This paper shows that the matching function and the Beveridge curve in the United States exhibit strong nonlinearities over the business cycle. These patterns can be replicated by enhancing a search and matching model with idiosyncratic productivity shocks for new contacts. Large negative aggregate shocks move the hiring cutoff point into a part of the idiosyncratic density function with higher density and thereby generate large, asymmetric job-finding rate and unemployment reactions. Our proposed mechanism is of high relevance as it leads to time varying effects of certain policy interventions.