Efficient Search on the Job and the Business Cycle

We build a directed search model of the labor market in which workers' transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states affects neither the agents' values and strategies nor the market tightness. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large countercyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies.