Stock-flow matching

We develop the implications of the stock-flow matching model for unemployment, vacancies, and worker flows. Workers and jobs are heterogeneous, so most worker-job pairs cannot profitably match, leading to the coexistence of unemployment and vacancies. Productivity shocks cause fluctuations in the number of jobs, which in turn cause fluctuations in other labor market variables. We derive exact expressions for employment and for worker transition rates in a finite economy and analyze their limiting behavior in a large economy. A calibrated version of the model is consistent with the observed co-movement and volatility of labor market variables.