dimension. For each value
of C,b∗is chosen to maximize zso the outcome Yobserved is the locus of optima along the red
line.
Let C1be a benchmark climate at which we are evaluating Y(C). If we differentiate Yby the
kth element of C, by the chain rule we have
dY(C1)
dCk
=∂z[b∗(C1),c(C1)]
∂Ck
+
N
#
n=1
∂z[b∗(C1),c(C1)]
∂bn
dbn
dCk
+
K
#
κ=1
∂z[b∗(C1),c(C1)]
∂cκ
dcκ
dCk
,(15)
where
∂z
∂Ck
=0,(16)
because the climate, as summary statistics of a probability distribution, cannot affect any outcome
by a pathway other than through the weather realizations it causes and actions based on beliefs
regarding its structure. Because Yis the outcome when zhas been optimized through all possible
adaptations, and it is differentiable in b,wealsoknow
∂z[b∗(C1),c(C1)]
∂bn
=0 (17)
for all Ndimensions of the action space. Thus, Equation 15 simplifies to
dY(C1)
dCk
=
K
#
κ=1
∂z[b∗(C1),c(C1)]
∂cκ
dcκ
dCk
=
K
#
κ=1
∂Y(C1)
∂cκ
dcκ
dCk
.(18)
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RE08CH04-Hsiang ARI 2 September 2016 8:33
ab
cd
c
c
Y
Y
YY
b
z(b,c)
Y(b*(C),c(C))
Y(b*(C),c(C)) z(b*(C1),c(C))
z(b*(C1),c(C))
Yi=2(b*(C),c(C))
= ∫∂Y(C)/∂cdC + Φi=2
Yi=1(b*(C),c(C))
= ∫∂Y(C)/∂cdC + Φi=1
Yi=1(C1) + ∂Y(C1)/∂c × (C – C1)
cross section
Y(b*(C1),c(C1))
Yi=2(C2)Yi=1(C1)
Yi=1(C2)
∂Y(C1)/∂c
∂Y(C2)/∂c
∂Y(C2)/∂c∂Y(C1)/∂c
∂Y(C1)/∂c
c(C1)
c(C2)
c(C2)
b*(C1) b*(C2)bc
c(C1)
c(C2) c(C1)
Y(b*(C2),c(C2))
Y(b*(C2),c(C2))
Figure 3
(a) Outcome generating function z(c,b)overweatheroutcomec(C)thatreflectstheclimateanddecisionb(C)thatrespondstobeliefs
about the climate. An implicit fourth dimension not pictured is climate C,whereweletE[c(C)] =Cfor simplicity. The red line is the
value function Y(C), the optimum achieved via maximization over z(.), conditional on a given value for C, which agents cannot control.
(b) The rotated view looking at the c-Yplane. Local variations in the outcome due to small changes in weather (blue arrows)aretangent
to the locus of optima. (c) Rotated view looking at the b-Yplane. The locus of optima (red line)isachievedbecauseofadaptationto
changes in climate, indicated by shifts in the bdimension. If agents beginning at C1could not adapt, they would be constrained to
points on the outcome-generating function along the blue line. (d) This panel shows the same view as panel b. The red line is Y(C) for
location i=1. The locus of points along the no-adaptation blue curve (as in panel c)liesbelowtheactualoptimumforallvaluesexcept
C1. The green line shows extrapolation of the marginal effect of the climate measured at C1. The orange line is Y(C)forlocationi=2,
where the integration constant φiis different than for i=1. The black line marks the cross-sectional relationship that would be
recovered if Yi=1(C1)andYi=2(C2) were the sample.
Note that for any marginal change in the distribution of weather, there exists a marginal change
in climate that is equal in magnitude and structure such that
dcκ
dCk
=.1 for κ=k
0 otherwise .(19)
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Focusing only on these analogous measures of weather and climate,5we have
dY(C1)
dCk
=∂Y(C1)
∂ck
,(20)
which says that the total marginal effect of the kth dimension of the climate, evaluated at C1,
is equal to the partial derivative of the outcome with respect to the same dimension of weather,
also evaluated at C1. Locally, the marginal effect of the climate on Yis identical to the marginal
effect of the weather. Equation 20 implies that Equation 9, the marginal treatment comparability
assumption, holds.
The equivalence between marginal effects of climate and weather can be used to construct
estimates for nonmarginal effects of the climate by integrating marginal effects of weather. For
an arbitrary climate C2, we know from the Gradient Theorem that we can solve for Y(C2) by
computing a line integral of the gradient in Yalong a continuous path through the k-dimensional
climate space from C1→C2,startingfromY(C1):
Y(C2)=/C2
C1
dY(C)
dC·dC+φ=/C2
C1
∂Y(C)
∂c·dC+φ=/C2
C1
∇cY(C)·dC+φ,(21)
where the substitution from Equation 20 is made for each of the Kelements of the gradient vector
∇cY(C)=[∂Y(C)
∂c1,..., ∂Y(C)
∂cK]. Here, φ=Y(C1) is the constant of integration, which is usually
unknown, although, in virtually all applications, changes in Yare the focus of investigation and
integration constants are differenced out. The vector of differentials ∇cY(C) describes all the
marginal effects of the weather measured locally at C, which can be estimated empirically by
restricting the sample of observations to those near Cand applying Equation 10:
∇cY(C)=ˆ
βTS000C.(22)
This estimate can then be substituted into Equation 21 to construct an exactly identified change
in Ythat occurs as the climate is varied from C1to C2, in the presence of adaptation adjustments
in b, using only time-series estimates:
Y(C2)−Y(C1)=/C2
C1
ˆ
βTS000C·dC.(23)
The difference in outcomes due to a change in the climate is computed by integrating a sequence of
weather-derived marginal effects evaluated at each intermediate value of C.Figure 3billustrates
this integration along the envelope of the function z(.), and Figure 3cdemonstrates how the locus
of points along this integration allows for all adaptations to climatic changes that occur through
adjustment of b, reflecting beliefs that evolve with C. As illustrated in Figure 3d, the integral in
Equation 23 differs from extrapolation of marginal weather effects (green line) or changes along
a path on the outcome-generating function z(.) where bis held fixed, which would occur if agents
were constrained not to adapt (blue curve).
To summarize, if the outcome is a solution to a maximization problem (Equation 14) for a
function z(.) that is continuous and differentiable in the space of all adaptive actions b, then by
application of the Envelope Theorem (Equation 18) we know that the marginal effect of the climate
is exactly the same as the marginal effect of an equally structured change in the weather distribution
(Equation 20), if both are evaluated locally relative to an initial climate. By the Gradient Theorem
we know that a sequence of marginal effects of the weather empirically estimated via time-series
5This focus on the effects of climate and weather where κ=kis consistent with interpreting multiple regression coefficients
as causal effects of Ckwhen other dimensions of Care fully and simultaneously accounted for.
