Labor Market Dynamics with Sorting

I propose a frictional search model of the labor market with worker and firm heterogeneity, sorting, and aggregate uncertainty. My main contribution is to show that labor market sorting, arising from a production complementarity between worker skills and firm productivities, can improve our understanding of the cyclical dynamics of the labor market. The model incorporates two new quantitatively important transmission channels. First, the model endogenously generates a wage rigidity of an empirically reasonable magnitude. Second, the firms form expectations about the endogenous distribution of unemployed worker types and the match surplus. The surplus function and distributions change with the aggregate state, which leads to the amplification of shocks. The model is calibrated to produce realistic degrees of wage dispersion and sorting. I propose a numerical procedure to keep track of the model’s complex state space. Labor market sorting considerably propagates the model’s response to shocks and brings it on par with empirical moments of labor market data, including vacancy dynamics.