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 se- lected from a general distribution, subject to some weak regularity require- ments, and the firms direct their job offers to workers. We identify conditions under which some fraction of the workforce will be "unemployable": no firm will approach them even though they offer positive surplus. For large mar- kets 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 unemployable workers, and a measure of heterogeneity (κ).The equilibrium unemployment rate is increasing in κ and, under cer- tain circumstances, is increasing in the productivity of highly skilled workers, despite endogenous entry. A key empirical prediction of the theory is that κ ≥ 1. We examine this prediction, using data from several countries.