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RE08CH04-Hsiang ARI 2 September 2016 8:33
variation at sequential values of Ccan then be integrated to compute the effect of nonmarginal
climate changes (Equation 23).
Note that this result does not depend on the nature of individuals’ expectations.
It is straightforward to extend this result to cases in which the climate exerts direct effects on
the outcome by altering a constraint on a maximization problem, rather than entering through
arguments to the maximand (Mas-Colell et al. 1995).
The black curve in Figure 3ddemonstrates how a cross-sectional regression, as in
Equation 8, may produce different results than the integration of weather effects proposed here.
Cross-sectional analysis does not difference out the integration constant φ, so if φi=1̸=φi=2for
pairs of observations, then a cross-sectional regression will not recover the red curve. For cross-
sectional regressions to recover the effect of Con Yin this context, we require all of the above
assumptions as well as the additional assumption that integration constants are identical:
dφ
di=0,(24)
which implies the strong form of the unit homogeneity assumption that units are comparable in
levels conditional on the climate (Equation 6). Thus, the set of assumptions necessary for valid
cross-sectional identification in this setting is strictly larger than the set of assumptions required
for valid time-series identification.
To my knowledge, the above result has not been previously established, and as such, existing
empirical papers leveraging weather variation do not explicitly check the assumptions critical
to this result: that Yis the solution to a (constrained) maximization, that adaptations btake on
continuous values, and that the maximand function z(.) is differentiable in b. Further, many prior
studies do not properly compute climate effects via Equation 23, with the notable exception of
Schlenker et al. (2013) and Houser et al. (2015), who essentially implement a form of this approach
explicitly. Total effects of climatic changes in Equation 23 are also computed correctly in studies
where marginal effects of weather are allowed to change based on underlying climatic conditions.
These evolving marginal weather effects are integrated to compute the cost of shifting climatic
conditions, as in Hsiang & Narita (2012) and Burke et al. (2015c). Finally, those studies in which
the marginal effects of weather are approximately invariant in climate, such as Ranson (2014) and
Deryugina & Hsiang (2014), also basically estimate Equation 23 when they linearly extrapolate
weather effects because the two calculations are equivalent.
3. MEASUREMENT OF CLIMATE VARIABLES
The measurement of climate variables is a critical methodological step in identifying climate
effects, regardless of the research design used. Early analyses concerned only with measuring
whether climatic factors had a nonzero effect, or the sign of an effect, used simple measures
of climate such as latitude or a single indicator variable that is one if a population is exposed
to a predefined event (e.g., a drought) and is zero otherwise. This approach is internally valid
but has important limitations that are often underappreciated in the literature. First, coarse
climate measures introduce large measurement errors that will cause attenuation bias, leading to
under-rejection of the null hypothesis. Second, the structure of a dose-response function
E[Y|c]=f(c)(25)
is often of interest. For example, we may be interested in nonlinearities or whether multiple
dimensions of climate interact in important ways, requiring that measures of climate variables
be near continuous and multidimensional. Third, if measures of cdo not reflect scalable physical
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quantities in the real world, we may have little confidence that estimated effects are externally
valid to other locations or to periods when the climate may change. For example, it is impossible
to consider how cyclone intensification may affect outcomes if cyclone exposure is measured only
as a binary variable. Fourth, pooling a sample of different locations may provide a valid average
treatment effect of climatic conditions on the sample, but it may be a poor predictor of outcomes
at any actual locations if the physical properties of events coded as similar are not actually
physically similar. Finally, the result derived in the previous section, that time-series variations
can be used to exactly identify marginal effects of the climate, can only hold if climatic variations
are measured in such a way that an econometrician can identify marginal effects. For example,
binary treatments are not differentiable, and so it may be difficult to determine if changing from
no treatment to treatment is a marginal change.
For all of the above reasons, many of the major innovations covered in the literature over the
past decade have resulted from improvements in the measurement of climate variables, contribut-
ing at least as much to recent advances, if not more, than functional form innovations (discussed
in Section 4). For example, using spatial interpolation techniques, Schlenker & Roberts (2009)
developed estimates of temperature with high spatial and temporal resolution, which allowed
them to construct precise measures of degree-days that integrate cumulative exposure to specific
temperature ranges (Figure 4a). Deschˆ
enes & Greenstone (2011) introduced a related approach
in which days are counted based on their average temperature [see Deryugina & Hsiang (2014)
for a derivation of this approach]. Yang (2008) estimated the effect of tropical cyclones by cod-
ing a storm’s maximum windspeed at landfall, an approach enriched further by Nordhaus (2010)
and Mendelsohn et al. (2012) who used additional landfall statistics; Hsiang (2010) expanded
the measurement of cyclone exposure by integrating wind speed exposure at all points through-
out the lifetime of a storm (Figure 4b). Guiteras et al. (2015) implemented a novel technique
for detecting surface flooding using satellite imagery. Auffhammer et al. (2006) used an atmo-
spheric circulation model to estimate overhead aerosol exposure. Hsiang et al. (2011) developed
a method to identify the ENSO exposure of countries (Figure 4c). Fishman (2016) utilized sev-
eral metrics to characterize the evenness of rainfall distributions that are similar in total rainfall
(Figure 4d). In several cases, researchers find that established linear or nonlinear transforma-
tions of fundamental climatic measures, such as temperature, rainfall, and humidity, are useful in
explaining patterns of outcomes, such as the standardized precipitation evapotranspiration index
(Harari & La Ferrara 2013), drought indices (Couttenier & Soubeyran 2014), vapor pressure
deficit (Urban et al. 2015), heat indices (Baylis 2015), or malaria ecology indices (McCord 2016).
In all cases, these various measures can be understood as approaches to collapsing the dimen-
sionality of cin a manner that efficiently describes patterns that matter from an economic or
social standpoint. In most of these cases, alternative approaches to measuring climate variables
cannot be viewed as objectively wrong; rather there are many ways of describing data in cthat
do not efficiently describe those components of variation that most strongly influence the out-
comes of interest. Blunt climate measures are not wrong, they just introduce large measurement
errors.
