We study the quantitative properties of trade equilibrium models with vertical differentiation and heterogeneous goods. We propose a model of vertical differentiation with many heterogeneous goods and many countries. Each country produces a continuous set of differentiated goods, and each good is vertically differentiated with a high- and a low- quality version. We focus on a class of costs and preferences for goods with two quality versions that makes expenditures linear in terms of the marginal utility of income and therefore keeps the general equilibrium model highly tractable. To focus on the effect of product quality, we isolate the effect of extensive margins.
We express a gravity equation that relates exports to trade costs, wages and populations and remoteness indices. The main contribution lies in the estimation of this new model on OECD countries. We estimate the bilateral trade costs, labor prices and average costs of quality upgrades. We use the estimated coefficient of the gravity equation to recover general equilibrium parameters. We recover quality parameters from the estimation of the production costs. This allows us to quantify the effect of trade costs, terms of trade, population sizes, local productivity and local income on the quality margins and welfare.