Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV

Xiaohong Chen (), Timothy M. Christensen and Sid Kankanala
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Xiaohong Chen: Cowles Foundation, Yale University, https://economics.yale.edu/people/faculty/xiaohong-chen
Timothy M. Christensen: Department of Economics, New York University
Sid Kankanala: Department of Economics, Yale University

No 2292, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We introduce computationally simple, data-driven 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 bootstrap-based, data-driven choice of sieve dimension for sieve nonparametric instrumental variables (NPIV) estimators. When implemented with this data-driven choice, sieve NPIV estimators of $h_0$ and its derivatives are adaptive: they converge at the best possible (i.e., minimax) sup-norm rate, without having to know the smoothness of $h_0$, degree of endogeneity of the regressors, or instrument strength. Our second procedure is a data-driven approach for constructing honest and adaptive uniform confidence bands (UCBs) for $h_0$ and its derivatives. Our data-driven UCBs guarantee coverage for $h_0$ and its derivatives uniformly over a generic class of data-generating processes (honesty) and contract at, or within a logarithmic factor of, the minimax sup-norm rate (adaptivity). As such, our data-driven 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 nd evidence against common parameterizations of the distribution of unobserved firm productivity.

Keywords: Honest and adaptive uniform confidence bands; Minimax sup-norm rate-adaptive estimation; Nonparametric instrumental variables; Bootstrap (search for similar items in EconPapers)
JEL-codes: C13 C14 C36 (search for similar items in EconPapers)
Pages: 89 pages
Date: 2021-07
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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