Betting on Exports: Trade and Endogenous Heterogeneity

We study the determinants of firm-level heterogeneity in a model where innovation choices upon entry affect the variance of productivity draws. In equilibrium, productivity is Pareto distributed with a shape parameter that depends on industry-level characteristics. We show that export opportunities, by increasing the pay-offs in the tail, induce firms to invest in bigger projects with more dispersed outcomes. When more productive firms pay higher wages, trade amplifies wage dispersion by making firms more unequal. These results are consistent with how firm size, innovation and wage heterogeneity vary in a panel of US industries and states.