Uniform confidence bands for functions estimated nonparametrically with instrumental variables

Abstract. This paper is concerned with developing uniform con-fidence bands for functions estimated nonparametrically with in-strumental variables. We show that a sieve nonparametric instru-mental 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 uni-form 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