Fixed Effects Binary Choice Models with Three or More Periods

Laurent Davezies; Xavier D'Haultfoeuille; Martin Mugnier

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arXiv · 2009.08108

Fixed Effects Binary Choice Models with Three or More Periods

Laurent Davezies·Xavier D'Haultfoeuille·Martin Mugnier

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Abstract

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).

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Laurent Davezies, Xavier D'Haultfoeuille, Martin Mugnier. 2022-09-29. Fixed Effects Binary Choice Models with Three or More Periods. https://arxiv.org/abs/2009.08108

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