Essays on International Economics

A DISSERTATION

SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA

BY

Mauŕıcio Barbosa-Alves

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

Doctor of Philosophy

Manuel Amador, Co-Advisor

Timothy J. Kehoe, Co-Advisor

June, 2025



Acknowledgements

I am profoundly grateful to Manuel Amador, Tim Kehoe, and Doireann Fitzgerald

for their exceptional guidance and mentorship throughout my academic journey. Beyond

economics, each of you fostered a humane and supportive environment that shaped not only

my research but also the kind of mentor I hope to become. I am also sincerely thankful

to Mike Waugh for his remarkable accessibility and insightful feedback throughout the

development of this thesis. I thank Javier Bianchi for the opportunity to collaborate and

for the meaningful interactions that ultimately helped shape my research perspective.

I feel extraordinarily fortunate to have had Braulio Britos as both a close friend and

co-author. Our collaboration gave me the freedom to explore my curiosity about economic

phenomena. It helped sharpen my intuition and analytical skills. The time we spent

working—and laughing—together will remain unmatched.

I am deeply thankful to Vladimir Kuhl Teles, who recognized my potential during

my master’s studies in Brazil and strongly advocated for me. I am also grateful to my

master’s co-advisor, Luis Araujo, and to Professor Tiago Cavalcanti, whose unwavering

support during that formative period was greatly appreciated.

I’m also particularly grateful for the support and encouragement from Brazilian col-

leagues and friends whose long-distance support was essential: Douglas Bokliang, Nicolas

Borsoi, Augusto Chaparin, Diego de Sousa Rodrigues, Thiago Ferreira, Gabriela Fonseca,

Liz Matsunaga, Luis Menon, Artur Nascimento, Victor Wong, and Lucas Zaniboni.

Many friends and colleagues offered invaluable comments and posed challenging ques-

tions that significantly enriched my work. I am especially thankful for the many conver-

sations shared with Diego Ascarza-Mendoza, Gabriel Devoto, René Dı́az de León, Jakub

Pawelczak, and Tomas Rose. With each of them, I shared not only research discussions

i



but also meaningful friendships, something I will deeply miss. I appreciate the cheer and

support from Pilar Barros, Teresa Balestrini, Hasan Cetin, and Angelo Mendes. I have

also greatly benefited from feedback during presentations and informal conversations with

many others. In particular, I would like to thank Ricardo Alves Monteiro, Marco Bassetto,

Illenin Kondo, Joseph Mullins, and Kjetil Storesletten.

Ultimately, I am grateful to my family for their tenacious support and encouragement

throughout every stage of my education. None of this would have been possible without

them. I am deeply grateful to my parents, Eliana and Josafá, and my brothers, Gabriel and

Pedro. My grandparents, João Diońısio and Maria, instilled in me the strongest parts of

my work ethic. I owe much of the curiosity that led me here to the inspiring conversations

I shared with my Uncle Rogério and my Aunt Eudes—two honorable role models in many

dimensions. Lastly, I am especially grateful to my wife, Bruna, whose indefatigable belief

in me has been a constant source of strength, joy, and energy.

ii



Dedication

To my extended family,

who took turns sleeping in front of a school when I was six just so I could have a place

there. Those three days planted the seed for everything that followed.

To my mother, Eliana,

who sacrificed her career so I could attend a better school on a scholarship during my

early years. That act of love and selflessness has shaped my view of education—and my

life.

To my wife, Bruna,

who selflessly put her own life on hold to follow me through every step of this Ph.D.

journey. Your support made this journey possible.

iii



Abstract

This dissertation comprises three interconnected chapters, each co-authored with Braulio

Britos. The first chapter provides an extensive literature review that sets the stage and

informs the analyses in the subsequent chapters. We synthesize existing research on the

economic implications of climate change, with a focus on adaptation strategies that in-

volve migration and trade. The following chapters share common features, including the

role of adaptation strategies, the frictions that hinder such adaptation, and how we utilize

short-run variations in weather to recover estimates of the severity of these frictions. We

then use these estimated frictions to estimate the effects of new long-term productivity

distributions, both over time and across space, on variables of interest.

In Chapter 2, we investigate the influence of climate change on patterns of international

migration, utilizing census data from Guatemala. We uncover novel empirical evidence in-

dicating that regions experiencing higher temperatures see a decrease in migration during

the subsequent year, with this effect being particularly pronounced in rural areas. We

propose that elevated temperatures temporarily diminish rural productivity, consequently

reducing the capacity of credit-constrained workers to afford migration costs. Thus, climate

change exerts dual pressures: while diminished rural productivity potentially enhances the

incentive to migrate, it simultaneously restricts individuals’ financial capacity to do so.

We develop and estimate a dynamic, incomplete-markets migration model featuring credit

constraints and explicit migration costs, where increased temperatures negatively impact

agricultural productivity. By calibrating our model to replicate the empirical temperature-

migration relationship, we project future rural productivity under various climate scenarios.

Our findings indicate a gradual increase in migration rates across all scenarios as workers

preemptively save to afford migration, reflecting a substantial degree of anticipation. Ad-

ditionally, we demonstrate that weather-contingent financial transfers, though potentially

assisting in covering migration expenses, paradoxically reduce migration by providing in-

surance against temperature-induced income losses, thus making staying in affected areas

relatively more attractive.

In Chapter 3, we analyze the impacts of climate change on food prices across regions

iv



and income groups, looking into Brazilian data. As climate change alters comparative

advantages in food production across goods and over space, existing trade frictions impede

effective adaptation through sourcing adjustments, compelling reliance on local sourcing,

and thereby pushing up food prices. Low-income households are relatively more exposed to

food price fluctuations, as they tend to have higher food expenditure shares. We construct

a spatial trade model that incorporates income heterogeneity and two distinct categories

of food goods, characterized by varying degrees of costs associated with transportation

and trade. This approach enables us to break down welfare losses attributable to climate

change into specific contributions from food expenditure shares, trade shares, and pro-

ductivity shifts. Leveraging Brazilian data, we estimate intranational trade relationships

by observing responses to short-term weather variability, price fluctuations, and driving

times between locations. Our empirical results indicate that trade costs for fresh foods

are twice as sensitive to driving time as those for commodity goods, which incur relatively

lower trade costs. Counterfactual analyses based on projected productivity changes reveal

notable welfare losses, as well as substantial heterogeneity. The most exposed households

would be willing to compromise approximately 3% of their income to prevent anticipated

productivity deterioration. Finally, we argue that investments aimed at enhancing road

infrastructure emerge as an effective mitigation strategy, as they decrease trade costs, and

promote integration. Households in certain states would be willing to pay up to 0.8% of

their income to achieve a 10% improvement in average driving speeds nationwide.

v



Contents

Acknowledgements i

Dedication iii

Abstract iv

List of Tables x

List of Figures xii

1 Critical Review of the Literature 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Productivity Changes and Distributional Effects . . . . . . . . . . . . . . . 2

1.3 Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Trade Frictions and Price Pass-Through . . . . . . . . . . . . . . . . . . . . 6

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Climate Change and International Migration 8

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 High Heat and Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2 Reduced-Form Estimates . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 A Model of Migration and High-Heat Shocks . . . . . . . . . . . . . . . . . 19

2.3.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.2 The Migration Problem . . . . . . . . . . . . . . . . . . . . . . . . . 22

vi



2.3.3 The Importance of Monetary Migration Costs . . . . . . . . . . . . . 24

2.4 Model Solution and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4.1 Externally Calibrated Parameters . . . . . . . . . . . . . . . . . . . 26

2.4.2 Link between High-Heat Shocks and Rural Productivity . . . . . . . 27

2.4.3 Simulated Method of Moments . . . . . . . . . . . . . . . . . . . . . 28

2.4.4 Migration and Savings Decisions . . . . . . . . . . . . . . . . . . . . 30

2.4.5 Climate Change Projections . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 The Effects of Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5.2 The Role of Anticipation . . . . . . . . . . . . . . . . . . . . . . . . 40

2.6 Unconditional Cash Transfers and Migration . . . . . . . . . . . . . . . . . 41

2.6.1 Universal Cash Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6.2 Cash Transfer Conditional on Bad Weather . . . . . . . . . . . . . . 44

2.6.3 Comparing the Transfer Schemes . . . . . . . . . . . . . . . . . . . . 45

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 Climate Change, Food Prices, and Inequality 51

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2.1 The Trade Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 Equivalent Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3.1 Climate change through the lens of the Model . . . . . . . . . . . . . 61

3.4 Recovering the Trade Frictions . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4.1 From Heat Shocks to Prices Changes . . . . . . . . . . . . . . . . . . 64

3.4.2 Weather Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.4.3 Consumer Price Index Data . . . . . . . . . . . . . . . . . . . . . . . 66

3.4.4 Structure for the Trade Shares . . . . . . . . . . . . . . . . . . . . . 68

3.5 Preferences and Model Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.5.1 Utility Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.5.2 Calibrating the Parameters . . . . . . . . . . . . . . . . . . . . . . . 80

3.6 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.6.1 Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

vii



3.6.2 Climate Change Scenarios . . . . . . . . . . . . . . . . . . . . . . . . 86

3.6.3 Improving the Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.7 Discussion and Potential Extensions . . . . . . . . . . . . . . . . . . . . . . 97

3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

References 101

Appendix A. Appendix to Chapter 2 111

A.1 Reduced-form Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

A.1.1 Exposure and Migration Rates . . . . . . . . . . . . . . . . . . . . . 112

A.1.2 Link Between Weather and Rural Transitory Shocks . . . . . . . . . 113

A.2 Other Specification Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

A.2.1 A model with non-monetary migration costs . . . . . . . . . . . . . . 116

A.2.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . 119

A.3 Estimation of ση . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A.3.1 Main Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A.3.2 Alternative Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A.4 Simulated Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . 128

A.4.1 Computing the Stationary Distribution . . . . . . . . . . . . . . . . 128

A.4.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

A.4.4 Dealing with the Stochastic βe . . . . . . . . . . . . . . . . . . . . . 131

A.4.5 Sampling from the stationary Distribution . . . . . . . . . . . . . . . 132

A.5 Climate Change Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

A.5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

A.5.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A.6 Additional Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

A.6.1 Stock of Migrants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

A.6.2 Stationary Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 140

A.6.3 Probability of Receiving the Transfer . . . . . . . . . . . . . . . . . . 144

A.6.4 Alternative Cash-Transfers Amounts for same UCT schemes . . . . . 145

A.7 Interpretation of ν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

viii



A.8 Identification of Estimated Parameters . . . . . . . . . . . . . . . . . . . . . 151

Appendix B. Appendix to Chapter 3 156

B.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

B.1.1 Exposure Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

B.1.2 Crop Production Data . . . . . . . . . . . . . . . . . . . . . . . . . . 159

B.1.3 CPI Data — Additional Details . . . . . . . . . . . . . . . . . . . . . 164

B.1.4 Brazilian Central Bank Classification for Goods and Services . . . . 170

B.1.5 Matching Crops from IBGE and GAEZ . . . . . . . . . . . . . . . . 171

B.1.6 Construction of µxℓ and T xℓ . . . . . . . . . . . . . . . . . . . . . . . 171

B.1.7 Construction of the Relative Wages . . . . . . . . . . . . . . . . . . 176

B.1.8 Counterfactual Measures of µxℓ . . . . . . . . . . . . . . . . . . . . . 178

B.2 Model: Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

B.2.1 Ideal Price Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

B.2.2 Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

B.2.3 Trade Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

B.2.4 Indirect Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

ix



List of Tables

2.1 Exposure on Rural Migration Rate . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Externally calibrated parameters . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3 Targeted Moments and Parameter Results . . . . . . . . . . . . . . . . . . . 29

2.4 Stock of Migrants in the U.S. under different Transfer Schemes and Scenarios 46

2.5 Annual Cost of the Unconditional Cash Transfers . . . . . . . . . . . . . . 48

3.1 Descriptive statistics for alternative measures of Driving Distance . . . . . 72

3.2 Regression (3.32), estimated by Nonlinear Least Squares . . . . . . . . . . . 75

3.3 Outcome for regression (3.32) under alternative regressors . . . . . . . . . . 77

3.4 Model parameters under the benchmark calibration . . . . . . . . . . . . . 84

A.1 Effect of Exposure on Corn yields . . . . . . . . . . . . . . . . . . . . . . . . 113

A.2 Effect of Exposure on Migration Rate by Percentage of Rural Population . 114

A.3 Effect of Exposure on Emigration Rate for Different Temperature Thresholds115

A.4 Regression estimating ηi . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

A.5 Interval allowed for each parameter . . . . . . . . . . . . . . . . . . . . . . . 130

A.6 Stock of Migrants in the U.S. under different Scenarios and Policies (5%

transfer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

A.7 Annual Cost of the Unconditional Cash Transfers Policies (5% transfer) . . 146

A.8 Stock of Migrants in the U.S. under different Scenarios and Policies (20%

transfer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

A.9 Annual Cost of the Unconditional Cash Transfers Policies (20% transfer) . 148

A.10 Interval allowed for each parameter . . . . . . . . . . . . . . . . . . . . . . . 151

A.11 Statistical Description over 2,500 sampled pairs for (me, ν) . . . . . . . . . . 153

A.12 Covariance Matrix over 2,500 sampled pairs for (me, ν) . . . . . . . . . . . 154

x



A.13 Model’s moment and estimated parameters . . . . . . . . . . . . . . . . . . 154

B.1 Regression (B.3) results: Rice . . . . . . . . . . . . . . . . . . . . . . . . . 161

B.2 Regression (B.3) results: Soybean . . . . . . . . . . . . . . . . . . . . . . . 162

B.3 Regression (B.3) results: Beans . . . . . . . . . . . . . . . . . . . . . . . . . 163

B.4 Locations for which CPI data is available . . . . . . . . . . . . . . . . . . . 166

B.5 Crops matched between GAEZ and the IBGE . . . . . . . . . . . . . . . . 173

xi



List of Figures

2.1 Migration Rates and High Temperatures . . . . . . . . . . . . . . . . . . . 15

2.2 Effect of Exposure on Migration Rate by Percentage of Rural Population . 18

2.3 Probability of Migration for low and high productivity workers . . . . . . . 31

2.4 Savings Decisions for low and high productivity workers by high-heat shocks 32

2.5 Average Productivity Relative to Baseline by Scenario . . . . . . . . . . . . 35

2.6 Effect of Climate Change on Migration Flows . . . . . . . . . . . . . . . . . 37

2.7 Effect of Climate Change on the High-Heat Migration link (βe) . . . . . . . 39

2.8 Effect of Anticipation on Migration Flows by Scenario . . . . . . . . . . . . 40

2.9 Effect of a Universal UCT on Migration Flows . . . . . . . . . . . . . . . . 42

2.10 Effect of a Bad-Weather UCT on Migration Flows . . . . . . . . . . . . . . 44

3.1 Spatial Correlations of Heat and Inflation . . . . . . . . . . . . . . . . . . . 76

3.2 Food Expenditure Share Across the Income Distribution . . . . . . . . . . 83

3.3 Percent Change in Yields, Optimistic Scenario, 2040 . . . . . . . . . . . . . 89

3.4 Log change in µxℓ across the states, Optimistic Scenario, 2040. . . . . . . . . 90

3.5 Percent Change in Average Potential Productivity, µ̂xℓ , Optimistic Scenario,

2040 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.6 Equivalent Variation across the states, Optimistic Scenario, 2040 . . . . . . 92

3.7 Equivalent Variation and change in HTC productivity . . . . . . . . . . . . 93

3.8 Alternative measures of driving frictions . . . . . . . . . . . . . . . . . . . . 95

3.9 Equivalent Variation from Road Improvement, first income decile, . . . . . 97

A.1 Effect of Exposure on Rural Migration Rates by Temperature Threshold . 112

A.2 Targeted moments as a function of τ . . . . . . . . . . . . . . . . . . . . . 117

A.3 Permanent productivity grid . . . . . . . . . . . . . . . . . . . . . . . . . . 122

xii



A.4 Asset grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

A.5 Implied mass of agents trying to Emigrate . . . . . . . . . . . . . . . . . . . 134

A.6 Temperature Increase by Climate Change Scenario . . . . . . . . . . . . . . 135

A.7 Exposure Distribution for Baseline (1995-2014) and by Scenario in 2100 . . 137

A.8 Effect of Climate Change on Stock of Migrants . . . . . . . . . . . . . . . . 139

A.9 Effect of Anticipation on Stock of Migrants . . . . . . . . . . . . . . . . . . 140

A.10 Stock of Migrants by Productivity at the Initial and Final stationary state

for each Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

A.11 Final Asset PDF at the Initial and Final stationary state for each Scenario 142

A.12 Stock of Migrants by Productivity for each Scenario and UCT scheme at the

Final stationary state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

A.13 Probability of Receiving the Transfer . . . . . . . . . . . . . . . . . . . . . 144

A.14 High-heat migration link and stock of migrants in the U.S. by migration cost 152

A.15 High-heat migration link and stock of migrants in the U.S. by disutility of

living in the U.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

B.1 Exposure to temperature thresholds . . . . . . . . . . . . . . . . . . . . . . 157

B.2 Locations for which the CPI data is available . . . . . . . . . . . . . . . . . 165

B.3 Measures for the historical µxℓ for LTC and HTC food goods. . . . . . . . . 174

B.4 Spatial correlation for µxℓ for LTC and HTC food goods. . . . . . . . . . . 175

B.5 Relative wage costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

xiii



Chapter 1

Critical Review of the Literature

1.1 Introduction

This chapter reviews the literature that underpins the analyses in Chapters 2 and

3. Chapter 2 examines migration as an adaptation strategy to confront the challenges of

climate change, with a focus on data from Guatemala. Chapter 3 examines trade as a

channel of adaptation, utilizing data from Brazil to investigate how food prices respond

and how these responses vary across income distribution and different regions.

The discussion in the following chapters draws on several interconnected strands of

literature related to the economic impacts of climate change. Bilal and Stock (2025) present

a recent and valuable overview of the macroeconomic consequences of climate change. We

build on that by reviewing work related to migration and trade as adaptation strategies

alongside the theoretical frameworks that guide our analysis.

We structure the literature review around three main themes. The first section exam-

ines how climate change affects the productivity of production factors and the resulting

sectoral and distributional consequences. The second section focuses on models of migra-

tion, particularly those that address climate-induced migration and recent developments

in migration theory. The third section investigates trade costs and the pass-through of

shocks to prices and other economic outcomes.

1



1.2 Productivity Changes and Distributional Effects

Climate Change will transform agricultural productivity, crop by crop and location

by location (Gutiérrez et al., 2021). Using a version of the Global Agro-Ecological Zones

(GAEZ) dataset crafted by the Food and Agriculture Organization (FAO) of the United

Nations, Costinot et al. (2016) analyzes how living standards across the globe would change

due to these changes in agricultural productivity, developing a model in the family of Eaton

and Kortum (2002). A pivotal contribution is to demonstrate how to integrate the latent

variable of potential productivity across the spectrum of crops, from specialist estimates,

into economic models of specialization and trade. The key idea exploited by the authors is

that changes in productivity are heterogeneous both across crops and within a country, as

well as across countries. As a result, new comparative advantages emerge, and re-optimized

production and trade patterns serve as a device to undo potentially adverse consequences

of Climate Change.

Bilal and Känzig (2024) constructs a long panel of temperature innovation at the coun-

try level and uses it to document substantial and persistent declines in global economic

activity following a temperature shock. The authors then use their estimates to motivate

and estimate a macroeconomic model with the main features of Nordhaus (1992) and lever-

age it to structurally estimate the damage functions to capital associated with temperature

increases.

Cruz and Rossi-Hansberg (2024) estimates productivity and amenity losses due to

rising temperatures, predicting welfare costs of up to 20% in parts of Africa and Latin

America, when considering the most extreme scenario provided in Gutiérrez et al. (2021).

Despite these significant losses, frictions in trade and migration open up opportunities for

substantial gains in some locations, with the welfare of some countries increasing by 5

Nath (2025) shows that rising temperatures tend to decrease labor productivity, with

the effects being more pronounced in the agricultural sector relative to the nonagricultural

sector of an economy. Then, the author articulates that high trade costs, together with

non-homothetic preferences, limit the capacity for sectoral reallocation from agriculture to

non-agriculture in countries experiencing climate change and at the early stages of economic

development.

2



Similarly, Somanathan et al. (2021) documents productivity declines in Indian manu-

facturing due to high-temperature exposure. Castro-Vincenzi et al. (2024) illustrates firms’

adaptive strategies in response to climate-induced supply chain disruptions. The key mech-

anism is that firms diversify their suppliers when they face disruptions from flooding, a

common event in India. The authors show that firms decide to source from suppliers that

are more expensive and far apart. The extent to which this adaptation takes place is

limited by trade frictions across space.

Do rising temperatures affect the total factor productivity (TFP) level or growth rate?

Casey et al. (2023) argues that rising temperatures affect the level of TFP but not its

growth rate. As a result, the per capita GDP growth rate slows temporarily but not

permanently, leading to sizable costs associated with climate change, albeit smaller than

those reported in existing literature.

Adamopoulos and Restuccia (2022) draws on the GAEZ dataset (GAEZ, 2000) to

document how frictions lead to misallocation in terms of crop choice. Due to existing

frictions in trade and financing, farmers often choose crops that are not necessarily the

ones with the highest attainable yields for their land. Depending on the pattern of changes

in productivity across crops and space, these frictions can be exacerbated, leading to further

misallocation.

Hsiang and Jina (2014) builds a panel of occurrences of cyclones across countries

between 1950 and 2008 to study how natural disasters affect capital, investment, and

income. The authors document substantial and robust declines in income that persist even

after twenty years. Using U.S. county-level data for daily temperature, precipitation, and

windspeed, Bilal and Rossi-Hansberg (2023) documents that an increase of 1◦C in global

temperature increased the probability of extreme events such as storms and heatwaves.

The authors then examine the responses of employment, investment, and income to such

extreme events, particularly in coastal regions.

Multiple theoretical contributions enabled researchers to overcome the computation

burden necessary to understand the distributional consequences of changes to economic

fundamentals, such as productivity. Fajgelbaum and Khandelwal (2016) builds a method-

ology to measure gains from trade across the income distribution within countries up to a

change in fundamentals. The key idea is that households’ expenditure shares vary across

3



the income distribution, and these shares serve as a measure of “exposure” to changes in

the fundamentals of these sectors.

Similarly, Adao et al. (2017) develops a method that allows for the computation of

welfare analysis under counterfactual scenarios without imposing structure on production

or preferences for a class of models of international trade. Costinot et al. (2016) uses the

“first-order” approach to compute welfare changes associated with productivity changes

in agriculture. The authors build around the insight that land usage shares across crops

within a country serve as the measure of exposure to productivity changes across the

crop spectrum. These approaches draw parallels with “static hat algebra” (Costinot and

Rodŕıguez-Clare, 2014) and the dynamic version of it (Caliendo et al., 2019).

Related to climate change and adaptation, Barreca et al. (2016) suggests that adapta-

tion to air conditioning is a margin of adjustment to higher temperatures and preventing

heat-related death in the United States. Fried (2024) explores how shifts in the distribu-

tion of temperature induced by Climate Change induce heterogeneous welfare costs. The

author focuses on the use of capital and energy in cooling and heating, as well as the

costs associated with equipment acquisition and usage. The key findings show substan-

tial heterogeneity across the income distribution and locations in the United States. Oni

(2024) analyzes energy price volatility, highlighting disproportionate economic impacts on

lower-income households in a setting.

1.3 Migration

Migration serves as a significant adaptive response to climate change, particularly in

developing regions where agricultural livelihoods are highly vulnerable to environmental

fluctuations (Clement et al., 2021; Mbow et al., 2019).

Bazzi (2017) provides evidence for the case of Indonesia, documenting that positive in-

come shocks from agriculture notably increase international migration, particularly among

financially constrained rural populations. In Chapter 2, we distill a similar effect but look

into international migration. Using data from Guatemala, we demonstrate that adverse

productivity shocks result in declines in international migration outflows.

Cattaneo and Peri (2016) analyzes the rural migration to cities or internationally by

using data from 115 countries between 1960 and 2000. The authors document that the

4



migration response to warming temperatures over time depends on the stage of development

of the affected country. For middle-income countries, warming temperatures increase rural

migration, whereas they decrease in low-income countries. The authors argue that liquidity

constraints are relatively more significant for rural residents of low-income households.

Using a detailed panel of rural houses in Mexico, Jessoe et al. (2018) investigate the

effects of high temperatures on local employment and wages. The authors document that

high temperatures lead to a reduction in local employment. On the migration side, they

argue that extreme heat increases domestic migration to urban areas and internationally

to the United States. Similarly, our study in Chapter 2 emphasizes the importance of

accounting for heat realization during the growing season of the main crops. A key depar-

ture in our paper is not to extrapolate the short-run findings; instead, we will use weather

innovations as a device to estimate migration costs.

The theoretical model of migration we develop builds on Lagakos et al. (2023), which

articulates the view that migration is a costly, long-run, forward-looking decision by pre-

senting a structural framework explicitly linking credit market imperfections to restricted

migration opportunities. Bilal and Rossi-Hansberg (2023), who use spatial migration mod-

els to evaluate anticipated changes in regional amenities and capital depreciation rates in

the United States. The authors emphasize the anticipatory behavior of migrants: the ex-

pectation that more challenging local conditions will prevail induces households to migrate

and anticipate migration behavior. Caliendo et al. (2019) presents a model of migration

and trade in a dynamic setting without asset accumulation on the household side.

Conte (2024) studies the effects of Climate Change on migration and welfare, focusing

on the countries in sub-Saharan Africa. The region is of particular interest since both

migration and trade costs are salient across the countries in the region, rendering the

welfare costs substantially higher than reduced-form estimates from the literature. The

author finds a trade-off between lowering migration barriers and promoting heterogenous

effects within the region. The key to this trade-off is that households would leave poor,

low-productivity areas if migration costs were to decrease.

Focusing on Brazil, Pellegrina and Sotelo (2024) shows that reducing migration costs

through improved road infrastructure allows farmers to take advantage of previously un-

tapped comparative advantages. As connectivity between regions improves, farmers move

5



westward and specialize in crops that are globally tradable commodities by gaining access

to high-productivity land.

1.4 Trade Frictions and Price Pass-Through

Anderson and Van Wincoop (2004) offers a comprehensive literature review on trade

costs. Trade frictions and costs limit the extent to which trade can serve as an adaptation

strategy in addressing climate-related productivity changes (Cruz and Rossi-Hansberg,

2024). A variety of models provide log-linear relationships between trade flows between

locations and trade costs, and predominantly the one developed in (Eaton and Kortum,

2002). The usual approach in the international trade literature is to project bilateral

trade flows on source and destination fixed effects, together with a set of variables that

are associated with barriers to trade, such as distance, common language, and shared

border. Baier et al. (2018) offers an excellent treatment of this approach, from modeling

to estimation.

For studies of trade within a country (also known as intra-national trade), trade flows

are generally not readily available. Agnosteva et al. (2014) exploits the availability of such

trade flow from Canada to estimate the intra-national cost. Otherwise, Atkin and Don-

aldson (2015) offers a summary of the challenges in measuring intra-national trade costs.

Researchers have developed various approaches to overcome this limitation. Advocating for

the importance of intra-national trade costs, Ramondo et al. (2016) argues that accounting

for domestic frictions to trade helps improve model fit to the data relative to international

trade models that assume complete frictionless domestic integration.

A large portion of the literature infers these trade costs from observed price differ-

entials across locations with a country (Allen and Atkin, 2022; Donaldson and Hornbeck,

2016; Pellegrina, 2022), exploiting different margins of either their setting or their available

data. Donaldson (2018) looks into archival data from Colonial India and argues that price

differences between locations for a commodity produced in a single area reflect the cost

of transporting that commodity from the origin to the destination where it is consumed.

With a similar approach, Asturias et al. (2019) utilizes price differentials of intermediary

inputs produced under monopolistic conditions to estimate trade frictions, directly relating

these price dispersions to spatial distances and infrastructure quality.

6



In the context of agricultural markets, Sotelo (2020) uses price dispersion in Peruvian

coffee markets along with road quality data to estimate trade costs. Similarly, Pellegrina

(2022) examines Brazilian agricultural markets, using deviations in farm gate prices to

derive trade elasticities and their relationship with transportation time. This literature

highlights substantial variability in trade friction sensitivities between perishable and non-

perishable goods.

Further, the literature on pass-through effects examines how shocks influence con-

sumer prices. Auer et al. (2022) investigates differential impacts of exchange rate shocks,

while Fitzgerald (2008) analyzes how trade costs mediate the transmission of exchange rate

volatility to consumer prices. Faccia et al. (2021) explores the impact of extreme weather

events on price dynamics, documenting heterogeneous responses based on the level of devel-

opment of the country and the relative price of food goods. Fitzgerald (2012) uses bilateral

trade flow data to study the extent to which trade and asset frictions impede risk sharing

among countries. Fitzgerald (2008) studies how trade costs preclude the pass-through from

exchange rate movements to consumer prices.

1.5 Conclusion

The literature on the economic effects of climate change has recently developed quickly.

The existence and availability of granular weather data allowed researchers to correlate

locally exogenous events from the weather and economic outcomes of interest. As expressed

above and pointed out in Bilal and Stock (2025), there is, however, substantial debate and

uncertainty regarding the extent to which these estimates are globally robust, whether they

are helpful as predictions for what can happen in the long run because of Climate Change.

The subsequent chapters share several common themes: exploring the role of adapta-

tion strategies, identifying frictions that impede these adaptations, and leveraging short-

term weather variations to estimate the severity of these frictions. We then use these

estimated frictions to project the effects of long-term changes in productivity distribu-

tions—both over time and across different regions—on key economic outcomes: migration

flows and local food prices, for example.

7



Chapter 2

Climate Change and International

Migration

2.1 Introduction

Migration is one of the main adaptation mechanisms individuals have against climate

change. By 2050, climate change could lead to more than 216 million internal migrants

alone (Clement et al., 2021). Effects are likely to be stronger in developing rural countries,

where elevated temperatures can cause reductions in crop yields and suitable lands for

farming (Mbow et al., 2019). Using census and satellite weather data for Guatemala, we

document a negative link between high temperatures and migration rates to the U.S. We

postulate that the mechanism behind this relationship arises from high heat reducing rural

productivity and preventing credit-constrained workers from migrating. Under this setting,

the effects of climate change are two-sided. The decline in rural productivity generated

by climate change impoverishes stayers, making migration more appealing. On the other

hand, it makes it harder for workers to pay the associated monetary migration costs.

We quantify the effects of climate change on international migration flows from Guatemala

to the U.S. We build a dynamic incomplete-markets model with migration and estimate it

to match our high-heat migration link observed in the data. In our model, workers observe

the future decline in rural productivity due to climate change and react to it. At the same

time, they are subject to high-heat shocks that translate into lower rural productivity,

8



affecting their income and the possibility of migration. The model predicts an increase

in migration once workers become aware of climate change. The increase is slowed by

the necessity for low-income workers to accumulate enough assets to cover the migration

cost. This increase is sustained as climate conditions deteriorate. Our findings also reveal

significant but delayed anticipation effects. Under a scenario where workers cannot antici-

pate the decline in rural productivity, initial migration flows are marginally lower than in

our baseline scenario with perfect foresight. Over time, however, the gap between these

scenarios widens considerably as migrants in the no-anticipation scenario are delayed in

initiating savings for migration.

Policies seeking to provide financial support to countries disproportionately affected by

climate change are focal points of discussions in international policy circles1. We use the

model to analyze the effects of these policies under the form of unconditional cash transfers

(UCTs) for two eligibility schemes, where we allow an external agent to give transfers to

workers subject to eligibility criteria. In the first scheme, the transfer is given to every

worker in the home economy. Under this policy, we find that migration flows increase in

most cases, as the transfer helps low-income workers to accumulate assets and eventually

pay the migration cost. In the second scheme, the policy consists of a transfer to workers

in regions that suffered an extreme high-heat shock,2 a policy comparable to anticipatory

weather-contingent cash-transfers programs3. We find that migration flows decrease as the

transfer helps risk-averse households to hedge against negative weather shocks, reducing

incentives to migrate. Counterintuitively, although these weather-contingent transfers can

facilitate covering migration costs, their insurance effect makes staying in Guatemala more

attractive.

A crucial element in our analysis is to estimate the relationship between high heat and

migration. For this estimation, we obtain hourly data on temperature for Guatemala at a

high degree of spatial granularity. Using this dataset, we compute the number of hours, in

1At the 27th United Nations Climate Change Conference (COP27), climate reparation or “loss and

damages” policies were a key item in the agenda (UNFCCC, 2023).
2We define the extreme high-heat shock as a drop in productivity of 40%.
3Similar programs have been implemented by the United Nations Office for the Coordination of Hu-

manitarian Affairs (OCHA) in Somalia, Ethiopia, and Bangladesh, targeting regions pre-emptively before

severe weather impacts (Chaves-Gonzalez et al., 2022).

9



days, that temperature is above 30
◦
C (86

◦
F) during the main crop season for every year.

This chosen temperature threshold is aligned with the documented negative effects on crop

yields found in Schlenker and Roberts (2009). Finally, we aggregate our measure of high

heat at the municipality level to merge it with census data on migration to the U.S.

We perform a fixed-effect estimation, controlling for municipality heterogeneity and

aggregate yearly shocks. The regression results show that when a municipality experiences

temperatures above 30
◦
C during the crop season for 24 hours, the migration rate drops

by 0.88 migrants per 10,000 people. The coefficient is larger for rural areas compared to

urban. In highly urbanized areas, we find no significant effects.

Bazzi (2017) finds a positive relationship between positive agricultural income shocks

and international migration in Indonesia and highlights how credit constraints limit migra-

tion in poor rural areas. Our results align with his findings. According to the International

Organization for Migration (IOM), Guatemalan migrants face high migration costs of ap-

proximately two times the annual average wage4. Additionally, Guatemala exhibits low

financial inclusion metrics. Only 12.7% of individuals aged over fifteen have borrowed from

a financial institution or used a credit card; 12.1% have saved at a financial institution; and

merely 10.3% have used a debit or credit card to make a purchase in the past year5. To

gauge the effects of climate change, we need a model that lines up with the salient features

of our data.

We build a dynamic migration model with uninsurable shocks as in Aiyagari (1994)

and a non-contingent asset that resembles Lagakos et al. (2023). Every period, households

choose between staying and working in the rural sector or paying the migration cost today

and moving to the U.S. next period. At home, they are subject to weather shocks that affect

their effective income. We assume that in the U.S., they receive a fixed level of consumption.

Apart from the high migration costs, migration does not happen with certainty. We allow

a migration success rate lower than 100%, which reflects how many migrants get detained

at the border, and a deportation probability once in the U.S. We show that in our setting,

a high-heat shock decreases the probability of migration. We then estimate the model to

build a tight connection between the moment we document from the data and the change

in the migration probability the model delivers.

4The average cost of traveling with a smuggler is between $6000 and $7000 (IOM, 2016).
5Data obtained from The Global Findex Database 2021, World Bank, for the year 2017.

10



Using crop yield data, we estimate the effect of exposure to high heat on crop yields,

obtaining the link between high heat and rural productivity. Next, we estimate the model

to match the coefficient of our high heat migration link and also the stock of Guatemalan

migrants in the U.S. We show that a standard migration model with non-monetary utility

costs cannot match the negative link observed in the data. The parameters we estimate

are the monetary migration cost and the disutility of living in the U.S. The link we observe

is informative about the workers that only migrate in case a good rural shock happens,

closely related to the migration cost.

Next, we leverage temperature projections for different climate change scenarios from

Gutiérrez et al. (2021) and construct the distribution of high-heat shocks for Guatemala

and their effect on rural productivity shocks for every year until 2100. We fed our model

with such projections. In this exercise, we assume that workers have perfect foresight of the

exact path of distributions of high-heat shocks and the scenario they are facing. We start

from a point where workers are unaware of climate change. In the first period, households

learn about climate change, and they start reacting to it.

