Repeated Moral Hazard with Worker Mobility via Directed On-the-Job Search

I develop a model of dynamic employment contracts by integrating an optimal contracting problem into an equilibrium search framework. The proposed framework enables us to analyze the interaction between the contracting problem and the endogenously evolving outside environment via worker mobility, and I characterize the optimal long-term wage contract as well as the optimal incentive compatible effort-tenure profile. The optimal contract exhibits an increasing wage-tenure profile for two reasons: 1) it induces the workers to be more likely to stay in their current contracts, and 2) it can induce the workers to make efforts when the current up-front wages cannot. The optimal incentive-compatible effort also has an increasing profile due to an interaction between 1) the workers' fear of losing their jobs, and 2) their incentive to obtain better outside offers. I then show the existence of an equilibrium. The equilibrium inherits the ``block recursivity'' developed by Shi (2008) and Menzio and Shi (2008); that is, individuals' optimal decisions and optimal contracts are independent of the distribution of workers.