Gravity Equations: Workhorse, Toolkit and Cookbook - Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook GRAVITY EQUATIONS: WORKHORSE,TOOLKIT, AND COOKBOOK Keith Head

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  • C E N T R ED T U D E S P R O S P E C T I V E SE T D I N F O R M A T I O N SI N T E R N A T I O N A L E S

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    Gravity Equations:Workhorse,Toolkit, and Cookbook

    Keith Head and Thierry Mayer

  • CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook

    TABLE OF CONTENTSHighlights and Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Points clefs et rsum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.1. Gravity features of trade data . . . . . . . . . . . . . . . . . . . . . 61.2. A brief history of gravity in trade . . . . . . . . . . . . . . . . . . . . 8

    2. Microfoundations for Gravity Equations . . . . . . . . . . . . . . . . . . . 112.1. Three Definitions of the Gravity Equation . . . . . . . . . . . . . . . . 112.2. Assumptions underlying structural gravity . . . . . . . . . . . . . . . . 132.3. Main variants of gravity for trade . . . . . . . . . . . . . . . . . . . . 142.4. Gravity models beyond trade in goods . . . . . . . . . . . . . . . . . . 23

    3. Theory-consistent estimation . . . . . . . . . . . . . . . . . . . . . . . 233.1. Proxies for multilateral resistance terms . . . . . . . . . . . . . . . . . 243.2. Iterative structural estimation . . . . . . . . . . . . . . . . . . . . . 243.3. Fixed effects estimation. . . . . . . . . . . . . . . . . . . . . . . . 253.4. Ratio-type estimation . . . . . . . . . . . . . . . . . . . . . . . . 263.5. Other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.6. Monte Carlo study of alternative estimators . . . . . . . . . . . . . . . . 283.7. Identification and estimation of country-specific effects . . . . . . . . . . . 31

    4. Gravity estimates of policy impacts . . . . . . . . . . . . . . . . . . . . . 334.1. Meta-analysis of policy dummies . . . . . . . . . . . . . . . . . . . . 334.2. The elasticity of trade with respect to trade costs . . . . . . . . . . . . . . 364.3. Partial vs general equilibrium impacts on trade . . . . . . . . . . . . . . 394.4. Testing structural gravity . . . . . . . . . . . . . . . . . . . . . . . 44

    5. Frontiers of gravity research . . . . . . . . . . . . . . . . . . . . . . . 455.1. Gravitys errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2. Causes and consequences of zeros . . . . . . . . . . . . . . . . . . . 505.3. Firm-level gravity, extensive and intensive margins . . . . . . . . . . . . . 56

    6. Directions for future research . . . . . . . . . . . . . . . . . . . . . . . 627. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

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  • CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook

    GRAVITY EQUATIONS:WORKHORSE,TOOLKIT, AND COOKBOOK

    Keith Head and Thierry Mayer

    HIGHLIGHTS

    We review the microfoundations of gravity equationsWe review the theory-consistent methods of estimating gravity equationsWe provide a literature review of the effect of certain policies, based on gravity estimatesWe specify some frontiers of research on gravity equations

    ABSTRACT

    This chapter focuses on the estimation and interpretation of gravity equations for bilateral trade. Thisnecessarily involves a careful consideration of the theoretical underpinnings since it has become clearthat naive approaches to estimation lead to biased and frequently misinterpreted results. There are nowseveral theory-consistent estimation methods and we argue against sole reliance on any one method andinstead advocate a toolkit approach. One estimator may be preferred for certain types of data or researchquestions but more often the methods should be used in concert to establish robustness. In recent years,estimation has become just a first step before a deeper analysis of the implications of the results, notablyin terms of welfare. We try to facilitate diffusion of best-practice methods by illustrating their applicationin a step-by-step cookbook mode of exposition.