In our main exercise, we see a substantial increase in the migration flows under all

climate change scenarios. By 2040, relative to initial migration, flows increase by 106%

in the worst scenario and by 35% in the best scenario. Under climate change, workers

foresee a reduction in future income prospects, rendering migration more appealing. In

our setting, even with forward-looking workers, migration takes time, as workers need to

build up the savings necessary to afford the migration cost.

In a second exercise, we estimate the anticipatory effects of climate change by com-

paring our main results versus a counterfactual where workers are not forward-looking,

an exercise that is analogous to the one conducted by Bilal and Rossi-Hansberg (2023).

We find strong but delayed anticipation effects. In the short run, migration flows from

our main results are slightly higher than those in the no-anticipation case. While in the

medium and long run, migration flows substantially exceed the no-anticipation case. Be-

fore the year 2040, migration flows under our baseline scenario are 77% higher than the

no-anticipation case for the worst climate change scenario and 30% for the best scenario.

The exercise shows that when workers are able to foresee the rural productivity path, they

seek to migrate. However, the necessity to accumulate assets for migration costs delays

11



this transition.

Finally, we estimate the impact of two foreign-aid-funded unconditional cash transfers

(UCTs) with different eligibility schemes. These transfers are allocated to the workers

throughout their lives while residing in Guatemala. The first policy is a universal UCT of

10% of initial average income, given to all workers in the home economy independent of

types or shocks. The second policy is a transfer, targeted to workers who experienced an

extremely bad weather shock, defined as a drop in productivity of at least 40%.

Our findings reveal that a universal UCT increases migration for most climate change

scenarios. However, the magnitude is small. This transfer alters the profile of migrant

types, shifting from high-productivity types to lower ones. The transfer increases the

appeal of staying for the high types while it eases the financial burden of paying for the

migration cost for the low ones. In the case of the bad-weather UCT, migration flows

decrease across all scenarios, and the effect is large. Under the best climate change scenario,

migration under the weather-contingent transfer is 30% lower than those of our baseline

results. Although the weather-contingent UCT alleviates the financial burden of migration

following a severe heat shock, it simultaneously insures the workers against bad shocks,

increasing the incentive to stay.

Our paper fits in the macro-development literature of migration and occupational

choice with credit market frictions (Lagakos et al., 2023; Buera et al., 2020). We abstract

from urban workers and model the rural sector, focusing our attention on modeling intrinsic

aspects of migration to the U.S. that migrants must navigate. Additionally, our model

introduces uncertainty in migration success and incorporates a deportation risk, presenting

an additional layer of risk migrants bear.

The main contribution of our paper is the estimation of the climate change effects

on international migration in a developing country. Research such as Bilal and Rossi-

Hansberg (2023) studies the effects of climate change in a spatial migration model along

the lines of Caliendo et al. (2019) and Artuç et al. (2010). In their paper, climate change

affects amenities and local depreciation rates of capital across the U.S. In our model, we

abstract from capital and non-monetary migration costs to take into account household

heterogeneity, credit constraints, asset holdings scarcity, and monetary migration costs, all

salient features of developing economies. Also, our reduced-form estimations contribute

12



to the literature on weather events on migration (Bazzi, 2017; Cattaneo and Peri, 2016;

Jessoe et al., 2018).

2.2 High Heat and Migration

In this section, we show the link between weather and migration. We show the link is

stronger in rural areas and propose the mechanism behind this relationship. We will use the

resulting reduced-form coefficient from our main specification as an input to estimate the

structural model we build in the next section. We proceed as follows. First, we describe

the dataset that we use to estimate the impact of weather on migration flows. Second,

we provide details about the reduced-form formulation for the estimation and discuss the

results. Third, we show the estimation results for rural areas and discuss the mechanism

behind our findings.

2.2.1 Data

We use two datasets. The first is household-level microdata from Guatemala’s most

recent national census, conducted by the National Statistical Institute (INE) in 2018.

In this dataset, we observe migration decisions from previous household members who

currently reside abroad and migrated during the 2002-18 period. The second dataset

corresponds to satellite weather data. We extract hourly land temperature observations at

a high-resolution raster from Copernicus Climate Change Service (2019) for the 1950-2022

period. Next, we provide more details on both datasets.

Migration data. Our primary dataset is from the “XII National Population and

VII Housing Census 2018”. This comprehensive dataset incorporates information about

international migrants who left their households between 2002 and 2018. The dataset

provides details about the geographical location of each household down to the municipality

level, as well as the destination country for each emigrant. This level of detail enables us

to determine migration flows from specific municipalities to international destinations.

We compute the municipal migration rate as the total of international migrants from

rural households in a specific year and then divide it by the total rural population, as

reported in 2018 in the census. We calculate it for every year and municipality. In our

13



estimations, we consider only migration from individuals between 15 and 65 years of age,

as these migrants are mainly incentivized by economic reasons.

Satellite temperature data. We use hourly average land temperature data at the

raster level of 0.1
◦
by 0.1

◦6 and calculate the number of days of exposure to temperatures

above 30
◦
C/86

◦
F. For example, in case hourly temperatures exceed 30

◦
C for 6 hours, this

counts as 0.25 days of exposure. We then aggregate exposure over the main crop season

to obtain the total number of days of exposure for that raster7. To match our raster-level

exposure data with our municipal-level data, we compute the weighted municipal average

of exposure over the rasters that are partially and completely contained in the municipal

boundary. We weigh the rasters by area and the 2010 value of total crop production using

satellite data from International Food Policy Research Institute (2019)8.

We select 30
◦
C as our temperature threshold based on the negative effects of exposure

to this temperature on crop yields documented in Schlenker and Roberts (2009). Their

paper finds non-linear temperature effects for maize, cotton, and soybean yields. We are

interested in estimating the effect of high heat through rural productivity on international

migration.

In Figure 2.1, we map the average rural migration rate and exposure to high tem-

peratures across municipalities. In both panels, white indicates low migration/exposure,

while red indicates high values. Figure 2.1a shows that the distribution of migrants is

concentrated in certain regions of the country, primarily in the Western Highlands (west

region of the map) and the Dry Corridor (east), regions marked by high agricultural activ-

ity, poverty levels, and susceptibility to climate change (INE, 2015; Bouroncle et al., 2015,

2017). Figure 2.1b shows the spatial distribution of high temperatures. Regions such as

Pacifico-Bocacosta (south) and Peten-Izabal (north and northeast) are most exposed to

high temperatures, while the Western Highlands region, due to its elevation, is the least.

This regional heterogeneity requires controlling for such variations in our estimation of the

high-heat migration link.

6Roughly 11 by 11kms, or 6.5 by 6.5 miles.
7For Guatemala, the main crop season goes from April to September (World Food Program, 2015).
8The size of this weighting raster is 0.083

◦
by 0.083

◦
, smaller than our weather raster.

14



Figure 2.1: Migration Rates and High Temperatures

(a) Rural Migration Rate

0 30 6090
Migrants per 10,000 people

(b) Exposure to High Temperatures

0 10 2030
Days of Exposure to Temperatures above 30C

Note: Panel (a) shows the rural migration rate, defined as the average number of international

rural migrants from 2002 to 2018, divided by the total rural population in 2018 for each municipal-

ity. Panel (b) shows the average number of days each municipality was exposed to temperatures

above 30
◦
C during the 2002-18 period. In both panels, grey areas indicate missing data.

15



2.2.2 Reduced-Form Estimates

The spatial granularity of our data allows us to estimate the effect of weather on

migration, taking into account heterogeneity in municipalities and aggregate shocks. We

use a fixed-effects estimation that allows us to account for municipal differences in weather

and migration flows. It also controls by time-invariant municipal factors such as the degree

of violence, political instability, economic conditions, infrastructure, environmental factors,

land quality, cultural aspects, and more. We also include a year fixed-effect term to account

for national aggregate shocks specific to the year. Our baseline specification is the following

ymt = βeExposuremt−1 + αm + ηt + εmt , (2.1)

where ymt is the rural migration rate at the municipality-year level; Exposuremt−1 is the

number of days during the main crop season a municipality has been exposed to temper-

atures above 30
◦
C/86

◦
F for the previous year; αm and ηt are the municipality and year

fixed effects, respectively; εmt is the error term.

We introduce the lag of our temperature variable rather than its contemporary value,

largely due to the timing of the main crop season in Guatemala, which goes from April to

September. Given we are interested in estimating the effect of a bad crop on the migration

flows, using contemporary values might be misleading. First, our migration data is annual,

and the harvest happens in September. Second, we suspect that the migration decision

precedes the actual move. That is, given the cost of migrating to the U.S., households

might need time to gather resources and make necessary arrangements before migrating.

On a second specification, we show that the effect of the contemporary value is lower than

the lagged. Furthermore, we add a specification controlling for departmental9 aggregate

shocks specific to the year. These terms clean for unobservable and observable aggregate

year changes at the department level, such as fluctuations in violence, income, and weather,

among other patterns.

Our main interest is in the coefficient βe. This value captures the change of an increase

in the duration of exposure on the migration rate of the following year. Given an increase in

the number of days, a negative coefficient represents a reduction in the municipal migration

9In Guatemala, a department is an administrative region that is above the municipality. There are

twenty-two in the country.

16



rate.

Table 2.1: Exposure on Rural Migration Rate

(1) (2) (3)

Variables Rural Mig. Rate Rural Mig. Rate Rural Mig. Rate

Lagged Exposure -0.880*** -0.762*** -0.426**

(0.152) (0.132) (0.182)

Contemporary Exposure -0.405***

(0.090)

Constant 8.964*** 10.156*** 7.779***

(0.753) (0.720) (0.925)

Observations 5,236 5,236 5,236

R2 0.263 0.264 0.545

Number of Municipalities 309 309 309

Time and Municipality FE YES YES YES

Department x Time FE NO NO YES

Note: The table shows the effect of exposure on the rural migration rate across several

specifications. FE stands for Fixed-Effect. Robust standard errors are in parentheses.

*** p<0.01, ** p<0.05, * p<0.1

Results are reported in Table 2.1. As we can see, the coefficients are negative and sig-

nificant. Going to the first column, an increase in lagged exposure decreases the municipal

rural migration rate by 0.88 migrants in 10,000 rural inhabitants. Put into practical terms,

a 10-day increase in exposure reduces the migration rate by 8.8 migrants per 10,000 indi-

viduals, which represents a 44% decrease in the average rural migration rate. In our second

specification, we find the effect of lagged exposure to be roughly the same as in the first

specification. The effect of the contemporary value of exposure is lower than its lag and

significant. Finally, our third specification shows the same relationship, but the magnitude

decreases. To summarize, we ultimately find, across the three specifications, a persistent

17



negative link between high heat during the crop season and international migration flows.

Next, we run our baseline fixed-effects specification in (2.1) by categories of munici-

palities according to quintiles of their percentage of rural population. We summarize our

results in Figure 2.2. Further details about the regression results can be found in Table

A.2 of the Appendix. We plot our point-estimate value for βe; the grey band represents the

95% confidence interval. From the graph, we see how the effect of exposure on migration

is larger and more significant for municipalities in rural areas. For urbanized areas, the

effect is not significant and close to zero. This outcome suggests that elevated temperatures

affect migration decisions in rural households more than their urban counterpart.

Figure 2.2: Effect of Exposure on Migration Rate by Percentage of Rural Population

Note: The plot shows the coefficients of lagged exposure from specification (2.1), for different

samples of municipalities according to their share of rural population. In particular, we created

five bins following the percentage of rural population each municipality has. We report the

point-estimate for each bin in green, and the 95% confidence interval in gray.

18



Our findings seem to align with Bazzi (2017). Our interpretation of the results is

that when a region experiences high heat, it leads to a decrease in rural productivity, and

with workers facing credit constraints and high migration costs, fewer will be able to pay

the migration cost, reducing the municipal migration rate. Also related is Amirapu et al.

(2022), who exploit extreme high-heat variation over time and space to study political

participation in India. Their main hypothesis is that high heat depletes crop productivity.

They find stronger effects in rural areas, consistent with our findings for Guatemala.

We also do a similar exercise estimating the effect of exposure on rural migration

for different temperature thresholds. Results are shown in Figure A.1 of the Appendix.

The effect on migration rates is stronger for exposure at higher temperatures. This aligns

with the non-linear effects of temperature exposure found for crop yields in Schlenker and

Roberts (2009)10.

2.3 A Model of Migration and High-Heat Shocks

In this section, we describe our model, building on the work of Lagakos et al. (2023).

As we will see, the model is able to match the negative short-run link between migration

and high-heat shocks. In our setting, workers are subject to income shocks due to extreme

weather conditions (i.e., high heat) that affect rural productivity. Every period, workers

choose to stay and work in the rural sector or try to migrate to the U.S. Workers choosing

to stay are able to save to smooth uninsurable income fluctuations, as in Aiyagari (1994).

Those choosing to migrate pay a monetary migration cost today and arrive in the U.S. the

next period, subject to being detained by immigration authorities. Once in the U.S., the

worker receives a fixed level of consumption every period and is subject to deportation,

which occurs stochastically. Finally, we model climate change as changes in the distribution

of high heat along a transition, making rural yields decrease over time. Next, we proceed

to describe the setup in more detail.

10Although the coefficients are significant with respect to zero, we cannot confirm that there are signifi-

cant differences in the coefficients.

19



2.3.1 Model Setup

Preferences. The economy is populated by a continuum of infinitely-lived workers.

Workers maximize expected utility over their lifetime with a discount factor of β ∈ (0, 1).

There is a single consumption good, and they have constant relative risk aversion prefer-

ences:

u(ct) =
c1−σt

1− σ
, (2.2)

where σ is the relative risk aversion coefficient. Workers that migrated and live in the U.S.

receive a constant level of consumption c∗ and get a taste parameter ν multiplicative to

utility, making u(c∗)ν the period utility of being in the U.S. The value of c∗ captures the

consumption gap between Guatemalans in the U.S. and workers in Guatemala, while ν

represents the non-monetary costs of being away from family and adapting to new rules

and language, among others.

Worker’s Productivity. Each worker at home is endowed with time-invariant rural

productivity η, drawn, at the beginning of time, from a log-normal distribution, ln (η) ∼
N (µη, ση). In our setting, η is the number of efficiency units provided by the worker’s labor.

An increase in ση implies a higher dispersion in rural productivity and, as we will see next,

worker’s income. The worker’s productivity at home does not affect the consumption level

or earnings in the U.S.11

Production. There is a continuum of competitive firms employing labor. Their

production function is Yt = Lαt , where Lt is the number of efficiency units employed, and

α is the returns to scale parameter. The firms pay the workers wt for every efficiency unit

of labor.

Income and High-Heat Shocks. Every period workers in Guatemala, providing η

units of labor, and receive a transitory high-heat shock zt that is uninsurable and iid across

workers (Aiyagari, 1994). zt is the effect of high heat on rural productivity. Effective hours

11One interpretation is that the workers have access to labor income that is independent of their rural

productivity in the home economy, such as knowing techniques and inputs useful for production in the

home economy but not in the U.S. Additionally, in the literature Adamopoulos et al. (2022) calibrates the

correlation between agricultural and non-agricultural abilities to find this correlation to be 0.289.

20



are then given by

ℓ(η, zt) = ηzt (2.3)

With wages equal to wt per efficiency unit, we have that labor income is wtℓ(η, zt) = wtηzt.

We further assume zt has the following form

ln (zt) = ln (1− χ)× ht (2.4)

where χ is the drop in rural yields by one complete day of exposure, and ht is the number

of hours of exposure above 30
◦
C, in equivalent days. Further details about the distribution

of exposure are provided in Section 2.4.2.

Savings. Workers in Guatemala are able to save in a risk-free asset a ∈ A, where A
is a finite grid12. The asset’s price is given by q > β, which is exogenous in our model. We

assume workers cannot borrow, meaning asset holdings must satisfy a ≥ 0 at all periods.

Migration. Besides savings and consumption, workers have the option to migrate.

Every period, the worker in Guatemala decides either to stay and work, or pay a monetary

migration cost of me and try to migrate to the U.S. In the case the worker chooses to

migrate, it is subject to an exogenous probability of successfully migrating of ϕ ∈ (0, 1].

With probability (1 − ϕ), the worker is unsuccessful and returns to the home economy.

The parameter ϕ represents the probability of a worker successfully arriving in the U.S.

and evading immigration controls at the border. We also assume the worker cannot bring

assets into the U.S.

We follow the recent quantitative literature on migration (Artuç et al., 2010; Kennan

and Walker, 2011; Caliendo et al., 2019; Lagakos et al., 2023; Bilal and Rossi-Hansberg,

2023) and introduce idiosyncratic taste shocks to the migration decision. That is, each

worker receives a pair of shocks regarding the decision of staying or migrating, {εs, εe}
distributed according to an Extreme Value Type-1 (Gumbel) distribution with scale pa-

rameter κ, that enter additively to their value functions. These shocks make the migration

decision probabilistic from an ex-ante perspective.

Living in the U.S. Once a worker arrives in the U.S., he/she receives the flow util-

ity mentioned above. Every period, the migrant is subject to an exogenous deportation

12In Section A.2.2 of the Appendix, we provide further detail about this approach.

21



probability of ψ ∈ [0, 1), representing the risk of being caught by immigration authorities

in the U.S. In this case, the worker is sent back to the home economy.

Climate Change. We assume climate change increases the mean of the temperature

distribution over time. This affects the distribution of high-heat shocks, potentially making

them worse and more frequent year after year. Workers at home can foresee this and make

decisions accordingly. We also assume climate change has no effect on the consumption

levels of migrants in the U.S.

2.3.2 The Migration Problem

We now write the problems in their recursive formulation. A worker with permanent

productivity η has two state variables: the level of assets a and the idiosyncratic transitory

heat shock z. We start with the migration problem faced by workers in the home economy.

Value at the Home Economy. We denote the ex-ante value function as the expec-

tation over the taste shocks as Vt(a, z; η). Workers at home solve

Vt(a, z; η) = Eε [max {V s
t (a, z; η) + εs, V e

t (a, z; η) + εe}] , (2.5)

where a worker with productivity η chooses between migrating or staying, with V s
t (a, z; η)

representing the value of staying, and V e
t (a, z; η) the value of migrating. Assuming the

taste shocks are iid across workers and options, we obtain the probability of migrating in

closed form under distributional assumptions for these shocks13. In general, an increase

in the variance of these shocks tends to increase the importance of non-economic reasons

leading to migration.

Value of Staying. Conditional on staying, the worker solves the following problem

V s
t (a, z; η) = max

a′∈A

{
u(wzη + a− qa′) + βEt

[
Vt+1(a

′, z′; η)
]}

(2.6)

The staying worker only chooses consumption and savings levels. Borrowing is not

allowed, meaning a′ ≥ 0, or equivalently, 0 is the lowest point in A. Combined with the

budget constraint, savings decisions pin down the consumption level, now equal to the

wages received by the worker, plus the level of assets at the beginning of the period minus

the expenditure on assets for the next period. The second term inside the maximization

13We show further details on Appendix A.2.2.

22



problem corresponds to the discounted continuation value of being at the home economy.

The value depends on the future realization of the transitory high-heat shock, z′, and the

asset holdings carried forward, a′. In the model, workers save either to smooth consumption

or to migrate eventually.

Value of Migrating. The value of migrating is the following

V e
t (a, z; η) = u(wzη + a−me) + β

[
Et
[
ϕV ∗

t+1(η) + (1− ϕ)Vt+1(0, z
′; η)

]]
(2.7)

with V e
t (a, z; η) = −∞ if wzη+ a < me. The migrant’s problem is passive. First, since the

worker cannot take assets abroad, the budget constraint pins down the consumption level

today. The worker can only migrate if the budget constraint is satisfied and consumption is

non-negative, i.e., if it can pay the migration cost. Aside from the taste shock, a necessary

condition for the worker to migrate is that the future expected utility in the U.S. must

be higher than the one at home. In this problem, the discounted continuation value has

two components. With probability ϕ, the worker successfully migrates, and next period

obtains a value of V ∗(η), which represents the value of living in the U.S. With probability

(1−ϕ), the worker is detained while trying to migrate and is sent back to the home economy

without any assets, a′ = 0 and will be subject to a high-heat shock z′ next period.

Value of Living in the U.S. When the worker is living in the U.S. the value is the

following

V ∗
t (η) = u(c∗)ν + β

{
Et
[
(1− ψ)V ∗

t+1(η) + ψVt+1(0, z
′; η)

]}
(2.8)

The worker in the U.S. receives a risk-free consumption level every period of c∗, inde-

pendent of η. However, the period-flow utility is discounted by ν, which is the disutility

of adapting to the U.S.14 The discounted expected continuation value of being in the U.S.

will be affected by the probability of being sent back home ψ. With probability (1 − ψ),

the worker stays one more period in the U.S. and obtains V ∗(η). With probability ψ, the

worker is sent back to the home economy without assets and is subject to a high-heat shock

the next period. Given the possibility of returning to the home economy, the value of being

in the U.S. depends on the permanent productivity level η. The value does not depend on

the current heat shock z, since these shocks are iid and do not affect the period utility in

the U.S.

14In Appendix A.7, we provide a comprehensive discussion about this parameter ν.

23



Stationary Distribution. If the distribution of high-heat shocks is constant, the

model exhibits a stationary distribution of wealth. We then can drop the subscript t of the

value functions. We use this approach to estimate the model, as we discuss in Section 2.4.

Here, we provide a short description of the stationary distribution and refer to Appendix

A.2.2 for further technical details.

In the model, there is a unitary mass of workers. This mass is composed by workers

living in Guatemala, which we denote the mass as µ(a, z, η), and Guatemalan migrants

in the U.S., M . Workers in Guatemala are subject to shocks z and hold asset position

a. The migration and savings policy functions, together with the success and deportation

probabilities, in addition to the exogenous law of motion of shocks, imply the laws of

motion for the stock of workers in Guatemala, µ(a, z, η), and in the U.S.,M(η). Workers in

Guatemala can either stay or migrate, and conditional on staying, they choose a particular

asset position a′ given their state (a, z, η), and will receive a shock z′ next period. Some

workers will successfully migrate to the U.S., while others will be detained at the border or

deported back to Guatemala. The stationary distribution is a pair (µ,M) such that these

flows remain constants across the state space (a, z, η).

2.3.3 The Importance of Monetary Migration Costs

Before proceeding to the estimation, we discuss the role of the monetary migration costs

when estimating migration dynamics. We show how a non-monetary utility migration cost,

standard in dynamic migration models for developed countries (Artuç et al., 2010; Kennan

and Walker, 2011; Caliendo et al., 2019; Bilal and Rossi-Hansberg, 2023), cannot by itself

generate the high-heat migration link we document from the data.

The data shows a link between current temperature and subsequent migration across

space. In our model, good weather conditions translate into generous income and allow

workers to pay the migration cost. In general, with low-productivity workers, the consump-

tion level conditional on staying is higher than the one conditional on migrating, leading

to a higher valuation of extra income for the migrant than for the stayer. Thus, when the

weather conditions dry up and income falls, the value of emigrating falls more than the

value of staying. As a result, in general, the migration probability decreases under a low

realization of z, holding a and η fixed.

24



To show the importance of the monetary migration cost to match our high-heat mi-

gration link, we modify our model to incorporate a non-monetary migration cost, and we

shut down ingredients of our model that are not part of the standard migration model.

In this version, workers do not face a monetary migration cost. Additionally, they don’t

have any asset holdings or saving technology available. Instead, workers face a disutility

of migration in terms of utility, τ ≥ 0, which is independent of z. workers are still subject

to the same economic environment, facing high-heat shocks z.

The disutility cost of migrating, τ , makes migrating more or less attractive relative to

staying, and hence, is useful to estimate the stock of migrants in the U.S., M , as we do in

Section 2.4 for our model. A higher value of τ tends to decreaseM monotonically. However,

it cannot produce the high-heat migration link from Table 2.1. In Section A.2.1 of the

Appendix, we show this in more detail. The economic intuition is as follows. The disutility

migration cost, τ , does not affect the relative utility between staying and migrating under

different shock realizations, z. Meanwhile, a monetary migration cost makes it very costly

to migrate, in terms of period utility, when the worker suffers a bad high-heat shock. The

worker needs to sacrifice current consumption to pay for the migration cost.

Aside from being able to match the high-heat migration link, monetary migration costs

are important for two reasons. First, workers need to save to migrate, which slows down

migration flows in our model. This contrasts with a setting with migration disutility costs,

where workers are able to migrate immediately without the need for savings. Second,

as climate change lowers productivity and income, staying becomes less desirable. This

is true for both models. Yet, when accounting for monetary migration cost, the declining

trajectory sharply reduces the incentive to migrate as the cost becomes increasingly difficult

to pay. In this framework, the dominating effect is not straightforward to determine. The

increasing difficulty of paying the migration cost, a factor absent in the disutility cost

model, has a strong effect on migration decisions.

2.4 Model Solution and Estimation

In this section, we describe our estimation strategy, the model’s solution in a stationary

equilibrium and the negative link between high heat and migration produced by the model,

and climate change projections.

25



First, we start by assigning values to specific parameters that are either directly ob-

served in the data, standard in the literature, or estimated externally. Second, we use

indirect inference to jointly estimate the monetary migration cost, me, and the disutility

of living abroad, ν; these parameters are key to our negative heat-migration link and the

stock of Guatemalan migrants in the US. For estimation purposes, we assume the economy

is initially at a stationary distribution and climate is not changing. Third, we discuss the

model’s migration and savings decisions and how they produce the negative high-heat mi-

gration link. Finally, we obtain temperature projections for each climate change scenario in

the region of Guatemala; then, we derive the trajectories of high-heat shock distributions

and compute the paths for rural yields. In the next subsection, we proceed to describe the

externally calibrated parameters.

2.4.1 Externally Calibrated Parameters

We set parameters to values that can be directly observed in the data or obtained from

the existing quantitative macroeconomic literature. Table 2.2 summarizes the externally

calibrated parameters. We choose the time period to be a year. We set the coefficient of

relative risk aversion σ to be 2, and the discount factor β to 0.95. These are standard

values in the macroeconomics literature for the annual frequency. Additionally, we set the

taste shock scale parameter, κ, to 0.478, as found in Bilal and Rossi-Hansberg (2023).

We determine the gross rate of return on savings, q−1, as the average difference, for the

2011-18 period, between the interest rate of deposits in Guatemala and the inflation rate

(World Bank, 2023); the result is a 1.27% annual real interest rate. We obtain the success

probability of Guatemalan migrants arriving in the U.S., ϕ, from Carare et al. (2023); this

is equal to 0.50. We calculate the deportation probability, ψ, as the ratio of average annual

removals for 2011-18 (US DHS, 2022), divided by the total undocumented population in

the U.S. for 2019 (MPI, 2023); thus, we set the probability to 0.0329. The consumption

level for Guatemalan migrants in the U.S., c∗, is calculated as the average annual personal

income of Guatemalans in the U.S. for 2016 (Ruggles et al., 2023), divided by the average

annual personal income in Guatemala (INE, 2016), both values are in PPP for the year

2016 (IMF, 2023); the resulting ratio is 4.29. We then multiply it by the average realization

of the high-heat shock on rural productivity under the average η.

26



Table 2.2: Externally calibrated parameters

Parameter Value Explanation Reference

σ 2.00 CRRA coefficient Standard

β 0.95 Discount factor Standard

κ 0.478 Scale of taste shocks ϵe, ϵs Bilal and Rossi-Hansberg (2023)

q (1.0127)−1 Inverse of rate of return of asset Deposits - Inflation rate

ϕ 50% Success probability Carare et al. (2023)

ψ 3.29% Deportation probability Removals/Unauthorized Population

c∗ 4.29× E[z] Consumption level in the U.S. U.S.-Guatemala wage ratio, PPP adjusted

µη 0.00 Mean of log(η) Normalization

ση 0.71 Standard deviation of log(η) SD[log(η)|stay] = 0.71

α 1.00 Production return to scale Constant Return to Scale

χ 2.30% High-heat yield drop See Section 2.4.2

We normalize the mean of the distribution for the worker’s time-invariant productivity,

µη, to 0. To determine the standard deviation of the distribution, ση, we use the latest

agricultural census data and estimate the standard deviation of observed yields among

farmers. This results in 0.71; thus, we set ση to that value. An in-depth explanation of

the methodology employed in constructing the farmers’ yields is available in Section A.3.1

of the Appendix.

We set the parameter controlling the returns to scale in the production function, α,

to 1. A direct implication is that the wage rate remains unaffected by variations in the

amount of efficient labor units in the home economy. Hence, the wage level, wt, is equal

to 1 for every period. Finally, the yield drop induced by one complete day of exposure to

temperatures above 30
◦
C, χ, is set to 2.3%. The next subsection provides further details

on this.

2.4.2 Link between High-Heat Shocks and Rural Productivity

Since rural productivity data from Guatemala is not readily available, we compute the

productivity drop from one day of exposure using the dataset from Schlenker and Roberts

27



(2009), which uses U.S. data. We opt to use the estimate for corn, given its predominance

in Guatemala’s agriculture, occupying 36.6% of croplands as indicated in (FAO, 2023; INE,

2020). We run a fixed-effect specification with log corn yields against exposure and several

other control variables. Further details about the specification and the results can be found

in Section A.1.2 of the Appendix. The estimated effect of exposure on log yields is -0.023,

meaning an increase in one exposure day decreases corn production by 2.3%. Therefore,

we set our χ to be 0.023. Subsequently, we compute the distribution for z, combining our

estimated χ and the exposure distribution for Guatemala. Further details can be found in

Section A.2.2 of the Appendix.

2.4.3 Simulated Method of Moments

We have two remaining parameters: me and ν. We estimate them using Simulated

Method of Moments (SMM). In this approach, we choose the parameter vector that mini-

mizes the distance between the moments in the data and the simulated ones in the model.

In Section A.4 of the Appendix, we highlight the more salient details on the computational

implementation of the SMM.

The parameters we estimate are the monetary migration cost, me, and the disutility

of being abroad, ν. We then choose two data moments to match, for which our parameters

are informative. The first targeted moment is the coefficient of the high-heat migration

link we report in Table 2.1. The second moment is the share of Guatemalans in the U.S.,

which is equal to 7.4%15.

Computation of Model’s Moments. The model generates two moments for com-

parison with their empirical counterparts. The first, βe, is the analog regression coefficient

to that found in Table 2.1 and is subject to sampling variation. The second, the stock of

migrants in the U.S., M , emerges from the model’s stationary distribution. To evaluate

the distance between data and model, we start by choosing a tentative parameter vector.

We solve the policy functions and find the stationary distribution; here, we compute the

model’s simulated stock of migrants, M . We then randomly sample workers in the model

from the stationary distribution and estimate the model’s βe. The sampling procedure is

15In Section A.8 of the Appendix, we show how the parameters identify the moments and other robustness

exercises.

28



simulated a thousand times to calculate the model’s average coefficient, β̂e, across samples.

Finally, the distance between the moments is evaluated, and a new parameter vector is cho-

sen. This process is done iteratively until the distance between data and model moments

is close enough.

Estimation Results. Below, we report and discuss the estimated parameters. Table

2.3 shows the actual data moments, the corresponding moments generated by the model,

and the values of the estimated parameters. The model does a good job of delivering the

targeted moments. The estimated model slightly overestimates the impact of the high-heat

shocks on migration and the share of migrants in the U.S.

Table 2.3: Targeted Moments and Parameter Results

Moments Data Model

Migration drop induced by exposure, βe -0.880 -0.882

Migrant share of Guatemalans in the U.S., M 0.074 0.076

Parameter Value

Migration cost, me 2.47

Disutility of living in the U.S., ν 2.58

Note: This table shows the actual data moments, the moments generated by the

model, and the values of the estimated parameters. Please note that the disutility

of living in the U.S., ν, is positive, consistent with a CRRA utility function where σ

equals 2, implying negative utility function values. ν > 1 represents a lower utility of

living abroad, while 0 < ν < 1 does the opposite.

Both parameters, {me, ν}, are tightly related to the stock of migrants. A higher

migration cost, me, lowers the period utility of the potential migrant, making migration

less attractive. A higher disutility of living abroad, ν, decreases the utility in the U.S.,

decreasing migration incentives. Ultimately, this leads to a lower stock of migrants in the

U.S.

29



However, the migration cost, me, is more closely related to the sensitivity of the migra-

tion rates to the high-heat shocks, βe, than the disutility of living abroad. This important

difference arises from the impact of me on the relative valuation of an extra amount of

income, which translates partially or fully into consumption under the path of staying or

migrating. This stark economic intuition lies in the deep core of our model.

Model Fit. Using data from the “Survey on International Migration of Guatemalan

Persons and Remittances 2016”, we estimate the average migration cost of hiring a smuggler

in proportion to the average wage in Guatemala (INE, 2016), this results in 1.92 for the

year 2016. In the context of the model, it is approximated to be 1.92×E[z], under η = 1.0.

The estimated parameter me is 2.47 and, hence, is slightly higher than the equivalent of

the data counterpart. This result should not be surprising, as a higher me cost detains

migration — it is, in fact, capturing other forces that disincentive migration that we do

not model explicitly.

Additionally, we set ση so that the standard deviation of log(η) conditional on staying

is approximately 0.71. We take this route because we can observe, in the data, only

individuals who stayed in Guatemala. This moment in the model is clearly endogenous: it

depends on the self-selection of heterogeneous workers who decide to stay. The result after

the estimation is 0.72.

2.4.4 Migration and Savings Decisions

In this section, we present the model’s migration probabilities and savings decisions.

First, we show how the migration decision depends on the high-heat shock, the level of

assets, and the worker’s productivity. Second, we discuss the savings policy functions for

the same workers under two high-heat shocks and how they relate to migration decisions.

Figure 2.3 depicts the migration probability across different asset levels and high-heat

shocks for two distinct worker types. The left panel represents a worker with productivity

below the median, while the right panel shows one above the median. The vertical axis

represents the magnitude of the high-heat shock, whereas the horizontal axis indicates the

worker’s asset level. The color pallet in the vertical-right-axis represents the probability

of migrating. A darker color means a higher probability of migrating, while lighter hues

imply a lower probability.

30



For both types, a high-heat shock that decreases rural productivity z also decreases

the probability of migrating in regions of the heatmap where the asset level is close to the

migration cost. A worker with assets approximating the migration cost can pay the cost

under a positive shock. However, migration is either unfeasible or very costly in terms

of period utility under an unfavorable shock. This result aligns with the data moment

we match βe: negative shocks decrease migration rates. The moment sheds light on the

fluctuating migration probabilities for workers with credit constraints under different high-

heat shocks.

Figure 2.3: Probability of Migration for low and high productivity workers

(a) Migration Probability for low-productivity type (b) Migration Probability high-productivity type

Note: Panel (a) shows the migration probability for a worker with permanent productivity η

equals to 0.8. The vertical axis is the realization of the high-heat shock, z, and the horizontal

axis shows the current asset holdings a. Panel (b) shows the same migration policy function, but

for η equals to 1.3.

For regions in the heatmap close to the migration cost, the probability of migration

is higher for the low-productivity worker compared to the high-productivity16. This par-

tially comes from the fact that the worker with lower productivity has a lower expected

16For even lower-productivity workers, the migration cost is equivalent to several years of income. Con-

sidering the chance of being detained at the border and losing all their assets, it is optimal for such workers

not to migrate, even if they can afford to migrate.

31



Figure 2.4: Savings Decisions for low and high productivity workers by high-heat shocks

(a) Savings decisions for low-productivity type (b) Savings decisions for high-productivity type

Note: Panel (a) shows the asset holdings chosen for the next period by a worker with permanent

productivity η equals to 0.8. The vertical axis is the next-period asset holdings, a′, and the

horizontal axis shows the current asset holdings a. The blue curve represents the best shock

(z = 1, no heat), and the red shows the worst (z = 0.39). Panel (b) shows the same savings

policy function, but for η equals to 1.3.

