- Fixed Effects Binary Choice Models with Three or More Periods (with Xavier D'Haultfœuille and Laurent Davezies), submitted.
We consider fixed effects binary choice models with a fixed number of periods T and without a large support condition on the regressors. If the time-varying unobserved terms are i.i.d. with known distribution F, Chamberlain (2010) shows that the common slope parameter is point-identified if and only if F is logistic. However, he considers in his proof only T=2. We show that actually, the result does not generalize to T>2: the common slope parameter and some parameters of the distribution of the shocks can be identified when F belongs to a family including the logit distribution. Identification is based on a conditional moment restriction. We give necessary and sufficient conditions on the covariates for this restriction to identify the parameters. In addition, we show that under mild conditions, the corresponding GMM estimator reaches the semiparametric efficiency bound when T=3.