Discussion Paper
Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation
This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of the structural function h0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h0 and its derivatives when h0 is approximated via a spline or wavelet sieve.