Optimal Sup-Norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression

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

No 1923R2, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h_0 and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of h_0 and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating h_0 and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when h_0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal root-mean-squared rates for severely ill-posed problems, and are only a logarithmic factor slower than the optimal root-mean-squared rates for mildly ill-posed problems. Third, we use our sup-norm rates to establish the uniform Gaussian process strong approximations and the score bootstrap uniform confidence bands (UCBs) for collections of nonlinear functionals of h_0 under primitive conditions, allowing for mildly and severely ill-posed problems. Fourth, as applications, we obtain the first asymptotic pointwise and uniform inference results for plug-in sieve t-statistics of exact consumer surplus (CS) and deadweight loss (DL) welfare functionals under low-level conditions when demand is estimated via sieve NPIV. Empiricists could read our real data application of UCBs for exact CS and DL functionals of gasoline demand that reveals interesting patterns and is applicable to other markets.

Keywords: Series 2SLS; Optimal sup-norm convergence rates; Uniform Gaussian process strong approximation; Score bootstrap uniform confidence bands; Nonlinear welfare functionals; Nonparametric demand with endogeneity (search for similar items in EconPapers)
JEL-codes: C13 C14 C36 (search for similar items in EconPapers)
Pages: 94 pages
Date: 2013-11, Revised 2017-01
Note: Includes Supplimental Material
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Optimal sup‐norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2018)
Working Paper: Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression (2017)
Working Paper: Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2017)
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