32



income flow at home compared to the high-productivity worker. Additionally, the high-

productivity worker does not benefit from such productivity upon migrating to the U.S.

Lastly, workers with more assets tend to have lower migration probabilities. This

is especially pronounced for workers with low productivity. In this case, workers prefer

consuming their assets before migrating, given their inability to transport them to the

U.S.

Even though migration probabilities might suggest higher migration flows coming from

low-productivity workers, we need to analyze the savings’ policy functions. In Figure 2.4,

we plot the savings policy functions for the same workers from Figure 2.3. Here, the blue

line indicates the policy function under a good productivity shock (absence of high heat),

while the red illustrates the function for the worst high-heat shock. The horizontal axis

represents the current worker’s asset level, while the vertical axis represents the worker’s

asset level for the next period, a′.

Both workers accumulate assets during good times up to some asset thresholds. In

our model, there are two main reasons why workers save. The first one is the standard

precautionary motives: upon receiving good shocks and by the concavity of the utility

function, the worker is better off by consuming some extra income today and saving some

of it for the next period, insuring against a bad shock. Note that when workers receive

an unfavorable high-heat shock, they consume part of their assets to smooth consumption,

effectively dis-saving.

The second reason why workers save is to pay the migration cost in the future. For

example, looking at the low-productivity worker in Figure 2.4a, under a good shock, if her

assets holdings are between 1.5 and me, she would accumulate assets. The observed jump

at approximately a = 1.5 points towards workers starting to save to pay the migration cost

and migrate potentially upon receiving a sequence of favorable shocks17. However, in the

stationary state, the low-productivity worker does not migrate. Assuming the worker can

afford the migration cost, eventually, it returns home with zero assets18. Once back in the

17Figure 2.3a shows at this asset level and under this shock, the probability of migration is zero: the

worker will have to save for migrating later, eventually, upon facing a sequence of good shocks.
18Every period, there is a share of migrants being detained at the border or deported. Recall that upon

trying to migrate, workers face a success probability equal to ϕ < 1. Additionally, every period upon being

in the U.S., there is a probability of facing deportation, ψ > 0. Thus, upon trying to migrate, every worker

33



home economy, the worker accumulates assets under positive shocks up to approximately

a = 0.5. Beyond this point, the worker ceases to accumulate. Considering that the proba-

bility of migration is zero at this asset level, this worker will not migrate in the stationary

state.

Analyzing the high-productivity worker, we see positive migration flows in the station-

ary state. Under a sequence of good shocks, the worker will accumulate assets, eventually

reaching an asset level that puts her in a region of the heatmap, Figure 2.3b, where she is

willing to pay the migration cost, increasing the migration probability.

The dynamics exposed in this section show that the link between high heat and mi-

gration does not depend on the worker’s productivity type. For both low and high types,

the migration probability decreases when the worker suffers a high-heat shock. In the

stationary state, we do not see migration flows coming from the low type in our model,

but we do from the high type. Given that higher types generate more income, they are

less constrained to migrate; however, the reduction in current consumption associated with

paying the migration cost and a high-heat shock makes it very costly to migrate and delays

this decision.

2.4.5 Climate Change Projections

We obtain temperature projections for different climate change scenarios from the

Intergovernmental Panel on Climate Change (IPCC) (Gutiérrez et al., 2021). These pro-

jections are specific to the Central American region during the main crop season from

April to September. We consider three climate change scenarios: optimistic, moderate,

and pessimistic19.

In Figure A.6 of the Appendix, we plot the projected temperature increases across the

distinct scenarios relative to the 1995-2014 period and their quadratic fit20. The optimistic

scenario indicates temperatures will peak around 2050 and gradually decline, reaching

eventually returns to Guatemala, either from being detained at the border or from deportation procedures.
19The scenarios correspond to the scenarios defined by the IPCC as RCP2.6 (optimistic), RCP4.5 (mod-

erate), and RCP8.5 (pessimistic). We collect the projection numbers in July 2023.
20A quadratic fit offers a good balance between simplicity and goodness of fit. In particular, for the

optimistic scenario, but also for the moderate one, temperatures rise up to a point and then decrease. A

linear fit seems, therefore, inappropriate.

34



a final increase in temperature of 0.7◦C by 2100. The moderate scenario anticipates a

temperature increase of 1.6◦C by 2100. The pessimistic scenario forecasts an increase of

3.3◦C. In our analysis, we assume that temperatures stop changing by 2100.

Using these projections, we compute a distribution for Z for every projected year and

scenario. Details about the construction of the Z distribution for every year of the transi-

tion can be found in Section A.5 of the Appendix21. Figure 2.5, plots the projected average

productivity path relative to the initial average for the three scenarios. In the optimistic

scenario, the drop in average productivity is around 3% by 2070, slightly recovering at the

end of the period as temperatures start to cool down. In the moderate scenario, the drop

resembles a linear one, dropping by 10% in average productivity at the end of the period.

The drop is more accelerated and pronounced for the pessimistic scenario, with average

productivity plummeting by around 25% by 2100.

Figure 2.5: Average Productivity Relative to Baseline by Scenario

Having projected the entire distribution of productivity shocks for every scenario over

the years, we feed these sequences into the model. For our main results, we designate 2023

21Additionally, in Figure A.7 of the Appendix, we plot the initial distribution of exposure and the final

distribution for every scenario in the year 2100, the last year of the transition.

35



as the year in which workers become aware of climate change and can foresee changes in

productivity. In our analysis, there is no uncertainty about the climate change scenario

workers will experience. Workers know the entire path for the distribution of productivity,

and they make decisions accordingly. Workers are still subject to idiosyncratic shocks

throughout the transition path, but the current and future distributions are perfectly

foreseeable to the individuals.

2.5 The Effects of Climate Change

In this section, we present a series of results and counterfactuals to analyze different

scenarios. First, we present the main results from our model. Second, we isolate the

effects of anticipation, comparing our main results to a scenario where workers take the

current transitory productivity distribution as permanent sequentially. The key results

are intuitive: as soon as workers are aware of climate change, migration flows increase;

additionally, anticipation effects are strong, workers with perfect foresight exhibit higher

migration flows in the short and medium run than workers who cannot anticipate climate

change. Next, we present our main results.

2.5.1 Main Results

We start with an economy in the stationary state with workers distributed according

to their ergodic distribution. In 2023, workers become aware of climate change and learn

the entire transitional path of productivity distribution.

Figure 2.6 displays the annual migration flows of Guatemalans migrating to the U.S.

in the model. The y-axis represents the percentage of the Guatemalan population that

has chosen to migrate22. Looking at the figure, we see that migration flows increase under

all scenarios. The increase is most pronounced in the pessimistic scenario and least in

the optimistic one. Relative to initial migration, by 2040, migration flows increase by

106%, 71%, and 35% in the pessimistic, moderate, and optimistic scenarios, respectively,

22Percentages are over the total Guatemalan population located in Guatemala and the U.S. Also, it

is important to distinguish between the decision to migrate and successfully arriving in the U.S. Workers

succeed in migrating at a rate of ϕ.

36



marking the peak for the moderate and optimistic scenarios. In the pessimistic case, by

2070, the increase in migration flows relative to the initial period is 179%, reaching its peak.

Migration flows reach a stationary level. By 2100, the stock of Guatemalan migrants in the

U.S. rises by 138%, 63%, and 17% for the pessimistic, moderate, and optimistic scenarios,

respectively23.

Figure 2.6: Effect of Climate Change on Migration Flows

Note: The vertical axis represents the percentage of the Guatemalan population that decides to

migrate. It is important to distinguish between the decision to migrate and successfully arriving

in the U.S. Workers succeed in migrating at a rate of ϕ. Furthermore, the percentages are over

the total Guatemalan population located in Guatemala and the U.S.

Under climate change, workers anticipate a reduction in future income in Guatemala,

increasing migration’s appeal. This happens for all workers under all scenarios. Figure

A.10 of the Appendix highlights this pattern, where we can see how the stock of migrants

in the final stationary state increases for all productivity types compared to our initial

state.

Diving a bit more into the dynamics, the increase in migration flows is smooth and

23The evolution of the stock of migrants can be found in Figure A.8 of the Appendix.

37



gradual. The smoothness is attributed to the large mass of low-productivity workers willing

to migrate but initially constrained by insufficient assets. These individuals must build up

savings over time until they reach a level of assets that allows them to pay the migration

cost. The lower the worker’s productivity, the longer it takes to save enough to afford

the migration cost. Specifically, in the pessimistic case, the fall in income is so strong

that, close to the year 2050, a new lower-productivity worker starts saving for migration,

explaining the acceleration in the migration flows for the subsequent periods.

Additionally, in the pessimistic scenario,24 the stock of migrants overshoots (Figure

A.8 of the Appendix). The overshooting is a byproduct of the combination of anticipation

and future conditions. Workers not only anticipate things will get worse trying to migrate

early but also know it will be harder to migrate later as income decreases. This leads

to some workers migrating during the transition but not in the final stationary state, as

during the transition, when things are not as bad, it is easier for them to save up and pay

the migration cost. After peaking,25 the stock starts decreasing. Before the end of the

productivity transition, income is so low that migration becomes too costly.

Even though the high-heat migration link, βe, might suggest that under climate change,

more people would be constrained and unable to migrate, our main results indicate the

opposite. How is this result consistent with the heat-migration link? We proceed to

answer this question by analyzing Figure 2.7. This graph plots the model’s estimated

heat-migration link for every year and scenario. The vertical axis represents the regression

coefficient β̂e for each point in time. The followed procedure to compute β̂e is the same we

used to compute the coefficient for the SMM estimation26.

As we can see in Figure 2.7, the high-heat migration link is consistently negative for

all periods and scenarios, meaning our main results are consistent with the link. We see

major fluctuations in magnitude across the transition, with the highest for the pessimistic

scenario and the least for the optimistic.

24Looking at the optimistic scenario, there seems to be overshooting; however, a big part of this is

because, in this scenario, things get better after the year 2070. This is shown in Figure 2.5.
25A decrease in the stock of migrants implies a negative net migration. This happens as more people

are being deported than the ones that are migrating, as migration is getting increasingly costly.
26This is described in Section 2.4.3.

38



Figure 2.7: Effect of Climate Change on the High-Heat Migration link (βe)

-0.88

Note: The vertical axis represents the regression coefficient β̂e from the specification in Equation

(2.1) over the transition for different climate change scenarios. The solid black line shows the

regression coefficient reported in Table 2.1. For each point in time, the plotted series follow the

same computational procedure of β̂e described in Section 2.4.3. At each point in time, we collect

1,000 samples with a size of 10,000 individuals. We run a regression for each sample, record

the estimated βe coefficient, and compute the average across samples, β̂e. The plot shows this

average at every point in the figure.

39



2.5.2 The Role of Anticipation

To account for how much of the migration is attributable to workers anticipating the

effects of climate change, we perform an exercise analogous to Bilal and Rossi-Hansberg

(2023). In this counterfactual, workers do not foresee future changes in weather. They

observe past today’s realization of shocks. They update their expectations according to

that distribution. This allows us to isolate the migration due to workers anticipating

climate change.

Figure 2.8: Effect of Anticipation on Migration Flows by Scenario

Note: The vertical represents the difference between the workers that migrated in our baseline

model and the no-anticipation case, normalized by the latter. Differences are expressed in per-

centages.

Figure 2.8 shows the percentage differential in migration flows relative to the no-

anticipation case. We see that when workers can anticipate the effects of climate change,

migration flows are slightly higher than the no-anticipation case in the short run. Migration

becomes significantly higher in the medium and long run across all scenarios. As workers

anticipate the drop in productivity caused by climate change, they seek to migrate in the

earlier periods. However, they cannot afford the migration cost in the early years, forcing

40



them to accumulate assets in order to cover migration costs. The difference between the

two cases widens, and before 2040, migration flows in our baseline exceeded those in the

no-anticipation case by 77%, 50%, and 30% for the pessimistic, moderate, and optimistic

scenarios, respectively. After those peaks, the differential in flows starts decreasing, ulti-

mately turning negative. In the long run, the stock of workers migrating with or without

anticipation must be the same.

The figure indicates a strong but delayed anticipation effect. This delay stems from

the necessity for workers to save a sufficient level of assets to cover migration costs. In this

setting, the cost of migration slows the transition, posing additional challenges for workers

seeking to migrate. The impact on the stock of migrants is further illustrated in Figure A.9

of the Appendix. In the year 2075, the stock of Guatemalan migrants in the U.S. surpasses

that of the no-anticipation case by 49%, 15%, and 4% for the pessimistic, moderate, and

optimistic scenarios, respectively.

2.6 Unconditional Cash Transfers and Migration

We now analyze the effects of unconditional cash transfers (UCTs) on migration under

climate change. For this exercise, we assume transfers are given to the workers over their

lifetime as long as they stay in Guatemala. Workers believe they will obtain the same

transfer for the next periods. Furthermore, we assume the transfer is funded with foreign

resources. We study two different eligibility schemes. The first scheme is a universal cash

transfer given to all workers in the home economy independent from types or shocks. The

second scheme targets workers who suffered an extreme high-heat shock, defined as a drop

in productivity of at least 40%. The transfer is not proportional to the innate productivity

η and appears additively in the budget constraint in Equations (2.6) and (2.7).

2.6.1 Universal Cash Transfer

In the first transfer scheme, all workers in Guatemala receive a transfer equivalent to

10% of the 2023 average income. We assume workers were not expecting the transfer. They

start receiving the transfer as they learn about climate change in the first period.

Figure 2.9 shows the effect of the universal transfer on migration flows over different

41



Figure 2.9: Effect of a Universal UCT on Migration Flows

Note: On the vertical axis, we plot the difference between the migration flows under the transfer

and our baseline in Section 2.5.1, dividing it by the baseline. The policy considered here is the

Universal UCT, in which every worker receives a cash transfer. The cash transfer is equivalent

to 10% of the initial average income.

42



climate change scenarios. In the early periods of the transition, migration flows under the

universal UCT are approximately 10% lower than the baseline. This is explained by high-

productivity workers deciding to stay instead of migrating, as the cash transfers increase

their value of staying relative to their value of migrating. At some point, the negative

difference shrinks, driven by an acceleration in the migration flows from low-productivity

workers helped by the transfer. From there, we see different effects for different scenar-

ios. In the pessimistic scenario, the negative difference quickly becomes positive as the

transfers keep easing the credit constraints for the low-productivity workers, accelerating

the migration process. Subsequently, the difference reaches a maximum and starts ceasing

down. This is explained by the time it takes the low-productivity worker to save in order to

migrate, an aspect that the transfer accelerates. In the long run, under the new stationary

distribution of high-heat shocks, the flow and stock of migrants will be higher with the

universal UCT. This also holds for the moderate but not for the optimistic, where the flow

is consistently lower.

The transfer shifts the composition of migrating worker types. In all scenarios, transfers

shift migration from high-productivity workers to lower ones27. The transfer increases

income flows every period, making staying more appealing. However, the value of migrating

increases as well, given the transfer helps to afford the migration cost. For high-productivity

workers, the increase in transfers has a higher effect on the valuation of staying. Before

the transfer, their income flow in Guatemala was already high, and in case they needed

to migrate, with relatively low savings, they could afford the migration cost; this makes

the effect of the transfer over the value of migrating relatively small. For low-productivity

workers, the transfers have a higher impact on the value of migrating. The transfer eases

the financial constraint, making it easier to save towards paying the migration cost without

sacrificing large consumption levels every period.

27In Figure A.12 of the Appendix, we plot the Stock of migrants by type at the final stationary state

under both transfers. The shift is observed on the plots located to the left. Although not plotted because

of the large amount of periods and types, the same shift is observed during the transition to the stationary

state.

43



2.6.2 Cash Transfer Conditional on Bad Weather

In this transfer scheme, every worker who receives a bad realization of the high-heat

shock receives a transfer. To ease comparisons, the transfer amount is the same as in the

case of the Universal UCT, 10% of average income. Workers are eligible to receive the

transfer if they receive a high-heat shock that causes a drop in productivity of at least

40% for that period. The transfer has a relatively small effect on the average income flow

workers receive, as the annual probability of receiving the transfer is 8.4% at the beginning

of the transition in 2023. The transfer mainly provides insurance, increasing income under

a bad realization of the shock reducing the risk. As before, we assume workers were not

expecting the transfer, and they received them the first period as they learn about the

climate change scenario.

Figure 2.10: Effect of a Bad-Weather UCT on Migration Flows

Note: On the vertical axis, we plot the difference between the migration flows under the transfer

and our baseline in Section 2.5.1, dividing it by the baseline. The policy considered here is the

High-Heat UCT, in which workers receive a cash transfer in case they suffer a drop in productivity

of at least 40%. The cash transfer is equivalent to 10% of the initial average income.

Figure 2.10 shows the effect of the bad-weather cash transfer on migration flows over

44



different climate change scenarios. On the y-axis, we plot the difference between the

migration flows under the weather-contingent transfer and our baseline in Section 2.5.1,

dividing it by the baseline. Years are plotted on the x-axis.

Examining the dynamics of migration flows, we observe these are consistently below

the baseline case for all climate change scenarios. The transfer does not have an immediate

effect on the migration trajectories. At the beginning of the period, changes in migration,

with respect to the baseline results, are small. After the first few years, transfers start

having a larger effect. Migration flows sharply decrease under all scenarios. The effect is

more pronounced for the optimistic scenario, where flows under the transfer are 30% lower

than those of the baseline results. Under the moderate scenario, migration flows drop

up to 20% in 2040, relative to our baseline. After subsequent fluctuations, it eventually

converges at approximately 15%. In the pessimistic scenario, migration flows drop up to

22% in 2060, relative to the baseline. Ultimately, the difference shrinks and settles at 5%

in the long run.

The decrease in migration flows is generated by the insurance effect of the transfer,

especially on the low-productivity migrating workers. The high-heat cash transfer mitigates

risk against bad shocks, increasing the worker’s value of staying. However, given that

the magnitude of the transfer is not dependent on the worker’s productivity type, the

insurance effect of the transfer is larger for the low-productivity worker compared to the

high-productivity.

2.6.3 Comparing the Transfer Schemes

In our last subsection, we compare two cash transfer schemes, evaluating them concern-

ing migrant stocks and associated costs. Our findings indicate that the transfer conditional

on bad weather events not only incentivizes more people to stay in Guatemala but also its

cost is significantly lower than a universal cash transfer. We now proceed to compare the

stock of migrants under these two transfer schemes.

In Table 2.4, we show the stock of migrants in our baseline and under the two transfer

schemes. We present the stocks for every climate change scenario and different years. The

stocks are expressed in percentages of the total Guatemalan population living in Guatemala

and in the U.S.

45



Table 2.4: Stock of Migrants in the U.S. under different Transfer Schemes and Scenarios

Case 2023 2040 2060 2080 2100 2120

Baseline

Optimistic 7.6 8.2 9.2 9.3 8.9 8.8

Moderate 7.6 8.9 10.8 11.7 12.3 12.5

Pessimistic 7.6 9.5 13.4 17.1 18.0 16.8

Universal

Optimistic 7.6 8.0 8.8 8.9 8.6 8.4

Moderate 7.6 8.6 10.5 11.8 12.6 12.9

Pessimistic 7.6 9.3 13.9 17.5 18.8 17.8

Bad-Weather

Optimistic 7.6 7.5 6.8 6.2 5.8 5.5

Moderate 7.6 8.3 9.7 10.6 11.0 10.9

Pessimistic 7.6 9.0 11.8 15.0 17.1 16.4

Note: This table shows the stock of migrants in the U.S. for the Optimistic, Moderate,

and Pessimistic scenarios for our baseline, Universal UCT, and High-Heat UCT. Baseline

refers to our main results (no cash transfer). Universal refers to the case in which every

worker receives a cash transfer. Bad-Weather refers to the case in which the cash transfer

is received only by workers who suffered a drop in productivity of at least 40%. The cash

transfer used for these exercises is equivalent to 10% of the initial average income.

Upon examining Table 2.4, we can observe that the stock of migrants in the U.S. is

lower under the bad-weather cash transfer for all climate change scenarios. By 2040, in the

medium run, differences with the baseline scenario are 0.7, 0.6, and 0.5 percentage points

(p.p.) for the optimistic, moderate, and pessimistic scenarios, respectively. In contrast,

the universal cash transfer diminishes migration flows by 0.2 (optimistic), 0.3 (moderate),

and 0.2 p.p. (pessimistic).

In subsequent decades, the disparity between the migrant stocks under the high-heat

cash transfer and the baseline becomes increasingly pronounced. By 2080, the difference

reaches 3.1 (optimistic), 1.1 (moderate), and 2.1 p.p. (pessimistic). For the same year and

under the universal transfer, migrant stocks are similar to the baseline. Notice, for the

moderate and pessimistic scenarios, the stocks of migrants are higher than the baseline but

46



lower in the optimistic.

The bad-weather cash transfer is more effective in discouraging migration, as it mit-

igates risk, bolstering the appeal of staying for risk-averse individuals across all climate

change scenarios. Conversely, the universal transfer increases cash availability at all times

for workers, thereby reducing the financial burden of migration costs and making migration

more attractive under most scenarios. We now proceed to a comparative analysis of the

costs of each transfer scheme.

In Table 2.5, we report the cost of unconditional cash transfers (UCTs) and the cost

ratio. The first two rows show the annual cost of the universal and the bad-weather cash

transfers for each climate change scenario, quantified as a percentage of initial average

income28. The last row shows the cost ratio of the two UCTs, also reported in percentages.

As the transfer amount is the same in both schemes, and the only modification is the

eligibility criteria, the bad-weather transfer is naturally less costly as it has fewer eligible

recipients. However, notice that the cost is changing; this is because of two factors. One

is the composition of migrants and stayers; the more people stay, the more people will

receive the transfer. The second factor only pertains to the bad-weather cash transfer;

with climate change, the probability of receiving a high-heat shock increases, increasing

the number of eligible workers for the transfer29.

The initial cost associated with a universal transfer equals 8.3% of the average annual

income for each worker in Guatemala. In contrast, the bad-weather transfer is 0.7%, making

the bad-weather transfer approximately twelve times cheaper than the universal. Notice

the cost trajectory of the universal transfer scheme is solely due to changes in the stock of

migrants. A decrease in the cost indicates a decline in the Guatemalan population living

at home, given the transfer amount is the same across time and workers. In the case of the

bad-weather transfer, we see a different cost evolution for each scenario. In the optimistic,

the cost remains fairly the same, as the drop in productivity generated by climate change

is not as severe as in other scenarios, and overall, there is an improvement in weather

conditions. In the case of the moderate and pessimistic scenarios, we see a steeper increase

in the cost, mainly associated with a higher probability of receiving the negative high-heat

28Initial average income is the average income in Guatemala for 2023.
29In Figure A.13 of the Appendix, we show how the probability of receiving such transfer evolves as the

productivity becomes less favorable along the transition for each scenario.

47



Table 2.5: Annual Cost of the Unconditional Cash Transfers

Case 2023 2040 2060 2080 2100 2120

Universal

Optimistic 8.3 8.2 8.2 8.2 8.2 8.2

Moderate 8.3 8.2 8.0 7.9 7.8 7.8

Pessimistic 8.3 8.1 7.7 7.4 7.3 7.4

Bad-Weather

Optimistic 0.7 0.8 1.0 1.0 0.8 0.8

Moderate 0.7 1.0 1.4 1.7 1.8 1.8

Pessimistic 0.7 1.1 1.8 2.4 2.9 3.0

Bad-Weather
Universal (%)

Optimistic 8.4 10.2 11.8 11.8 10.0 10.0

Moderate 8.4 12.4 17.2 21.1 23.0 23.1

Pessimistic 8.4 13.8 23.0 32.1 40.5 40.4

Note: This table shows the cost of the UCTs for the Optimistic, Moderate, and Pessimistic

scenarios. In the first two rows, the cost is annual and measured as a percentage of initial

average income. The last row indicates the ratio between the cost of the High-Heat and the

Universal cash transfer, expressed in percentages. The cash transfer used for these exercises

is equivalent to 10% of the initial average income.

shock. As the cost of the bad-weather transfer goes up, so does the ratio in the third row.

However, notice that the most expensive the bad-weather transfer reaches is 40.5% of the

universal transfer’s cost.

These findings show that not only does the high-heat transfer mitigate risk and make

staying more appealing, but it is also significantly less expensive than an alternative where

the transfer is given to everyone. However, both exercises come with caveats. Note we

assume that the transfer is given throughout the transition, and workers believe that as

well. In case workers believe the policy is temporary instead of permanent, results might

be different. Indeed, we could expect transfers to further fuel migration flows, as people are

not expecting the policy to last for long. In this case, the institution giving the transfers

must have credibility.

48



2.7 Conclusion

This paper studies the effects of climate change on international migration flows. Lever-

aging on census and granular land temperature data for Guatemala, we document a robust

negative link between exposure to high heat during the crop season and next year’s migra-

tion rate to the U.S. We further establish the effect to be stronger in rural areas.

Next, we build a quantitative dynamic migration model in which workers are subject

to unfavorable transitory heat shocks that affect their rural yield. At the core of our

model, high heat decreases income, which ultimately limits workers’ ability to migrate.

Upon receiving a high-heat shock, the migration cost becomes hard to afford, as sacrificing

current consumption has a strong effect on the period’s utility. This lowers the worker’s

migration probability. We show that the mechanism in our model lines up with the feature

of our data, something that the standard migration model cannot generate.

We then use the model to study how climate change shapes migration dynamics. There

are mainly two major forces affecting migration incentives. On one hand, climate change

makes migration more appealing, as rural productivity decreases over time, impoverishing

individuals who stay. On the other hand, the worse weather conditions over time reduce

available income, making it harder to save and eventually migrate.

We show the effects of two different unconditional cash transfers, funded by foreign

aid, on migration flows. In our results, providing a universal cash transfer proves to be

both expensive and inefficient. On one hand, providing cash to some workers makes mi-

gration economically viable and triggers migration. On the other, some workers would

never migrate regardless of the transfer, and resources are wasted. A scheme that favors

insurance against bad shocks decreases migration flows and costs only a fraction of the

universal scheme. While we do not provide an explicit objective to be fulfilled with these

schemes, the results suggest that there is plenty of room for better targeting and richer

schemes.

Our paper abstracts from several mechanisms that can be potentially important for

migrating decisions. For example, we do not consider any feedback between workers that

stay and factor prices, such as wages or land prices. As more people leave, labor becomes

scarce and land abundant. The former tends to make it easier to afford the migration

costs, while the latter tends to decrease migration incentives. These simple forces lead to

49



a rich set of possibilities. Furthermore, we assume workers know the scenario they end

up experiencing, and they know exactly the entire productivity distribution path. Future

work tackling these two assumptions can inform about migrant selection and the role of

uncertainty in international migration flows.

50



Chapter 3

Climate Change, Food Prices, and

Inequality

3.1 Introduction

Climate change is expected to reshape the spatial patterns of agricultural produc-

tivity. One adaptive strategy involves leveraging novel comparative advantages through

the re-optimization of food sourcing. Nevertheless, due to the high costs associated with

transporting goods over distances, trade barriers restrict the degree to which this process

can happen. For items that incur substantial transportation costs, the significance of local

productivity becomes paramount. With the rise in food prices, the welfare implications are

not uniformly distributed across various income levels, as lower-income households usually

spend a higher proportion of their budget on food.

What effects will climate change have on food prices and how will it influence indi-

viduals across various income levels? To address this question, we develop a spatial model

of food production and trade, building on Eaton and Kortum (2002) and Costinot et al.

(2016). Our model incorporates rich heterogeneity in four dimensions. First, to examine

the importance of trade ease, we distinguish between two types of food goods, each facing

different trade costs. Second, locations vary in productivity for each type of food. Third,

locations are distinct regarding their degree of connectedness to others. Fourth, income

levels within each location vary, with both relatively richer and poorer households.

51



In our model, locations produce goods based on their productivity and engage in trade.

Food goods face varying trade costs, which distort the comparative advantages of locations

and influence trade patterns. Goods with higher trade costs exhibit a greater spatial price

dispersion compared to those with lower trade costs. For high-trade-cost goods, local

productivity is especially critical, as lower productivity leads to higher prices.

We calculate the welfare effects stemming from changes in food prices. In our setting,

shifts in utility caused by climate change are driven solely by changes in food prices, as

household income is constant. We decompose the equivalent variation from climate change

into three components, drawing on standard demand theory. The first is the food expendi-

ture share: poorer households, with higher food expenditure shares, are more sensitive to

changes in food prices. The second is the trade shares between locations, which reflect how

regions are affected by productivity changes in other regions they trade with, including

themselves. The third component captures changes in potential food productivity across

different areas.

We apply the model to Brazil, treating each state as a separate location. Given Brazil’s

vast latitude range and tropical climate, there are significant productivity differences across

regions and crops. The country’s extensive land coverage and reliance on road-based trans-

portation make the movement of goods challenging. Additionally, income inequality is

pronounced both within and across states.

Trade flows and frictions are central to our model, but not directly observed in the data.

This is a frequently encountered issue in domestic trade is the necessity for comprehensive

information on trade flows among sub-national units, hardly observed in the data. As in

many studies of intra-national trade, e.g, Ramondo et al. (2016), Pellegrina (2022), Sotelo

(2020), the trade flows are not directly observable in data between Brazilian states1. To

overcome this data constraint, we incorporate the model structure with the inclusion of

short-term weather variances, allowing us to derive a correlation between price fluctuations

and weather anomalies, both quantifiable in the data. We then employ this observed

variation in prices and weather disturbances to extract estimates of these trade barriers

for different types of food goods.

1This feature is common across most countries. Canada is a noticeable exception, which releases

interprovincial trade flows. See, e.g., Agnosteva et al. (2014)

52



In our model, heat shocks reduce food productivity, driving up prices. Neighboring

states are also affected, as they import food from the impacted state. Thus, the observed

price change in any state reflects a weighted average of heat shocks between states, with

the weights determined by trade shares. These shares depend on average potential produc-

tivity, labor costs, and bilateral trade frictions. To capture this structure, we combine a

panel of Consumer Price Index (CPI) data with a panel of heat shocks. Drawing from crop

science literature, e.g. Schlenker and Roberts, 2009, we focus on a temperature threshold

of 30
◦
C/86

◦
F, known to harm crop yields. Using satellite weather data Copernicus Climate

Change Service (2019), we construct a panel tracking the number of hours (in days) that

temperatures exceeded this threshold in each city. We leverage these heat shocks to esti-

mate trade frictions from variations in prices and temperatures and validate the threshold

by showing evidence of yield declines when crops are exposed to such temperatures during

the growing season.

To the extent that most cargo transportation within Brazil rely on trucks via roads

(World Bank, 2022), we model trade frictions as a function of driving time between states2.

We build on a classification of food goods’ tradability developed by the Brazilian Central

Bank for tracking the CPI. Using this classification, we compute the price index for baskets

of food products, in a panel of locations. One index includes goods that are frequently

traded on the international market, such as commodities, while the other represents items

that are less commonly traded globally, typically more perishable, fresh goods. We sepa-

rately estimate the elasticity of trade costs with respect to the driving time for each basket.

Our findings suggest that this elasticity is nearly double for goods with elevated trade costs,

such as fresh goods, compared to those with reduced trade costs, such as commodities.

We examine how the spatial correlation of heat and price changes shape our results.

While heat shocks naturally show positive spatial correlation, we document that a similar

pattern for inflation dynamics across locations. Specifically, as driving time between loca-

tions increases, making them less connected, the inflation correlation decreases, especially

for goods with higher trade costs. Our model capture this feature of the data: locations

farther apart experience different heat shocks, and substantial trade frictions make local

2World Bank (2022) shows data for 2021, with the estimated share of cargo transported by road is 66%.

Railroads correspond to 18% and waterways other 15%.

53



prices more dependent on nearby conditions. Thus, inflation correlations decline more

sharply for high-trade-cost goods, with a more modest decline observed for low-trade-cost

goods.

With these estimates of trade frictions and trade shares, we proceed to do counter-

factual exercises. Actual production data often suffers from selection bias in Ricardian

models, as locations tend to produce goods where they have a comparative advantage.

Hence, the productivity across the spectrum of goods is latent: in the actual production

data, we observe only partially these productivities. To address this, we use the potential

productivity of crops across regions for each type of food good. Following our equivalent

variation decomposition, we incorporate proportional changes in average potential produc-

tivity into the model. These estimates are sourced from the GAEZ project by FAO and

IIASA (2022), based on various climate change scenarios.

The GAEZ project also provides data on the historical levels of this potential produc-

tivity. We employ this historical data for two reasons. First, it serves as an input to recover

trade frictions. Second, it provides a benchmark to compare with alternative productivity

forecasts from the GAEZ project. In our equivalent variation decomposition, changes in

average potential productivity are central, making historical estimates a crucial basis for

comparison.

The GAEZ project provides detailed data on agricultural productivity under various

climate change scenarios, covering different time horizons and intensities of productivity

shifts linked to greenhouse gas concentrations. Given the higher uncertainty over longer

horizons, we focus our results using the optimistic scenario (RCP 2.6) for the period ending

in 20403.

We show that even under the most optimistic climate change scenario, there is sig-

nificant variation in potential productivity changes across states compared to historical

baselines. Furthermore, there is substantial heterogeneity in the effect of climate change

on productivity between food types, with high-trade-cost foods experiencing more pro-

nounced declines in average potential productivity.

Using our equivalent variation analysis, we estimate how much households would be

3The GAEZ data employs four Representative Concentration Pathways (RCPs): 2.6, 4.5, 6.0, and 8.5

to construct scenarios. These values represent radiative forcing levels by 2100, reflecting greenhouse gas

concentrations, with lower values indicating cooler temperatures and stricter mitigation policies.

54



willing to pay to avoid the productivity changes linked to climate change. While food prices

are an aggregate at the state level, within-state income heterogeneity leads to differentiated

welfare effects of price increases. Due to non-homothetic preferences, food expenditure

shares decline with income, consistent with observed data. Households in the lowest income

decile are more vulnerable to changes in food prices, as they allocate a larger share of their

income to food4. Under the optimistic scenario, households in the first income decile in

some states would be willing to forgo up to 3% of their income to avoid these productivity

shifts.

Finally, we argue that an effective adaptation strategy is to improve road quality. Since

trade frictions are modeled as a function of driving time between states, increasing average

road speed effectively reduces trade barriers. We derive a formula for the equivalent vari-

ation under this scenario, involving three components similar to the productivity change

decomposition: food expenditure shares, trade shares between states, and the estimated

elasticity of trade frictions with respect to driving time. We find that, given these elastici-

ties, the sufficient statistic for the equivalent variation is the own trade share of each state,

linking to findings from the international trade literature, (Arkolakis et al., 2012). For a

10% improvement in road quality, households in the lowest income decile would be willing

to pay up to 0.8% of their income under the optimistic scenario.

Outline. The remainder of the paper is organized as follows. Section 2 presents the

trade component of the model. Section 3 derives a welfare change formula to highlight

key elements for the counterfactual exercises. Section 4 introduces a perturbation to re-

cover missing trade shares. Section 5 develops the demand side, specifying preferences

and parameter calibration. Section 6 presents results from the counterfactuals, includ-

ing the policy scenario on road infrastructure. Section 7 discuss limitations and potential

extensions. The final section summarizes the findings.

3.2 Model

We develop a spatial model of food production and trade, incorporating heterogeneity

along four dimensions: the tradability of different types of food, the productivity of each

4We show this pattern in figure 3.2.

55



location for each food type, the degree of connectedness between locations, and income

heterogeneity within each location.

