Directed Search for Equilibrium Wage-Tenure Contracts

I construct a theoretical framework in which firms offer wage-tenure contracts to direct the search by risk-averse workers. All workers can search, on or off the job. I characterize an equilibrium and prove its existence. The equilibrium generates a non-degenerate, continuous distribution of employed workers over the values of contracts, despite that all matches are identical and workers observe all offers. A striking property is that the equilibrium is block recursive; that is, individuals' optimal decisions and optimal contracts are independent of the distribution of workers. This property makes the equilibrium analysis tractable. Consistent with stylized facts, the equilibrium predicts that (i) wages increase with tenure, (ii) job-to-job transitions decrease with tenure and wages, and (iii) wage mobility is limited in the sense that the lower the worker's wage, the lower the future wage a worker will move to in the next job transition. Moreover, block recursivity implies that changes in the unemployment benefit and the minimum wage have no effect on an employed worker's job-to-job transitions and contracts.