Structural Constrained ANOVA-type Estimation of Gravity Panel Data Models

In most gravity model applications, general equilibrium effects are disregarded altogether or ”controlled for” by country or country-time fixed effects, and the parameter estimates on observable trade cost variables are falsely interpreted as reduced-form marginal effects rather than only direct effects of such variables on trade. This paper proposes an empirical approach which employs panel data and, apart from bilateral trade data, employs fixed country-pair effects and fixed country-time effects only. Parameters are estimated by Poisson pseudo-maximum likelihood, imposing structural constraints that ensure alignment of estimation with theory. This approach represents a large class of trade models in both estimation and comparative static analysis. Mainly due to the presence of country-pair fixed effects, the framework exhibits a high explanatory power which considerably exceeds the one of traditional models that are based on observable trade cost variables. In a panel data-set of bilateral trade among OECD countries, the correlation coefficient between the model predictions and the data amounts to 0.96. We illustrate how general equilibrium consistent comparative static analysis can be conducted, and how the results compare with non-structural direct effects.