Trade, Gravity, and Aggregation

Gravity equations are an important tool in empirical international trade research. We study to what extent sector-level parameters can be recovered from aggregate gravity equations estimated via Poisson pseudo maximum likelihood. We show that in the leading case where trade cost regressors do not vary at the sector level, estimates obtained with aggregate data have a clear interpretation as a weighted average of sectoral elasticities. Otherwise the estimates are biased, but researchers may possibly infer the direction of the bias. We illustrate our results by revisiting Baier and Bergstrand's (2007) influential study of the effects of free trade agreements.