Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation

Xiaohong Chen () and Timothy Christensen
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Timothy Christensen: Dept. of Economics, Yale University

No 1923R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 h_0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h_0 and its derivatives when h_0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L^2-norm rates for severely ill-posed problems, and are only up to a [log(n)]^epsilon (with epsilon

Keywords: Ill-posed inverse problems; Series 2SLS; Optimal sup-norm convergence rates; Adaptive estimation; Random matrices; Bootstrap uniform confidence bands; Nonlinear welfare functionals; Nonparametric demand analysis with endogeneity (search for similar items in EconPapers)
JEL-codes: C13 C14 C32 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2013-11, Revised 2015-04
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (13)

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Working Paper: Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation (2015)
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