Particular caution is needed when applying the natural logarithm transformation standard in
many economic applications to climate measures, as it is not always sensible. For example, using
log(temperature) in Equation 10 is challenging to interpret because a 1% change in temperature—
used in the interpretation of the resulting coefficients—has a different meaning depending on
whether temperature is measured in Fahrenheit, Celsius, or Kelvin. In other cases, such trans-
formed data can be fit to a model, but the standard interpretation is inconsistent with physical
phenomena. For example, Nordhaus (2010) and Mendelsohn et al. (2012) model hurricane dam-
age using log(windspeed) and conclude that damage is superelastic because it appears to grow up to
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RE08CH04-Hsiang ARI 2 September 2016 8:33
29°C
mmmm
100
200
0
Daily rainfall in Ahmedabad, Gujarat
0 50 100 150 200
0
100
200
Days (May 1st–Nov 1st)
1996
Total rainfall: 642 mm
Rainy days: 77
2000
Total rainfall: 635 mm
Rainy days: 47
Meters per second
0
20
40
60
Kilometers
east
Kilometers
north
Meters per second
40
20
0
200
–200
0
0
–200
200
Teleconnected
locations
Tem p era t ure
Time
24 h 24 h
Degree days >29°C Total wind speed
at surface
Tmax
Tmax
Tmin Tmin Tmin
ab
cd
Figure 4
Examples of innovations in climate measurement. (a) Construction of degree-days measures using hourly temperature data interpolated
between daily minimum and maximum temperature in Schlenker & Roberts (2009). (b) Wind field model used to reconstruct wind
exposure along the path of tropical cyclones (inset is computed exposure of super typhoon Joan) in Hsiang & Jina (2014).
(c) Identification of “teleconnected” pixels (red) that have temperature and rainfall strongly coupled to the El Ni ˜
no-Southern
Oscillation in Hsiang et al. (2011). (d) Example rainfall distributions used to construct the rainy days count as a measure of within-year
rainfall dispersion across two years with similar total rainfall in Fishman (2016).
six exponents faster than the energy of the storm—a misinterpretation that is readily reconciled
with physics when the log transformation is simply not applied (Camargo & Hsiang 2016).
Many dimensions of the climate, such as persistent drought and sea level, remain poorly cap-
tured in econometric models due to measurement challenges. Future innovations will further
improve our understanding of these climate effects substantially.
4. ECONOMETRIC MODELS
Having selected a research design and constructed appropriate climate measures, an econometri-
cian must select a model that is fitted to the data. Here I discuss five aspects of modeling that have
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been particularly important in the measurement of climate effects: nonlinearities, displacement,
uncertainty, adaptation, and cross-study comparisons.
The discussion here is focused on the measurement of climate effects by applying a reduced
form approach to construct a dose-response surface. Such an approach does not necessarily specify
a single pathway through which the climate affects social outcomes, and in many cases it is likely
that several pathways play a role. Hsiang et al. (2013) suggest that to reject potential pathways in
any given context, researchers must look for natural experiments in which a particular pathway is
obstructed due to external factors and then examine whether reduced form effects persist; studies
by Sarsons (2015) and Fetzer (2014) are useful examples of this strategy.
It is worth noting that a large number of studies in economics utilize variation in weather
as an instrumental variable to study the effect of an intermediary variable on an outcome. This
strategy relies on the assumption of an exclusion restriction, i.e., that the employed weather
variation only affects the outcome through the specified intermediary variable. This assumption is
untestable, although the large number of studies utilizing exogenous variation in weather to study
a large number of outcomes through various proposed pathways seems to be evidence that this
assumption cannot be true in many cases.
4.1. Nonlinear Effects
The interpretation and estimation of nonlinear effects depend heavily on whether observations
are highly resolved in space and time or whether they are highly aggregated. Because weather
data are often available at high resolution, even when outcome data are not, it is often possible
to recover microlevel response functions, below the level of aggregation in the outcome data, by
carefully considering the data generating process.
4.1.1. Recovering local, microlevel, and instantaneous nonlinear effects. Local effects of
climatic variables are often nonlinear in important ways, such as extreme cold days and extreme heat
days generating excess mortality (Deschˆ
enes & Greenstone 2011) or extreme heat hours causing
damage to crop yields (Schlenker & Roberts 2009). In some cases, such as Aroonruengsawat &
Auffhammer (2011) and Graff Zivin & Neidell (2014), outcomes are measured at the same daily
frequency as these nonlinear effects manifest, rendering their measurement straightforward using
standard techniques. However, in most cases nonlinear effects manifest over timescales (e.g., hours)
and spatial scales (e.g., pixels) that are much finer than the periodicity and spatial scale at which
outcome data are measured (e.g., annually by country). Similarly, local effects may differ between
multiple locations within a unit of observation. Despite aggregation of the outcome across space
and over moments in time, it is possible to recover nonlinear relationships at the spatial and
temporal scale at which climatic data are recorded. Suppose outcome Yiτis observed over regions
i(e.g., provinces) made up of more finely resolved positions s(e.g., pixels) during intervals of time
τ(e.g., years) comprised of shorter moments t(e.g., days). Let the instantaneous nonlinear effect
of climate at a moment and position be f(cst), which we approximate as a linear combination of
Msimple nonlinear functions (e.g., polynomial terms)
f(cst)≈β1f1(cst)+β2f2(cst)+...+βMfM(cst)=
M
#
m=1
βmfm(cst),(26)
where the βs are constant coefficients. In practice, f(.) has been successfully modeled as an
M-piecewise linear function, as in degree-day models; an Mth order polynomial or restricted
cubic spline (Miller et al. 2008, Schlenker & Roberts 2009); interactions between multiple climate
measures (Urban et al. 2015), options which have efficiency and (local) differentiability benefits;
60 Hsiang
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RE08CH04-Hsiang ARI 2 September 2016 8:33
or an M-piecewise constant or “binned” function (Deryugina & Hsiang 2014, Desch ˆ
enes & Green-
stone 2011), a flexible nonparametric option.
Under the assumption of temporal and spatial separability, i.e., that the outcome of interest is
a linear sum of f(.) across positions and moments, weighted by the number of affected economic
units gs(e.g., crop fields) at those positions, then the regressions in Equations 8, 10, and 11 are
modified to the form
Yiτ=αi+1#
s∈i#
t∈τ
f(cst)gs2+xiτγ+θ(i)(τ)+ϵiτ,(27)
where the index and functions of τand region effects αiare omitted in the cross-sectional case.
Notably, as demonstrated in Welch et al. (2010), the structure of f(.) may differ between subperiods
in τso that Equation 27 becomes
Yiτ=αi+.#
s∈i1#
t∈τa
fa(cst)gs+#
t∈τb
fb(cst)gs23+xiτγ+θ(i)(τ)+ϵiτ,(28)
if τaand τbrepresent a partition of period τ. Focusing on Equation 27 for simplicity, we can
substitute the approximation from Equation 26 and interchange the order of summation to obtain
Yiτ≈αi+.#
s∈i#
t∈τ1M
#
m=1
βmfm(cst)gs23+xiτγ+θ(i)(τ)+ϵiτ
=αi+
M
#
m=1
βm1#
s∈i#
t∈τ
fm(cst)gs2
$%& '
˜
fmiτ
+xiτγ+θ(i)(τ)+ϵiτ(29)
=αi+
M
#
m=1
βm˜
fmiτ+xiτγ+θ(i)(τ)+ϵiτ,
which can be estimated with a linear regression using data at the region-period (iτ) level. Note
that the regressors ˜
fmiτare weighted sums across space and time of the mth nonlinear function
evaluated at locations sand moments tthat are not resolved in the outcome data. Estimation
of Equation 29 via regression recovers estimates for βmdescribing the local and instantaneous
function f(.), even though it uses coarser data.
