Endogenous Heteroskedasticity in Linear Models

Abstract: Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous regressors-i.e., endogenous heteroskedasticity. We show that the presence of endogenous heteroskedasticity in the structural regression renders the two-stage least squares estimator inconsistent. To address this issue, we propose sufficient conditions and a control function approach to identify and estimate the causal parameters of interest. We establish the limiting properties of the estimator--namely, consistency and asymptotic normality--and propose inference procedures. Monte Carlo simulations provide evidence on the finite-sample performance of the proposed methods and evaluate different implementation strategies. We revisit an empirical application on job training to illustrate the methods.