We show that a general class of frictional labor market models with a participation margin and an individual-specific state can only match labor market transition rates within a certain range, which we characterize analytically. Transition rates in the data are outside the range the model can match, which explains the failure of previous papers to calibrate to these flows. We also examine whether extending the model can bring it closer to the data, and find that endogenous search intensity and state-dependent separation rates do not help, but misclassification, persistently inactive workers, and modifications of the productivity process such as learning on the job can match the gross flows.