Binary choice panel data models with predetermined variables

We present a class of binary choice models for panel data with the following features: (i) The explanatory variables are predetermined but not strictly exogenous. This includes lagged dependent variables as well as other forms of unspecified feedback. (ii) Individual effects are allowed to be correlated with the explanatory variables. Dependence is specified through the conditional expectation of the effects which is let to be non-parametric. We also present a GMM estimator for these models, which is consistent and asymptotically normal for fixed T and large N. We study its finite sample properties in an autoregressive model by means of Monte Carlo simulations. Finally, as an empirical illustration, we estimate a female labour force participation equation with predetermined children using PSID data.