ABSTRACT

Title of Dissertation: ESSAYS ON PRODUCTION NETWORKS
AND INTERNATIONAL MACROECONOMICS

Alvaro Nicolas Silva Uribe
Doctor of Philosophy, 2024

Dissertation Directed by: Professor Şebnem Kalemli-Özcan
Department of Economics

This dissertation includes three chapters on the role of production networks in (interna-

tional) macroeconomics.

In the first chapter, “Inflation in Disaggregated Small Open Economies,” I study the conse-

quences of these production networks for our understanding of inflation in small open economies.

I show that the production network alters the elasticity of the consumer price index (CPI) to

changes in sectoral technology, factor prices, and import prices. Sectors can import and export

directly but also indirectly through domestic intermediate input-output linkages. Indirect export-

ing dampens the inflationary pressure from domestic forces, such as adverse sectoral technology

shocks and increases in factor prices. In contrast, indirect importing increases the inflation sen-

sitivity to import price changes. Computing these CPI elasticities requires knowledge of the

production network structure as these do not coincide with typical sufficient statistics used in

the literature, such as sectoral sales-to-GDP ratios (Domar weights), factor shares, or imported

consumption shares. Using input-output tables, I provide empirical evidence that adjusting CPI



elasticities for indirect exports and imports matters quantitatively for small open economies. I

then use the model to illustrate the importance of production networks during the recent COVID-

19 inflation in Chile and the United Kingdom.

In Chapter 2, “Business Cycle Asymmetry and Input-Output Structure: The Role of Firm-to-

Firm Networks” co-authored with Jorge Miranda-Pinto and Eric R. Young, we study the network

origins of business cycle asymmetries using cross-country and administrative firm-level data. At

the country level, we document that countries with a larger number of non-zero intersectoral

linkages (denser networks) display a more negatively skewed cyclical component of output. At

the firm level, firms with more suppliers and customers display a more negatively skewed dis-

tribution of their output growth. To rationalize these findings, we construct a multisector model

with input-output linkages. We show that the relationship between output skewness and network

density naturally arises once we consider non-linearities in production. In an economy with low

production flexibility, denser production structures imply that relying on more inputs becomes

a risk that further amplifies the effects of negative productivity shocks. On the contrary, when

firms display high production flexibility, having more inputs to choose from becomes an oppor-

tunity to diversify the effects of negative productivity shocks. We calibrate the model using our

rich firm-to-firm network Chilean data and show that (i) more connected firms experience larger

declines in output in response to a COVID-19 shock, and (ii) the cross-sectional distribution of

output growth in the model displays a fatter left tail during downturns. The previous result is

shaped by the interplay between production complementarities and network interconnectedness

rather than by the asymmetry of the shocks. The size of the shock determines the strength of the

relationship between degrees and output decline, highlighting the importance of non-linearities

and the limitations of local approximations.



In Chapter 3, “Commodity Prices and Production Networks in Small Open Economies” co-

authored with Petre Caraiani, Jorge Miranda-Pinto, and Juan Olaya-Agudelo, we study the role of

domestic production networks in the transmission of commodity price fluctuations in small open

economies. We provide empirical evidence of strong propagation of commodity price changes

to quantities produced in domestic sectors that supply intermediate inputs to commodity sectors

(upstream propagation) and muted propagation to sectors using commodities as intermediate

inputs (downstream propagation). We develop a small open economy production network model

to explain these transmission patterns. We show that the domestic production network is crucial

for shaping the propagation of commodity prices. The two key mechanisms that rationalize the

evidence are (i) the foreign demand channel and (ii) the input-output substitution channel. These

two channels amplify the upstream propagation of commodity price changes by increasing the

demand for non-commodity inputs, and, at the same time, they mitigate the downstream cost

channel by allowing firms to use relatively cheaper primary inputs in production.



ESSAYS ON PRODUCTION NETWORKS AND INTERNATIONAL
MACROECONOMICS

by

Alvaro Nicolas Silva Uribe

Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Doctor of Philosophy

2024

Advisory Committee:
Professor Şebnem Kalemli-Özcan, Chair
Professor Pierre de Leo
Professor Thomas Drechsel
Ph.D. Julian di Giovanni
Professor Liu Yang



© Copyright by
Alvaro Nicolas Silva Uribe

2024



Dedication

A Luna y mi familia.

ii



Acknowledgments

We always want to write this kind of text because it means we are closing a stage in our

lives. To me, the motivation is the opposite: I would like to thank many people for helping me

open this new door. Let me get to it.

I want to thank my advisor Şebnem for her invaluable guidance, support, and encourage-

ment. You always had the right word and the right thought, even if it took me months and

sometimes years to realize. This paragraph lets you know that you were instrumental and essen-

tial to my development as a researcher, for which I will forever be in debt. You did the right push

at the right moment, moving me away from my fears and low self-esteem to work on the things I

always liked but did not dare to pursue out of cowardice. Without your guidance, I do not know

what kind of thesis I would have written. Your support was not only academic but also emotional.

Thanks for always being there as a pillar, which, from time to time, got me out of the emotional

holes that research led us to. As you know, I am a man of few words, and this is an attempt

to express my sincere gratitude towards you as an advisor, researcher, and, most importantly, a

human being. Please, keep doing what you do.

I would also like to thank my dissertation committee members. Pierre, for the countless

discussions, comments, and chats about research and life in general. Thanks for constantly push-

ing me to go deeply into intuition and empirical facts. All these greatly contributed to this thesis.

I know I am stubborn, but you made me a little less so. Ultimately, as we joke about it, it is

iii



a matter of personality, but thanks for always being there when I needed it. To Thomas, thank

you for your sharp comments and suggestions, which greatly improved this thesis. I took the

first class you ever taught at Maryland, and together with Seho, we are the first students you

foresee all the way through. I hope we fulfill your expectations. To Julian, whom I met later in

the process thanks to Şebnem, your sharpness and insistence on understanding all the fine details

made me a better researcher. As I told you once, part of my inspiration to become a researcher

started when I read your papers. Getting to know you and working with you later as a co-author

is one of the beautiful things about the profession: one day, you read their papers; the next, you

put a face to that piece of paper and, if you are lucky, the next day you are working with them. I

would also like to thank Prof. Liu Yang for kindly agreeing to serve on my committee as a Dean’s

representative.

I want to express my gratitude to many people. Unfortunately, writing all them down would

require a book. If you are not listed here, please do not take it personally.

Rodrigo Cerda, Felipe Saffie, and Sergio Urzúa deserve a special thank from my part. You

guys trusted me from the beginning of my career until today. These “tiny” pushes really made a

difference in the grand scheme of things. I hope I fulfilled some of your expectations of me. If

not, rest assured that I am doing my best.

To my coauthors, from whom I have learned along the way. Special thanks go to Jorge

Miranda-Pinto for always having my back since my third year and constantly helping me get out

of the research holes with Marcelo Bielsa’s quotes; it is hard not to be motivated by those. I

have learned a lot from you, and I hope to continue doing so. To Muhammed Yıldırım for our

countless discussions about research and life in general. Let us keep those rolling.

To my friends in College Park, especially Cata and Titi, thanks for always being there for

iv



me, especially our family with Luna. To my classmates Seho Kim and Michael Navarrete, thanks

for all the support over the years, especially during the challenging market. To Gonzalo Garcı́a

and Rodrigo Heresi for their support over all these years and patience with my dumb questions.

To the Shannon community, thank you for all those friendly times that allowed us to escape from

academic life and remember that working is not what life is all about.

I thank my mother, Rosa, for always listening to me. You are one of a kind and have been

my role model all along. I am proud of being your son, and I hope you are as well. To my brother,

Marco, for our good laughs when we are together. Those bring life back to me. To those who are

no longer with me: my father Bernardino, my grandmother Maria, my father-in-law Jorge, and

my grandfather-in-law Felix. I hope that wherever you are, you are proud. Many other milestones

are to come, so do not celebrate too effusively.

Finally, to the most important person in my life, my wife Luna. I am a better researcher

because you are there with me. I am a better person because you are there with me. But above

all, I am complete when you are there with me. Thanks for always being there in the good and

the bad, always smiling, supporting me, always scolding me when I did something wrong, and

being happy when I did something right. This is one of the good, and it is, of course, because and

for you. I finally understood that life is life because I got to share it with you; how lucky I am! I

love you.

v



Table of Contents

Preface ii

Dedication ii

Acknowledgements iii

Table of Contents vi

List of Tables ix

List of Figures x

Chapter 1: Inflation in Disaggregated Small Open Economies 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 A Small Open Economy Model with Production Networks . . . . . . . . . . . . 10

1.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.2 Sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.4 Characterizing Changes in the Price Index . . . . . . . . . . . . . . . . . 15
1.2.5 An alternative representation of factor markets: from factor prices to fac-

tor supplies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3 The empirical relevance of adjustments of CPI elasticity . . . . . . . . . . . . . . 25

1.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.4 The evolution of inflation in Chile and United Kingdom during COVID-19 . . . . 34
1.4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.4.2 Mapping the model to the data . . . . . . . . . . . . . . . . . . . . . . . 38
1.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Chapter 2: Business Cycle Asymmetry and Input-Output Structure: The Role of
Firm-to-Firm Networks 46

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2 Cross-country evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3 Firm-level evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.3.1 Data Description and Sample construction . . . . . . . . . . . . . . . . . 56
2.3.2 Firm-level networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

vi



2.3.3 Firm-level output asymmetry and networks . . . . . . . . . . . . . . . . 62
2.3.4 Firm-level resilience and networks during downturns . . . . . . . . . . . 64

2.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4.1 Representative Consumer . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.2 Producers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.4.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.4.4 Useful Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.4.5 Aggregate Impact of Sectoral Technology Shocks . . . . . . . . . . . . . 73

2.5 Quantitative Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5.1 Intersectoral linkages and skewness across countries . . . . . . . . . . . 79
2.5.2 Firm-to-firm network in Chile . . . . . . . . . . . . . . . . . . . . . . . 80

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Chapter 3: Commodity Prices and Production Networks in Small Open Economies 86
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.2 Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3 Commodity prices via production networks . . . . . . . . . . . . . . . . . . . . 97

3.3.1 Measuring Network Spillovers . . . . . . . . . . . . . . . . . . . . . . . 98
3.3.2 Network propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.4.1 Representative Consumer. . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.4.2 Non-Tradable Sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.4.3 Commodity Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.4.4 Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.4.5 Comparative Statics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

3.5 Quantitative exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.5.1 The Case of Non-Unitary Elasticities in Production . . . . . . . . . . . . 118
3.5.2 A Calibrated Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Appendix A: Appendix to Chapter 1 125
A.1 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A.1.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.1.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.1.3 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

