Gravity Equations: Workhorse,Toolkit, and Gravity Equations: Workhorse,Toolkit, and Cookbook Keith Heady

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  • Gravity Equations:

    Workhorse,Toolkit, and Cookbook∗

    Keith Head† Thierry Mayer‡

    April 7, 2013

    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 misin-

    terpreted 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 estima-

    tor 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 wel-

    fare. We try to facilitate diffusion of best-practice methods by illustrating their application in

    a step-by-step cookbook mode of exposition.

    JEL code: F1

    Keywords: bilateral trade, heterogeneous firms, distance, borders, trade cost elasticity, poisson

    ∗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 understanding 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 Rodŕıguez-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, João Santos Silva, 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 Anderson, 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, keith.head@sauder.ubc.ca ‡Sciences Po, CEPII, and CEPR, thierry.mayer@sciences-po.fr

    1

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

  • Contents

    1 Introduction 3

    1.1 Gravity features of trade data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    1.2 A brief history of gravity in trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    2 Microfoundations for Gravity Equations 7

    2.1 Three Definitions of the Gravity Equation . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.2 Assumptions underlying structural gravity . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.3 Main variants of gravity for trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.4 Gravity models beyond trade in goods . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    3 Theory-consistent estimation 19

    3.1 Proxies for multilateral resistance terms . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.2 Iterative structural estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.3 Fixed effects estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    3.4 Ratio-type estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    3.5 Other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    3.6 Monte Carlo study of alternative estimators . . . . . . . . . . . . . . . . . . . . . . . 23

    3.7 Identification and estimation of country-specific effects . . . . . . . . . . . . . . . . . 27

    4 Gravity estimates of policy impacts 29

    4.1 Meta-analysis of policy dummies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    4.2 The elasticity of trade with respect to trade costs . . . . . . . . . . . . . . . . . . . . 32

    4.3 Partial vs general equilibrium impacts on trade . . . . . . . . . . . . . . . . . . . . . 34

    4.4 Testing structural gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    5 Frontiers of gravity research 41

    5.1 Gravity’s errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    5.2 Causes and consequences of zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    5.3 Firm-level gravity, extensive and intensive margins . . . . . . . . . . . . . . . . . . . 51

    6 Directions for future research 57

    7 Conclusions 57

    References 57

    2

  • 1 Introduction

    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.1 Over the last decade, concentrated

    efforts of trade theorists have established that gravity equations emerge from mainstream 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 determinants 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 theory, we use graphical displays to lay out the factual basis for taking gravity

    equations seriously. The first key feature of trade data that mirrors the physical gravity equation

    is that exports rise proportionately with the economic size of the destination and imports rise in

    proportion to the size of the origin economy. Using GDP as the economy size measure, we illustrate

    this proportionality using trade flows between Japan and the European Union. The idea is that the

    European Union’s area is small enough and sufficiently far from Japan that differences in distance

    to Japan can be ignored. Similarly because the EU is a customs union, each member applies the

    same trade policies on Japanese imports. Japan does not share a language, religion, currency or

    colonial history with any EU members either.

    Figure 1 (a) shows Japan’s bilateral exports on the vertical axis and (b) shows its imports.

    The horizontal axes of both figures show the GDP (using market exchange rates) of the EU trade

    partner. The trade flows and GDPs are normalized by dividing by the corresponding value for

    1Other examples of social physics include power function distributions thought to characterize incomes, firm and city sizes, and network linkages.

    3

  • Figure 1: Trade is proportional to size

    (a) Japan’s exports to EU, 2006 (b) Japan’s imports from EU, 2006

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