Identification and estimation of heteroscedastic binary choice models with endogenous dummy regressors

In this paper, we consider the semiparametric identification and estimation of a heteroscedastic binary choice model with endogenous dummy regressors and no parametric restriction on the distribution of the error term. Our approach addresses various drawbacks associated with previous estimators proposed for this model. It allows for: general multiplicative heteroscedasticity in both selection and outcome equations; a nonparametric selection mechanism; and multiple discrete endogenous regressors. The resulting three‐stage estimator is shown to be asymptotically normal, with a convergence rate that can be arbitrarily close to n−1/2 if certain smoothness assumptions are satisfied. Simulation results show that our estimator performs reasonably well in finite samples. Our approach is then used to study the intergenerational transmission of smoking habits in British households.