The model includes three productive sectors: one referred to as the outside good sector,

and two sectors producing different types of food, distinguished primarily by their degree

of tradability. We classify the food sectors into two groups: one facing low trade costs and

the other facing high trade costs. Each location is endowed with a distribution of potential

productivities for goods of each type of food, and the outside good. Within each location, a

population of households resides and supplies labor inelastically. These households do not

migrate, and differ in their effective labor hours, generating income heterogeneity within

each location.

Our approach proceeds as follows. First, we present the model without considering

any shocks — either transitory shocks from weather or “permanent” shocks from climate

change. As we develop the theoretical framework, we identify key missing data necessary for

estimating the model, most notably detailed information on trade flows. We then introduce

a transitory weather shock into the model and derive the link between price movements

and the realization of these transitory shocks. This relationship is used to estimate trade

frictions and recover trade shares. Finally, we discuss the sources of exogenous variation

that underpin the counterfactual analysis.

3.2.1 The Trade Block

Our environment is static and there is no storage technology available. There are L

locations, indexed by ℓ in the set L ≡ {1, 2, . . . , L}. A mass of households Λℓ lives in

location ℓ. Locations are endowed with productivity parameters, described momentarily.

Sectors, Goods, and Market Structure. There are three sectors: one producing an

outside good, indexed by o, and sectors producing two types of food goods. One type faces

low trade costs between regions, denoted by c, and another faces high trade costs, denoted

by q. One might fix ideas by thinking of goods of type c as easily traded commodities, such

as rice, soybean, corn, and wheat, and think of goods indexed q as harder to trade or more

perishables, such as tomatoes and lettuce. We denote x ∈ X ≡ {c, q} to ease the notation

later. For each food type x, there is a unitary mass of goods, each indexed by ω ∈ [0, 1].

56



We call a variety a pair of type and good (x, ω). In all that follows, we assume all markets

are perfectly competitive so that prices are pinned down by the marginal production costs,

on top of any transportation costs.

Transportation Costs. We model trade frictions as iceberg costs, and let the outside

good o be traded without friction. As a result, the price of the outside good is the same

across locations and, therefore, is well suited to serve as the numeraire.

For food products, all varieties of a given type x face a trade cost τxj,ℓ for the location

pairs (j, ℓ) and the good type x ∈ {c, q}. As usual, the interpretation of τxj,ℓ is that a

sourcing location ℓ needs ship τxj,ℓ units of a variety (x, ω) so that the location j receives

one unit.

We normalize τxℓ,ℓ = 1 for all locations ℓ and types x. Whenever j ̸= ℓ, we require

that τxj,ℓ ≥ 1. We further require that the triangle inequality be satisfied: for any triplet of

locations (j, k, ℓ), the following τxj,ℓ ⩽ τxj,kτ
x
k,ℓ, so that there is no arbitrage opportunities in

moving the goods around.

Variety Aggregation. Varieties are aggregated by type x with a CES function5. For

each type of food, there is a unitary mass of varieties, which we denote by ω:

ccℓ =

(∫ 1

0
ccℓ(ω)

νc−1
νc dω

) νc

νc−1

and cqℓ =

(∫ 1

0
cqℓ(ω)

νq−1
νq dω

) νq

νq−1

(3.1)

where cxℓ (ω) denotes the consumption of variety (x, ω) in location ℓ. The CES structure

delivers the ideal price indexes for each type of food as follows:

P cℓ =

(∫ 1

0
pcℓ(ω)

1−νcdω

) 1
1−νc

and P qℓ =

(∫ 1

0
pqℓ(ω)

1−νqdω

) 1
1−νq

(3.2)

Our trade structure can be solved independently from the preference block, provided that

this CES structure is imposed. Hence, we proceed with a general formulation and later

specialize on the outer utility function.

5One alternative interpretation is that in each location there is a mass of competitive grocery shops

that aggregate all varieties (x, ω) of each type x into a composite that the households buy by means of a

CES production function.

57



Production. There is a single production factor, labor. Production is linear in labor in

all sectors. The productivity on the outside good sector at location ℓ ∈ L is given by Zoℓ ,

so its inverse denotes the input requirement to produce a unit of output:

Y o
ℓ = ZoℓN

o
ℓ (3.3)

where No
ℓ is the amount of labor allocated to such production. Letting wℓ denote the wage

rate prevailing at the location ℓ. The cost of producing one unity of the outside good is

given
wℓ
Zoℓ

(3.4)

For the food goods, we model their production following Eaton and Kortum (2002) model.

We denote by Zxℓ (ω) the efficiency of location ℓ in producing the variety ω of food type

x ∈ {c, q}. The production technology takes the form of

Y x
ℓ (ω) = Zxℓ (ω)N

x
ℓ (ω) (3.5)

so that the cost per unit for producing good variety (x, ω) at location ℓ is given by

wℓ
Zxℓ (ω)

(3.6)

Good sourcing. Consider the problem of a family living in location j ∈ L deciding

where to source from. The cost in location j ̸= ℓ ∈ L to acquire a variety (x, ω) from

location ℓ takes into account the production cost in location ℓ and the transportation costs

from ℓ to location j, that is:

pxj,ℓ(ω) ≡
(

wℓ
Zxℓ (ω)

)
τxj,ℓ (3.7)

Under the working assumption of perfect competition, location j buys from location

ℓ if ℓ is able to supply at the lowest delivery cost, taking into account both production

and transportation costs. The price that location j pays for the variety (x, ω) is the lowest

among all potential sourcing locations:

pxj (ω) ≡ min
{
pxj,ℓ(ω) : ℓ ∈ L

}
(3.8)

58



Food Production Technology. We assume that the productivity draws follows the

structure of Eaton and Kortum (2002). We denote by Zxℓ (ω) the productivity of variety

(x, ω) at location ℓ, which we refer to as “EK term” below.

For each type of good-variety pair (x, ω), a location receives a productivity draw from a

location-specific Fréchet probability distribution with the cumulative distribution function:

F xℓ (z̃) = e−T
x
ℓ z̃

−θx

. (3.9)

The draws are independent across varieties (x, ω) within and across locations. The param-

eter T xℓ , or “State of Technology,” defines the mean productivity and reflects the absolute

advantage of location ℓ for type x Eaton and Kortum (2002). The parameter θx, uniform

across locations, governs the dispersion of productivity draws, with higher values implying

narrower comparative advantages. As in Simonovska and Waugh (2014), θx represents the

trade elasticity.

Price Determination. Below, we state the main results of the model and refer to a

complete derivation in appendix B.2. As in Eaton and Kortum (2002), location j faces a

probability distribution of prices of a variety

Gxj,ℓ(p) = 1− e−[Tx
ℓ (wℓτ

x
j,ℓ)

−θx ]pθ
x

(3.10)

Because the productivity draws are i.i.d, this probability is the same for every variety

(x, ω). This term gives the probability of location j being supplied by location ℓ with the

price up to p for type x. Since location j buys from the lowest cost supplier, we next show

the probability location j buy type-variety pair (x, ω) of a price of at most p. This requires

that there is at least one location that supplies at the price not higher than p, as follows

Gxj (p) = 1−
∏
ℓ∈L

[1−Gxj,ℓ(p)] (3.11)

Plugging equation (3.10) into (3.11), we recover

Gxj (p) = 1− e−Φx
j p

θx

(3.12)

where

Φxj ≡
∑
ℓ∈L

T xℓ (wℓτ
x
j,ℓ)

−θx (3.13)

59



The term Φxj shows how the State of Technology, T xℓ , the input cost of production wℓ,

and the trading frictions τxj,ℓ between each location ℓ and j ultimately shape the price

distribution faced at the location j.

Price of Basket. As we shall see next, the state of these three forces across all locations

and their interaction describes the price level in each location j ∈ L. Equation (3.12) allows

us to recover the ideal price indexes for each good type, in equation (3.2) , as follows:

P xj =

(∑
ℓ∈L

T xℓ (wℓτ
x
j,ℓ)

−θx
)− 1

θx

γx for (3.14)

where γx is a time-invariant constant6.

Trade Shares. We need to find out how trade flows are pinned down with given prices.

To achieve that goal, let us start by computing the probability location j buys a given

variety to location supplied by location l ∈ L. Because the productivity draws are iid, and

since there is a continuum of goods for each type, this probability turns out to be the share

of goods that ℓ ∈ L supply to j ∈ L.
We denote by πxj,ℓ the fraction of goods of type x that location j ∈ L buys from location

ℓ ∈ L, which is given by

πxj,ℓ =
T xℓ

(
wℓτ

x
j,ℓ

)−θx
Φxj

≡
T xℓ

(
wℓτ

x
j,ℓ

)−θx
∑
ℓ∈L

T xℓ (wℓτ
x
j,ℓ)

−θx
(3.15)

In order to find out the total cost of these expenditures, we need to calculate the price

of the goods that location j bought from location ℓ. Due to the Fréchet distribution for

the productivity draws, the distribution of paid prices faced by location j ∈ L of varieties

coming from ℓ ∈ L conditional on ℓ being the cheapest supplier turns out to be equal to

the distribution of prices coming from ℓ ∈ L to j ∈ L, that is

Pr

{
pxj,ℓ(ω) ≤ p̃ | pxj,ℓ(ω) ≤ min

k∈L−ℓ

pxj,k(ω)

}
= Gxj (p̃) (3.16)

6This constant is equal to Γ
(

θx+1−νx

θx

) 1
1−νx

. Γ(u) is the Gamma function, given by
∫∞
0
xu−1e−xdx,

for u > 0. As we show later, once we apply logs and take differences, this constant disappears entirely

60



The result in (3.16) implies that the share of expenditures on type x in the location j

that is supplied by location ℓ is also given by πxj,ℓ.

3.3 Equivalent Variation

In what follows, we borrow insights from the standard demand theory, in the spirit of

Fajgelbaum and Khandelwal (2016) to shed light on why the separation between the trade

and the demand blocks we propose is particularly useful. In particular, as we show next,

because of free mobility of labor across sectors, and because the changes in productivity

affect only the agricultural sector, by assumption, income in terms of the outside good is

constant. Hence, changes in utility from the productivity in the food sector come from the

changes the relative price of food alone.

3.3.1 Climate change through the lens of the Model

The average potential productivity of the food-producing sectors is defined to be µxℓ ≡
E[Zxℓ (ω)]. Because the draws for each ω ∈ [0, 1] comes from a Frechét distribution, this

average productivity relates to T xℓ according to the formula

T xℓ =
[
µxℓ

]θx
κx (3.17)

where κx is a time-invariant constant common to all locations7. In what follows, we will

assume that climate change affects T xℓ , by looking at µxℓ , which we can read from the GAEZ

dataset.

Let Vi,j ≡ V (P cj , P
q
j , yi) be the indirect utility of an individual with income yi in

a location j, where prices are P cj and P qj . Notice that because the outside good is the

numeraire, its prices do not appear in the indirect utility. Taking the log of Vi,j and its

total derivative with respect to log prices and log income, we have:

V̂i,j =
∑
x∈X

∂ log(Vi,j)
∂ logP xj

P̂ xj +
∂ log(Vi,j)
∂ log yi

ŷi (3.18)

7This constant is equal to Γ
(

θx−1
θx

)−θx

. Γ(u) is the Gamma function, given by
∫∞
0
xu−1e−xdx, for

u > 0.

61



where we use the convention ẑ ≡ d log(z) representing the log change in a variable z. Let

EVi,j be the equivalent variation associated with the prices changes as the proportional

change in income, at pre-shock prices, which would generate the same change in utility as

the total derivative above:

V̂i,j =
∂ log(Vi,j)
∂ log yi

EVi,j (3.19)

Here, EVi,j is the variation in income that would be necessary to achieve the same variation

in utility that would have happened from the variation in prices and income above, that is

V̂i,j .
We recover the following formula for the Equivalent Variation using Roy’s Identity,

while noticing that ŷi = 0 since in our setting, due to the free mobility of labor across

sectors and the assumption that Zoℓ is not affected by Climate Change, income is constant8:

EVi,j =
∑
x∈X

−sxi,jP̂
x
j (3.20)

where sxi,j is the expenditure share on good x with income i at location j, at the pre-shock

prices. The interpretation of EVi,j is the consumer’s willingness to pay to avoid the price

changes.

The prices changes P̂ xj for each x happen due to changes in the productivity in each

crop, in each location. Through the lens of our model, we map climate change into a change

in the parameter µxℓ , implemented as a change the parameter T xℓ , per equation (3.17). In

particular, we have

P̂ xj =
∑
ℓ∈L

∂ log(P xj )

∂ log(µxℓ )
µ̂xℓ (3.21)

Using (3.14), (3.17), and (3.15) we have

∂ log(P xj )

∂ log(µxℓ )
= −πxj,ℓ (3.22)

So that the change in the price of basket of type x in location j relates to changes in the

average productivity in location ℓ according to the trade share, πxj,ℓ. Using this result in

(3.20), we recover

EVi,j =
∑
x∈X

sxi,j
∑
ℓ∈L

πxj,ℓµ̂
x
ℓ (3.23)

8It is straightforward to relax this assumption.

62



Equation (3.23) shows that the equivalent variation depends on the components. First,

it depends on the expenditure share on type x under income i and location j , sxi,j . This

information is recoverable from the data, by means of exploit the latest consumer expen-

diture survey, provided a classification for what should be in each basket x. The second

component is the trade-share between location j and all other suppliers locations ℓ, given

the the type x, which is πxj,ℓ. This component is not observed directly in the intra-national

data, and one needs to estimate it. Finally, the last component is the proportional change

in the average potential productivity, µ̂xℓ .

Next, we show how we perturb the model in order to recover the estimate for πxj,ℓ. The

key idea is to introduce a transitory weather shock that is observed in the data and can be

useful to backout these estimates, provided the structure of the model and the available

data.

3.4 Recovering the Trade Frictions

Our main goal in this section is to estimate the trade shares, which are not directly

observed in the data. In order to do so, we introduce a transitory component to agriculture

productivity that depends on the realization of a weather shock.

Weather Shocks. At each period, a weather shock realizes, which we denote by h ≡
{hℓ}ℓ∈L, where a location ℓ receives hℓ. As we explain below, these weather shocks affect

the productivity of food-producing sectors, affecting their production costs. For simplicity,

we assume that these heat shocks do not affect the productivity of the outside sector. In

what follows, we suppress hℓ from the notation to limit notation clutter.

In this perturbed environment, there are two terms that define the productivity of the

food-producing sectors. The first is a permanent productivity that follows the structure of

Eaton and Kortum (2002), while the second term captures the transitory effects of heat in

the productivity of crops.

We denote by Z̃xℓ (ω) the permanent productivity of variety (x, ω) at location ℓ, which

we refer to as “EK term” above. The second term accounts for how the weather realizations

affect productivity temporarily, and we denote it by Gx(hℓ). We emphasize that the first

63



term is time-invariant and the second is stochastic. The “effective efficiency” Zxℓ (ω) is then

Zxℓ (ω) = Z̃xℓ (ω)︸ ︷︷ ︸
EK term

× Gx(hℓ)︸ ︷︷ ︸
Weather Shock

(3.24)

Different realizations of the weather variable hℓ map into different levels of “effective pro-

ductivity”. These effects are invariant to the location — there is no subscript ℓ in the

function Gx(·)— but we allow food types to have different sensitivities to heat. The uni-

tary cost of production variety (x, ω) is given by

w̃xℓ ≡ wℓ
Gx(hℓ)

(3.25)

From the expressions above for the prices and trade shares, Equations (3.14) and (3.15),

the key change is the replacement of wℓ by w̃
x
ℓ :

P xj =

(∑
ℓ∈L

T xℓ (w̃
x
ℓ τ

x
j,ℓ)

−θx
)− 1

θx

γx and πxj,ℓ =
T xℓ

(
w̃xℓ τ

x
j,ℓ

)−θx
∑
ℓ∈L

T xℓ (w̃
x
ℓ τ

x
j,ℓ)

−θx
(3.26)

The log linearity of the price of the basket and the trade shares allows us to derive

link between the incidence of heat and changes in prices. We exploit this link to recover

estimates of these trade frictions.

3.4.1 From Heat Shocks to Prices Changes

In this section, we show how we recover estimates of trade costs for each type of food

good. First, we develop the results that we need in order to run the structural regression.

For a type x of food, the model implies a close relationship between logarithmic changes

in price and the occurrence of heat in every location. In the model, heat reduces the

productivity of each sector, effectively increasing the unitary cost of production: more

labor is required to produce one unit of output. Then, because the locations trade among

themselves, the higher production cost in one location translates into higher bundle cost

in all other locations, with the relative importance given by the trade shares. Next, we

formalize this intuition.

64



Consider a location j of interest and a location ℓ that receives a heat shock. The price

at the location j increases with an increase in the cost of production at the location ℓ

according to
∂ log(P xj )

∂ log(w̃xℓ )
= πxj,ℓ (3.27)

Equation (3.27) shows that the elasticity of the price index at j with respect to production

costs at location ℓ is given by the expenditure share of location j from location ℓ. Intuitively,

location j is more exposed to shocks at ℓ with the higher importance of ℓ as a supplier. This

production cost increases with the realization of heat. By our formulation, this implies

∂ log(w̃xℓ )

∂hℓ
= −∂ log(G

x(hℓ))

∂hℓ
≡ ηx (3.28)

This delivers a single semi-elasticity that is one output of our estimation procedure. Notice

that we assume, for simplicity, that ηx is homogeneous between locations. This is an

identification assumption. Putting all together, we recover

∂ log(P xj )

∂hℓ
≡
∂ log(P xj )

∂ log(w̃xℓ )

∂ log(w̃xℓ )

∂hℓ

= πxj,ℓ × ηx (3.29)

The logarithm increase in the cost of a basket x in a location j goes up with a shock

realized at location ℓ with two components. The first is how much location j is exposed to

shocks in ℓ through trade, πxj,ℓ multiplied by how much the production cost in ℓ increases

upon the realization of heat, at the margin.

This gives the price change up to a first-order approximation, with “one unit” of the

hℓ. In reality, shocks would affect each region. To take all this into account, we take the

total derivative of the price with respect to heat shocks in each location and sum it across

all locations.

∆ log(P xj ) ≈ ηx
L∑
ℓ=1

πxj,ℓ∆hℓ (3.30)

In our approach is then to use variation from observed price changes and heat shock

realizations to infer the trade shares πxj,ℓ. The key idea is to use the structure of these

trade shares in the model, together with observables in the data to recover the trade costs,

65



allowing us to retrieve the missing shares. Toward this goal, we next describe the data we

use.

3.4.2 Weather Data

Our weather satellite data is extracted from Copernicus Climate Change Service (2019)

for the 1950-2021 period. We use the hourly average land temperature at the raster level

of 0.1
◦
by 0.1

◦9. We calculate the number of days of exposure to temperatures above

30
◦
C/86

◦
F at the quarterly level. We convert the raster-level exposure data to the munic-

ipal level by computing the municipal average exposure over the rasters contained in the

municipal boundary. Ultimately, we calculate the weighted state-level average of exposure,

weighting municipalities by the average annual value of municipal crop production from

1999 to 2021. The crop production data comes from the Systematic Survey of Agricultural

Production collected by IBGE, which we describe in more detail in the Appendix B.1.2.

We choose 30
◦
C as our temperature threshold, given the adverse effects that tem-

peratures above this threshold have on crop yields, as well documented in Schlenker and

Roberts (2009). They find non-linear effects of exposure to high temperatures on maize,

cotton, and soybean yields. We validate this choice for the temperature threshold. As

documenting the link between heat exposure and crop yields is not entirely novel in the

literature, we include them in the Appendix B.1.2. Our analysis shows a contraction in

crop yields after exposure to temperatures above 30
◦
C in the crop growing season. The

estimates are statistically significant and economically relevant. After controlling for state-

year factors, the semi-elasticity is around −0.4% for rice, −0.6% for soybeans, and 0.6%

for beans.

3.4.3 Consumer Price Index Data

We use data from the official Consumer Price Index (CPI) in Brazil, taken from

IBGE10. The most detailed data are available at the “sub-item” level (e.g., banana, bus

fare, t-shirt) at the monthly frequency, which aggregates into baskets called “items” (e.g.,

9Equivalent to 11 by 11kms, or 6.5 by 6.5 miles. Owing to the curvature of the earth, the area covered

in the grids increases as we approach the equator line.
10In Portuguese, it is the IPCA — Índice de Preços ao Consumidor Amplo.

66



fruits, public transportation, youths apparel), and further aggregates named “groups”(e.g.,

food and beverages, transportation, apparel). Nationwide, IBGE tracks a basket of sub-

item prices, mimicking the average consumption basket of a family with income ranging

from 1 to 40 minimum wages and living in urban areas11.

The raw microdata consists of a panel of locations and price changes at sub-item, item,

and group levels, together with the monthly weights. Our sample starts in August 1999, a

date that we chose given the history of hyperinflation before 1994 and the pegged exchange

rate from mid-1994 until early 1999. The last observation date is December 2023. The

panel is unbalanced, with 11 locations at the beginning of the sample and 16 at the end of

the sample. A location is either a metro area or a municipality (state capital), and there

is at most one location per state. More details in these locations, and their relevance are

relegated to Appendix B.1.3.

The price levels are not directly available, so we construct price indices. For each

location, we use the raw microdata to construct the price level for a variety of baskets. For

a given basket, we renormalize the weights of the sub-items that are part of the basket so

that they sum up to one hundred and compute the weighted average inflation. Then, we

recover the price index for each basket by compounding its inflation over time. We refer

to appendix B.1.3 for further details on the CPI data and the steps taken to recover the

price levels.

We borrow a tradability classification from the Brazilian Central Bank (BCB) in order

to construct low-trade-cost and high-trade-cost food baskets. The BCB calls goods “trad-

able” and “non-tradable”, respectively. In the classification, “non-tradable” is not literal :

these are goods and services that are produced and consumed primarily domestically, with

a minor role played by international trade. Examples of “Tradable Food” are soybean, rice,

wheat, sugar, and their derivatives, while beans and fresh food such as tomatoes, lettuce,

and kale are examples of “Non-tradable Food”. We refer to appendix B.1.4 for further

details on the BCB classification. In order to avoid any confusion, we call the “tradable”

basket as low-trade-cost “LTC” and the “non-tradable” as HTC.

11This income range covers around 90% of the families in the latest Consumer Expenditure Survey, from

2017-2018. The national minimum wage in 2018 was R$ 954. The average commercial exchange rate against

the U.S. dollar fr 2018 was approximately R$ 3,65 per US$, so the minimum wage was approximately US$

260 in 2018.

67



3.4.4 Structure for the Trade Shares

We use the functional form for the trade shares shares from Equation (3.15) in a

non-linear estimation approach. Specifically, we estimate the parameters [T xℓ ], wages [w̃
x
ℓ ],

and a parameter θx, while imposing a functional form on trade frictions [τxj,ℓ] based on

observables. We then maximize the fit of the model by aligning it with this structure.

For the trade cost functional form τxj,ℓ, we adopt a straightforward approach, using

driving time between state capitals with a constant elasticity. A non-linear least squares

method allows us to estimate the elasticity δx separately for each food type.

The following sections outline the data sources and processing methods used to con-

struct the trade shares

Technology Level T xℓ

The State of Technology parameter T xℓ relates to the average potential productivity

of a location ℓ for type x, as Equation (3.17) highlights. It is important to note that

this Equation does not allow us to identify the parameter θx separately. This is a common

feature in the trade models, where some parameters cannot be separately identified. Hence,

we take a value from the literature, in particular Astorga-Rojas (2024) and Albert et al.

(2024).

The GAEZ data come in raster form for 53 crops, for the historical crop yields for

the period of 1981-2010. The unit of measurement is kilograms per hectare. For each

of the these 53 crops, we calculate the potential yield at the state level. There are two

adjustments that we need to perform with these data so that we can arrive at an estimate

for T xℓ .

First, since our model considers labor as the sole production factor, we must translate

land productivity into labor productivity. To accomplish this, we rely on data from Brazil’s

most recent agricultural census, which took place in 2017. We utilize the national average

for input requirements per crop, which indicates the number of workers employed per

unit of land. Two fundamental assumptions underpin this approach. Firstly, a Leontief

production function is employed, implying a fixed ratio between land and workers across

different locations. This ratio varies based on the crop: some crops require more land,

while others demand more labor. Secondly, it is assumed that land is relatively abundant,

68



implying that production is contingent on labor allocation rather than the land’s quantity.

The subsequent adjustment involves incorporating averaging. This step is crucial as

the units after the initial adjustment, and even before, do not align across different crops,

resulting in kilograms per worker. By converting land productivity into worker produc-

tivity measured in kilograms, we address the issue by multiplying labor productivity by

the historical average price per crop at the national level. Consequently, we map µxℓ to

the revenue productivity within the dataset. The source of the crop price data is the

Systematic Survey of Agricultural Production (SSAP)12. We used the ratio between the

total production value divided by the total production quantity at the national level per

year from 2002 to 202213. Then, we take the average over the years. The use of national

price is intended to mitigate the issue of the state price incorporating the trade frictions

themselves, as the local price in isolated places tends to be higher.

For the second adjustment, we aligned the FAO potential crop yields with those moni-

tored by the SSAP. Altogether, there are 29 crops that were mapped between these datasets.

These 29 crops are categorized as either low-trade-cost or high-trade-cost based on their

names’ correspondence with CPI food items. Specifically, 17 crops fall under LTC, while

12 are designated as HTC. These matched crops represent on average, across time, 90 per-

cent of all crop production value and 95 percent of land utilization nationwide. Appendix

B.1.5 contains a complete list of these crops, along with further details on these adjustment

factors.

Finally, since the trade share in Equation (3.15) is homogeneous of degree 0 in the

vector of productivities, we choose the state of São Paulo as a reference and normalize the

other states T xℓ as a ratio of the level of São Paulo. The resulting measure for µxℓ for each

food type is show in Appendix B.1.5.

Wage level w̃xℓ

We borrow wages from the Continuous National Household Sample Survey14 conducted

by the IBGE. This is a household survey that started in 2012 and is ongoing. The data is

12In Portuguese, “Levantamento Sistemático da Produção Agŕıcola”.
13The records for 2001 and before of the prices were measured as local currency per unit or bunch for

some crops, especially fruits.
14PNAD Cont́ınua, in Portuguese

69



released at the state level at a quarterly frequency.

We make two decisions. First, similarly to the parameters T xℓ , the trade share is

Equation (3.15), it is homogeneous to zero degree in the wages vector. Hence, we work

again with São Paulo as a reference state: the wage cost normalized to 1 and fed into the

estimation procedure the relative wage of all states to the level in São Paulo.

Furthermore, given that the temporal coverage is less than half of that provided by the

CPI data, utilizing the time series of relative wages would result in a loss of approximately

half of our sample size. To address this limitation, we opt to use a singular representative

value for the wage in each state. Specifically, we compute the varying ratios of relative

wages compared to São Paulo and subsequently determine the average of this time series.

Through the lens of our model, one might interpret this strategy as follows: we take a

first-order approximation of this trade shares with respect to w̃xℓ around a zero heat shock

position h = 0 and let fixed effects and the residuals soak the approximation error. If this

relative rate shows any particular seasonal pattern, the state-season fixed effects that we

include in the regression would capture such a pattern. The series we use is the average

usually received wage in all occupations. For our purposes, this serves as a proxy for Zoℓ .

There are two main implications resulting from taking this approach. First, since the

wage is constant, it follows that the trade shares are constant - the state of technology,

trade frictions, and the parameter θx are assumed to be invariant in this stage. In reality,

these trade shares probably fluctuate, but these are all unobserved fluctuations. Second,

the wage level that we input into the estimation procedure is the same regardless of the

type of food. The values for the wage we use for each state can be found here in Appendix

B.1.5.

Trade Elasticity θx

There is great variability in the estimates of trade elasticity in the empirical appli-

cations of trade models. As discussed above, we borrow the trade elasticity parameter

θx from Astorga-Rojas (2024). The author leverages the construction of Brasilia and the

project to connect the newly created national capital city to other state capitals as a nat-

ural experiment. Using archival data with state-to-state trade flows from 1942 to 1949

and 1968 to 1974; the author recovers an estimate for the trade elasticity from a gravity

70



equation using the construction plan for roads connecting Brasilia to other state capitals

as an instrument. The value he finds is θx = 3.39. The value is the same used in Albert

et al. (2024) and within the range proposed in the literature. Notice that we use the same

trade elasticity for both types of food.

Pellegrina (2022) relies on archival data from Brazil together with the price of agri-

cultural goods finds a trade elasticity θx around 3.90 for perishable agricultural products

(vegetables and fruits), and θx around 5.1 and 5.6 for cereals (rice, soybeans, corn, and

wheat) and other non-perishable agricultural products, respectively. The value we use,

θx = 3.39, is within the range proposed in Simonovska and Waugh (2014) and similar to

the value of 4 commonly assumed when this parameter is not directly estimated. Ramondo

et al. (2016) uses a value of 4 when studying domestic frictions in the US.

Trade Frictions Specification

We need to discipline one matrix of trade costs per type of food, totaling values of

parameters 27× 27× 2. Given the assumed full integration within each state (τxj,j = 1), we

impose symmetry (τxj,ℓ = τxℓ,j) of the trade costs reduces the number of parameters. The

lack of trade data within subparts of a nation is common (Ramondo et al., 2016; Pellegrina,

2022; Sotelo, 2020). Approximately two thirds of the cargo in Brazil is conducted by trucks

via roads (World Bank, 2022), we impose that these trade costs are a function of the driving

time between state capitals.

Precisely, the functional form that we use is

log(τxj,ℓ) =

0 if j = ℓ

δx log(dj,ℓ) if j ̸= ℓ
(3.31)

The variable variable dj,ℓ ≥ 0 is a measure of distance between the capital of states j and ℓ.

As we explained in the model, we set τj,ℓ = 1 whenever j = ℓ. For all the other cases, the

distance is non-zero, and we assume that the trade friction τxj,ℓ exhibits a constant elasticity

with respect to the measure of the distance. We allow this elasticity to be different for the

two types of food goods, low-trade-cost and high-trade-cost.

We measure the distance dj,ℓ by the driving time, in hours, from the capitals of j and

ℓ. We collect this information from Open Street Maps in July 2024. Similarly, Pellegrina

71



(2022) uses Google Maps data for the driving time for some of his estimation. The infor-

mation contains the driving distance in kilometers and the driving time in hours - which

allows us to compute the average speed, measured in kilometers per hour. Since there is

substantial heterogeneity in the average speed between locations, we interpret this as a

sign of heterogeneous road quality across the nation.

Table 3.1: Descriptive statistics for alternative measures of Driving Distance

Measure Origin Capital N Mean SD Min p25 p50 p75 Max

Driving Distance, km

All 702 2619 1443 112 1534 2430 3597 6702

Manaus 26 4050 1403 754 3420 4392 4988 6020

São Paulo 26 2152 1220 408 956 2309 2935 4653

Porto Alegre 26 2975 1312 473 1884 3427 4000 5236

Driving Time, hours

All 702 38 22 2 21 34 53 100

Manaus 26 65 20 13 56 68 77 90

São Paulo 26 30 19 6 13 30 39 73

Porto Alegre 26 41 19 6 26 45 53 81

Average Speed, km/hour

All 702 70 6 52 66 71 75 82

Manaus 26 62 4 52 60 62 65 67

São Paulo 26 73 5 63 69 74 77 81

Porto Alegre 26 74 4 65 70 75 77 78

Notes: The table displays the statistics for driving distance, driving time and average speed

between all pairs of state capitals in Brazil. There are 27 states, with 702 (27× 26) unique

pairs of origin-destinations. Swapping the order of origin and destination within the pair might

lead to different estimates for the three variables shown in the table. The reason is that the

exact route might not be two-ways all along. The differences are usually smaller than 1%,

considering absolute deviation from the mid-point. Manaus is the capital of Amazonas, in the

Norte Region in the Amazon. São Paulo is the capital of São Paulo and Porto Alegre is the

capital of Rio Grande do Sul, the state most to the South. Data is from Open Street Maps,

collected in July 2024. p25 stands for the percentile 25% in the distribution, while p75 stands

for the percentile 75%.

Table 3.1 shows some descriptive statistics for all unique origin-destination pairs of

state capitals (“All”), and some selected capitals. Brazil is a large country, so driving

distance measured in kilometers between state capitals go as high as 6700 km. The median

travel time is 34 hours, spamming from 2 to 100 hours. There is substantial dispersion

72



in road quality, proxied by the average speed: the interquantile interval for the average

speed is 9 km, from 75km/h to 66km/h, while the range of this variable is from 52km/h

to 82km/h.

To further illustrate the dispersion in road quality and remoteness, we include three

state capitals in Table 3.1 for reference. We choose Manuas, the state capital of Amazonas,

to be a representative location of a reasonably dense location that is somewhat far from

other state capitals. Manaus is situated in the center of the Amazon rainforest, an area

that remains fairly secluded, with road travel speeds being quite modest. The median

driving time from Manaus to other capitals is 68 hours, with the median speed being 62

km. It is not only about how distant Manaus is, but how difficult or costly, in time, to get

there.

We added two other capitals for easing the comparison. São Paulo, the capital of the

homonymous state, is the richest capital and amounts to the most populated capital. The

median and average driving time is 30 hours, with a median speed of 74 km/hour. Porto

Alegre is the state capital of Rio Grande do Sul, the state that is most to the south. Almost

by construction, Porto Alegre is “far” from many states, specially the ones from the North

and Northeast. This pattern can be seen from the driving distances and driving times,

that are offset relatively to São Paulo, that is somewhat more central. It is somewhat

remarkable that the average speed departing from São Paulo or from Porto Alegre are very

much lined up.

Having gotten a sense of these differences in the driving time, we next describe the

estimating regression that we run to recover the trade costs.

Estimating Equation and Results

We are now in place to implement our specification, as in (3.30). The estimating

regression is

ln(pxj,t)− ln(pxj,t−1) = ηx
L∑
ℓ=1

πxj,ℓHeatℓ,t + ξt + χℓ,s + ϵj,t (3.32)

The dependent variable is the log change in prices for a basket x in a location j between

period t and t−1. The baskets that we consider are the low-trade-cost and the high-trade-

cost food, from the CPI data. The independent variable is a weighted average of the heat

73



across all states, with the weights given by the trade shares between the reference state j

and all others, indexed by ℓ. The heatℓ,t variable is the number of hours, measured in days,

state ℓ was exposed to the temperature of 30
◦
C during quarter t. We run the regression

at the quarterly frequency.

Because there is variation in the price data that are non-necessarily related to the

realizations of heat, we further include two types of fixed effects. First, ξt is the quarterly

date fixed effect. This term captures forces that push inflation up and down in all locations

regardless of the heat shocks, such as the business cycle or the nominal interest rate. In

addition, we also have a fixed effect interacting with location and season, namely ξℓ,s. In

Brazil, the seasons are summer, fall, winter, and spring from quarter one to four of the

calendar year. These dummies are meant to capture seasonal patterns that are specific

to each location. Because Brazil is very vast across the latitudes and relatively to the

east coast, there is substantial heterogeneity in the seasonal patterns of heat — and hence

prices. For example, locations in the North and Northeast are closer to the Equator line

and then to be relatively warmer.

The multiplying coefficient ηx is an outcome of the procedure. This is the semi-

elasticity of the yields in a given location with respect to the heat that is realized at that

location, as in Equation (3.29). We first discuss the results regarding δx, later focusing on

the discussion for ηx.

Table 3.2 shows the results from the non-linear least square estimate of Equation (3.32).

For goods classified as low-trade-cost, the elasticity of the trade friction with respect to the

driving time is about 0.30, while this elasticity is around 0.56 for the high-trade-cost food

goods. We bootstrapped the confidence interval for this elasticity using 300 repetitions,

with 95% of the sample clustered at the state level. The coefficients are statistically different

from zero and each other.

