A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade

Rodolfo Metulini,Roberto Patuelli,Daniel Griffith

doi:10.3390/econometrics6010009

Abstract

Nonlinear estimation of the gravity model with Poisson-type regression methods has become popular for modelling international trade flows, because it permits a better accounting for zero flows and extreme values in the distribution tail. Nevertheless, as trade flows are not independent from each other due to spatial and network autocorrelation, these methods may lead to biased parameter estimates. To overcome this problem, eigenvector spatial filtering (ESF) variants of the Poisson/negative binomial specifications have been proposed in the literature on gravity modelling of trade. However, no specific treatment has been developed for cases in which many zero flows are present. This paper contributes to the literature in two ways. First, by employing a stepwise selection criterion for spatial filters that is based on robust (sandwich) p-values and does not require likelihood-based indicators. In this respect, we develop an ad hoc backward stepwise function in R. Second, using this function, we select a reduced set of spatial filters that properly accounts for importer-side and exporter-side specific spatial effects, as well as network effects, both at the count and the logit processes of zero-inflated methods. Applying this estimation strategy to a cross-section of bilateral trade flows between a set of 64 countries for the year 2000, we find that our specification outperforms the benchmark models in terms of model fitting, both considering the AIC and in predicting zero (and small) flows.

Highlights

A traditional gravity model describing trade in its simple form asserts that the volume of trade between a country pair is proportional to the product of their gross domestic products and inversely related to a measure of distance separating them, where distance is broadly defined as a function of several variables that can be viewed as trade resistance factors
The log-linear specification of the gravity model along with ordinary least squares (OLS) estimation has been widely used in the empirical literature, mostly because of its good empirical performance and, in later years, for the strong theoretical foundations provided in papers such as Anderson (1979) and Anderson and Wincoop (2003)
We focus on an eigenvector spatial filtering (ESF) approach (Griffith 2003), within a Zero-inflated specifications of Poisson models (ZIP)

Summary

Introduction

A traditional gravity model describing trade in its simple form asserts that the volume of trade between a country pair is proportional to the product of their gross domestic products and inversely related to a measure of distance separating them, where distance is broadly defined as a function of several variables that can be viewed as trade resistance factors. A “structural break” in applied trade modelling is represented by the work of Santos Silva and Tenreyro (2006), who show that log-linearization of the gravity model leads to inconsistent estimates in the presence of heteroscedasticity in trade. Econometrics 2018, 6, 9 levels (and because of Jensen’s inequality). They propose a Poisson-type specification of the gravity model along with a Poisson pseudo-maximum likelihood (PPML) estimator, somehow to the Poisson approach proposed much earlier by Flowerdew and Aitkin (1982). Santos Silva and Tenreyro (2006, 2011) provide simulation evidence that the PPML estimator is well-behaved even when the conditional variance is far from being proportional to the conditional mean. Several studies in trade have since applied the PPML estimator (see Linders et al 2008; Martin and Pham 2015; Burger et al 2009; Martínez-Zarzoso 2013)

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Conclusion