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Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV

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Abstract

We introduce computationally simple, data-driven procedures for estimation and inference on a structural function $h_0$ and its derivatives in nonparametric models using instrumental variables. Our first procedure is a bootstrap-based, data-driven choice of sieve dimension for sieve nonparametric instrumental variables (NPIV) estimators. When implemented with this data-driven choice, sieve NPIV estimators of $h_0$ and its derivatives are adaptive: they converge at the best possible (i.e., minimax) sup-norm rate, without having to know the smoothness of $h_0$, degree of endogeneity of the regressors, or instrument strength. Our second procedure is a data-driven approach for constructing honest and adaptive uniform confidence bands (UCBs) for $h_0$ and its derivatives. Our data-driven UCBs guarantee coverage for $h_0$ and its derivatives uniformly over a generic class of data-generating processes (honesty) and contract at, or within a logarithmic factor of, the minimax sup-norm rate (adaptivity). As such, our data-driven UCBs deliver asymptotic efficiency gains relative to UCBs constructed via the usual approach of undersmoothing. In addition, both our procedures apply to nonparametric regression as a special case. We use our procedures to estimate and perform inference on a nonparametric gravity equation for the intensive margin of firm exports and nd evidence against common parameterizations of the distribution of unobserved firm productivity.

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  • Xiaohong Chen & Timothy M. Christensen & Sid Kankanala, 2021. "Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV," Cowles Foundation Discussion Papers 2292, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2292
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    1. Xiaohong Chen & Timothy M. Christensen, 2018. "Optimal sup‐norm rates and uniform inference on nonlinear functionals of nonparametric IV regression," Quantitative Economics, Econometric Society, vol. 9(1), pages 39-84, March.
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    Cited by:

    1. Zhu, Ying, 2025. "Phase transitions in nonparametric regressions," Journal of Econometrics, Elsevier, vol. 252(PB).
    2. Jiafeng Chen & Xiaohong Chen & Elie Tamer, 2021. "Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators," Papers 2110.06763, arXiv.org, revised Oct 2022.
    3. Chen, Jiafeng & Chen, Xiaohong & Tamer, Elie, 2023. "Efficient estimation of average derivatives in NPIV models: Simulation comparisons of neural network estimators," Journal of Econometrics, Elsevier, vol. 235(2), pages 1848-1875.
    4. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Cowles Foundation Discussion Papers 2238R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    5. Ziyu Wang & Yuhao Zhou & Jun Zhu, 2022. "Fast Instrument Learning with Faster Rates," Papers 2205.10772, arXiv.org, revised Oct 2022.

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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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