Spatial Correlation, Trade, and Inequality:
Evidence from the Global Climate*
Jonathan I. Dingel
Chicago Booth, NBER & CEPR

Kyle C. Meng
UC Santa Barbara & NBER

Solomon M. Hsiang
UC Berkeley & NBER
22 July 2023

Abstract

Global phenomena, such as climate change, often have local impacts that are spatially correlated. We show that greater spatial correlation of productivities can increase international
inequality by increasing the correlation between a country’s productivity and its gains fromtrade. We confirm this prediction using a half-century of exogenous variation in the spatial correlation of agricultural productivities induced by a global climatic phenomenon. We introduce
this general-equilibrium effect into projections of climate-change impacts that typically omit
spatial linkages and therefore do not account for the global scope of climate change. We projectgreater international inequality, with higher welfare losses across Africa.

Keywords: climate change, inequality, spatial correlation, gains from trade, El Niño, agricultural trade
JEL codes: F11, F14, F18, O13, Q17, Q54, Q56*

Dingel and Meng contributed equally to this work. We thank Rodrigo Adão, Treb Allen, Costas Arkolakis, Mark
Cane, Chris Costello, Arnaud Costinot, Tatyana Deryugina, Pedro DiNezio, Dave Donaldson, Robert Feenstra, Kinda
Hachem, Christian Hansen, Matthew Kahn, Yuhei Miyauchi, Brent Neiman, Ben Olken, Esteban Rossi-Hansberg,
Veronica Rappaport, and Michael Waugh for valuable discussions and suggestions. Thanks to seminar participants
at numerous institutions and conferences for helpful comments. Kevin Dano provided excellent research assistance.
This work was completed in part with resources provided by the University of Chicago Research Computing Center.
Dingel thanks the James S. Kemper Foundation Faculty Research Fund at the University of Chicago Booth Schoolof Business for financial support. A previous version of this paper circulated as “The Spatial Structure of Productivity, Trade, and Inequality: Evidence from the Global Climate.” jdingel@chicagobooth.edu, kmeng@bren.ucsb.edu,
shsiang@berkeley.edu.

1Introduction

Global phenomena often have heterogeneous local impacts. In many cases, these impacts are
spatially correlated: neighboring locations experience similar conditions, a pattern dubbed the“first law of geography” (Tobler, 1970). The effects of anthropogenic climate change on cereal
yields, depicted in Figure 1, offer a prime example. Projected productivity losses are spatiallyconcentrated near the equator, while economies that will experience smaller losses and even somegains tend to be in mid-latitude locations. That is, a key feature of global climate change is thatan economy suffering reduced productivity will tend to have neighboring economies that also havelowered productivity.1 Empirical studies of climate change impacts have largely neglected theconsequences of such spatial correlation, and thus the global nature of climate change, by studying
isolated local temperature variation.
Figure 1: Change in log cereal yields under climate change (2013-2099)

Notes: Map shows the projected change in country-level log cereal yields under climate change between 2013–2099.
See details in Section 5.1.

This paper shows that greater spatial correlation of productivities increases welfare inequality
by altering the pattern of international trade. Theoretically, the spatial structure of productivity shapes countries’ gains from trade because they trade more with their neighbors than distantcountries. Our empirical investigation leverages exogenous variation in the spatial correlation ofagricultural productivities induced by a naturally-occurring global climatic phenomenon over thelast half-century. We find that gains from trade respond to spatial correlation in a manner that
increases international inequality. When we amend projections of anthropogenic-climate-change
impacts based on quasi-experimental estimates to incorporate this general-equilibrium effect, projected international inequality rises.
Trade theory links the spatial correlation of productivities and international inequality, as we
explain in Section 2. A country benefits by trading with more productive counterparts to the extent
1

Other examples of global events with spatially correlated local consequences include the Great Recession (Piskorski and Seru, 2018), food price shocks (McGuirk and Burke, 2020), and pandemics (Barro, Ursúa and Weng, 2020;
Dong, Du and Gardner, 2020).

1

that they demand more of its exports and sell it cheaper imports. Since trade costs increase withgeographic distance, a country enjoys larger gains from trade when its neighbors, rather than its
distant trading partners, are more productive. We show that when productivities are more spatiallycorrelated, more productive countries gain more from trade because they are near other productive
countries, while less productive countries gain less from trade because they are far from productive
trading partners. All else equal, greater spatial correlation raises welfare inequality.
Our main contribution is to estimate the empirical relationship between the spatial correlationof productivities and the distribution of gains from trade. Estimating causal effects of common
shocks is generally challenging because there are few or no unaffected units (Donaldson, 2015;
Fuchs-Schündeln and Hassan, 2016; Nakamura and Steinsson, 2018; Ramey, 2019). In our setting,the treatment of interest affects the entire global trading network. Thus, comparisons must be
made across time using exogenous variation from a global common shock. That is, one needs anatural experiment at a global scale.
To that end, our empirical investigation exploits a naturally-occurring climatic phenomenon
known as the El Niño-Southern Oscillation (ENSO), described in Section 3. In years when ENSO
is strong, there is a large, spatially contiguous region across the tropics that experience hotter
conditions, shown in red in Figure 2. As a result, ENSO approximates the ideal experiment by
increasing the global spatial correlation of cereal productivities without altering their mean orvariance.
Figure 2: ENSO and the global spatial structure of temperature

Notes: This map depicts pixel-level correlations between ENSO in December and average temperature during thefollowing February for 1961–2013. Red areas are hotter with warmer ENSO conditions. Blue areas are cooler withwarmer ENSO conditions.

In Section 4, we examine the effect of this global natural experiment on the distribution of
the gains from trade in cereals. In an important class of trade models, a country’s gains fromtrade are revealed by the share of its expenditure devoted to imports (Arkolakis, Costinot and2Rodrı́guez-Clare, 2012). We estimate how local temperature-driven and global ENSO-driven variation in cereal productivities affect these expenditure shares. When productivities are more spatiallycorrelated, more productive countries import more. According to the model, greater spatial correlation of productivities causes more productive countries to gain relatively more from trade andless productive countries to gain less. Specifically, increasing the cross-sectional spatial correlationof cereal productivities by one standard deviation increases the inequality of welfare attributableto cereal consumption by 2%.
We take several steps to validate this interpretation of the difference in trade patterns. In
particular, our welfare quantification relies on a class of trade models in which there is no spatial
correlation in the pattern of comparative advantage within the cereals sector. In alternative trademodels with spatially correlated comparative advantage (see Appendix A.4), a country may havelower gains from trade when its neighbors are more productive, so that higher spatial correlationof all-cereals productivity would decrease welfare inequality. Three results suggest this is unlikely.
First, sufficiently spatially correlated comparative advantage within cereals would imply that ENSO
would alter the expenditure-productivity relationship with the opposite sign of our estimated effect. Second, gravity regressions do not reject the hypothesis that the trade elasticity is invariant tobilateral distance, suggesting comparative advantage within the cereals sector is not spatially correlated. Third, we examine an alternative outcome variable that accommodates arbitrary patternsof comparative advantage: a local approximation of the change in the terms of trade (Dixit andNorman, 1980). This measure also shows that greater spatial correlation of all-cereals productivity
increases welfare inequality.
Understanding the consequences of global phenomena like anthropogenic climate change requires
quantifying both local direct effects and indirect effects due to spatial linkages. Researchers often
face a trade-off between using plausibly exogenous variation to estimate treatment effects andcapturing indirect effects due to spatial linkages. Quasi-experimental research designs typicallyestimate local direct effects but ignore spatial linkages, while structural models quantify indirect
effects but impose many functional-form assumptions.
In Section 5, we develop a hybrid approach that incorporates the spatial correlation of productivities when projecting climate-change impacts without imposing the full structure of quantitative trade models. A growing empirical literature examines how economic outcomes respond toquasi-experimental variation in local temperatures.2 Typically, projected climate impacts for any
location are the product of these estimated effects and that location’s temperature trajectory underclimate change, holding temperatures in other locations fixed. The projected global impact of climate change is then the sum of these isolated impacts across locations. This calculation, however,amounts to asking what would happen if, say, Kenya were to warm by itself, without acknowledging that global climate change will also simultaneously warm Ethiopia, Tanzania, and Canada. In
doing so, this approach fundamentally overlooks the global scope of anthropogenic climate change
2

Following seminal studies of the United States (Deschênes and Greenstone, 2007a,b; Schlenker and Roberts,2009), quasi-experimental local temperature variation has been used to study various economic effects around theworld (e.g., Dell, Jones and Olken 2012; Burke, Hsiang and Miguel 2015; Carleton et al. 2020).

3

(Dell, Jones and Olken, 2014; Hsiang, 2016; Auffhammer, 2018; Deschênes and Meng, 2018).
We produce new climate impact projections that leverage quasi-experimental estimates whileaccounting for changes in the spatial correlation of cereal productivity. Prior quasi-experimental
studies project increased dispersion in various economic outcomes across countries (Dell, Jones and
Olken, 2012; Burke, Hsiang and Miguel, 2015). We show that incorporating spatial linkages leads
to a 20% greater increase in the inequality of welfare from cereal consumption by the end of thetwenty-first century. Notably, a projection that omits the change in spatial correlation considerably
understates the climate-driven welfare losses for most countries in Africa because these countries
jointly experience larger productivity losses. While these projections are not literal forecasts offuture climate impacts because they abstract from adaptation, migration, and other possible responses, they demonstrate how one can extend quasi-experimental research designs to examine theconsequences of spatial interdependence. In doing so, this paper brings the quasi-experimental
approach to climate-change impacts conceptually closer to recent structural analyses of the spatial
distribution of economic activity under climate change (Brock, Engström and Xepapadeas, 2014;
Desmet and Rossi-Hansberg, 2015; Conte et al., 2021; Cruz and Rossi-Hansberg, 2021; Nath, 2021;
Krusell and Smith, 2022).
This paper connects studies of environmental determinants of economic outcomes to the literature on economic geography. Local environmental conditions alter economic activity by influencing
factor productivities, human capital accumulation, and institutional quality (Bloom and Sachs,
1998; Easterly and Levine, 2003; Nordhaus, 2006; Bleakley, 2007; Nunn and Puga, 2012). We
explore how local economic outcomes depend on environmental conditions elsewhere via trade.
Generally, countries with better access to trading partners have higher incomes (Head and Mayer,
2004; Redding and Venables, 2004). Our results link the distribution of the gains from trade to
the spatial correlation of productivities. The most closely related study of global agricultural trade
is by Costinot, Donaldson and Smith (2016), who examine the consequences of climate changeusing a model of international trade and an agronomic productivity forecast. While we focus on
the spatial correlation of absolute advantage, they focus on changes in comparative advantage andwithin-country crop switching. While they employ agronomic forecasts to predict changes in tradeflows, we investigate the trade effects of historical variation in agricultural productivities.

2

Theoretical framework

This section introduces a theoretical framework to show how the spatial correlation of productivities
may affect international inequality and to guide our empirical investigation of this prediction.
Section 2.1 introduces a class of models in which a country’s gains from trade are revealed by theshare of its expenditure devoted to its own output. We use a stylized example to illustrate how
the spatial correlation of the productivity distribution affects welfare inequality by altering thecovariance between a country’s productivity and its domestic share of expenditure.3 Section 2.2
3

Spatial correlation of productivity need not alter average welfare: on a symmetric geography, proximity to
productivity is necessarily zero-sum. Hence our focus on its consequences for international inequality.

4

describes how we can estimate this relationship using panel data and why we study the cereals
sector. Further details and derivations are available in Appendix A.

2.1

Spatial correlation and welfare inequality

We study the class of models characterized by Arkolakis, Costinot and Rodrı́guez-Clare (2012),
in which the gains from trade can be inferred from the domestic share of expenditure. This classincludes Armington (1969), Krugman (1980), Eaton and Kortum (2002), and Melitz (2003) witha Pareto productivity distribution.4 We summarize the perfect-competition case in the main text,
while Appendix A.1 provides details and covers the monopolistic-competition models. The world
economy consists of j = 1, . . . , N countries.
Preferences. Individuals in country j have constant-elasticity-of-substitution preferences overgoods.
Production. There is one factor of production. Perfectly competitive firms employ a production technology that exhibits constant returns to scale and depends on productivity Aj . Eachcountry j inelastically supplies Lj units that earn factor price wj , so national income is Yj = wj Lj .
Trade costs. There are iceberg trade costs, such that selling one unit of a good to j from i
requires producing τij ≥ 1 units, with τii = 1.
Gravity equation. Denote sales from i to j by Xij and j’s total expenditure by Xj ≡PN

i=1 Xij .

The share of expenditure by j on goods from i, λij , is given by a gravity equation:
λij =

Xij
Aϵ (τij wi )−ϵ,= PN iϵ (τ w )−ϵ
Xj
A
lj
l
l=1 l

where ϵ is the “trade elasticity” governing how bilateral expenditures respond to bilateral trade
costs.
Equilibrium. In equilibrium, labor markets clear, goods markets clear, and budget constraints
are satisfied such that income Yi equals expenditure Xi . Thus, equilibrium incomes {Yi }N
i=1 satisfy
PN
Yi = j=1 λij Yj .
A country’s welfare is the sum of its welfare in autarky and its gains from trade, and in thisclass of models the latter can be inferred from expenditure shares. Real consumption per capita isln (Ci /Li ) = ln Ai + γ −1
ln λii ,ϵ(1)where γ is a model-specific constant unrelated to productivity. The former term, ln Ai + γ, is per
capita welfare in autarky. Absent trade, a country’s welfare depends on only its own productivity:
it purchases only its own goods, so λii = 1 and ln λii = 0. The latter term, − 1ϵ ln λii , is its
gains from trade relative to autarky. This sufficient statistic depends on the trade elasticity ϵ andthe country’s expenditure share on its own goods, which is a function of trade costs and all othercountries’ productivities. When a country imports goods from other countries, λii < 1 and its gains
4

As is common in trade theory, we abstract from dynamics and risk by studying static models.

5

from trade are positive.5 Importantly, the domestic share of expenditure is an observed outcome
capturing the gains from trade: given the trade elasticity, a lower domestic share of expenditure
implies larger gains from trade.
From equation (1), the variance of welfare across countries is the sum of the variance of productivity, the covariance of productivities and gains from trade, and the variance of those gains.
1var (ln (Ci /Li )) = var (ln Ai ) + 2cov ln Ai , − ln λii
ϵ




+ var

1
ln λiiϵ(2)The spatial correlation of productivities affects international inequality through the second term:
the covariance of productivity and gains from trade.6
By making neighboring countries have more similar productivities, spatial correlation interacts
with two key features of international trade. First, a country benefits by trading with more productive counterparts, which demand more of its exports and sell it cheaper imports. Second, trade
costs increase with geographic distance (Disdier and Head, 2008). Thus, when proximate countries
have more similar productivity levels, more productive countries tend to enjoy greater gains fromtrade because more productive trading partners are nearby. Conversely, less productive countries
experience lower gains from trade because more productive trading partners are farther away. When
more productive countries gain more from trade than less productive countries, welfare inequality isgreater. Appendix A.2 makes this argument in detail, presenting results of a local approximation,an analytical proof for a four-country model, and numerical simulations of a many-country modelwith a realistic geography.7 Here, we present the results from a highly stylized model in order toillustrate the economic logic and relevant empirical considerations.
The stylized model has productivity follow a sine wave over a one-dimensional space. There are
N countries with equal population sizes evenly spaced on the unit circle. Trade costs depend only
on distance: the log trade cost between two countries is proportionate to the log distance between
them. The trade elasticity is ϵ = 1, so that welfare is ln Ai − ln λii , a difference that is easy to
depict visually. Productivity ln Ai follows a sine-wave distribution, with an integer frequency of θ
over the circle’s circumference. This distribution has two convenient properties. First, its spatial
correlation is governed by θ: lower frequencies exhibit greater spatial correlation. Second, its mean,variance, skewness, and kurtosis are independent of this frequency.
The left panel of Figure 3 depicts the spatial distributions of productivities (ln Ai , in black),
welfare (ln Ci , in blue), and domestic shares of expenditure (ln λii , in red) in this circular economy
for the cases in which the sine wave has frequencies of θ = 1 and θ = 4. It is clear that the spatial
correlation of productivities is greater in the θ = 1 case, as location “zero” divides the circle into
5

Since expenditure shares depend on relative prices, this share is closely linked to the country’s terms of trade,which is the relative price of its exports compared to its imports. We return to this insight later when considering
an alternative gains-from-trade measure under weaker theoretical assumptions.
6
The first term, the variance of productivity, is invariant to spatial correlation by definition. For empirically
relevant values of ϵ, the third term is an order of magnitude smaller than the second term, as explained in Appendix
A.1.
7
To examine our prediction with realistic productivities and trade costs, we simulate a global economy made up
of 158 countries whose geographic coordinates, cereal yields, and crop areas are their 1961–2013 averages in our data.

6

two contiguous regions with above-average and below-average productivity. In this case, productive
economies only need to ship their goods a short distance to reach the most productive economy,
while the least productive country must ship its goods halfway around the world to reach it. This
contrasts with the θ = 4 case, in which distances between the most and least productive countries
are shorter.
Figure 3: Circular geography with productivity sine wave
1.0
0.4
0.3

0.5

ln λii (demeaned)

0.2

0.0

-0.5

0.1
0.0
-0.1
-0.2
-0.3

-1.0
-3

-2

-1

0

1

2

3

-0.4

Countries’ locations on [−π, π]ln Ai , θ = 1
ln Ai , θ = 4

ln λii , θ = 1
ln λii , θ = 4

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

ln Ai (demeaned)ln Ci , θ = 1
ln Ci , θ = 4

θ = 1, I = 0.24

θ = 2, I = 0.05

θ = 3, I = 0.02

θ = 4, I = −0.01

Notes: This figure depicts an economy with a circular geography and a productivity distribution that follows a sine
wave with frequency θ. There are N = 50 locations evenly spaced on the unit circle. Bilateral log trade costs areproportionate to the log length of the arc between two points on the circle. The trade elasticity is ϵ = 1, so thatwelfare is simply the difference ln Ai − ln λii . See Appendix A.2.3 for parameterization details. By Theorem 1 ofAllen, Arkolakis and Takahashi (2020), the equilibrium solution depicted for each set of parameter values is unique.
The left panel depicts the (demeaned) distributions of productivities, equilibrium domestic shares of expenditure,
and welfare are depicted for the cases of θ = 1 and θ = 4. The right panel depicts the ln λii –ln Ai relationship for thecases of θ = 1, 2, 3, 4. The right panel’s legend reports the value of Moran’s I for each sine wave.

The frequency of the exogenous productivity sine wave affects the amplitude of the endogenous
welfare sine wave. In the case of higher spatial correlation (θ = 1), the amplitude of the welfare series
is greater than in the θ = 4 case. This follows from the fact that the equilibrium domestic share of
expenditure series has a smaller amplitude in the θ = 1 case, and welfare is the difference between
the productivity and expenditure-share series. In other words, with greater spatial correlation, theexpenditure series follows the productivity series less closely: cov(ln Ai , ln λii ) is smaller and thus
2cov ln Ai , − 1ϵ ln λii is greater.8
The right panel of Figure 3 depicts the relationship between productivity and the domestic
share of expenditure for more values of the sine-wave frequency, θ. The scatter plot reveals analmost perfectly linear relationship between ln λii and ln Ai . The slope of this relationship, which is
proportionate to cov(ln Ai , ln λii ), systematically varies with the spatial correlation of the sine wave.
When the productivities are more spatially correlated, a location’s domestic share of expenditure isless responsive to its own productivity level. Our empirical investigation examines the relationshipbetween these observable outcomes to discern the consequences of spatial correlation for welfare
inequality.
8

We assume here that the trade elasticity ϵ is invariant to the global spatial correlation of productivities. Section 3.2
and Appendix C show that our empirical setting satisfies this assumption.

7

2.2

From theory to empirics

We have illustrated the consequence of spatial correlation of productivities for global welfare inequality in an ideal environment that holds fixed all other economic elements. Our empiricalinvestigation of how spatial correlation affects the covariance of productivity and gains from trademust further allow for a realistic geography, arbitrary productivity distributions, the presence ofother determinants of equilibrium trade flows, and multiple sectors. Appendix A.2 presents a number of models with these features to motivate our empirical research design and Appendix A.3
shows that our prediction holds for each sector in a multi-sector gravity model. To summarize
our empirical implementation, we examine our ceteris paribus prediction by exploiting year-to-year
variation in the global cross-sectional spatial correlation of productivities for our sector of interestin a panel-data setting.
To accommodate a realistic geography, we measure the global spatial correlation of productivities in year t using Moran’s I, a measure defined on any geography endowed with a distancemetric:N
It ≡ P Pi

P P

j̸=i ωiji
ln Ait − ln At ln Ajt − ln At
.
2
P
ln
A
−
ln
A
t
ℓt
ℓ

j̸=i ωij

In this formula, N is the number of countries, ωij = ωji is a symmetric spatial weight that depends
Pon the distance between countries i and j, and ln At ≡ N1 i ln Ait is average productivity in year
t. In the circular sine-wave economy of Section 2.1, Moran’s I is 0.242 and -0.011 for the θ = 1 andθ = 4 cases, respectively.
We use panel data to address other determinants of the domestic share of expenditure that may
be correlated with productivity. For example, remote countries face higher-than-average trade costs
that raise their domestic share of expenditure and remote countries may also exhibit lower productivities. In our panel setting, time-invariant country characteristics that influence the domestic
share of expenditure and might be correlated with productivity can be absorbed by country fixed
effects.9 Likewise, year fixed effects absorb potentially confounding time-varying global shocks, andcountry-specific trends absorb secular local growth in productivity and trade.
Using a panel of countries at an annual frequency, we estimate the following regression:ln λiit = β0 ln Ait + β1 It ln Ait + Π′ Zit + µit ,(3)

where λiit is country i’s domestic share of expenditure in year t, Ait is its productivity, It is theMoran’s I statistic for the spatial correlation of productivities, and the vector Zit includes country
fixed effects, year fixed effects, and country-specific time trends. µit is a residual due to unobserved
shocks and the linear approximation.
β0 and β1 are reduced-form parameters describing the covariance of interest. β0 captures therelationship between a country’s gains from trade and productivity when Moran’s I is zero. β1
captures the degree to which the global spatial correlation of productivities mediates this covariance9

Appendix A.2.3 illustrates this logic for the case of heterogeneous population sizes.

