Endogenous Heteroskedasticity in Linear Models

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