    JEL Classification: F10

    Keywords: Gravity equations, International trade

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  • CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook

    GRAVITY EQUATIONS:WORKHORSE,TOOLKIT, AND COOKBOOK

    Keith Head and Thierry Mayer

    POINTS CLEFS

    Nous exposons les diffrentes micro-fondations thoriques dont peuvent dcouler les mod-les de gravitNous dtaillons les mthodes destimation conformes la thorieNous proposons une revue de littrature des tudes fondes sur des modles de gravit et quicherchent mesurer limpact de certaines politiques sur le commerce.Nous dgageons quelques frontires de la recherche sur les quations de gravit

    RSUM

    Cet article porte sur lusage des quations de gravit, dans le cadre gnral de la recherche sur le com-merce international. Nous dtaillons les diffrentes mthodes destimation, ainsi que leurs interprtationspossibles. En amont des estimations, nous retraons lvolution des fondements thoriques sur lesquelssappuient les quations de gravit. Ces fondations thoriques nont t labores que tardivement, aprsavoir constat le caractre biais des estimations athoriques. Les quations de gravit reposent dsor-mais sur plusieurs socles thoriques. Nous recommandons une approche plurielle plutt quune approchesappuyant sur un modle thorique unique. Nous proposons donc une boite outils plutt quun cadrethorique fig. De manire gnrale, comparer les rsultats issus de plusieurs mthodes nous semble trela meilleure manire dtablir la robustesse des conclusions. Il reste toutefois envisageable quun modleou un estimateur particulier sapplique mieux une question prcise ou un type spcifique de don-nes. Ces dernires annes, les quations de gravit ont trouv un nouvel usage. Elles peuvent dsormaisconstituer la premire tape dune tude plus approfondie portant sur les effets dune politique donnesur le bien-tre. En rsum, nous nous proposons de diffuser les thories les plus abouties ainsi que lesmthodes destimation qui nous semblent les meilleures.

    Classification JEL : F10

    Mots cls : Equations de gravit, Commerce international

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  • CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook

    GRAVITY EQUATIONS:WORKHORSE,TOOLKIT, AND COOKBOOK1

    Keith Head and Thierry Mayer

    1This is a draft of a chapter to appear the Handbook of International Economics Vol. 4, eds. Gopinath, Helpman,and Rogoff. The chapter has a companion website, https://sites.google.com/site/hiegravity/, with anappendix, Stata code, and related links. We thank Leo Fankhnel and Camilo Umana for outstanding assistancewith the programming and meta-analysis in this chapter, Soledad Zignago for great help with providing and un-derstanding subtleties of some of the data used, and Julia Jauer for her update of the gravity data. Scott Baier,Sebastian Sotelo, Joo Santos Silva generously provided computer code. Andres Rodrguez-Clare answered manyquestions we had about welfare calculations but is not responsible of course, for any mistakes we may have made.Arnaud Costinot, Gilles Duranton, Thibault Fally, Mario Larch, Marc Melitz, Gianmarco Ottaviano, and DanielTrefler made very useful comments on previous drafts. We are especially grateful to Jose de Sousa: his carefulreading identified many necessary corrections in an early draft. Participants at presentations Hitotsubashi GCOEConference on International Trade and FDI 2012, National Bank of Belgium, Clemson University also contributedto improving the draft. Finally, we thank our discussants at the handbook conference, Rob Feenstra and Jim An-derson, for many helpful suggestions. We regret that because of limitations of time and space, we have not beenable to fully respond to all of the valuable suggestions we received. This research has received funding from theEuropean Research Council under the European Communitys Seventh Framework Programme (FP7/2007-2013)Grant Agreement no. 313522.Sauder School of Business, University of British Columbia and CEPR, keith.head@sauder.ubc.caSciences Po, CEPII and CEPR, thierry.mayer@sciences-po.fr

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    https://sites.google.com/site/hiegravity/

  • CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook

    1. INTRODUCTION

    As the name suggests, gravity equations are a model of bilateral interactions in which size anddistance effects enter multiplicatively. They have been used as a workhorse for analyzing thedeterminants of bilateral trade flows for 50 years since being introduced by Tinbergen (1962).Krugman (1997) referred to gravity equations as examples of social physics, the relativelyfew law-like empirical regularities that characterize social interactions.2 Over the last decade,concentrated efforts of trade theorists have established that gravity equations emerge from main-stream modeling frameworks in economics and should no longer be thought of as deriving fromsome murky analogy with Newtonian physics. Meanwhile empirical workguided in varyingdegrees by the new theoryhas proceeded to lay down a raft of stylized facts about the deter-minants of bilateral trade. As a result of recent modelling, we now know that gravity estimatescan be combined with trade policy experiments to calculate implied welfare changes.

    This chapter focuses on the estimation and interpretation of gravity equations for bilateral trade.This necessarily involves a careful consideration of the theoretical underpinnings since it hasbecome clear that naive approaches to estimation lead to biased and frequently misinterpretedresults. There are now several theory-consistent estimation methods and we argue against solereliance on any one method and instead advocate a t