A.2 Two period model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.2.1 Solving for consumption at time 0. . . . . . . . . . . . . . . . . . . . . . 131
A.2.2 Mapping the net transfer, T . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.3 A Small Open Economy Dynamic Model with Production Networks . . . . . . . 135
A.3.1 Calibration and Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

A.4 Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.4.1 Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
A.4.2 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.4.3 Market clearing conditions and substitution patterns . . . . . . . . . . . . 149

vii



A.4.4 Putting all equations together . . . . . . . . . . . . . . . . . . . . . . . . 153

Appendix B: Appendix to Chapter 2 154
B.1 Cross-Country Evidence: Real GDP Detrending . . . . . . . . . . . . . . . . . . 154
B.2 Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Appendix C: Appendix to Chapter 3 159
C.1 Data Sources and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
C.2 Additional Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

C.2.1 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
C.2.2 Extra Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

C.3 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
C.4 Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

C.4.1 Non-Tradable Producers . . . . . . . . . . . . . . . . . . . . . . . . . . 176
C.4.2 Commodity Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
C.4.3 Allen-Uzawa Elasticities of Substitution . . . . . . . . . . . . . . . . . . 178

Bibliography 181

viii



List of Tables

1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Average Inflation, 2020 – 2022. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.1 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Size and Interconnectedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3 Sales Growth Skewness and Network Degrees . . . . . . . . . . . . . . . . . . . 65
2.4 Employment Growth Skewness and Network Degrees . . . . . . . . . . . . . . 66

3.1 Ranking of Network Centrality of Commodity Sectors in 1995 . . . . . . . . . . 95
3.2 Average Pairwise Correlation across Commodity Prices . . . . . . . . . . . . . . 96
3.3 Network Effects of Commodity Price Changes on Non-Commodity Sectors . . . 102

A.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

B.1 Cross-Country Relationship between Real GDP Cyclical Component Skewness
and Network Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

B.2 Annual labor productivity growth . . . . . . . . . . . . . . . . . . . . . . . . . . 158

C.1 Sectors in WIOD Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
C.2 Commodities and WIOD Industries. . . . . . . . . . . . . . . . . . . . . . . . . 163
C.3 Calibration Exercises: The Role of Upstreamness . . . . . . . . . . . . . . . . . 164
C.4 Calibration Exercises: The Role of Downstreamness . . . . . . . . . . . . . . . . 164
C.5 Network Effects of Commodity Price Changes on Non-Commodity Sectors With-

out Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

ix



List of Figures

1.1 CPI Inflation in Small Open Economies. . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Export and Network-Export adjusted Domar weights. . . . . . . . . . . . . . . . 28
1.3 Three sectors with largest adjustments: United Kingdom. . . . . . . . . . . . . . 29
1.4 Country and sector fixed effects: export-network adjusted - export adjusted. . . . 31
1.5 Labor share adjustments for different countries. . . . . . . . . . . . . . . . . . . 34
1.6 Country and sector fixed effects: export-network adjusted sector-specific factor

shares - export adjusted sector-specific factor shares. . . . . . . . . . . . . . . . 35
1.7 Direct and Network-Adjusted import consumption shares. . . . . . . . . . . . . . 36
1.8 Chile Inflation under different models. . . . . . . . . . . . . . . . . . . . . . . . 42
1.9 United Kingdom Inflation under different models. . . . . . . . . . . . . . . . . . 43

2.1 Skewness of Cyclical Component of Real GDP (1985 – 2019) . . . . . . . . . . 47
2.2 Input-Output Structure: Chile in 1995 . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 Cross-Country Production Network Density and Skewness . . . . . . . . . . . . 55
2.4 Chilean Firm-to-Firm Network: Random Sample of 2000 firms . . . . . . . . . . 58
2.5 Network degrees distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Output asymmetry and firm level networks . . . . . . . . . . . . . . . . . . . . . 63
2.7 Output growth distribution recessions and expansions . . . . . . . . . . . . . . . 67
2.8 Output growth distribution during COVID-19 . . . . . . . . . . . . . . . . . . . 67
2.9 Coefficient of regressing output growth against log degrees . . . . . . . . . . . . 69
2.10 Aggregate Output Response to a Technology Shock in Sector 2 . . . . . . . . . . 76
2.11 Changes in Domar Weight of Sector 2 after a positive technology shock . . . . . 77
2.12 Simulated Skewness as a Function of the Elasticity . . . . . . . . . . . . . . . . 78
2.13 Skewness of real GDP (model) . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.14 Model Implied Relationship Production Network Density and Skewness . . . . . 81
2.15 Model implied distribution of output growth distribution . . . . . . . . . . . . . 83
2.16 Coefficient of regressing output growth against log degrees . . . . . . . . . . . . 84

3.1 Domestic Production Network Australia . . . . . . . . . . . . . . . . . . . . . . 94
3.2 Upstream and Downstream Propagation . . . . . . . . . . . . . . . . . . . . . . 100
3.3 Sectoral Propagation of a Mining Price Shock: The Role of Elasticities . . . . . . 121
3.4 Sectoral Propagation of a Mining Price Shock: the Role of the Export Share . . . 122

A.1 Inflation Impulse Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

x



B.1 Chilean Real GDP Cyclical Components under different detrending procedures . 155
B.2 Cross-Country Skewness of Real GDP Cyclical Components . . . . . . . . . . . 156

C.1 Commodity Price Changes: Agriculture and Forestry . . . . . . . . . . . . . . . 165
C.2 Commodity Price Changes: Mining and Quarrying . . . . . . . . . . . . . . . . 166
C.3 Commodity Price Changes: Food Products and Beverages . . . . . . . . . . . . . 166

xi



Chapter 1: Inflation in Disaggregated Small Open Economies

1.1 Introduction

In 2022, inflation reached 8 percent in the United States, its highest level in 40 years.

The picture was similar on the other side of the Atlantic: Euro Area inflation was 8.4 percent,

the highest since its creation. Explanations include shocks to commodity prices (Blanchard and

Bernanke, 2023; Gagliardone and Gertler, 2023), sectoral demand changes (Ferrante et al., 2022),

fiscal stimulus (Bianchi et al., 2023; di Giovanni et al., 2023b), and supply chain disruptions

(di Giovanni et al., 2022, 2023a; Comin et al., 2023). As shown in Figure 1.1, high inflation was

not restricted to these two economies: the median small open economy experienced an inflation

rate of around 10 percent in 2022. However, inflation in this group of countries has been less

studied during the current episode. This paper attempts to fill this gap using both theory and data.

My starting point is the multi-sector and multi-factor production network closed economy

model in Baqaee and Farhi (2019b). It provides a useful benchmark to analyze inflation during

macroeconomic shocks such as COVID-19, a combination of sectoral and aggregate shocks.

Given my focus on small open economies, I augment this model to feature imports and exports at

the sectoral level, adapting the production network model to the small open economy case. I use

the model to study how the consumer price index (CPI) reacts to changes in sectoral technology,

factor prices, and import prices, going from the micro to the macro level.

1



I show that openness and production networks affect our understanding of inflation in small

open economies via two distinct channels. On the one hand, exporting, either directly or indi-

rectly through other economic producers, dampens the effect of sectoral technology shocks and

factor price changes relative to a closed economy. On the other hand, direct importing gives rise

to the problem of imported inflation as the domestic consumer’s basket now contains imported

goods. On top of this channel, production networks imply that domestic goods are manufactured

using imported inputs indirectly. As a result, production networks amplify imported inflation.1

Uncovering these effects and quantifying their importance is only possible when both openness

and network linkages are explicitly considered.

The key economic intuition is that opening up the economy is one of the ways to break the

link between what the country produces and what is consumed by domestic consumers. In an

efficient closed economy — an economy without distortions — with intersectoral linkages and

domestic final consumption only, everything produced is consumed by the domestic consumer.

Network-adjusted domestic consumption, by which I mean domestic consumption adjusted by

domestic production network linkages, is thus equivalent to sales in the closed economy.2 That

domestic households consume everything produced, directly or indirectly, is one of the key build-

ing blocks of why the production network structure is irrelevant to first-order for macroeconomic

outcomes such as real GDP or welfare in closed economies. This irrelevance result is a useful

benchmark. It allows us to use the ratios of sectoral sales to nominal GDP (the so-called “Do-
1This channel is distinct from inflation resulting from imported intermediate goods, as models can have inter-

mediate goods without intersectoral linkages. See Svensson (2000) for an early analysis of imported inflation via

intermediate goods.
2This definition is deliberately reminiscent of the network-adjusted labor share introduced in Baqaee (2015).

2



Figure 1.1: CPI Inflation in Small Open Economies.

-2.5

0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0
Ye

ar
-o

n-
Ye

ar
 In

fla
tio

n,
 %

20
05

m1

20
07

m1

20
09

m1

20
11

m1

20
13

m1

20
15

m1

20
17

m1

20
19

m1

20
21

m1

20
22

m12

Median
Percentile 10/90

Note: The figure shows the median inflation rate (solid lines) and 10th and 90th percentile (dashed lines). Small

open economies are economies that represent less than 5 percent of world GDP and have a trade openness larger than

30 percent of GDP. See section 1.3.1 for more details. Plot shows an unbalanced panel of 46 small open economies

over time. Source: Bank for International Settlements.

mar weights”) and factor payments to nominal GDP (factor shares) as sufficient statistics for the

pass-through of sectoral technology changes or factor price changes to the CPI, respectively.3

Increases in sectoral technology decrease consumer inflation by the Domar weight of the sector,

while increases in factor prices increase inflation by the factor share.

I show that this irrelevance result no longer holds for consumer inflation in small open

economies, without the need for second-order approximations, as in Baqaee and Farhi (2019b),

3As I show in the theory section, this can be thought of as a corollary of Hulten’s theorem (Hulten, 1978a) but

for the CPI rather than for real GDP. Recall that for real GDP, Hulten’s theorem states that in an efficient closed

economy with inelastic factor supplies, the first-order effect of sectoral technology on real GDP is given by the

Domar weights, and the first-order effect of changes in factor supply is given by its factor share.

3



or distortions, as in Baqaee and Farhi (2020) and Bigio and La’o (2020a).4 The reason is as

follows. Consider first the impact of sectoral technology shocks on the CPI. In a small open

economy, there are two final uses for goods produced within borders: domestic consumption or

exports. Unlike the closed economy case, sectoral sales do not map to the network-adjusted do-

mestic consumption for two reasons: (i) direct exports and (ii) indirect exports through domestic

production network linkages. Instead, sectoral sales map to network-adjusted domestic consump-

tion plus network-adjusted exports. Since what matters for the CPI is network-adjusted domestic

consumption, one must subtract network-adjusted exports from sectoral sales. Hence, relative

to a closed economy, a consumer is weakly less exposed to changes in sectoral technology. Im-

portantly, we require knowledge of the domestic production network structure to compute these

network-adjusted domestic consumption measures.

