Abstract: We study a labor market where workers search for jobs both on the job and off the job. In the model, there are aggregate productivity shocks and match-specific shocks. We outline the proof of existence of an equilibrium which we call a block recursive equilibrium (BRE), in which individuals' decisions and market tightness are independent of the distribution of workers over wages or contracts. A critical assumption that is responsible for a BRE to exist is that search is directed by firms' posting of contracts. We explain why a BRE does exist under the assumption of directed search and why it does not under the assumption of random search. Finally, we generalize the proof of existence of a BRE to allow workers to be ex-ante heterogeneous with respect to some observable characteristics such as education and skill.
Keywords: Directed Search; On the Job Search; Heterogeneity; Aggregate Fluctuations
JEL Classification: E24; E32; J64