Structural Gravity with Dummies Only

The measurement of trade costs and their effects on outcome is at the heart of a large quantitative literature in international economics. The majority of the recent significant contributions on the matter assumes that trade consists of a product of exporter-time-specific factors, importer-time-specific factors, and country-pair-time-specific trade costs, and that log trade costs are additively composed of a parameterized part and a residual part. We demonstrate that residual trade costs are relatively important and that the parameters on observable trade-cost measures as well as the structural country-time-specific variables or parameters are inevitably biased no matter of whether models are estimated by ordinary least-squares or by exponential-family models. The reason is that the country-specific variables are endogenous to the residual trade costs, regardless of whether they are captured by iteratively-solved structural terms or by country-time fixed effects. As a result, quantifications of effects of trade costs and comparative static results are also biased. Apart from diagnosing this problem, the paper provides remedies for it. All of the proposed remedies involve binary indicator variables (fixed effects) only, and they are nonlinear in both variables and parameters. We therefore dub these approaches as ones of a constrained analysis of variance (CANOVA) of bilateral exports or imports. We propose saturated as well as unsaturated versions of the CANOVA approach for both cross-section and panel data. The saturated approach uses up all degrees of freedom and estimates as many parameters as there are observations on bilateral exports or imports, providing an exact decomposition of bilateral trade into trade costs and country-specific parameters. The unsaturated approaches do not use up all degrees of freedom and estimate fewer parameters than there are observations on bilateral exports or imports, providing an approximate decomposition of bilateral trade into trade costs and country-specific parameters. We demonstrate that with panel data an unsaturated model with exporter-time, importer-time and country-pair effects works quite well relative to both the saturated model as well as models with parameterized trade-cost functions. The conclusions of the CANOVA models regarding the importance of trade costs for trade turn out to be substantially different from the ones implied by the conventional parameterized trade-cost-function models