Testing the binomial fixed effects logit model; with an application to female labor supply

Regression models for proportions are frequently encountered in applied work. The conditional expectation is bound between 0 and 1 and, therefore, must be non-linear which requires non-standard panel data extensions. The quasi-maximum likelihood estimator of Papke and Wooldridge (1996) suffers from the incidental parameters problem when including fixed effects. In this paper, we re-consider the binomial panel logit model with fixed effects (Machado, 2004). We show that the conditional maximum likelihood estimator is very easy to implement using standard software. We investigate the properties of the estimator under misspecification and derive a new test for overdispersion in the binomial fixed effects logit model. Models and test are applied in a study of contracted work-time percentage, measured as proportion of full-time work, for women in Switzerland.