Seminar

Optimal Uniform Convergence Rates, Adaptive Estimation, and Inference for Nonparametric Instrumental Variables Estimation

Timothy Christensen (New York University)

November 18, 2014, 15:30–17:00

Room MS 001

Econometrics and Empirical Economics Seminar

Abstract

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) estimation in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We contribute to the NPIV literature as follows. First, we establish an upper bound on the uniform (i.e. sup-norm) convergence rates of sieve NPIV estimators. We then derive the minimax lower bound in sup-norm loss and show that spline and wavelet sieve NPIV estimators can achieve the optimal sup-norm rates. Second, we introduce a data-driven procedure for choosing the sieve dimension. Our procedure is adaptive in the sense that spline and wavelet sieve NPIV estimators that use the data-driven choice can attain their optimal sup-norm rates. Third, we establish uniform limit theory for plug-in estimators and sieve t-statistics of nonlinear functionals of the unknown structural function under mild conditions. To illustrate the usefulness of our results, we derive asymptotically exact uniform confidence bands for nonlinear functionals of the unknown structural function. Finally, we discuss application of our results to nonparametric estimation of exact consumer surplus allowing for endogeneity of prices and incomes. With Xiaohong Chen (Yale).