Simple Estimators for Binary Choice Models with Endogenous Regressors

This paper provides simple estimators for binary choice models with endogenous or mismeasured regressors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can be used with limited, censored, continuous, or discrete endogenous regressors, and they also allow for latent errors having heteroskedasticity of unknown form, including random coefficients. The variants of special regressor based estimators we provide are numerically trivial to implement. We illustrate these methods with an empirical application estimating migration probabilities within the US.