with Rodrigo Adao and Sharat Ganapati

How does firm heterogeneity affect the aggregate consequences of international trade shocks? In the workhorse monopolistic competition model, we show that the distribution of firm fundamentals affects aggregate equilibrium outcomes only through the shape of two univariate functions of the exporter firm share. These functions determine semiparametric gravity equations for the extensive and intensive margins of firm exports, yielding bilateral elasticities of trade flows to trade costs that vary with the exporter firm share. We show that the shape of these elasticity functions is sufficient to compute (i) counterfactual changes in aggregate outcomes and (ii) expressions for welfare gains. We estimate these elasticity functions using the model-implied semiparametric gravity equations of firm exports. Our estimates imply that bilateral trade is less sensitive to trade shocks when the exporter firm share is high. Firm heterogeneity leads to a 15% change in the gains from trade (compared to the constant elasticity gravity benchmark) that are higher in countries with a higher exporter firm share.

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