A similar intuition holds for how factor price changes affect CPI. The relevant statistic here

is the network-adjusted domestic factor share: how much of each factor is embedded in goods

consumed domestically after considering domestic production network linkages (in the spirit of

the domestic factor demand concept in Adao et al. (2022)). The total amount of a factor available

in the economy can be “consumed” by domestic or foreign consumers,5 with the production

network potentially reshaping these patterns. While factor shares are sufficient statistics in the

closed economy, in the small open economy with production networks we need to subtract from

4Strictly speaking, those papers I cited sought ways to break Hulten’s theorem in closed economies, which refer

to quantities meaning the effect of sectoral technology changes or distortions on real GDP. However, since, as a

corollary of Hulten’s theorem, we can back out changes in CPI, I referenced them here.
5Here, consumers do not directly consume factors but goods. Given that goods are ultimately made of factors of

production, we can think of consumers implicitly consuming them. This notion can be found in the reduced factor

demand system proposed by Adao et al. (2017).

4



factor shares the fraction of each factor that is exported either directly or indirectly via production

networks. This means that relative to a closed economy, the domestic consumer is weakly less

exposed to changes in factor prices.

The effect of import prices on the CPI, on the other hand, is amplified in a small open econ-

omy with production networks relative to a small open economy without production networks.

The relevant statistics here are network-adjusted import consumption shares. Since the domestic

consumer directly imports, the direct consumption share captures part of the exposure to im-

port price changes. However, if there are intersectoral linkages across producers, domestic good

producers may end up importing intermediate inputs either directly, by buying from abroad, or

indirectly, by buying from domestic sectors that buy from abroad or that buy from sectors that buy

from abroad, and so on. This means that the imported content of domestically produced goods in-

creases in the presence of production networks. To the extent that domestic goods increase their

reliance on imported intermediate goods, so does the domestic consumer. Thus, the domestic

consumer’s exposure to import prices must account for both direct and indirect exposure, which

are encapsulated in the network-adjusted import consumption shares.

Guided by the model, I turn to the data to measure the importance of these production

network adjustments. I find that these adjustments matter quantitatively using data from the

World Input-Output Tables. I illustrate these adjustments by focusing on the three sources of

variation I have considered so far: sectoral technology, factor prices, and import prices.

First, consider the electricity sector in the United Kingdom (UK). The Domar weight of

this sector is around 5.95 percent. Once we consider direct exports (but not indirect exports), the

relevant ratio for the pass-through to CPI decreases to 5.90 percent, a negligible change. This

is expected, as the UK electricity sector hardly exports directly to other countries. Yet, when

5



considering indirect exporting, the network-adjusted domestic consumption share decreases to

4.4 percent, a 25 percent decrease relative to the Domar weight benchmark. This is because

other export-heavy sectors in the UK use electricity as a production input either directly or in-

directly. Thus, Domar weights would overestimate the impact of a change in productivity in the

UK electricity sector on the domestic CPI.

Second, consider the role of wage changes in the CPI. In a closed economy, the labor

share is the relevant statistic for how wage changes pass through to the CPI. In the data, the

labor share for the average small open economy is around 57 percent. However, the small open

economy model with production networks suggests that we need to subtract from the labor share

the portion that is exported directly or indirectly. After accounting for network-adjusted exports,

this average labor share decreases to 39 percent. This means that the same increase in domestic

wages has a 32 percent lower impact on inflation in a small open economy relative to a closed

economy.

Finally, let me consider the role of import prices. In the data, the average small open

economy exhibits a direct import consumption share of around 17 percent of its total expenditure.

Yet, on average, the network-adjusted import consumption share is 30 percent. This implies that

the impact of import prices on domestic inflation is (almost) twice what would be implied by a

measure ignoring indirect linkages.

In the last section of the paper, I use the model to analyze the recent inflation in two small

open economies: Chile and the United Kingdom. I chose these two countries as (i) they fit into

the small open economy definition, (ii) they have experienced high inflation in recent years, and

(iii) they allow me to compute and contrast between emerging and developed markets. Using

these countries, I show that network adjustment on exports and imports provides a quantitative

6



improvement in matching data moments over both closed economy models and small open econ-

omy models without production networks.

Between 2020 and 2022, the average annual inflation rate in Chile was 6.13 percent, with

a standard deviation of 3.89. A quantitative closed economy model with production networks

implies an average inflation rate of 0.98 percent with a standard deviation 9.69. A small open

economy model without production networks delivers an average inflation rate of 1.45 percent

with a standard deviation 6.88. Finally, the small open economy model with production networks

delivers an average inflation rate of 2.41 with a standard deviation 6.67. Overall, the small open

economy with production networks better matches the mean and the standard deviation.

For the United Kingdom, average inflation rate was 3.69 percent over the same period, with

a standard deviation of 3.11. The closed economy model with production networks implies an

average inflation rate of 2.27 percent with a standard deviation 2.57. The small open economy

model without network adjustments exhibits an average inflation rate of 2.72 percent with a

standard deviation of 2.64. The small open economy model with production networks shows an

average inflation rate of 3.21 percent with a standard deviation 3.00. As in the Chilean case, the

production network coupled with openness helps to get closer to the date moments of United

Kingdom inflation.

The measurement and application sections illustrate that the required network adjustments

in a small open economy matter for our understanding of inflation not only as a theoretical cu-

riosity but also in practice.

Related Literature. This paper relates to several strands of the literature. The first one studies

inflation in closed economies with production networks (Basu, 1995; La’o and Tahbaz-Salehi,

7



2022; Guerrieri et al., 2022; Baqaee and Farhi, 2022b; Luo and Villar, 2023; Afrouzi and Bhat-

tarai, 2022; Ferrante et al., 2022; Rubbo, 2023; Minton and Wheaton, 2023; di Giovanni et al.,

2023a,b; Lorenzoni and Werning, 2023).6 These studies consistently find that the interaction be-

tween sectoral price/wage rigidities and production networks is key to understanding the behavior

of inflation, which has implications for the conduct of monetary policy, such as what inflation rate

to target. This paper focuses on how introducing production networks in a small open economy

model helps us to understand the pass-through of different shocks to inflation. Although there is

no price rigidity in the model, and thus I cannot speak about the optimal conduct of monetary

policy, I contribute to this literature by showing that the production network can have a first-

order impact on inflation beyond its role in the sales share distribution without the need for any

distortions.

Second, this paper relates to the literature on inflation in small open economies. In the sec-

ond part of the 20th century, Latin America experienced episodes of high and persistent inflation,

a term later coined as “chronic inflation”. In response, there was extensive literature during the

1990s on how to best control chronic inflation and the impact of different nominal and real policy

rules in small open economies (see Calvo and Végh, 1995; Calvo et al., 1995; Calvo and Végh,

1999, and especially the last one, for an overview of this earlier literature). Modern treatments

that introduce New Keynesian features such as sticky prices and monopolistic competition into

small open economy models include Gali and Monacelli (2005) and Faia and Monacelli (2008)7.

6There is also extensive literature on multisector models with sticky prices that do not necessarily feature a

production network structure, so I omit them from the main text. For earlier contributions, see Woodford (2003) and

the references therein.
7There is also a large literature focusing on two or more countries. My work is not directly related to these models

as I focus on small open economies. I refer the interested reader to Corsetti and Pesenti (2007) and Corsetti et al.

8



These models have been augmented to include intersectoral linkages and applied to understand

the recent inflationary episode, focusing on the United States (Comin and Johnson, 2020; Comin

et al., 2023). Relative to this literature, I explicitly analyze the role of production networks on

inflation for small open economies. I show how the production network interacts with trade,

affecting how domestic and foreign shocks ultimately affect CPI inflation both theoretically and

quantitatively. Moreover, the fact that I use a first-order approximation allows me to consider

unrestricted intersectoral linkages, in the sense of not needing to assume any functional forms for

production or utility. Finally, the model also features multiple factors of production, while the

previous models typically focus on only one factor (labor).

Finally, in focusing on the role of network-adjusted exports and imports, this paper con-

tributes to the literature on indirect trade (Huneeus, 2018; Adao et al., 2022; Dhyne et al., 2021,

2023; Muñoz, 2023). This literature focuses on the firm-level consequences of indirect trade,

which is equivalent to my trade network-adjustments. For example, Dhyne et al. (2021) use

Belgian firm-to-firm level transaction data and find that the relevant concept for a firm sales’

exposure to international markets is total exports (network-adjusted exports), while its exposure

in costs is total imports (network-adjusted import share). My contribution to this literature is to

embed indirect trade into a small open economy model to analyze how it matters for aggregate

inflation.

(2010) for an overview of such models. Recent literature focusing on inflation using multi-country and multi-sector

models include, for example, Auer et al. (2019) and Ho et al. (2022) during non-Covid-19 times and di Giovanni

et al. (2022) and Andrade et al. (2023) during COVID-19.

9



Outline. The rest of this paper is structured as follows. Section 1.2 describes the model I use to

understand inflation in small open economies. Section 1.3 measures the importance of production

networks and trade for inflation comparing across sectors and countries. Section 1.4 applies the

model to Chile and the United Kingdom. Finally, Section 1.5 concludes.

1.2 A Small Open Economy Model with Production Networks

Environment. There is a set of domestically produced goods that I denote by N with

typical element i. These goods can be consumed domestically, used as intermediate inputs by

other domestic sectors, and exported. I denote the imported goods set byM , with typical element

m. These imported goods can be used as intermediate inputs to produce domestic goods or as

final consumption. Finally, there is a set F of factors with typical element f .

Notation. I denote matrices and vectors using bold i.e., Y . I denote the transpose of a matrix

as Y T . Unless otherwise noted, vectors are always column vectors. For example, the vector of

Domar weights, defined below, is λ = (λ1, λ2, ..., λN)
T . Log changes are expressed as d log Y =

Ŷ .

Table 1.1 shows the different shares and matrices that are key for the analysis. I use a bar

over a variable for shares based on total expenditure, while GDP-based measures do not contain

a bar.