74



Table 3.2: Regression (3.32), estimated by Nonlinear Least Squares

LTC Food Goods HTC Food Goods

log(dj,ℓ), δ
x 0.303*** 0.561***

(0.053) (0.083)

Observations 1,211 1,211

R-squared 0.89 0.82

States 16 16

Fixed Effects:

Quarterly Date ✓ ✓

State-Season ✓ ✓

Note: Bootstrapped standard errors clustered at

State level. We performed 300 repetitions, with 95%

of the sample for each state. Significance levels: p <

*** 1%

By construction, these elasticities get the dynamics of both price and heat shocks from

the data as close as possible to the ones that the model implies. We now offer some heuristic

explanations on why the ordering of these elasticity turns out to be consistent with the

ordering low-versus-high trade cost in the classification.

Heat shocks are naturally spatially correlated. Panel (a) of Figure 3.1 shows the

correlation of heat shocks between pairs of states plotted against the driving time between

their capitals. Nearby states, with shorter driving times, experience similar shocks, leading

to high correlations.

Panel (b) of Figure 3.1 reveals a less intuitive pattern: nearby locations also exhibit

closely related inflation dynamics, with correlations decreasing as driving time increases.

Unlike heat shocks, inflation correlations remain above 0.50 even for distant locations. This

persistence reflects other nationwide drivers of inflation, such as monetary policy and the

business cycle15.

A notable feature in Panel (b) is that the decline in inflation correlation is sharper for

high-trade-cost (HTC) food goods.16 Due to higher trade costs, states are more likely to

15Although not depicted in the figure, components that are entirely immobile, such as “food away from

home,” exhibit an average correlation of 0.30, which remains constant regardless of driving time.
16This pattern is supported by regression analysis showing statistically different slopes for high- and

75



Figure 3.1: Spatial Correlations of Heat and Inflation

(a) Heat shocks (b) Inflation of Food Goods

Note: For both panels, the horizontal axis is the driving time between the pair of state capitals,

in log scale. Panel (a) shows the spatial correlation of the heat shocks. The vertical axis is the

correlation across the time series of these heat shocks for each pair of states. Panel (b) shows

the correlation of food good inflation for each pair of states, by tradability classification. Here

P̂ x
j ≡ log(P x

t ) − log(P x
t−1). In yellow, we have the low-trade-cost food goods, while in green we

have the high-trade-cost goods.

76



source HTC goods from nearby states, making local inflation more sensitive to local con-

ditions. Since heat shock correlations drop off quickly with distance, inflation correlations

for HTC goods decline faster than for low-trade-cost goods. Thus, the higher elasticity

δx for HTC goods aligns with the observed correlation patterns of both heat shocks and

inflation across the cross-section.

Table 3.3: Outcome for regression (3.32) under alternative regressors

Dependent variable: 100× (log(pxj,t)− log(pxj,t−1))

LTC Food HTC Food LTC Food HTC Food

(1) (2) (3) (4)

Heatt,j 0.049*** 0.104*

(0.017) (0.058)∑L
ℓ=1 π

x
j,ℓHeatt,ℓ, η

x 0.113*** 0.120*

(0.039) (0.066)

Observations 1,211 1,211 1,211 1,211

R-squared 0.89 0.82 0.89 0.82

States 16 16 16 16

Fixed Effects:

Quarterly Date ✓ ✓ ✓ ✓

State-Season ✓ ✓ ✓ ✓

Note: Robust Driscroll-Kraay standard errors. Significance levels:

p < *** 1%, ** 5%, * 10%. Columns (1) and (2) show the result of

the regression in (3.32) by imposing πx
j,j = 1, that is including only

the own shock to state j. Columns (3) and (4) exhibit the results for

the weighted average of the heat shocks and with the estimation

conducted by NLS.

A notable feature in Table 3.3 is the change in estimated coefficients when comparing

regressions using only own-state shocks versus those including shocks from all states. Since

states trade with one another, heat shocks affecting sourcing states influence the price

dynamics of destination states. By considering only the own-state shock, relevant variables

are omitted, leading to biased coefficients in columns (1) and (2). Accounting for shocks

from all states, through the structure of the model for πxj,ℓ, effectively incorporates these

low-trade-cost goods.

77



variables under the assumption that ηx remains consistent across states.

The relationship between the coefficients under different specifications also connects

to the elasticity estimate δx for each food type. For high-trade-cost (HTC) goods, the

elasticity δq is relatively high, resulting in low trade shares for states other than the own

state (ℓ ̸= j). Consequently, the coefficients in columns (2) and (4) are similar, reflecting

a near-autarky situation for HTC goods. In contrast, for low-trade-cost (LTC) goods, the

lower elasticity δc leads to more interstate trade, with πcj,j deviating from unity. As a

result, including previously omitted variables causes a significant shift in the estimated

coefficients between columns (1) and (3). Interestingly, the resulting semi-elasticity of crop

yields to heat, ηx, remains consistent across both food types.

The heat elasticity ηx, detailed in Table 3.3, reflects short-term elasticity, measuring

the change in log yields from one additional day above 30
◦
C in a quarter. It is not intended

to predict long-term productivity changes under climate change scenarios.

While ηx is not useful for counterfactual exercises, it validates the model by aligning

implied semi-elasticities of crop yields to heat shocks with estimates from crop production

data (Appendix B.1.2). Column (5) of Tables B.1, B.2, and B.3 report elasticities of

0.4%–0.6% for rice, soybeans, and beans, slightly higher than the 0.11% and 0.12% in

Table 3.3, columns (3) and (4). Differences arise, for example, because crop production

data are annual, focusing on critical growth cycles, while regression (3.32) is quarterly and

averages sensitivity across crops and seasons.

3.5 Preferences and Model Fit

3.5.1 Utility Function

We employ a non-homothetic utility function, which aligns the income’s share allocated

to food with observed data by depending on income. We use a Stone-Geary utility function

that involves a minimum level of food consumption cf . Although the utility function

remains consistent across regions, disparities in the costs of these minimum levels create

state-specific effects. These are due to regional differences in food prices, leading to uneven

minimum consumption costs. In addition, regional income variations influence the relative

burden of these costs on households in different states.

78



U(coi,ℓ, c
f
i,ℓ) = (1− αf ) log(coi,ℓ) + αf log(cfi,ℓ − cf ) (3.33)

where coi,ℓ is the consumption of the outside good, cfi,ℓ is the food consumption and cf is

the minimum consumption of good. The indices (i, ℓ) refer to income i in location ℓ.

Food is a composite of low- and high-trade-cost food CES aggregators. We assume for

now that this composite is a Cobb-Douglas function, as follows:

cfi,ℓ = αc log(cci,ℓ) + αq log(cqi,ℓ) (3.34)

cci,ℓ is the consumption of the low-trade-cost food composite and cqi,ℓ is the high-trade-cost

food composite, with income i in location ℓ. This formulation allows us to write the price

of food in location ℓ as a function of the price of each type-specific basket:

P fℓ =

(
P cℓ
αc

)αc (
P qℓ
αq

)αq

(3.35)

Notice that the income level does not appear in this price: regardless of income, the

price of food depends on the location ℓ where it is consumed. However, due to the non-

homotheticity of the utility function, households with different incomes in the same location

will face distinct burdens to pay for the floor consumption of food. Precisely, the food

expenditure share is given by

sfi,ℓ = αf + (1− αf )
P fℓ c

f

yi,ℓ︸ ︷︷ ︸
ψi,ℓ

(3.36)

The term ψi,ℓ captures the subsistence share: the share of income required to pay the floor

consumption of food. Given the Cobb-Douglas aggregator for the food composite, the food

expenditure share for each type is given by

sxi,ℓ = αxsfi,ℓ, x ∈ {c, q} (3.37)

Income. For the household in group i living in location ℓ, its income is simply their

effective hours supply, ei,ℓ, times the wage prevailing at that location, wℓ. Because of free

mobility across sectors, the wage is pinned down by the productivity in the outside sector,

wℓ = Zoℓ . The income yi,ℓ = ei,ℓwℓ = ei,ℓZ
o
ℓ .

79



3.5.2 Calibrating the Parameters

In our setting, since markets are competitive, prices are given by the marginal cost

of production. Per equation (3.14), the prices of the baskets x are pinned down by State

of Technology, T xℓ , the wages w̃xℓ and the trade frictions between locations, τxj,ℓ. Because

labor is fully mobile across the sectors, as in Costinot et al. (2016), the productivity of the

outside sector Zoℓ determines the labor cost in each state. As in Eaton and Kortum (2002),

the income is hence exogenously given by the effective labor hours and the productivity

Zoℓ . The key implication is a separation between price determination and the demand side.

In contrast, the preference parameters and the income pin down the expenditure shares,

for each household in each location. Given that the wage rate is governed by the produc-

tivity of the outside sector, Zoℓ , introducing income heterogeneity is straightforward. We

take the route of allowing households in each location to have heterogeneous endowments

of effective labor hours. Facing the same hourly wage, the differences in effective labor

hours generate mechanically income heterogeneity. Given the income for each household

in each location, our goal is to calibrate the preference parameters to match the food ex-

penditure shares as closely as possible, taking as given the production structure and the

implied prices. In our setting, we need to assign values for 6 parameters, two that are

general (αf , cf ), and one pair for each type of food (αx, νx) for x ∈ {c, q}. Next, we discuss
the role of each of these parameters.

First, αf approximates the food expenditure share as the subsistence ratio ψi,ℓ gets

close to 0. Hence, this parameter is disciplined mostly by the behavior of the food ex-

penditure share for the highest income decile. Conversely, when ψi,ℓ increases, so does

the food expenditure share. Hence, the food expenditure share of the lowest-income decile

disciplines the choice of cf , which drives ψi,ℓ.

For the parameters of each food type, we set αc = αq = 0.5, based on average food

expenditure shares. The CPI data includes both goods and services, such as “Food away

from home,” which falls under food services. In the BCB basket, the “tradable” (low-

trade-cost) basket consists only of goods, while the “non-tradable” (high-trade-cost) basket

includes both goods and services. Historically, the tradable basket accounts for around 50%

of the food category in the CPI. Within the non-tradable basket, the representative family

tracked by the official CPI (IPCA) allocates approximately 40% to goods and 60% to

80



services. Since our model does not explicitly include food services, we incorporate the

entire non-tradable basket into the high-trade-cost category.17

For the remaining parameters, we set νc = 3 and νq = 3. In our model, these pa-

rameters influence the price level, as shown in equation (3.14) through γx.18 A higher νx,

provided the condition νx < 1 + θx is met, results in a lower price level. As long as this

constraint is satisfied, the specific values of νc and νq are not critical, as they primarily

serve to rescale the productivity vectors T xℓ .

We want to estimate the parameters (αf , cf ). Our goal is, given prices and income,

pick (αf , cf ) to describe the food expenditure shares as best as possible. Concretely, the

estimated parameters solve

̂(αf , cf ) ∈ argmin

[∑
i

∑
ℓ

Λi,ℓ

(
sf,datai,ℓ − sf,model

i,ℓ (αf , cf )
)2]

where we weighted the deviations by the population shares in income decile i in state ℓ,

Λi,ℓ. As explained earlier, the income brackets are defined at the national level, so the

within state population is not necessarily even across i. In addition, the average income

for each bracket i is not even across the states. We use this heterogeneity to discipline the

effective hours, ei,j as follows: together with the level of Zoj , we calibrate ei,j to match the

income level for each bracket at each state, according to yi,j = ei,jZ
o
j .

Our data for the expenditure shares come from the latest Consumer Expenditure

Survey19, conducted between 2017 and 2018. The coverage for the survey is national, and

the unit of aggregation is the household level. In total, 57 920 households were interviewed,

aiming to be representative of 69 017 704 households nationwide. The average family size

is 3.00 persons per household.

From the microdata, we recover three estimates that are useful for our purposes: (i)

the population distribution, measured by the number of households in each state; (ii) the

income distribution at each state; (iii) the food expenditure shares at each state given an

income bracket. Let i denote an income decile and ℓ denote a state. We take the income

17If we only considered food goods, excluding services, the shares would be αc = 0.70 and αq = 0.30.
18As in Eaton and Kortum (2002), these parameters must satisfy νx < 1 + θx to ensure that basket

prices are well-defined.
19Pesquisa de Orçamentos Familiares, POF, in Portuguese. The two other more recent versions are from

2008-2009 and 2002-2003.

81



distribution at the national level and define brackets based on their deciles. Then, we take

the microdata conditional for each state and recover the number of families within the

brackets, together with their average income within the bracket. This process retrieves a

matrix Λi,ℓ with the share of families living in state ℓ with income decile i, relative to the

number of families across the country, together with a matrix Yi,ℓ with the average income

under bracket i in state ℓ. We sum all expenditures and income for a given pair (i, ℓ) and

take their ratio to recover the expenditure shares on a particular good type.

Calibration and Fit. The outcome of our estimation is αf = 0.1694, cf = 0.0321.

The calibration approach mechanically gives more weight to the fit for states that have

relatively more households, because Λi,ℓ for such states is higher. One alternative weighting

scheme for this loss function is to attribute the same weight for the states, by setting an

alternative weight that give the same weight for each bin (i, ℓ) in the loss function. The

resulting parameters are qualitatively and quantitatively alike.

82



Figure 3.2: Food Expenditure Share Across the Income Distribution

Notes: The figure shows the relationship between food expenditure shares and

income deciles, comparing the model’s predictions (blue solid line) with the actual

data (red dashed line). The y-axis represents the percentage of total expenditure

allocated to food, while the x-axis corresponds to income deciles, from the lowest

(1st decile) to the highest (10th decile).

The model fit, with the food expenditure share at the national level, is shown in Figure

3.2. Figure illustrates the relationship between food expenditure shares and income deciles,

comparing model predictions with actual data. The y-axis represents the percentage of total

expenditure allocated to food, while the x-axis displays income deciles, ranging from the

lowest (1st decile) to the highest (10th decile). As income increases, the food expenditure

share tends to decline, in the data and in the model. In the model, the decline is tied

to the decrease in ψfi,ℓ as increase increase. This variable captures the cost of the floor

consumption of food relative to total income. The severity of this cost depends on the

state, as the price of food is dispersed across space due to the trade frictions.

The model provides a close fit to the actual data, particularly in the lower and middle-

income deciles, where the predicted and observed shares are closely aligned. However,

there is a slight divergence in the higher income deciles, where the model underestimates

83



Table 3.4: Model parameters under the benchmark calibration

Parameter Value Source

Productivity

T xℓ State of Technology [†] Average potential productivity, section 3.4.4

Zoℓ Outside Good Productivity [†] Household labor survey, section 3.4.4

Trade

τxj,ℓ Trade Frictions [‡] Specification in Equation 3.31

δc Trade cost elasticity, LTC 0.30 Regression of price on heat shocks, section 3.4.4

δq Trade cost elasticity, HTC 0.56 Regression of price on heat shocks, section 3.4.4

θx Trade elasticity for LTC and HTC 3.39 Literature, section 3.4.4

Preferences

αf Food weight in utility function 0.16 Joint estimation for (αf , cf ), section 3.5.2

cf Minimum consumption of food 0.03 Joint estimation for (αf , cf ), section 3.5.2

νc Elasticity of Substitution across LTC food 3.00 Normalization of Price level, section 3.5.2

νq Elasticity of Substitution across HTC food 3.00 Normalization of Price level, section 3.5.2

αc LTC expenditure share within food 0.50 Consumer Prince Index basket, section 3.5.2

αq HTC expenditure share within food 0.50 Consumer Prince Index basket, section 3.5.2

Distributions: Population and Income

Λi,ℓ Population shares under income i in location ℓ [‡] Consumer Expenditure Survey, section 3.5.2

Yi,ℓ Income level for location [‡] Consumer Expenditure Survey, section 3.5.2

Notes: [†] refers to either a vector of values, while [‡] refers to a matrix of values.

the share of expenditure on food compared to the observed data. Table 3.4 summarizes all

the parameters for the calibration of the baseline, using the benchmark calibration.

3.6 Counterfactuals

With the baseline parameters established for the model, we proceed to outline the two

counterfactual analyses we conduct. The first analysis explores how climate change impacts

different regions and varies across income levels, focusing on changes in food prices. To

84



assess this, we employed GAEZ projections under different scenarios for potential produc-

tivity concerning each food type x. The second analysis examines how enhancing trans-

portation infrastructure in Brazil might reduce the negative impacts of climate change by

decreasing trade expenses.

3.6.1 Climate Change

In order to shed light on the main ingredients for our counterfactuals, we rewrite the

equivalent variation formula, as in equation (3.23):

EVi,j =
∑
x∈X

sxi,j
∑
ℓ∈L

πxj,ℓµ̂
x
ℓ

In our model, we derive sxi,j and πxj,ℓ, and use µ̂xℓ directly from the data. Alternatively,

the expenditure shares sxi,j can also be extracted directly from the Consumer Expenditure

Survey microdata, offering more precise estimates by closely matching the actual data.20

We determine the percentage change µ̂xℓ by using the same methodology for calculating

trade shares and determining T xℓ , as detailed in subsection 3.4.4.

Our initial parameters include values for µxℓ , which we convert into values for T xℓ . To

determine the counterfactual value for these terms, we conduct the same procedures used

to estimate T xℓ in the baseline scenario, as outlined in section 3.4.4. The main distinction

is that we now incorporate FAO projections for the potential yield of each crop under

different Climate Change scenarios, replacing historical potential levels.

The procedure we undertake comprises the following steps. Initially, for each crop

and location, we consider a set of counterfactual potential productivities. We perform two

adjustments similar to those used to derive the metric µxℓ in the historical baseline scenario.

First, land productivity is transformed into labor productivity using the input requirements

from the most recent agricultural census. Following this, labor productivity is converted

into a standardized unit by multiplying it by average historical prices. Ultimately, this

provides a measurement of units of local currency per worker. For both adjustments,

national averages are employed as a benchmark to minimize any interaction between trade

frictions and revenue productivity, which could occur if location-specific input requirements

and historical prices were used.

20We are currently recovering exact shares from the microdata directly.

85



In an alternative scenario, µx′ℓ is defined as the average of this revenue productivity,

serving as our measure for µxℓ . From the construction in equation (3.17), a corresponding

State of Technologies vector, represented by (T xℓ )
′, is derived to allow for the complete

re-computation of the model. This lets us compare the results with those of the first-order

method. For the results of the first-order approach, the logarithmic variations in µxℓ are

used, which are determined by

µ̂xℓ ≡ log(µx′ℓ )− log(µxℓ ) (3.38)

Importantly, similar to the approach in Costinot et al. (2016), in which the productivity

of the outside sector is maintained constant, we assume that climate change does not

influence productivity in the outside sector. If it did, an additional component would

appear in the equivalent variation formula, as shown in equation (3.23), to account for

changes in income. Although broadening the analysis within the model is straightforward,

addressing the measurement concerns about changes in non-agricultural productivity is

itself challenging, as noted in some strands of the literature (Bilal and Känzig, 2024; Bilal

and Rossi-Hansberg, 2023; Cruz and Rossi-Hansberg, 2024). We proceed with a discussion

of the data relevant to these hypothetical climate change scenarios.

3.6.2 Climate Change Scenarios

The GAEZ dataset offers numerous alternative forecasts for global crop potential pro-

ductivity under various scenarios, presented as rasters. To determine potential productiv-

ities per state, we convert the raster data to align with state boundaries, yielding area-

weighted potential productivity for each crop under each scenario, exactly as we did for

the baseline model.

Apart from the assumptions regarding input intensity and irrigation practices, each

scenario is characterized by three critical dimensions: the forecast timeline, the intensity

of greenhouse gases responsible for warming, and the model that translates greenhouse

gases concentration and other socioeconomic assumptions into temperature increases. We

employed the high-input (maximum yield assumption with modern machinery) and rain-fed

settings from the GAEZ portal. Costinot et al. (2016) uses this same high-input, rain-fed

setup based on an earlier version (v3) of the GAEZ dataset.

86



Time Horizon. The first dimension concerns the time horizon. The GAEZ data set

shows the historical potential productivity from 1981 to 201021. The alternative scenarios

present data for three 30-year periods, each with a point estimate. For these intervals —

2010-2040, 2041-2070, and 2071-2100 –— the reported crop potential yields are the simple

average across the series, subject to all settings except time.

Greenhouse Gas Concentration. The second dimension considers future greenhouse

gas concentrations under each scenario. Various assumptions correspond to distinct Rep-

resentative Concentration Pathways (RCPs), as defined by the Intergovernmental Panel

on Climate Change (IPCC) (Gutiérrez et al., 2021). These pathways are characterized by

their radiative forcing levels, expressed in W/m2. Four main trajectories include RCP 2.6,

4.5, 6.0, and 8.5. Generally, a lower value indicates a cooler Earth (less greenhouse forcing)

and demands more stringent mitigation efforts to maintain that scenario.

Climate Models. The GAEZ offers crop potential yields derived from five distinct cli-

mate models, integrating RCPs as input22. For our analysis, we utilized the average yield

from these models for each time frame (2040, 2070, 2100) and RCP (2.6, 4.5, 6.0, 8.5).

These averages are applied at the crop level to determine the counterfactual average pro-

ductivity, µx′ℓ .

Summary. There are 60 triplet assortments, composed of three time horizons, four RCPs,

and five climate models. Initially, we fix a time horizon and an RCP and then average

potential crop yields over the climate models, reducing combinations to 12. Due to higher

uncertainty in longer horizon estimates, our analysis concentrates on the 2040 time horizon

and the optimistic scenario (RCP 2.6) concerning greenhouse gas concentrations. The

choice for this Optimistic scenario is illustrative. Even for the lowest greenhouse gases

contraction, there is already wide variability in the changes in productivity.

212010 marks the most recent year of available historical data. The project compiles several data sources

to make these historical evaluations and forecasts, including temperature, precipitation, wind, and soil

characteristics.
22The models include GFDL-ESM2m, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, and

NorESM1-M.

87



Details on the Productivity Changes

Significant variability exists in the percentage change of potential yield over short

timescales among different crops and regions. Figure 3.3 illustrates this heterogeneity by

depicting the change in potential yield under the Optimistic scenario for wetland rice in

panel (a), cassava in panel (b), soybean in panel (c), and beans in panel (d) by 2040.

Rice yields drop by more than 20% in certain states. In contrast, cassava yields may

increase by up to 15% in some southern areas, while others might see reductions over 10%.

This divergence is rooted in the distinct needs for temperature, humidity, wind, soil, and

terrain among crops, indicating that productivity changes result from factors beyond just

a warming climate.

Figure 3.3 illustrates the diverse shifts in crop productivity across different regions.

Our model requires an estimate of the average potential productivity for each food type,

denoted as µxℓ . As outlined in section 3.4.4, and using the baseline productivity data,

we determine the counterfactual values for µxℓ . With equation (3.38), we calculate the

log change in this potential productivity and apply the equivalent variation formula from

Equation (3.23).

Prior to examining the effects of productivity changes, we present the counterfac-

tual measures µxℓ for various food types and regions. Figure 3.4 illustrates the smoothed

histogram of these variations, highlighting two notable observations. There is notable vari-

ability across states for a given food type. The range of variation is around 40 percentage

points: from -40% to 0% for HTC and -20% to 20% for LTC. Additionally, the distri-

bution for HTC items skews more leftward. On average, the decline in productivity is

more pronounced than that of LTC. Figure 3.5 illustrates the geographic spread of these

productivity shifts, in two maps.

88



Figure 3.3: Percent Change in Yields, Optimistic Scenario, 2040

(a) Wetland Rice (b) Cassava

(c) Soybean (d) Beans

Notes: The maps illustrate the percentage shift in potential yield for Wetland Rice, Cassava,

Soybean, and Beans, represented in panels (a), (b), (c), and (d), respectively, by 2040 under

the Optimistic scenario (RCP 2.6). The counterfactual yield is based on the average from five

climate models, as described in section 3.6.2.

89



Figure 3.4: Log change in µxℓ across the states, Optimistic Scenario, 2040.

Notes: The figure shows the kernel density estimate for the log

changes in the expected productivity of the food sectors, indexed

by x, across the states. The change is given as equation (3.38),

relative to the historical counterpart of the appropriate object.

90



Figure 3.5: Percent Change in Average Potential Productivity, µ̂xℓ , Optimistic Scenario,

2040

(a) LTC (b) HTC

Note: The maps present the percentage change in average potential yield, µx
ℓ , compared to

historical data for each state: panel (a) for LTC and panel (b) for HTC. This is projected for

2040 under the Optimistic scenario, RCP 2.6. The counterfactual yields represent the average

from five climate models, detailed in section 3.6.2. Note that the heatmap color scales differ.

Equivalent Variation

Upon obtaining the variations in average potential productivities, we apply the equiv-

alent variation formula, as in equation (3.23). For households residing in a specific location

j, the trade shares between states, πxj,ℓ, and alterations in average potential productivities,

µ̂xℓ , remain constant. The heterogeneity of outcomes within the region, due to productivity

changes, is attributed to disparities in the food expenditure share, sxi,j , with the lowest

income deciles being relatively more exposed.

Figure 3.6a presents the findings for the lowest income decile across states, focusing on

this group due to its highest food expenditure share within each state. The central insight is

related to productivity changes illustrated in Figure 3.4. Since productivity shifts in HTC

91



Figure 3.6: Equivalent Variation across the states, Optimistic Scenario, 2040

(a) First income decile

(b) Last income decile

Note: The figures illustrate the equivalent variation for the lowest income decile, in panel (a), and

the highest income decile, in panel (b). Green bars represent the HTC food goods contribution,

whereas yellow bars indicate the LTC contribution. States are arranged from left to right, from

the most adverse to the least adverse total change.

92



goods are predominantly negative, their impact is adverse. Conversely, LTC productivity

changes are approximately centered around zero. With minor trade costs, states engage

more in LTC goods trading, making them more susceptible to inter-state changes. As

a result, LTC contributions are less significant than HTC, and, for some states, even

positive. We examine the impact of local productivity on the results, especially noting

Figure 3.7: Equivalent Variation and change in HTC productivity

Notes: The figure displays a scatter plot illustrating the equiva-

lent variation for the first decile in different states against changes

in productivity for HTC food goods. The x-axis is reversed, indi-

cating a decrease in productivity as one moves from left to right.

Bubble size corresponds to population shares.

that the primary influence appears to be the goods facing high trade costs. Figure 3.7

depicts the relationship between the equivalent variation for the lowest income decile and

the variation in productivity for HTC food goods. For these goods, the trade costs are

sufficiently high that πxj,ℓ approaches zero when j ̸= ℓ. Consequently, in equation (3.23),

HTC’s contribution arises mainly from changes in productivity within the same region,

93



resulting in the marked correlation seen in figure 3.7.

Figure 3.6b shows the counterpart of the equivalent variation for the highest-income

decile. Notice that because of dispersion in the food price and in the income at the top of

the distribution across states, the ordering of the states is not the same as in Figure 3.6a.

3.6.3 Improving the Roads

Next, we proceed to the second counterfactual analysis, which emphasizes the role of

roads in serving as a mitigation mechanism. We examine the structure applied to trade

frictions, which are modeled based on driving time between states. Better road quality

decreases these frictions, facilitating trade between locations. Consequently, reduced trade

barriers enhance the adaptation mechanism for sourcing food goods. In Table 3.1 and the

related text, we briefly described driving times between locations. Since the driving time

between state capitals served as a proxy, the discussion was concise. Given the importance

of driving time in this counterfactual analysis, we revisit the data.

Figure 3.8a presents a scatter plot illustrating driving distances (x-axis) versus driving

times (y-axis) from three Brazilian state capitals, as detailed in Table 3.1. Distances and

times are recorded in kilometers (km) and hours, respectively, with data points for each

of the other 26 state capitals. Manaus, marked by red circles, is relatively isolated in the

Amazon, averaging more than 1,000 kilometers from the nearest three capitals and often

over 3,000 kilometers from many others. In contrast, Porto Alegre (green triangles) and

São Paulo (blue squares) are closer to other capitals, resulting in shorter driving times.

A best-fit line is included, showing average speeds as distance over time. For Manaus,

this line is noticeably higher than those of Porto Alegre and São Paulo, indicating greater

distances and reduced average speeds, as evidenced in Table 3.1.

Figure 3.8b provides an alternative perspective on average speed heterogeneity. This

illustration includes the same three state capitals, but the y-axis now displays the average

speed from each origin to all other state capitals. Notably, for Porto Alegre and São Paulo,

the average speed remains relatively stable across distances, centered around 75 km/h, with

fluctuations from approximately 65 to 80 km/h. São Paulo, being more centrally located,

has numerous state capitals within a 3,000 km radius. In contrast, Manaus exhibits a

consistently lower average speed across the distance range, with an observable increase in

94



speed as the distance grows, highlighting low speeds near Manaus. This suggests that

considering distance can overlook the additional travel cost in areas with lower average

speeds.

Figure 3.8: Alternative measures of driving frictions

(a) Driving Time, hours (b) Average Speed, km per hour

Notes: Two scatter plots are depicted, with Driving distance (km) on the horizontal axis versus

two distinct driving metrics. Panel (a) presents driving time in hours, and panel (b) illustrates

average speed in km/h. Each point represents data from one origin compared to all 26 Brazil-

ian state capitals: Manaus (red, circles), Porto Alegre (green, triangles), and São Paulo (blue,

squares). These origins correspond to those in Table 3.1.

Consider now our counterfactual scenario. Assume an increase in the average road

speed by ϕ%. Since the trade friction is a constant elasticity function of driving time, the

reduction in trade cost corresponds to this elasticity as follows:

∂ log(τxj,ℓ)

∂ log(di,j)
= δx (3.39)

assuming j ̸= ℓ. Consequently, a rise in average speed by ϕ% results in a trade cost

adjustment of −ϕδx. This reduction in trade barriers decreases price levels at each location

according to:
∂ log(P xj )

∂ log(τxj,ℓ)
= πxj,ℓ (3.40)

95



The equivalent variation is

EVi,j =
∑
x∈X

sxi,j
∑
ℓ̸=j

πxj,ℓδ
xϕ

=
∑
x∈X

sxi,j(1− πxj,j)δ
xϕ (3.41)

The initial row acknowledges τxj,j = 1, while the final row considers that total trade shares

equal 1. Equation (3.41) stresses the significance of the own-trade share, as discussed in

Arkolakis et al. (2012). With given expenditure shares sxi,j and elasticity δx, the own-trade

share πxj,ℓ provides a sufficient metric for calculating equivalent variation to first-order.

The first-order method offers a streamlined formulation to separate each type of food’s

contribution to the equivalent variation. Although the elasticity of trade friction to driving

time for high-trade-cost foods, δq, is double that for low-trade-cost foods, δc, typically

the own-trade share is larger for high-trade-cost foods. These opposing factors introduce

variability in the policy impacts.

96



Figure 3.9: Equivalent Variation from Road Improvement, first income decile,

Notes: The figure illustrates the equivalent variation for the lowest income

decile across states, following a 10% increase in average road speed post-

climate change. The green indicates HTC food goods’ impact, whereas

the yellow represents LTC’s contribution. States are arranged from left to

right, from the worst to best total change.

3.7 Discussion and Potential Extensions

In this section, we discuss key assumptions and potential extensions of the model.

While our framework focuses on the main forces of production and trade pattern shifts

driven by new comparative advantages, it omits other adaptation margins, such as migra-

tion and the role of immobile factors like land and housing.

Migration. Significant differences in productivity changes across states suggest that

households might be less inclined to stay in regions likely to face reduced productivity,

particularly if they are remote. By constraining migration in our model, we may overstate

the adverse effects on these households. Barbosa-Alves and Britos (2023) highlights how

financial frictions and declining productivity prospects influence migration. Our approach

aligns with the baseline model of Ramondo et al. (2016), which excludes migration to focus

97



on domestic trade frictions, a central element of our analysis.

Although our model does not predict migration flows, the relative productivity changes

and their effects on utility across regions can indicate potential migration directions. For

example, if a state like Tocantins is expected to face declining productivity, residents may

consider relocating. The scale and economic impact of such migration is a quantitative

question, and incorporating migration into the model would be a valuable extension for

future research.

Lower transportation costs could also encourage migration. Recent studies show how

reduced transport costs have spurred migration and enabled the exploration of new com-

parative advantages. For Brazil, Morten and Oliveira (2024) documents how the transport

network developed around Braśılia in the 1950s boosted both trade and internal migration.

Similarly, Pellegrina and Sotelo (2024) attributes the “March to the West” in Brazil dur-

ing the late 20th and early 21st centuries to improved road infrastructure, which arguably

have lowered migration costs and shaped regional productivity. In a way, this argument

connects to Donaldson and Hornbeck (2016), where the authors utilize the expansion of

railroads in the late 19th-century United States as a means to investigate the revaluation

of land due to surge in new comparative advantages.

Immobile Factors. As shifts in comparative advantage drive migration, immobile fac-

tors such as land and housing can limit these movements. For regions experiencing an

outflow of residents, land and housing would become relatively abundant, potentially lead-

ing to a decline in their prices. This could deter further migration, as lower costs of living

might encourage households to stay. Donaldson and Hornbeck (2016) illustrates how re-

duced trade barriers, through railway expansion in the late 19th century U.S., led to higher

land values. A similar example is seen in Donaldson (2018).

Incorporating land as an explicit production factor could further enhance the ability

to test the goodness of fit of the model. This addition would allow for validation against

land use patterns observed in the data, as explored in studies like Costinot et al. (2016),

Sotelo (2020), and Pellegrina (2022). Our model implicitly assumes a Leontief production

function between land and labor, where land is relatively abundant, making labor the

binding constraint on food production.

98



Other Considerations. The actual price of food also reflects processing costs beyond

raw agricultural products. Ignoring these costs may lead us to overstate the effects of

declines in crop productivity on overall food prices. Additionally, we classify foods as either

low-trade-cost (LTC) or high-trade-cost (HTC), but some goods, like animal products, may

fall between these categories due to transportation needs such as refrigeration. While these

products are included in the LTC group because of their classification as “tradables” by the

Brazilian Central Bank, they may warrant separate analysis. Pellegrina (2022) finds that

trade distance elasticities for cereals and “other non-perishable” foods, including beef, are

similar. Further refining the model to incorporate a more detailed breakdown of consumer

food costs would enhance our estimates.

3.8 Conclusion

In this paper, we developed a multi-location model of food production and trade to

analyze the effects of climate change on food prices and income inequality. The framework

incorporates heterogeneity in food tradability, location-specific productivity, regional con-

nectivity, and income distribution within each location. We applied the model to Brazil, a

country with significant geographical and climatic diversity, to examine how these factors

interact to shape food prices and household welfare under climate change.

The results indicate that trade frictions play a central role in limiting regional adapta-

tion to changes in local food productivity, particularly for goods with high trade costs. As

climate change alters agricultural productivity, the limited adaptability of high-trade-cost

goods underscores the importance of these trade frictions. This dynamic poses greater

risks for poorer households, which allocate a larger share of their income to food and are

therefore more susceptible to price increases. Consequently, the uneven impacts of climate

change on food prices have implications for existing income inequalities within and across

regions.

Our counterfactual analysis suggests that reducing trade frictions through improve-

ments in road infrastructure can serve as an adaptation strategy. Enhanced connectivity

lowers trade costs, enabling regions to source food more efficiently from more productive

areas, which helps mitigate local price pressures. This, in turn, can dampen adverse wel-

fare effects, particularly for low-income households that are more exposed to food price

99



increases. Although the findings are specific to Brazil, the mechanisms and methods de-

veloped here can be applied to other regions with similar vulnerabilities, such as India or

parts of Africa, where climate change and transportation infrastructure constraints are also

pertinent issues.