4.1.2. Nonlinearity in regional summary measures due to local nonlinearities. Many analy-
ses do not estimate Equation 29 but instead examine whether nonlinear relationships exist between
summary statistics of climate data and aggregated outcome data, because constructing ˜
fusually
involves highly disaggregated climate data and is therefore challenging. The most common sum-
mary statistic of ckiτ,thekth element of ciτ, is a weighted average value over region iand period τ
ckiτ=#
s∈i#
t∈τ
cks t gs.(30)
For example, Dell et al. (2012) construct measures of population-weighted average temperature
over entire countries during an entire year. These region-by-period summary statistics may then
be used to construct regressors in a nonlinear model, such as the Q-order polynomial
Yiτ=ˆ
αi+
Q
#
q=1
ˆ
βq(ckiτ)q+xiτˆ
γ+ˆ
θ(i)(τ)+ˆ
ϵiτ,(31)
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120
150
–40
–20
March
1997
April
1997
Longitude
Latitude
10˚C
0%
30%
20˚C
30˚C
Temperature
Cropland
Annual temperature
slope b1
slope b1
mass m1
mass m2
Daily
temperature
Daily impact
Annual impact
a
b
c
d
e
Years have dierent
distributions of daily
temperature exposure
over cropland weights gS.
slope = m1b1 + m2b2
slope = m1b1 + m2b2
Figure 5
(a) Heterogenous temperatures across locations swithin a region are aggregated based on the distribution of units of analysis gs,inthis
case the spatial distribution of croplands (b). This aggregation means that if climate affects outcomes at a highly localized level (c), shifts
in the regional distribution of climatic exposure of gs(d) will generate an aggregate response to aggregated climate measures that is
generally smoother (e). Figure adapted from Burke et al. (2015c).
a widely used approach. Equation 31 differs from Equation 29 such that the two approaches
should not recover identical coefficients, even if the microlevel nonlinear data generating process
is unchanged. Burke et al. (2015c) demonstrate that the marginal effects recovered in Equation 31
should equal the weighted-average marginal effect at the local level (as estimated in Equation 29),
averaged across locations and moments, that is associated with a one-unit shift in the distribution
of local climatic conditions (Figure 5). Importantly, it is the spatial covariance between weights gs
and climatic conditions within periods of observation that determines how local nonlinear effects
appear in region-level models such as Equation 31. In general, a wider dispersion of conditions
experienced across locations and moments within a summarized region leads to greater smooth-
ing and flattening of the response in Equation 31 relative to the local instantaneous response
(Figure 5c–e). Thus, we expect that larger and more heterogenous regions with longer periods of
observation should produce smoother and flatter responses to summary climate measures, even if
local nonlinear effects are unchanged.
4.1.3. Global nonlinear effects. The distribution of climatic conditions experienced over time
within one region often differs substantially from distributions in other regions. In these cases,
average marginal effects should differ if response functions are nonlinear. Marginal effects that
change as a function of mean climate conditions are easily modeled as an interaction between
average climatic conditions and realizations of climatic variables such that
∂Yiτ
∂ciτ
=β(¯
ci),(32)
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β = α1 + α2T
–
T
–
1T
–
2
T
–
1
T
–
2
T
Y
T
YY
β(T
–)
β1β2
ba
T
Y = α0 + (α1 + α2T
–
) × TY = γ0 + γ1T × γ2T2
c
T
d
PDF of T
at i = 1
Figure 6
Different marginal effects βestimated from variation within different locations with different average
climates (a)mayresultfromaninteractionwithaverageclimaticconditions(b). In a panel data setting, this
can be modeled using an interaction (c), where each panel unit is a local linearization of a nonlinear function,
or a global nonlinear function can be estimated using the full sample (d). Abbreviation: PDF, probability
distribution function.
as illustrated in Figure 6a,b. Should an underlying global nonlinear response exist, it could be
recovered by estimating a single model that is nonlinear in climate variable realizations, with
a response surface that is only locally identified by the time-series variation among units that
experience realizations in the neighborhood of a tangency point (Figure 6c). This is conceptually
analogous to integrating Equation 32 to recover the global response surface (Figure 6d), which
holds exactly as lim ciτ→¯
ci.
4.2. Displacement and Delay
In many contexts, it is plausible that climatic events at moments in the past or at nearby locations
affect an outcome at a specific time and place, much like the surface of a pond observed at any
moment and location might depend on whether a raindrop disturbed that location or a nearby
point on the pond surface moments before. When using time-series identification of climate
effects, it is crucial to account for these ripple effects so that a local transient response is not
mischaracterized as a persistent effect. Of particular concern is whether climatic events have a net
effect on outcomes, or whether they simply displace outcomes across time and/or space.
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All-cause daily male mortality rate
following temperature exposure
(per 100,000 individuals)
GDP loss surrounding cyclone
exposure after 15 years
(% per meter per second)
ab
00–
400 400–
800 800–
1,200 1,200–
1,600 1,600–
2,000
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
–0.02
0.00
051015202530
Eect of neighbor’s exposure
Eect of own
cyclone exposure
0.02
0.04
0.06
0.08
0.10
Days after temperature exposure Distance from exposed country (km)
Eect of day with mean temperature <30°F
Eect of day with mean temperature >80°F
Figure 7
(a) Temporal lag effects of hot and cold days on all causes of male mortality based on data from Deschˆ
enes & Moretti (2009). (b) Spatial
lag effects of tropical cyclones on own and neighbors’ GDP 15 years after exposure; inset shows example annuli used to construct spatial
lags around Haiti. Adapted from Hsiang & Jina (2014).
Thus far, we have only considered contemporaneous effects of the vector ciτon outcome Yiτ.
We now consider the influence of the entire vector field c(s,t) defined across all positions sand
moments ton the outcome Yiτ.
