Conditional inference for binary panel data models with predetermined covariates

A fixed-effects logit model that accounts for feedback effects of the dependent variable on the covariates is proposed. The model is formulated by including leads of the predetermined covariates among the regressors and it is proved to satisfy certain theoretical properties under some regularity conditions on the distribution of the covariates. Estimation is based on the Conditional Maximum Likelihood (CML) method for the static logit model and the Pseudo-CML (PCML) method for the corresponding dynamic formulation. Both methods have good finite-sample properties even when the required regularity conditions are not satisfied. An application is provided about female labor supply where we jointly account for the predetermined number of children and husbands’ income. Differently from previous studies, it emerges that female employment history does not affect future fertility choices and the husband's earnings, as no evidence of feedback effects is found.