1.2.1 Households

There is a representative household that consumes domestically produced goods and for-

eign goods. It has an instantaneous utility function that I denote by U(CD,CM), where CD =

10



Table 1.1: Definitions

Name Notation Expression Goods/Factors

GDP-based

Domar Weight λi
PiQi

GDP
for i ∈ N

Consumption Share bi
PiCi

GDP
for i ∈ N

Imported Consumption Share bm
PmCm

GDP
for m ∈M

Export Share xi
PiXi

GDP
for i ∈ N

Factor Shares Λ Λf =
WfLf

GDP
for f ∈ F

Expenditure-based

Domar Weight λ̄i
PiQi

E
for i ∈ N

Consumption Share b̄i
PiCi

E
for i ∈ N

Imported Consumption Share b̄m
PmCm

E
for m ∈M

Export Share x̄i
PiXi

E
for i ∈ N

Factor Shares Λ̄ Λ̄f =
WfLf

E
for f ∈ F

Sector-level Shares

Input-Output Matrix Ω Ωij =
PjMij

PiQi
j ∈ N

Leontief-Inverse Matrix ΨD = (I −Ω)−1 Ψij =
∞∑
s=0

Ωs
ij i, j ∈ N

Factor Spending Matrix A aif =
WfLif

PD
i Qi

i ∈ N ; f ∈ F

Intermediate Import Spending Matrix Γ Γim = PmMim

PiQi
i ∈ N ;m ∈M

{Ci}i∈N denotes the vector of domestically-produced goods consumption and CM = {Cm}m∈M

is the vector of foreign goods consumption. These consumption vectors have associated vector

prices PD = {Pi}i∈N and PM = {Pm}m∈M . Unless otherwise stated, all prices are denomi-

11



nated in local currency. I assume the utility function U(.) is homogeneous of degree one in its

arguments. The representative consumer also owns all factors of production and supplies them

inelastically at the given factor prices.

Given a vector of prices, both domestically produced and foreign goods, the cost-minimization

problem satisfies

PC = min
CD,CM

∑
i∈N

PiCi +
∑
m∈M

PmCm subject to U(CD,CM) ≥ Ū . (1.1)

Solving this problem delivers a price index that is a function of good prices. I denote this

price index by P = P (PD,PM). As a reminder, notice that up to a first-order approximation,

changes in this price index satisfy

P̂ = b̄TDP̂D + b̄TM P̂M , (1.2)

where

b̄D = {b̄i} =
PiCi

E
; b̄M = {b̄m} =

PmCm

E
; E = P T

DCD + P T
MCM = PC,

are the expenditure share on domestically produced goods (b̄i), imported goods (b̄m), and total

expenditure (E), respectively.

The consumer budget constraint reads

PC + T =
∑
f∈F

WfLf +
∑
i∈N

Πi,

where T is an exogenous net transfer to the rest of the world as in Baqaee and Farhi (2022b).

In Appendix A.2, I provide a justification for having such a force in the current model using a

two-period model without changing the main results.

12



1.2.2 Sectors

There is a representative firm in each i sector that produces according to the following

production function

Qi = ZiF
i ({Lif}f∈F , {Mij}j∈N , {Mim}m∈M) , (1.3)

where Zi is a sector-specific productivity, Lif is demand for factor f by firm i, Mij represents

intermediate input demand for good j ∈ N by firm i, and Mim represents input demand for

imported good m ∈M . We can write cost-minimization firm i as

TCi = min
{Lif}Ff=1,{Mij}j∈N ,{Mim}m∈M

∑
f∈F

WfLif +
∑
j∈N

PjMij +
∑
m∈M

PM
m MM

im

subject to ZiF
i ({Lif}f∈F , {Mij}j∈N , {Mim}m∈M) ≥ Q̄i.

This delivers a marginal cost function that only depends on prices and technology due to

the constant returns to scale assumption. In particular,

MCi =MCi(Zi,PD,PM ,W ), (1.4)

where W = {Wf}f∈F is a vector of factor prices.

We can get conditional factor and intermediate input demand by applying Shephard’s

lemma to the optimized total cost, TCi, such that

∂MCi

∂Wf

Qi = Lif for each f ∈ F, (1.5)

∂MCi

∂Pj

Qi =Mij for each j ∈ N, (1.6)

∂MCi

∂Pm

Qi =Mim for each m ∈M. (1.7)

13



Due to constant returns to scale and perfectly competitive good and factor markets, each firm i

makes zero profit:

PiQi =
∑
f∈F

WfLif +
∑
j∈N

PjMij +
∑
m∈M

PmMim for all i ∈ N. (1.8)

1.2.3 Equilibrium

Market clearing conditions for good and factor markets satisfy

Qi = Ci +Xi +
∑
j∈N

Mji for each i ∈ N. (1.9)

Equation (1.9) is the good market clearing condition. I assume Xi is exogenous as in Adao et al.

(2022) so that a price clearing the market always exists for each domestically produced good even

if it is exported.

Since this is a real model, nominal prices are indeterminate unless I supplement one addi-

tional equation. To do so, I impose the following

PC ≤ M = E,

where M is the money supply that I take as exogenous in what follows. This is a cash-in-

advance constraint used, for example, in La’o and Tahbaz-Salehi (2022) and Afrouzi and Bhat-

tarai (2022).8 We can think of this restriction as the small open economy’s central bank effectively

pinning down total nominal expenditure (E), providing an exogenous nominal anchor. It is appar-

ent that the central bank, conditional on knowing C, which is determined by real variables, can

8It can be shown that this “constraint” is isomorphic to a model with money in the utility function that is sepa-

rable from aggregate consumption. The cash-in-advance constraint thus serves no other purpose than pinning down

nominal variables without affecting real allocations in this model.

14



implement any price level, P , that it desires consistent with C. This model features the classical

dichotomy, where real variables are determined independently of the nominal side.9 Under these

assumptions, one should interpret the results as highlighting the role of production networks for

the consumer price index, conditional on an exogenous central bank monetary policy.

Similar to Baqaee and Farhi (2019a), I define an equilibrium in this economy using a dual

approach in which feasible and equilibrium allocations are found by taking as given factor prices

W and a level of expenditure, E, as follows

1. Given sequences (W ,PD,PM ,Π) and exogenous parameters (T ), the household chooses

(CD,CM) to maximize its utility subject to its budget constraint.

2. Given (W ,PD,PM ) and production technologies, firms choose (Li,Mi) to minimize their

cost of production.

3. Given X , goods markets clears.

4. The cash-in-advance constraint holds with equality PC = M = E

1.2.4 Characterizing Changes in the Price Index

Having defined the environment, optimality, and equilibrium conditions, I can now study

changes in the consumer price index, P̂ . Inflation here consists of a log-linear approximation

around the initial price level equilibrium. The purpose of the model is to distill whether and how

the production network may matter for inflation, which in the model is a cross-sectional statement

rather than a dynamic statement. “Inflation” in this context can thus be understood in the space
9The converse is not true as real shocks can affect nominal variables. See Végh (2013) chapter 5, especially

footnote 11.

15



rather than the time dimension. This concept has been used, for example, to study inflation in

the US during the COVID-19 period (Baqaee and Farhi, 2022b; di Giovanni et al., 2022), and the

role of sticky prices in production networks (La’o and Tahbaz-Salehi, 2022; Baqaee and Rubbo,

2023).

The following result characterizes how the consumer price index reacts to changes in ex-

ogenous variables.

Proposition 1. Consider a perturbation (Ẑ, Ŵ , P̂M) around some initial equilibrium. Up to a

first order, changes in the aggregate price index, P̂ , satisfy

P̂ = −
(
λ̄T − λ̃T

)
Ẑ +

(
Λ̄T − Λ̃T

)
Ŵ + (b̄TM + b̃TM)P̂M , (1.10)

where

λ̃T = x̄TΨD; Λ̃T = x̄TΨDA; b̃TM = b̄TDΨDΓ

Proof. See Appendix A.1.1.

The above expression highlights how opening up the economy to goods trade and introduc-

ing a production network structure alter the usual prediction of closed economy models. I now

proceed with some illustrations that provide intuition for this expression.

Illustration 1: Closed economy. The following proposition characterizes CPI in a closed econ-

omy.

Proposition 2. In a closed economy, equation (1.10) reduces to

P̂ = −λT Ẑ +ΛTŴ ,

16



Proof. See Appendix A.1.2. Proposition 2 shows the exact form of changes in the CPI in a

closed economy (see Baqaee and Farhi, 2022b). Intuitively, CPI changes are a weighted average

of changes in productivity (weighted by the Domar weights, λ) and factor prices (weighted by

the factor shares, Λ).

Equation (1.10) extends this for small open economies with production networks. There are

four differences between the closed economy expression and equation (1.10). First, of course,

inflation now depends on import price changes. Second, the Domar weights and factor shares

in equation (1.10) are now based on expenditure rather than on nominal GDP. This distinction

arises in small open economies that feature trade imbalances, in which the income from domestic

production need not equal what they consume. Since what matters for the CPI is what domestic

consumers spend, nominal expenditure is the relevant object for dividing sales and factor pay-

ments.

Third, the effect of sectoral productivity changes on the CPI is dampened relative to a

closed economy or a small open economy without production networks. To see this, note that the

relevant statistic for the effect of sectoral productivity changes on the CPI is λ̄T−λ̃T , and thus the

Domar weight λ̄T is no longer the sufficient statistic for understanding how sectoral productivity

changes affect CPI. Importantly, the relevant elasticity requires adjusting the expenditure-based

Domar weight λ̄ by substracting λ̃T = x̄TΨD. This adjustment comes from the fact that what

matters is the domestic consumer’s exposure to changes in sectoral productivity.

To be precise, let me write the price index as a function of domestic and imported goods

prices, i.e., P = P(PD,PM). Suppose there is a change in the productivity of sector k, Ẑk,

with no changes in factor or import prices. This shock impacts all domestic goods prices due to

input-output linkages. Its propagation to the CPI is a tale of two elasticities. First, how exposed

17



is the consumer to changes in domestic good prices ∂ logP
∂ logPi

, for all i. By the envelope theorem,

this elasticity is simply the consumption share of the good at the initial equilibrium, b̄i. Second,

the impact depends on how productivity passes through to each domestic goods price, ∂ logPi

∂ logZk
.

This last term is simply given by −Ψik, which measures the sensitivity of the price of good i to

a change in productivity of sector k after taking into account all direct and indirect linkages via

the production network. Collecting all these pieces, we can write:

P̂ =
∑
i∈N

∂ logP
∂ logPi︸ ︷︷ ︸

=b̄i

∂ logPi

∂ logZk︸ ︷︷ ︸
=−Ψik

Ẑk = −b̄TDΨ(:, k)Ẑk,

where Ψ(:, k) is the kth column of the Leontief-inverse matrix Ψ. Note that again, the reason

why b̄TDΨ is not equivalent to the vector of sales share is precisely because this is not the relevant

exposure of the domestic consumer in the presence of input-output linkages and international

trade.

