The deep deterioration in the labor market during the Great Recession, the subsequent slow recovery, and the missing disinflation are hard to reconcile for standard macroeconomic models. We develop and estimate a New-Keynesian model with financial frictions, search and matching frictions in the labor market, and endogenous intensive and extensive labor supply decisions. We conclude that the estimated combination of the low degree of nominal wage rigidities and high degree of real wage rigidities, together with the small role of pre-match costs relative to post-match costs, are key in successfully forecasting the slow recovery in unemployment and the missing disinflation in the aftermath of the Great Recession. We find that endogenous labor supply data are very informative about the relative degree of nominal and real wage rigidities and the slope of the Phillips curve. We also find that none of the model-based labor market gaps are a sufficient statistic of labor market slack, but all contain relevant information about the state of the economy summarized in a new indicator for labor market slack we put forward.