On the inefficiency of matching models of unemployment with heterogeneous workers and jobs when firms rank their applicants

In a circular matching model with bargained wages, firms rank their applicants and pick the most suitable one. Job creation appears to lower the average output. As firms do not internalize this effect, there are too many jobs in a laissez-faire equilibrium under the Hosios condition. By contrast, job rejection is efficient for the equilibrium value of market tightness. Consequently, introducing unemployment compensation raises the aggregate income by lowering market tightness. Due to the isomorphism between the two models, these results extend to match-specific productivities. However, competitive search restores market efficiency.