While the model emphasizes trade frictions, it abstracts from other adaptation strate-

gies that may also be significant. For example, migration between regions could serve as

a response to changes in local productivity. Although migration flows are not estimated,

differences in cross-state effects from the equivalent variation analysis offer insights into po-

tential migration directions. Barbosa-Alves and Britos (2023) discusses how local changes

in agricultural productivity can influence migration. Another relevant consideration is

the valuation of fixed factors, such as land and housing. Extending the framework to in-

clude these factors could provide a more comprehensive understanding of the adaptation

mechanisms and is a potential area for future research.

100



References

Adamopoulos, T., Brandt, L., Chen, C., Restuccia, D., and Wei, X. (2022). Land Security

and Mobility Frictions. Working Papers tecipa-717, University of Toronto, Department

of Economics.

Adamopoulos, T. and Restuccia, D. (2022). Geography and agricultural productivity:

Cross-country evidence from micro plot-level data. The Review of Economic Studies,

89(4):1629–1653.

Adao, R., Costinot, A., and Donaldson, D. (2017). Nonparametric counterfactual pre-

dictions in neoclassical models of international trade. American Economic Review,

107(3):633–689.

Agnosteva, D. E., Anderson, J. E., and Yotov, Y. V. (2014). Intra-national trade costs:

Measurement and aggregation. Technical report, National Bureau of Economic Research.

Aiyagari, S. R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly

Journal of Economics, 109(3):659–684.

Albert, C., Bustos, P., and Ponticelli, J. (2024). The effects of climate change on labor and

capital reallocation. Unpublished manuscript.

Allen, T. and Atkin, D. (2022). Volatility and the gains from trade. Econometrica,

90(5):2053–2092.

Amirapu, A., Clots-Figueras, I., and Rud, J. P. (2022). Climate change and political

participation: Evidence from india.

101



Anderson, J. E. and Van Wincoop, E. (2003). Gravity with gravitas: A solution to the

border puzzle. American economic review, 93(1):170–192.

Anderson, J. E. and Van Wincoop, E. (2004). Trade costs. Journal of Economic literature,

42(3):691–751.

Arkolakis, C., Costinot, A., and Rodŕıguez-Clare, A. (2012). New trade models, same old

gains? American Economic Review, 102(1):94–130.

Armington, P. S. (1969). A theory of demand for products distinguished by place of

production (une théorie de la demande de produits différenciés d’après leur origine)(una

teoŕıa de la demanda de productos distinguiéndolos según el lugar de producción). Staff

Papers-International Monetary Fund, pages 159–178.

Artuç, E., Chaudhuri, S., and McLaren, J. (2010). Trade shocks and labor adjustment: A

structural empirical approach. American Economic Review, 100(3):1008–45.

Asensio, J. C., Kato, T., and Shin, H. (2021). Lessons on engaging with the private sector

to strengthen climate resilience in guatemala, the philippines and senegal. (96).

Astorga-Rojas, D. (2024). Access to markets and technology adoption in the agricultural

sector: Evidence from brazil. Unpublished manuscript.

Asturias, J., Garćıa-Santana, M., and Ramos, R. (2019). Competition and the welfare gains

from transportation infrastructure: Evidence from the golden quadrilateral of india.

Journal of the European Economic Association, 17(6):1881–1940.

Atkin, D. and Donaldson, D. (2015). Who’s getting globalized?: The size and implications

of intra-national trade costs. (w21439).

Auer, R., Burstein, A., Lein, S. M., and Vogel, J. (2022). Unequal expenditure switching:

Evidence from switzerland. Technical report, National Bureau of Economic Research.

Backus, D. K., Kehoe, P. J., and Kydland, F. E. (1992). International real business cycles.

Journal of political Economy, 100(4):745–775.

102



Baier, S. L., Kerr, A., and Yotov, Y. V. (2018). Gravity, distance, and international

trade. In Handbook of international trade and transportation, pages 15–78. Edward

Elgar Publishing.

Barbosa-Alves, M. and Britos, B. (2023). Climate change and international migration.

Barreca, A., Clay, K., Deschenes, O., Greenstone, M., and Shapiro, J. S. (2016). Adapting

to climate change: The remarkable decline in the us temperature-mortality relationship

over the twentieth century. Journal of Political Economy, 124(1):105–159.

Barrozo, M. (2023). Where is the beef? supply chains and carbon emissions in the amazon.

Technical report, Working Paper.

Bazzi, S. (2017). Wealth heterogeneity and the income elasticity of migration. American

Economic Journal: Applied Economics, 9(2):219–55.

Bilal, A. and Känzig, D. R. (2024). The macroeconomic impact of climate change: Global

vs. local temperature. Technical report, National Bureau of Economic Research.

Bilal, A. and Rossi-Hansberg, E. (2023). Anticipating climate change across the united

states. Working Paper 31323, National Bureau of Economic Research.

Bilal, A. and Stock, J. H. (2025). Macroeconomics and climate change.

Bouroncle, C., Imbach, P., Läderach, P., Rodriguez, B., Medellin, C., Fung, E., Martinez-

Rodriguez, M. R., and Donatti, C. I. (2015). La agricultura de guatemala y el cambio

climático: ¿dónde están las prioridades para la adaptación? [In Spanish].

Bouroncle, C., Imbach, P., Rodriguez-Sanchez, B., Medellin, C., Martinez-Valle, A., and

Läderach, P. (2017). Mapping climate change adaptive capacity and vulnerability of

smallholder agricultural livelihoods in central america: ranking and descriptive ap-

proaches to support adaptation strategies. Climate Change, 141:123–137.

Brazilian Central Bank (2019). Ipca weighting structure updates and repercussions in its

classifications. Box, Brazilian Central Bank. Available at: https://www.bcb.gov.br/

content/ri/inflationreport/201912/ri201912b7i.pdf.

103

https://www.bcb.gov.br/content/ri/inflationreport/201912/ri201912b7i.pdf
https://www.bcb.gov.br/content/ri/inflationreport/201912/ri201912b7i.pdf


Buera, F. J., Kaboski, J. P., and Shin, Y. (2020). The Macroeconomics of Microfinance.

The Review of Economic Studies, 88(1):126–161.

Burke, M., Hsiang, S. M., and Miguel, E. (2015). Global non-linear effect of temperature

on economic production. Nature, 527(7577):235–239.

Caliendo, L., Dvorkin, M., and Parro, F. (2019). Trade and labor market dynamics:

General equilibrium analysis of the china trade shock. Econometrica, 87(3):741–835.

Carare, A., Koh, C., and Yakhshilikov, Y. (2023). Northern triangle undocumented migra-

tion to the united states. IMF Working Papers, 2023(017):A001.

Casey, G., Fried, S., and Goode, E. (2023). Projecting the impact of rising temperatures:

The role of macroeconomic dynamics. IMF Economic Review, 71(3):688–718.

Castro-Vincenzi, J., Khanna, G., Morales, N., and Pandalai-Nayar, N. (2024). Weather-

ing the storm: Supply chains and climate risk. Technical report, National Bureau of

Economic Research.

Cattaneo, C. and Peri, G. (2016). The migration response to increasing temperatures.

Journal of Development Economics, 122:127–146.

Chaves-Gonzalez, J., Milano, L., Omtzigt, D.-J., Pfister, D., Poirier, J., Pople, A., Wittig,

J., and Zommers, Z. (2022). Anticipatory action: Lessons for the future. Frontiers in

Climate, 4.

Clement, V., Rigaud, K. K., de Sherbinin, A., Jones, B., Adamo, S., Schewe, J., Sadiq,

N., and Shabahat, E. (2021). Groundswell part 2: Acting on internal climate migration.

License: CC BY 3.0 IGO.

Comin, D., Lashkari, D., and Mestieri, M. (2021). Structural change with long-run income

and price effects. Econometrica, 89(1):311–374.

Conte, B. (2024). Climate change and migration: the case of africa. Unpublished

manuscript.

Conte, B., Desmet, K., Nagy, D. K., and Rossi-Hansberg, E. (2021). Local sectoral spe-

cialization in a warming world. Journal of Economic Geography, 21(4):493–530.

104



Copernicus Climate Change Service (2019). ERA5-Land hourly data from 2001 to present.

Costinot, A., Donaldson, D., and Smith, C. (2016). Evolving comparative advantage and

the impact of climate change in agricultural markets: Evidence from 1.7 million fields

around the world. Journal of Political Economy, 124(1):205–248.

Costinot, A. and Rodŕıguez-Clare, A. (2014). Trade theory with numbers: Quantifying the

consequences of globalization. In Handbook of international economics, volume 4, pages

197–261. Elsevier.

Cruz, J.-L. and Rossi-Hansberg, E. (2024). The economic geography of global warming.

Review of Economic Studies, 91(2):899–939.

Donaldson, D. (2018). Railroads of the raj: Estimating the impact of transportation

infrastructure. American Economic Review, 108(4-5):899–934.

Donaldson, D. and Hornbeck, R. (2016). Railroads and american economic growth: A

“market access” approach. The Quarterly Journal of Economics, 131(2):799–858.

Eaton, J. and Kortum, S. (2002). Technology, geography, and trade. Econometrica,

70(5):1741–1779.

Faccia, D., Parker, M., and Stracca, L. (2021). Feeling the heat: extreme temperatures

and price stability.

Fajgelbaum, P. D. and Khandelwal, A. K. (2016). Measuring the unequal gains from trade.

The Quarterly Journal of Economics, 131(3):1113–1180.

FAO (2023). Faostat. License: CC BY-NC-SA 3.0 IGO. Accessed on 29 September 2023

at https://www.fao.org/faostat/en/#data.

FAO and IIASA (2022). Global agro-ecological zones (gaez v4) - data portal. https:

//gaez.fao.org/. Accessed: 2024-10-16.

Fitzgerald, D. (2008). Can trade costs explain why exchange rate volatility does not feed

into consumer prices? Journal of monetary Economics, 55(3):606–628.

105

https://www.fao.org/faostat/en/#data
https://gaez.fao.org/
https://gaez.fao.org/


Fitzgerald, D. (2012). Trade costs, asset market frictions, and risk sharing. American

Economic Review, 102(6):2700–2733.

Fried, S. (2024). A macro study of the unequal effects of climate change. Federal Reserve

Bank of San Francisco.

GAEZ (2000). Global agro-ecological zones, version 3.0. https://www.gaez.iiasa.ac.

at/. Food and Agricultural Organization (FAO) and International Institute for Applied

Systems Analysis (IIASA).

Guren, A., McKay, A., Nakamura, E., and Steinsson, J. (2021a). What do we learn from

cross-regional empirical estimates in macroeconomics? NBER Macroeconomics Annual,

35(1):175–223.

Guren, A. M., McKay, A., Nakamura, E., and Steinsson, J. (2021b). Housing wealth effects:

The long view. The Review of Economic Studies, 88(2):669–707.

Gutiérrez, J., Jones, R., Narisma, G., Alves, L., Amjad, M., Gorodetskaya, I., Grose, M.,

Klutse, N., Krakovska, S., Li, J., Mart́ınez-Castro, D., Mearns, L., Mernild, S., Ngo-Duc,

T., van den Hurk, B., and Yoon, J.-H. (2021). Atlas. Cambridge University Press. In

Press. Interactive Atlas available from http://interactive-atlas.ipcc.ch/.

Hazell, J., Herreno, J., Nakamura, E., and Steinsson, J. (2022). The slope of the phillips

curve: evidence from us states. The Quarterly Journal of Economics, 137(3):1299–1344.

Heathcote, J. and Perri, F. (2002). Financial autarky and international business cycles.

Journal of monetary Economics, 49(3):601–627.

Heathcote, J. and Perri, F. (2004). Financial globalization and real regionalization. Journal

of Economic Theory, 119(1):207–243.

Hsiang, S. M. and Jina, A. S. (2014). The causal effect of environmental catastrophe on

long-run economic growth: Evidence from 6,700 cyclones. Technical report, National

Bureau of Economic Research.

IMF (2023). World economic outlook database, april 2023. Accessed on 25 August 2023

at https://www.imf.org/en/Publications/WEO/weo-database/2023/April.

106

https://www.gaez.iiasa.ac.at/
https://www.gaez.iiasa.ac.at/
http://interactive-atlas.ipcc.ch/
https://www.imf.org/en/Publications/WEO/weo-database/2023/April


INE (2015). Republica de guatemala: Encuesta nacional de condiciones de vida 2014,

principales resultados. [In Spanish].

INE (2016). Encuesta nacional de empleo e ingresos enei 1-2016. Technical report, Instituto

Nacional de Estad́ıstica de Guatemala.

INE (2020). Encuesta nacional agropecuaria año agŕıcola 2019–2020. Technical report,

Instituto Nacional de Estad́ıstica.

International Food Policy Research Institute (2019). Global Spatially-Disaggregated Crop

Production Statistics Data for 2010 Version 2.0.

IOM (2016). Encuesta sobre migración internacional de las personas guatemaltecas y

remesas 2016. Tech. rep., International Organization for Migration. United Nations

Migration Agency.

Jessoe, K., Manning, D. T., and Taylor, J. E. (2018). Climate Change and Labour Al-

location in Rural Mexico: Evidence from Annual Fluctuations in Weather. Economic

Journal, 128(608):230–261.

Jordà, Ò. (2005). Estimation and inference of impulse responses by local projections.

American economic review, 95(1):161–182.

Kennan, J. and Walker, J. R. (2011). The effect of expected income on individual migration

decisions. Econometrica, 79(1):211–251.

Krugman, P. (1991). Increasing returns and economic geography. Journal of political

economy, 99(3):483–499.

Lagakos, D., Mobarak, A. M., and Waugh, M. E. (2023). The welfare effects of encouraging

rural–urban migration. Econometrica, 91(3):803–837.

Mbow, C., Rosenzweig, C., Barioni, L. G., Benton, T. G., Herrero, M., Krishnapillai, M.,

Liwenga, E., Pradhan, P., Rivera-Ferre, M. G., Sapkota, T., Tubiello, F. N., and Xu, Y.

(2019). Food security. Intergovernmental Panel on Climate Change.

McAuliffe, M. and Triandafyllidou, A., editors (2021). World Migration Report 2022.

International Organization for Migration (IOM), Geneva.

107



Melitz, M. J. (2003). The impact of trade on intra-industry reallocations and aggregate

industry productivity. econometrica, 71(6):1695–1725.

Montiel Olea, J. L. and Plagborg-Møller, M. (2021). Local projection inference is simpler

and more robust than you think. Econometrica, 89(4):1789–1823.

Morten, M. and Oliveira, J. (2024). The effects of roads on trade and migration: Evidence

from a planned capital city. American Economic Journal: Applied Economics, 16(2):389–

421.

MPI (2023). Migration data hub. Migration Policy Institute’s Migration Data

Hub. Accessed on 25 August 2023 at http://www.migrationpolicy.org/programs/

migration-data-hub.

Nath, I. (2025). Climate change, the food problem, and the challenge of adaptation through

sectoral reallocation. Journal of Political Economy. Published ahead of print.

Nordhaus, W. D. (1992). An optimal transition path for controlling greenhouse gases.

Science, 258(5086):1315–1319.

Obstfeld, M. and Rogoff, K. (2000). The six major puzzles in international macroeconomics:

is there a common cause? NBER macroeconomics annual, 15:339–390.

Oni, M. H. (2024). Commuting, home utilities, and production: The distributional effect

of energy price shocks. Unpublished manuscript.

Parker, M. (2018). The impact of disasters on inflation. Economics of Disasters and

Climate Change, 2(1):21–48.

Pellegrina, H. S. (2022). Trade, productivity, and the spatial organization of agriculture:

Evidence from brazil. Journal of Development Economics, 156:102816.

Pellegrina, H. S. and Sotelo, S. (2024). Migration, specialization, and trade: Evidence from

brazil’s march to the west. Journal of Political Economy (Forthcoming).

Plagborg-Møller, M. and Wolf, C. K. (2021). Local projections and vars estimate the same

impulse responses. Econometrica, 89(2):955–980.

108

http://www.migrationpolicy.org/programs/migration-data-hub
http://www.migrationpolicy.org/programs/migration-data-hub


Pople, A., Hill, R., Dercon, S., and Brunckhorst, B. (2021). Anticipatory Cash Transfers in

Climate Disaster Response. CSAE Working Paper Series 2021-07, Centre for the Study

of African Economies, University of Oxford.

Ramondo, N., Rodŕıguez-Clare, A., and Saboŕıo-Rodŕıguez, M. (2016). Trade, domestic

frictions, and scale effects. American Economic Review, 106(10):3159–3184.

Redding, S. and Venables, A. J. (2004). Economic geography and international inequality.

Journal of international Economics, 62(1):53–82.

Redding, S. J. (2010). The empirics of new economic geography. Journal of regional science,

50(1):297–311.

Redding, S. J. and Rossi-Hansberg, E. (2017). Quantitative spatial economics. Annual

Review of Economics, 9:21–58.

Ruggles, S., Flood, S., Sobek, M., Brockman, D., Cooper, G., Richards, S., and

Schouweiler, M. (2023). Acs 2016. IPUMS USA: Version 13.0. Accessed on 25 August

2023 at https://doi.org/10.18128/D010.V13.0.

Samuelson, P. A. (1954). The transfer problem and transport costs, ii: Analysis of effects

of trade impediments. The Economic Journal, 64(254):264–289.

Schlenker, W. and Roberts, M. J. (2009). Nonlinear temperature effects indicate severe

damages to us crop yields under climate change. Proceedings of the National Academy

of sciences, 106(37):15594–15598.

Simonovska, I. and Waugh, M. E. (2014). The elasticity of trade: Estimates and evidence.

Journal of international Economics, 92(1):34–50.

Somanathan, E., Somanathan, R., Sudarshan, A., and Tewari, M. (2021). The impact of

temperature on productivity and labor supply: Evidence from indian manufacturing.

Journal of Political Economy, 129(6):1797–1827.

Sotelo, S. (2020). Domestic trade frictions and agriculture. Journal of Political Economy,

128(7):2690–2738.

109

https://doi.org/10.18128/D010.V13.0


Tauchen, G. (1986). Finite state markov-chain approximations to univariate and vector

autoregressions. Economics letters, 20(2):177–181.

UNFCCC (2023). Report of the conference of the parties on its twenty-seventh session,

held in sharm el-sheikh from 6 to 20 november 2022, addendum. part two: Action taken

by the conference of the parties at its twenty-seventh session. Conference of the Parties.

US DHS (2022). 2021 yearbook of immigration statistics. Technical report, U.S. Depart-

ment of Homeland Security, Office of Immigration Statistics, Washington, D.C.

Vogt-Schilb, A., Walsh, B., Feng, K., et al. (2019). Cash transfers for pro-poor carbon

taxes in latin america and the caribbean. Nature Sustainability, 2:941–948.

World Bank (2022). Brazil infrastructure assessment (p174544) synthesis report.

World Bank (2023). World development indicators. Accessed on 25 Au-

gust 2023 at https://databank.worldbank.org/reports.aspx?source=

world-development-indicators.

World Food Program (2015). Initial analysis of the impact of the drought on food security

in guatemala, el salvador, and honduras.

110

https://databank.worldbank.org/reports.aspx?source=world-development-indicators
https://databank.worldbank.org/reports.aspx?source=world-development-indicators


Appendix A

Appendix to Chapter 2

111



A.1 Reduced-form Estimations

A.1.1 Exposure and Migration Rates

In this exercise, we show the different coefficients of exposure on migration rates by

changing the temperature threshold of exposure. Following the same specification as in

Equation (2.1), in Figure A.1, we plot the βe coefficient for exposure to temperatures above

30, 31, 32, 33, 34, and 35
◦
C. The bands correspond to the 95% confidence interval. Results

of the specification can be found in Table A.3 of the Appendix.

Figure A.1: Effect of Exposure on Rural Migration Rates by Temperature Threshold

112



A.1.2 Link Between Weather and Rural Transitory Shocks

We obtain the link between high temperatures and rural transitory shocks by regressing

log yields of corn with exposure during the crop season, March to August for the U.S., using

U.S. data. We take the dataset from Schlenker and Roberts (2009) and run the following

Fixed-effects regression:

ycst = α+ β1Exposurecst + δRaincst + δ2Rain
2
cst + ηsD

∗
st+ ηs2D

∗
st

2 + κc + εcst

Where ycst is the ln yield of corn for county c, state s and year t; Exposurecst is the

number of days during the corn crop season a county has been exposed to temperatures

above 86F/30C; Raincst and Rain2cst is the total precipitation during the season and its

quadratic term, respectively; D∗
st and D

∗
st

2 is a state time trend and its quadratic term,

respectively; κc and ηt are the fixed effect terms for county and year respectively; εct is the

error term.

Table A.1: Effect of Exposure on Corn yields

Variables Corn yields (in logs)

Exposure to 30C -0.023***

(0.001)

Constant 3.619***

(0.061)

Observations 128,169

R2 0.850

Precipitation controls YES

County FE YES

State time trends YES

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

113



A.2 Other Specification Results

Table A.2: Effect of Exposure on Migration Rate by Percentage of Rural Population

(1) (2) (3) (4) (5)

Variables Mig Rate Mig Rate Mig Rate Mig Rate Mig Rate

0-20% 20-40% 40-60% 60-80% 80-100%

Lagged Exposure 0.059 -0.540** -1.026*** -1.040*** -0.906***

(0.299) (0.207) (0.322) (0.253) (0.302)

Observations 636 778 1,341 1,630 1,257

R2 0.072 0.207 0.228 0.309 0.341

Number of Municipalities 38 46 79 96 74

Time and Municipality FE YES YES YES YES YES

Note: This table shows the results of the specification in (2.1), by segmenting the sample

according to the share of rural population of each municipality. For example, the first

column shows the results of the specification for municipalities that have a share of rural

population that is between 0-20%. This table is used as an input for Figure 2.2. Robust

standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

114



Table A.3: Effect of Exposure on Emigration Rate for Different Temperature Thresholds

(1) (2) (3) (4) (5)

Variables Rural Rural Rural Rural Rural

Mig Rate Mig Rate Mig Rate Mig Rate Mig Rate

Lagged Exposure 30C -0.880***

(0.152)

Lagged Exposure 31C -0.999***

(0.191)

Lagged Exposure 32C -1.172***

(0.242)

Lagged Exposure 33C -1.210***

(0.280)

Lagged Exposure 34C -1.117***

(0.298)

Observations 5,236 5,236 5,236 5,236 5,236

R2 0.263 0.260 0.258 0.256 0.256

Number of Municipalities 309 309 309 309 309

Time and Municipality FE YES YES YES YES YES

Note: This table shows the results of different temperature thresholds. For example, the

first column shows the results when the exposure is calculated with a threshold of 30C.

This table is used as an input for Figure A.1. Robust standard errors in parentheses. ***

p<0.01, ** p<0.05, * p<0.1

115



A.2.1 A model with non-monetary migration costs

In what follows, we provide the model with non-monetary migration costs instead of

having the monetary cost. We focus on the stationary version of the model for simplicity.

We proceed by formulating the key differences and ultimately show the importance of

monetary migration costs.

Key differences. In this version of the model, agents are subject to the same dis-

tribution of temporary productivity shocks (high-heat shocks) as in our baseline model.

However, agents do not have access to a savings technology, implying a = a′ = 0, the

monetary cost of migration is zero, me = 0, and but face an additive migration disutility

τ ≥ 0.

Value at the Home Economy. We denote the ex-ante value function as the expec-

tation over the taste shocks as V(z, η). agents at home solve

V(z; η) = Eε [max {V s(z; η) + εs, V e(z; η) + εe}] (A.1)

Value of Staying. Conditional on staying, the agent’s value is

V s(z; η) = u(wzη) + βE
[
V(z′; η)

]
(A.2)

Value of Migrating. The value of migrating is the following

V e(z; η) = u(wzη)− τ + β
[
E
[
ϕV ∗(η) + (1− ϕ)V(z′; η)

]]
(A.3)

Value of Living in the U.S.. When the agent is living in the U.S., the value is the

following

V ∗(η) = u(c∗)ν + β
{
E
[
(1− ψ)V ∗(η) + ψV(z′; η)

]}
(A.4)

Having the value functions defined, we proceed to set the externally calibrated param-

eters as in Table 2.2. Among the two parameters that we estimated, me is set to zero by

construction, and we set ν equal to 1.1

Below, we conduct the following exercise. We set τ ∈ T ≡ {0, 1, 2, . . . , 48, 49, 50}.
Solve the policy functions, find the stationary distribution, obtain 1, 000 cohorts of 10, 000

1Setting ν to the estimated value in our baseline model implies a different quantitative result for τ that

matches the mass of migrants in the U.S., but does not modify the qualitative conclusions that we layout

here, specifically regarding the model not producing βe.

116



individuals from the stationary distribution, and then run the regression we have in Equa-

tion (2.1) for each sample and then average out across samples, the same approach that

we follow for the baseline model. Recalling that βe is stochastic,2 we run this exercise 30

times for each τ ∈ T , record the values for each βe and report the range of these estimates,

together with an average.3

Figure A.2: Targeted moments as a function of τ

(a) βe range for various τ (b) M for various τ

Note: Panel (a) depicts the range of average βe, over 30 simulations for the average β̂e of 1,000 cohorts of

10,000 agents each. The gray region is the range, while the black solid line shows the mean over the 30

experiments. Panel (b) exhibits the mass of migrants, M , for each level of τ . This moment is not stochastic

— it is computed as a fixed point, as explained in Appendix A.2.2. The respective target for each moment

is shown as the red dashed line.

Looking at Figure A.2, when τ is close to 0, the reference calibration implies that the

variability of the estimate for βe is large.4 Observe that M is large when τ is close to 0:

the value in the U.S., V ∗(η) is high relative to E[V s(z, η)]. As τ increases, the value of

migrating decreases and makes the stock of migrants in the U.S. get closer to the target

of 7.4%. At the same time, the variability of βe shrinks; migration probabilities decrease,

making sample selection error less important.

2The output of the regression depends on the sample selection the regression was run on.
3We observe that increasing the number of sampled individuals, cohorts, or experiments makes the

average of all these βe approaches zero for each τ .
4Increasing sample size used for the regression decreases the variability of βe.

117



Evidently, increasing the number of experiments, samples, and sampled individuals

tends to push the average across experiments closer to 0 in the case of βe. We conclude

that this version of the model, with non-monetary migration costs, can deliver the stock

of migrants in the U.S., M , but not the high-heat migration link we document from the

data βe.

118



A.2.2 Computational Details

Solution Method for the Baseline Model

We refer to the Baseline model as the one in which agents do not take into account

any Climate Change. We solve the model using standard Value Function Iteration. Since

we have the taste shocks for the migrating-staying decision, we do not rely on any type of

interpolation.

We start by constructing the set of permanent types, which we denote by η, and

assigning a relative share for each node, µη. The result is a tuple list {ηi, µiη}
nη

i=1. Next, we

set a grid for assets, A, and a grid for the transitory (weather) shocks, Z.

We set a tolerance ϵ = 10−10 and a relaxation parameter ξ ∈ (0, 1] to allow for slow

updating of values, in case ξ < 1. 5 We set an iteration counter t = 1 and initialize a guess

for the value functions as follows

Vt(a, z; η) = V e
t (a, z; η) = V s

t (a, z; η) = V ∗
t (η) = 0.0, ∀(a, z, η)

Then we proceed to find policy functions for savings fa(a, z; η), migrating fe(a, z; η) as

follows:

1. Update the value of being abroad, V ∗
t+1(η) as

V ∗
t+1(η) = u(c∗)ν + β

[
(1− ψ)V ∗

t (η) + ψEz′
[
Vt(0, z′; η)

]]
2. Compute V e

t+1(a, z, η) as

V e
t+1(a, z; η) = u(wzη + a−me) + β

[
ϕV ∗

t (η) + (1− ϕ)Ez′
[
Vt(0, z′; η)

]]
3. Compute V s

t+1(a, z, η) and fa,t+1(a, z; η) as

V s
t+1(a, z; η) = max

a′∈A

{
u(wzη + a− qa′) + βEz′

[
Vt(a, z′; η)

]}
and

fa,t+1(a, z; η) = argmax
a′∈A

{
u(wzη + a− qa′) + βEz′

[
Vt(a, z′; η)

]}
5In practice, the problem is well-behaved and imposing ξ = 1 does not prevent convergence. Otherwise,

ξ < 1 requires more iterations to converge.

119



4. Next, compute Vt+1(a, z; η) and fe,t+1(a, z; η) as follows
6

Vt+1(a, z; η) = κ× ln

(
exp

(
V e
t+1(a, z; η)

κ

)
+ exp

(
V s
t+1(a, z; η)

κ

))
and

fe,t+1(a, z; η) =
exp

(
V e
t+1(a,z;eta)

κ

)
exp

(
V e
t+1(a,z;η)

κ

)
+ exp

(
V s
t+1(a,z;η)

κ

)
5. Check for convergence:

(a) if ∥Vt+1(a, z; η)− Vt(a, z; η)∥∞ ⩽ ϵ, abort — the solution was found.

(b) if ∥Vt+1(a, z; η)− Vt(a, z; η)∥∞ > ϵ, update the ex-ante value function as

Vt+1(a, z; η) ≡ ξ × Vt+1(a, z; η) + (1− ξ)× Vt(a, z; η)

replace the indexer t by t+ 1 and go back to step 1.

Computing the Stationary Distribution

Once we find the policy functions for savings and migrating, we compute the stationary

distribution as follows.

We initialize from an arbitrary distribution (µt(a, z; η),Mt(η)) (that has to be con-

formable with {µiη}
nη

i=1), we compute the next-period distribution (µt+1(a, z; η),Mt+1(η))

by applying the tautologies below:

Mt+1(η) =Mt(η)(1− ψ) + Et(η)ϕ

where

Et(η) =
∑
a∈A

∑
z∈Z

µt(a, z, η)fe(a, z; η)

6To render the computation numerically stable, we apply in reality

Vt+1(a, z; η) = Vmax + κ× ln

(
exp

(
V e
t+1(a, z; η)− Vmax

κ

)
+ exp

(
V s
t+1(a, z; η)− Vmax

κ

))
with Vmax ≡ max {V s

t+1(a, z; η), V
e
t+1(a, z; η)} and, for the migrating policy function,

fe,t+1(a, z; η) =
1

1 + exp
(

V s
t+1(a,z;η)−V e

t+1(a,z;η)

κ

)

120



and

µt+1(a
′, z′, η) =

∑
a∈A

∑
z∈Z

µt(a, z, η)1
{
fa′(a, z; η) = a′

}
(1− fe(a, z; η)) Pr(z

′)

+1
{
a′ = 0

}
Pr(z′) [Mt(η)ψ + Et(η)(1− ϕ)]

We proceed iteratively until the following condition is met

∥µt+1(a, z; η)− µt(a, z; η)∥∞ + ∥Mt+1(η)−Mt(η)∥∞ ≤ 10−6

Our initial guess is given by M0(η) = 0.0 and µ0(0, z, η) = Pr(z) × µη. There is nothing

in particular to this guess, any arbitrary (conformable) distribution would converge to the

same distribution, up to the numerical inaccuracy tolerated.

Details on Grids

Permanent productivity, η. In our analysis, we impose ln(η) ∼ N(µη, σ
2
η). We

chose nη = 17 as the number of grid points. We set the lowest η to exp(µη − 3ση), while

the highest η is given by exp(µη+3ση), and choose the intermediary points equally distant

from each other (in logs) with using the procedure proposed by Tauchen (1986). Figure A.3

shows the resulting grid together with the mass of agents of each type, under the baseline

parametrization.7

Asset grid, A. Since we do not rely on interpolating, we choose a na = 100 as grid

points. We set the lower bound to A as the 0.0 and the upper bound as max{A} = 10.0,

by experimentation.8 We choose the grid points to be more concentrated around the lower

bound, where even small differences in asset holds can give substantial increases in utility.

We choose the following scheme to distribute the grid points. We start by splitting the

interval [0, 1] as follows (equally spaced points){
xj : xj ≡

j − 1

na − 1
, j = 1, 2, . . . , na

}

7For each type η, the mass µη will be, in the stationary distribution, either domestically or abroad.
8Aiming at making sure we get max{A} > sup{fa(a, z; η)}, ∀(a, z, η) for possibles combinations of

parameters in the estimation procedure.

121



Figure A.3: Permanent productivity grid

122



Then we set a parameter θ = 2.25 and compute the A grid as follows, for j ∈ {1, 2, . . . , na}

aj = amin + (amax − amin)x
θ
j

Figure A.4 shows the asset grid for our baseline specification — θ = 2.25 — and two other

alternatives. Given θ > 1, there are more grid points around amin than around amax. If

θ = 1, then the asset grid would be just linearly spaced. If instead θ = 3.5, we would

observe even more grid points around amin.

Figure A.4: Asset grid

High Temperature Shocks, Z. To build our Z grid, first, we obtain the distribution

of exposure at the municipality-year level for the period of analysis 2011-18. Second, we

calculate the CDF weighted by the rural population of the municipality. Third, from

the CDF, we compute the probability of having 0 days of exposure and the following

intervals: (0,2], (2,5], (5,10], (10,20], (20,35], and more than 35. This sets our number of

grid points for Z to 7, i.e., nZ = 7. Once the probabilities are calculated, we compute the

weighted average of exposure for 0 days and every interval. Ultimately, we calculate the

123



corresponding Z according to Equation (2.4). The probability for every Z point is the one

calculated in the third step.

124



A.3 Estimation of ση

A.3.1 Main Estimation

To obtain the value of ση we estimate rural yields from farmers in Guatemala. For

this we use microdata from the last agricultural census in Guatemala ”IV Censo Nacional

Agropecuario 2003”, corresponding to the crop year 2002–03 conducted by the National

Statistical Institute (INE). The census includes information on quantities produced, labor,

land size, input use, machinery and equipment, as well as geographic location, however, it

does not include any information on prices, sales or costs.

Given we only observe quantities produced, we obtain data on market prices of several

crops for the year 2003 from the Ministry of Agriculture, Livestock and Food. We compute

the total revenue of the farm by multiplying the market prices to each crop and adding

them up by producer. Then, we divide the revenue by total harvested area in hectares and

total labor employed by the producer. Because we do not have data on the cost or use

intensity of intermediate inputs, only if they were used in production, we estimate etai as

the residual of the following reduced-form estimation

ln (revip) = γXi + αp + ln (ηi) (A.5)

where revip is the total revenue per hectare and labor of producer i; Xi is a vector of

controls and inputs which are included the household over total labor ratio, if the producer

has machinery, equipment, uses high-performance seeds, organic and chemical fertilizer, if

it has irrigation and number of cultivated crops; αp is the fixed-effect term for populated

place which is a subdivision of municipality. The results of the regression can be seen in

Table A.4. After recovering the residual, we calculate the standard deviation which is equal

to 0.71.

A.3.2 Alternative Estimation

Considering the lack of data regarding cost of intermediate inputs, we estimated the

value of ση using the 2014 National Survey of Living Conditions (ENCOVI) compiled by

INE. This is a household survey representative at the national level. The dataset includes

125



Table A.4: Regression estimating ηi

Variables Revenue (in logs)

Household Labor/Total Labor 1.110***

(0.035)

If has machinery -0.047***

(0.016)

If has equipment -0.027***

(0.009)

If uses high-performance seeds -0.010

(0.015)

If uses organic fertilizer -0.026***

(0.008)

If uses chemical fertilizer -0.043*

(0.023)

If uses pesticide -0.008

(0.016)

If has irrigation system 0.022

(0.017)

Number of crops -0.418***

(0.019)

Observations 580,267

R-squared 0.561

Populated Place FE YES

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

126



a module detailing agricultural production with information on quantities produced, sales,

labor, land size, input use, and costs.

