This paper formulates and estimates an extension of the medium-scale labor matching model of Gertler and Trigari (2009) with endogenous separations, sticky prices, and sticky wages using postwar US data and an array of commonly-discussed shocks. Several results stand out. It appears that the baseline model and a number of other model specifications might be misspecified along the hiring margin; the model actually matches the job destruction margin fairly well. The model also faces a serious tradeoff: It can perform well at generating short-run volatility, or else it can match the negative relationship between inflation and employment in the long run. It cannot do both.s. Based on the timing of observed fluctuations in interest rates, inflation, and productivity, it appears that the vast majority of observed fluctuations in the real economy remain unexplained by standard real and nominal shocks.