Efficient Semiparametric Instrumental Variable Estimation under Conditional Heteroskedasticity

We consider the estimation of a semiparametric regression model where the data is independently and identically distributed. Our primary interest is the estimation of the parametric vector, where the associated regressors are correlated with the errors, contain both continuous and discrete variables, and the error term is conditionally heteroskedastic. Under general conditional heteroskedasticity that depends on both excluded and included exogenous variables, we propose a new estimator based on Yao and Zhang’s (2011, Efficient semiparametric instrumental variable estimation, working paper, Economics Department, West Virginia University) framework and establish its asymptotic properties. It is consistent and asymptotically normally distributed. It allows the reduced form to be nonparametric and is efficient as it reaches the semiparametric efficiency bound. Furthermore, it is asymptotically equivalent to a GMM estimator that optimally select the instrumental variables with conditional moment restriction, and thus is also efficient among a class of semiparametric IV estimators. We perform a Monte Carlo study, which illustrates its finite sample properties and confirms our theoretical result.