To estimate ηi, first we compute the value added of production. Given problems with

outliers, we calculate the implicit sale price for each crop, dividing total sales (in Quetzales,

the Guatemalan currency) by total quantities sold. After that, we multiply the price by

the total quantities produced for every crop, ultimately adding all the crops and resulting

in total revenue. Then we proceed to subtract intermediate inputs costs involved in the

crop production. These inputs include seeds or plants, organic and chemical fertilizers,

pesticides, packaging, and fuel.

After obtaining the value added, we divide it by total land, and by the implicit labor

cost. As most producers employ family members for agricultural activities, we calculate

the median profits of producers and take this as the implicit wage of producer, and any

household member that reports working at the establishment, as their main job. We finally

add any hired labor wages to the total implicit wage, to have our measure of implicit labor

cost.

Lastly, we estimate ηi as the residual of the following regression

ln (value addedij) = αj + ln (ηi) (A.6)

where value addedij is the value added per hectare and labor cost of producer i in

department j; αj is the Fixed Effects term at department-area level.9 When we recover

the residual, the standard deviation is equal to 0.81, higher than our estimate from the

agricultural census.

9Data on municipality is not available, department is a geographical administrative level above munic-

ipality. Area refers if the household is located in a rural or an urban setting.

127



A.4 Simulated Method of Moments

A.4.1 Computing the Stationary Distribution

In our model, a unitary mass of agents is split between either in the Home economy

or abroad. Let µ(a, z, η) be the mass of agents at Home with the state vector (a, z, η), and

M(η) the mass of agents abroad with innate productivity η. Agents abroad do not carry

any asset a, and their value is independent of the temporary idiosyncratic shock z that

affects the rural production in the Home economy.

Given a current distribution of agents, i.e., the pair (µ⃗, M⃗) ∈ D ⊂ R3
+ × R, the

transitory shock distribution, say {(z,Pr(z))}z∈Z , the exogenous probability of deportation

ψ, and the success rate of migration ϕ, we can write the law of motion of distribution of

agents as10

M ′(η) =M(η)(1− ψ) + E(η)ϕ (A.7)

where

E(η) =
∑
a∈A

∑
z∈Z

µ(a, z, η)fe(a, z, η) (A.8)

and

µ′(a′, z′, η) =
∑
a∈A

∑
z∈Z

µ(a, z, η)1
{
fa′(a, z, η) = a′

}
(1− fe(a, z, η)) Pr(z

′)

+1
{
a′ = 0

}
Pr(z′) [M(η)ψ + E(η)(1− ϕ)] (A.9)

Equations (A.7)-(A.9) define implicitly an operator T : D 7→ D. We call a stationary

distribution an element (µ⃗, M⃗) ∈ D such that T
(
(µ⃗, M⃗)

)
= (µ⃗, M⃗), that is a fixed-point

of T .

Equation (A.7) shows that for the following period, the mass of agents equipped with

a particular productivity level η that will be abroad, M ′(η), is given by the agents that are

currently abroad M(η) times the probability of not being deported (1− ψ) plus the mass

of agents that successfully migrated in the current period and will be abroad next period,

E(η)ϕ.

10In particular, for the migrating policy function, the law of large numbers gives that the probability of

migration is equal to the proportion of agents migrating, condition on a triplet state.

128



Equation (A.8) shows the definition of agents that tried to migrate in the current

period. By the law of large numbers, a fraction ϕ of them will be abroad next period,

while the remaining fraction 1−ϕ will be detained and sent back to the Home economy. It

is the sum of the mass of agents with assets a, temporary productivity z, and permanent

productivity η, µ(a, z, η), times the migration probability, fe(a, z, η).

Equation (A.9) is the stock of agents in the Home economy with a state vector (a′, z′, η).

There are two elements. The first term consists of agents that are in the Home economy and

do not migrate, which happens with probability 1−fe(a, z, η), and have chosen fa′(a, z, η) =

a′, and drawing transitory productivity z′, which happens with probability Pr(z′), taking

into account the initial mass µ(a, z, η). The second term is the mass of agents that were

deported and are sent back with zero assets —a′ = 0, M(η)ψ, times the probability of

drawing the transitory productivity z′, Pr(z′). In addition, there is a mass of agents that

tried to migrate but failed, E(η)(1− ϕ).

As we discussed, we use the stationary distribution to estimate some parameters of

the model. In addition, the stationary distribution of agents is a helpful tool for analyz-

ing terminal outcomes under climate change projections after any transition dynamics is

concluded.

A.4.2 Procedure

Let θ be the p× 1 vector of parameters to be estimated. Let gd be the m× 1 vector of

moments in the data that we want to replicate and g(θ) the m × 1 vector counterpart of

these moments as a function of the parameter vector θ.

We define the vector of of model error as the gap between the model implied moments

g(θ) and the corresponding vector of moments from the data gd:

e(θ) ≡ g(θ)− gd (A.10)

The loss function we consider is

L(θ) ≡ e(θ)TWe(θ) (A.11)

where W is a m ×m positive semi-definite matrix of weights. Observe that L : Θ 7→ R+.

The objective is to find a vector θ∗ in a space Θ that attains the minimum of the loss

129



function, that is:

θ∗ ∈ argmin
θ∈Θ

L(θ) (A.12)

A.4.3 Implementation

In our implementation, we estimate two parameters and target two moments, that is

p = 2 and m = 2. Hence, the system is identified. The parameters that we estimate are

θ ≡ [me, ν].

We implement the Nelder-Mead algorithm with (p + 1) (randomly chosen) vectors as

an initial simplex to minimize the loss function. We set the weighting matrix W to be the

identity matrix.

We experiment with some combinations of θ to figure out a tentative candidate for

the argument that minimizes the loss function. Then, we create a large interval for each

parameter around this tentative solution to construct a parameter space for the Nelder-

Mead search. We set the parameter space Θ for the search as a box. The relevant space Θ

is the Cartesian product over these intervals.

Table A.5: Interval allowed for each parameter

Parameter θlbi θubi

me 1× E[z] 3× E[z]
ν 1.0 3.0

Note: θlbi and θubi stand for the lower-bound and upper-bound, respectively, for parameter θi.

Yielding Θ ≡ [1× E[z], 3× E[z]]× [1.0, 3.0].

The Nelder-mead algorithm is implemented without any constraints. To achieve that,

we performed a logistic transformation over each interval, for each parameter, according

to the formula11:

yi(x) = θlbi +
1

1 + exp(−λx)
(θubi − θlbi ), λ > 0

11In our implementation we set λ = 1.

130



implying

lim
x→−∞

yi(x) = θlbi and lim
x→+∞

yi(x) = θubi

Defining the map that performs the logistic transformation as

H(y) : R2 7→ Θ

we rewrite the loss function as

L̃ : R2 7→ R+

explicit as the composition L̃ = (L ◦ H)(y) ≡ L(H(y)). The problem we input to the

Nelder-Mead algorithm is then

min
y∈R2

L̃(y)

Once a candidate solution is found for the minimum, y∗ ∈ R2, we applied the logistic

transformation to figure out the relevant parameter factor that gives the minimum, i.e,

θ∗ ≡ H(y∗).

A.4.4 Dealing with the Stochastic βe

As in the main specification from the empirical part, we got a connection between

high heat and migration. In disciplining the model, we explicitly build the link between

weather conditions and rural productivity. In the model, we get a connection between rural

productivity and migration probability. To get in the model a regression, such as in the

data, of migration rate on the high-heat shocks, we proceed as follows. We first solve the

model given a vector of parameters and find the stationary distribution. Next, we draw

1, 000 samples of 10, 000 individuals indexed by i from it and run the following regression:

fe(a, z, η)i = γ0 + γ1 log(zi) + ϵi (A.13)

where fe(a, z, η) is the migration probability under state (a, z, η). In what follows, we let

the estimate of γ1 under sample s to be γ̂s. Intuitively, the value of γ̂s should be positive.

A higher temporary productivity (i.e., higher z) relaxes the budget constraint and makes

it more likely to afford the migration cost. It also increases the value of staying. As in

general, cs(a, z, η) ≫ ce(a, z, η), the valuation of an extra unit of resources is higher under

migrating than staying, and thus, a higher z tends to increase the probability of migrating.

131



The value of γ̂ that feeds in the loss function in Equation (A.11) is the average of the

1, 000 estimates, one for each sample. That is, denoting a sample by s ∈ {1, 2, . . . , 1000},
we input in the loss function

γ =
1

1000

1000∑
s=1

γ̂s

To make gd comparable to this γ̂, we convert the estimated coefficient in the regression in

Table 2.1 into the effect of one extra day of exposure above 30
◦
C/86

◦
F in the productivity,

according to

ln(z) = ln(1− χ)× h (A.14)

where χ = 0.023 is the estimated average decrease in the yield for an extra day of exposure

to a temperature above 30
◦
C/86

◦
F. Hence

∂ ln(z)

∂h
= ln(1− χ) (A.15)

and so the target for the parameter γ is, adjusting per the success rate of migration, ϕ:

gd ≡
β̂e

10, 000

1

ϕ

1

ln(1− χ)
(A.16)

It is important to recall that the definition of the migration rate reported in Table 2.1 is

per 10,000 individuals. Hence, we need to adjust the estimated value to according to the

normalization. We adjust by the success rate of migration since we only observe in the

data the effective migration, not the attempts to migrate.

A.4.5 Sampling from the stationary Distribution

When estimating the model, we collected 1,000 samples of 10,000 individuals from the

stationary distribution to compute the regression coefficient γ̂ from Equation (A.13) from

the main text. In this appendix, we show a checker on the sampling procedure. These

individuals are sampled from the mass of households that are “currently” in Guatemala,

that is µ(·) rather than M(·).
From the stationary distribution in the baseline model, we derive the implied flow of

households as

E ≡
∑
η

E(η) =
∑
η

∑
a

∑
z

µ(a, z, η)fe(a, z; η)

132



Alternatively, it is easy to show that, in the stationary distribution,

E =
ψ

ϕ
×M ≡ ψ

ϕ
×
∑
η

M(η)

From regression (A.13), its counterpart in the regression is given by

Ereg ≡ (γ̂0 + γ̂1E [ln(z)])

In reality, we need to multiply the number by∑
η

∑
a

∑
z

µ(a, z, η),

an adjustment to take into account that, in the stationary distribution, the mass of agents

in the home economy does not sum to 1. The remaining fraction is abroad, in the U.S.

Figure A.5 below shows the model implied flow of tentative migrants from the station-

ary distribution, with the dotted black line and its counterpart implied by the regression.

The former is computed without sampling and does not depend on the sample size.

The implied flow computed from the regression does depend on the particular sample.

The plot shows in the x-axis an increasing (in log10 scale) the sample size. Then, for 1000

samples in total, we computed the implied emigration flow from each regression, given a

sample size, and restored the results. Then, we compute 5 and 95 percentiles and the

mean. The plot shows that as the sample size grows, the implied flow from the regression

converges to the one computed directly from the stationary distribution.

The punchline is that the sampling from the stationary distribution is not flawed.

133



Figure A.5: Implied mass of agents trying to Emigrate

Note: The dotted black line shows the implied (tentative) emigration flow from the stationary

distribution, which does not rely on sampling. The regression we run to estimate the model does

rely on sampling. The plot shows the lines for the sampling exercises. For each sample size, in

the x-axis, we sample 300 samples, run the regression, and collect the implied, by each regression,

the tentative emigration flow. Then, with the data from the 300 samples, we compute the 5 and

95 percentiles in blue and red, respectively. The mean over is in solid green.

134



A.5 Climate Change Transitions

A.5.1 Data

In this section, we explain in more detail how we construct the transitory productivity

grid points and their respective probabilities. Figure A.6 shows the increases in temperature

projected for each scenario and its quadratic fit, as we discussed in the main text. We take

these projections and calculate the quadratic fit for every scenario as follows:

Pt = α+ β1
∗t+ β2

∗t2 + εt (A.17)

Figure A.6: Temperature Increase by Climate Change Scenario

To get the Z grid points along the transition, we compute them in a similar fashion as

our baseline Z grid for every projected year. First, we take the satellite temperature data

from Copernicus Climate Change Service (2019) at the raster-hourly level for the 1995-

2014 period, and we add the quadratic fit estimated in (A.17), P̂t. Second, we calculate

135



the exposure to temperatures above 30
◦
C during the main crop season and collapse the

raster level projections into the municipal level, as described in Section 2.2 of the paper.

Third, we compute our Z points and the respective probabilities as in Section A.2.2 of the

Appendix.

We apply this procedure for every projected year from 2023 to 2100. After 2100, we

assume temperatures are the same for every scenario. Therefore, the Z grid after 2100 is

the same as in 2100. In Figure A.7, we plot the histogram for the distribution of exposure

for our baseline and for the different climate change scenarios in the year 2100. As we can

see, the distribution for the optimistic case is similar to our baseline, while for the moderate

case, we see a shift towards more exposure days. For the pessimistic case, the shift is more

pronounced as the probability of experiencing many days above 30
◦
C increases.

A.5.2 Model

Forward-looking agents

This is our main exercise. For agents that are forward-looking, we assume that agents

have Rational Expectations and learn at date t = 0, still under the baseline distribution of

the weather shocks, the whole path for the transitory shocks, Z. This is a perfect foresight

exercise regarding the path of distributions.

In order to solve the value functions, policy functions, and distributions along the

transition, we follow these steps:

1. Solve the Value Functions and Policy Functions at date t = T as if the shocks were

to be forever as in the last period of the transition.

2. Starting at t = T , set the Continuation Values as V ∗
t (a, z; η) and Vt(a, z; η)

3. From t = (T − 1) to t = 0, decreasing one by one the time iterator t, use the

appropriate distribution of shocks at date t, Zt, to solve backward the sequence of

Value Functions and Policy Functions.

4. Having found the complete sequence of policy functions, iterate forward to using

the policy functions, the adequate z → z′ transitions, and the initial distribution of

136



Figure A.7: Exposure Distribution for Baseline (1995-2014) and by Scenario in 2100

(a) Baseline (b) Optimistic

(c) Moderate (d) Pessimistic

137



agents, to compute the mass of agents in the Home economy, the mass of agents

trying to emigrate and the mass of agents abroad.

After completing all these steps, we own the following objects.

Value Functions.

{V e
t (a, z; η), V

e
t (a, z; η),Vt(a, z; η), V ∗

t (η)}
T
t=0

Policy Functions.

{fa,t(a, z; η), fe,t(a, z; η)}Tt=0

Distribution of Agents and Flow of Tentative Migrants.

{µt(a, z, η),Mt(a, z, η), Et(a, z, η)}Tt=0

After t = T , all these objects will be equal to the baseline model computed under the

appropriate distribution of shocks, which is ZT .

Non-Forward Looking Agents

For the case of non-forward looking agents, we assume that they do observe the entire

distribution of shocks at (and up to) date t, but they expect to have the current (period

by period) distribution going forward. Our preferred interpretation is that they believe

in what they see, but think the future is not going to get worse. In this sense, they are

backward-looking agents.

There is one main difference relative to the case agents having perfect foresight regard-

ing the future productivity distribution’s path. Period by period along the transition, we

update the current realization of shocks. Then, using similar steps to A.2.2, we compute the

fixed-point value functions to get the continuation value for the households, using the cur-

rent distribution of transitory shocks as “permanent”. Equipped with these continuation

values, we then solve for the policy functions period by period.

138



A.6 Additional Results

A.6.1 Stock of Migrants

Figure A.8: Effect of Climate Change on Stock of Migrants

139



Figure A.9: Effect of Anticipation on Stock of Migrants

A.6.2 Stationary Distributions

140



Figure A.10: Stock of Migrants by Productivity at the Initial and Final stationary state

for each Scenario

(a) Initial (b) Final Optimistic

(c) Final Moderate (d) Final Pessimistic

141



Figure A.11: Final Asset PDF at the Initial and Final stationary state for each Scenario

(a) Initial (b) Final Optimistic

(c) Final Moderate (d) Final Pessimistic

142



Figure A.12: Stock of Migrants by Productivity for each Scenario and UCT scheme at the

Final stationary state

(a) Optimistic, Universal Cash Transfer (b) Optimistic, Bad-Weather Cash Transfer

(c) Moderate, Universal Cash Transfer (d) Moderate, Bad-Weather Cash Transfer

(e) Pessimistic, Universal Cash Transfer (f) Pessimistic, Bad-Weather Cash Transfer

143



A.6.3 Probability of Receiving the Transfer

Figure A.13: Probability of Receiving the Transfer

Note: This figure exhibits the probability of an individual receiving the transfer for each scenario

over time. In the exercises, we attribute the transfers for individuals that receive a transition

shock equal or lower to z = 0.60. In general, this probability rises over time: the distribution of

high heat is changing over time in the direction of high heat becoming more likely, and hence, a

lower z becomes more likely.

144



A.6.4 Alternative Cash-Transfers Amounts for same UCT schemes

Effect of a 5% Average Income Cash Transfer

Table A.6: Stock of Migrants in the U.S. under different Scenarios and Policies (5% transfer)

Case 2023 2040 2060 2080 2100 2120

Baseline

Optimistic 7.6 8.2 9.2 9.3 8.9 8.8

Moderate 7.6 8.9 10.8 11.7 12.3 12.5

Pessimistic 7.6 9.5 13.4 17.1 18.0 16.8

Universal

Optimistic 7.6 8.1 9.0 9.1 8.8 8.6

Moderate 7.6 8.8 10.6 11.7 12.4 12.6

Pessimistic 7.6 9.4 13.6 17.3 18.3 17.2

Bad-Weather

Optimistic 7.6 7.9 8.3 8.2 7.8 7.5

Moderate 7.6 8.6 10.3 11.1 11.4 11.4

Pessimistic 7.6 9.3 12.4 16.1 17.4 16.4

Note: This table shows the stock of migrants in the U.S. for the Optimistic, Moderate, and

Pessimistic scenarios for our baseline, universal UCT, and Bad-Weather UCT. Baseline

refers to our main results (no cash transfer). Universal refers to the case in which every

agent receives a cash transfer. Bad-Weather refers to the case in which the cash transfer

is received only by agents who suffered a drop in productivity of, at least, 40%. he cash

transfer used for these exercises is equivalent to 5% of the initial average income.

145



Table A.7: Annual Cost of the Unconditional Cash Transfers Policies (5% transfer)

Case 2023 2040 2060 2080 2100 2120

Universal

Optimistic 4.1 4.1 4.1 4.1 4.1 4.1

Moderate 4.1 4.1 4.0 3.9 3.9 3.9

Pessimistic 4.1 4.1 3.9 3.7 3.7 3.7

Bad-Weather

Optimistic 0.3 0.4 0.5 0.5 0.4 0.4

Moderate 0.3 0.5 0.7 0.8 0.9 0.9

Pessimistic 0.3 0.6 0.9 1.2 1.5 1.5

Bad-Weather
Universal (%)

Optimistic 8.4 10.2 11.8 11.7 9.8 9.8

Moderate 8.4 12.4 17.1 20.9 22.8 22.9

Pessimistic 8.4 13.8 22.8 31.7 39.8 39.7

Note: This table shows the cost of the UCTs for the Optimistic, Moderate, and Pessimistic

scenarios. In the first two rows, the cost is annual and measured as a percentage of initial

average income. The last row indicates the ratio between the cost of the bad-weather and

the universal cash transfer, expressed in percentages. The cash transfer used for these

exercises is equivalent to 5% of the initial average income.

146



Effect of a 20% Average Income Cash Transfer

Table A.8: Stock of Migrants in the U.S. under different Scenarios and Policies (20%

transfer)

Case 2023 2040 2060 2080 2100 2120

Baseline

Optimistic 7.6 8.2 9.2 9.3 8.9 8.8

Moderate 7.6 8.9 10.8 11.7 12.3 12.5

Pessimistic 7.6 9.5 13.4 17.1 18.0 16.8

Universal

Optimistic 7.6 7.7 8.4 8.4 8.1 7.9

Moderate 7.6 8.3 10.3 12.0 13.0 13.2

Pessimistic 7.6 9.1 14.2 17.7 19.3 18.3

Bad-Weather

Optimistic 7.6 7.4 6.4 5.7 5.1 4.9

Moderate 7.6 7.9 7.9 8.7 9.4 9.5

Pessimistic 7.6 8.5 10.8 12.9 14.4 13.8

Note: This table shows the stock of migrants in the U.S. for the Optimistic, Moderate, and

Pessimistic scenarios for our baseline, universal UCT, and Bad-Weather UCT. Baseline

refers to our main results (no cash transfer). Universal refers to the case in which every

agent receives a cash transfer. Bad-Weather refers to the case in which the cash transfer

is received only by agents who suffered a drop in productivity of, at least, 40%. he cash

transfer used for these exercises is equivalent to 20% of the initial average income.

147



Table A.9: Annual Cost of the Unconditional Cash Transfers Policies (20% transfer)

Case 2023 2040 2060 2080 2100 2120

Universal

Optimistic 16.5 16.5 16.4 16.4 16.5 16.5

Moderate 16.5 16.4 16.1 15.8 15.6 15.5

Pessimistic 16.5 16.3 15.4 14.7 14.4 14.6

Bad-Weather

Optimistic 1.4 1.7 1.9 1.9 1.6 1.6

Moderate 1.4 2.0 2.8 3.4 3.7 3.7

Pessimistic 1.4 2.3 3.6 4.8 6.0 6.1

Bad-Weather
Universal (%)

Optimistic 8.4 10.2 11.9 11.9 10.0 10.0

Moderate 8.4 12.4 17.6 21.6 23.5 23.6

Pessimistic 8.4 13.9 23.4 32.6 41.6 41.5

Note: This table shows the cost of the UCTs for the Optimistic, Moderate, and Pessimistic

scenarios. In the first two rows, the cost is annual and measured as a percentage of initial

average income. The last row indicates the ratio between the cost of the bad-weather and

the universal cash transfer, expressed in percentages. The cash transfer used for these

exercises is equivalent to 20% of the initial average income.

148



A.7 Interpretation of ν

In the main text, we assume that ν is a multiplicative term to the utility valuation of

consumption in the U.S., c∗. In this appendix, we explain in more details this assumption.

Introducing the parameter ν > 0 allows the model more degrees of freedom to match

the mass of Migrants that would live in the U.S. Given that the utility function is CRRA,

u(c) =
c1−σ

1− σ

with σ > 1. The value of being abroad is given by

V ∗(η) =
u(c∗)ν + βψEz′ [V(0, z′; η)]

1− β(1− ψ)

Because the utility level is negative, a higher ν implies a higher disutility of being abroad.

We think of this disutility as capturing the non-consumption enjoyment of being away from

its mother tongue, different culture, and nourishment, among others.

Ceteris Paribus, a higher level of ν tends to lower the value of emigrating, V e(a, z; η),

relative to the value of staying, V s(a, z; η), and avert migration. This results in both a

lower mass of migrants and a lower sensitivity of migration probability (or migration rate),

the two moments that we target. The more prominent effect tends to be on the mass of

migrants, and, in general, ν is much more informative about M than about β1.

Our estimate for c∗ comes directly from the data.12 An alternative to introducing ν is

estimating c∗ directly, since there is another level of consumption c̃ such that

u(c∗)ν = u(c̃)

which imply

c̃ = c∗ν
1

1−σ

Under our parametrization, σ = 2 and the expression becomes

c̃ =
c∗

ν

Hence, a larger ν would be equivalent — in terms of utility — to a lower level of consump-

tion. Using c∗ = 4.29E × [z] and the result from the SMM procedure for ν is 2.58, we

find
12See Section 2.4.1

149



c̃ =
4.29

2.58
× E[z] = 1.66× E[z]

The implied valuation of consumption in the U.S. is, therefore, higher than the one of

an individual that chooses qaa
′ = a, conditional on the median productivity η = 1. In this

case, consumption is simply cs = wzη — which occurs if a = a′ = 0 or a′ − a = a r
1+r .

In general, the lower the η, the more attractive is c̃ relative to E[z]. Another feature

is that c∗ is risk-free, while consumption in Guatemala is risky. Thus, the higher the

productivity, η, the higher the variance of income and, hence, consumption. So, the higher

the η, the feature of c∗ being risk-free becomes more attractive to the individual. These

two forces that go in opposite directions result in a selection that most migration comes

from individuals with η > 1.

150



A.8 Identification of Estimated Parameters

In the main text, we approach the quantitative problem by pre-setting some parame-

ters that are readily available in from the data, well-established in the literature or used

by reference papers in the literature. We then estimate two parameters using the Simu-

lated Method of Moments, which are the monetary migration cost me and the disutility

parameter of living in the U.S. ν.

In this appendix, we shed some light on the robustness of our modeling estimates. We

show how each parameter we estimate relates to the targeted moments we consider. We

start by fixing all pre-set parameters to the ones in the text. Next, we sample pairs of

(me, ν) and show how each pair relates to the targeted moments. This approach is similar

to the one ? employ.

We sample 2,500 pairs of the parameters we estimate, (me, ν). For each pair, we

solve the policy functions and stationary distribution of agents, next sampling cohorts,

and finally run a regression in the spirit of Equation 2.1 for each cohort. We start by

specifying an interval that specifies the range of reasonable values for each parameter after

some experimentation. The numbers are contained in Table A.10 below.

Table A.10: Interval allowed for each parameter

Parameter Lower-bound Upper-bound

me 2.01 2.92

ν 0.00 4.00

Then, we sample 5,000 draws from a normal distribution with zero mean and unitary

variance, N(0, 1). 2,500 of these draws pin down me and 2,500 of these draws pin down

ν, making the 2,500 pairs. Equipped with 2,500 pairs of normally distributed sampled

variables, we applied the logit transformation explained in Section A.4 of the Appendix,

yielding 2,500 pairs of (me, ν) that lie in the specified range for each parameter. A desired

implication of the use of normality together with the logit transformation is that the

sampled points are relatively more concentrated in the centroid of the box.

Given a pair of (me, ν) and the remaining parameters, we then solve the stationary

151



distribution and compute the two moments that we target. These two moments are the

sensitivity of the migration probability (and therefore migration rates) to the weather

shock, βe, and the stock of Guatemalans in the U.S., M .

Figure A.14: High-heat migration link and stock of migrants in the U.S. by migration cost

Note: The plot shows 2,500 dots, one for each combination of (me, ν), and the respective values of the βe

regression coefficient analogous to the one in Equation (2.1) and Table 2.1, in the left panel, and the stock

of migrants, M , in the right panel. The horizontal axis shows the value of me, while the vertical axis shows

the appropriated values for model moments. The horizontal red lines exhibit the target for each moment,

while the green vertical line highlights the estimated value for the parameter. Fixing a given level of me,

the variation observed along the vertical line associated with this level of me for each moment (each panel)

is driven by different values of ν that was paired with the fixed me.

152



Figure A.15: High-heat migration link and stock of migrants in the U.S. by disutility of

living in the U.S.

Note: The plot shows 2,500 dots, one for each combination of (me, ν), and the respective values of the βe

regression coefficient analogous to the one in Equation (2.1) and Table 2.1, in the left panel, and the stock

of migrants, M , in the right panel. The horizontal axis shows the value of ν, while the vertical axis shows

the appropriated values for model moments. The horizontal red lines exhibit the target for each moment,

while the green vertical line highlights the estimated value for the parameter. Fixing a given level of ν, the

variation observed along the vertical line associated with this level of ν for each moment (each panel) is

driven by different values of me that was paired with the fixed ν.

Table A.11: Statistical Description over 2,500 sampled pairs for (me, ν)

Symbol Mean SD Min q25 Median q75 Max

me 2.46 0.21 2.01 2.30 2.47 2.63 2.92

ν 2.58 0.21 2.10 2.42 2.59 2.74 3.06

βe -1.03 0.90 -4.63 -1.56 -0.86 -0.19 -0.02

M (%) 8.68 7.53 0.69 1.20 7.60 13.95 32.54

Note: SD stands for standard deviation, Min for minimum, q25 is the 25 percentile, q75 is 75 percentile

and Max is the maximum.

153



Table A.12: Covariance Matrix over 2,500 sampled pairs for (me, ν)

Symbol me ν βe M(%)

me 0.04 0.00 0.11 -0.86

ν 0.00 0.05 0.14 -1.26

βe 0.11 0.14 0.80 -6.74

M(%) -0.86 -1.26 -6.74 56.75

Note: Numbers are rounded to the second decimal place.

Table A.13: Model’s moment and estimated parameters

(1) (2) (3) (4)

Variables βe M me ν

me 2.5623*** -0.2014*** -0.0137

(0.0262) (0.0020) (0.0204)

ν 3.1642*** -0.2779*** -0.0131

(0.0256) (0.0019) (0.0195)

Observations 2,500 2,500 2,500 2,500

R2 0.91 0.92 0.00 0.00

Note: Standard errors reported. *** p<0.01, ** p<0.05, * p<0.1.

In column (1) of Table A.13, we run a regression of βe on me, ν, and a constant

(not reported). In column (2), we run a similar regression but using M as the dependent

variable. Columns (3) and (4) highlight that the draws for me and ν are not correlated.

Analyzing the numbers from Tables A.12 and A.13, we observe that, conditional on

the values for the pre-set parameters, the parameter controlling the disutility of migration

drives a slightly larger share of the results. While it is true for both moments individually,

154



ν is particularly important for the mass of migrants in the U.S., the importance of me is

relatively higher for the regression coefficient, βe.

155



Appendix B

Appendix to Chapter 3

B.1 Data

B.1.1 Exposure Data

Figure B.1 exhibits the temperature observed on a hypothetical day. The day starts at

around 10
◦
C and ends at around 14

◦
C. As the temperature rises, it eventually surpasses the

threshold of 30
◦
C at around 8 a.m. and remains above this threshold until approximately

4:30 p.m., so the total exposure to 30
◦
C is 8.5/24 ≈ 0.3541 day. The temperature remains

above 35
◦
C between 10:30 a.m. and 2 p.m., so the exposure to 35

◦
C is 3.5/24 ≈ 0.1458

day.

156



Figure B.1: Exposure to temperature thresholds

Exposure 30°C

Exposure 35°C

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour of the Day

Te
m

pe
ra

tu
re

 (
°C

)

Notes: The figure illustrates the exposure to different temperature cutoffs throughout a hypo-

thetical day.

157



Our weather data is hourly. We compute the exposure to different temperature thresh-

olds for each municipality and month, combining the weather data and the official munic-

ipality boundaries from IBGE for the year 2022. We then aggregate it at the quarterly

frequency.

Since the CPI data is available at the location level that is unique for each state, the

regression uses the exposure measure at the state level. We first compute the exposure

at the municipality level and then weigh each municipality within the state by the crop

production value as follows

Heatℓ,t ≡
∑
l∈Mℓ

Heatl,t × w̃l,ℓ =
∑
l∈Mℓ

Heatl,t ×

 wl,ℓ∑
l∈Mℓ

wl,ℓ

 (B.1)

where Mℓ is the set of all municipalities in state ℓ. The weight is wl,ℓ for municipality l at

state ℓ, and is given by

wl,ℓ =

2021∑
y=1999

CPVl,y
22

(B.2)

where CPVl,y is the total crop production value. As we detail in Appendix B.1.2, the

data for such series comes at annual frequency, at crop and municipality level. The data

starts in 1974 and finishes in 2021. We use the data from 1999 to be lined up as much as

possible with the CPI coverage. Hence, wl,ℓ is the time average crop production value at

the municipality l. This weight is time-invariant throughout the sample.

158



B.1.2 Crop Production Data

We use the Systematic Survey of Agricultural Production1 from IBGE as the main

source for crop production data. Our data comes in annual frequency and provides the

value of production, planted area, harvest area, quantity produced, and average yield at

the level of crop and municipality. We refer to appendix B.1.2 for a detailed list of crops

that are covered.

The data covers the years 1974 to 2021. We use the production value data to weigh the

observations (municipalities) around a reference city for the metro area when constructing

the exposure measure we use to run the regression in (3.32). Specifically, we first compute

the exposure to a given threshold of temperature for each municipality at the monthly

frequency. Then, for each metro area in our CPI data, we consider all cities that are within

the state limits for that metro area. The measure of exposure for each metro area is the

weighted average of exposure of all municipalities within the state boundaries, and the

relative weight is given by the total (nominal) crop production value, averaged from 1999

to 2021, to overlap with our CPI data coverage, as much as possible.

Link between Heat Exposure and Crop Yields

We use a long panel of data to examine the relationship between heat exposure and

crop yields. Our findings show that temperatures exceeding 30
◦
C tend to reduce crop

yields, consistent with Schlenker and Roberts (2009) based on U.S. data. We estimate this

effect using a panel regression where the dependent variable is yield, regressed on heat

exposure at a specified cutoff, T . As in the main text, we set T = 30
◦
C. Heat exposure is

measured during the crop season, defined from September to May, which covers the most

significant crops in terms of production value that share a common or overlapping growing

period.

log(yieldℓ,t) = β0 + βhHeatt,ℓ + ΓXℓ,t + αℓ + αt + ϵℓ,t (B.3)

1In Portuguese, “Levantamento Sistemático da Produção Agŕıcola”.

159



Here, t represents time, and ℓ denotes location. The variable Heatt,ℓ measures exposure

above the temperature of 30
◦
C. We include location fixed effects to control for time-

invariant, location-specific factors, and time fixed effects to account for aggregate shocks.

The vector Xt, ℓ comprises additional controls for robustness checks, including state and

regional trends, as well as interactions of states and regions with years.

For brevity, we show three regressions here. The crops for these regressions are rice,

soybean, and beans. Rice and soybeans are classified as “tradable” in the Brazilian Central

Bank CPI classification, while beans are classified as “non-tradable”. Again, “tradable”

refers to our low-trade-cost, LTC, and “non-tradable” refers to our high-trade-cost, HTC.

We ran one regression separately per crop to allow the fixed effect to control for crop-

specific forces at locations and aggregate effects. Alternatively, one could interact with

each fixed effect with a crop dummy together with the exposure variable.

The coefficient βh is a semi-elasticity. For example, one additional day of exposure

above 30
◦
C during the crop season decreases the rice yield by 0.40% and the beans yield

by 0.6%, after controlling for state-year fixed effects.

160



Table B.1: Regression (B.3) results: Rice

Dependent variable: 100× log(yieldt,ℓ)

(1) (2) (3) (4) (5)

Heatt,ℓ -1.40∗∗∗ -1.37∗∗∗ -0.795∗∗∗ -1.41∗∗∗ -0.392∗∗∗

(0.0512) (0.0494) (0.0519) (0.0471) (0.0554)

Observations 154501 154501 154501 154501 154501

R-squared 0.172 0.185 0.273 0.198 0.376

Number of Municipalities 4837 4837 4837 4837 4837

Municipality FE ✓ ✓ ✓ ✓ ✓

Year FE ✓ ✓ ✓ ✓ ✓

Regional Trend ✓

Regional Dummy x Year ✓

State Trend ✓

State Dummy x Year ✓
Note: This table shows the results of regression (B.3), with several controls. Robust standard

errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. All regressions include both Mu-

nicipality and Year Fixed Effects. The regression in Column (1) does not include any other

controls. Column (2) adds the control for the Regional Trend. Column (3) adds an interaction of

a Regional Dummy with Year. Column (4) adds a State Trend. Column (5) adds an interaction

between a State Dummy and Year.

161



Table B.2: Regression (B.3) results: Soybean

Dependent variable: 100× log(yieldt,ℓ)

(1) (2) (3) (4) (5)

Heatt,ℓ -0.951∗∗∗ -1.05∗∗∗ -0.891∗∗∗ -0.951∗∗∗ -0.599∗∗∗

(0.0345) (0.0362) (0.0382) (0.0365) (0.00037)

Observations 73240 73240 73240 73240 73240

R-squared 0.508 0.51 0.583 0.522 0.66

Number of Municipalities 2881 2881 2881 2881 2881

Municipality FE ✓ ✓ ✓ ✓ ✓

Year FE ✓ ✓ ✓ ✓ ✓

Regional Trend ✓

Regional Dummy x Year ✓

State Trend ✓

State Dummy x Year ✓
Note: This table shows the results of regression (B.3), with several controls. Robust standard

errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. All regressions include both Mu-

nicipality and Year Fixed Effects. The regression in Column (1) does not include any other

controls. Column (2) adds the control for the Regional Trend. Column (3) adds an interaction of

a Regional Dummy with Year. Column (4) adds a State Trend. Column (5) adds an interaction

between a State Dummy and Year.

