- 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, Chamberlianin (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.
- A Note on the Existence of Conditional Maximum Likelihood Estimates of the Binary Logit Model with Fixed Effects
By exploiting McFadden (1974)'s results on conditional logit estimation, we show that there exists a one-to-one mapping between existence and uniqueness of conditional maximum likelihood estimates of the binary logit model with fixed effects and the spatial configuration of data points. Our results extend those in Albert and Anderson (1984) for the cross-sectional case and can be used to build a simple algorithm that detects spurious estimates in finite samples. Importantly, we show an instance from artificial data for which the STATA's command clogit returns spurious estimates.