Block Recursive Equilibria for Stochastic Models of Search on the Job

In this paper, we develop a general stochastic model of directed search on the job. Analogous to models of random search on the job, the state of the economy in our model includes the infinite-dimensional distribution of workers across different employment states (unemployment, and employment at different wages). Unlike the models of random search on the job, our model admits an equilibrium in which agents' value and policy functions do not depend on the distribution of workers. We refer to this type of equilibrium as a Block Recursive Equilibrium (BRE). Therefore, while solving the equilibrium of a random search model in a stochastic environment is a difficult task both analytically and computationally, solving the Block Recursive Equilibrium of our model is as easy as solving a representative agent model. We prove existence of a BRE under various specifications of workers' preferences and contractual environments, including dynamic contracts and fixed-wage contracts.