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Honest Confidence Sets in Nonparametric IV Regression and Other Ill-Posed Models

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  • Andrii Babii

Abstract

This paper develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). Since it is impossible to have inferential methods based on the central limit theorem, we develop two alternative approaches relying on the concentration inequality and bootstrap approximations. We show that expected diameters and coverage properties of resulting sets have uniform validity over a large class of models, i.e., constructed confidence sets are honest. Monte Carlo experiments illustrate that introduced confidence sets have reasonable width and coverage properties. Using U.S. data, we provide uniform confidence sets for Engel curves for various commodities.

Suggested Citation

  • Andrii Babii, 2016. "Honest Confidence Sets in Nonparametric IV Regression and Other Ill-Posed Models," Papers 1611.03015, arXiv.org, revised Dec 2020.
  • Handle: RePEc:arx:papers:1611.03015
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    Cited by:

    1. Andrii Babii & Jean-Pierre Florens, 2017. "Are Unobservables Separable?," Papers 1705.01654, arXiv.org, revised Mar 2021.
    2. Andrii Babii, 2020. "High-dimensional mixed-frequency IV regression," Papers 2003.13478, arXiv.org.
    3. Kengo Kato & Yuya Sasaki & Takuya Ura, 2018. "Inference based on Kotlarski's Identity," Papers 1808.09375, arXiv.org, revised Sep 2019.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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