This paper shows two business cycle facts for the United States. First, the job-finding is very asymmetric over the business cycle and moves a lot more in recessions than in booms. Second, there is a positive correlation between the job-finding rate and the matching efficiency. We provide an explanation for both business cycle facts by enhancing a search and matching model with idiosyncratic shocks for match formation and by solving the full nonlinear structure of the model. Understanding the sources of these nonlinearities is very important. In our calibration, government interventions (such as wage subsidies and government spending) are three times more effective in a heavy recession than in a boom. In
addition, shifts of the matching efficiency are not necessarily a sign for higher structural unemployment.