This paper shows analytically and numerically that there are two ways of generating an observationally equivalent comovement between matches, unemployment, and vacancies in dynamic labor market models: either by assuming a standard Cobb-Douglas contact function or by combining a degenerate contact function with idiosyncratic productivity shocks for new jobs. Despite this observational equivalence, we provide several reasons for why it is important to understand what happens inside the black box of job creation. We calibrate a combined model with both mechanisms to administrative German wage and labor market flow data. In contrast to the model without idiosyncratic shocks, the combined model is able to replicate the observed negative time trend in estimated matching functions. In addition, the full nonlinear combined model generates highly asymmetric business cycle responses to large aggregate shocks.