8between gains from trade and productivity.10 When β1 < 0, greater spatial correlation lowers thecovariance of productivity and the domestic share of expenditure, implying a higher covariance
between productivity ln Ai and the sufficient statistic for the gains from trade, −1
ϵ ln λii . When
greater spatial correlation of productivities causes more productive countries to experience greater
gains from trade and less productive countries to experience lower gains from trade, international
inequality increases.
Our choice of empirical setting is guided by four criteria. First, trade flows must decline with
distance so that countries tend to trade with their neighbors. Second, examining the role of the spatial correlation of productivities across a trade network requires a measure of productivity reported
in comparable terms across the globe. Third, examining global spatial correlation requires sufficient
time-series variation to identify its effects. Fourth, the identifying variation in productivities andtheir global spatial correlation needs to be plausibly exogenous to infer a causal relationship.
To satisfy these criteria, we study the cereals sector, which we define as the top eight cereals that
account for more than 99% of global cereal production and trade.11 Trade in cereals declines with
distance: column 1 of Table C.1 shows that bilateral trade in cereals declines with physical distancewith an elasticity and overall explanatory power that is typical of prior estimates for aggregate tradeflows (Head and Mayer, 2014). Cereals satisfy the second and third criteria because a measure of
productivity, cereal yield (the output-land ratio), is available at the country-year level with nearly
global coverage since 1961 from the United Nations Food and Agriculture Organization (FAO).12,13
Our fourth criteria requires exogenous variation in national cereal productivities and their global
spatial correlation. Estimating equation (3) by ordinary least squares (OLS) is uninformative if
expenditure shares and productivity are simultaneously determined or if there are omitted determinants of expenditure shares that are correlated with productivity.14 In an ideal experiment, a10
While equation (3) is a reduced-form regression, Appendix A.2.4 shows that it captures 93% of the welfare
variance generated under our most realistic trade model.
11
These cereals are barley, maize, millet, oats, rice, rye, sorghum, and wheat. According to the FAO, these eight
cereals constituted 99.3% of global production (in metric tons) and 99.6% of global trade (in nominal US dollars)
during 1961–2013. These cereals are not homogeneous goods. FAO data report quantities of wheat produced, buttrade data distinguish durum and non-durum wheat. Trade data distinguish four types of rice, but the International
Rice Genebank holds more than 125,000 rice varieties, which are differentiated by quality, appearance, and taste(Agcaoili-Sombilla and Rosegrant, 1994). Quantitative trade models make common predictions about trade flows
while making different assumptions about the set of goods in the utility function. We study expenditure shares, so
we need not map our data sources’ product definitions to goods indexed by ω in the theoretical framework.
12
If land and other inputs are perfect complements in the production of cereals, yield equals total factor productivity(TFP) (Costinot, Donaldson and Smith, 2016). More generally, land productivity and TFP may differ, in which caseone needs an instrument for yield that shifts its TFP component. Using weather as a source of exogenous variationin cereal yields is a popular research design (e.g., Roberts and Schlenker 2013) that dates to the first application of
instrumental variables (Wright, 1928).
13
Unfortunately, data on other sectors’ expenditure shares and productivities lack the spatial and temporal coverage
necessary for our empirical analysis. Data availability also necessitates studying cereal trade at the level of countries.
Annual data on agricultural productivity, internal trade, and population counts for subnational spatial units have notbeen collected by most countries for most years. We therefore focus on international trade and the spatial correlationof productivities across countries.
14
For example, demand shocks could affect expenditure shares and elicit supply responses that change average
yields. Similarly, if domestic cereal production employs imported intermediate goods, then unobserved trade-cost
shocks could jointly affect domestic cereal yields and the domestic share of expenditure.

9researcher would manipulate productivities around the world in a way that alters the global spatial
correlation of productivities without changing the global mean or variance of productivities. Suchan experiment is obviously not possible. However, because of the well-established sensitivity of cereal yields to environmental conditions (Schlenker and Roberts, 2009; Hsiang and Meng, 2015), weare able to approximate this ideal experiment by exploiting productivity variation attributable totemperature variation and a global climatic phenomenon known as the El Niño-Southern Oscillation(ENSO), described in the following section.
Finally, translating the consequences of spatial correlation for trade patterns into welfare consequences relies on the assumptions made in the Arkolakis, Costinot and Rodrı́guez-Clare (2012)class of models. In particular, this theoretical framework assumes that the pattern of comparativeadvantage within the sector is symmetric across countries so that the exports of neighboring anddistant economies are similarly substitutable.15 Most quantitative trade models assume this pattern of comparative advantage.16 However, as Appendix A.4 shows, in alternative trade models
with spatially correlated patterns of comparative advantage, a country may have lower gains fromtrade when its neighbors are more productive.
Three empirical findings address this potential concern about spatially correlated comparativeadvantage. First, if comparative advantage were sufficiently spatially correlated, β1 in equation (3)would be positive (see Appendix A.4). Our estimates of β1 in Sections 4.2 and 4.3 are negative.
Second, per Lind and Ramondo (2019), spatially correlated comparative advantage would require
the trade elasticity to vary with the distance between trading partners. Gravity regressions cannot
reject the hypothesis that the trade elasticity is invariant to bilateral distance (see column 3 ofTable C.1), suggesting comparative advantage within cereals is not spatially correlated. Third,
we find qualitatively consistent results when examining an alternative outcome variable that is
informative under much weaker theoretical assumptions.
Specifically, we examine changes in the terms of trade – changes in the prices of exports relative
to imports – as measured by the product of price changes and the previous period’s traded quantities(Dixit and Norman, 1980, p.132). A country’s terms of trade improve if its initial net import vector
is cheaper at the new prices than at the old prices.17 This measure is attractive because it only
requires a revealed-preference argument. Unfortunately, unlike the domestic share of expendituremodeled in equation (3), this measure limits any conclusions about the welfare consequences oftrade to its sign: whether a country’s terms of trade improved or deteriorated. We use this outcome
variable in Section 4.4 and find the same welfare consequences of greater spatial correlation as we
15
Comparative advantage causes countries to gain by specializing and trading with each other. Absolute advantage
affects how these gains from trade are divided between countries through the terms of trade. Our prediction concerns
the spatial correlation of absolute advantage. In Appendix A.4, we examine how the spatial correlation of comparativeadvantage may interact with the spatial correlation of absolute advantage.
16
A notable exception is recent work by Lind and Ramondo (2019) that generalizes quantitative Ricardian models
by tractably relaxing this assumption.
17
To see the connection between gains from trade and terms of trade in quantitative trade models, consider theArmington case detailed in Appendix Section A.1. In that model, the gains from trade are given by the price of a
hP
i−1/ϵ
−1
N
−ϵ
.
country’s export relative to its consumer price index, λii ϵ = pi /l=1 (pli )10

do when making stronger assumptions.

3

The El Niño-Southern Oscillation

This section first summarizes the basic physics of ENSO and then empirically demonstrates that it
drives annual variation in the global spatial correlation of cereal productivity.

3.1

Background

ENSO is a naturally occurring, annual climatic phenomenon characterized by mutually reinforcing
circulation patterns between the atmosphere and the tropical Pacific ocean. While ENSO originatesin the tropical Pacific, it is a major determinant of weather conditions around the world. Indeed,at an annual frequency, ENSO is often recovered as the first principal component of various local
atmospheric or oceanographic variables across the planet (Sarachik and Cane, 2010).
ENSO is often colloquially described as consisting of one neutral state and two extreme states.
These conditions are broadly characterized by the amount of heat that is released from the tropical
Pacific ocean into the atmosphere (Cane and Zebiak, 1985). In typical “ENSO neutral” years,
normal circulation patterns pushing westward hold a pool of warm water against Indonesia andother land masses in the South Pacific. A positive “El Niño” state occurs when this circulation
pattern weakens such that this pool of warm water spills eastward across a large area of theequatorial Pacific Ocean. With warm water exposed to the atmosphere over a greater sea surface
area, El Niño years release more ocean heat into the atmosphere over a relatively short period. The
opposite occurs during the negative “La Niña” state. In La Niña years, stronger circulation patterns
push the same volume of warm water more firmly against the Indonesian landmass, reducing seasurface contact with the atmosphere and thus reducing heat released from the ocean. While thesethree distinct states are descriptively convenient, there is in fact a continuum of ENSO conditions
corresponding to the amount of heat released into the tropical atmosphere.
ENSO conditions in the tropical Pacific affect the spatial pattern of weather conditions acrossthe planet due to how heat travels when released in the tropics. Because there is almost no
Coriolis effect near the equator (a result of the simple facts that the Earth is round and spins),
atmospheric signals propagate rapidly throughout the tropics. During a positive ENSO event, thewarm air initially released above the tropical Pacific Ocean is propagated throughout the tropics bya transport mechanism in the atmosphere known as an equatorial Kelvin wave that sweeps acrossthe globe, altering weather conditions almost simultaneously throughout the tropics (Chiang andSobel, 2002).18 For this reason, it is often said that the tropical atmosphere is “teleconnected”
during a positive ENSO event, as atmospheric conditions in locations distant from each other are
linked through this mechanism. Because the equatorial Kelvin wave that connects local weather
around the equator is confined primarily to the tropics, the weather conditions that prevail during
18
This tropical phenomenon is described in Hsiang and Meng (2015). For a complete scientific treatment of ENSO
physics, see Sarachik and Cane (2010).

11

a positive ENSO event do not generally extend to higher latitudes, which may in fact experience
opposing weather conditions because of changes to atmospheric circulation.
This physical mechanism allows ENSO to induce large areas of the planet to experience similar
local temperature, precipitation, humidity, and other weather conditions. The spatial consequencesof a positive ENSO event are perhaps best illustrated by temperature.19 During a positive ENSO
event, temperature conditions around the world are reorganized such that there is a spatiallycontiguous area of relatively warm temperatures across the tropics and subtropics while almost
simultaneously there is a spatially contiguous area of relatively cooler temperatures in higherlatitude locations. The opposite occurs during negative ENSO events: less heat is released into theatmosphere and temperatures across the globe are less spatially organized.
ENSO conditions are typically summarized by the average sea-surface temperature over a fixedarea in the tropical Pacific. In our main analysis, we employ the widely used NINO4 index, astatistic defined as average ocean temperature (in degrees Celsius) over a rectangular area boundedby 5◦ S - 5◦ N, 160◦ E - 150◦ W (see Figure E.2).20 Figure 4 plots this monthly ENSO index for
1856–2013, which extends back further than our estimation sample period of 1961–2013. There
are two important features of ENSO relevant for our empirical application: (i) the monthly timingof a typical ENSO event and (ii) how an ENSO event influences local temperatures around theplanet both spatially and temporally. Due to ENSO’s tropical origins, the timing of ENSO events

2

Figure 4: Monthly ENSO index (1856–2013)-2

Monthly ENSO index (degrees Celsius)-10
1

Sample period

1860

1880

1900

1920

1940
Year

1960

1980

2000

2020

Notes: This figure depicts the monthly ENSO index (i.e., NINO4) during 1856–2013. The shaded area shows our
1961–2013 sample period.

is phase-shifted relative to the calendar year. Figure E.3 illustrates this timing by plotting themonthly ENSO index 12 months before and after a given December for the 10 most positive ENSO
19

ENSO alters the spatial structure of other weather variables but these effects tend to be of smaller spatial scales.
For example, during positive ENSO events there is typically flooding over the Pacific coast of South America while
the Atlantic coast of South America primarily experiences droughts (Ropelewski and Halpert, 1987).
20
In robustness checks, we show that using other measures of ENSO yields similar empirical results.

12events during 1961–2013. An ENSO event generally begins during April-May of a given year andlasts until the following April-May, an interval known as the “tropical year.” Because the ENSO
index typically peaks in December, the cleanest annual measure of any ENSO event is simply theDecember value of the index.21 In all following empirical analyses, we use December values as our
year-to-year measure of ENSO.
A typical ENSO event affects local temperatures around the planet in a spatially and temporally
distinct manner. Figure 5 depicts the month-by-month structure of warming that occurs when the
ENSO index increases. Each map displays the time-series correlation of monthly temperatures foreach pixel during the specified month and ENSO in month zero, defined as December. Yellow,
orange, and red colors indicate locations that warm as the ENSO index increases; blues indicate
locations that cool. In the May before a December ENSO event (month -7), the east equatorial
Pacific begins to warm. Regions throughout the tropics, both over land and the oceans, continue
to warm for the next several months, peaking in the eastern Pacific in December (month 0) andover the rest of the tropics in March and April (months +3 and +4). This warming then dissipates
across the tropics, with little effect visible more than a year after the December peak. Higher
latitudes experience some cooling through these months, though the effect is weaker.
Figure 5 also shows that the local impacts on temperatures around the planet from a single
ENSO event straddles two calendar years. When using annual socioeconomic data reported bycalendar years, one must therefore examine how outcomes in a given year depend on both ENSO
in that year and ENSO in the previous year.

3.2

ENSO and the spatial correlation of cereal productivity

The spatial and temporal patterns shown in Figure 5 suggest that ENSO could drive the spatial
correlation of cereal yields. Figure 6 shows country-level responses of log cereal yields to a 1-degreeincrease in the sum of contemporaneous and lagged December ENSO indices.22 Consistent with theclimatic dynamics described above, increases in the ENSO index tend to lower cereal productivities
in countries near the equator and raise cereal productivities in countries far from the equator. Thispattern suggests an increase in the spatial correlation of cereal yields.
To quantify global spatial correlation in each year, we construct an annual Moran’s I statistic
for country-level log cereal yields.23 Figure 7 shows the relationship between ENSO and the global
spatial correlation of cereal productivity. To characterize the ENSO phenomenon in terms of ascalar, we plot the sum of December ENSO indices in years t and t − 1 on the horizontal axis andMoran’s I in year t on the vertical axis. An increase in the ENSO index raises this measure of
21

This measure of ENSO is stationary and does not exhibit serial correlation. A Dickey-Fuller test strongly rejects
the presence of a unit root in favor of stationarity (p=4.15e-21). We do not detect any statistically significant
coefficients when estimating a time series regression of our annual December NINO4 measure of ENSO on a constant,a linear trend, and five lagged terms with optimal bandwidth Newey-West standard errors.
22
Our country-by-year measure of aggregate cereal yield is the harvested area-weighted cereal-level yield across theeight major cereals. See Appendix B for data details.
23
In our empirical applications, we use spatial weights ωij = 1/(dij + 1), where dij is the great-circle distance
between the two countries’ area-weighted centroids.

13

Figure 5: Lead and lag local temperature correlation with December ENSO

Notes: Each panel shows pixel-level (0.5◦ latitude by 0.5◦ longitude resolution) correlation between the ENSO
index in December and pixel-level monthly temperatures for 11 months before (lead) and 12 months after (lag)December. Blue shows areas with negative correlation. Red shows areas with positive correlation.

14

Figure 6: ENSO’s effects on cereal yields

Notes: This map shows the linear coefficient on the sum of contemporaneous and lagged ENSO for each country’s
log cereal yield. Each country-specific time-series model includes a constant and a linear time trend.

spatial correlation. ENSO, in this simple bivariate model, explains 12% of annual variation in thespatial correlation of cereal productivities.
Figure 7: Moran’s I for log cereal yields and ENSO

.18

Moran's I of log cereal yield
.2
.22

.24

coef=0.005, se=0.002, R2=0.12

-2.5

-2

-1.5
-1
-.5
0
.5
1
1.5
Sum of contemp. and lagged December ENSO index

22.5

Notes: Figure shows the relationship between Moran’s I of crop-weighted country-level log cereal yields in year t
and the sum of contemporaneous and lagged December ENSO. The solid line depicts the line of best fit and thedashed series is a local polynomial.

To relax the timing simplification used in Figure 7, Table 1 presents regressions of the annual
Moran’s I statistic for log cereal yields on flexible polynomial functions of December ENSO in
15

years t and t − 1. Each model includes a linear time trend and reports standard errors robust
to serial correlation and heteroskedasticity. In column 1, we include only linear contemporaneousand lagged ENSO terms. Column 2 adds quadratic contemporaneous and lagged ENSO terms
and a linear interaction term. Column 3 estimates the linear and quadratic effects for the sumof contemporaneous and lagged ENSO. This more parsimonious specification effectively imposes acommon coefficient for EN SOt and EN SOt−1 and a common coefficient for EN SOt × EN SOt−1 ,2 . Looking across the columns of Table 1, two results are evident. First,
EN SOt2 , and EN SOt−1

both contemporaneous and lagged ENSO affect the spatial correlation of cereal productivity but
only after controlling for higher-order terms, as shown in column 2. Second, the model in column 3
produces a stronger fit than that in column 2, as summarized by a lower Bayesian Information
Criterion (BIC) value. To strike a balance between non-linear flexibility and avoiding overfitting,
we use the functional form in column 3 to model the relationship between ENSO and the global
spatial correlation of cereal productivity throughout Section 4.
It is natural to wonder whether one could simply drive global spatial correlation of cereal
productivity using the global spatial correlation of temperatures rather than ENSO. That measure
would capture temperature variation caused by both ENSO and other climatic factors. Column 4shows that, while the annual Moran’s I statistic for temperatures is correlated with the annual
Moran’s I for cereal productivities, it has lower predictive power than ENSO, as reflected by ahigher BIC statistic. This may be because cereal yields depend on other environmental conditions
besides temperature, such as precipitation and humidity, many of which also become more spatiallycorrelated under a positive ENSO event. These other environmental channels are captured by ENSO
in columns 1–3 and not by the global spatial correlation of only temperature in column 4. For thisreason, our benchmark regression in the following section uses ENSO directly. Consistent withcolumn 4 of Table 1, we show that the regression coefficients are less precisely estimated when we
use the spatial correlation of temperatures in place of ENSO.
Finally, consistent with our thought experiment in Section 2.1, ENSO affects neither the global
mean nor the variance of cereal productivity, as shown in Figure 8. We have also assumed thatthe trade elasticity is unaffected by changes in the spatial correlation of productivities. Consistent
with this assumption, column 2 of Table C.1 shows that the estimated coefficient on distance in a
gravity model of bilateral trade flows is invariant to ENSO. We also present a more direct test ofwhether ENSO affects comparative advantage within cereals in Section 4.3.

16

Table 1: Moran’s I in cereal productivity and ENSO
Outcome is Moran-I in log cereal yields
(1)
(2)
(3)
EN SOt0.008(0.002)[0.000]0.003(0.002)[0.121]

EN SOt−1

EN SOt x EN SOt−1

EN SOt2
2
EN SOt−1

(4)

0.008
(0.002)[0.000]0.005(0.002)[0.008]0.004(0.003)[0.148]-0.001(0.002)[0.639]0.004(0.003)[0.197](EN SOt + EN SOt−1 )0.006(0.001)[0.000]0.002(0.001)[0.070](EN SOt + EN SOt−1 )2

It (Tit )0.541(0.163)[0.001]

BIC
Observations-275.8453-267.2153-276.6353-272.95
53

Notes: Time-series regressions of Moran’s I in log cereal yields
on nonlinear functions of contemporaneous and lagged December
ENSO. All models include a linear time trend. Serial correlation andheteroskedasticity-robust standard errors with optimal bandwidth inparentheses (Newey and West, 1987); p-values in brackets.

Figure 8: Global cross-sectional mean and variance in cereal productivity and ENSO
coef=0.003, se=0.013, R2=0.001.3.2

Global annual mean of log cereal yields
.4
.6
.8

Global annual variance of log cereal yields
.4
.5
.6
.7

1

coef=0.007, se=0.020, R2=0.002

-2.5

-2

-1.5
-1
-.5
0
.5
1
1.5
Sum of contemp and lagged December ENSO index

2

2.5

-2.5

-2

-1.5
-1
-.5
0
.5
1
1.5
Sum of contemp and lagged December ENSO index

22.5

Notes: The left (right) panel shows the relationship between the mean (variance) of cross-sectional country
log cereal yields and the sum of contemporaneous and lagged December ENSO. Linear fit shown as solid line.
Local polynomial fit shown as dashed line.

17

4

Empirical results

The theoretical results in Section 2 suggest that the covariance between agricultural productivity, ln Ai , and the domestic share of expenditure, ln λii , should be lower when productivities are
more spatially correlated. This section examines this relationship using exogenous temperatureand ENSO-driven changes in productivities and their global spatial correlation. We describe ourestimation strategy in Section 4.1, present the main empirical results in Section 4.2, examine aseries of robustness checks in Section 4.3, and corroborate our results using terms-of-trade changes
in Section 4.4. Appendix B details our data sources.

4.1

Estimation strategy

To estimate equation (3), we employ an instrumental-variables (IV) strategy that exploits plausibly
exogenous variation in local yields and the global spatial correlation of yields. To drive local
yields, we use country-level crop-area-weighted annual temperature, Tit , constructed using datafrom Willmott and Matsuura (2001) (see Appendix B). As described in Section 3, global spatial
correlation of yields is driven by contemporaneous and lagged ENSO.
Equation (3), our second-stage equation, has two endogenous variables, ln Ait and It ln Ait . We
instrument for them using the following first-stage equations:′′ln Ait = α11f (Tit ) + α12f (Tit )g(EN SOt + EN SOt−1 ) + Γ′1 Zit + υ1it

(4)

′
′
It ln Ait = α21
f (Tit ) + α22
f (Tit )g(EN SOt + EN SOt−1 ) + Γ′2 Zit + υ2it

(5)

where the vector of semi-parametric controls, Zit , includes the same variables as equation (3).
′ , α′ , α′ , and α′ are vectors of first-stage coefficients. f () captures the relationship between
α11
12
21
22

local temperature and yield; nonlinearity in f () is well documented (Schlenker and Roberts, 2009;
Schlenker and Lobell, 2010; Welch et al., 2010; Moore and Lobell, 2015; Proctor et al., 2018). In
particular, we model f () as a restricted cubic spline of local temperature; the choice of the numberof splines is detailed below. g() captures the relationship between ENSO and the global spatial
correlation of yields. Following the model-selection results in Table 1, g() is a quadratic functionof (EN SOt + EN SOt−1 ). υ1it and υ2it are error terms.
Nonlinear functional forms for f () and g() are necessary to capture nonlinearities in our firststage equations, but this means that we have more than two instruments for the two endogenous
variables. Two-stage least squares (2SLS) estimation in such over-identified IV settings can exacerbate issues with biased point estimates and incorrectly sized inference. These issues worsen if themany instruments are also weak (Bound, Jaeger and Baker, 1995).24
We address this concern using several weak-instrument diagnostics. First, we employ the limited
24

Indeed, the use of local temperature in first-stage equations (4) and (5) is intended to ameliorate the overidentification problem. One could alternatively predict ln Ait and It ln Ait using flexible functions of country-specific
ENSO effects. However, that approach would involve many more instruments as our sample has over 130 countries.
Our benchmark specification for equations (4) and (5) employs 12 instruments.

18

information maximum likelihood (LIML) IV estimator, which is approximately median-unbiased forover-identified models (Mariano, 2001). Second, we conduct tests to detect weak instruments in our
LIML estimator. Third, we conduct inference that is robust to the presence of weak instruments.

4.2

Main results

To begin, consider OLS estimates of β0 and β1 from equation (3), reported in column 1 of Table 2.
The OLS estimate of β0 has the expected sign and is statistically distinct from zero, but the OLS
estimate of β1 is indistinct from zero and, in fact, positive.
Columns 2 through 6 of Table 2 report IV estimates that address the potential bias of the OLS
estimates. Across columns, we vary the number of spline terms in the temperature function f ().
Column 2 has two spline terms, the minimum needed to capture nonlinearity in f (). Each subsequent column adds another spline term in f ().25 Because all models include a quadratic functionof the sum of contemporaneous and lagged ENSO, this corresponds to 6, 9, 12, 15, and 18 instruments used jointly across the first-stage equations (4) and (5).26 Panel A shows 2SLS estimates,
while panel B shows LIML estimates. Because ENSO varies only in the time dimension, we cluster
standard errors by year to allow arbitrary forms of spatial correlation and heteroskedasticity acrosscountries within a given year. In robustness checks, we consider other error structures, including
the Bekker (1994) adjustment that accounts for LIML standard errors being potentially too small
in the presence of many weak instruments.
The OLS estimate of β0 appears to be biased downward relative to the IV estimates, suggestingthat ln Ait and µit are negatively correlated. One potential source of such OLS bias would bedemand shocks for domestic output, as a positive shock would raise the value of the dependent
variable and lower the average-productivity regressor if domestic production exhibited decreasing
returns. Similarly, an exogenous increase in trade costs could increase the value of the dependent
variable and decrease cereal yields if production employs imported inputs.
The 2SLS estimates reported in panel A of Table 2 show βb0 > 0 and βb1 < 0, with little
variation in the point estimates across columns 2 to 6. The 2SLS estimates of both parameters
are also statistically different from the OLS estimates, suggesting that the 2SLS estimates do notexhibit the same bias as the OLS estimates and thus are not the result of completely uninformative
instruments. However, in over-identified IV settings, 2SLS estimates are still biased and incorrectly
sized. This is evident in that the Cragg and Donald (1993) joint F-statistic for both first-stage
regressions is well below the Stock and Yogo (2005) critical values for 10% maximal 2SLS bias and25

Two to six spline terms correspond to three to seven knots. Knots are placed between equally spaced percentilesof the temperature empirical distribution according to Harrell (2001).
26
′
′
′
′
Columns 1–5 of Table F.1 show first-stage statistics for α11
and α12from equation (4) and α21
and α22fromequation (5), corresponding to the IV specifications shown in columns 2–6 of Table 2. They show p-values from F-tests
examining the joint significance of elements in each vector of first-stage coefficients. As expected, uninteracted local
temperature is consistently a strong predictor of local cereal yields in first-stage equation (4). For the interaction
between local yields and the global spatial correlation of yields in first-stage equation (5), both uninteracted local
temperature (i.e., 0th order ENSO) and local temperature interacted with ENSO (i.e., 1st and 2nd order ENSO) arestrong predictors.

