We consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables, lags of the endogenous dependent variable as well as unobservable individual-specific effects. For the logit specification we propose an estimator that is consistent and asymptotically normal, although its rate of convergence is slower than the inverse of the square root of the sample size. In the semiparametric case the proposed estimator is shown to be consistent. The finite sample properties of the proposed estimators are investigated in a small Monte Carlo simulation study.