This paper discusses the estimation of binary choice panel data models. We begin with different versions of the static random effects model when the explanatory variables are strictly exogenous. Depending on the autocorrelation structure of the errors, different estimators are available and we detail their attractiveness in each situation by trading-off their efficiency and robustness with respect to misspecification. Then, we consider the static model when a time invariant unobservable variable is correlated with the time varying explanatory variables. The non-linearity of binary choice models makes it pretty hard to eliminate individual fixed effects in likelihood functions and moment conditions, because the usual differencing out that works for the linear model does not work here except in special cases. Imposing quite restrictive assumptions is the price to pay to estimate consistently parameters of dynamics for fixed and random effects, in other words cases when the explanatory variables include lagged endogenous variables or are weakly exogenous only.