Third, the effect of factor prices on the CPI is also dampened relative to the closed economy

benchmark or a small open economy without production networks. Although the logic is similar

to that of how productivity changes pass through CPI, I analyze the factor price case in detail in

the next example, as it also allows me to relate equation (1.10) to a well-known concept in the

trade literature: the factor content of exports.

Illustration 2: Domestic factor demand and the factor content of exports. This example helps

to illustrate how the fact that exports used domestic factors lowers the sensitivity of prices to

changes in domestic factor prices. Equation (1.10) highlights a tension between domestic factor

demand and the factor content of exports, in the spirit of Adao et al. (2022). When an economy

exports, some of its factors of production end up meeting foreign demand which, everything else

18



equal, reduces domestic factor demand. These factors meet foreign demand because they are used

to produce domestic goods that are exported. As a result, factor price changes put less pressure

on the price index10. Moreover, this channel is in place whenever an economy exports to the rest

of the world, even if there is no production network. To see this, notice that factor payments to a

given factor f can be written as

WfLf =
∑
i∈N

WfLif =
∑
i∈N

aifλi. (1.11)

Without intermediate inputs, the Domar weight of each sector, λi, is simply that sector’s share in

total final demand

Qi = Ci +Xi =⇒ λi = bi + xi. (1.12)

Combining equations (1.11) and (1.12), I get

WfLf −
∑
i∈N

aifxi︸ ︷︷ ︸
Factor Content of Exports

=
∑
i∈N

aifbi︸ ︷︷ ︸
Domestic Factor Demand

. (1.13)

This equation shows the tension: a rise in exports – higher xi – must be balanced out by a fall

in domestic factor demand on the right-hand side, conditional on aggregate payments to factor

f being constant. This is one of the mechanisms through which exports cause domestic factor

prices to put less pressure on domestic consumer prices.

When we allow for a production network and trade, sectors that do not export much directly

(have low xi) could end up exporting indirectly via other producers. The case I analyzed above,

without a production network, is a particular case in which Ω = 0N×N and thus ΨD = I .

10Though the factor content of exports is already well known in the trade literature, I am unaware of previous

work linking this precise notion to inflation.

19



What this suggests is that in the presence of intermediate input linkages, what matters for the

price index changes is not just how much each sector exports directly, xT , but also how much

it exports indirectly through intermediate input linkages, xTΨD (see Dhyne et al., 2021). This

mechanism also affects how much each factor ends up being exported and how much factor price

changes are passed through to the CPI, since xTΨDA represents the factor content of exports

when there are intermediate input linkages across sectors and -
(
λ̄T − x̄TΨD

)
is the relevant

“Domar weight” for the pass-through of sectoral technology shocks to inflation.

Illustration 3: Import price changes with intersectoral linkages and the network-adjusted import

consumption share. This example illustrates that intersectoral linkages amplify the influence of

import price changes on inflation. In the presence of intermediate input linkages and imported

intermediate inputs, the direct import consumption shares b̄TM are not a sufficient statistic for

the effect of import prices on the CPI. To see this, fix factor prices and assume no productivity

shocks, Ŵ = 0F and Ẑ = 0N . Then

P̂ =
(
b̄TM + b̄TDΨDΓ

)︸ ︷︷ ︸
Network-adjusted import consumption share

P̂M

As was the case for the factor content of exports, this equation shows the importance of network-

adjusted import consumption shares. While domestic consumers purchase imports directly as

final consumption (b̄M ), they also consume imports indirectly by purchasing domestically pro-

duced goods that directly or indirectly use imported intermediate inputs. This channel is captured

by the second term on the right-hand side, b̄TDΨDΓ, which captures the total import content of

each domestically produced good when we account for intermediate input linkages. Intuitively, a

rise in the price of import goodm raises the marginal cost of a given producer h by Γhm. This rise

in the marginal cost implies that Ph raises. This increase in Ph, through intermediate input link-

20



ages, raises the price of (say) good i, by Ψih, which denotes the exposure of sector i to changes

in the price of sector h after taking into account intermediate input linkages. This increase in the

price of good i, in turn, is passed through to the consumer price index via b̄i.

Additional Models. I provide two additional models in Appendix A.2 and A.3. In Appendix

A.2, I provide a detailed two-period model of a small open economy to show that the simplified

model presented here shares the same intuition. The key idea follows Baqaee and Farhi (2022b),

who in turn build on Krugman (1998) and Eggertsson and Krugman (2012), where we can sep-

arate a dynamic problem into two sub-periods: the present and the future. All action happens

in the present, while the future can be taken as given. Shocks occur during the present and last

only for that period, wherein the “future”, the economy returns to its initial no-shock equilib-

rium. Conditional on this interpretation, the model in this section is isomorphic to a multi-period

model.

In Appendix A.3, I provide a three-sector (exportable, importable, and non-tradable) canon-

ical small open economy dynamic model, as in Chapter 8 of Uribe and Schmitt-Grohé (2017).

There, I embed a production network structure and show that the results also hold in that en-

vironment. In working out these additional models, I contribute to the literature by effectively

embedding production networks into a small open economy setup and studying its consequences

for inflation.

21



1.2.5 An alternative representation of factor markets: from factor prices to fac-

tor supplies

Factor price changes on the right-hand side of the equation (1.10) are exogenous and thus

can be considered primitives in my exercise. However, typical neoclassical models treat factor

prices as endogenous and factor supply as exogenous. Writing the problem considering factor

prices as given simplified the intuition for the main result of this paper. It also allowed me to

differentiate the proximate causes of inflation between my model and a closed economy with

or without production networks.11 I now show that the same intuition holds if we reverse the

ordering, treating factor prices as endogenous outcomes and factor supply as exogenous objects.

1.2.5.1 Solving in terms of factor supply quantities

The key difference when solving for factor prices as endogenous objects is that we need to

introduce factor market clearing conditions introduced below:

∑
i∈N

Lif = L̄f ∀f ∈ F,

where the left-hand side is factor demand, and the right-hand side is factor supply. In what

follows, I assume that factor supplies, L̄f , are exogenous.

Recall that the expenditure-based share of factor f can be written as

Λ̄f =
Wf L̄f

M ,

where I have imposed the factor market clearing condition and the cash-in-advance constraint.
11This is also the route followed by Baqaee and Farhi (2019a) when studying aggregation in disaggregated

economies via aggregate cost functions rather than aggregate production functions.

22



Thus, changes in factor prices can be written as

Ŵf = ̂̄Λf + M̂ − ̂̄Lf , (1.14)

which in vector form is

Ŵ = ̂̄Λ+ 1FM̂ − ̂̄L.
Intuitively, factor prices can go up because (i) demand is reallocated toward that factor, as cap-

tured by ̂̄Λ; (ii) aggregate demand is going up (M̂); and (iii) there is a decrease in (inelastic)

factor supply ( ̂̄L). As shown in the proposition below, this decomposition allows me to write

changes in the price index as a function of sectoral and aggregate shocks and also changes in

these expenditure-based factor shares.

Proposition 3. Consider a perturbation (M̂, dT, Ẑ, P̂M , X̂, ̂̄L) around some initial equilibrium.

Up to a first order, changes in the aggregate price index, P̂ , satisfy

P̂ = −
(
λ̄T − λ̃T

)
Ẑ − Λ̃T ̂̄Λ−

(
Λ̄T − Λ̃T

) ̂̄L+
dT

M +
(
1− Λ̃T1F

)
M̂︸ ︷︷ ︸

Factor Price Changes

+
(
b̄TM + b̃TM

)
P̂M , (1.15)

Proof. See Appendix A.1.3.

Proposition 3 is an ex-post sufficient statistics results in the spirit of Baqaee and Farhi

(2022a) since there is still one endogenous vector that needs to be solved for, namely ̂̄Λ. Con-

ditional on knowing this vector, we can compute the response of the CPI to changes in the other

primitives. Note that in a closed economy, this term would be zero, since in this case Λ̃ = 0F

and thus factor share reallocation would not have any first-order effect on inflation.

23



Note that the only difference relative to the model with exogenous factor price changes

is that we are now mapping factor price changes to other exogenous objects (M̂, dT, ̂̄L). As in

Baqaee and Farhi (2022b), decreases in factor supply are inflationary because they increase factor

prices conditional on factor demands. The impact on inflation of money supply changes, M̂, is

dampened relative to the closed economy because factor prices have less pass through to infla-

tion. Increases in net transfers to the rest of the world, dT , also increase CPI inflation because,

conditional on money supply, they increase nominal GDP and thus increase factor prices. In

this sense, factor price changes are “sufficient statistics” for how money supply and net transfer

changes affect the CPI.

A few additional remarks regarding Proposition 3 are in order. First, note that sectoral

export demands, X , do not appear directly in this equation. It means that it can only affect

inflation through its effect on ̂̄Λ. Second, as I show in Appendix A.4, ̂̄Λ can be found by solving

a linear system of equations. This system of equations depends on primitives, the production

network structure, and the elasticities of substitution for producers and consumers. Thus, solving

for ̂̄Λ requires us to take a stand on the values of elasticities of substitution of producers across

different inputs and of consumers across different goods. Perhaps more important than this is that

through this endogenous vector, elasticities of substitution matter to a first-order for CPI inflation

in small open economies. Hence, even with a simple, sufficient statistics framework, elasticities

of substitution matter to a first-order for inflation in small open economies, a result that contrasts

with the closed-economy benchmark.

24



1.3 The empirical relevance of adjustments of CPI elasticity

This section examines the quantitative relevance of the proposed production network ad-

justments for inflation across small open economies. I start by describing the data sources and

how I classify countries as small open economies. I then present three different results. First, I fo-

cus on the network-adjusted domestic consumption shares, which are the relevant elasticities for

the pass-through of sectoral technology shocks to inflation. Second, I examine the adjustments to

labor shares once we account for indirect exports. Finally, I compare direct and network-adjusted

import consumption shares.

1.3.1 Data

Although network-adjusted shares require more information than sales and factor shares,

they are still easily computable from available data. In this subsection, I briefly describe the

necessary data to compute them.

Input-Output Tables. I calculate the objects (Ω, x̄, b̄D, b̄M , λ̄) using domestic input-output ta-

bles from the World Input-Output database release 2016, the latest available.

Penn World Tables (PWT). I use version PWT 10.01. This dataset contains income, input,

output, and productivity information between 1950 and 2019 for 183 countries. This database is

freely available to download at https://www.rug.nl/ggdc/productivity/pwt/?lang=en.

