Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression

Xiaohong Chen () and Timothy M. Christensen
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Timothy M. Christensen: Institute for Fiscal Studies

No CWP09/17, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h0 and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS) estimators of h0 and its derivatives. Second, we derive a lower bound that describes the best possible (minimax) sup-norm rates of estimating h0 and its derivatives, and show that the sieve NPIV estimator can attain the minimax rates when h0 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 con dence bands (UCBs) for collections of nonlinear functionals of h0 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. This April 2017 version is an updated version of the January 2017 version. The original version of the working paper is available here.

Keywords: Series 2SLS; Optimal sup-norm convergence rates; Uniform Gaussian process strong approximation; Score bootstrap uniform con dence 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)
Date: 2017-02-13
New Economics Papers: this item is included in nep-ecm and nep-ore
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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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