Estimating the gains from trade in frictional local labor markets

We develop a theory and an empirical strategy to estimate the welfare gains of economic integration in economies with frictional local labor markets. The model yields a welfare formula that nests previous results in the literature and features an additional adjustment margin, via the employment rate, that generates new insights. We show that the quantitative impact of this new channel depends on the goods market structure and on the degree of firm heterogeneity. To obtain causal estimates of the two key structural parameters needed for the welfare analysis, the trade elasticity and the elasticity of substitution in consumption, we propose a theoretically-consistent identification strategy that exploits exogenous variation in production costs driven by differences in industrial composition across local labor markets. As an application, we exploit Germany's rapid trade integration with China and Eastern Europe between 1988 and 2008 to assess the quantitative importance of accounting for unemployment changes when computing the gains from trade across local labor markets in West Germany. Under monopolistic competition with free entry and firm heterogeneity, the median welfare gains in the frictional setting are 6% larger relative to the frictionless setting. The relative welfare gains are typically more modest under alternative market structures.