Using this database, I construct two measures. First, I denote the share of world GDP

25

https://www.rug.nl/ggdc/productivity/pwt/?lang=en


accounted for by country c as αc. Formally,

αc =
nGDPc

nGDPW

, nGDPW =
∑
c∈C

nGDPc

I measure nGDPc using the series cgdpo, which corresponds to the Output-side real GDP at

current PPP’s (in 2017 US$ millions).

To measure trade openness, I use the series csh x and csh m in the PWT. The first corre-

sponds to the ratio of merchandise exports over nominal GDP, while the second corresponds to

imports over nominal GDP at current PPP’s. I define the trade openness of country c as

Opennessc =
Exportsc + Importsc

nGDPc

= csh xc − csh mc,

where the last line follows since in the data csh mc = − Importsc
nGDPc

Classifying Small Open Economies. I apply two criteria to separate countries into small and

non-small open economies according to the data. First, an economy is small if αc ≤ 0.05.

Second, an economy is open if Opennessc ≥ 0.3. A country is a small open economy if it

satisfies both conditions.

1.3.2 Results

In this subsection, I compare the network-adjusted objects with their closed economy and

no-network adjustment counterparts whenever possible. All cross-sectional plots are based on

the year 2014 unless stated otherwise.

26



1.3.2.1 Network-adjusted domestic consumption shares

I start by showing results for network-adjusted domestic consumption shares λ̄ − x̄TΨD.

Figure 1.2 shows three scenarios for the average sector in small open economies in panel (a) and

for non-small open economies in panel (b). The x-axis shows the unadjusted Domar weights,

while the y-axis shows the adjusted objects. Light squares in these figures refer to the export-

adjusted weights, while dark points are export-network-adjusted weights. Thus, the dark points

in these plots are the network-adjusted domestic consumption shares. As we can see, the adjust-

ments are stronger for small open economies than non-small open economies. Moreover, we can

see that the average Domar weight in small open economies is around 4 percent; it decreases to

around 2.84 percent with the export adjustment and to around 2.31 percent when adjusting for

network-adjusted exports. This is a non-negligible change. It suggests that the inflation impact of

a given sized sectoral productivity shock in an average-sized sector will be dampened by around

50 percent for the average small open economy relative to the closed economy benchmark.

To provide a more concrete example, Figure 1.3 shows the three sectors for which network-

export adjustment is the largest in the United Kingdom: administrative support, legal and ac-

counting, and electricity, gas, and water. The latter sector is illustrative. Its Domar weight is

around 5.95 percent. This number goes down only to 5.9 percent when we subtract direct ex-

ports. For all practical purposes, this means this sector is non-tradable. Once we consider in-

direct exports, however, the network-adjusted consumption share decreases to 4.4 percent. This

illustrates how indirect linkages are quantitatively relevant and provide information beyond the

direct export share.

27



Figure 1.2: Export and Network-Export adjusted Domar weights.

(a) Small Open Economies

AUS

AUT BEL
BGRCAN

CHE

CYP

CZE

DEU
DNK

ESP

EST

FIN
FRAGBR

GRC
HRV HUN

IRL

ITA

KOR

LTU

LUX

LVA

MEX
MLTNLDNOR

POL

PRT
SVK

SVN
SWEAUS

AUT
BEL

BGRCAN
CHE

CYP

CZE

DEU

DNKESP

EST

FINFRAGBR
GRC

HRV HUN

IRL

ITA

KOR

LTU
LUX

LVA

MEX

MLTNLD

NOR POL

PRT
SVKSVN

SWE

0

1

2

3

4

5

6

7

Ad
ju

st
ed

 D
om

ar
 W

ei
gh

ts

2 3 4 5 6 7
Domar Weights, λT

Export Adjusted Domar Weight
Export + Network Adjusted Domar Weight

(b) Non-Small Open Economies

BRA

CHN

IDNINDJPN
RUS

TUR
USA BRA

CHN

IDNINDJPN RUS

TURUSA

0

1

2

3

4

5

6

7

Ad
ju

st
ed

 D
om

ar
 W

ei
gh

ts

2 3 4 5 6 7
Domar Weights, λT

Export Adjusted Domar Weight
Export + Network Adjusted Domar Weight

Note: This figure shows the average Domar weight for each country. The x-axis corresponds to the average Domar

weight computed as in the closed economy model, λT . The gray squares subtract only for direct exports i.e. λ̄T−x̄T .

The black circles further consider the production network structure, λ̄T − x̄TΨD. Panel (a) shows the results for

small open economies, while Panel (b) shows the results for non-small open economies.

28



Figure 1.3: Three sectors with largest adjustments: United Kingdom.

Administrative support Legal and accounting Electricity, gas, and water
0

2

4

6

8
D

om
ar

W
ei

gh
ts

,
%

Unadjusted Export Adjustment Export + Network Adjustment

Note: This figure shows the three sectors with the largest export network-adjusted share for the United Kingdom.

Regression framework. Which sectors and countries are most affected by network adjustments?

To answer this question, I estimate the following cross-sectional regression

ysc = αs + αc + εcs, (1.16)

where ysc represents the difference between a measure for the small open economy with a pro-

duction network relative to the small open economy without networks for a given country c and

sector s. αs is a sector-specific fixed effect, αc is a country-specific fixed effect, and εcs is an error

term. From this regression, I get estimates of sector and country-specific fixed effects. Notice

that these are identified up to a normalization, which in my case is that
∑
s∈S

α̂s = 0 and
∑
c∈C

α̂c = 0.

All fixed effects are interpreted as deviations from the average fixed effects.

In Panel (a) of Figure 1.4, I show the country-fixed effect estimates when the left-hand

side variable is the difference between the network-adjusted export share and the direct export

29



share. Note that these country-fixed estimates tell us the average difference between these shares

— as a fraction of aggregate expenditure — across sectors within a country. We can see that

the countries with the largest adjustments are Luxembourg, Slovak Republic, Malta, and Latvia,

while countries with the smaller adjustments are Korea, Hungary, and Mexico. These numbers

indicate that the export sectors of the latter economies do not rely much on inputs from the

domestic economy, not exporting much indirectly.12

Panel (b) does the same exercise for the sector-fixed effect estimates. These estimates tell

us the average difference between shares across countries within a sector. Financial services is

the sector with the largest average production network adjustment. Note that the Electricity, Gas,

and Water (EGSA) is the seventh sector with the largest difference, while Legal and accounting is

the sixth sector. Thus, the examples cited above are not specific to the United Kingdom but have

consistently large network adjustments across countries. Intuitively, these sectors are important

suppliers for domestic sectors that export directly or indirectly.

These exercises suggest that accounting for the production network is important in comput-

ing inflation elasticities and that the adjustment varies substantially across countries and sectors.

1.3.2.2 Network-adjusted domestic factor demand

I now conduct a similar exercise to examine the importance of network adjustments for

factor shares. First, I study how the aggregate labor share in different countries varies depending

on the export and network export adjustment. I then consider how sector-specific labor shares

vary when considering direct and indirect exports.

12Remember that it does not need to be confused with a country that does not export at all.

30



Figure 1.4: Country and sector fixed effects: export-network adjusted - export adjusted.

(a) Country Fixed Effects

K
or

ea

Hun
ga

ry

M
ex

ico

Cze
ch

Rep
ub

lic

Nor
way

Cro
at

ia

Sw
ed

en

Den
m

ar
k

G
re

ec
e

Aus
tr

al
ia

Pol
an

d

Can
ad

a

Cyp
ru

s

Fr
an

ce

Uni
te

d
K

in
gd

om

Por
tu

ga
l

Bul
ga

ria

Lith
ua

ni
a

Sp
ai

n

Fin
la

nd

Aus
tr

ia
Ita

ly

Ire
la

nd

Sl
ov

en
ia

G
er

m
an

y

Sw
itz

er
la

nd

Est
on

ia

Belg
iu

m

Net
he

rla
nd

s

Lat
vi

a

M
al

ta

Sl
ov

ak
Rep

ub
lic

Lux
em

bou
rg

−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

F
ix

ed
E

ff
ec

ts
N

et
w

or
k

-
N

o
N

et
w

or
k

(P
er

ce
nt

ag
e

p
oi

nt
s)

(b) Sector Fixed Effects

O
th

er
H
H

ac
tiv

iti
es

Fish
in

g
an

d
aq

ua
cu

ltu
re

R
es

ea
rc

h
an

d
de

ve
lo
pm

en
t

W
at

er

O
th

er
tr
an

sp
or

t eq
ui

pm
en

t

H
um

an
he

al
th

A
ir

tr
an

sp
or

t

M
ot

io
n

pi
ct

ur
e

W
at

er
tr
an

sp
or

t

Fu
rn

itu
re

d

Tex
til

es
, wea

rin
g

ap
pa

re
l an

d
lea

th
er

Elec
tr
ica

l eq
ui

pm
en

t

Prin
tin

g
an

d
m

ed
ia

Edu
ca

tio
n

Pap
er

Com
pu

te
r,

ele
ct

ro
ni

c
an

d
op

tic
al

Pub
lis

hi
ng

Pub
lic

A
dm

in
ist

ra
tio

n

O
th

er
pr

of
es

sio
na

l ac
tiv

iti
es

Pha
rm

ac
eu

tic
al

O
th

er
no

n-
m

et
al
lic

m
in

er
al
s

A
cc

om
od

at
io
n

M
ac

hi
ne

ry
an

d
eq

ui
pm

en
t

Se
wer

ag
e

Fo
re

st
ry

W
oo

d
pr

od
uc

ts

Pos
ta

l ac
tiv

iti
es

Che
m

ica
ls

R
ub

be
r an

d
pl

as
tic

O
th

er
se

rv
ice

s

M
in

in
g

R
ep

ai
r of

m
ac

hi
ne

ry

M
ot

or
ve

hi
cle

s

A
rc

h/
en

gi
ne

er
in

g
ac

tiv
iti

es

A
dv

er
tis

in
g

R
ep

ai
r of

m
ot

or
ve

hi
cle

s

Cok
e
an

d
re

fin
ed

pe
tr
ol
eu

m

In
su

ra
nc

e

Bas
ic

m
et

al
s

Tele
co

m
m

un
ica

tio
ns

R
et

ai
l tr

ad
e

In
fo

rm
at

io
n

se
rv

ice
s

A
gr

icu
ltu

re

Fo
od

, be
ve

ra
ge

an
d

to
ba

cc
o

Fa
br

ica
te

d
m

et
al
s

Con
st
ru

ct
io
n

R
ea

l es
ta

te

Lan
d

tr
an

sp
or

t

EG
SA

Leg
al

an
d

ac
co

un
tin

g

A
dm

in
ist

ra
tiv

e
su

pp
or

t

W
ar

eh
ou

sin
g

Fin
an

cia
l se

rv
ice

s

W
ho

les
al
e
tr
ad

e

Fin
an

cia
l se

rv
ice

s
au

x.
−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

F
ix

ed
E

ff
ec

ts
N

et
w

or
k

-
N

o
N

et
w

or
k

(P
er

ce
nt

ag
e

p
oi

nt
s)

Note: This figure shows fixed effects from estimating equation (1.16) where the dependent variable is the difference

between the network-adjusted export share and the direct export share. Panel (a) shows country fixed effects esti-

mates, while Panel (b) shows sector fixed effects. 31



Labor share. Figure 1.5 shows the labor share for different economies on the x-axis and the net-

work export-adjusted labor share on the y-axis. Black diamons shows small open economies and

gray circles represents non-small open economies. As we can see, the adjustments are again sig-

nificant for small open economies but not for non-small open economies. The average labor share

across non-small open economies is 53 percent, while the network export-adjusted labor share

is 50 percent, a negligible change. In contrast, the average labor share in small open economies

is around 57 percent, while the network export-adjusted labor share is only 39 percent. This

means the impact of a given wage increase will be 32 percent lower in a small open economy

with production networks relative to an otherwise similar closed economy.