4.2.1. Temporal displacement. Aclimaticeventattimetmight bring an event that would
otherwise occur at time t+1 forward in time, an effect known as temporal displacement or
harvesting. For example, Deschˆ
enes & Moretti (2009) highlight the importance of this concept by
demonstrating that many deaths that occur during hot days in the United States would have likely
occurred within the subsequent two months even in the absence of a hot day; they thus conclude
that an effect of a heat wave will influence the timing of deaths within a relatively narrow window,
in addition to creating some entirely new deaths (Figure 7a). Mathematically, the signature of
temporal displacement is for periods following a climatic event to have a response that is opposite
in sign to the contemporaneous response. A challenge to identifying these lagged effects is that
the climatic histories of sequential moments overlap, so it may not be the case that outcomes at
any moment are only a response to a single historical climate event. Rather, outcomes at each
moment represent a superposition of many historical events each at a different moment in time.
This issue can be resolved by conditioning expected outcomes on the complete history of climatic
events using a distributed lag model:
Yiτ=ˆ
αi+
L
#
l=04ci,τ−lˆ
βl5+xiτˆ
γ+ˆ
θ(i)(τ)+ˆ
ϵiτ,(33)
where lis a lag length measured in periods (l=0 indicates a contemporaneous observation),
and the maximum lag length considered is L. The identifying assumption to this approach is
that the influence of a climate event at τ0on outcomes at τ1is determined by the length of
time τ1−τ0separating the observations. As written, this model also assumes additive separability
between lagged effects, although this assumption can be relaxed by interacting lagged terms. It is
somewhat standard in the literature to sometimes include negative lags (leads) in Equation 33 as a
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falsification exercise, as it is generally assumed that future climatic events do not affect outcomes
substantially.
The net effect of a one-unit climatic event after λperiods is the cumulative effect
ˆ
.λ=
λ
#
l=0
ˆ
βl.(34)
If all of the effects of a climate event displace outcomes in time, then ˆ
.λ=Lwill be zero, whereas
a positive or negative cumulative effect indicates that climatic events caused additional changes
beyond altering the timing of events. It is worth noting that when the outcome is a growth rate,
then these cumulative effects represent changes in levels, as explored and discussed by Dell et al.
(2012) and Hsiang & Jina (2014). Burke et al. (2015c) compute .λin a nonlinear context.
4.2.2. Delayed effects. Equation 33 is also used to detect delayed effects, which may arise even if
contemporaneous effects ( ˆ
βl=0) are small or zero but lagged effects ( ˆ
βl>0) are large. In several cases,
such as the effect of cold days on mortality (Figure 7a)(Deschˆ
enes & Moretti 2009) or the effect of
tropical cyclones on employment and income (Anttila-Hughes & Hsiang 2012, Deryugina 2015),
delayed effects are of first-order relevance, dominating contemporaneous effects.
4.2.3. Spatial displacement and remote effects. Similar to temporal displacement and delay,
it is possible that climatic events cause outcomes to be displaced across space or trigger remote
outcomes (analogous to delayed effects in space) even if local effects are limited, perhaps because
markets and price signals efficiently transmit the influence of the climate across locations. For
example, Hsiang & Jina (2014) examine whether cyclone strikes displace income growth to nearby
countries (Figure 7b). The econometric challenge associated with identifying these effects is
analogous to the temporal case, as overlapping spatial effects may complicate the spatial distribution
of outcomes, similar to multiple simultaneous raindrops generating overlapping rings of waves
in a pond. The solution is also similar and involves estimating a spatial lag model analogous to
Equation 33, but where lags are applied to the index i,ratherthanτ, based on the distance between
contemporaneous observations; effects at all distances are estimated simultaneously. Similar to
temporal lags, the net effect of a climatic event can be considered by summing lags, although
care must be taken because the number of observations at varying distances may not necessarily be
constrained and will depend on the spatial arrangement of units. This approach performs especially
well when it is applied to data on a regular grid, as demonstrated by Harari & La Ferrara (2013).
In cases where remote effects may be delayed, then a model with spatial-temporal lags is required:
Yiτ=ˆ
αi+
L
#
l=0
/
#
π=0
{c[j|D(i,j)=π],τ−lˆ
βlπ}+xiτˆ
γ+ˆ
θ(i)(τ)+ˆ
ϵi,(35)
where c[j|D(i,j)=π],τ−lis the average climate exposure of all locations jthat are at a distance πfrom
location i(where the outcome is observed) at time τ−l.D(i,j ) is the distance from ito j. For
example, Figure 7bdisplays the cumulative growth effect of a cyclone as a function of distance
from the event.
4.3. Statistical Uncertainty
Uncertainty estimates for regressions must account for the strong spatial and temporal autocor-
relation in climatic exposure, regardless of the research design employed. The concern is that
unobservable omitted variables may also be autocorrelated, such that spurious correlations with
climate events occur with greater frequency than they would if all observations were independently
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distributed—this will cause bias in estimates of standard errors even though estimated climate ef-
fects ˆ
βmay be unbiased (Bertrand et al. 2004, Moulton 1986). The extent of the bias in standard
errors depends on the spatial scale and sampling frequency of the data relative to natural patterns
of autocorrelation in the climatic variations of interest. Data that are aggregated to large scales
are generally less problematic, and different solutions come at different computational cost and
may be appropriate in different contexts. Schlenker & Roberts (2009) propose applying Conley
spatial standard errors (Conley 1999) that nonparametrically estimate the variance-covariance
matrix of βby estimating cov(ϵi,τ,ϵj,τ) using ξ[D(i,j)]ˆ
ϵi,τˆ
ϵj,τ,whereξ[D(i,j)] is a kernel function
that weights these terms based on D(i,j), the distance between observations iand j. Hsiang (2010)
combines this approach with Newey-West heteroskedastic6and auto-correlation robust (HAC)
standard errors (Newey & West 1987) to also account for temporal autocorrelation within panel
units. Hsiang & Jina (2014) demonstrate that this spatial-HAC adjustment was correctly sized in
one context by estimating pseudoexact p-values via randomizing their data in multiple dimensions
and reestimating their model many times. Fetzer (2014) expands this approach to an instrumental
variables context.
The spatial-HAC approach is computationally intensive, as distances between every pair of
observations must be computed and transformed, and it does not guarantee a positive-definite
estimate for the covariance matrix of residuals. Thus, it may often be reasonable to estimate
approximate standard errors using simpler techniques, verifying that spatial-HAC adjustments
do not alter the result substantively. For example, Dell et al. (2012) simply cluster their standard
errors within panel units to account for temporal autocorrelation. Burke & Emerick (2016) cluster
standard errors for county-level observations in a long-differences model by state to account for
within-state spatial correlation; cross-state residual correlations in errors are assumed to be small
after conditioning on state fixed effects. Hsiang et al. (2013) employ a block bootstrap in a fully
nonparametric regression and block-resample entire cross sections of a panel data set to account for
spatial autocorrelation among contemporary observations. Hsiang et al. (2011) collapse a global
panel to a single time series when examining ENSO effects, as the treatment generates spatial
correlations at continental (or larger) scales.
