We measure the role of firm heterogeneity in counterfactual predictions of monopolistic competition trade models without parametric restrictions on the distribution of firm fundamentals. We show that two bilateral elasticity functions are sufficient to nonparametrically compute the counterfactual aggregate impact of trade shocks, and recover changes in economic fundamentals from observed data. These functions are identified from two semiparametric gravity equations governing the impact of bilateral trade costs on the extensive and intensive margins of firm-level exports. Applying our methodology, we estimate elasticity functions that imply an impact of trade costs on trade flows that falls when more firms serve a market because of smaller extensive margin responses. Compared to a baseline where elasticities are constant, firm heterogeneity amplifies both the gains from trade in countries with more exporter firms, and the welfare gains of European market integration in 2003-2012.
How do shocks to economic fundamentals in the world economy affect local labor markets? In a framework with a flexible structure of spatial linkages, we characterize the model-consistent shock exposure of a local market as the exogenous shift in its production revenues and consumption costs. In general equilibrium, labor outcomes in any market respond directly to the market’s own shock exposure, and indirectly to other markets shocks exposures. We show how spatial linkages control the size and the heterogeneity of these indirect effects. We then develop a new estimation methodology - the Model-implied Optimal IV (MOIV) - that exploits quasi-experimental variation in economic shocks to estimate spatial linkages and evaluate their counterfactual implications. Applying our methodology to US Commuting Zones, we find that difference-in-difference designs based on model-consistent measures of local shock exposure approximate well the differential effect of international trade shocks across CZs, but miss around half of the aggregate effect, partly due to the offsetting action of indirect effects.