Directed Search for Equilibrium Wage-Tenure Contracts

I analyze the equilibrium in a labor market where firms offer wage-tenure contracts to direct the search of employed and unemployed workers. Each applicant observes all offers and there is no coordination among individuals. Workers' applications (as well as firms' recruiting decisions) are optimal. This optimality requires the equilibrium to be formulated differently from the that in the literature of undirected search. I provide such a formulation and show that the equilibrium exists. In the equilibrium, individuals explicitly tradeoff between an offer and the matching rate at that offer. This tradeoff yields a unique offer which is optimal for each worker to apply, and applicants are separated endogenously according to their current values. Despite such uniqueness and separation, there is a non-degenerate and continuous wage distribution of employed workers in the stationary equilibrium. The density of this distribution is increasing at low wages and decreasing at high wages. In all equilibrium contracts, wages increase with tenure, which results in quit rates to decrease with tenure. Moreover, the model makes novel predictions about individuals' job-to-job transition and comparative statics.