The Employed, the Unemployed, and the Unemployable: Directed Search with Worker Heterogeneity

We examine the implications of worker heterogeneity on the equilibrium matching process, using a directed search model. Worker abilities are selected from a general distribution, subject to some weak regularity requirements, and the firms direct their job offers to workers. For large markets we derive a simple closed form expression for the equilibrum matching function. This function has constant returns to scale and two new terms, which are functions of the underlying distribution of worker productivities: the percentage of workers who are employable, and a measure of heterogeneity (kappa). The equilibrium unemployment rate is increasing in kappa and, under certain circumstances, is increasing in the productivity of highly skilled workers, despite endogenous entry.