Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation
Xiaohong Chen () and
Timothy M. Christensen
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Timothy M. Christensen: Institute for Fiscal Studies
No CWP32/15, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
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 h0 and its derivatives. Second, we show that a computationally simple sieve NPIV estimator can attain the optimal sup-norm rates for h0 and its derivatives when h0 is approximated via a spline or wavelet sieve. Our optimal sup-norm rates surprisingly coincide with the optimal L2-norm rates for severely ill-posed problems, and are only up to a [log(n)]? (with ?
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)
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Working Paper: Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:ifs:cemmap:32/15
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