Latent Multilateral Trade Resistance Indices: Theory and Evidence

DOIhttp://doi.org/10.1111/sjpe.12074
Date01 July 2015
Published date01 July 2015
LATENT MULTILATERAL TRADE
RESISTANCE INDICES: THEORY
AND EVIDENCE
Wilfried Koch* and James P. LeSage**
ABSTRACT
Anderson and van Wincoop (American Economic Review (2003), 69:106)
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 sta-
tistical approach that has advantages over the non-stochastic numerical
approach used by Anderson and van Wincoop (2003) to solve for these
indices.
II
NTRODUCTION
Past literature on empirical modeling of trade flows using gravity models
relies on least-squares estimates, which assume the dependent variable
observations representing trade flows from all regions ito all other regions
jare 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 relation 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, and flows should be inversely related to distance between
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
*Universit
eduQu
ebec
a Montr
eal and CIRP
EE
**Texas State University
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12074, Vol. 62, No. 3, July 2015
©2015 Scottish Economic Society.
264
different theories. None lead to traditional gravity [...]’ (p. 706). In addition,
Anderson and van Wincoop (2003) argue that traditional least-squares esti-
mates of the gravity equation are biased due to the 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 interde-
pendence that is functionally related to trade costs.
A variety of approaches have been taken to estimating the gravity relation-
ship 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 parameters included in the regression relationship to proxy multilateral
resistance terms. Ranjan and Tobias (2007) use semi-parametric effects param-
eters in an application to international trade flows, where the effects parame-
ters 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 around a free trade world leads to a set of theoretically determined
inward and outward multilateral resistance indices. These latent unobservable
resistance parameters exhibit an implicit structure of dependence that we use
as the basis for a Bayesian prior structure to produce estimates of the latent/
unobservable resistance indices.
A secondary contribution is to show that our model subsumes that of Feen-
stra (2002, 2004) that relies on origin- and destination-specific fixed effects
parameters included in the regression relationship to proxy multilateral resis-
tance terms, and Ranjan and Tobias (2007) where the effects parameters are
modeled as a (semi-parametric) function of an exogenous variable measuring
bilateral trade resistance between origin-destination dyads. We argue that all
of these models relax multilateral aspects of the dependence structure in favor
of bilateral dependence, or a specification based on heterogeneity rather than
simultaneous/multilateral dependence. This may be important since Behrens
et al. (2012), indicate that models/specifications that control for regional/
observational heterogeneity do not necessarily capture the full structure of
interdependence between trade flows implied by theory. They derive a ‘ dual’
version of the Anderson and van Wincoop (2003) model using a model based
on quantity competition that also implies a simultaneous structure of interde-
pendence between observed trade flows.
Section II sets forth a derivation of the gravity equation from a CES expen-
ditures system following work of Anderson and van Wincoop (2003), while
Section III turns attention to the econometric specification. An empirical
application to a sample of 2004 trade flows between 80 countries is described
in Section IV along with a demonstration of the implications of a change in
trade openness arising from the simultaneous dependence structure of multi-
lateral resistance.
LATENT MULTILATERAL TRADE RESISTANCE INDICES 265
Scottish Journal of Political Economy
©2015 Scottish Economic Society

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