Structural gravity with dummies only: Constrained ANOVA-type estimation of gravity models

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 is log-linear in exporter-specific factors, importer-specific factors, and log trade costs that are additively composed of a parameterized part and a residual part. We demonstrate that, under standard assumptions in the literature, the magnitude of unobservable, residual trade costs is large, and that their ignorance leads to a bias of the importance of observable trade-cost measures as well as of country-specific variables that are either solved implicitly through structural estimation or estimated explicitly as fixed effects. The reason is that, due to general-equilibrium linkages, some country-specific variables are endogenous to 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 by proposing theory-consistent approaches including a two-step procedure that permits identifying partial effects of observable gravity variables on total trade costs and trade flows which do not suffer from the unobserved-trade-cost bias.