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

Xiaohong Chen, Timothy Christensen
2017 Social Science Research Network  
Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression cemmap working paper, No. CWP09/17 Provided in Cooperation with: Institute for Fiscal Studies (IFS), London Suggested Citation: Chen, Xiaohong; Christensen, Timothy M. (2017) : Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression, cemmap working paper, No. CWP09/17, Centre for Microdata Methods and Practice (cemmap), London, http://dx.
more » ... ://dx. Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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.
doi:10.2139/ssrn.2916740 fatcat:46e45r52zjd2rli6h2ycnjwi5u