This paper develops and implements semiparametric methods for estimating binary response (binary choice) models withcontinuous endogenous regressors. It extends the existing literature on semiparametric estimation in single index binary response models to the case of endogenous regressors.
It develops a control function approach to accounting for endogeneity in triangularand fully simulataneous binary response models. An application is given to the case of estimating the income effect in a labor market participationproblem using a large micro data set from the British FES. The semiparametric estimator is found to perform well detecting a significant attenuation bias. The proposed estimator is contrasted to the corresponding Probit and Linear Probability specifications.