Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Abstract

This paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables. We show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed. The asymptotic normality result holds in both mildly and severely ill-posed cases. We present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values. Monte Carlo experiments illustrate the finite-sample performance of the uniform confidence band.