19

Table 2: Domestic shares of expenditure and the spatial correlation of productivities
Outcome is log domestic share of expenditure
(1)
(2)
(3)
OLS
IV
IV

(4)
IV

(5)
IV

(6)
IV

Panel A: 2SLS estimatesln Ait (β0 )ln Ait × It (β1 )Pct. change in welfare variancefrom 1 s.d. increase in It

0.284(0.119)[0.021]0.758(0.487)[0.126]1.541(0.515)[0.004]-3.321(2.071)[0.115]1.746(0.542)[0.002]-3.440(2.148)[0.115]1.696(0.412)[0.000]-3.391(1.476)[0.026]1.701(0.425)[0.000]-3.350(1.493)[0.029]1.654(0.431)[0.000]-3.290(1.555)[0.039]-0.353(0.226)[0.119]1.536(0.976)[0.116]1.591(1.023)[0.120]1.568(0.716)[0.029]1.549(0.728)[0.033]1.521(0.754)[0.044]

Panel B: LIML estimatesln Ait (β0 )ln Ait × It (β1 )Pct. change in welfare variancefrom 1 s.d. increase in It

2.110(0.837)[0.015]-4.530(2.752)[0.106]2.380(0.847)[0.007]-4.907(2.937)[0.101]2.114(0.604)[0.001]-4.144(1.834)[0.028]2.196(0.669)[0.002]-4.218(1.949)[0.035]2.308(0.771)[0.004]-4.463(2.194)[0.047]2.091(1.407)[0.137]2.264(1.497)[0.131]1.914(0.954)[0.045]1.948(1.035)[0.060]2.060(1.191)[0.084]

Number of temperature splines in f ()
2
3
4
5
6
ENSO polynomial order in g()
2
2
2
2
2
Number of instruments
6
9
12
15
18
Cragg-Donald F-stat
7.052
5.832
5.174
4.324
3.801
Stock-Yogo crit. value: 10% max 2SLS bias
9.480
10.43010.78010.93011.000Stock-Yogo crit. value: 10% max 2SLS size
21.68027.51032.88038.08043.220Stock-Yogo crit. value: 10% max LIML size
4.060
3.700
3.580
3.540
3.560
Kleibergen-Paap F-stat
6.100
5.664
3.963
3.332
3.069
Anderson-Rubin weak-id robust joint p-value
0.000
0.000
0.000
0.000
0.000
BIC for first stage equations-30933.7 -30917.4 -31134.0 -31120.2 -31091.8
Observations
5452
5452
5452
5452
5452
5452
Notes: This table reports estimates of β0 and β1 from equation (3). Column 1 shows OLS estimates. Columns
2–6 show IV estimates that vary by the number of temperature spline terms in f (). Panel A (B) shows 2SLS
(LIML) IV estimates. All models include quadratic EN SOt + EN SOt−1 terms and incorporate country fixed
effects, year fixed effects, and country-specific linear trends as included instruments. Standard errors, clusteredby year, in parentheses; p-values in brackets. Appendix D.1 describes how we compute the percentage change inthe variance of welfare for a one-standard-deviation increase in Moran’s I relative to the historical mean assuming
ϵ = 8.59, with those standard errors calculated using the delta method.

size across columns 2 to 6 of Panel A.
As an alternative to 2SLS, panel B of Table 2 presents LIML estimates. Again, we find very
similar point estimates for βb0 > 0 and βb1 < 0 across the varying number of temperature splines incolumns 2 to 6. The LIML estimates are even farther away from the OLS estimates than the 2SLS
estimates, suggesting that the LIML estimator mitigates biases in our 2SLS estimates.
LIML is an approximately median-unbiased estimator in over-identified settings, but its stan-20

dard errors may still be incorrectly sized in the presence of weak instruments. We report two tests
to assess whether weak instruments are a concern. First, across columns 2 to 6, the Cragg-Donald
joint F-statistic for both first-stage regressions is above the Stock-Yogo critical values for 10% maximal LIML size, which rejects the presence of weak instruments. However, the Stock-Yogo criticalvalues are only valid for iid errors. While we also report the Kleibergen-Paap F-statistic, which
is more appropriate given our clustered error structure (Kleibergen and Paap, 2006), there are no
established critical values for non-iid errors. We therefore cannot entirely rule out the presence of
weak instruments solely by looking at first-stage F-statistics. Second, we turn to inference methods
that are robust to the presence of weak instruments. For each IV model in columns 2 to 6, we
present the p-value from the Anderson-Rubin test of the null hypothesis that β0 and β1 in equation (3) are jointly zero (Anderson and Rubin, 1949). This null hypothesis is strongly rejected.
The combined evidence from these various diagnostics suggests that weak instruments are not aconcern. This gives us confidence that our LIML estimates are unbiased and correctly sized.
Which number of spline terms in the temperature function f () yields the most informative estimates of our parameters of interest? Note that this model selection is not crucial to our conclusions:
across columns 2 through 6, the point estimates of β0 and β1 do not vary much. All the estimates ofβ0 have p-values near or below 0.01, and the LIML estimates of β1 have p-values ranging from 0.03
to 0.11. To select one specification, we employ the Bayesian Information Criterion (BIC) statistic from a joint seemingly unrelated regression of first-stage equations (4) and (5) to address thetrade-off between capturing nonlinearities in f () and having too many spline terms in f (). Table 2
shows that the BIC statistic is minimized with four temperature spline terms in column 4. This
corresponds to the specification with the most precise LIML estimates of β0 and β1 , with p-valuesof 0.001 and 0.03, respectively, and will serve as our benchmark model moving forward.
Per the theoretical framework in Section 2, our empirical estimates suggest that the spatial
distribution of productivity affects a country’s terms of trade, as revealed by its domestic shareof expenditure. The positive relationship between its own productivity and domestic share of
expenditure (β̂0 > 0) reveals that higher productivity worsens the terms of trade. This deteriorationis dampened when productivities are more spatially correlated (β̂1 < 0) since higher productivity
in neighboring countries improves a country’s terms of trade.27 We corroborate this terms-of-tradeinterpretation using observed changes in unit values in Section 4.4.
For the class of models introduced in Section 2, these estimated effects imply an increase in the
global variance of welfare. Suppose that the cross-sectional global spatial correlation of agricultural
productivity were to increase by one standard deviation relative to the historical mean. Applying
the expression for the variance of welfare in equation (2) to our benchmark LIML estimates in column 4, panel B of Table 2, we find that a one-standard-deviation increase in the spatial correlationof productivities leads to a statistically significant 2% increase in the global variance of welfare.28
27

At empirically observed levels of spatial correlation, this does not reverse the positive relationship between ln Ait
and ln λiit . As shown in Figure 7, the spatial correlation of cereal yields lies between 0.17 and 0.25 in our estimation
sample. Thus, β̂0 + β̂1 × It > 0 at all historical values of It for the estimates reported in Table 2.
28
See Appendix D.1 for details. As a point of comparison, Kopczuk, Saez and Song (2010) find that the annual

21

4.3

Additional robustness checks

This section presents several robustness checks of our main empirical result. They are designed
to test the validity of our statistical assumptions, the interpretation of our results, and the consequences of our data-construction choices. Our benchmark model throughout is that shown incolumn 4, panel B of Table 2.
Randomization inference

Our main source of identifying variation is time-series fluctuationsin the global ENSO cycle, shown in Figure 4. While it is plausible that ENSO is uncorrelated withunobserved determinants of domestic shares of expenditure over a large sample of years, spurious
correlations could occur within a 53-year sample.
To examine the relevance of this small-sample concern, we conduct a placebo test by randomly
reshuffling years (i.e., drawn without replacement) of our panel data, breaking the time-series link
between domestic shares of expenditure and ENSO-driven changes in country-level cereal yields
and the global spatial correlation of yields. This allows us to obtain an empirical distributionof our estimated reduced-form coefficients, βb0 and βb1 , under placebo conditions and compute theprobability of observing our benchmark estimates if years were randomly assigned.
The left and right panels of Figure 9 show the empirical distribution for βb0 and βb1 , respectively,
for 10,000 samples. The vertical lines show the location of our estimated βb0 and βb1 from theobserved data. It is highly unlikely that our main result is due to small-sample bias.

.06
.04
0

.02

Randomization distribution

.06
.04
.02
0

Randomization distribution

.08

.08

Figure 9: Randomization inference

-1

0

1

2

-4

β0

-2

0

2

4

β1

Notes: Empirical distributions of βb0 (left panel) and βb1 (right panel) from 10,000 samples of 53 years drawn fromthe original data without replacement. Vertical lines show βb0 and βb1 from observed data estimated using benchmark
model in column 4, panel B of Table 2.

Standard errors

Standard errors are clustered by year in our benchmark model because ENSO

varies in the time dimension. Table F.2 considers alternative error structures. Column 1 reproduces
our benchmark results. To account for serial correlation, column 2 allows year-level clustering andvariance of log earnings across U.S. workers increased on average by 2% per year between 1970–2003.

22

common serial correlation across countries within a 20-year rolling window following Driscoll andKraay (1998). Column 3 allows differential serial correlation and heteroskedasticity across countries
over our entire sample period by clustering standard errors by both year and country. Allowing
both forms of serial correlation has little effect on standard errors. Finally, if instruments are weak,standard errors from the LIML estimator may be too small (Hansen, Hausman and Newey, 2008).
Column 4 applies the Bekker (1994) adjustment to our benchmark LIML estimates. This only
slightly inflates our standard errors, which is unsurprising given that the various tests in Table 2
do not suggest the instrumental variables are weak.
Controlling for time-varying trade costs

Our IV model correctly identifies β0 and β1 when

ENSO conditions influence a country’s domestic share of cereal expenditure only through its effects
on local yields and the global spatial correlation of yields.29 While it is unlikely that ENSO, as anaturally occurring climatic phenomenon, is affected by economic activity, the exclusion restriction
could be violated if ENSO affects domestic cereal expenditure outside of its influence on cereal
yields. For example, a violation would occur if ENSO directly affected trade costs.
To address this potential violation of the exclusion restriction, Table F.3 augments our benchmark model with additional controls designed to capture time-and-country-varying trade costs.
Column 1 replicates our benchmark result. In column 2, we add a proxy for country-year-specifictrade costs by interacting the global annual crude oil price with the country’s average log domestic
share of expenditure over our sample period. Column 3 uses an alternative measure of crosssectional trade openness by interacting the global oil price with a country’s centrality, measured as
the average of its inverse distance to every other country weighted by that trading partner’s longrun average log agricultural output. In both cases, these proxies for time-varying trade costs do notmeaningfully alter our estimates of β0 and β1 . Columns 4 and 5 provide more flexible specifications
by interacting year fixed effects with the two cross-sectional measures of trade openness used incolumns 2 and 3. Again, our coefficients of interest are relatively unaffected by the inclusion ofthese controls, suggesting that unobserved shocks to trade costs are not correlated with our ENSOdriven instruments. Cereals may be subject to export restrictions that are imposed in response to
productivity shocks. In column 6, we include a dummy variable that indicates if a country imposeda new export restriction on cereals that year, using data from the UNCTAD TRAINS database.
Controlling for such export restrictions does not alter our result. ENSO also alters local precipitation. If precipitation is also a determinant of trade costs, there may be an exclusion restriction
29

For example, Hsiang, Meng and Cane (2011) show that warmer ENSO conditions increase the likelihood of civil
conflicts in the tropics over the same period. This relationship, however, need not imply an exclusion-restriction
violation. Suppose ENSO increases civil conflicts in the tropics only through lowered cereal yields. In that scenario,
civil conflict would serve as a “bad control” in our IV specification, potentially biasing our coefficients of interest(see Angrist and Pischke 2009, p. 64-68). Our exclusion-restriction assumption is invalid only if ENSO increases
civil conflicts partially through non-agricultural channels and if civil conflicts affect domestic share of expenditureby, for example, raising international trade costs relative to internal trade costs. Because the current climate-conflict
literature currently supports both agricultural and non-agricultural channels (Hsiang, Burke and Miguel, 2013),
the inclusion of conflict as a control would not deliver a unique interpretation: it would either jeopardize a valid
identification strategy or suggest that our instrumental-variables strategy is invalid.

23

violation. In column 7, we include quadratic terms for total annual precipitation for each country
and find that it does not affect our result.
Large economies

Our estimate of β̂0 > 0 implies that a positive productivity shock worsens

an economy’s terms of trade. This is at odds with the small-open-economy assumption that theterms of trade are exogenous to local conditions.30 Of course, some economies must influence world
prices, but since our estimating equation treats each country as an informative observation without
weighting by size, our results suggest that the “typical” economy is not small. To examine thismore explicitly, column 2 of Table F.4 excludes the ten largest economies that account for morethan half of world cereal production from our estimation sample. The resulting estimates of β̂0 andβ̂1 are very similar to our benchmark estimates. This finding is consistent with the idea that trade
costs make all markets “local”, so that no exporter is a price taker.
Dynamic effects Table F.5 estimates dynamic responses that the static model presented in
Section 2 necessarily omits. Column 1 replicates our benchmark contemporaneous-productivity
specification for a sample in which t is restricted to 1962–2012, the sample period that allows forboth lead and lagged yields. Before discussing these results, it is important to note that because
current productivity is affected by EN SOt and EN SOt−1 , we would not expect lead productivity,
driven in part by EN SOt , or lagged productivity, driven in part by EN SOt−1 , to have zero effecton current domestic share of expenditure. Rather, the absence of dynamics would produce leadand lagged effects that are muted compared with the contemporaneous effect.
Improvements since the 1980s in the forecasting of strong ENSO events (Chen et al., 2004;
Shrader, 2017) could allow the domestic share of expenditure to respond to future ENSO-driven
cereal yields. To examine whether agricultural trade anticipates future ENSO events, column 2
tests for the effects of lead log yields, as instrumented by ENSO in years t + 1 and t and local
temperature in year t + 1. Lead effects are much smaller in magnitude than contemporaneous
effects and are not statistically significant.
Past yields might influence the domestic share of expenditure if past productivity affects contemporary productivity through intertemporal channels such as depletion of soil nutrients or if
past output is stored to facilitate current consumption. Cereal storage, in particular, has beenshown to facilitate consumption smoothing in many settings (Williams and Wright, 2005; Roberts
and Schlenker, 2013). We address this in two ways. Column 3 examines the effects of lagged log
yields generally, as instrumented by ENSO in years t − 1 and t − 2 and local temperature in yeart − 1. Compared with contemporaneous effects, lagged effects are smaller in magnitude and not
significant at conventional levels. Our measure of domestic expenditure is contemporaneous output
minus exports; this includes potential changes in stored cereal inventories. In column 4, we use a30

Prior empirical work, which “typically assumes that countries are small and that the terms of trade are exogenous”(Debaere and Lee, 2003, 1), has primarily focused on the consequences of external shocks to countries’ commodity
terms of trade. Notable exceptions are Acemoglu and Ventura (2002) and Debaere and Lee (2003), which study theeffects of capital accumulation on the terms of trade.

24

measure of domestic expenditure that removes changes in cereal inventory using cereal storage datafrom the FAO.31 The estimated coefficients are smaller in absolute magnitude than our benchmark
estimates; however, they are not statistically different.
The static model of Section 2 assumes that trade is balanced. To verify the plausibility ofthis assumption, we have estimated a variant of the regression specification in equation (3) inwhich the dependent variable is instead country i’s aggregate goods trade deficit in year t. Neither
instrumented cereal productivity nor its interaction with Moran’s I for cereal productivities havestatistically significant effects on the trade deficit.
Sample split

One may wonder if β0 and β1 vary over the sample, particularly given improvements

in ENSO forecasts since the 1980s. Table F.4 reports separate estimates for the two halves of ourestimation sample, 1961–1987 and 1988–2013. While the estimated coefficients for the second half
are smaller in absolute magnitude than those for the first half, these differences are not statisticallysignificant.
ENSO and local temperature definitions Table F.6 considers alternative definitions of ENSO
and country-level local temperatures. Column 1, panel A reproduces our benchmark results using
the NINO4 measure as our ENSO index and crop-area-weighted country-level temperatures. In
columns 2, 3 and 4, we use the NINO3, NINO34, and NINO12 indices, alternative measures of
ENSO that differ by the spatial area over which average sea-surface temperature is calculated (seeFigure E.2). In panel B, we construct country-level temperatures from pixel-level temperature databy taking the average across the total area of each country rather than across crop areas.32 Our
results are largely unaffected by these two data-construction choices.
Our identification strategy need not require ENSO per se. Rather, one needs an exogenous
driver of the global spatial correlation of cereal yields that exhibits a sufficiently strong first stage.
In Table F.7, we report estimates produced by replacing g(EN SOt +EN SOt−1 ) in equations (4) and(5) with the annual global spatial correlation of temperature, It (Tit ).33 While the point estimatesin Table F.7 do not differ drastically from the corresponding estimates in panel B of Table 2, thefirst-stage regressions are generally weaker. This is consistent with Table 1, which shows that It (Tit )does not predict the global spatial correlation of cereal yields as strongly as ENSO. In short, basedon the strength of the first-stage relationship, we prefer to use ENSO as the source of exogenous
31

This measure is contemporaneous output minus exports minus change in cereal inventory, where the latter isdefined as the difference in stored cereals in year t minus stored cereals in year t − 1. This implicitly assumes thatall stored cereals are domestically produced. The sample is smaller due to observations with missing storage data.
32
Our sample of countries increases slightly when using total-area-weighted temperature compared with using croparea-weighted temperature because a handful of small-sized countries have no agricultural activity in the Ramankutty
et al. (2008) dataset.
33
When considering temperature-driven only variation, instead of using It (Tit ) in equations (4) and (5), one could
alternatively use the vector of country-specific local temperature-predicted productivity to construct a predicted\
Moran’s I statistic. Such an approach, however, implicitly assumes that It ({lnAit (Tit )}) is the correct functional
relationship between local temperature and the global spatial correlation in yields. Our approach, which follows
Kelejian (1971) and Amemiya (1974), allows for more flexible estimation and in general produces a more efficient IV
estimator.

25

variation in the global spatial correlation of cereal yields rather than the spatial correlation of anintermediate local weather variable.
Domestic expenditure share construction As detailed in Appendix B, we do not observe
cereal prices for all cereal-country-year observations with positive cereal output. Our benchmark
measure of domestic share of expenditure imputes missing cereal-level prices using the averageexport-volume-weighted cereal export unit value for that country and year. While this imputation
increases the number of observations in our estimation sample, this procedure could bias our estimates if it introduces measurement error into the outcome variable that is correlated with the
instrumented regressors.
Table F.8 presents alternative approximations for the domestic expenditure share. Column 1
reproduces our benchmark result. Columns 2 through 4 employ alternative price imputations.
Column 2 imputes missing export unit values using producer prices.34 Columns 3 and 4 impute
missing cereal prices using the lowest and highest observed export unit values, rather than the
average, for a given country and year. All three alternative imputation methods yield estimates ofβ0 and β1 that are statistically indistinguishable from the benchmark estimate in column 1. To see
if our benchmark result is sensitive to the source of trade data, in column 5 we compute domestic
expenditure shares using trade data from Comtrade instead of FAO. Finally, in column 6 we drop
observations where our benchmark measure of log domestic expenditure share is in the bottom andtop 1% of its unconditional distribution. Neither robustness check alters our conclusions.
Comparative advantage within the cereals sector

In principle, ENSO might affect not only

the spatial correlation of absolute advantage but also the spatial correlation of comparative advantage within the cereals sector. In the Eaton and Kortum (2002) model, comparative advantage
is governed by the trade-elasticity parameter. The gravity regression reported in column 2 of Table C.1 shows that ENSO does not alter the distance elasticity, consistent with an unaltered tradeelasticity. As a more direct test, we estimate our benchmark first-stage equations (4) and (5) for
cereal-specific yields and test whether these cereal-specific coefficients differ from the corresponding aggregate cereals coefficients. Table F.9 reports p-values for these tests for each of the eight
cereals. The large p-values on all ENSO coefficients suggest that ENSO does not alter patterns ofcomparative advantage within the cereals sector.

4.4

Estimates using terms-of-trade outcomes

Thus far, the outcome variable in our empirical investigation has been the domestic share of expenditure, a sufficient statistic for welfare under the modeling assumptions described in Section 2.1.
That theoretical result leverages assumptions that restrict admissible combinations of consumer
preferences, production technologies, and market structure. While widely used, this class of models
may be regarded as narrow.
34

See discussion in Appendix B regarding concerns with using FAO’s producer prices.

26

We now investigate how the spatial correlation of productivities affects the gain from trade using
an outcome variable that captures welfare changes under much weaker assumptions. We examinechanges in the terms of trade as measured by the product of price changes and the previous period’s
traded quantities. Appendix B describes how we construct this variable using trade data. Thismeasure identifies whether a country’s terms of trade locally improve or deteriorate under the
relatively weak assumptions required for the revealed-preference argument of Dixit and Norman(1980).
Since this outcome variable is defined in terms of changes from the previous year, we timedifference our estimating equations so that we relate changes in the terms of trade to changes in log
productivity and changes in the product of spatial correlation and log productivity. In particular,
we employ first-differenced versions of the second-stage and first-stage equations (3, 4, 5). The
second-stage equation is now
arcsinh(∆ToTit ) = ς0 (ln Ait − ln Ait−1 ) + ς1 (It ln Ait − It−1 ln Ait−1 ) + ζi + ξt + εit ,(6)

where ζi and ξt are country and year fixed effects that correspond to the country-specific trends
and differences in year fixed effects in the levels second-stage equation (3), respectively.35 εit is anerror term that we cluster by year. To facilitate interpretation of ς0 and ς1 as elasticities (as with β0
and β1 ), we use an inverse hyperbolic sine transformation of ∆ToTit on the left side of equation (6)(Bellemare and Wichman, 2020).36 The terms-of-trade interpretation of our main empirical results
predicts that ς0 < 0 and ς1 > 0. The two first-stage equations are:ln Ait − ln Ait−1 = ϱ′11 (f (Tit ) − f (Tit−1 ))+ ϱ′12 (f (Tit )g(EN SOt + EN SOt−1 ) − f (Tit−1 )g(EN SOt−1 + EN SOt−2 ))+ ζ1i + ξ1t + φ1it

(7)

It ln Ait − It−1 ln Ait−1 = ϱ′21 (f (Tit ) − f (Tit−t ))+ ϱ′22 (f (Tit )g(EN SOt + EN SOt−1 ) − f (Tit−1 )g(EN SOt−1 + EN SOt−2 ))+ ζ2i + ξ2t + φ2it(8)

where φ1it and φ2it are error terms. Consistent with the benchmark expenditure share specificationin column 4, panel B of Table 2, f (·) is a restricted cubic spline function with four terms and g(·)
is a quadratic function.
Table 3 reports LIML IV estimates of equation (6). Column 1 examines changes in the terms oftrade for cereals. An increase in productivity worsens a country’s terms of trade (ˆς0 < 0), but thiseffect is dampened when productivities are more spatially correlated (ˆς1 > 0). This corroborates
the interpretation of our expenditure-share results as reflecting terms-of-trade effects. To broaden
the economic scope, Column 2 examines changes in the terms of trade for all commodities in the
35
36

The country fixed effects of equation (3) are eliminated by taking the difference.
Since changes in the terms of trade can be positive or negative, a log transformation is infeasible.

