ASYMPTOTIC NORMALITY OF A NONPARAMETRIC INSTRUMENTAL VARIABLES ESTIMATOR∗

This article gives conditions under which the nonparametric instrumental variables estimator of Hall and Horowitz (Annals of Statistics 33 (December 2005), 2904–2929) is asymptotically normally distributed. With sufficiently large samples, the asymptotic normality result can be used to form confidence intervals for the unknown function that is estimated by the Hall–Horowitz procedure. The article reports the results of a Monte Carlo investigation of the finite-sample coverage probabilities of the confidence intervals.