Increasing Marginal Costs, Firm Heterogeneity, and the Gains from “Deep” International Trade Agreements

Two parameters are central to several modern quantitative models of bilateral international trade flows: the elasticity of substitution in consumption (σ) and the inverse index of heterogeneity of firms’ productivities (θ). However, structural parameter estimation applications using the seminal Feenstra econometric methodology typically focus on estimates of only σ and a bilateral export supply elasticity – which we will term γ. Separately, modern trade agreements are increasingly “deep,” meaning they reduce fixed trade costs alongside variable trade costs (such as tariffs). Although Melitz models of international trade recognize both trade costs theoretically, very little is known quantitatively about their relative impacts on trade and welfare. In this paper, we offer three contributions. First, in the spirit of Arkolakis (2010), we extend the canonical Melitz model of trade to allow for increasing marginal market-penetration costs, alongside fixed marketing costs, to show theoretically the importance of accounting for increasing marginal costs (via γ) – in the presence of firm heterogeneity – in understanding the relative impacts on trade, extensive margins, intensive margins, and welfare of reducing fixed trade costs and variable trade costs. Second, we provide a microeconomic foundation for estimating all three parameters using the Feenstra econometric methodology alongside a gravity equation. Third, we demonstrate the importance of increasing marginal costs using two counterfactual exercises. One illustrative quantitative implication for U.S. trade policy is that, under (empirically rejected) constant marginal costs, fixed trade costs would have to be reduced by 57 percent for a welfare-equivalent reduction in variable trade costs of 3 percent; by contrast, under (empirically supported) increasing marginal costs, fixed trade costs would have to be reduced by only 14 percent.