This paper introduces quality innovations with endogenous sunk costs in a heterogeneous firm model of international trade and derives implications for the gravity equation. The model predicts that the effect of fixed costs on exports and on the share of exporters is lower in industries with a higher degree of vertical product differentiation. We use both aggregate trade data and firm-level data to estimate gravity equations and find strong evidence for a dampening effect of vertical differentiation on the fixed costs elasticity in international trade. Moreover, we estimate the parameters of our model and simulate the effects of a reduction in fixed trade barriers. Accounting for quality lowers the positive gains from trade and leads to more heterogeneous effects across industries compared to a trade model without quality investments. Consistent with our theory, vertical differentiation affects exports via sunk costs and the extensive margin, whereas the effect of variable trade costs does not depend on quality.
international trade heterogeneous firms gravity product quality