It remains an open question what the most general and efficient approach to estimating statis-
tical uncertainty is in most climate econometrics applications. For example, what is the optimal
selection of kernel-weighting functions for contemporaneous and serial observations in the spatial-
HAC approach? Also, many climate data sets are derived from gridded data, which themselves
might be spatially interpolated from station data or augmented with a physics-based model—such
as reanalysis products (Auffhammer et al. 2013)—and it remains unknown how these procedures
influence the statistical uncertainty of resulting parameter estimates.
4.4. Adaptation
As discussed above, climate affects economic outcomes through belief effects and direct effects,
and it is generally thought that most belief effects are adjustments that individuals make to cope
with their expected distribution of direct effects. For this reason, belief effects are often described
as adaptations to a climate, although this need not always be true (e.g., beliefs about the climate
could serve simply as a coordinating mechanism). In this framework, adaptations can be defined
as belief effects that interact with direct effects; for example, some agents believe it will be cold
sometimes at a location, causing them to purchase coats (a belief effect), which reduces the chance
6Note that the Conley approach employed by Schlenker & Roberts (2009) was also robust to heteroskedasticity.
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they become ill after cold days (a direct effect). Multiple approaches have been used to document
and quantify these adaptations.
4.4.1. Indirect measurement via a cross section of levels. One strategy for measuring the
influence of adaptations is to estimate the effect of climate on some outcome that is influenced
by adaptation using a cross-sectional research design (Equation 8). The central benefit of this
approach is that it captures all belief effects, including adaptations that interact with direct effects
of the climate. For example, farm prices in Mendelsohn et al. (1994) should reflect any effects
that beliefs over Chave, including the net present value of all future revenues that result from
realizations of c, which are mediated by these beliefs and the resulting management practices.
There are two weaknesses to measuring adaptations using this approach: Measurement relies on
the strongest form of the unit homogeneity assumption (Equation 6), and the cross-sectional
approach cannot separately disentangle belief effects that do not interact with direct effects, belief
effects that do, and the integrated effect of all direct effects. However, an approach proposed by
Moore & Lobell (2014) combines this approach with time-series identification in an effort to
partially isolate these effects from one another.
4.4.2. Explicit observation of adaptation. Another approach to documenting adaptations is to
estimate the effect of climate directly on outcomes that are known (or thought) to be adaptations
to climate. For example, Hornbeck (2012) and Hidalgo et al. (2010) estimate the effect of drought
on migration of agricultural households, and Kurukulasuriya & Mendelsohn (2008) measure how
climate influences the selection of crops that farmers choose to plant. This approach can be adopted
in a cross-section, times-series, or long-differences framework. A benefit is that the adaptive action
is known and observed directly, rather than indirectly. However, a limitation is that this approach
does not recover the overall effectiveness of these adaptations, i.e., the extent to which the altered
actions interact with direct effects of climate.
4.4.3. Measurement of implicit adaptation combining time-series variation with stratifi-
cation. The one approach able to isolate the effectiveness of adaptations is to use a time-series
research design (Equation 10) for an outcome affected by adaptation, stratifying the sample—or
estimating interactions—using variables that are thought to predict the extent of adaptation. For
example, Auffhammer & Aroonruengsawat (2011) estimate the effect of daily temperature on en-
ergy consumption while stratifying by long-run average temperatures, demonstrating that energy
demand is higher on hot days in counties that are usually hotter on average. This result suggests that
the adoption of air conditioning, which is unobserved but assumed to be higher in counties that are
hotter on average, increases the effect of temperature on electricity demand. Roberts & Schlenker
(2011) effectively stratify a panel of counties by year, implemented by interacting a response func-
tion with a nonlinear trend, to understand if innovation over time or learning reduced the heat
sensitivity of maize in Indiana [Lobell et al. (2014) ask a similar question by examining how cross-
sectional estimates of climatic effects on yields evolve over a sequence of years]. Hsiang & Narita
(2012) derive a theory describing when such stratification works to reveal the total effectiveness of
adaptations. According to these authors, a benefit of this approach is its ability to measure the over-
all net effectiveness of all adaptive actions that project onto the interacted proxy variables, whereas
a weakness is that the costs of indirectly observed adaptations are unknown. To partially address
this weakness, Schlenker et al. (2013) propose an approach to measure adaptation costs in terms of
the outcome variable, although it is possible that additional costs or benefits may be unobserved.
Another key challenge of this approach is that those measures used as correlates for adaptations,
such as income (Hsiang & Narita 2012), urban status (Burgess et al. 2014), historical experience
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with climatic events (Hsiang & Jina 2014), or access to crop insurance (Annan & Schlenker 2015)
are not exogenous and vary primarily in cross section. This means it may be difficult to determine
whether changes to the measured variable are a cause of adaptation, an effect of adaptation, or
driven by an omitted variable that determines both. This drawback can be partially solved in cases
where plausibly exogenous circumstances change an influential factor, enabling a researcher to
more credibly identify whether a specific factor constrains adaptation. This approach is applied by
Hornbeck & Keskin (2015) to estimate the effect of groundwater discovery on agricultural adap-
tation and by Barreca et al. (2013) to estimate the effect of residential air conditioning technology
on health-related adaptation.
4.5. Comparisons and Synthesis of Results Across Studies
Unlike many other econometric studies, such as those that study policy changes, regressors in cli-
mate econometric studies are generally physical quantities that have similar or identical meaning
at all times and at any location on the planet. Because of this, comparisons across contexts are
thought to have clearer interpretations, often demonstrating replicability or highlighting impor-
tant differences across samples. For example, Hsiang & Narita (2012) and Hsiang & Jina (2014)
demonstrate notable global uniformity in the response to cyclones. In some cases, such as Guo
et al. (2014) examining mortality and Hsiang et al. (2013) examining social conflict, standardization
of cto a z-score based on historical variance brings parameter estimates into alignment—perhaps
because populations form beliefs and adapt effectively to distributions of historical conditions.
In some sectors, notably agricultural impacts and climatic effects on social conflict, explicit
comparisons of seemingly contradictory findings have generated substantial controversy. In the
case of agriculture, much of this disagreement can be reconciled by accounting for inconsistent
aggregation of data in the presence of local nonlinearities (see Section 4.1). In the case of social
conflict, much of this disagreement can be reconciled by accounting for statistical uncertainty in
parameter estimates (Hsiang & Meng 2014, Hsiang et al. 2015).
Hierarchical meta-analysis has played a role in synthesizing generalizable findings and quan-
tifying the extent of agreement in the literature (Hsiang et al. 2013) as well as in constructing
composite estimates for use in the climate projections discussed below (Houser et al. 2015). These
approaches do not assume globally uniform effects but instead model parameter estimates from the
literature in a random-effects framework, where populations experience different true effects of
the climate but may exhibit a generalizable component that is common across populations (Burke
et al. 2015b, Gelman et al. 2004).
