Oxford’s Alberto Behar and Ben Nelson are working to build a really rigorous trade gravity model. They combine Anderson and van Wincoop’s general equilibrium multilateral resistance approach with Helpman, Melitz, and Rubinstein’s emphasis on firm heterogeneity and the extensive margin.

We argue that one needs to take both AvW and HMR’s findings into account, otherwise interpretation of the effects of trade frictions will be misleading. We therefore unite these two strands of the literature. We derive a theoretically grounded gravity equation and then extend a method of approximating MR [multilateral resistance] terms, developed by Baier and Bergstrand (2009), to the case of firm heterogeneity…

For all our observations, traditional linear estimates bias downwards the effect of observable trade barriers on country-level trade flows. This difference, rather than the firm-level bias in the opposite direction highlighted by HMR, is arguably more relevant for policy…

Consistent with AvW’s “Implication 1”, larger countries have larger firm-level elasticities of bilateral trade in response to multilateral changes in trade costs. However we show that, once firm entry into trade is accounted for, this is no longer unambiguously true in theory for overall elasticities at the country level. Moreover, on balance we find a negative correlation in the data between country size and bilateral trade elasticities once changes in the extensive margin are accounted for.