A Simple Estimator for Binary Choice Models with Endogenous Regressors

This paper provides a few variants of a simple estimator for binary choice models with endogenous or mismeasured regressors, or with heteroskedastic errors, or with panel fixed effects. 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 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.