5. ATTRIBUTION AND PROJECTION
Two objectives of understanding the effect of climate on societies are to understand what ele-
ments of the modern world might be attributable to climatic factors and to inform projections of
future outcomes under different climate scenarios. Both are cases in which parameters recovered
empirically are put to work. Note that in the following, I retain only the time index for simplicity.
5.1. Historical Attribution
Having identified the effect of current and previous climatic conditions Con outcome Y, it is
natural to ask, what counterfactual outcomes would we have observed historically under a different
climate? In our one realization of history, we observed Ytand Ctand estimated a response surface
ˆ
f(C) that described deviations from some benchmark outcome Y0associated with the benchmark
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climate C0. In estimation, these benchmark levels are usually nuisance parameters absorbed by
various fixed effects, trends, and controls. Observed outcomes are then
Yt=Y0+ˆ
f(Ct)−ˆ
f(C0),(36)
where Y0can be solved for but is not observed. Writing an analogous equation for an arbitrary
counterfactual climate Ct+%Ctand an associated unknown counterfactual outcome Yt+%Yt,
we difference these equations to obtain
%ˆ
Yt=ˆ
f(Ct+%Ct)−ˆ
f(Ct),(37)
which allows us to estimate %ˆ
Yt,thealterationofanoutcomethatwewouldexpectduetoa
change in historical climate by %Ct. This approach was used by Lobell et al. (2011) to estimate
the historical effect of observed warming on global crop yields, by Hsiang et al. (2011) to estimate
the historical influence of ENSO on global conflict, by Hsiang & Jina (2014) to estimate historical
influence of tropical cyclones on national income trajectories, and by Carleton & Hsiang (2016)
to attribute impacts based on a variety of results from the literature. Importantly, these estimates
should be viewed as partial equilibrium estimates insofar as ˆ
f(.) captures a partial equilibrium re-
sponse. Costinot et al. (2016) and Desmet & Rossi-Hansberg (2015) demonstrate more structured
approaches that can be used to attribute historical impacts in a general equilibrium framework.
Application of Equation 37 must be implemented cautiously, as counterfactual outcomes are
not observed and thus cannot be verified. One indirect test of this approach, useful when ˆ
f(.) is
identified via time-series variation, is to examine how closely predictions from Equation 37 match
historical cross-sectional patterns. Dell et al. (2009) run such a test for effects of temperature
on income, arguing that adaptation and growth convergence must explain the difference. Graff
Zivin et al. (2015) arrive at similar conclusions when comparing time-series estimates with long
differences in measures of human capital. Hsiang & Jina (2015) compare predictions based on
microlevel estimates with macrolevel cross sections for tropical cyclone impacts and conclude
that results are largely consistent. In a remarkable higher-order test, Barreca et al. (2015) find that
cross-sectional variation in the intra-annual variance in temperature, when applied to Equation 37,
is a good predictor of cross-sectional patterns of intra-annual variance in birth rates.
5.2. Projecting Future Effects of Climate Changes
Projecting impacts of climate changes is analogous to applying Equation 37, except that Ctis
replaced with a benchmark future scenario—usually a “no change” scenario based on historical
distributions of variables—and %Ctis an anthropogenic alteration to the climate. Early economic
analyses used simple, spatially uniform, general estimates of %Ct, such as imposing a flat +5◦F
warming and +8% rainfall across the United States (Mendelsohn et al. 1994). In the econometrics
literature, Schlenker et al. (2006) and Desch ˆ
enes & Greenstone (2007) introduce the use of spatially
and temporally resolved global climate model simulations to construct %Ct.Lobelletal.(2008)
and Burke et al. (2009) demonstrate that when applying climate model projections in Equation 37,
accounting for climate model uncertainty in %Ctmay be as important as accounting for statistical
uncertainty in ˆ
f(.) See Burke et al. (2015a) for additional exploration of this issue.
The above approaches generally assume that ˆ
f(.) has a fixed structure throughout the duration
of the projection simulation, perhaps a reasonable assumption in cases where historical changes in
ˆ
f(.) have been limited. However, as demonstrated in Section 2.4 (recall Figure 3d), the marginal
effect of climate identified via weather and captured in ˆ
f(.)maybecomeincreasinglyincorrect
as climatic conditions deviate from baseline conditions during a projection simulation and these
adaptations [or other factors, such as those described in Lobell et al. (2014)] alter ˆ
f(.). To partially
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address this issue, Houser et al. (2015) demonstrate how multiple empirical estimates, capturing
both cross-sectional heterogeneity and trends in ˆ
f(.), could be combined to construct projections
where ˆ
f(.) evolves throughout the projection simulation to reflect historical patterns and rates of
adaptation.
5.2.1. Top-down and bottom-up approaches. Optimal climate policy requires understanding
the full economic burden of potential climate trajectories. Empirical estimates can be used to gen-
erate projections of this total cost using either a top-down estimate, where the modeled outcome
Ytis some aggregate proxy for well-being, such as GDP (Burke et al. 2015c, Dell et al. 2012,
Deryugina & Hsiang 2014, Nordhaus 2006), or constructing bottom-up estimates for multiple
outcomes representing different sectors of the economy that are modeled and summed, sometimes
called the enumerative approach (Houser et al. 2015, Tol 2002). In principle, both approaches
can be comprehensive, so long as top-down estimates are augmented with nonmarket impacts. In
practice, bottom-up estimates may better account for the distributional costs of climate change
(Houser et al. 2015), although it is theoretically possible for them to perform equally well. When
applying Equation 37 to bottom-up projections, it is important to account for the covariance of
impacts across different sectors to accurately construct the distribution of aggregate losses (Houser
et al. 2015), an effect that is thought to be mostly captured in the estimated responses used for
top-down projections.
6. REMAINING CHALLENGES
In addition to challenges described in the sections above, there are four major areas where I see
methodological innovation as necessary and likely to be successful in the near future.
6.1. Matching Effects and Mechanisms
Regardless of the research design, most estimated effects of climate are reduced from estimates
that capture influences on an outcome through all possible pathways. Developing strategies and
techniques that can isolate and characterize a specific mechanism is critical for understanding
why climatic factors matter. Testing for interactions with potential mediating factors that are
plausibly exogenous (Barreca et al. 2013), exploiting natural experiments where specific pathways
are shut down (Fetzer 2014), and matching detailed patterns of climate influence on outcomes and
potential mediating factors (Anttila-Hughes & Hsiang 2012) are all approaches that have been
somewhat successful in specific contexts, although additional innovations in this area are needed,
as these strategies are not always available.
