Identification and estimation using heteroscedasticity without instruments

Abstract

Lewbel (2012) provides an estimator for linear regression models containing an endogenous regressor, when no outside instruments or other such information is available. The method works by exploiting model heteroscedasticity to construct instruments using the available regressors. Some authors have considered the method in empirical applications where an endogenous regressor is binary (e.g., endogenous Diff-in-Diff or endogenous binary treatment models), without proving validity of the estimator in that case. The present paper shows that the assumptions required for Lewbel's estimator can indeed be satisfied when an endogenous regressor is binary.