27

Table 3: Changes in terms of trade
Outcome is asinh(change in terms of trade)(1)
Cereals∆ ln Ait (ς0 )∆ ln Ait × It (ς1 )Cragg-Donald F-stat
Stock-Yogo crit. value: 10% max LIML size
Kleibergen-Paap F-stat
Observations

(2)
Food

-1.886(1.015)[0.069]8.756(5.058)[0.089]-1.354(1.273)[0.292]
6.625(6.643)[0.323]10.054
3.580
3.347
5747

10.054
3.580
3.347
5747

Notes: This table reports estimates of equation (6). Column 1 examineschange in the terms of trade for cereals. Column 2 examines change in theterms of trade for all commodities in Standard International Trade Classification (SITC) section 0 (food and live animals). Standard errors are reported
in parentheses; p-values in brackets.

commodity section “food and live animals,” which includes cereals. Consistent with the discussionof multi-sector models in Appendix Section A.3, these welfare effects are somewhat dampened
when we incorporate a broader set of goods. The standard errors in column 2 are also larger
than in column 1, perhaps unsurprisingly given that the dependent variable uses a broader set ofunit values, which are noisy proxies for prices, and cereal imports are only 25% of food imports
for the average observation.

The dampened coefficients and larger standard errors render theseestimates statistically insignificant at conventional thresholds. We therefore find that countries’
terms of trade in cereals respond in the predicted manner to greater spatial correlation of cereal
productivities, but we lack the statistical power to trace these effects through to economy-widechanges in the terms of trade.37

5

Application: Inequality under future climate change

In this section, we demonstrate how to incorporate the role of spatial interdependence via trade into
projections of economic outcomes when the spatial correlation of productivities changes. Recent
reviews of quasi-experimental studies that inform climate-change impact projections emphasize
the need to consider spatial linkages (Dell, Jones and Olken, 2014; Hsiang, 2016; Auffhammer,
2018; Deschênes and Meng, 2018). In this growing literature, the effect of local temperature onan economic outcome is first estimated using quasi-experimental variation that implicitly holds
37

Estimates of the coefficients ς0 and ς1 for other 1-digit commodity sections are not statistically significant andoften have the opposite sign of those found for the “food and live animals” section.

28

temperatures in other locations fixed. These estimates are then used to compute the local consequences of anticipated future warming and the sum of these projected local impacts is used toquantify climate change’s global impact. However, by using estimates that hold fixed the spatial
structure of temperature, these projections amount to considering many scenarios in which eachscenario has only a single location experiencing warming. This exercise misses the global nature ofclimate change, in which all locations experience warming simultaneously.
To that end, we amend this approach to incorporate changes in the spatial correlation of productivities due to climate change.38 By allowing the expenditure-productivity relationship to dependon spatial correlation, this approach incorporates spatial interdependence without imposing thefull structure of quantitative trade models. This strategy is similar to that of Monte, Redding
and Rossi-Hansberg (2018), who use observables to account for heterogeneous local employment
elasticities implied by a quantitative model of commuting flows. More broadly, we posit that this approach can be applied to studying other determinants of productivity, provided that the researcher
observes exogenous variation in that determinant that also alters its global spatial correlation.
Because this exercise serves only to highlight the implications of incorporating this particularmechanism, we emphasize that it omits other potential general-equilibrium effects of climate change.
First, these projections study changes in cereal productivity due to climate-driven changes in local
temperatures over the twenty-first century in isolation. We fix all other variables, such as the spatial
pattern of comparative advantage within cereals, at recent historical values. Thus, we do not take
into account important trends such as technological change. Second, we apply estimates based on
past exogenous annual changes in cereal productivity to future long-term productivity changes due
to climate change. This implies that we omit possible adaptations in anticipation of future climatechange (Deschênes and Greenstone, 2007c; Hsiang, 2016). Third, we do not consider other potential
adjustments such as factor reallocation across sectors and across crops within the agricultural
sector. All three practices are standard in this climate-impacts literature, due to the absence ofcredible estimates of the relevant mechanism, and these assumptions may ultimately cause theseprojections to differ from realized climate impacts. Our objective is merely to demonstrate how
the economic consequences of spatial correlation, estimated using quasi-experimental variation, canbe incorporated into projections of climate impacts. As such, this exercise helps bridge the gap
between quasi-experimental approaches and structural models of climate impacts (Brock, Engströmand Xepapadeas, 2014; Desmet and Rossi-Hansberg, 2015; Costinot, Donaldson and Smith, 2016;
Krusell and Smith, 2022).
We first report climate change’s projected effects on the global variance and spatial correlationof cereal productivity. We then show how incorporating these changes in the spatial correlation of
productivities alters welfare projections.
38

There is currently no scientific consensus on how ENSO will be affected by anthropogenic climate change (Stocker
et al., 2013). Our projection exercise therefore assumes ENSO is stationary over the twenty-first century and does
not contribute to long-run changes in the global spatial correlation of cereal productivities.

29

5.1

Cereal productivity under climate change

To examine how climate change will affect cereal productivity, we estimate a nonlinear log cereal
yield response function using historical variation in annual temperatures across countries and years.
Specifically, for the period 1961–2013, we estimate:ln Ait = k(Tit ) + Ψ′ Xit + νit(9)where k() is a restricted cubic spline function and the benchmark set of controls in Xit include
country fixed effects, year fixed effects, and country-specific quadratic trends. Figure 10 shows theestimated cubic spline response function, k(), using four temperature spline terms. It also shows
two cross-sectional temperature distributions: observed temperatures in 2013 and the forecast
for 2099 under a business-as-usual (Representative Concentration Pathway 8.5) climate scenario
obtained from the Coupled Model Intercomparison Project (CMIP5) multi-model ensemble mean.39
Column 1 of Table F.10 shows that the coefficients of k() shown in Figure 10 are jointly statisticallysignificant with a productivity-maximizing temperature around 9◦ C.40 Table F.10 also indicatesthat the predicted optimal temperature is relatively insensitive to the number of knots in the spline
function and to the inclusion of precipitation controls. Next, we combine the estimated coefficientsin equation (9) with local temperature projections under a business-as-usual climate scenario toproject log cereal yields in the 2014–2099 period. All other variables in equation (9) are fixed at2013 levels (see Appendix D.2 for details).
Climate change alters two important moments of the cross-country cereal productivity distribution. First, the variance of cereal productivity increases. In 2013, 10 of the 12 countries withtemperatures below the global productivity-maximizing temperature had productivities above thecross-sectional mean (see Figure E.4).41 As climate change raises temperatures, these more productive countries will gain further by moving towards the productivity-maximizing temperature shownin Figure 10. Concurrently nearly all other countries will experience productivity losses as they
move away from the optimal temperature. Because the gains from climate change will be experienced almost exclusively by more productive countries, the cross-country variance of productivity
will rise, as depicted by the black line in the left panel of Figure 11.
Second, as temperatures increase across the planet, the spatial correlation of cereal productivities increases. This is again due to the non-monotone yield response function shown in Figure 10
and the fact that surface temperatures are generally decreasing in distance to the equator. Absent
39
CMIP5 is a coordinated effort by the climate-science community to harmonize model runs across various climate
models. The average climate projection across CMIP5 models is known as the multi-model ensemble mean. CMIP5
was used to inform the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (see Taylor,
Stouffer and Meehl (2012) for details).
40
Using similar country-by-year-level data but for the 1983–2009 period, Proctor et al. (2018) find a similar
productivity-maximizing temperature.
41
Figure E.4 shows that the unconditional relationship between log productivity and temperature is very similar
to the conditional relationship depicted in Figure 10, k(Tit ). Thus, we can describe how climate change alters thevariance and spatial correlation of productivities in terms of the nonlinear shape of k(Tit ), even though productivity
incorporates other determinants contained in controls Ψ′ Xit and residual νit from equation (9).

30Figure 10: Estimated temperature response function for log cereal yields
0Predicted yield for hist. temp.

Temperature-predicted log cereal yields
-1.5
-1
-.5

Predicted yield for future temp.
2013 country temp. distribution

0 .05 .1
Distribution

2099 country temp. distribution

-5

0

5

10
15
20
Temperature (C)

25

30

35

Notes: Gray solid line shows k() in equation (9), the predicted relationship between crop-area-weighted countrylevel temperature and log cereal yields, estimated during 1961–2013. Restricted cubic spline function is estimatedusing four spline terms with knot placements according to Harrell (2001). Gray dashed line shows predicted log cereal
yields using extrapolated temperature in 2099. Estimated model corresponds to column 1 of Table F.10. Orange
line shows distribution of observed country-level temperatures in 2013. Red line shows distribution of projected
country-level temperature in 2099 from CMIP5 ensemble mean under a business-as-usual (RCP 8.5) scenario.

Figure 11: Variance in climate-driven welfare over the 21st century

Notes: The left panel shows the change in the global variance (black line) and Moran’s I (blue line) of log cereal
yields over the twenty-first century under climate change. The right panel shows the percent change in the varianceof welfare omitting (gray line) and including (red line) changes in the spatial correlation of log cereal yields over thesame period. Climate projections are from CMIP5 ensemble mean under a business-as-usual (RCP 8.5) scenario.
Appendix D.2 describes the welfare calculations assuming ϵ = 8.59.

climate change, mid-latitude locations experience the productivity-maximizing temperature. Locations closer to and farther from the equator both generally exhibit lower yields. As climate change
31increases temperatures, latitudes closer to the poles will experience the productivity-maximizing
temperature, and less productive countries will be more bunched around the equator. This bifurcation of global agriculture into high-productivity poles and a low-productivity band around theequator would increase the spatial correlation of cereal productivity.42 The resulting increase in
Moran’s I for cereal productivity under climate change is depicted by the blue series in the left
panel of Figure 11.

5.2

Welfare projections and changes in spatial structure

Greater spatial correlation of cereal productivity due to climate change matters for global welfare
inequality. To demonstrate this, we combine projected local cereal productivity under climatechange with the estimates of βb0 and βb1 from Section 4 to project future domestic shares of expenditure via equation (3) and welfare variance via equation (2) (see Appendix D.2 for details). We
consider two scenarios with different terms-of-trade effects.43 In the first scenario, we fix the spatial
correlation of temperature-predicted cereal productivities to its 2013 value. In the second scenario,
we allow climate change to increase the spatial correlation of productivities as depicted by the blue
series in the left panel of Figure 11.
The projected change in the variance of welfare over the twenty-first century is shown in the rightpanel of Figure 11. The gray line shows the projection that omits changes in spatial correlation andthe red line shows the projection that include such changes. Omitting changes in spatial correlation,
the projected increase in the variance of cereal productivity generates a projected increase in thevariance of welfare. The projection that incorporates increases in the spatial correlation of cereal
productivity due to climate change predicts a 20% greater increase in welfare inequality between
2013–2099 compared to the projection that holds spatial correlation fixed.
How do the projections differ across countries? Figure 12 maps the difference between the two
projections.44 Including an increase in the spatial correlation of productivities causes the gains
from trade to be lower in less productive countries and higher in more productive countries than ina projection that holds spatial correlation fixed. In particular, Figure 12 shows that most countries
in Africa, and a few in Asia and South America have lower gains from trade in the projection thatincorporates changes in spatial correlation. This is because the relatively high local temperaturesthat drive yield losses in these countries are compounded by similar temperatures simultaneously
experienced by neighboring countries. In the simplest terms, a key feature of climate change
is that it makes Ethiopia and Kenya less productive at the same time, lowering the gains from
42

Additionally, the country-specific shift in temperature due to climate change is not spatially uniform. Becauseof surface albedo changes due to polar ice melt, there will be greater warming near the poles. However, this latitudedependent gradient is relatively small compared to the average global temperature change and thus plays a secondorder role in determining changes in the spatial correlation of productivities. For example, the projected temperaturechange over the twenty-first century for Gabon, the country located closest to the equator, is 3.4◦ C. For Finland, thecountry located closest to the north pole, the projected temperature change is 2.9◦ C.
43
In autarky, the variance of welfare would be proportionate to the variance of productivity. Since a productivity
increase is associated with worse terms of trade, an increase in the variance of productivity causes a smaller increasein the variance of welfare when there is international trade.
44
See equation (D.12) at the end of Appendix D.2.

32

Figure 12: Differences in projected welfare changes due to change in spatial correlation (2013–2099)

Notes: Map shows the difference in projected country-level welfare change over 2013–2099 between projections
that include and omit changes in spatial correlation. Climate projections from CMIP5 ensemble mean under abusiness-as-usual (RCP 8.5) scenario. Appendix D.2 describes welfare calculations assuming ϵ = 8.59.

Spatial structure
reduces loss

Spatial structure
amplifies gain

Spatial structure
amplifies loss

Spatial structure
reduces gain-.01

Difference in welfare projection
-.005
0
.005

.01

Figure 13: Differences in welfare projections from projected changes in spatial correlation and yields

-.5

-.4

Africa

Asia

-.3
-.2
-.1
Projected yield change
EuropeN. America

S. America

0.1
Pacific

Notes: Scatter shows the difference in projected country-level welfare change between projections that include
and omit changes in spatial correlation (from Figure 12) plotted against change in log cereal yields over 2013–
2099 under climate change. Countries are color-coded by continent. See Figure E.5 for the same plot withcountry identifiers. Appendix D.2 describes welfare calculations assuming ϵ = 8.59.

33

trade compared to a scenario in which each country warms independently. By the same logic,
parts of Europe and North American have higher gains from trade when the projection includes
increases in spatial correlation. The relatively milder temperatures experienced by these countries
are accompanied by similar temperatures over neighboring locations.
Figure 13 depicts climate-change forecasts for each country in terms of the predicted change
in cereal productivity and the difference in projected welfare from omitting the change in spatial
correlation shown in Figure 12 on the vertical axis. The vast majority of countries suffer a decreasein cereal productivity as a result of increased temperature. As in Figure 12, the strongest contrast
in Figure 13 is between outcomes for African and European economies. While there is substantial
heterogeneity in the productivity declines across countries within each continent, most economies
in Africa, and a few in South America and Asia, experience productivity losses that would beconsiderably amplified by changes in spatial correlation. By contrast, most European economies
have reduced projected welfare losses when the change in spatial correlation is incorporated. For the
few economies with increased productivity under climate change, the differences across projections
are close to zero.

6

Conclusion

This paper studies how the spatial structure of the global productivity distribution shapes the
distribution of welfare across countries. In particular, we use a benchmark trade model with
distance-related trade costs to show that, all else equal, greater spatial correlation of productivities
can increase welfare inequality. The increase in spatial correlation causes high-productivity locations to enjoy larger gains from trade than they would if productivity were spatially uncorrelated.
In settings in which welfare differences are arbitraged away by mobile factors of production, greater
spatial correlation of productivities would make population density, rather than welfare per capita,
more unequal across locations.45
To investigate the empirical relationship between the spatial correlation of productivities andthe distribution of gains from trade, we exploit a global natural experiment. Specifically, we use the
El Niño-Southern Oscillation, a naturally occurring global climatic phenomenon, which exogenously
alters the annual spatial correlation of cereal productivity around the planet. We examine how thespatial correlation of cereal productivity governs the response of the domestic share of expenditure,a sufficient statistic for the gains from trade in a broad class of trade models, to local productivity.
Using data from the past five decades of cereal trade, we find that high-productivity countries
enjoy larger gains from trade when cereal productivities are more spatially correlated, as predicted.
More broadly, our empirical approach advances the use of causal-inference techniques to estimate
general-equilibrium predictions.
In our application, we demonstrate that incorporating changes in the spatial correlation of
productivities substantially alters predictions about global welfare inequality when forecasting the45

Appendix A.5 proves that this is the case for a symmetric geography with four locations.

34

consequences of anthropogenic climate change. This interplay between the spatial structure of
productivity and welfare inequality is potentially important in many other domains. Many determinants of productivity – such as demographics, political institutions, and natural endowments– tend to exhibit substantial spatial correlation. For natural endowments in particular, spatial
correlation may change following the relocation of existing endowments (e.g., migrating wildlife
stocks), the discovery of new uses for them (e.g., solar and wind availability), or the discovery of
new endowments (e.g., fossil fuel deposits). This paper provides a framework for analyzing thewelfare consequences of such widespread productivity changes.

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Appendix – For Online Publication
A

Theory appendix

A.1

General economic environment

This appendix section provides details of the perfect-competition results presented in Section 2 andextends them to the Krugman (1980) model of monopolistic competition.
Preferences. Individuals in country j have constant-elasticity-of-substitution preferences overgoods indexed by ω. The accompanying price index isZPj =pj (ω)1−σ1/(1−σ)
dω

.

ω

A.1.1

Perfect-competition microfoundations

Production. Productivity Aj has a model-specific microeconomic interpretation. In the Armington model, each country i produces a distinct variety using a linear production technology such that
one unit of labor yields Ai units of output. Under perfect competition, its price is wi /Ai and thusP
1/(1−σ)N
1−σthe Dixit-Stigliz price index is Pj =
(w
τ
/A
)
. In the Eaton and Kortum (2002)
i
ij
i
i=1
model, there is a continuum of varieties, and each country’s efficiency in producing them follows aFréchet distribution with location parameter Ti and dispersion parameter ϑ. The equivalence with
the Armington model requires Ti = Aϵi .
Gravity equation. Written in terms of expenditure shares, the gravity equation is
λij =

Xij
χi (τij wi )−ϵχi (τij wi )−ϵ
=
= PN
,
−ϵ
Xj
Φj
l=1 χl (τlj wl )(A.1)

where χi is a function of Ai and other structural parameters that are not trade costs, ϵ is theP−ϵis the “inward multilateral resistance” term (Head“trade elasticity”, and Φj ≡ N
l=1 χl (τlj wl )and Mayer, 2014). Φj is a (decreasing) transformation of j’s price index that summarizes consumers’
access to goods from every source. In the Armington model, ϵ = σ − 1 and χi = Aϵi . In the EatonKortum model without intermediate inputs, ϵ = ϑ and χi = Ti . Thus, the equilibrium trade flows
associated with a productivity distribution {Ai }i and trade elasticity ϵ in the Armington model are
equal to the equilibrium trade flows for an Eaton-Kortum model in which efficiency distributions
have location parameters Ti = Aϵi . As a result, we can replace χi in the gravity equation by Aϵi , asdone in the main text.
Welfare. Equation (1) is an immediate consequence of the main result in Arkolakis, Costinot
and Rodrı́guez-Clare (2012). They show that, in a broad class of models, the gains from traderelative to autarky are equal to − 1ϵ ln λii . In our theoretical environment, autarky welfare is equal
to ln Ai + γ, as implied by equation (1). γ is a function of structural parameters. In the Armington model with symmetric preferences, γ is zero. In the Eaton and Kortum (2002) model,42
1/(1−σ), where Γ is the gamma function.
γ = Γ 1 + 1−σθSpatial correlation and welfare. To examine the role of spatial correlation, consider two
productivity distributions, a correlated state c and an uncorrelated state u, with the same unconditional variance of productivities, var(ln Aci ) = var(ln Aui ). The difference in welfare dispersion
between these states is2
var (ln (Cic /Li )) − var (ln (Ciu /Li )) = − [cov (ln Aci , ln λcii ) − cov (ln Aui , ln λuii )]ϵ1+ 2 [var (ln λcii ) − var (ln λuii )] .
ϵ

(A.2)

The latter term should make only a second-order contribution to the difference in welfare dispersion, since ϵ12 is an order of magnitude smaller than 2ϵ for empirically relevant values of the tradeelasticity.46
A.1.2

Krugman (1980) microfoundations

We now discuss the case of monopolistic competition with homogeneous firms, in which the measureof varieties available in equilibrium is endogenously determined. Consider a many-country versionof the Krugman (1980) model in which costs may vary across countries. Denote the equilibrium
number of homogeneous firms producing in country j by nj .
Production function. Homogeneous firms produce differentiated varieties under monopolisticcompetition. Denote their fixed costs by fj and constant marginal costs by cj . Productivity Aj
may be a shifter of fixed costs or marginal costs for all firms.
Gravity equation. In the free-entry equilibrium, the gravity equation (A.1) holds with ϵ =σ − 1, ni = Li / (σfi ), and χi = ni c−ϵ
i .
Welfare. In this setting, real per capita consumption isln (Ci /Li ) =1
ln ni − ln ci + ln
ϵ



σ−1
σ


−

1
ln λiiϵIf population size Li and fixed costs fi are country-invariant (ni = n ∀j) and we interpret
productivity as shifting marginal costs, Ai = c−1
i , then this is equivalent to equation (1) withσ−11
γ = ϵ ln n + ln σ . If population size Li and marginal costs ci are country-invariant and we−1/ϵinterpret productivity as shifting fixed costs, Ai = fiwith γ = 1ϵ ln (L/σ) + ln σ−1σc .

, then this is equivalent to equation (1)In the case of countries with heterogeneous population sizes, equation (1) must be extended to46

Typical estimates of the aggregate trade elasticity are between 4 and 8. Caliendo and Parro (2015) estimatethat the trade elasticity for agricultural goods is between 8 and 17. Provided that var (ln λcii ) − var (ln λuii ) is thesame order of magnitude or smaller than cov (ln Aci , ln λcii ) − cov (ln Aui , ln λuii ), this means that the second termon the right side of equation (A.2) is an order of magnitude smaller than the first term. Appendix A.1.3 showsthat cov (ln Aci , ln λcii ) − cov (ln Aui , ln λuii ) is the same order of magnitude as var (ln λcii ) − var (ln λuii ) if trade costs are
symmetric (τij = τji ) and countries equal sized (Li = L ∀i). This is also overwhelmingly true in numerical simulations
featuring countries of different sizes reported in Appendix Figure E.1. Nonetheless, our welfare calculations, laid out
in Appendix D, incorporate ϵ12 [var (ln λcii ) − var (ln λuii )].

43

replace γ with a location-specific γi that depends on structural parameters other than productivity.
For example, if productivity shifts marginal costs, Ai = c−1
i , then we obtainlnwhere γi = 1ϵ ln ni + ln

σ−1
σ



Ci
Li


= ln Ai + γi −1
ln λii ,
ϵ

(1′ )

.

Spatial correlation and welfare. If we assume that cov(ln Aui , γi ) = cov(ln Aci , γi ), we obtainan extension of equation (A.2):
2
var (ln Cic /Li ) − var (ln Ciu /Li ) = − [cov (ln Aci , ln λcii ) − cov (ln Aui , ln λuii )]ϵ2− [cov (γi , ln λcii ) − cov (γi , ln λuii )]ϵ1+ 2 [var (ln λcii ) − var (ln λuii )] .
ϵ(A.2′ )

Similar results hold for the Melitz (2003) model of heterogeneous firms under monopolisticcompetition when the productivity distribution of country j is a Pareto distribution with location
parameter Aj .
A.1.3

The case of symmetric trade costs

The case of symmetric trade costs (τij = τji ∀i, j) is illuminating because it allows us to define theequilibrium in terms of one vector of endogenous outcomes (Φi ) and relevant because it connects
more closely with measures of spatial correlation, which use symmetric spatial weights. Startingfrom the equilibrium system of equations and using the assumption of symmetric trade costs:
Yi = wi Li =X  wi −ϵ
j

Ai

τij−ϵ

wj Lj
=
Φj



wi
Ai

−ϵ
Ωi

 1
ϵ+1
Ωi
Ai L i −ϵ X
X
ϵ
−ϵ wj
−ϵ
⇒ Φi =
τji=
τji(Aj Lj /Ωj ) ϵ+1
Aj
j
j
X
ϵ
−ϵ
=
τji (Aj Lj /Φj ) ϵ+1

wi
⇒
=
Ai



j

The last equality exploits the fact that we can normalize incomes such that Φi = Ωi when tradeis balanced and τij−ϵ is symmetric, as established in Anderson and van Wincoop (2003) and Headand Mayer (2014).
−ϵi)
Combining λii = (wi /A, the above expression for wi /Ai , and the assumption of symmetricΦi44trade costs yields the result that−ϵϵ
− 2ϵ+1(Ωi /(Ai Li )) ϵ+1= (Ai Li ) ϵ+1 Φi ϵ+1 .
λii =
Φi

ϵ
Thus, in the case in which Li = L ∀i, var(ln λii ) = ϵ+1
cov(ln Ai , ln λii ) − 1+2ϵ
1+ϵ cov(ln Φi , ln λii ).

