Gravity Equations: Workhorse, Toolkit and Cookbook
Total Page：16
File Type：pdf, Size：1020Kb
No 2013 – 27 September CENTRE D’ÉTUDESPROSPECTIVES ETD’INFORMATIONS INTERNATIONALES DOCUMENTDETRAVAIL Gravity Equations: Workhorse,Toolkit, and Cookbook Keith Head and Thierry Mayer CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook TABLE OF CONTENTS Highlights and Abstract...........................3 Points clefs et résumé............................4 1. Introduction..............................6 1.1. Gravity features of trade data.....................6 1.2. A brief history of gravity in trade....................8 2. Microfoundations for Gravity Equations................... 11 2.1. Three Definitions of the Gravity Equation................ 11 2.2. Assumptions underlying structural gravity................ 13 2.3. Main variants of gravity for trade.................... 14 2.4. Gravity models beyond trade in goods.................. 23 3. Theory-consistent estimation....................... 23 3.1. Proxies for multilateral resistance terms................. 24 3.2. Iterative structural estimation..................... 24 3.3. Fixed effects estimation........................ 25 3.4. Ratio-type estimation........................ 26 3.5. Other methods........................... 27 3.6. Monte Carlo study of alternative estimators................ 28 3.7. Identification and estimation of country-specific effects........... 31 4. Gravity estimates of policy impacts..................... 33 4.1. Meta-analysis of policy dummies.................... 33 4.2. The elasticity of trade with respect to trade costs.............. 36 4.3. Partial vs general equilibrium impacts on trade.............. 39 4.4. Testing structural gravity....................... 44 5. Frontiers of gravity research....................... 45 5.1. Gravity’s errors........................... 46 5.2. Causes and consequences of zeros................... 50 5.3. Firm-level gravity, extensive and intensive margins............. 56 6. Directions for future research....................... 62 7. Conclusions.............................. 63 References................................ 63 2 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 equations We review the theory-consistent methods of estimating gravity equations We provide a literature review of the effect of certain policies, based on gravity estimates We specify some frontiers of research on gravity equations ABSTRACT 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 has become clear that naive approaches to estimation lead to biased and frequently misinterpreted results. There are now several theory-consistent estimation methods and we argue against sole reliance on any one method and instead advocate a toolkit approach. One estimator may be preferred for certain types of data or research questions 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, notably in terms of welfare. We try to facilitate diffusion of best-practice methods by illustrating their application in a step-by-step cookbook mode of exposition. JEL Classification: F10 Keywords: Gravity equations, International trade 3 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 différentes micro-fondations théoriques dont peuvent découler les mod- èles de gravité Nous détaillons les méthodes d’estimation conformes à la théorie Nous proposons une revue de littérature des études fondées sur des modèles de gravité et qui cherchent à mesurer l’impact de certaines politiques sur le commerce. Nous dégageons quelques frontières de la recherche sur les équations de gravité RÉSUMÉ Cet article porte sur l’usage des équations de gravité, dans le cadre général de la recherche sur le com- merce international. Nous détaillons les différentes méthodes d’estimation, ainsi que leurs interprétations possibles. En amont des estimations, nous retraçons l’évolution des fondements théoriques sur lesquels s’appuient les équations de gravité. Ces fondations théoriques n’ont été élaborées que tardivement, après avoir constaté le caractère biaisé des estimations athéoriques. Les équations de gravité reposent désor- mais sur plusieurs socles théoriques. Nous recommandons une approche plurielle plutôt qu’une approche s’appuyant sur un modèle théorique unique. Nous proposons donc une boite à outils plutôt qu’un cadre théorique figé. De manière générale, comparer les résultats issus de plusieurs méthodes nous semble être la meilleure manière d’établir la robustesse des conclusions. Il reste toutefois envisageable qu’un modèle ou un estimateur particulier s’applique mieux à une question précise ou à un type spécifique de don- nées. Ces dernières années, les équations de gravité ont trouvé un nouvel usage. Elles peuvent désormais constituer la première étape d’une étude plus approfondie portant sur les effets d’une politique donnée sur le bien-être. En résumé, nous nous proposons de diffuser les théories les plus abouties ainsi que les méthodes d’estimation qui nous semblent les meilleures. Classification JEL : F10 Mots clés : Equations de gravité, Commerce international 4 CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook GRAVITY EQUATIONS: WORKHORSE,TOOLKIT, AND COOKBOOK1 Keith Head∗ and Thierry Mayery 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 an appendix, Stata code, and related links. We thank Leo Fankhänel and Camilo Umana for outstanding assistance with 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, João Santos Silva generously provided computer code. Andres Rodríguez-Clare answered many questions 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 Daniel Trefler made very useful comments on previous drafts. We are especially grateful to Jose de Sousa: his careful reading identified many necessary corrections in an early draft. Participants at presentations Hitotsubashi GCOE Conference on International Trade and FDI 2012, National Bank of Belgium, Clemson University also contributed to 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 been able to fully respond to all of the valuable suggestions we received. This research has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) Grant Agreement no. 313522. ∗Sauder School of Business, University of British Columbia and CEPR, [email protected] ySciences Po, CEPII and CEPR, [email protected] 5 CEPII Working Paper Gravity Equations: Workhorse,Toolkit, and Cookbook 1.I NTRODUCTION As the name suggests, gravity equations are a model of bilateral interactions in which size and distance effects enter multiplicatively. They have been used as a workhorse for analyzing the determinants 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 relatively few 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 from some murky analogy with Newtonian physics. Meanwhile empirical work—guided in varying degrees by the new theory—has 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 estimates can 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 has become clear that naive approaches to estimation lead to biased and frequently misinterpreted results. There are now several theory-consistent estimation methods and we argue against sole reliance on any one method and instead advocate a toolkit approach. One estimator may be preferred for certain types of data or research questions 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, notably in terms of welfare. We try to facilitate diffusion of best-practice methods by illustrating their application in a step-by-step cookbook mode of exposition. 1.1. Gravity features of trade data Before considering