Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV
Abstract
We introduce computationally simple, datadriven procedures for estimation and inference on a structural function $h_0$ and its derivatives in nonparametric models using instrumental variables. Our first procedure is a bootstrapbased, datadriven choice of sieve dimension for sieve nonparametric instrumental variables (NPIV) estimators. When implemented with this datadriven choice, sieve NPIV estimators of $h_0$ and its derivatives are adaptive: they converge at the best possible (i.e., minimax) supnorm rate, without having to know the smoothness of $h_0$, degree of endogeneity of the regressors, or instrument strength. Our second procedure is a datadriven approach for constructing honest and adaptive uniform confidence bands (UCBs) for $h_0$ and its derivatives. Our datadriven UCBs guarantee coverage for $h_0$ and its derivatives uniformly over a generic class of datagenerating processes (honesty) and contract at, or within a logarithmic factor of, the minimax supnorm rate (adaptivity). As such, our datadriven UCBs deliver asymptotic efficiency gains relative to UCBs constructed via the usual approach of undersmoothing. In addition, both our procedures apply to nonparametric regression as a special case. We use our procedures to estimate and perform inference on a nonparametric gravity equation for the intensive margin of firm exports and find evidence against common parameterizations of the distribution of unobserved firm productivity.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.11869
 Bibcode:
 2021arXiv210711869C
 Keywords:

 Economics  Econometrics;
 Statistics  Methodology;
 Statistics  Machine Learning
 EPrint:
 The datadriven choice of sieve dimension in this paper is based on and supersedes Section 3 of the preprint arXiv:1508.03365v1