Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors

Previous estimators of binary choice panel data models with fixed effects require strong parametric error asumptions, strictly exogeneous regressors, or both. This is because nonlinearity of the model precludes the use of the "moment conditions on differences" based estimators that are generally employed for linear models without strictly exogeneous regressors. Based on the cross section binary choice estimator in Lewbel (2000a), we show how discrete choice panel data models with fixed effects can be estimated with only predetermined regressors. The estimator is semiparametric in that the error distribution is not specified, it allows for some general forms of heteroskedasticity, and converges at rate root n.