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Latent Multilateral Trade Resistance Indices: Theory and Evidence

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Niveau: Supérieur, Doctorat, Bac+8
Latent Multilateral Trade Resistance Indices: Theory and Evidence? Wilfried Koch† James P. LeSage‡ October 9, 2009 Abstract Anderson and van Wincoop (2003) make a convincing argument that traditional gravity equation estimates are biased by the omission of multilateral resistance terms. They show that these multilateral resistance terms are implicitly defined by a system of non-linear equations involving all regions' GDP shares and a global interdependence structure involving trade costs. We show how linearizing the system of non-linear relationships around a free trade world leads to an interdependence structure that can be used as a Bayesian prior to produce statistical estimates of the inward and outward multilateral resistance indices. This reflects a statistical approach that has advantages over the non-stochastic numerical approach used by Anderson and van Wincoop (2003) to solve for these indices and other approaches proposed in the literature. KEYWORDS: gravity equations; multilateral resistance indices; Bayesian hier- archical models JEL: C11; F12; R12 ?The authors wish to thank R. K. Pace and Olivier Parent for valuable comments. The usual disclaimer applies. †LEG, Universite de Bourgogne, France. E-mail: , corresponding au- thor. ‡McCoy College of Business, Texas State University-San Marcos, USA 1

  • gravity equation

  • squares estimates

  • regions using only

  • xij ?

  • resistance between

  • multilateral resistance

  • bilateral trade

  • involving all regions'

  • trade flows


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Multilateral Trade Resistance Theory and Evidence
Wilfried Koch
James P. LeSage
October 9, 2009
Abstract
Indices:
Anderson and van Wincoop (2003) make a convincing argument that traditional gravity equation estimates are biased by the omission of multilateral resistance terms. They show that these multilateral resistance terms are implicitly defined by a system of non-linear equations involving all regions’ GDP shares and a global interdependence structure involving trade costs. We show how linearizing the system of non-linear relationships around a free trade world leads to an interdependence structure that can be used as a Bayesian prior to produce statistical estimates of the inward and outward multilateral resistance indices. This reflects a statistical approach that has advantages over the non-stochastic numerical approach used by Anderson and van Wincoop (2003) to solve for these indices and other approaches proposed in the literature.
KEYWORDSequations; multilateral resistance indices; Bayesian hier-: gravity archical models JEL: C11; F12; R12
 TheR. K. Pace and Olivier Parent for valuable comments.The authors wish to thank  usual disclaimer applies. LeEBGo,uUrngiovgersit´ed.e-EamlienF,arcn:kod.@uchilwiefrf.enruob-gogr, corresponding au-thor. McCoy College of Business, Texas State University-San Marcos, USA
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1 Introduction
Past literature on empirical modeling of trade flows using gravity models rely on least-
squares estimates that require the strong assumption that the dependent regression variable
representing trade flows from all regionsito all other regionsjare independent of other
flows,i, j= 1, . . . , n. For example, McCallum (1995), among others, assume independence
and use least-squares to estimate a traditional gravity that attempts to explain variation
in trade flows between regions using only GDP of the origin and destination regions and
distance between regions as explanatory variables. Trade interaction in the gravity relation
should be directly proportional to a product of regional size measures, with regional GDP
typically used to reflect economic size of the regions. Flows should be inversely related to
distance between regions and inclusion of this variable is thought to eliminate geographical
or spatial dependence in flows from nearby regions.
Anderson and van Wincoop (2004) provide a theoretical basis for this literature, and
noted that: “Gravity equations can be derived from a variety of different theories. None
lead to traditional gravity [...]” (p.706). In addition, Anderson and van Wincoop (2003)
argue that traditional least-squares estimates of the gravity equation produces estimates
that are biased due to omission of multilateral resistance terms. These resistance terms are
implicitly defined by a system of non-linear equations involving all regions’ GDP shares and
a global interdependence that is functionally related to trade costs.
A variety of approaches have been taken to estimating the gravity relationship in such
a way as to avoid the omitted variables bias arising from ignoring multilateral resistance
terms. These include a mixed numerical-statistical approach by Anderson and van Wincoop
(2003) that numerically solves for multilateral resistance terms in a first step and uses these
in the second step estimation procedure. A fixed effects regression approach was proposed
by Feenstra (2002, 2004) who relies on origin- and destination-specific fixed effects included
in the regression relationship to proxy multilateral resistance terms. Ranjan and Tobias
(2007) use semi-parametric effects in an application to international trade flows, where
the effects are modeled as a function of an exogenous variable measuring bilateral trade
resistance between origin-destination dyads.
Our contribution is to show that a linearization of the non-linear system of equations
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