This paper assesses how various approaches to modeling the separation margin affect the ability of the Mortensen-Pissarides job matching model to explain key facts about the aggregate labor market. Allowing for realistic time variation in the separation rate, whether exogenous or endogenous, greatly increases the unemployment variability generated by the model. Specifications with exogenous separation rates, whether constant or time-varying, fail to produce realistic volatility and productivity responsiveness of the separation rate and worker flows. Specifications with endogenous separation rates, on the other hand, succeed along these dimensions. In addition, the endogenous separation model with on-the-job search yields a realistic Beveridge curve correlation and performs well in accounting for the productivity responsiveness of market tightness. While adopting the Hagedorn-Manovskii calibration approach improves the behavior of the job finding rate, the volume of job-to-job transitions in the on-the-job search specification becomes essentially zero.