162



Table B.3: Regression (B.3) results: Beans

Dependent variable: 100× log(yieldt,ℓ)

(1) (2) (3) (4) (5)

Heatt,ℓ -1.04∗∗∗ -0.895∗∗∗ -0.721∗∗∗ -0.941∗∗∗ -0.604∗∗∗

(0.0372) (0.0345) (0.0363) (0.0341) (0.0404)

Observations 207222 207222 207222 207222 207222

R-squared 0.172 0.217 0.269 0.24 0.371

Number of Municipalities 5522 5522 5522 5522 5522

Municipality FE ✓ ✓ ✓ ✓ ✓

Year FE ✓ ✓ ✓ ✓ ✓

Regional Trend ✓

Regional Dummy x Year ✓

State Trend ✓

State Dummy x Year ✓
Note: This table shows the results of regression (B.3), with several controls. Robust standard

errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1. All regressions include both Mu-

nicipality and Year Fixed Effects. The regression in Column (1) does not include any other

controls. Column (2) adds the control for the Regional Trend. Column (3) adds an interaction of

a Regional Dummy with Year. Column (4) adds a State Trend. Column (5) adds an interaction

between a State Dummy and Year.

163



B.1.3 CPI Data — Additional Details

Locations and Broad Baskets

Table B.4 reveals details for the locations we consider in the analysis. There are 16

locations in the panel, most of which are metro areas. All the locations that are labeled

as “municipality” are the state capital. For each state, there is at most one location, but

not all states are covered by the CPI data, as figure B.2 shows. Out of 27 states, 16 are

currently tracked in the CPI data, either by its capital or the metroarea that include its

capital.

The weight of each location when constructing the national index is highly variable,

as the column “Location” highlights. Locations with high total household income receive

higher weights, conditioning on income from 1 to 40 minimum wages. For example, the

location of “São Paulo” has the highest weight because it is the most populated state in

Brazil and has a relatively high household income2. These location weights are not used

directly in our estimation.

The table shows the weight in the CPI basket for Food overall and breaks down these

weights into “Tradable” and “Nontradable” according to the Central Bank Classification

exposed in B.1.4. The range for the weight of Food in the basket is 26.6 percent to 16.8

percent.

The table also illuminates regional differences in the consumption basket. Locations

with lower weight are usually poorer and tend to have a relatively high expenditure share

on Food. On the other hand, locations with higher weights tend to consume a relatively

larger share of Nontradable food within the group “Food”. The reason is that the “Food”

group contains subitems related to services, such as eating out, which tend to be a relatively

larger share of the expenditure as income increases.

Figure B.2 brings a map of the state boundaries and the year when the locations

associated with each state became available in our sample. The sample we consider starts

in 1999, and by that year, there were already 11 locations in the CPI. In January 2014,

Campo Grande (MS) and Vitória (ES) became covered. In May 2018, Rio Branco (AC),

São Luis (MA), and Aracaju (SE) data became available.

2For brevity of the exposition, we omitted these two information from the table.

164



Figure B.2: Locations for which the CPI data is available

Notes: The figure shows the state boundaries. The legend reads as the year in which the metro

area or capital city was introduced in the CPI panel. Many locations were introduced before

1999, so the map reads as 1999 all the cities which were already available in that year. For

locations in gold, the CPI coverage started before 1999. For locations in light blue, the coverage

started in 2014. For locations in darker blue, the coverage started in 2018. Locations for which

CPI data is unavailable are marked in gray.

165



Table B.4: Locations for which CPI data is available

Weights (%)

Location Type State Acronym Location Food LTC Food HTC Food

Rio Branco Municipality Acre AC 0.5 23.3 12.8 10.4

Belém Metroarea Pará PA 3.9 26.6 15.9 10.7

São Lúıs Municipality Maranhão MA 3.5 25.5 16.3 9.2

Fortaleza Metroarea Ceará CE 3.2 23.9 13.0 10.9

Recife Metroarea Pernambuco PE 3.9 23.5 11.8 11.6

Aracaju Municipality Sergipe SE 1.0 21.7 10.9 10.8

Salvador Metroarea Bahia BA 6.0 22.4 11.7 10.7

Belo Horizonte Metroarea Minas Gerais MG 9.7 21.7 11.2 10.6

Vitória Metroarea Esṕırito Santo ES 1.9 17.4 9.3 8.1

Rio de Janeiro Metroarea Rio de Janeiro RJ 9.4 20.2 10.4 9.8

São Paulo Metroarea São Paulo SP 32.3 20.0 9.7 10.3

Curitiba Metroarea Paraná PR 8.1 20.9 11.7 9.2

Porto Alegre Metroarea Rio Grande do Sul RS 8.6 21.1 11.1 10.0

Campo Grande Metroarea Mato Grosso do Sul MS 1.6 21.5 11.9 9.6

Goiânia Municipality Goiás GO 4.2 20.5 11.1 9.4

Braśılia Federal District Distrito Federal DF 4.1 16.8 7.1 9.7

Brazil Country - BR 100.0 21.0 10.9 10.1

Notes: The table shows every location we consider in the analysis. The location weights are the officially

released figures from the IBGE and were computed from the latest Consumer Expenditure Survey conducted

in 2017 and 2018. Location weights come from regional differences in household income. The weights for

“Food”, LTC Food and HTC Food refers to the data for December 2023. “LTC Food” is “tradable” food,

while “HTC Food” is “nontradable” food, according to the latest Central Bank Classification, as exposed

in B.1.4. Occasional rounding errors occur.

Basket of Items Covered in the CPI

Within our sample coverage, the basket of nationally covered sub-items changed three

times, so there were baskets that were tracked. These changes happen mainly due to new

information available from updated versions of Consumer Expenditure Survey (CES)3.

The editions of the survey post stabilization of hyperinflation took place in 1995-1996,

3In Portuguese, Pesquisa de Orçamentos Familiares — POF

166



2002-2003, 2008-2009 and 2017-2018.

At the beginning of our sample, in 1999, the reference CES was the version conducted

in 1995-1996. The CES version 2002-2003 was incorporated into the CPI basket in 2006.

The next CES version, 2008-2009, led to a change in the CPI basket in 2012. The latest

CES, from 2017-2018, was introduced to the CPI basket in 2020 and was current until the

end of our sample.

Computing the Time Series of Price Changes

Let i be a sub-item (e.g., rice, bus fare, dress), ℓ be a location (e.g., São Paulo, Belo

Horizonte, Rio Branco), and t a month. The CPI data provides (i) a monthly weight

associated with the sub-item at that location, which we denote by wi,ℓ,t; and (ii) a monthly

percent change in prices, which we denote by πi,ℓ,t ≡
pi,ℓ,t
pi,ℓ,t−1

− 1.

The official data provides the inflation level and the weight for “Food and Beverages”

for each date t and location ℓ. Below, we explain how we construct the inflation measures

for the baskets of “Non-Food,” “Food Tradable”, and “Food Nontradable”.

Price Changes of an Arbitrary Basket We let the set of all sub-items be denoted by

I. Each sub-item is part of exactly one “item” Ik, forming a partition K

I ≡
⋃
k∈K

Ik : Ik
⋂
k ̸=k′

Ik
′
= {∅}

Let Ik be an item (e.g., fruits, public transportation, women’s apparel), which is a

set of similar sub-items. Normalize, at the location and monthly level, the weight of each

sub-item of Ik so that they sum up to 1. The monthly price change for the item Ik at

location ℓ at time t is equal to

πIk,ℓ,t ≡
∑
i∈Ik

πi,ℓ,t × w̃i,ℓ,t ≡
∑
i∈Ik

πi,ℓ,t ×
wi,ℓ,t∑

i∈Ik
wi,ℓ,t

(B.4)

Let G be a group (e.g., Food and Beverages, Transportation, Apparel), which is a set

a set of similar items. Normalize, at the location and monthly level, the weight of each

sub-item of Ik so that they sum up to 1. The price change for a group G at location ℓ at

167



time t is equal to

πG,ℓ,t ≡
∑
i∈G

πi,ℓ,t × w̃i,ℓ,t ≡
∑
i∈G

πi,ℓ,t ×
wi,ℓ,t∑

i∈G
wi,ℓ,t

(B.5)

Constructing the Non-Food basket. Let Ft,ℓ denote the group of items that are

classified as “Food”. We then compute the inflation level for the basket of “Non-Food”

sub-items by constructing a group NFt,ℓ as follows. First, we construct the group NFt,ℓ as

NFt,ℓ ≡ {i ∈ I : i /∈ Ft,ℓ} (B.6)

πNF,ℓ,t ≡
∑

i∈NFℓ,t

πi,ℓ,t × w̃i,ℓ,t ≡
∑

i∈NFℓ,t

πi,ℓ,t ×
wi,ℓ,t∑

i∈NFℓ,t

wi,ℓ,t
(B.7)

Constructing the Tradable and Nontradable Food baskets. We borrow from the

Brazilian Central Bank a classification of which items are classified as “Tradable” and

which ones are Classified as “Non-Tradable”, which we use in particular for the group of

“Food and Beverages”, which we refer generically as “Food”4 The set of sub-items that are

classified as “Food” form a partition of items that are “Tradable” and “Nontradable”. Let

TFℓ,t be the set of tradable food sub-items at location ℓ and time t. We let NTFℓ,t denote

the set of nontradable food sub-items.

Fℓ,t ≡ TFℓ,t
⋃
NTFℓ,t such that TFℓ,t

⋂
NTFℓ,t = {∅} (B.8)

The inflation of tradable food at location ℓ at date t is given

πTF,ℓ,t ≡
∑

i∈TFℓ,t

πi,ℓ,t × w̃i,ℓ,t ≡
∑
TFℓ,t

πi,ℓ,t ×
wi,ℓ,t∑

i∈TFℓ,t

wi,ℓ,t
(B.9)

while for the nontradable food, we have

πNTF,ℓ,t ≡
∑

i∈NTFℓ,t

πi,ℓ,t × w̃i,ℓ,t ≡
∑

NTFℓ,t

πi,ℓ,t ×
wi,ℓ,t∑

i∈NTFℓ,t

wi,ℓ,t
(B.10)

4See Appendix B.1.4 for further detail on such classification.

168



Computing the Price Level of A Basket. Once we compute the series of inflation

for each basket B ∈ {F,NF, TF,NTF}, The time series for the price for that basket is

computed as

pB,ℓ,t = pB,ℓ,0

t∏
τ=0

(1 + πB,ℓ,τ ) (B.11)

where we set pB,ℓ,0 = 100 without loss of generality. Applying the natural logs and taking

the difference between period t+ h and t− 1, where h stands for the horizon, recovers the

dependent variable in the regressions we use throughout the main text.

169



B.1.4 Brazilian Central Bank Classification for Goods and Services

Our CPI data come from IBGE. We would like to use a measure of the tradability of

goods and services. Since such a classification is not directly available from the IBGE, we

rely on the classification developed by the Brazilian Central Bank (BCB).

The BCB uses data on import, export, and production to classify goods and services

as “Tradable” and “Nontradable”. There is a third category called “Regulated”, for sub-

items whose prices are controlled by contracts by the competent government (such as bus

fare, eletricity fee). These three categories form a partition. Methodological notes with

updates to this classification were last posted on Brazilian Central Bank (2019).

We use this classification exclusively for Food goods and services5. In such group, there

are not “regulated” sub-items, so the goods and services are either classificied as tradable

or non-tradable.

Within our sample, there were four versions of the Consumer Expenditure Survey (see,

for further details, B.1.3). For each of these versions, the IBGE defines a national basket

of goods and services whose prices will be tracked. The basket of goods actually tracked

at each location is a subset of this national basket and depends on regional differences in

the consumption habits.

5In Portuguese, “Alimentação e Bebidas”.

170



B.1.5 Matching Crops from IBGE and GAEZ

In this appendix, we list all crops that are matched from the GAEZ dataset and the

IBGE crop production data.

These crops correspond to around 90% of total crop production value for the years

between 2002 and 2022. The corresponding metric for the share of total land used for

crops is even higher, around 95%.

B.1.6 Construction of µxℓ and T x
ℓ

In the main text, we show that the Frechet draws for the productivity imply a link

between the State of Technology parameter T xℓ , and the average (or expected) potential

productivity, µxℓ . In the text, this relationship appears in Equation (3.17), which we

reproduce here

T xℓ =
[
µxℓ

]θx
κx

In order to recover a measure of average productivity in a way that makes sense in our

model, we perform the two adjustments: converting from land to labor productivity and

standardizing the units — so we can take an average. The formula to recovering µxℓ is

µxℓ =
1

Nx

∑
ω

Zxℓ (ω)ν(ω)p(ω) (B.12)

where Nx is the number of goods of type x in the Table B.5, Zxℓ (ω) is the productivity

of crop ω in location ℓ, measured in Kg/Ha, ν(ω) is the input requirement, measured in

Wokers/Ha, and p(ω), is the price in local currency/Kg. The resulting unit is a measure

of local currency per worker.

Notice that ν(ω) is given by the inverse of labor intensity in Table B.5. This is im-

portant since a low input requirement means that the crop is relatively intense in land

— soybean is a prominent example. In this case, by construction in equation (B.12), the

relatively more land-intense crops receive a relatively high weight.

Observe that both the input requirement, ν(ω), and the price, p(ω), do not take the

index ℓ. Both are based on the national average. The reason is that both conventions are

done so that average is sensitive and the final measure corresponds to labor productivity.

Using local prices or local input requirements might contaminate the averaging with the

171



connectedness of each location — e.g., the price of a good in a relatively isolated place

would be higher, but this would reflect trade costs rather than higher productivity.

Once the measure of µxℓ , we construct the variable T xℓ . The constant κx is absorbed

into a normalizing scale: all we need is the relative value of T xℓ to construct πxj,ℓ, as this

variable is homogeneous of degree zero in the vector [T xℓ ], as shown in Equation (3.15).

Results for µxℓ .

172



Table B.5: Crops matched between GAEZ and the IBGE

Crop Name GAEZ Acronym Tradability Actvitity Labor Intensity

Banana bana HTC Fruits 149

Barley barl LTC Cereals 82

Beans bean HTC Other seasonal crops 165

Cacao coco HTC Cacao 101

Cassava casv HTC Other seasonal crops 165

Citrus citr HTC Organge 107

Coconut cocn HTC Fruits 149

Coffee coff LTC Coffee 157

Corn maiz LTC Cereals 82

Cotton cott LTC Cotton 14

Cowpea cowp HTC Other seasonal crops 165

Dry peas dpea HTC Vegetables and Legumes 304

Flax fibre flax LTC Oilseeds 169

Groundnut grnd LTC Other seasonal crops 165

Oat oats LTC Cereals 82

Oil palm oilp LTC Other permanent crops 110

Olive oliv LTC Other permanent crops 110

Onion onio HTC Other seasonal crops 165

Rye ryes LTC Cereals 82

Sorghum bsrg LTC Cereals 82

Soybean soyb LTC Soybean 13

Sugar Cane sugc LTC Sugarcane 45

Sunflower sunf LTC Oilseeds 169

Sweet Potato spot HTC Other seasonal crops 165

Tea teas LTC Other permanent crops 110

Tomato toma HTC Vegetables and Legumes 304

Wetland rice ricw LTC Cereals 82

Wheat whea LTC Cereals 82

White Potato wpot HTC Other seasonal crops 165

Notes: Labor intensity is measured as the number of workers per 1,000 hectares, rounded to the

nearest whole number. Since labor intensity data is not directly available for each crop, we assign

the value from the closest corresponding group whenever necessary. “Activity” is the group de-

fined in the 2017 agricultural census conducted in Brazil. These groups are: “Cereals,” “Fruits,”

“Oilseeds,” “Other Seasonal Crops,” “Other Permanent Crops,” and “Vegetables and Legumes.”

The “Fruits” category excludes oranges and grapes, while “Oilseeds” excludes soybeans.

173



Figure B.3: Measures for the historical µxℓ for LTC and HTC food goods.

(a) LTC: µc
ℓ

(b) HTC: µq
ℓ

Notes: Panel (a) displays the relative average potential productivity of each state for LTC

(low-temperature crop) food goods, while panel (b) shows the corresponding values for HTC

(high-temperature crop) food goods. In both panels, productivity levels are expressed relative

to the state of São Paulo, which is set to 100 for reference. Each bar represents the productivity

value for a given state, with states arranged on the horizontal axis in increasing order from left

to right.

174



Figure B.4: Spatial correlation for µxℓ for LTC and HTC food goods.

(a) LTC: µc
ℓ

(b) HTC: µq
ℓ

Notes: Panel (a) exhibits the relative average potential productivity of each state for the LTC

food goods, while panel (b) exhibits the analogue for the HTC food goods. Both measures are

relative to the level of the state of São Paulo, which is normalized to 100. The color scale for

each location is comparable.

175



B.1.7 Construction of the Relative Wages

In the construction of the trade shares, as in Equation 3.15, we need a measure of the

wages costs in each location. For that, we took the average wage for all occupations from

Continuous National Household Sample Survey (PNAD Cont́ınua, in Portuguese).

The trade share is homogeneous of degree 0 in the vector of wages. Hence, similar to

the case of recovering µxℓ and T xℓ , we choose one state as a reference and normalize the

average wage to the level observed in the State of São Paulo. Since the series started in

2012, we took an average over time, otherwise we would lose more than half of the CPI

sample that we use to run the regression Equation 3.32. The CPI data in our sample starts

in 1999.

In the model, πxj,ℓ fluctuates because of fluctuations in w̃xℓ . Hence, taking the average

over time for the relative wage level in each state renders the trade share constant. The

resulting average wage is shown below, in figure B.5.

176



Figure B.5: Relative wage costs

(a) Ordered Wages

(b) Spatial Dispersion

Notes: Panel (a) exhibits the relative wage of each state, ordered from left to right; Panel (b)

exhibits the same information in a map, highlighting the spatial dispersion of wages.

177



B.1.8 Counterfactual Measures of µxℓ

Relative to the baseline, the key change in the construction of the counterfactual µxℓ ,

denoted by µx′ℓ , is the new draws in Zxℓ (ω), which we denote by Zxℓ (ω)
′.

Applying the formula in Equation (B.12), we have the following:

µx′ℓ =
1

Nx

∑
ω

Zx′ℓ (ω)ν(ω)p(ω) (B.13)

Letting gxℓ (ω) be the net growth rate of land productivity for variety (x, ω) in location ℓ,

we have by construction:

Zx′ℓ (ω) = Zxℓ (1 + gxℓ (ω)) (B.14)

Hence, we can rewrite the rate of change in µxℓ as

µx′ℓ − µxℓ
µxℓ

=
∑
ω

µ̃xℓ (ω)g
x
ℓ (ω) (B.15)

where

µ̃xℓ ≡
Zxℓ (ω)ν(ω)p(ω)∑
ω

Zxℓ (ω)ν(ω)p(ω)
(B.16)

gives the of contribution of good ω into µxℓ . Up to a first-order approximation, provided

that gxℓ (ω)

log(µx′ℓ )− log(µxℓ ) = log
(µx′ℓ
µxℓ

)
≈
µx′ℓ − µxℓ
µxℓ

=
∑
ω

µ̃xℓ (ω)g
x
ℓ (ω) (B.17)

Therefore, up to a first-order approximation the proportional change in the average poten-

tial productivity can be decomposed into a weighted average of growth rate of each crops’

productivity, gxℓ (ω) and the weights are given by the pre-change contributions toward µxℓ ,

that is, µ̃xℓ (ω).

178



B.2 Model: Derivations

In this appendix, we provided a detailed derivation of the results for the main model.

B.2.1 Ideal Price Index

From the nested-CES structure of the utility, the ideal price index for each good type

at location ℓ ∈ L

P cℓ =

(∫ 1

0
pcℓ(ω)

1−νdω

) 1
1−ν

and P qℓ =

(∫ 1

0
pqℓ(ω)

1−νdω

) 1
1−ν

We will use this expressions later on in the derivation.

B.2.2 Prices

Let the adjusted bundle cost of inputs at location ℓ ∈ L and good type x be

w̃xℓ ≡ wℓ
Gx(s)

The cost of location faced by location j if it were to buy variety ω from location ℓ is given

by

pxj,ℓ(ω) =
w̃xℓ

Z̃xℓ (ω)
τxj,ℓ

where τxj,ℓ is trade cost of good type x from location ℓ to j and Z̃xℓ (ω) is the productivity

of location ℓ to produce variety ω of good type x, which we label as “EK term” in (3.24).

These EK productivities are independently drawn across locations, varieties, and types

from a location-type specific Fréchet Distribution, as in (3.9):

F xℓ (z̃) = e−T
x
ℓ z̃

−θx

.

179



The probability that location ℓ can supply variety ω of type x to location j at a price at

most p is given by

Gxj,ℓ(p) ≡ Pr
{
pxj,ℓ(ω) ≤ p

}
= Pr

{
w̃xℓ

Z̃xℓ (ω)
τxj,ℓ ≤ p

}

= Pr

{
w̃xℓ
p
τxj,ℓ ≤ Z̃xℓ (ω)

}
= 1− Pr

{
Z̃xℓ (ω) ≤

w̃xℓ
p
τxj,ℓ

}
= 1− F xℓ

(
w̃xℓ
p
τxj,ℓ

)
= 1− exp

{
−T xℓ

(
w̃xℓ τ

x
j,ℓ

)−θ
pθ
}

(B.18)

Location j buys from the lowest-cost supplier. The probability of location j pays at

most p for the type-variety pair (x, ω) is given by

Gxj (p) ≡ Pr

{
min
ℓ∈L

pxj,ℓ(ω) ≤ p

}
= 1− Pr

{
min
ℓ∈L

pxj,ℓ(ω) ≥ p

}
= 1− Pr

{⋂
ℓ∈L

(
pxj,ℓ(ω) ≥ p

)}
= 1−

∏
ℓ∈L

(
1−Gxj,ℓ(p)

)
(B.19)

Using (B.18) into (B.19)

Gxj (p) = 1−
∏
ℓ∈L

exp
{
−T xℓ

(
w̃xℓ τ

x
j,ℓ

)−θ
pθ
}

= 1− exp

{
pθ
∑
ℓ∈L

−T xℓ
(
w̃xℓ τ

x
j,ℓ

)−θ}
= 1− exp

{
−pθΦxj

}
(B.20)

where

Φxj ≡
∑
ℓ∈L

T xℓ
(
w̃xℓ τ

x
j,ℓ

)−θ
180



The ideal price index for location good type x is given by at location j solves(
P xj
)1−ν ≡

∫ 1

0
pxℓ (ω)

1−νdω

=

∫ ∞

0
p1−νdGxj (p)

=

∫ ∞

0
p1−ν

(
d

dp
(1− exp

{
−pθΦxj

})
dp

=

∫ ∞

0
p1−νθpθ−1Φxj exp

{
−pθΦxj

}
dp

= θΦxj

∫ ∞

0
pθ−ν exp

{
−pθΦxj

}
dp

≡
∫ ∞

0

(
y

Φxj

) 1−ν
θ

exp {−y} dy

=
(
Φxj
)− 1−ν

θ

∫ ∞

0
y

1−ν
θ exp {−y} dy

=
(
Φxj
)− 1−ν

θ Γ

(
θ + 1− ν

θ

)
≡
(
Φxj
)− 1−ν

θ γ (B.21)

where we used, in the sixth row, the change of variable y ≡ pθΦxj , which implies dy =

θpθ−1Φxj dp. The Gamma function that appears in the eighth row is given by Γ (t) ≡∫∞
0 yt−1 exp {−y} dy, for t > 1. We let

γ ≡ Γ

(
θ + 1− ν

θ

)
The price index P xj is then given by

P xj =
(
Φxj
)− 1

θ γ
1

1−ν

≡

(∑
ℓ∈L

T xℓ
(
w̃xℓ τ

x
j,ℓ

)−θ)− 1
θ

γ̄ (B.22)

where we let γ̄ ≡ γ
1

1−ν

B.2.3 Trade Flows

The trade flows expressions are standard expressions in the Eaton and Kortum (2002)

framework. Below we show a detailed derivation. There is a continuum of varieties of each

181



type, and the productivity draws are independent across varieties, types and locations. This

implies that the probability a location j ∈ L buys a variety ω ∈ [0, 1] of type x ∈ {c, q} is

equal to the proportion of goods of this type that location j ∈ L will buy from ℓ ∈ L. We

denote this trade share by πxj,ℓ.

To find out this share, let us start with the probability that j ∈ L buys ω ∈ [0, 1] from

ℓ ∈ L. In what follows, let L−ℓ ≡ {j ∈ L : j ̸= ℓ}, the set of all locations but ℓ.

πxj,ℓ ≡ Pr

{
pxj,ℓ(ω) ≤ min

k∈L−ℓ

pxj,k(ω)

}
=

∫ ∞

o
Pr

{
min
k∈L−ℓ

pxj,k(ω) ≥ p

}
dGxj,ℓ(p)

=

∫ ∞

o
Pr

 ⋂
k∈L−ℓ

(
pxj,k(ω) ≥ p

) dGxj,ℓ(p)

=

∫ ∞

o

 ∏
k∈L−ℓ

(1−Gxj,k(p))

 dGxj,ℓ(p)
=

∫ ∞

0

 ∏
k∈L−ℓ

(
exp

{
−T xk

(
w̃xkτj,k
p

)−θ
}) dGxj,ℓ(p)

=

∫ ∞

0

exp
pθ ∑

k∈L−ℓ

−T xk
(
w̃xkτ

x
j,k

)−θ
 dGxj,ℓ(p)

=

∫ ∞

0

exp
pθ ∑

k∈L−ℓ

−T xk
(
w̃xkτ

x
j,k

)−θ
( d

dp

(
1− exp

{
−T xℓ

(
w̃xℓ τj,ℓ
p

)−θ
}))

dp

182



Now, using equation (B.18), we get

πxj,ℓ ≡
∫ ∞

0

exp
pθ ∑

k∈L−ℓ

−T xk
(
w̃xkτ

x
j,k

)−θ
T xℓ (w̃xℓ τj,ℓ)

−θ θpθ−1 exp
{
−T xℓ (w̃xℓ τj,ℓ)

−θ pθ
}
dp

= T xℓ (w̃xℓ τj,ℓ)
−θ
∫ ∞

0
θpθ−1 exp

{
−pθΦxj

}
dp

= T xℓ (w̃xℓ τj,ℓ)
−θ Φ

x
j

Φxj

∫ ∞

0
θpθ−1 exp

{
−pθΦxj

}
dp

=
T xℓ (w̃xℓ τj,ℓ)

−θ

Φxj

∫ ∞

0
θpθ−1Φxj exp

{
−pθΦxj

}
dp

=
T xℓ (w̃xℓ τj,ℓ)

−θ

Φxj

[
− exp

{
−pθΦxj

}]∞
p=0

=
T xℓ (w̃xℓ τj,ℓ)

−θ

Φxj
(B.23)

B.2.4 Indirect Utility

Under the assumption of the Stone-Geary utility function, the indirect utility is given

by

U(coi,j , c
f
i,j) = (1− αf ) log(coi,j) + αf log(cfi,j − cf ) (B.24)

The outside good is a numeraire, the price of food is P fj and the income is yi,j . Thus, the

demand for each good is

Coi,j = (1− αf )(yi,j − cfP fj ) (B.25)

Cfi,j = cf + αf
(yi,j − cfP fj )

P fj
(B.26)

Hence, the food expenditure share is given by

sfi,j ≡
Cfi,jP

f
j

yi,j
= αf + (1− αf )ψfi,j (B.27)

where ψfi,j is the subsistence ratio, the share of income that is needed to pay for the

minimum food consumption:

ψfi,j ≡
cfP fj
yi,j

(B.28)

183



Plugging the demand for each good into the utility, we recover the indirect utility function:

Vi,j ≡ V (yi,j , P
f
j ) = (1− αf ) log(1− αf ) + αf log(αf )︸ ︷︷ ︸

≡α̃

+ log(yi,j − cfP fj )− αf log(P fj )

(B.29)

We write

Vi,j = α̃+ log(yi,j − cfP fj )− αf log(P fj ) (B.30)

Effect of Increasing Food Prices

The derivative of the indirect function with respect to the food prices is given by

∂Vi,j
∂P fj

=
−cf

yi,j − cfP fj
− αf

1

P fj

=
−cf

yi,j − cfP fj

P fj

P fj
− αf

1

P fj

= − 1

P fj

(
cfP fj

yi,j − cfP fj
+ αf

)

= − 1

P fj

(
ψfi,jyi,j

yi,j − ψfi,jyi,j
+ αf

)

= − 1

P fj

(
ψfi,j

1− ψfi,j
+ αf

)

= − 1

P fj

(
αf + ψfi,j(1− αf )

1− ψfi,j

)

This derivative is more negative: increasing food prices decreases the indirect utility ceteris

paribus. This derivative also gets more negative as ψfi,j increases.

Exact Income Compensation

Suppose that the price of food change proportionally by a factor g:

P f ′j = P fj (1 + g) (B.31)

184



The goal of this section is to derive by which factor income ei,j needs to change to achieve

the same level of utility, at the initial prices. That is, ei,j that solves the following equation:

V (yi,j(1 + ei,j), P
f
j ) = V (yi,j , P

f
j (1 + g)) (B.32)

The equality requires

log(yi,j(1+ei,j)− cfP fj )−α
f log(P fj ) = log(yi,j− cfP fj (1+g))−α

f log(P fj (1+g)) (B.33)

Now, using the fact that

cfP fj = ψfi,jyi,j (B.34)

and that

cfP f ′j = cfP fj (1 + g) (B.35)

= ψfi,jyi,j(1 + g) (B.36)

we have that

log(yi,j(1+ei,j)−ψfi,jyi,j)−α
f log(P fj ) = log(yi,j−ψfi,jyi,j(1+g))−α

f log(P fj (1+g)) (B.37)

implying

(yi,j(1 + ei,j)− ψfi,jyi,j) = (yi,j − ψfi,jyi,j(1 + g))(1 + g)−α
f

(B.38)

or

(1 + ei,j)− ψfi,j = (1− ψfi,j(1 + g))(1 + g)−α
f

(B.39)

or

ei,j = ψfi,j + (1− ψfi,j(1 + g))(1 + g)−α
f − 1 (B.40)

or

ei,j = ψfi,j + ((1 + g)−α
f − 1)− ψfi,j(1 + g)1−α

f
(B.41)

so let us write

Ei,j(ψfi,j , g) ≡ ei,j = ψfi,j + ((1 + g)−α
f − 1)− ψfi,j(1 + g)1−α

f
(B.42)

Some properties of this function Ei,j are

[label=)]Ei,j(ψfi,j , 0) = 0 Decreasing in g Decreasing in ψfi,j if g > 0, and increasing in

ψfi,j if g < 0 Convex in g

185



Property (a) follows by construction.

For Property (b), observe that

∂Ei,j
∂g

= −αf (1 + g)−α−1 − ψfi,j(1− α)(1 + g)−α
f
< 0 (B.43)

Property (a) + (b) imply that households would be willing to pay not to face higher

prices. This is rather mechanical: the indirect utility is increasing in income and decreasing

in prices.

For property (c), observe that

∂Ei,j
∂ψfi,j

= 1− (1 + g)1−α
f

(B.44)

When g = 0, this derivative evaluates as 0. Now, using the fact that

∂Ei,j
∂g

∂Ei,j
∂ψfi,j

= −(1− αf )(1 + g)−α
f
< 0 (B.45)

we see that Ei,j is increasing in ψfi,j if g is negative and decreasing in g if positive.

Finally, for property (d), observe that the second derivative of Ei,j with respect to g is

positive:
∂2Ei,j
∂g2

= αf (1− αf )(1 + g)−α−1
[
(1 + g)−1 + ψfi,j

]
> 0 (B.46)

Exact Growth Rate in Food Prices

Owing to the Cobb-Douglas structure of the composite for the two goods, the price of

the food basket is given by

P fℓ =

(
P cℓ
αc

)αc (
P qℓ
αq

)αq

(B.47)

Let g be the (net) growth rate of price of food, gc and gq their analogue for the LTC and

the HTC. Hence, the final price is given by

P fℓ (1 + g) =

(
P cℓ (1 + gc)

αc

)αc (
P qℓ (1 + gq)

αq

)αq

(B.48)

or

P fℓ (1 + g) =

(
P cℓ
αc

)αc

(1 + gc)α
c

(
P qℓ
αq

)αq

(1 + gq)α
q

(B.49)

186



or

(1 + g) = (1 + gc)α
c
(1 + gq)α

q
(B.50)

Using a log approximation, the growth rate g can be written as a weighted average of the

changes gc and gq

g ≈ αcgc + αqgq (B.51)

The approximation is good with the growth rates (gc, gq) are small, but performance de-

teriorates for large changes - positive or negative. In our results, the changes in prices are

large. The underlying reason is that the changes in potential productivity, captured by µxℓ

are substantial.

187


	Acknowledgements
	Dedication
	Abstract
	List of Tables
	List of Figures
	Critical Review of the Literature
	Introduction
	Productivity Changes and Distributional Effects
	Migration
	Trade Frictions and Price Pass-Through
	Conclusion

	Climate Change and International Migration
	Introduction
	High Heat and Migration
	Data
	Reduced-Form Estimates

	A Model of Migration and High-Heat Shocks
	Model Setup
	The Migration Problem
	The Importance of Monetary Migration Costs

	Model Solution and Estimation
	Externally Calibrated Parameters
	Link between High-Heat Shocks and Rural Productivity
	Simulated Method of Moments
	Migration and Savings Decisions
	Climate Change Projections

	The Effects of Climate Change
	Main Results
	The Role of Anticipation

	Unconditional Cash Transfers and Migration
	Universal Cash Transfer
	Cash Transfer Conditional on Bad Weather
	Comparing the Transfer Schemes

	Conclusion

	Climate Change, Food Prices, and Inequality
	Introduction
	Model
	The Trade Block

	Equivalent Variation
	Climate change through the lens of the Model

	Recovering the Trade Frictions
	From Heat Shocks to Prices Changes
	Weather Data
	Consumer Price Index Data
	Structure for the Trade Shares

	Preferences and Model Fit
	Utility Function
	Calibrating the Parameters

	Counterfactuals
	Climate Change
	Climate Change Scenarios
	Improving the Roads

	Discussion and Potential Extensions
	Conclusion

	References
	 Appendix A.  Appendix to Chapter 2
	Reduced-form Estimations
	Exposure and Migration Rates
	Link Between Weather and Rural Transitory Shocks

	Other Specification Results
	A model with non-monetary migration costs
	Computational Details

	Estimation of 
	Main Estimation
	Alternative Estimation

	Simulated Method of Moments
	Computing the Stationary Distribution
	Procedure
	Implementation
	Dealing with the Stochastic e
	Sampling from the stationary Distribution

	Climate Change Transitions
	Data
	Model

	Additional Results
	Stock of Migrants
	Stationary Distributions
	Probability of Receiving the Transfer
	Alternative Cash-Transfers Amounts for same UCT schemes

	Interpretation of 
	Identification of Estimated Parameters

	 Appendix B.  Appendix to Chapter 3
	Data
	Exposure Data
	Crop Production Data
	CPI Data — Additional Details
	Brazilian Central Bank Classification for Goods and Services
	Matching Crops from IBGE and GAEZ
	Construction of x and Tx
	Construction of the Relative Wages
	Counterfactual Measures of x

	Model: Derivations
	Ideal Price Index
	Prices
	Trade Flows
	Indirect Utility