Comparing these outcomes for productivity distributions Ac and Au in the case in which Li = L ∀i,var(ln λcii ) − var(ln λuii ) =iϵ hcov(ln Aci , ln λcii ) − cov(ln Aui , ln λuii )ϵ+1i
1 + 2ϵ h−cov(ln Φci , ln λcii ) − cov(ln Φui , ln λuii ) .
1+ϵ

Heuristically, the latter term is of smaller magnitude, since Φi is a price-index term that is aweighted sum of all other countries’ prices. Thus, var (ln λcii ) − var (ln λuii ) is the same order ofmagnitude as cov (ln Aci , ln λcii ) − cov (ln Aui , ln λuii ).

A.2

Spatial correlation and the covariance of productivity and gains from tradeThis appendix section theoretically illustrates how the spatial correlation of productivities may
affect welfare inequality by altering the covariance between productivity and gains from trade.
We do so by a series of steps. First, we use a local approximation to show that the change inthe covariance of productivities and domestic shares of expenditure resulting from an infinitesimalchange in countries’ productivities depends on the change in a term akin to the Moran’s I spatialcorrelation statistic for productivity. Second, we allow for large productivity changes by proving
our theoretical prediction in a symmetric four-country model and showing that it holds in numericalsimulations with more countries. Third, we examine how to identify this ceteris paribus prediction inasymmetric environments in which countries differ by other, potentially confounding, determinantsof equilibrium trade flows, as well as allowing for realistic geography, productivities and trade
costs. These simulations motivate our use of panel data in our empirical investigation. Finally, weshow implications for our predictions for trade models with multiple sectors, spatial correlation incomparative advantage, and mobile labor.
A.2.1

A local approximation

A partial-equilibrium local approximation suggests that an increase in the spatial correlation of
productivities should decrease the covariance of productivities and domestic shares of expenditureand that Moran’s I captures part of this spatial interdependence. A general-equilibrium local
approximation that exploits the assumption of symmetric trade costs (τij = τji ) delivers a very
similar result, as shown below. We can regress ln λii on the interaction of log productivity andMoran’s I to estimate this relationship.
We first consider the effect of an infinitesimal change in countries’ productivities on the covariance of productivities and domestic shares of expenditure. Let {d ln Ai }i denote a set of local

45

productivity changes that do not alter the distribution’s variance (dvar(ln Ai ) = 0). The resulting
change in cov(ln λii , ln Ai ) can be written as the sum of four terms:
dcov(ln λii , ln Ai ) = ϵ dvar(ln Ai ) −ϵ cov(d ln wi , ln Ai ) − cov(d ln Φi , ln Ai ) +cov(ln λii , d ln Ai )
|
{z
}
|
{z
} |
{z
}
=0

=0 by P.E.

≈dI by P.E.

(A.3)
The first term is zero by the assumption that the distribution’s variance is unchanged. If wetake a partial-equilibrium perspective by assuming d ln wi = 0 ∀i, the second term is also zero.
Furthermore, in partial equilibrium the third term is closely related to the spatial correlation of
productivities. The following subsection shows that, if wages are unchanged, cov(d ln Φi , ln Ai )is akin to the change in Moran’s I if we set spatial weights equal to initial expenditure sharesωji = λji for j ̸= i.47 The fourth term, while not taking the form of a change in Moran’s I, is also
intuitively linked to spatial correlation. Conditional on Ai and Li , λii will be lower in countries
where neighboring countries are larger and more productive. An increase in spatial correlation willtend to raise productivity in countries with more productive neighbors, so the fourth term should
also be negative when spatial correlation increases.
Partial-equilibrium case
Using the facts that ln λii = ϵ ln Ai − ϵ ln wi − ln Φi and dcov(yi , xi ) = cov(dyi , xi ) + cov(yi , dxi ), we
can derive the following
dcov(ln λii , ln Ai ) = ϵdcov(ln Ai , ln Ai ) − ϵdcov(ln wi , ln Ai ) − dcov(ln Φi , ln Ai )= ϵdvar(ln Ai ) − ϵcov(d ln wi , ln Ai ) − ϵcov(ln wi , d ln Ai ) − cov(d ln Φi , ln Ai ) − cov(ln Φi , d ln Ai )= ϵ dvar(ln Ai ) −ϵ cov(d ln wi , ln Ai ) − cov(d ln Φi , ln Ai ) − cov(ϵ ln wi + ln Φi , d ln Ai ),
|
{z
}
|
{z
} |
{z
} |
{z
}
=0

=0 by P.E.

≈dI by P.E.

=cov(ln λii ,d ln Ai )which yields equation (A.3). The first two terms are zero by the assumptions of unchanged varianceand partial equilibrium, respectively. The fourth term is equivalent to cov(ln λii , d ln Ai ) because
ln λii = ϵ ln Ai − ϵ ln wi − ln Φi and dvar(ln Ai ) = 2cov(ln Ai , d ln Ai ) = 0. We proceed to show why
the third term is related to the change in Moran’s I, dI.
Starting from the definition of Moran’s I for productivity, we can write changes in Moran’s I
47

Moran’s I is a commonly used measure of global spatial correlation that can be computed for any geography
endowed with a distance metric. It takes values between -1 and 1. Moran’s I for productivity ln Ai is defined byP P
ln Aj − ln ANi
j̸=i ωij ln Ai − ln A
P
P
I≡
,
2
P
i
j̸=i ωijℓ ln Aℓ − ln A
where N is the number of countries, ωij = ωji is a symmetric spatial weight, and ln A is the cross-sectional average.

46

as a covariance of ln Ai and a weighted sum of d ln Aj .
N
I≡P P

XX


1
ωij ln Ai − ln A ln Aj − ln A2Pi
j̸=i ωij
i j̸=iℓ ln Aℓ − ln A
|
{z
}
≡Ω
XX




dI = Ω
ωij d ln Ai ln Aj − ln A + ln Ai − ln A d ln Aji= 2Ω

by dvar(ln A) = 0

j̸=i

XX
i


ωij ln Aj − ln A d ln Ai

by ωij = ωji ∀i, j

j̸=i= 2Ωcov Xby ωii = 0 ∀i

ωji d ln Aj , ln Ai j

The third term in equation (A.3) evaluated at fixed wages is a covariance of ln Ai and a weighted
sum of d ln Aj .
Φi =

X

−ϵ −ϵ
Aϵj τjiwjj
1 X ϵ −ϵ −ϵ 11d ln Φi =dAj −dwj
ϵAj τji wj
Φi
Aj
wj
j
X
=ϵ
λji (d ln Aj − d ln wj )j

cov(d ln Φ, ln Ai |d ln wi =0 ∀i ) = ϵcov X

λji d ln Aj , ln Ai 

j

As a result, this covariance would be proportionate to the expression for dI above if ωji = λji . It is
not identical to the change in Moran’s I because ωii = 0 and while spatial weights are symmetric,
ωji = ωij , the initial equilibrium’s expenditures shares need not be.
General-equilibrium case with symmetric trade costs
Assume that τij = τji ∀i, j. Using the two previously noted facts that dcov(yi , xi ) = cov(dyi , xi ) +ϵ− 2ϵ+1cov(yi , dxi ), and symmetric trade costs imply λii = (Ai Li ) ϵ+1 Φi ϵ+1 , we obtain the following
expression for dcov(ln λii , ln Ai ):dcov(ln λii , ln Ai ) = cov(d ln λii , ln Ai ) + cov(ln λii , d ln Ai )
2ϵ + 1ϵ 1=dvar(ln Ai ) + cov(d ln Li , ln Ai ) −cov(d ln Φi , ln Ai ) + cov(ln λii , d ln Ai )
{z
} |
{z
}
ϵ+1 2|
ϵ+1
=0

=0

47

Section A.1.3 showed that when τij = τji ∀i, j, we can characterize equilibria in terms of {Φi }i andexogenous variables. We therefore obtain an expression for d ln Φi .
Φi =X−ϵ ϵ −ϵτji
Aj wj =

j

X

ϵ

−ϵ
τji
(Aj Lj /Φj ) ϵ+1

j



ϵ
1 ϵ
1
1
−ϵ
ϵ+1
d ln Φi =dAj −dΦjτji (Aj Lj /Φj )Φi ϵ + 1
Aj
Φj
j
ϵ X
=
λji (d ln Aj − d ln Φj )
ϵ+1
X

(A.4)

j

To establish the connection between cov(d ln Φi , ln Ai ) and the change in Moran’s I, we switch
to matrix notation. Define the following matrices:
ln Ã ≡ ln Ai − ln A i

n-element vectord ln A ≡ {d ln Ai }in-element vector

W ≡ {ωij }i,jn-by-n matrix

Using these matrices, we can write the change in Moran’s I as
dI = 2ΩXXiωij ln Aj − ln A d ln Ai = 2Ω · ln Ã′ Wd ln A.

jϵ
If we define B as the matrix whose ij element is ϵ+1
λji , then equation (A.4) can be written as

d ln Φ = B (d ln A − d ln Φ)⇒ d ln Φ = (I + B)−1 Bd ln A,
where the inverse exists because I + B is diagonal-dominant. As a result
cov(ln Ai , d ln Φi ) =i
1 hln Ã′ (I + B)−1 Bd ln A .
NThis covariance would be proportionate to the change in the Moran’s I spatial-correlation statisticP
n+1 nfor {ln Ai }i if we were to use the spatial weight matrix W = (I + B)−1 B = ∞B .
n=1 (−1)
That is, if the spatial weights were equal to the infinite sum of expenditure-share interactions thatsummarize the entire trading network, the change in Moran’s I would capture cov(d ln Φi , ln Ai ).
The first term in this infinite sum, B, is the “direct effect” in which productivity changes are
simply weighted by their expenditure share. Since the gravity equation relates expenditure sharesto bilateral distances, we thus expect the change in spatial correlation to affect dcov(ln λii , ln Ai ).

48

Figure A.1: Four-country example: Productivity distributions
High

Low

High

High

Low

High

Low

Low

“Regional” arrangement“Alternating” arrangement

A.2.2

Four-country case

A symmetric four-country model is the simplest possible environment in which one can demonstrate
our result for large productivity changes. Consider four countries of equal size evenly spaced ona symmetric geography. Each country is “near” two neighbors and farther from the remaining
country. Thus, the trade cost matrix is

1

d1 d2 d1
d1 1 d1 d2 

,
τ ≡

d
d
1
d
2
1
1


d1 d2 d1 1

1 < d1 < d2 < d21(A.5)

where the trade costs d2 > d1 , a mnemonic for distance, obey the triangle inequality: d2 < d21 .
For these four countries, consider a mirror-image productivity distribution in which two countries have high productivity and the other two countries have low productivity. These productivities
might alternate – high, low, high, low – or the world may be divided into a high-productivity region
and a low-productivity region. Figure A.1 depicts the two possible spatial arrangements. What are
the consequences for trade and welfare?
Proposition 1 shows that the “regional” arrangement of productivities exhibits greater spatial
correlation, as measured by Moran’s I. As a result, the covariance of productivity and the domestic
share of expenditure is lower when productivities are distributed this way. That makes the varianceof welfare across countries greater. The proof of Proposition 1 follows below.
Proposition 1 (Four-country case). Consider an economy in which N = 4, Li = L ∀i, ϵ ≥ 1,
and trade costs τij are given by condition (A.5). Comparing the productivity distributions Ac =(ã, ã, 1, 1) and Au = (ã, 1, ã, 1), where ã > 1,
 Ac is more spatially correlated than Au in the sense that the value of Moran’s I for ln Ac isgreater for any spatial weight matrix that is a one-to-one mapping between ωij and τij andassigns a higher weight to the pairs with τij = d1 than pairs with τij = d2 .
 Equilibrium income inequality, given by Y1 /Y4 , is greater for the more spatially correlated pro-ductivity distribution, Ac . Equivalently, the more productive economies’ equilibrium double49

factoral terms of trade are greater for the more spatially correlated productivity distribution.
 The covariance of productivity and the domestic share of expenditure is lower for the more

spatially correlated productivity distribution: cov(ln Aci , ln λcii ) < cov(ln Aui , ln λuii ).
 The variance of welfare across countries is greater for the more spatially correlated productivity

distribution: var(ln(Cic /L)) > var(ln(Ciu /L)).
This four-country case illustrates our prediction linking the spatial correlation of productivities
to welfare inequality.
Ac is more spatially correlated than Au
Proof. Recall that Moran’s I is given byN
I(ln A, W ) = P P

P

i

j ωij

i

P

ln Ai − ln Aj ωij ln Aj − ln A
,
2
P
ln
A
ln
A
−
i
i

where ωij are spatial weights. Define the spatial weight matrix

ω0

ω1
{ωij } = 
ω
 2
ω1

ω1 ω2 ω1
ω0 ω1 ω2 .
ω1 ω0 ω1 
ω2 ω1 ω0Thus, there is a one-to-one mapping between ωij and τij . ω1 is the spatial weight associated withtrade cost d1 ; ω2 is the spatial weight associated with trade cost d2 .
The average log productivity is given by ln A = 21 ln ã. For the correlated state, ln Ac =[(ln ã, ln ã, 0, 0), so the demeaned log productivity vector is equal to ln
Ac = ( 1 ln ã, 1 ln ã, − 1 ln ã, − 1 ln ã).
2

2

2

2

[
For the uncorrelated state, ln Au = (ln ã, 0, ln ã, 0) and ln
Au = ( 12 ln ã, − 21 ln ã, 12 ln ã, − 12 ln ã).
Piln Ac is more spatially correlated than ln Au if and only if I(ln Ac , W ) > I(ln Au , W ) ⇐⇒
P
P
P
[
[
[
[
ln
Ac
ωij lnAc >lnAuωij ln
Au .
i

j

i

j

i

j

j

The relevant terms are as follows:(X[ωij ln
Acj =

j

X

[
ln
Aci

i

X

for i = 3, 4[
ωij lnAcj = (ω0 − ω2 ) (ln ã)2(ji

for i = 1, 2

j

X
X

1
2 (ω0 − ω2 ) ln ã− 12 (ω0 − ω2 ) ln ã

[
ln
Aui

X

[
ωij lnAuj =12 (ω0 − 2ω1 + ω2 ) ln ã− 21 (ω0 − 2ω1 + ω2 ) ln ã

for i = 1, 3
for i = 2, 4[
ωij lnAuj = (ω0 − 2ω1 + ω2 ) (ln ã)2j

I(ln Ac , W ) > I(ln Au , W ) ⇐⇒ ω0 − ω2 > ω0 − 2ω1 + ω2 ⇐⇒ ω1 > ω2 .
50

Equilibrium for the correlated state: Ac = (ã, ã, 1, 1)
By symmetry, the equilibrium incomes and market access of countries 1 and 2 are identical, Y1 = Y2
and Φ1 = Φ2 . Similarly, countries 3 and 4 have identical outcomes: Y3 = Y4 and Φ3 = Φ4 . As
PN
a result, the equilibrium incomes that solve Yi =j=1 λij Yj can without loss of generality be
characterized by the scalar x ≡ Y1 /Y4 , the relative income levels.
Y1 = λ11 Y1 + λ12 Y2 + λ13 Y3 + λ14 Y4 ⇒ x =λ13 + λ14
1 − λ11 − λ12ϵEquilibrium expenditure shares can be expressed as λij = Aϵi Yi−ϵ τij−ϵ /Φj . Thus λij A−ϵi Yi =

τij−ϵ /Φj and
x=

−ϵ
−ϵ
τ13
/Φ3 + τ14
/Φ4
.
−ϵ
−ϵ
ϵ
ã−ϵ Y1 − τ11 /Φ1 − τ12/Φ2−ϵ ϵ −ϵ−ϵ−ϵ −ϵUsing the facts that Φ1 = Φ2 = Y1−ϵ ãϵ (1 + d−ϵ1 ) + Y3 (d2 + d1 ) and Φ3 = Φ4 = Y1 ã (d2 +
−ϵ
−ϵ
d−ϵ
1 ) + Y3 (1 + d1 ), it can be shown that the equilibrium value of x is the solution to the equationx2ϵ+1 +

−ϵ

d−ϵ
ϵ
ϵ+1
2 + d1− xϵ − ã2ϵ = 0.
−ϵ ã x1+d| {z 1 }

(A.6)

≡rc

Equilibrium for the uncorrelated state: Au = (ã, 1, ã, 1)Analogous to the correlated state, this case can be solved by exploiting the facts that countries
1 and 3 have identical outcomes, Y1 = Y3 and Φ1 = Φ3 , and countries 2 and 4 have identicaloutcomes: Y2 = Y4 and Φ2 = Φ4 . The equation that characterizes equilibrium relative income x is
x2ϵ+1 +

−ϵ

d−ϵ
ϵ
ϵ+1
1 + d1− xϵ − ã2ϵ = 0.
−ϵ ã x1+d| {z 2 }

(A.7)

≡ru

Note that 0 < rc < ru < 1 since d21 > d2 > d1 > 0.
Comparing equilibria
Equations (A.6) and (A.7) show that relative income in each equilibrium is given by the zeros of
the following generalized polynomialR(x; r) = x2ϵ+1 + rãϵ xϵ+1 − xϵ − ã2ϵwhen r > 0 is evaluated at rc and ru , respectively. By Descartes’ rule of signs, R(x; r) has exactly
one real positive zero (for a given value of r) (Jameson, 2006).48 Denote this zero of R(x; r) byx∗ (r).
48

It also has either 0 or 2 negative zeros that are obviously not of interest.

51

We prove that x∗ (r) is decreasing by contradiction. Let r1 < r2 and denote by x∗1 and x∗2their respective unique positive zeros. Suppose that x∗1 < x∗2 . Consider the function F (x) =R(x; r2 ) − R(x; r1 ) = (r2 − r1 )ãϵ xϵ (x − 1). It is evident that F (0) = F (1) = 0, F (x) < 0 ∀x ∈ (0, 1),
and F (x) > 0 ∀x > 1. When evaluated at x∗1 , F (x∗1 ) = R(x∗1 ; r2 ) − R(x∗1 ; r1 ) = R(x∗1 ; r2 ), since x∗1
is a zero of R(x; r1 ).
Note that R(x; r) is continuous in x and that R(0; r) < 0. Therefore, R(x; r2 ) < 0 ∀x ∈ (0, x∗2 ).
Since x∗1 ∈ (0, x∗2 ) by assumption, F (x∗1 ) = R(x∗1 ; r2 ) < 0. Since F (x) > 0 ∀x > 1, we conclude thatx∗1 ∈ (0, 1). We also know that ∀x > x∗1 , R(x; r1 ) > 0 since R(x∗1 ; r1 ) = 0 and limx→+∞ R(x; r1 ) =+∞. Together, these results imply that R(1; r1 ) > 0. Yet, R(1; r1 ) = 1 − ã2ϵ < 0 as ã > 1. Thus,
we have a contradiction. We conclude that r1 < r2 ⇒ x∗1 > x∗2 .
Denote the equilibrium relative incomes by xc and xu . Since ru > rc , xu < xc . The ratio of
equilibrium incomes is greater in the correlated case. Since the countries are of equal size, the ratioof equilibrium incomes x is also the more productive economy’s “double-factoral terms of trade”.
Thus, the more productive economies’ double-factoral terms of trade are greater in the correlatedcase.
cov(ln Ai , ln λii ) is lower in the spatially correlated case
Proof. Equilibrium domestic shares of expenditure can be expressed as λii = Aϵi Yi−ϵ /Φi . For the−ϵ ϵ −ϵ−ϵ−ϵ −ϵcorrelated state Ac , Φ1 = Φ2 = Y1−ϵ ãϵ (1 + d−ϵ1 ) + Y3 (d2 + d1 ) and Φ3 = Φ4 = Y1 ã (d2 +
−ϵ
−ϵ
d−ϵ
1 ) + Y3 (1 + d1 ), so

1

1

1

1

λc11 = λc22 = Aϵ1 Y1−ϵ /Φ1 =−ϵ =−ϵ ϵ −ϵ−ϵ ϵ c
1 + d−ϵ(1 + d−ϵ1 + ã xc (d2 + d1 )
1 )(1 + ã xc r )λc33 = λc44 = Aϵ3 Y3−ϵ /Φ3 =−ϵ =ϵ −ϵ −ϵϵ −ϵ c
1 + d−ϵ(1 + d−ϵ1 + ã xc (d2 + d1 )
1 )(1 + ã xc r )

−ϵ
−ϵ −ϵ
For the uncorrelated state Au , Φ1 = Φ3 = Y1−ϵ ãϵ (1 + d−ϵ2 ) + 2Y2 d1 and Φ2 = Φ4 = Y2 (1 +−ϵ ϵ −ϵd−ϵ2 ) + 2Y1 ã d1 , so1

1

λu11 = λu33 = Aϵ1 Y1−ϵ /Φ1 ==−ϵ ϵ −ϵ−ϵ ϵ u1 + d−ϵ(1 + d−ϵ2 + 2ã xu d1
2 )(1 + ã xu r )λu22 = λu44 = Aϵ2 Y2−ϵ /Φ2 =

1
1
=
−ϵ
ϵ x−ϵ d−ϵu1 + d−ϵ
+
2ã
(1
+
d
)(1
+ ãϵ x−ϵ
u 1
u r )
2
2

Thus, we obtain the following demeaned values of the log domestic shares of expenditure\ln
λ11 = − 21 [ln (1 + xϵ ã−ϵ r) − ln (1 + ãϵ x−ϵ r)]\\ln
λ44 = −lnλ11when evaluated at (rc , xc ) and (ru , xu ) for the two respective equilibria.

52

The covariance of productivity and the domestic share of expenditure is therefore
cov(ln Ai , ln λii ) =




−1
ln ã ln 1 + xϵ ã−ϵ r − ln 1 + ãϵ x−ϵ r
4Recall that ϵ and ã are fixed parameters while x is a function of r. This covariance is positive
because ã > x.49
It can be shown that cov(ln Ai , ln λii ) is increasing in r.
dcov(ln Ai , ln λii )
∝−
dr

d ln



1+xϵ ã−ϵ r1+ãϵ x−ϵ rdr ϵ   dxã
x ϵ rϵ −>0∝−
2 + xϵ ã−ϵ + x−ϵ ãϵ
x
ã
x
dr
{z
}
|{z}
|
|
{z
}
>0

>0

<0

Since ru > rc , the covariance of productivity and the domestic share of expenditure is lower
for Ac than Au . Thus, the covariance of productivity and the equilibrium gains from trade,cucov(ln Ai , −1
ϵ ln λii ), is greater for A than A .

var(ln(Ci /L)) is greater in the spatially correlated case
Proof. In both equilibria,var(ln λii ) =4ϵ22  \ 2 2  \ 2  \ 2ln λ11 +ln λ44 = ln λ11 =44(ln ã)22
1
cov(ln Ai , − ln λii ) .
ϵTherefore
1−1
ln λii ) + 2 var(ln λii )
ϵ
ϵ

2
4
1
−1
= var(Ai ) + 2cov(ln Ai ,ln λii ) +cov(ln Ai , − ln λii )ϵ(ln ã)2ϵvar(ln(Ci /L)) = var(Ai ) + 2cov(ln Ai ,This is increasing in cov(ln Ai , −1
ϵ ln λii ) if and only if1182+
cov(ln Ai , − ln λii ) > 0 ⇐⇒ ln ã > ln2(ln ã)ϵϵ

1 + ãϵ x−ϵ r
1 + xϵ ã−ϵ rThis inequality is true. The triangle inequality for trade costs, d2 < d21 , implies that ru < 1. If√√
r < 1 and ϵ ≥ 1, then R( ã; r) ≤ 0.50 Thus, x∗ (r) ≥ ã ∀r ∈ (0, 1). That implies the following
49ã > x because x is the largest positive zero of R(x; r), R(x′ ; r) < 0 ∀x′ ∈ (0, x), and R(ã; r) = (1+r)(ã−1)ã2ϵ > 0.