Sector-specific labor shares. I now conduct a similar exercise to that of export and network-

adjusted export measures above. Here, I consider the dependent variable to be the difference

between the network-adjusted labor content of exports relative to the non-network-adjusted labor

content of exports.

This exercise illustrates the heterogeneity across sectoral labor markets. Before, I consid-

ered the aggregate labor share. However, this aggregate labor share is a weighted average of what

happens at the sectoral level. It can be a misleading statistic for certain questions, especially in

an environment such as COVID-19, where sectoral labor markets were hit differently.

Panel (a) of Figure 1.6 shows the results for the country-fixed effects, while Panel (b)

shows the same but for sector-fixed effects. Apart from Luxembourg, the ranking differs from

the network-adjusted domestic consumption share in Figure 1.4. Interestingly, countries where

sector-specific labor shares adjusted the most due to the domestic production network are the

Netherlands, Slovenia, and Germany, while the ranking at the bottom stays the same. This says

32



that Germany exhibits an average production network adjustment of sector-specific labor shares

0.15 percentage points larger than the adjustment for the average country.

Turning to the sector fixed-effects results, the sectors with the largest production network

adjustment are Legal and Accounting, Wholesale Trade, and Administrative support. Legal and

accounting, for example, has an average adjustment 0.6 percentage points larger than the average

sector. Since the 0.6 percentage point is an average across all countries, consider the Legal and

Accounting sector in Germany as a concrete example. The share of this sector’s labor on nominal

GDP is around 2.6 percent of GDP. It goes down to 2.3 percent when we subtract exports and

to 0.8 percent when we consider the domestic production network structure. Thus, ignoring

the production network adjustment would significantly overstate how much wage changes sector

pass-through to the CPI.

1.3.2.3 Network-adjusted import consumption shares

As a final empirical exercise, I consider import consumption shares. Figure 1.7, provides a

scatterplot of these shares across economies. On the x-axis, I show the direct import consumption

share, while on the y-axis, I show the network-adjusted import consumption share. The average

direct import consumption share across non-small open economies is 6.7 percent. It increases

to 9.3 percent when considering the production network structure. While it increases by almost

3 percentage points, this change is small relative to the one I find for small open economies.

The average direct import consumption share across small open economies is around 17 percent.

This number goes up to 30 percent when considering the production network structure. This is

a 13 percentage points increase. It suggests that the pass-through from import price changes to

33



Figure 1.5: Labor share adjustments for different countries.

AUS

AUT

BEL

BGR

CAN CHE

CYP

CZE

DEU

DNK

ESP

EST

FIN

FRA

GBR

GRC

HRV

HUN

IRL

ITA

KOR

LTU
LUX

LVA

MEX

MLT

NLD

NOR

POL

PRT

SVK

SVN

SWE

BRA

CHN

IDN
IND

JPN

RUS

TUR

USA

20

30

40

50

60

70
Ad

ju
st

ed
 L

ab
or

 S
ha

re

30 40 50 60 70
Labor Share, ΛL

Small Open Economy
Non Small-Open Economy

Note: This figure shows the average labor share on the x-axis and the export-network adjusted labor share for small

open economies in black diamonds and non-small open economies in gray circles.

inflation (almost) doubles when we introduce intersectoral linkages.

1.4 The evolution of inflation in Chile and United Kingdom during COVID-19

In this section, I use the model to study CPI inflation during the COVID-19 episode in

Chile and the United Kingdom.

This empirical examination requires more data relative to the previous section. While

the earlier section showed information on the CPI elasticities and compared these across coun-

tries and sectors using the WIOT alone, this section requires taking a stand on the processes

(Ŵt, P̂Mt, Ẑt), which are not readily available for most countries worldwide. Therefore, I picked

Chile and the United Kingdom, countries with all the necessary information to construct (Ŵt, P̂Mt, Ẑt)

34



Figure 1.6: Country and sector fixed effects: export-network adjusted sector-specific factor

shares - export adjusted sector-specific factor shares.

(a) Country Fixed Effects

K
or

ea

Hun
ga

ry

M
ex

ico

Cze
ch

Rep
ub

lic

Nor
way

Sw
ed

en

Cro
at

ia

Den
m

ar
k

Pol
an

d

Aus
tr

al
ia

G
re

ec
e

Can
ad

a

Bul
ga

ria

Por
tu

ga
l

Cyp
ru

s

Sp
ai

n

Lith
ua

ni
a

Fr
an

ce

Ire
la

nd

M
al

ta
Ita

ly

Lat
vi

a

Fin
la

nd

Est
on

ia

Sl
ov

ak
Rep

ub
lic

Aus
tr

ia

Uni
te

d
K

in
gd

om

Sw
itz

er
la

nd

Belg
iu

m

G
er

m
an

y

Sl
ov

en
ia

Net
he

rla
nd

s

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Note: This figure shows the fixed effects when the dependent variable is the difference between the network-adjusted

sector-specific factor shares and the direct export share adjusted sector-specific factor shares. Panel (a) shows this

difference for the country fixed effects estimates, while Panel (b) does the same for sector fixed effects.

35



Figure 1.7: Direct and Network-Adjusted import consumption shares.

AUS

AUT

BEL

BGR

CAN

CHE

CYP

CZE

DEU

DNK

ESP

EST

FIN

FRA

GBR
GRC

HRV HUN

IRL

ITA

KOR

LTU

LUX

LVA

MEX

MLT

NLD

NOR

POL

PRT

SVKSVN

SWE

BRA
CHNIDN

IND
JPN

RUS
TUR

USA

0

10

20

30

40

50

60
To

ta
l I

m
po

rt 
Co

ns
um

pt
io

n 
Sh

ar
e

0 10 20 30 40 50 60
Direct Import Consumption Share, (bM)T

Small Open Economy
Non Small-Open Economy

Note: This figure shows the direct import consumption share on the x-axis and the network-adjusted import con-

sumption share on the y-axis. Small open economies are the black diamonds, and non-small open economies are the

gray circles.

that also belong to the small open economy category.

This is an ex-post exercise using existing data to analyze the past behavior of inflation be-

tween 2020 and 2022. Yet, Proposition 1 is helpful for forecasting inflation and is thus a valuable

tool for policymakers in small open economies. Provided that we have forecast information on

the processes (Ŵt, P̂Mt, Ẑt), we can combine this information with input-output tables to get an

estimate of inflation. The accuracy of this exercise will depend on the accuracy of elasticities and

that of the forecasted series. Throughout this section, I focus on the former, as it is the main point

of this paper.

In what follows, I first describe the data. Then, I show how I map the model to the data.

36



Finally, I discuss the results for Chile and the United Kingdom.

1.4.1 Data

1.4.1.1 Chile

Input-Output Tables. Since Chilean data is unavailable from the WIOT, I resort to Chilean Na-

tional Accounts. I use Compilacion de Referencia for year 2013. The structure is similar to

that of the WIOT, having information on input-output linkages, final uses, and factor payments.

Moreover, it is quite disaggregated, containing information for up to 171 industries. I collapse

this data to a 17-sector classification due to data availability on sectoral wages. This 17-sector

classification is equivalent to SIC2.

Sectoral Productivity. The ideal measure of productivity from the model is total factor produc-

tivity (TFP). However, TFP measures are hard to come by, especially at high frequencies and at

the sectoral level. To circumvent this problem, I proxy sectoral TFP using sectoral labor produc-

tivity. I collect data on real GDP for the same 17 sectors and divide by total sectoral employment.

Real GDP and sectoral employment data come from the Central Bank of Chile (CBCh) and are

available quarterly from 1996 to 2022.

Sectoral Wages. I source sectoral nominal wages from the Chilean National Institute of Statis-

tics (INE) series Indice de Remuneraciones Nominal. This database is available monthly from

January 2016 to December 2022. To be consistent with the productivity data, I collapsed this data

to a quarterly frequency.

37



Import Prices. I use the import price index available from the CBCh quarterly from 2013 to

2022.

1.4.1.2 United Kingdom

Input-Output Tables. I source data from the WIOT domestic tables as in the previous empirical

section. I collapse these input-output tables into 20 industries to be consistent with the data on

sectoral wages.

Sectoral Productivity. I sourced data from the Office for National Statistics (ONS) of the United

Kingdom. I downloaded quarterly estimates of labor productivity from the Flash productivity

report.13 This contains information for up to 17 industries.

Sectoral Wages. I source this data from the ONS of the United Kingdom. In particular, I use

the dataset EARN03. This contains monthly information on average weekly earnings for around

20 industries. This dataset is available from 2000 to 2022.

Import Prices. I use the import price index from the ONS (series GD74, dataset: MM22). This

series is available at different frequencies. I use quarterly information from 2009 until 2022.

1.4.2 Mapping the model to the data

Before showing the results, a few remarks are in order. Since the model is static, all inherent

inflation dynamics will combine the dynamics of exogenous variables and their interaction with

the CPI elasticities.
13This data can be downloaded freely from the “Flash productivity by section” section at the ONS here.

38

https://www.ons.gov.uk/economy/economicoutputandproductivity/productivitymeasures/datasets/flashproductivitybysection


First, I take all series and compute their level deviations from their value in 2018Q4. For-

mally, the sources of variation I feed in to construct implied inflation from the different models

take the following form

ŷt = yt − y2018Q4,

where yt represents (the log) of any time series and y2018Q4 is its value in 2018Q4. Notice that

each vector now has a t subscript as they are deviations from 2018Q4 at each time t.

