  We consider fixed effects binary choice models with a fixed number of periods
$T$ and regressors without a large support. If the time-varying unobserved
terms are i.i.d. with known distribution $F$, \cite{chamberlain2010} shows that
the common slope parameter is point identified if and only if $F$ is logistic.
However, he only considers in his proof $T=2$. We show that the result does not
generalize to $T\geq 3$: the common slope parameter can be identified when $F$
belongs to a family including the logit distribution. Identification is based
on a conditional moment restriction. Under restrictions on the covariates,
these moment conditions lead to point identification of relative effects. If
$T=3$ and mild conditions hold, GMM estimators based on these conditional
moment restrictions reach the semiparametric efficiency bound. Finally, we
illustrate our method by revisiting Brender and Drazen (2008).
