Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation

Xiaohong Chen and Timothy M. Christensen

No 32/15, CeMMAP working papers from Institute for Fiscal Studies

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 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 ∈

Date: 2015-06-30
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Persistent link: https://EconPapers.repec.org/RePEc:azt:cemmap:32/15

DOI: 10.1920/wp.cem.2015.3215

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