This paper develops and implements semiparametric methods for estimating binary response (binary choice) models with continuous endogenous regressors. It extends existing results on semiparametric estimation in single-index binary response models to the case of endogenous regressors. It develops a "control function" approach to account for endogeneity in triangular and fully simultaneous binary response models. The proposed estimation method is applied to estimate the income effect in a labour market participation problem using a large micro data-set from the British Family Expenditure Survey. 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. Copyright 2004 The Review of Economic Studies Ltd.
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