50

 1

√
2ϵ+1
ϵ+1
ϵ
ϵ
1
R( ã; r) = ã 2 + rãϵ (ã 2 − ã 2 ) − ã2ϵ = ãϵ ã 2 + rã 2 (ã 2 − 1) − ãϵ
 1

 ϵ


ϵ
1
1
ϵ
≤ ãϵ ã 2 + ã 2 (ã 2 − 1) − ãϵ = −ãϵ ã 2 − ã 2
1 + ã 2 ≤ 0

53

inequality:
1 + ãϵ x−ϵ rãϵ x−ϵ (1 + r)≤=
1 + xϵ ã−ϵ rxϵ ã−ϵ (1 + r)
 2ϵ 
ã
ã 2ϵ
= ãϵ
≤ √
x
ã

Thus, var(ln(Ci /L)) is increasing in cov(ln Ai , −1
ϵ ln λii ).

This completes the proof of Proposition 1.
A.2.3

Circular geography

Next, we investigate a symmetric geography with more than four countries and more than two
productivity levels using numerical simulations. Figure 3 presents this illustrative example inwhich we parameterize Ai and τij on a circular geography. As stated in the main text, N = 50,πϵ = 1, and Li = 1 ∀i. Countries have locations given by li = N(2i − 1 − N ) for i = 1, . . . , N .

Productivity ln Ai has a mean value of 10 and follows a sine wave with amplitude 1 and frequency
θ.51 Bilateral trade costs are given by ln τij = .8 ln(1 + ∥li − lj ∥), where ∥li − lj ∥ is the distance
between locations i and j on the circle. Moran’s I is computed using spatial weight ωij = 1+∥l1i −lj ∥for i ̸= j. Figure 3 depicts demeaned distributions. Table A.1 reports the means and variances ofcountries’ welfare per capita under autarky and trade.
Table A.1: Outcomes for one-sector sine-wave economy
Frequency of ln A sine wave (θ)
Autarky welfare (ln A) varianceTrading-equilbrium welfare (ln C/L) variance

1

2

3

4

0.510204
0.298203

0.510204
0.226274

0.510204
0.203006

0.510204
0.184882

Economic characteristics other than productivity that influence domestic shares of expenditurecomplicate bivariate plots like the right panel of Figure 3. A simple example is heterogeneity
in country size Li : all else equal, larger economies have a larger domestic share of expenditure.
Variation in size orthogonal to productivity simply adds noise to the bivariate plot. However,variation in size correlated with productivity also introduces omitted variable bias. This can beaddressed by examining the covariance of the domestic share of expenditure and productivity
conditional on size. More generally, any time-invariant country characteristics that influence thedomestic share of expenditure and might be correlated with productivity can be absorbed bycountry fixed effects.
We illustrate this in Figure A.2, which depicts the relationship between ln λii and ln Ai in anenvironment that extends the circular geography and sine-wave productivity parameterization usedin Figure 3 to feature heterogeneous country sizes. In particular, size ln Li is the sum of a sine
51

The standard deviation of a sine wave is proportional to its amplitude and independent of its frequency. This istrue for both the function and our N -point discretization.

54

wave with mean value 10, amplitude 1, and frequency θL = 1 and Gaussian noise ∼ N (0, 1). Thus,
country size ln Li is positively correlated with productivity ln Ai in the θ = 1 state. The left
panel depicts the covariance of ln λii and ln Ai for the frequencies θ = 1 and θ = 4. The rightpanel depicts these covariances conditional on country fixed effects, which we estimated using theequilibrium outcomes of the five equilibria associated with θ = 1, 2, 3, 4, 5. While our ceteris paribus
prediction is not evident in the left panel due to omitted variable bias, the right panel shows thatthe covariance of ln λii and ln Ai is lower when θ is lower after country fixed effects absorb theconsequences of heterogeneous country sizes.
Figure A.2: Circular geography with heterogeneous sizes and productivity sine wave
ln λii (residuals)

ln λii (demeaned)

1.0
0.5
0.0
-0.5
-1.0
-1.5

0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

ln Ai (demeaned)ln Ai (residuals)

θ=1

θ=4

θ=1

Unconditional relationship

θ=4

Relationship conditional on fixed effects

Notes: This figure depicts the λii –Ai relationship for an economy with a circular geography and a productivity
distribution that follows a sine wave with frequency θ. Geographic locations, trade costs, and the trade elasticity
are the same as in Figure 3. Country sizes Li are positively correlated with Ai in the θ = 1 state. The residuals in
the right panel are obtained by subtracting the country-level mean values of ln λii and ln Ai across the five equilibria
associated with θ = 1, 2, 3, 4, 5. See Appendix A.2.3 for parameterization details.

The real world features productivities and trade costs that do not exhibit the symmetry of a sine
wave on a circle. Departing from the sine-wave distribution, Figure A.3 depicts the expenditureproductivity relationship for the circular geography with equal-sized countries when we shuffle a
productivity vector drawn from the normal distribution so as to vary its spatial correlation. They
were generated by shuffling a vector ln A0 that was drawn from N (0, 1). There is a clear negative
relationship: as Moran’s I increases, the equilibrium domestic share of expenditure is less responsive
to domestic productivity.
A.2.4

Calibrated geography

To examine our prediction with realistic geography, productivities and trade costs, we simulate a
global economy made up of 158 countries whose geographic coordinates, cereal yields, and cropareas are their 1961–2013 averages in our data. We impose distance-related trade costs and swap
pairs of countries’ productivity levels in order to vary spatial correlation without altering themean or variance of the productivity distribution.We recover the covariance of expenditure andproductivity in each equilibrium by regressing the domestic share of expenditure for country i at
55

Figure A.3: Circular geography with equal-sized countries and arbitrary productivities

0.8
0.6

ln λii (demeaned)

0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

ln Ai (demeaned)

I = 0.00

I = 0.09

I = 0.17

Notes: This figure depicts the λii -Ai relationship in an economy with a circular geography for three randomly
generated productivity distributions. Geography, equal-sized locations, and trade costs are the same as in Figure 3.

“time” t, where each t denotes an equilibrium associated with a different productivity distribution,
on its own productivity and fixed effects:
ln λiit = βt ln Ait + πiI + πtT + µit .

(A.8)

As in the right panel of Figure A.2, the country fixed effects πiI control for differences in countries’
time-invariant determinants of the domestic share of expenditure, such as size and remoteness. The“year” fixed effects πtT control for differences in the average domestic shares of expenditure acrossdifferent spatial distributions of productivity.
The coefficients βt in equation (A.8) characterize the conditional covariance of ln λii and ln Ai ineach equilibrium. Since the equilibrium value of ln λii depends on the entire vector of productivities
and not just ln Ai , as shown by the gravity equation (2.1), this covariance differs across equilibria.52 Relating the general-equilibrium elasticity βt to properties of the exogenous productivity
vector shows how this covariance’s contribution to welfare inequality depends on properties of the
productivity vector. Figure A.4 shows that this covariance exhibits a negative and roughly linear
relationship with Moran’s I, a statistic that captures the spatial correlation of productivities. On
this realistic geography, when productivities are less spatially correlated, the equilibrium covarianceof ln λii and ln Ai is more positive and thus welfare inequality is lower.
52

λii
For the same reason, we expect the elasticity ∂∂ ln
to vary across i, so that βt is an average elasticity.
ln Ai

56

.2

.21

∂lnλii / ∂lnAi
.22

.23

.24

Figure A.4: Real-world geography and bilateral productivity swaps

.125

.145

.165
.185
.205
Spatial correlation of log productivity

.225

.245

Notes: Each observation is the estimated productivity elasticity of domestic expenditure share and spatial correlationof productivities for the equilibrium resulting from a bilateral swap of two countries’ productivity levels. Countries’
productivities and factor endowments are set equal to their long-run averages of cereal yield and log crop area,
respectively. Bilateral trade costs are proportionate to bilateral distances between countries’ crop centroids. The
trade elasticity is set to 8.59 and the scale of trade costs is set so that the distance elasticity of trade is 1.46.
Equilibria computed for 7499 bilateral swaps of productivities. Linear fit shown as solid line. Local polynomial fit
for 1st through 99th percentiles of spatial correlation shown as dashed line. Equilibrium associated with long-run
averages shown as square.

While the line of best fit in Figure A.4 is not perfect, the Moran’s I statistic aptly summarizes
how the spatial structure of productivity affects welfare inequality. In the model, the covarianceof productivity and gains from trade is determined by the general-equilibrium solution of a system
of non-linear equations. In Appendix Figure E.1, we examine how well relating this covariance toMoran’s I for productivity captures changes in the variance of welfare per capita. For each of theequilibria depicted in Figure A.4, we compare the variance of welfare per capita in the model tothat predicted by using the line of best fit. Regressing variance of welfare per capita in the model on
its predicted value yields an R2 of .93. Thus, a log-linear specification employing Moran’s I aptly
captures how welfare inequality determined by the general-equilibrium model depends on the spatial
structure of productivity. Our empirical investigation will therefore estimate the expenditureproductivity relationship using a linear regression and exogenous variation in productivities without
imposing the full structure of a quantitative trade model.53
53

An alternative way to examine the predicted expenditure-productivity relationship would be to calibrate the trademodel to rationalize the observed data from one year, introduce a change in the spatial correlation of productivities,
and then examine how well the calibrated model’s predicted expenditure responses align with observed changes.

57

A.3

Multiple-sector case

We obtained predictions about the spatial correlation of absolute advantage Ai using a theoreticalframework that makes two important assumptions about the pattern of comparative advantage.
First, there is only one sector. Second, the pattern of comparative advantage across varieties withinthat sector is symmetric across countries. This appendix section extends the model to multiple
sectors. The following appendix section examines the case of correlated comparative advantage.
Our empirical investigation exploits exogenous variation in the spatial distribution of productivities in the agricultural sector, which constitutes a small share of global trade. What happens
in an economy with multiple sectors? This appendix section shows that our prediction linking the
spatial correlation of productivities and the productivity-expenditure relationship holds for eachsector in a multi-sector gravity model of trade. When consumers have Cobb-Douglas preferences
over sectors and CES preferences over varieties within sectors, there are multi-sector analoguesof equations (1), (2), and (A.2) that sum over sectors using their expenditure shares. Thus, theprevious section’s predictions about trade in one sector can be investigated in a multi-sector worldthat introduces an additional dimension of comparative advantage.
Preferences. Individuals in country i have preferences that are Cobb-Douglas over sectors
s = 1, . . . , S and constant elasticity of substitution (CES) within sectors. Thus, the relevant priceindices are
Pi =

S
Y
s=1

Pisαis and Pis =Zpi (ωs )1−σs1/(1−σs )
dωs

,

ωs

P
where αis ≥ 0 are expenditure shares ( Ss=1 αis = 1) and σs are sectoral elasticities of substitution
across varieties.
Production. Productivity in country j in sector s is Ais .
Trade costs. Selling one unit to j from i in sector s requires producing τijs ≥ 1 units, with
τiis = 1.
Gravity equation. Denote sales from i to j in sector s by Xijs and j’s total expenditure by
P PS
Xj ≡ N
s=1 Xijs . Across sectors, Cobb-Douglas preferences cause optimizing consumers toi=1
spend αjs of their total expenditure in sector s, Xjs = αjs Xj . Within each sector, CES preferences
result in the share of expenditure by j on goods from i in sector s taking the form of a gravity
equation:Xijs
χis (τijs wi )−ϵsχis (τijs wi )−ϵs
λijs =
= PN
=
.
−ϵs
Xjs
Φjs
l=1 χls (τljs wl )Equilibrium. In a competitive equilibrium, labor-market clearing, goods-market clearing, andThis approach would encounter two challenges. First, computing the spatial correlation of productivities requires
productivity levels. Common calibration procedures, such as “exact hat algebra” (Costinot and Rodrı́guez-Clare,2014), do not identify these productivity levels. One would therefore need to explicitly estimate many structuralparameters to pursue this approach. Second, since other shocks affect both expenditure shares and productivities, thisalternative approach would still require the researcher to select relevant exogenous variation and define a criterion forevaluating model fit. Our instrumental-variables approach employs standard statistical criteria to define appropriate
exogenous variation and perform causal inference.

58

budget constraints are satisfied such that total income Yi = wi Li and sectoral income Yis = wi LisPPSsatisfy Yis = N
s=1 Yis , and Xis = αis Yi for all countries. The equilibrium system
j=1 Xijs , Yi =of equations is
Yis =

N
X

λijs αjs

S
X

Yjs′ .

s′ =1

j=1

In this environment, real consumption per capita is

ln

Ci
Li


=

S
X
s=1



1
αis ln Ais + γs − ln λiis .
ϵsP
The first two terms, Ss=1 αis (ln Ais + γs ), are per capita welfare in autarky, and the final term,P− Ss=1 αϵis
ln λiis , summarizes the gains from trade.
s
Dispersion in per capita welfare across countries thus depends on the exogenous variation in
productivities Ais and the endogenous variation in domestic shares of expenditure λiis . For the sakeof expositional brevity, assume that expenditures shares are common across countries, αis = αs ∀i
In that case, the variance of per capita welfare is!
!
  
S X
S
S
S
X
X
X
Ci
αs αs′
αisvar ln= var
ln λiis − 2
cov (ln Ais , ln λiis′ )αis ln Ais + var
Li
ϵs
ϵs′
′
s=1

s=1

s=1 s =1

To examine the role of spatial correlation, consider two productivity distributions – a correlated
state c and an uncorrelated state u. Assume
unconditional varianceof the productivity that 

PS
PS
c
u
distributions is the same, var
s=1 αis ln Ais = var
s=1 αis ln Ais . The difference in welfare
dispersion then depends on the covariance of productivities and domestic shares of expenditure,both within and across sectors, and between domestic shares of expenditure.

var (ln (Cic /Li )) − var (ln (Ciu /Li )) = 2

S X
S
o
X
αs αs′ ncov (ln Auis , ln λuiis′ ) − cov (ln Acis , ln λciis′ )ϵs′′
s=1 s =1

S X
SoX
αs αs′ n−cov (ln λuiis , ln λuiis′ ) − cov (ln λciis , ln λciis′ )ϵs ϵs′′
s=1 s =1

(A.9)
α α

Just as in the single-sector case, for typical values of the sectoral trade elasticities, 2 sϵ ′s′ is ans

α αorder of magnitude larger than ϵss ϵ s′′ . Thus, the difference in welfare dispersion is governed by thescov (ln Ais , ln λiis′ ) terms, provided that the block of cov (ln Ais , ln λiis′ ) terms is the same order ofmagnitude as the block of cov (ln λiis , ln λiis′ ) terms.
Under what circumstances is studying differences in cov (ln Ais , ln λiis ) in one sector alone informative about welfare dispersion? For simplicity, consider the two-sector case and three possible
relationships between the two sectors: perfectly correlated productivities, perfectly anti-correlated59

Table A.2: Outcomes for two-sector sine-wave economy
Frequency of ln A1 sine wave (θ1 )Autarky welfare ( 12 ln A1 + 12 ln A2 ) varianceTrading-equilbrium welfare (ln C/L) variance

1

2

3

4

0.255102
0.114255

0.255102
0.097649

0.255102
0.092189

0.255102
0.087935

productivities, and orthogonal productivities.
In the perfectly correlated case, there is little scope for adjustment across sectors, and thus
outcomes are similar to those obtained in the one-sector environment. In fact, if all sectors haveperfectly correlated productivities (Ais ∝ Ai ∀s), perfectly correlated spatial linkages (τijs ∝ τij ∀s),and equal trade elasticities (ϵs = ϵ ∀s), then expenditure shares are equal across sectors, λijs = λij ,and the difference in welfare dispersion in equation (A.9) is exactly proportionate to the singlesector expression in equation (A.2).
If sectoral productivities are perfectly anti-correlated, then outcomes in one sector may be
exactly offset by outcomes in another, leaving welfare unchanged. That is, it is possible to constructcircumstances in which the sum of covariances of productivities and domestic shares of expenditure
within sectors is exactly the opposite of the sum of cross-sector covariances. Consider the two-sector
case with equal expenditure shares α1 = α2 = 21 ∀j and equal trade elasticities ϵ1 = ϵ2 = ϵ. If thetwo sectors’ productivities are perfectly anti-correlated, such that ln Ai1 + ln Ai2 is a constant, thenPPα αit can be shown that Ss=1 Ss′ =1 sϵ ′s′ cov (ln Ais , ln λiis′ ) = 0. Thus, our predictions about tradesflows are valid, but the welfare consequences of these changes are fully offset by the non-agricultural
sector’s anti-correlated changes.
What about the orthogonal case? Figure A.5 depicts a two-sector sine-wave economy with twosymmetric sectors that differ only in their sine-wave frequency. Table A.2 reports the means andvariances of countries’ welfare per capita under autarky and trade. Compared to Table A.1, thevariance of autarky welfare is lower because autarky welfare is the simple average of two sectors’ (orthogonal) productivities with the same mean and variance. The mean trading-equilibrium welfare
is higher (the gains from trade are larger) in the multi-sector case due to gains from specializationaccording to comparative advantage. This additional margin of adjustment also dampens the degree
to which greater spatial correlation of productivities in one of the two sectors affects the varianceof welfare in the trading equilibrium, but our main prediction still holds in this multi-sector settingwith orthogonal productivities.

A.4

Spatial correlation of comparative advantage

This appendix section addresses how the spatial correlation of comparative advantage interacts withthe spatial correlation of absolute advantage. Introducing spatially correlated comparative advantage could reverse how the expenditure-productivity relationship varies with the spatial correlationof absolute advantage.
60

Figure A.5: Two-sector sine-wave economy: cov(ln λii1 , ln Ai1 )0.6

ln λii1 (demeaned)

0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

ln Ai1 (demeaned)θ1 = 1θ1 = 4
Notes: This figure depicts the λiis –Ais relationship for s = 1 in a two-sector economy in which sectoral productivity
follows a sine wave with frequency θs . The two series depicted are frequencies θ1 = 1 and θ1 = 4 for the first
sector. The second sector has frequency θ2 = 10 in both cases. The two sectors have identical trade costs τijs ,expenditure shares αi1 = αi2 = 12 , and trade elasticities ϵ1 = ϵ2 . The two lines are the line of best fit for each series.
When productivities are more spatially correlated (when θ1 is lower), cov(ln λii1 , ln Ai1 ) is lower. See Table A.2 inAppendix A.3 for details of this example.

The predictions in the main text concern the spatial correlation of absolute advantage Ai whencomparative advantage is symmetric across countries. Most quantitative trade models assume thispattern of comparative advantage.54 In this appendix section, we relax this assumption to examine
how the spatial correlation of comparative advantage may interact with the spatial correlation ofabsolute advantage. Our thought experiment varies the spatial correlation of absolute advantage,holding the pattern of comparative advantage fixed.55
To consider the role of spatially correlated patterns of comparative advantage, we extend theEaton and Kortum (2002) model, in which comparative advantage is symmetric across countries, tohave “continents” of countries with correlated relative productivities. The world economy consistsof N countries partitioned across k = 1, . . . , K continents. Country i belongs to continent k(i) andits productivity in good ω is zi (ω). We depart from Eaton and Kortum (2002) by assuming thatthe vector of productivities (Z1 , . . . , ZN ) is drawn from a multivariate nested Fréchet distribution:


ρk 
K
 X

X
1

F (z1 , . . . , zn ) = exp −(Ti zi−ϑ ) ρk 
,


k=1

54

i:k(i)=k

A notable exception is recent work by Lind and Ramondo (2019) that generalizes quantitative Ricardian models
by tractably relaxing this assumption.
55
Consistent with this assumption, column 2 of Table C.1 shows that the distance elasticity of trade is unaffected by
ENSO, our source of exogenous variation in the spatial correlation of absolute advantage. In the Eaton and Kortum(2002) model, this elasticity embodies the pattern of comparative advantage.

61

Table A.3: Estimates of β1 and within-continent correlation 1 − ρWithin-continent correlation 1 − ρ
0.3
0.4
0.5
0.6

K

0

0.1

0.2

2
3
4

-0.112-0.112-0.112-0.111-0.110-0.108-0.108-0.106-0.103-0.101-0.099-0.094-0.090-0.088-0.082-0.073-0.071-0.064-0.049-0.048-0.041

0.7

0.8

0.9

-0.022-0.021-0.013

0.002
0.005
0.013

0.014
0.018
0.029

Notes: This table reports estimates of β1 obtained from the regression ln λiit = β0 ln Ait + β1 It ln Ait + πiI +
πtT + µit on equilibrium outcomes from a simulated global economy with 50 countries as described in the textof Appendix A.4. Moran’s I is computed using spatial weight ωij = 1+∥l1i −lj ∥ for i ̸= j. The correlation
parameter ρk = ρ ∀k, the dispersion parameter is ϑ = 8.28 (Eaton and Kortum, 2002), and the level parameterln Ti follows a sine wave, as in Section 2.1, with θ = 1, . . . , 8. In the standard model, 1 − ρ = 0.

where the location parameter Ti governs the absolute advantage of country i and the dispersion parameter ϑ is common across countries. Parameters (ρ1 , . . . , ρk ) govern the degree of within-continent
correlation in productivities, which is decreasing in ρk . When ρk = 1 ∀k, these productivities are
independent, as in Eaton and Kortum (2002). Note that λii is a sufficient statistic for welfare onlyin the case in which ρk = 1 ∀k. Here, we focus on the consequences of the spatial correlation ofcomparative advantage for how the observed expenditure-productivity relationship varies with thespatial correlation of absolute advantage.
After considerable algebraic manipulations, it can be shown that the gravity equation for thisgeneralized productivity distribution is1(Ti (wi τij )−ϑ ) ρk(i)

λij =
P

(Tm (wm τmj )−ϑ )

1
ρk(i)

Φk(i)j,Φjm:k(m)=k(i)where Φkj =P1−ϑ ) ρki:k(i)=k (Ti (wi τij )ρkand Φj =PK

k=1 Φkj .

To study the interaction of the spatial correlation of comparative advantage and the spatial
correlation of absolute advantage, we simulate a world economy with a symmetric geography anda sine-wave productivity distribution, as in Section 2.1. We divide the 50 countries into two, three,or four continents with ρk = ρ ∀k. As we increase within-continent correlation in comparativeadvantage by lowering ρ from 1.0 to 0.1 in steps of size 0.1, we find that the effect of spatial
correlation in absolute advantage is initially dampened and then reversed. As reported in Table A.3, for the highest values of 1 − ρ, the estimated β1 is positive. That is, for sufficiently highwithin-continent correlation of comparative advantage, the cov(ln λii , ln Ai ) relationship depicted
in Figure 3 becomes steeper with greater spatial correlation of Ai , not flatter. In short, whenneighboring countries specialize in similar products, a neighbor’s productivity improvement may
actually worsen a country’s terms of trade by increasing the world supply of that country’s exports
and thereby depressing its export price.
62

Thus, our empirical estimate of β1 in equation (3) captures the effect of spatial correlationin absolute advantage as mediated by the existing spatial correlation in comparative advantage.
Most quantitative trade models have symmetric patterns of comparative advantage, in which caseβ1 should be negative. If patterns of comparative advantage within cereals are very spatiallycorrelated, β1 could be positive. Our empirical estimates in Section 4 reject this possibility.

