We examine how firm heterogeneity influences aggregate welfare through endogenous firm selection. We consider a homogeneous firm model that is a special case of a heterogeneous firm model with a degenerate productivity distribution. Keeping all structural parameters besides the productivity distribution the same, we show that the two models have different aggregate welfare implications, with larger welfare gains from reductions in trade costs in the heterogenous firm model. Calibrating parameters to key U.S. aggregate and firm statistics, we find these differences in aggregate welfare to be quantitatively important (up to a few percentage points of GDP). Under the assumption of a Pareto productivity distribution, the two models can be calibrated to the same observed trade share, trade elasticity with respect to variable trade costs, and hence welfare gains from trade (as shown by Arkolakis, Costinot and Rodriguez-Clare, 2012); but this requires assuming different elasticities of substitution between varieties and different fixed and variable trade costs across the two models
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