Block recursive equilibria for stochastic models of search on the job

We develop a general stochastic model of directed search on the job. Directed search allows us to focus on a Block Recursive Equilibrium (BRE) where agents' value functions, policy functions and market tightness do not depend on the distribution of workers over wages and unemployment. We formally prove existence of a BRE under various specifications of workers' preferences and contractual environments, including dynamic contracts and fixed-wage contracts. Solving a BRE is as easy as solving a representative agent model, in contrast to the analytical and computational difficulties in models of random search on the job.