In the above equation, I call the deviation ŷt a “shock”. This differs from a structurally

identified shock because I feed variation directly from the data, taking it as given. With this

caveat in mind and throughout this section, I refer to these ŷt simply as shocks.

Using this procedure I construct counterparts to θt = (Ŵt, P̂Mt, Ẑt) in the model. I mea-

sure factor prices as sectoral wages. I assume segmented labor markets such that there are dif-

ferent wages across sectors to capture better the behavior of labor markets during the COVID-19

episode, as highlighted in the recent literature (Baqaee and Farhi, 2022b; di Giovanni et al., 2022,

2023a,b). Since I cannot observe sector-specific prices for other factors, such as capital or land, I

assume that those factor prices did not change over the sample period.

CPI inflation in the data πt, when t refers to a quarter, is

πt = logPt − logPt−4

Combining the model and shocks, I have P̂Model
t as

P̂Model
t = −

∑
i∈N

RCPI,Z
i Ẑit +

∑
f∈F

RCPI,W
f Ŵft +RCPI,M

M P̂Mt.

Note that here (RCPI,Z
i ,RCPI,W

f ,RCPI,M
M ) stand for the responses of the CPI to changes in sec-

toral technology, factor prices, and import price, respectively. These objects are model-dependent

39



and thus will be different when considering the closed economy model, the small open economy

model without production networks, and the small open economy with production networks.

Finally, inflation from the model is

πModel
t = P̂Model

t − P̂Model
t−4 .

The approach of taking log differences relative to some initial point is the most transparent

because it does not modify the data much, relative to other alternatives such as standard detrend-

ing procedures.

1.4.3 Results

In this subsection, I compare inflation implied by the models, πModel
t , and that in the data.

Figures 1.8 and 1.9 show inflation in the data and the one implied by the model for Chile

and the United Kingdom for 2020–2022, respectively. To highlight the distinct role of produc-

tion networks and openness, I consider three models: a closed economy model (Closed, pink

triangles), a small open economy without production networks (SOE no Network, green ∗), and

a small open economy with production networks (SOE - Network, orange circles). I plot the

model’s numbers using symbols rather than lines to emphasize the absence of dynamics within

the model apart from those generated by the shocks I am feeding in.

Although the empirical exercise is fairly simple, it captures the data patterns well and more

significantly for the small open economy with a production network in Chile and the United

Kingdom.

As pointed out, the model has no intrinsic dynamics: all the action over time comes from

the dynamics in θt. A more meaningful comparison is to compare the moments implied by the

40



model and those in the data. Table 1.2 does precisely this and shows the first two moments of

inflation in the data and the model. Panel (a) is for Chile, while Panel (b) shows the United

Kingdom.

The average annual inflation in Chile between 2020 and 2022 was 6.13 percent, with a stan-

dard deviation of 3.89. The closed economy model delivers substantially lower mean inflation

(0.98) and higher standard deviation (9.69) relative to the data. We can see that the sole introduc-

tion of a small open economy aspect, without production networks, gets us in the right direction

as it exhibits a larger mean relative to the closed economy benchmark (1.45) and a lower standard

deviation (6.88). The small open economy with production networks gets us closer to the data,

with an average inflation of 2.41 and a standard deviation of 6.67.

In the United Kingdom, the average inflation was 3.69 percent, almost half that of Chile

during the same period, with a standard deviation of 3.11. The closed economy benchmark

generates again too little average inflation (2.27 vs. 3.31) but now too low a standard deviation

(2.57 vs. 3.11). As was the case for Chile, introducing the small open economy aspect put us

in the right direction: inflation is higher on average (2.72) and has a higher standard deviation

(2.64). Considering production networks again improves the results: the model exhibits an even

higher mean (3.21) and standard deviation (3.00).

To sum up, this exercise suggests that a small open economy model with production net-

works better matches inflation moments during 2020 – 2022 than a closed economy model and

a small open economy model without production networks. To be fair, the small open economy

with production networks should indeed do better than the other two as it adds a piece of realism

missing from these other models, namely, intersectoral linkages. The question is how much. The

results here are suggestive evidence that this is quantitatively relevant. Of course, the stylized

41



Figure 1.8: Chile Inflation under different models.

20
20

Q
1

20
20

Q
2

20
20

Q
3

20
20

Q
4

20
21

Q
1

20
21

Q
2

20
21

Q
3

20
21

Q
4

20
22

Q
1

20
22

Q
2

20
22

Q
3

20
22

Q
4

−16

−12

−8

−4

0

4

8

12

16
A

n
nu

al
In

fla
ti

on
,

%

Data

Closed, R2-adj = 0.84

Open – No Network, R2-adj = 0.86

Open – Network, R2-adj = 0.92

Note: This figure shows inflation in the data and the one implied by the different models. The black line is the

data. The pink triangles correspond to the closed economy model. The green ∗ are the small open economy model

without production networks, and the orange circles correspond to the small open economy model with production

networks.

model has many missing parts, but remarkably, such a stylized exercise matches these inflation

data moments well.

42



Figure 1.9: United Kingdom Inflation under different models.

20
20

Q
1

20
20

Q
2

20
20

Q
3

20
20

Q
4

20
21

Q
1

20
21

Q
2

20
21

Q
3

20
21

Q
4

20
22

Q
1

20
22

Q
2

20
22

Q
3

20
22

Q
4

−4

−2

0

2

4

6

8

10

12

14
A

n
nu

al
In

fla
ti

on
,

%
Data

Closed, R2-adj = -0.01

Open – No Network, R2-adj = 0.19

Open – Network, R2-adj = 0.44

Note: This figure shows inflation in the data and the one implied by the different models. The black line is the

data. The pink triangles correspond to the closed economy model. The green ∗ are the small open economy model

without production networks, and the orange circles correspond to the small open economy model with production

networks.

1.5 Conclusion

I study inflation in small open economies with production networks. Theoretically and

empirically, I show that production networks matter for the effect of sectoral technology shocks,

factor prices, and import prices on CPI inflation. I argue that the reason why the interaction of

trade and production network matters is because opening up the economy is one of the ways to

break the equivalence between what is produced within borders and what is consumed by the

domestic consumer, for whom the CPI is relevant. Once we break that relationship, the pro-

duction network amplifies this discrepancy via indirect linkages: Non-exporters become indirect

exporters, while non-importers become indirect importers. This ultimately affects the exposure

43



Table 1.2: Average Inflation, 2020 – 2022.

Panel (a): Chile Panel (b): United Kingdom

Mean Std. Dev. Mean Std. Dev

Data 6.13 3.89 3.69 3.11

Model

Closed 0.98 9.69 2.27 2.57

SOE no Network 1.45 6.88 2.72 2.64

SOE - Network 2.41 6.67 3.21 3.00

Note: This table shows the mean and standard deviation of inflation for the data and the different models. The

Closed model uses the implied elasticities as if we consider the economies as closed. The SOE no network model

considers the elasticities in a small open economy that does not feature any production network. Finally, the SOE -

Network model accounts for network linkages.

of the domestic consumer to a different set of shocks. The production network thus has a first

order impact on inflation, with sales and factor shares no longer being sufficient statistics to study

how changes in sectoral technology or factor prices pass through to inflation, as it would be the

case in a closed economy.

In a small open economy with production networks, indirect exporting dampens domes-

tic shocks relative to an otherwise equivalent closed economy. Foreign shocks, such as import

price shocks, are amplified relative to an otherwise equivalent small open economy without pro-

duction networks. Which channels dominate at the aggregate level depends on the production

44



network structure and is, in the end, a quantitative question. I show that the production network

adjustments on both the export and import side matter quantitatively across a set of small open

economies. I apply the small open economy model with production networks to the recent in-

flationary episode in Chile and the United Kingdom. Including production networks helps better

match the mean and variance of inflation of these countries between 2020 and 2022.

45



Chapter 2: Business Cycle Asymmetry and Input-Output Structure: The Role

of Firm-to-Firm Networks

(with Jorge Miranda-Pinto and Eric R. Young. Published at the Journal of Monetary Eco-

nomics, 2023.)

2.1 Introduction

It is a general fact that recessions are shorter and more severe than expansions, i.e. they

are “sharper”. This asymmetry leads to a negatively-skewed distribution of real GDP growth as

documented in, for example, Ordonez (2013). Figure 2.1 shows this asymmetry for the cyclical

component of real GDP for a sample of 46 countries during 1985-2019. Out of the 46 countries,

43 display negatively-skewed business cycles. The primary explanation for this fact in the liter-

ature is the existence of financial constraints (Ordonez, 2013; Jensen et al., 2020). In this paper,

we offer a different explanation for the asymmetry based on the empirical importance of sectoral

shocks and the structure of input-output connections.

We use sectoral input-output data for 46 countries and firm-to-firm network data for the

Chilean economy to study the role of production networks in shaping the magnitude of macroe-

conomic downturns. In the cross-country data, we document strong correlations between the

skewness of the cyclical component of real GDP — our measure of the downturn’s severity—and

46



input-output structure (density of the network). We then use the firm-level network data to in-

vestigate to which extent production linkages at the firm level relate to firm-level output growth

skewness and firm-level output declines during COVID-19.

Figure 2.1: Skewness of Cyclical Component of Real GDP (1985 – 2019)

-3 -2 -1 0 1
Skewness Cyclical Component 1985-2019

United States
United Kingdom

Turkey
Switzerland

Sweden
Spain

South Africa
Singapore

Saudi Arabia
Romania

Republic of Korea
Portugal

Poland
Philippines

Norway
New Zealand
Netherlands

Mexico
Malta

Malaysia
Luxembourg

Japan
Italy

Israel
Ireland

India
Iceland

Hungary
Greece

Germany
France
Finland

Denmark
Cyprus

Costa Rica
Colombia

China
Chile

Canada
Cambodia

Bulgaria
Brazil

Belgium
Austria

Australia
Argentina

Note: This figure plots the skewness of countries’ annual cyclical component of real GDP for the period 1985-2019.

We compute the cyclical component following Hamilton (2018) and estimate it as the residual (εt) from a regression

of the form yt = β0 + β1yt−2 + β2yt−3 + εt country-by-country, where yt is log real GDP at time t.

Using OECD domestic input-output data, we show that — controlling for other impor-

tant cross-country characteristics — countries in which more input-output connections are active

(denser networks) display more negatively-skewed business cycles, as expressed by a more neg-

ative skewness of the cyclical component of real GDP for the period 1985-2019. Our estimates

imply that if a country with a network density of 0.69 (the average in the sample) were to increase

47



its active links by 10 percentage points (to 0.79), the skewness of the cyclical component of real

GDP would decrease from −0.68 to −0.98. To put the numbers