The paper develops a model of directed search on the job in which transitions of workers between unemployment and employment and across employers are driven by heterogeneity in the quality of firm-worker matches. The equilibrium is such that the agents’ value and policy functions are independent of the endogenous distribution of workers across employment states. Hence, the model can be solved outside of the steady state and used to measure the effect of cyclical productivity shocks on the labor market. Productivity shocks are found to generate large fluctuations in workers’ transitions, unemployment, and vacancies when matches are experience goods, but not when matches are inspection goods.

This paper studies the optimal redistribution of income inequality caused by the presence of search and matching frictions in the labor market. We study this problem in the context of a directed search model of the labor market populated by homogeneous workers and heterogeneous firms. The optimal redistribution can be attained using a positive unemployment benefit and an increasing and regressive labor income tax. The positive unemployment benefit serves the purpose of lowering the search risk faced by workers. The increasing and regressive labor tax serves the purpose of aligning the cost to the firm of attracting an additional applicant with the value of an application to society.