This paper considers the estimation of binary choice panel data models with discrete endogenous regressors. We present a switching probit model which accounts for selectivity bias as well as for other forms of time invariant unobserved heterogeneity. Individual effects are allowed to be correlated with the explanatory variables, which can be predetermined as opposed to strictly exogenous. This model is applied to estimate a female participation equation with endogenous fertility and predetermined existing children and with individual effects using PSID data. We use the family sex composition as an instrument for exogenous fertility movements. The results indicate that assuming the exogeneity of fertility induces a downward bias in absolute value in the estimated negative effect of fertility on participation, although the failure to account for unobserved heterogeneity exaggerates this effect. Moreover, the estimates that deal with the endogeneity of fertility and control for fixed effects, but treat existing children as strictly exogenous produce a smaller effect of fertility than those obtained treating this variable as predetermined.
Binary choice Panel data Endogenous variables Predetermined variables Labour force participation Fertility