A.5

Mobile labor

In an economic-geography model in which welfare differences are arbitraged away by mobile factorsof production (e.g., Allen and Arkolakis 2014), greater spatial correlation of productivities makes
population density, rather than welfare per capita, more unequal across locations. We demonstrate this using a symmetric geography with four locations, like the geography used in Appendix
Section A.2.2, in which the population of each location is endogenously determined. Locations’productivities vary exogenously, and their amenities are identical.
Given four locations with trade costs given by equation (A.5), total population L, and anelasticity of substitution σ, the endogenous populations {Li }4i=1 and welfare level W must satisfy
two equations:σ̃(σ−1)Lσ̃i = Ai
W 1−σ

4
X

1−σ (1−σ̃)(σ−1) σ̃
τji
Aj
Lj

and

j=1

L=

4
X

Lj ,

j=1

σ−1
where σ̃ ≡ 2σ−1
. Let L denote the vector containing L1 , . . . , L4 , let T denote the (symmetric)
1
matrix of trade costs raised (element-wise) to the power 1−σ, and let A denote the 4-by-4 diagonal

matrix with {A1 , . . . , A4 } on the diagonal.
The equilibrium equation of interest can then be written as

I−

1
W σ−1

A

σ̃(σ−1)TA(1−σ̃)(σ−1)

Lσ̃ = 0.

W σ−1 is the eigenvalue and Lσ̃ is the eigenvector of the matrix Aσ̃(σ−1) TA(1−σ̃)(σ−1) .
Let Ac and Au denote diagonal matrices whose diagonal elements are (ã, ã, 1, 1) and (ã, 1, ã, 1),
respectively, with ã > 1. Also, let ā ≡ ãσ−1 > 1, d¯1 ≡ d1−σ , and d¯2 ≡ d1−σ .

12σ̃(σ−1)(1−σ̃)(σ−1)σ−1σ̃Consider the eigenvalue λc = Wc
and eigenvector Lc associated with Ac
TAc
.
1−σ
1−σ
σ̃
1−σ̃
We can verify that the eigenvector Lc = (xc , xc , 1, 1) and the eigenvalue λc = ā(d1 +d2 )xc +1−σ
d1 + 1 satisfy the equation of interest. This implies that the equilibrium value of xc is given byā1−σ̃ (d¯1 + d¯2 )x21 − (ā − d¯1 − 1 + ād¯1 )x1 − (d¯1 + d¯2 )āσ̃ = 0.

(A.10)

Similarly, in the case of Au , consider the eigenvalue λu = Wuσ−1 and the eigenvector Lσ̃u asσ̃(σ−1)(1−σ̃)(σ−1). We can verify that the eigenvector Lσ̃u = (xu , 1, xu , 1) andthe eigenvalue λu = 2ā1−σ̃ d¯1 x2 + d¯2 + 1 satisfy the equation of interest. This implies that thesociated with Au

TAu

63

equilibrium value of xu is given by2ā1−σ̃ d¯1 x2u − (ā − d¯2 − 1 + ād¯2 )xu − 2āσ̃ d¯1 = 0.

(A.11)The quadratic equations (A.10) and (A.11) each have one positive and one negative root. Restricting attention to the positive roots, we can compare the relative sizes of xc and xu . It can beshown that xc > xu .
The equilibrium values of Lc and Lc are
 1
 1
σ̃
σ̃
x
 c1 xu  σ̃ 
1
L
L
xc 
 
Lc =
and
L
=


 1.
u
1
1
1
 
σ̃
σ̃
2xc + 2  
2xu + 2 xuσ̃ 11It can then be shown that cov(ln Ai , ln Li ) is greater for Ac than Au because xc > xu . Thus, withwelfare equalized across locations, the productivity-population relationship is more positive when
productivities are more spatially correlated.

B

Data sources and construction

Agricultural data Our cereal data cover barley, maize, millet, oats, rice, rye, sorghum, andwheat. We use cereal-level measures of output (in metric tons, 1961–2013), yield (in metric tons
per harvested hectare, 1961–2013), trade quantity (in metric tons, 1961–2013), trade value (innominal USD, 1961–2013), producer prices (in nominal local currency, 1966–2013), and change instorage (in metric tons, 1961–2013) for each country and year obtained from the FAO.56 Domestic
share of expenditure aggregated across cereals c = 1, . . . , C for country i in year t isPC
λiit = PC

c=1 Xciit

c=1 Xciit +

P

j̸=i

PC

c=1 Xcjit

where Xcjit is the value of cereal c sold to i by j in year t. We observe Xcjit for j ̸= i. We construct
Xciit using data on output quantities, export quantities, and prices. Xciit = (qcit − exportscit ) · pcit ,where qcit is domestic output quantity, exportscit is export quantity, and pcit is domestic price.
There are two potential data
P sources for price pcit , neither of which are ideal. The first data
source is export unit values,j̸=i Xcijt
exportscit , which are observed when a country exports a cereal.

Un-

fortunately, only 53% of the cereal-country-year observations in our sample with positive output
quantities have positive export quantities. The second price measure, producer prices in nominal
local currency, presents two challenges. First, producer prices are available for only 59% of thecereal-country-year observations with positive cereal output. Second, due to resource constraints
at the time, the FAO did not standardize the collection of 1966–1990 producer prices as it did for
56

Available at http://www.fao.org/faostat/en/#data.

64

prices since 1991. As such, the FAO warns against the combined use of the full 1966–2013 panel
and notes that it is “not in a position to give any explanation for the existing differences” between
1966–1990 and 1991–2013 producer prices.57 Thus, despite extensive efforts to convert 1966–1990
FAO producer prices into nominal US dollars, use of producer prices raises concerns.
In light of these limitations and to ensure sufficient statistical power in our estimation, we electPC
to approximate domestic expenditure
Xciit by domestic quantity times average export unit
 PC Pc=1 X PC
c=1
j̸=i cijt
PC
value,. This measure is available for every year thatc=1 (qcit − exportscit )c=1 exportscit

a country exports at least one cereal, yielding a sizable estimation sample. This approximation
Pof domestic expenditure C
c=1 Xciit makes our outcome variable a noisy measure of the domestic
share of expenditure. Table F.8 shows results for alternative approximations of the domestic shareof expenditure. Our country-year measure of aggregate cereal yield is harvested area-weighted
cereal-level yield.
For several robustness checks, we use bilateral trade data from the U.N. Comtrade database.58
Comtrade data has the disadvantage of using cereal codes that differ from that used by the FAO.
As such, despite careful matching of cereal categories across the two datasets, we prefer to use
production and trade data that is consistently reported by the FAO. However, trade data at thebilateral level is available from Comtrade starting in 1962, whereas it is only available from the
FAO starting in 1986. Thus, for the gravity equations estimated in Table C.1, we use Comtradebilateral trade data. As a robustness check, we show in column 5 of Table F.8 that our main result
is unaffected when we alternatively construct domestic expenditure share using Comtrade data.
We also use bilateral trade data from Comtrade to construct a measures of the change in acountry’s terms of trade each year. A country is better off if its initial net export vector is more
expensive at new prices than at old prices (Dixit and Norman, 1980, p.132). Define the normalized
net export vector for country i in year t − 1 by a vector whose 2 × C × (N − 1) elements areexportscijt−1 and −exportscjit−1 for j ̸= i multiplied by a scalar so that its norm is one.59,60 Define
the accompanying price-change vector for country i in year t by a vector whose 2 × C × (N − 1)elements are ∆pcijt and ∆pcjit for j ̸= i, where ∆ denotes the time difference operator. We
use changes in unit values of bilateral trade flows to proxy for these price changes. The change
in the terms of trade is the inner product of these two vectors, which we denote ∆ToTit , with
∆ToTit > 0 indicating an improvement in country i’s terms of trade. Our measure is imperfectbecause unit values are a noisy measure of prices and the price-change element ∆pcijt is not observed
if exportscijt = 0. Absent further information, we impose ∆pcijt = 0 for these elements. Beyond
cereals, the change in the terms of trade for a broader set of commodities, such as all products in
SITC sector 0 “food and live animals”, can be computed analogously using the quantities and unit
57

See here: http://fenixservices.fao.org/faostat/static/documents/PA/PA_e.pdf
Available at https://comtrade.un.org
59
Recall N is the number of countries. The normalizing scalar is P exports 1 +exports. Absent the normalcijt−1
cjit−1c,jization, larger economies would mechanically exhibit larger terms-of-trade changes.
60
Note that exportscijt−1 and −exportscjit−1 are distinct elements in this net export vector, so that the same cereal
imported and exported by the same country is not assumed to be a homogeneous good.
58

65

values reported in Comtrade data.
ENSO index

Annual ENSO variations can be detected using different indices, with the mostcommonly used being equatorial Pacific sea surface temperature (SST) anomalies. We primarily
utilize 1960-2013 values of the monthly Kaplan NINO4 index which averages SST over the area
5◦ S-5◦ N, 160◦ E-150◦ W. For robustness checks in Table F.6, we also use the NINO3 (5◦ S-5◦ N,
150◦ W-90◦ W), NINO34 (5◦ S-5◦ N, 170◦ W - 120◦ W), and NINO12 (10◦ S-0◦ , 90◦ W-80◦ W) indices(Kaplan et al., 1998).61
Historical temperature and precipitation

Global temperature (in degrees centigrade) and

precipitation (in mm/month) variables constructed from monthly gridded global weather data at
a 0.5◦ latitude by 0.5◦ longitude resolution were obtained from the Center for Climatic Researchat the University of Delaware (Willmott and Matsuura, 2001). 1960-2013 monthly data was first
spatially aggregated from pixel to country-level using cross-sectional crop-area weights in 2000 from
Ramankutty et al. (2008). For robustness checks in Table F.6, we also aggregate temperature frompixel to country-level using total country area. Annual values are then constructed by averaging
January-December monthly values.
Projected temperature under climate change

Global multi-model ensemble mean temper-

ature (in degrees centigrade) from monthly gridded global data at the 2.5◦ latitude by 2.5◦ longitude resolution from the Coupled Model Intercomparison Project version 5 (CMIP5).62 2014–2099
monthly data was first spatially aggregated from pixel to country-level using cross-sectional croparea weights in 2000 from Ramankutty et al. (2008). Annual values are then constructed byaveraging January-December monthly values.
Geography

Country latitude and longitude are defined as crop area-weighted average using the

global cross-sectional distribution of crop area in 2000 from Ramankutty et al. (2008). Great-circle
distances between these country centroids are computed using the haversine formula.
Global oil prices Monthly West Texas Intermediate crude oil spot price obtained from the St.
Louis Federal Reserve for 1961–2013.63 Annual values are then constructed by averaging JanuaryDecember monthly values.
Export restrictions Export restrictions come from the United Nations Conference on Tradeand Development’s (UNCTAD) TRAINS database.64 To construct the dummy variable used incolumn 6 of Table F.3, we employ all export-related measures (Chapter P of the International
Classification of Non-Tariff Measures), excluding export subsidies. The indicator equals one for
61

Available at http://iridl.ldeo.columbia.edu/SOURCES/.Indices/.nino/.EXTENDED/
Available at https://climexp.knmi.nl/selectfield_cmip5.cgi
63
Available at https://fred.stlouisfed.org/series/WTISPLC
64
Available at http://trains.unctad.org
62

66

country-year observations in which a new restriction on exporting any cereal to any trading partner
was introduced.
Tariffs

Importer-exporter-year ad-valorum tariff data at the cereal level come from the WorldBank’s World Integrated Trade Solution (WITS) database.65 We use the WITS-defined effective
tariff rate, which generally takes the lowest available value among Most-Favored Nation, Bound,and Preferential tariffs. To construct an aggregate cereal tariff value, we take the simple averageof nonmissing values across the eight major cereals.

C

Gravity regressions

The theoretical model of Section 2 implies that the value of cereals exported by exporter i toimporter j in year t satisfies a gravity equation:
ln Xijt = −ϵ ln τij + ln

χit
ϵ
wit




+ ln

Xjt
Φjt


.

(C.1)

Two assumptions embodied in this gravity equation are pertinent to our main empirical test inequation (3). First, trade costs τij must be positively related to bilateral distance for spatial
correlation of productivities to be relevant for welfare inequality. Second, we interpret equation (2)assuming that the trade elasticity, ϵ, is constant. In particular, we assume that time-series variationin the global spatial correlation of productivities does not alter the trade elasticity, allowing us to
use the observed change in the covariance between country productivity and own expenditure share
as a measure of the change in welfare inequality. Similarly, we assume that the trade elasticity does
not vary across trading partners. By contrast, in the model of spatially correlated comparativeadvantage in Section A.4, the trade elasticity for pairs of countries on the same continent is higher(in absolute value) when ρ < 1. The constant-elasticity assumption underlies the sufficient statistic
for welfare in Arkolakis, Costinot and Rodrı́guez-Clare (2012).
To examine these assumptions, Table C.1 reports several variants of gravity regressions. To
account for the typical preponderance of zero-valued bilateral trade observations (≈70% of sample),we use the Poisson pseudo-maximum likelihood estimator (Silva and Tenreyro, 2006). We find thatobserved trade in cereals declines with distance and is consistent with a constant trade elasticity.
Column 1 of Table C.1 estimates a standard gravity equation following Head and Mayer (2014)
using bilateral distance as a (time-invariant) source of variation in bilateral trade costs (τij ) andexporter-year (it) and importer-year (jt) fixed effects to capture the second and third terms ofequation (C.1) respectively. Unsurprisingly, bilateral trade declines with distance: the distanceelasticity of trade is -1.4. The modest distance elasticity is consistent with cereals produced by different countries serving as imperfect substitutes.66 The regression exhibits the typical explanatory
65

Available at https://wits.worldbank.org/tariff/trains/country-byhs6product.aspx?lang=en
Relatedly, there would be no two-way trade if cereals were perfectly homogeneous commodities. Yet, 63% ofcountries that trade cereals in a given year both import and export cereals that year. At the level of importer66

67

power, accounting for 87% of the variation in cereal trade flows.67
In column 2 of Table C.1, we examine whether the distance coefficient responds to global
ENSO time-series variation. To do so, we introduce an interaction between bilateral distance and aquadratic function of the sum of contemporaneous and lagged ENSO (i.e., ENSOt + ENSOt−1 ), thefunctional form for ENSO used for our main IV results in Table 2. We introduce importer-exporter
fixed effects that absorb time-invariant components, including (uninteracted) bilateral distance.
The distance elasticity of trade does not vary with ENSO: the coefficients on the interactions arevery close to zero. Assuming the distance elasticity of trade costs is also invariant to ENSO,
this supports the assumption that our plausibly exogenous variation in the spatial correlation of
productivities does not alter the trade elasticity.
Finally, we use bilateral tariff variation to examine whether the trade elasticity varies withthe bilateral distance between trading partners. Assuming full passthrough of tariffs to costs,
the coefficient on a bilateral ad valorem tariff is the trade elasticity. Following Lind and Ramondo(2019), we interact bilateral distance with time-varying tariffs to estimate distance-dependent tradeelasticities. Tariff data have two disadvantages: they are only available after 1990 and have many
missing values.68,69 With these caveats noted, column 3 reports a trade elasticity of ϵ = −7.7, which
is similar to the Caliendo and Parro (2015) estimate of ϵ = −8.59 that we employ in our welfare
calculations. If comparative advantage were spatially correlated, so that neighboring countries
have more similar productivity distributions across varieties, we would find a positive coefficient on
the interaction between tariffs and distance. To the contrary, column 3 shows a (noisily estimated)
negative coefficient. We cannot reject the hypothesis that the trade elasticity is invariant to bilateral
distance.

exporter pairs, 19% of trading pairs sell cereal in both directions.
67
The pseudo R-squared when omitting the distance covariate is 0.74, implying that distance explains 50% of theresidual variation after accounting for importer-year and exporter-year fixed effects.
68
The shorter time span means tariff data are not well suited for estimating whether the trade elasticity varies overtime with ENSO, the test in column 2 of Table C.1.
69
91% of Comtrade observations with positive trade value at the importer-exporter-cereal-year level have missing
WITS tariff values.

68Table C.1: Gravity regression for international trade in cereals
Outcome is bilateral trade value(1)
ln distanceij

(2)

(3)

-1.430(0.014)[0.000]ln distanceij × (EN SOt + EN SOt−1 )0.008(0.011)[0.491]
0.003(0.009)[0.730]ln distanceij × (EN SOt + EN SOt−1 )2

ln tariffijt-7.725(4.997)[0.122]-2.791(4.310)[0.517]ln tariffijt × ln distanceij

Observations
Sample period
Pseudo R-squared

640,482
1962-2013
0.869

466,364
1962-2013
0.952

10,028
1991-2013
0.997

Notes: The dependent variable is annual bilateral (importer-reported)cereal trade value from Comtrade. All models use the Poisson pseudomaximum likelihood estimator. Columns 1 and 2 include importer-yearand exporter-year fixed effects. Column 3 further includes importerexporter fixed effects. Standard errors, clustered by year, in parentheses; p-values in brackets.

69

D

Welfare calculations

This section details the welfare calculations in the main text.

D.1

Historical variance of welfare effectThis section details the within-sample welfare calculation discussed in Section 4.2 and shown in
Table 2. Recall the expression for the variance of welfare in equation (2):−1var (ln (Ci /Li )) = var (ln Ai ) + 2cov ln Ai ,ln λii
ϵ




+ var

1
ln λiiϵ

We employ this expression to quantify the magnitude of our regression results in welfare terms.
Consider the following thought experiment: suppose the spatial correlation of productivities increases from the 1961–2013 historical mean, I¯ = .214, by one standard deviation, σI = .0191.
What is the resulting percentage change in the cross-sectional variance of welfare, holding everything else fixed? We denote these two hypothetical states as uncorrelated state u and correlated
state c.
For the uncorrelated state, we define variance productivity as the average cross-sectional productivity variance during 1961–2013:
var(ln Aui ) ≡ Et [vari (ln Ait |t)](D.1)

Next, we define covariance between productivity and domestic share of expenditure during theuncorrelated state as the average cross-sectional covariance during 1961–2013:
cov(ln Aui , ln λuii ) ≡ Et [covi (ln Ait , ln λiit |t)](D.2)

We further define the variance of domestic share of expenditure during the uncorrelated states as
the average variance during 1961–2013:
var(ln λiiu ) ≡ Et [vari (ln λiit |t)]

(D.3)

Note that the values in definitions (D.1), (D.2), (D.3) can be directly computed from data sinceln Ait and ln λiit are observed.
For the correlated state c, var(ln Aci ) is also given by definitions (D.1) since we assume productivity variance is unaltered by changes in spatial correlation. cov(ln Aci , ln λcii ) and var(λcii ),however, have to be calculated as one does not directly observe data from a year in which only
It = I¯+σI while everything else is fixed at the historical mean. To do this, first recall the expression
for ln λit in equation (3):ln λiit = β0 ln Ait + β1 It ln Ait + Π′ Zit + µit

70Our estimates of this equation can be employed to construct each component of equation (2) for thecorrelated state. The covariance between productivity and domestic share of expenditure during
the correlated state is:cov(ln Aci , ln λcii ) ≡ (βb0 + βb1 (I¯ + σI ))Et [vari (ln Ait |t)]b ′ Zit |t)] + Et [covi (ln Ait , µ+ Et [covi (ln Ait , Π
bit |t)](D.4)

The variance of domestic share of expenditure during the correlated state is:var(ln λcii ) ≡ (βb02 + 2βb0 βb1 (I¯ + σI ) + βb12 (I¯ + σI )2 )Et [vari (ln Ait |t)]b ′ Zit |t)] + Et [vari (b+ Et [vari (Πµit |t)]b ′ Zit |t)]+ 2(βb0 + βb1 (I¯ + σI ))Et [covi (ln Ait , Π
bit |t)]+ 2(βb0 + βb1 (I¯ + σI ))Et [covi (ln Ait , µb ′ Zit , µ+ 2Et [covi (Πbit |t)](D.5)

Each term in equations (D.4) and (D.5) is either directly observable or can be obtained by estimating
equation (3). For example, for the model estimated in column 4, panel B of Table 2, with βb0 = 2.114
and βb1 = −4.144, we have:
Et [vari (ln Ait |t)] = .453
b ′ Zit |t)] = 1.04
Et [vari (ΠEt [vari (bµit |t)] = .083
b ′ Zit |t)] = −.497
Et [covi (ln Ait , Π
Et [covi (ln Ait , µ
bit |t)] = −.026
b ′ Zit , µEt [covi (Πbit |t)] = −.001
Applying equation (2), the percentage change in the variance of welfare in the correlated state,
relative to the uncorrelated state, is




Cc
Cu
var ln Lii − var ln Liivar(ln(Ciu /Li ))=var (ln Aci ) − 2ϵ cov (ln Aci , ln λcii ) + ϵ12 var (ln λcii )var (ln Aui ) − 2ϵ cov (ln Aui , ln λuii ) + ϵ12 var (ln λuii )

−1

(D.6)

To complete the calculation, let the agricultural trade elasticity be ϵ = 8.59 (Caliendo and Parro,
2015, Table A2). Values from equation (D.6) are shown in Table 2, with standard errors calculatedusing the delta method.

D.2

Change in country-level welfare and welfare variance under climate changeThis section discusses how we calculate the percentage change in the global variance of welfare
and the change in country-level welfare between the end of our estimation period, t̄ = 2013, and71

the end of our projection period, T = 2099, under climate change, holding everything else fixed.70
We compare two projections, one which omits climate-induced changes in the spatial structure of
agricultural productivity and another which allows for such changes.
We begin by showing how we quantify changes in country-level agricultural productivity as wellas the global variance and spatial correlation of agricultural productivity under climate change. We
then consider two projections of country-level domestic share of expenditure. The first projection,
which would be a typical projection of climate impacts, omits climate-induced changes in thespatial structure of agricultural productivity. The second projection includes such changes. We
then compare changes in the variance of welfare and in country-level welfare over the 20th century
across these two projections.
Projecting agricultural productivity

Recall equation (9) for ln Ait during the estimation

period, t ∈ [1961, 2013]:
ln Ait = k(Tit ) + Ψ′ Xit + νitColumn 1 of Table F.10 shows coefficients for bk() from our benchmark specification, which is alsoplotted in Figure 10. Using estimates from equation (9) and our business-as-usual CMIP5 ensemble
mean projected temperatures under climate change, Tbit , we first compute country-year agricultural
productivity under climate change during the projection period t ∈ [2014, 2099], holding everything
but temperature fixed to estimated t̄ = 2013 values:db ′ Xit̄ + νbit̄ln
Ait = bk(Tbit ) + Ψ

(D.7)

d
In the left panel of Figure 11, the black line shows var(lnAit ) while the blue line shows Moran’s I,d
Ibt computed using ln
Ait , for each projection year.
Projecting domestic share of expenditure omitting and including change in spatial
structure We consider two projections of the domestic share of expenditure: one which holds
the global spatial correlation of productivities fixed to the 2013 value and another which allows it
to vary under climate change. Both projections use our benchmark estimate of β1 and β2 fromequation (3), shown in column 4, panel B of Table 2.
Holding the spatial correlation of productivities fixed to the t̄ = 2013 value (along with otherunprojected determinants), the domestic share of expenditure during the projection period, t ∈[2014, 2099], is:nddb ′ Zi,t̄ + µln
λiit = (βb0 + βb1 It̄ )ln
Ait + κbIt̄ + Π
bit̄

(D.8)

where spatial correlation affects both the average domestic share of expenditure (κ) and its relationship to domestic productivity (β1 ).71
70

Compared with the welfare calculation described in Appendix D.1 and reported in Table 2, there is an addedcomplication as climate change also changes the variance of productivity.
71
To obtain κ, we first recover year fixed effects from equation (3). κ
b = 2.45 is the coefficient from a linear regressionof year fixed effects on It and a linear time trend.

