A simple alternative to the linear probability model for binary choice models with endogenous regressors

Dong and Lewbel have developed the theory of simple estimators for binary choice models with endogenous or mismeasured regressors, depending on a “special regressor” as defined by Lewbel (Journal of Econometrics, 2000). These estimators can be used with limited, censored, continuous, or discrete endogenous regressors and have significant advantages over the linear probability model. These estimators are numerically straightforward to implement. We present and demonstrate an improved version of a Stata routine that provides both estimation and postestimation features, and we give a simple example where the linear probability model fails to estimate any useful quantity.