Many labor market models use both idiosyncratic productivity and a vacancy free entry condition. This paper shows that these two features combined generate an equilibrium comovement between matches on the one hand and unemployment and vacancies on the other hand, which is observationally equivalent to a constant returns Cobb-Douglas function commonly used to model match formation. We use German administrative labor market data to show that the matching function correlation solely based on idiosyncratic productivity and free entry is very close to the empirical matching function. Consequently, we argue that standard matching function estimations are seriously biased if idiosyncratic productivity plays a role for match formation. In this case, they are not suitable for the calibration of labor market models.