Increasing marginal costs, firm heterogeneity, and the gains from “deep” international trade agreements

Two parameters are central to modern quantitative models of trade flows: the elasticity of substitution in consumption (σ) and the inverse index of heterogeneity of firms' productivities (θ). However, structural parameter estimation using the seminal Feenstra econometric methodology focuses on estimates of only σ and a bilateral export-supply elasticity (labeled γ). Separately, modern trade agreements are increasingly “deep,” meaning they reduce fixed trade costs alongside variable trade costs. First, in the spirit of Arkolakis (2010), we extend the Melitz model of trade to allow for increasing marginal market-penetration costs in an empirically tractable manner to help understand 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 methodology alongside a gravity equation. Third, we demonstrate the importance of increasing marginal costs for shallow and deep trade-agreement liberalizations using two counterfactual exercises.