72

Allowing the spatial correlation of productivities to vary under climate change, the domestic
share of expenditure during the projection period, t ∈ [2014, 2099], is:sddb ′ Zi,t̄ + µ
Ait + κbIbt + Πbi,t̄ln
λiit = (βb0 + βb1 Ibt )ln

Projecting changes in global welfare variance(D.9)

From equation (1), the expression for welfare

of country i in year t isln (Cit /Lit ) = ln Ait + γ −1
ln λiit .
ϵTo compute the change in variance of welfare from the end of the estimation period, t̄ = 2013, to
any year during the projection period, t ∈ [2014, 2099], we difference equation (2):dvar (ln(Cit /Lit )) − var (ln(Cit̄ /Lit̄ )) = [var(lnAit ) − var(ln Ait̄ )]dd− (2/ϵ)[cov(lnAit , lnλiit ) − cov(ln Ait̄ , ln λiit̄ )]d+ (1/ϵ2 )[var(lnλiit ) − var(ln λiit̄ )](D.10)For the projection which holds spatial structure fixed, equations (D.7) and (D.8) allow construction
n
n
d
d
d
of var(lnλ ) and cov(lnAit , lnλ ) for each year in the projection period. These then enter into
iit

iit

equation (D.10) to compute the change in welfare variance between 2014–2099 for the projectionn /Ln )) − var (ln (C /L )). That projectedthat omits changes in spatial structure, var (ln (CiT
it̄
it̄
iT

welfare variance is shown as the solid gray line in the right panel of Figure 11.
Similarly, for the projection that allows climate-induced changes in spatial structure, equassdddtions (D.7) and (D.9) allow construction of var(lnλ ) and cov(lnAit , lnλ ) for each year in
iit

iit

the projection period. These then enter into equation (D.10) to compute the change in welfare variance between 2014–2099 for the projection that includes changes in spatial structure,s /Ls )) − var (ln (C /L )). That projected welfare variance is shown as the solid redvar (ln (CiT
it̄
it̄
iT

line in the right panel of Figure 11.
We then calculate the percentage difference in the change in welfare variance between projections
that include and omit changes in spatial structure:s /Ls )) − var (ln (C /L ))var (ln (CiT
it̄
it̄
iT 
−1
n
n
var ln CiT /LiT − var (ln (Cit̄ /Lit̄ ))(D.11)

When applying baseline estimated parameters and an agricultural trade elasticity of ϵ = 8.59
(Caliendo and Parro, 2015, Table A2) to equation (D.11), we find that allowing climate change toalter the spatial correlation of productivities predicts a 20% greater increase in welfare variancethan when spatial correlation is held fixed.
Projecting changes in country-level welfare

For the projection that omits changes in spatial

structure, the difference in country i welfare from t̄ = 2013 to T = 2099 is:
h
i
n
d
d
ln(CiT/LniT ) − ln(Cit̄ /Lit̄ ) = [lnAiT − ln Ait̄ ] − (1/ϵ) (βb0 + βb1 It̄ )(lnAiT − ln Ait̄ )73

Likewise, for the projection that includes changes in spatial structre, the difference in country i
welfare from t̄ = 2013 to T = 2099 is:
i
h
s
d
d
AiT − (βb0 + βb1 It̄ ) ln Ait̄ + κb(IbT − It̄ )ln(CiT/LsiT )−ln(Cit̄ /Lit̄ ) = [lnAiT −ln Ait̄ ]−(1/ϵ) (βb0 + βb1 IbT )ln
The difference in country welfare between projections that include and omit changes in spatial
structure is:snd[ln(CiT/LsiT ) − ln(Cit̄ /Lit̄ )] − [ln(CiT/LniT ) − ln(Cit̄ /Lit̄ )] = −(1/ϵ)[(βb1 ln
AiT + κb)(IbT − It̄ )] (D.12)

Figures 12 and 13 show the country-level difference across projections.

E

Appendix figures.43

Welfare per capita variance (model)
.432
.434
.436

.438

Figure E.1: Welfare per capita, model vs approximation by linear regression

.43

.432
.434
.436
.438
Predicted welfare per capita variance (linear projection).44

Notes: For each equilibrium depicted in Figure A.4, we compute equilibrium welfare per capita in the model(vertical axis) and welfare per capita predicted by an estimated linear regression (horizontal axis). The regression
specification is akin to the line of best fit depicted in Figure A.4, see equation (3). Predicted welfare per capita iscomputed by plugging in predicted values of ln λii into equation (2). The R2 of the bivariate relationshipis .93.
cov (ln Ai , ln λii ) − cov ln Āi , ln λ̄ii is at least the same order of magnitude as var (ln λii ) − var ln λ̄ii in 99% of
swaps; it is an order of magnitude larger in 16%.

74

Figure E.2: Location of ENSO sea-surface temperature measurements

Notes: ENSO indices defined as average sea surface temperature over a region minus the long-term mean sea surface
temperature for that region. Spatial definitions for standard ENSO indices: NINO4 (5◦ S-5◦ N, 160◦ E-150◦ W),
NINO3 (5◦ S-5◦ N, 150◦ W-90◦ W), NINO34 (5◦ S-5◦ N, 170◦ W - 120◦ W), and NINO12 (10◦ S-0◦ , 90◦ W-80◦ W).

-2

Monthly ENSO index (degrees Celsius)
-1.5
-1
-.5
0
.5
1

1.5

Figure E.3: Monthly ENSO index for top 10 positive events

-12

-9

-6

-3
0
3
Months relative to Dec in year t

6

9

12

Notes: Time evolution of monthly ENSO index 12 months before and after the 10 most positive ENSO events over
1961–2013. ENSO events occur during the winters of 1965, 1972, 1982, 1986, 1991, 1994, 1997, 2002, 2006, and 2009.

75

-3

Demeaned log cereal yield in 2013
-2
-1
0
1

2

Figure E.4: Observed log cereal yields and temperature in 2013

-5

0

5

10
15
Temperature (C)

20

25

30

Notes: Observed country-level log cereal yields in 2013 with cross-sectional mean removed plotted against temperature in 2013. From equation (9), observed log cereal yield is sum of the nonlinear temperature relationship k(Tit ),controls Ψ′ Xit , and the residual term νit . Vertical line shows the predicted log yield maximizing temperature from
Figure 10.

.01

Figure E.5: Differences in welfare projections from projected changes in spatial correlation andyields
ARE

Spatial structure
reduces loss

Spatial structure
amplifies gain

KWT

OMN

Difference in welfare projection
-.005
0
.005

BEL
NLD
NZL
EGYCHL FRA
JPN
VNM
IDN
PNG
GUY
BRA
HUN
SUR
BGD
SLB
LAO
DOM
MYS
VEN
LKA
SAU
BLZ PHLPRY MMRROUECUMEX THACOL CRICIV KHM CUB
BTN INDPAN TLS
SLV
PAK
MDG
NPL
ZMB
ERI
BOL
NIC
GTM
IRQ
UGA
MWIDJI
SLE
GAB
TTO
KEN
CAF
GHA
HND
CMR
MLI
GIN
TZAGNBBEN
JAM
NGA LBR
MRT
BFA
SEN
HTI
BRN
YEM GMB
SOM
TCD
COG
TGO
AGO
LBY
COD
ZWE
MOZ
USA

KOR
CHN
ITA
ALB
ARG

BIH
GRC
PRT
ESP

PER

URY

BGR

ISR

ZAF
LBN

TUR

RWA
AUS

AFG
IRN

DZA

MAR

TUN
SYR

CYP
PSE

JOR
SWZ

LSO

BDI

IRL
DEU
GBR
DNK
CHE

AUT LUX
CZE

SWE
CAN

POL
PRK

FIN
NOR

FSU

MNG

SDN

-.01

NER
NAM

Spatial structure
amplifies loss-.5

Spatial structure
reduces gain

BWA

-.4

-.3
-.2
-.1
Projected yield change

0.1

Notes: Scatter shows the difference in projected country-level welfare change between projections that include andomit changes in spatial correlation (from Figure 12) plotted against change in log cereal yields over 2013–2099 underclimate change. Countries labeled by ISO3 identifier.

76

F

Appendix tables
Table F.1: Statistical significance of first-stage coefficients′ joint F-stat p-value
α11′ joint F-stat p-value
α12′ joint F-stat p-value
α21′ joint F-stat p-value
α22

(1)
0.022
0.006
0.071
0.041

(2)
0.007
0.038
0.004
0.062

(3)
0.011
0.097
0.007
0.028

(4)
0.011
0.178
0.006
0.041

(5)
0.008
0.218
0.003
0.071

Number of temperature splines in f ()Observations

2
5452

3
5452

4
5452

5
5452

6
5452

Notes: Shows p-values from joint significance F-tests across the elements of each vector′′′′of first-stage coefficients, α11and α12from equation (4), α21
and α22from equation (5).
Columns 1–5 correspond to the IV specifications in columns 2–6 of Table 2.

Table F.2: Alternative error structures
Outcome is log domestic share of expenditure
(1)
(2)
(3)
ln Ait (β0 )ln Ait × It (β1 )Clustering
Bekker adjustment
Observations

(4)

2.114
(0.604)[0.001]-4.144(1.834)[0.028]2.114(0.581)[0.001]-4.144(1.659)[0.016]2.114(0.830)[0.014]-4.144(2.157)[0.060]2.114(0.698)[0.004]-4.144(1.939)[0.037]

year cluster

year clusterand 20 year HAC
No
5452

year cluster
and cntry cluster
No5452

year cluster

No
5452

Yes
5452

Notes: Estimates of β0 and β1 from equation (3). Column 1 reproduces benchmark estimates fromcolumn 4, panel B of Table 2 with year-level clustered standard errors. Column 2 allows year-levelclustering and common serial correlation across countries within a 20-year window. Column 3 allows year
and country-level clustering. Column 4 allows year-level clustering with a Bekker (1994) adjustment.
Standard errors in parentheses; p-values in brackets.

77

Table F.3: Controlling for time-varying trade costs
Outcome is log domestic share of expenditure
(1)
(2)
(3)
(4)
ln Ait (β0 )ln Ait × It (β1 )2.114(0.604)[0.001]-4.144(1.834)[0.028]2.178(0.612)[0.001]-4.254(1.865)[0.027]2.163(0.593)[0.001]-4.189(1.825)[0.026]2.492(0.737)[0.001]-4.748(2.095)[0.028]

(5)

(6)

(7)

2.297
(0.641)[0.001]-4.227(1.844)[0.026]2.115(0.604)[0.001]-4.145(1.833)[0.028]2.270(0.796)[0.006]-4.281(1.985)[0.036]ln oil price × average ln λii
Yes
ln oil price × centrality
Yes
Year FE × average ln λii
YesYear FE × centrality
Yes
Export restrictions
Yes
Precipitation
Yes
Cragg-Donald F-stat
5.174
5.249
5.077
4.875
4.042
5.163
3.932
Stock-Yogo crit. value: 10% max LIML size
3.580
3.580
3.580
3.580
3.580
3.580
3.580
Kleibergen-Paap F-stat
3.963
3.911
3.903
4.146
3.523
3.967
3.497
Observations
5452
5452
5452
5452
5452
5452
5452
Notes: Estimates of β0 and β1 from equation (3). Column 1 replicates benchmark model from column 4, panel
B, of Table 2. Column 2 (3) controls for the interaction of global log oil price and cross-sectional average log
domestic share of expenditure (output-weighted inverse distance averaged across all other countries). Column 4(5) controls for the interaction of year fixed effects and cross-sectional average log domestic share of expenditure(output-weighted inverse distance averaged across all other countries). Column 6 controls for introductions of export
restrictions. Column 7 controls for quadratic precipitation terms. Standard errors, clustered by year, in parentheses;
p-values in brackets.

Table F.4: Sample splits
Outcome is log domestic share of expenditure(1)(2)
ln Ait (β0 )

(4)

2.114
(0.604)[0.001]-4.144(1.834)[0.028]2.152(0.595)[0.001]-4.226(1.925)[0.033]1.845(2.807)[0.517]-4.639(12.564)[0.715]1.692(0.511)[0.003]-2.708(1.627)[0.108]

No
1961-2013
5.174
3.580
3.963
0.000
5452

Yes
1961-2013
5.020
3.580
4.473
0.000
4952

No
1961-1987
1.628
3.580
1.137
0.000
2655

No
1988-2013
3.810
3.580
4.052
0.000
2793

ln Ait × It (β1 )Include large producers?
Sample period
Cragg-Donald F-stat
Stock-Yogo crit. value: 10% max LIML size
Kleibergen-Paap F-stat
Anderson-Rubin weak-id robust joint p-value
Observations(3)

Notes: Estimates of β0 and β1 from equation (3). Column 1 reproduces benchmark estimates from column 4,panel B of Table 2. Column 2 excludes the following ten countries, which together account for more than half ofworld cereal output in each year: China, United States, India, Former Soviet Union, France, Indonesia, Canada,
Brazil, Germany, and Bangladesh. Column 3 restricts sample to 1961–1987. Column 4 restricts sample to 1988–
2013. Standard errors, clustered by year, in parentheses; p-values in brackets.

78

Table F.5: Dynamic effects
Outcome is log domestic share of expenditure(1)(2)
ln Aitln Ait × It

2.217
(0.651)[0.001]-4.152(1.874)[0.031]ln Ait+1(4)
1.326(0.634)[0.041]-3.233(1.590)[0.047]0.724(0.503)[0.156]-0.830(1.642)[0.615]ln Ait+1 × It+1

ln Ait−1

0.851(0.526)[0.112]-2.039(1.354)[0.138]ln Ait−1 × It−1

2nd stage sample period
Include stored cereals?
Cragg-Donald F-stat
Stock-Yogo crit. value: 10% max LIML size
Kleibergen-Paap F-stat
Observations(3)

1962-2012
No
4.480
3.580
3.632
5237

1962-2012
No
5.688
3.580
2.592
5236

1962-2012
No
5.293
3.580
3.532
5235

1961-2013
Yes
5.345
3.580
3.622
5191

Notes: Estimates of β0 and β1 from equation (3). Column 1 reproduces benchmark model using log yields inyear t instrumented by December ENSO in years t and t − 1 and local temperature in year t. Column 2 uses log
yields in year t + 1, instrumented by December ENSO conditions in years t + 1 and t and local temperature inyear t + 1. Column 3 uses log yields in year t − 1, instrumented by December ENSO conditions in years t − 1 andt − 2 and local temperature in year t − 1. Column 4 uses log yields in year t to examine effects on a measure ofdomestic share of expenditure that includes stored cereals. Sample period for 2nd stage equation is 1962–2012 forcolumns 1-3 and 1961–2013 for column 4. Standard errors clustered by year in parentheses; p-values in brackets.

79

Table F.6: ENSO and local temperature definitions
Outcome is log domestic share of expenditure
(1)
(2)
(3)
Panel A: Crop-area-weighted country temperatureln Ait (β0 )2.114(0.604)[0.001]-4.144(1.834)[0.028]2.084(0.706)[0.005]-4.465(2.406)[0.069]2.722(0.987)[0.008]-6.026(3.127)[0.059]ENSO index
4334
Cragg-Donald F-stat
5.174
5.013
5.195
Stock-Yogo crit. value: 10% max LIML size 3.580
3.580
3.580
Kleibergen-Paap F-stat
3.963
2.897
3.993
Observations
5452
5452
5452
Panel B: Total-area-weighted country temperature

12
3.781
3.580
2.333
5452

ln Ait (β0 )ln Ait × It (β1 )ln Ait × It (β1 )ENSO index
Cragg-Donald F-stat
Stock-Yogo crit. value: 10% max LIML size
Kleibergen-Paap F-stat
Observations

2.108(0.715)[0.005]-4.064(2.414)[0.098](4)

1.632(0.500)[0.002]-3.960(1.617)[0.018]1.722(0.626)[0.008]-4.125(2.155)[0.061]

1.562(0.597)[0.012]-4.155(2.071)[0.050]1.871(0.729)[0.013]-4.517(2.331)[0.058]

4
4.423
3.580
3.490
5605

3
3.928
3.580
2.653
5605

34
4.186
3.580
3.344
5605

12
3.103
3.580
1.957
5605

Notes: Estimates of β0 and β1 from equation (3). Panel A uses crop-area-weighted country-level
temperatures. Panel B uses total-area-weighted country-level temperatures. Columns 1 to 4 use
NINO4, NINO3, NINO34, and NINO12 as ENSO index. Standard errors, clustered by year, inparentheses; p-values in brackets.

80Table F.7: Using spatial correlation of temperature instead of ENSO
Outcome is log domestic share of expenditure
(1)
(2)
(3)

(4)

(5)

2.486
(1.310)[0.063]-5.044(4.173)[0.232]1.647(0.618)[0.010]-2.348(1.943)[0.232]1.686(0.624)[0.009]-2.394(2.021)[0.241]ln Ait (β0 )ln Ait × It (β1 )2.540(1.182)[0.036]-5.135(4.011)[0.206]1.918(0.600)[0.002]-3.092(1.884)[0.107]

Number of temperature splines in f
2
3
4
5
6
Temperature Moran’s I polynomial order in g
1
1
1
1
1
Number of instruments
4
6
8
10
12
Cragg-Donald F-stat
6.407
5.267
6.161
5.428
4.846
Stock-Yogo crit. value: 10% max 2SLS bias
7.560
9.480
10.22010.58010.780Stock-Yogo crit. value: 10% max 2SLS size
16.87021.68025.64029.32032.880Stock-Yogo crit. value: 10% max LIML size
4.720
4.060
3.780
3.640
3.580
Kleibergen-Paap F-stat
2.813
2.217
2.145
2.389
2.061
BIC for first stage equations-30779.0 -30789.6 -30873.7 -30862.6 -30845.5
Observations
5452
5452
5452
5452
5452
Notes: LIML estimates of β0 and β1 from equation (3) with g(EN SOt + EN SOt−1 ) in first-stage
equations (4) and (5) replaced with the annual global spatial correlation of temperature, It (Tit ). Columns
show estimates that vary by the number of temperature spline terms in f (). All models include country
fixed effects, year fixed effects, and country-specific linear trends as included instruments. Standard
errors, clustered by year, in parentheses; p-values in brackets.

Table F.8: Alternative domestic expenditure share constructions
Outcome is log domestic share of expenditure
(1)
(2)
(3)
ln Ait (β0 )ln Ait × It (β1 )Price data
Price imputation
Drop outliers?
Cragg-Donald F-stat
Stock-Yogo crit. value: 10% max LIML size
Kleibergen-Paap F-stat
Observations

(4)

(5)

(6)

2.114
(0.604)[0.001]-4.144(1.834)[0.028]1.365(0.397)[0.001]-3.068(1.423)[0.036]1.825(0.559)[0.002]-3.622(1.585)[0.026]1.568(0.432)[0.001]-2.835(1.337)[0.039]1.249(0.430)[0.005]-2.452(1.152)[0.038]1.867(0.536)[0.001]-3.520(1.549)[0.027]

FAO
averageexport
No
5.174
3.580
3.963
5452

FAO
export+producer
No
8.049
3.580
3.864
2918

FAO
lowestexport
No
5.174
3.580
3.963
5452

FAO
highestexport
No
5.174
3.580
3.963
5452

Comtradeaverageexport
No
5.346
3.580
2.406
4148

FAO
averageexport
1%
5.259
3.580
3.832
5366

Notes: Estimates of β0 and β1 from equation (3). Column 1 reproduces benchmark estimates from column 4,panel B of Table 2 with average export-volume-weighted cereal export unit value used for imputing cereal-level
prices in constructing domestic expenditure share. Column 2 uses cereal-level export unit values with missing
observations imputed using producer prices to construct domestic expenditure. Columns 3 and 4 use cereal-level
export unit values with missing observations imputed using the lowest and highest observed export unit value fora given country and year, respectively. Column 5 replicates column 1 but constructs domestic expenditure shareusing Comtrade bilateral trade data instead of FAO trade data. FAO trade data available for 1961–2013. Comtrade
data available for 1962–2013. Column 6 replicates column 1 but drops observations with outcome variable being
in the bottom and top 1% of distribution. Standard errors, clustered by year, in parentheses; p-values in brackets.

81

Table F.9: Testing for heterogeneity in cereal-specific first-stage coefficientsFirst-stage equation (4)Temp. 1st term
Temp. 2nd term
Temp. 3rd term
Temp. 4th term
Temp. 1st term X (ENSOt + ENSOt−1 )Temp. 2nd term X (ENSOt + ENSOt−1 )Temp. 3rd term X (ENSOt + ENSOt−1 )Temp. 4th term X (ENSOt + ENSOt−1 )Temp. 1st term X (ENSOt + ENSOt−1 )2
Temp. 2nd term X (ENSOt + ENSOt−1 )2
Temp. 3rd term X (ENSOt + ENSOt−1 )2
Temp. 4th term X (ENSOt + ENSOt−1 )2BarleyMaize

Millet

Oats

Rice

Rye

Sorghum

Wheat

1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1

1
.048
2.3e-04
5.4e-03
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1
1
1
1
1

.7
1
.33
.41
1
1
1
1
1
1
1
1

First-stage equation (5)Temp. 1st term
1
1
1
1
1
1
1
.32
Temp. 2nd term
1
1
1
1
.45
1
1
1
Temp. 3rd term
1
1
1
1
.015
1
1
.11
Temp. 4th term
.87
1
1
1
.19
1
1
.095
Temp. 1st term X (ENSOt + ENSOt−1 )
1
1
1
1
1
1
1
1
Temp. 2nd term X (ENSOt + ENSOt−1 )
1
1
1
1
1
1
1
.33
Temp. 3rd term X (ENSOt + ENSOt−1 )
1
1
1
1
1
.57
1
.76
Temp. 4th term X (ENSOt + ENSOt−1 )
1
1
.6
1
1
1
.74
1
Temp. 1st term X (ENSOt + ENSOt−1 )2
1
1
1
1
1
1
1
1
Temp. 2nd term X (ENSOt + ENSOt−1 )2
1
1
1
1
1
1
1
1
Temp. 3rd term X (ENSOt + ENSOt−1 )2
1
1
1
1
1
1
1
1
Temp. 4th term X (ENSOt + ENSOt−1 )2
1
1
1
1
1
1
1
1
Notes: This table reports the p-values from tests that the coefficients from estimating first-stage equations (4)and (5) for cereal-specific yields for the cereal listed in each column are equal to the coefficients in our benchmark
first-stage estimates for aggregate cereal yields. The p-values of these pairwise cross-model tests incorporate a
Bonferroni correction for multiple-hypothesis testing.

82

Table F.10: Log cereal yield and local temperature
Outcome is log cereal yields
(1)
(2)
(3)
(4)
Temperature 1st term

Temperature 2nd term

Temperature 3rd term

Temperature 4th term

0.004
(0.009)[0.686]-0.183(0.041)[0.000]0.650(0.160)[0.000]-1.162(0.533)[0.034]0.004(0.009)[0.677]-0.165(0.040)[0.000]0.599(0.159)[0.000]-1.100(0.539)[0.047]

Temperature 5th term

0.005
(0.010)[0.629]-0.222(0.071)[0.003]0.418(0.196)[0.038]0.356(0.649)[0.586]-2.204(1.775)[0.220]0.005(0.010)[0.631]-0.203(0.071)[0.006]0.393(0.196)[0.050]0.248(0.644)[0.702]-1.801(1.760)[0.311]

Temperature 6th term

Precipitation

0.003(0.001)[0.000]-0.000(0.000)[0.000]Precipitation squared

Number of temperature splines
Precipitation
Temp. joint p-value
Optimal temp.
Observations

4No
0.0004
8.81
7226

4
Yes
0.0014
8.91
7226

(5)

(6)

0.007
(0.011)[0.519]-0.126(0.060)[0.041]0.020(0.212)[0.924]1.320(0.674)[0.056]-2.895(1.880)[0.130]1.830(3.814)[0.633]0.005(0.011)[0.623]-0.100(0.059)[0.093]-0.031(0.205)[0.882]1.394(0.658)[0.039]-3.370(1.864)[0.076]
3.213(3.791)[0.401]
0.003(0.001)[0.000]-0.000(0.000)[0.000]6No0.0015
7.80
7226

6
Yes
0.0049
7.70
7226

0.003
(0.001)[0.000]-0.000(0.000)[0.000]5No0.0009
8.87
7226

5
Yes
0.00308.94
7226

Notes: Estimates of cubic spline terms for k() in equation (9) during 1961–2013. The number of knots
placed along the temperature support according to Harrell (2001) varies across columns. Odd (even)numbered columns exclude (include) quadratic precipitation terms. P-value from a joint significance testof temperature terms shown. Standard errors, clustered by year, in parentheses; p-values in brackets.

83