6.2. Adaptation and General Equilibrium
As discussed above, adaptation to climate is thought to be economically important, but it has only
been characterized in a limited number of cases. Notably, the costs of adaptations are almost never
measured because they are usually not observed. Moreover, most measurements are partial equi-
librium responses, whereas general equilibrium responses to climate, such as factor reallocations
across space or time, are a form of adaptation thought to be important but about which little is
known. Further, general equilibrium changes will result in changing prices, and knowing these
adjustments is important for valuing quantity effects that are already understood. However, only
asmallnumberofstudieshavebegunexploringtheseeffects(Colmer2016,Costinotetal.2016,
Roberts & Schlenker 2013).
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RE08CH04-Hsiang ARI 2 September 2016 8:33
6.3. Unprecedented Events
In analyses of future climate changes, evaluating events that are unprecedented in recent history
is a major obstacle, and any empirical progress on these questions would be highly valuable.
Innovative strategies that can measure potential costs of unprecedented physical events, such as
rapid sea level rise or ocean acidification, or that characterize the likelihoods of unprecedented
social responses to climatic changes, such as mass migrations or state failures, are needed if these
impacts are to be accounted for systematically in assessment exercises.
6.4. Integration with Theory and Numerical Models
Numerous theoretical models, including many used for integrated assessment policy analysis,
have elements that describe climatic influence on economies (Nordhaus 1993, Stern 2006, Tol
2002) but are generally not based on empirically derived relationships. Incorporation of empirical
parameter estimates into process models (Houser et al. 2015, Lobell et al. 2013) and integrated
assessment models (Kopp et al. 2013, Moore & Diaz 2015) demonstrates promise, although much
innovation is needed if these theoretical models are to perform as well as analogous models in other
scientific fields. For example, it is unknown if empirical calibration improves the out-of-sample
forecast performance of these models or if all model parameters are even theoretically estimable
using existing techniques.
7. CONCLUSION
Recent years have seen rapid innovation in the methods used to identify climatic influences on
economies, with correspondingly rapid growth of insights that are reshaping how we understand
the breadth and importance of climate–society interactions (Carleton & Hsiang 2016, Dell et al.
2014). Key innovations have been in research design, the measurement of climatic factors, and
the formulation of econometric models. In sharp contrast to the folk wisdom that “climate is not
weather,” here I demonstrate that under fairly general conditions, weather variation, as it is used in
many recent studies, exactly identifies the effect of climate—although many studies to date have not
properly computed the effect of climatic changes when using these weather-derived parameters.
Aggregation and synthesis of econometric findings have demonstrated a striking replicability of
many recent findings across contexts, lending credibility both to the techniques that generate
these results and to exercises where these results are applied to simulations of recent history or
future climate changes. Many first-order partial equilibrium results are now well understood, yet
major methodological innovations are still required to (a) tackle the key challenges of identifying
mechanisms, (b) measure adaptation costs, general equilibrium, and price responses, (c) evaluate
the effects of unprecedented events, and (d) more deeply integrate with theoretical and numerical
policy models.
DISCLOSURE STATEMENT
The author is not aware of any affiliations, memberships, funding, or financial holdings that might
be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
I thank David Anthoff, Jesse Anttila-Hughes, Max Auffhammer, Alan Barrecca, Marshall Burke,
Tamma Carleton, Olivier Deschˆ
enes, Tatyana Deryugina, Ram Fishman, Michael Greenstone,
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Michael Hanemann, Wu-Teh Hsiang, Bob Kopp, David Lobell, Gordon McCord, Kyle Meng,
Billy Pizer, James Rising, Michael Roberts, Wolfram Schlenker, Christian Traeger, and seminar
participants at Berkeley and Harvard for discussions and suggestions. I thank Wolfram Schlenker
for generously sharing data.
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Annual Review of
Resource Economics
Volume 8, 2016 Contents
Prefatory Articles
Some Comments on the Current State of Econometrics
George Judge ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣1
Information Recovery and Causality: A Tribute to George Judge
Gordon Rausser and David A. Bessler ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣7
Early Pioneers in Natural Resource Economics
Gardner M. Brown, V. Kerry Smith, Gordon R. Munro, and Richard Bishop ♣♣♣♣♣♣♣♣♣♣♣♣25
Environment
Climate Econometrics
Solomon Hsiang ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣43
Welfare, Wealth, and Sustainability
Elena G. Irwin, Sathya Gopalakrishnan, and Alan Randall ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣77
Climate Engineering Economics
Garth Heutel, Juan Moreno-Cruz, and Katharine Ricke ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣99
Economics of Coastal Erosion and Adaptation to Sea Level Rise
Sathya Gopalakrishnan, Craig E. Landry, Martin D. Smith,
and John C. Whitehead ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣119
Drivers and Impacts of Renewable Portfolio Standards
Thomas P. Lyon ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣141
Designing Policies to Make Cars Greener
Soren T. Anderson and James M. Sallee ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣157
Resources
The Economics of Wind Power
G. Cornelis van Kooten ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣181
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Forest Management, Public Goods, and Optimal Policies
Markku Ollikainen ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣207
The Economics of Forest Carbon Offsets
G. Cornelis van Kooten and Craig M.T. Johnston ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣227
The Management of Groundwater: Irrigation Efficiency, Policy,
Institutions, and Externalities
C.-Y. Cynthia Lin Lawell ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣247
Development
Sustainability and Development
Edward B. Barbier ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣261
Resource-Dependent Livelihoods and the Natural Resource Base
Elizabeth J.Z. Robinson ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣281
Well-Being Dynamics and Poverty Traps
Christopher B. Barrett, Teevrat Garg, and Linden McBride ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣303
The Impact of Food Prices on Poverty and Food Security
Derek D. Headey and William J. Martin ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣329
Contract Farming in Developed and Developing Countries
Keijiro Otsuka, Yuko Nakano, and Kazushi Takahashi ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣353
Agriculture
University–Industry Linkages in the Support of Biotechnology Discoveries
Richard A. Jensen ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣377
The Political Economy of Biotechnology
Ronald Herring and Robert Paarlberg ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣397
Predicting Long-Term Food Demand, Cropland Use, and Prices
Thomas W. Hertel, Uris Lantz C. Baldos, and Dominique van der Mensbrugghe ♣♣♣♣♣417
The Economics of Obesity and Related Policy
Julian M. Alston, Joanna P. MacEwan, and Abigail M. Okrent ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣443
Media Coverage, Public Perceptions, and Consumer Behavior: Insights
from New Food Technologies
Jill J. McCluskey, Nicholas Kalaitzandonakes, and Johan Swinnen ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣467
Errata
An online log of corrections to Annual Review of Resource Economics articles may be
found at http://www.annualreviews.org/errata/resource
Contents xi
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