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Honest confidence sets in nonparametric IV regression and other ill-posed models

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  • Babii, Andrii

Abstract

This paper provides novel methods for inference in a very general class of ill-posed models in econometrics, encompassing the nonparametric instrumental regression, different functional regressions, and the deconvolution. I focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). I first show that it is not possible to develop inferential methods directly based on the uniform central limit theorem. To circumvent this difficulty I develop two approaches that lead to valid confidence sets. I characterize expected diameters and coverage properties uniformly over a large class of models (i.e. constructed confidence sets are honest). Finally, I illustrate that introduced confidence sets have reasonable width and coverage properties in samples commonly used in applications with Monte Carlo simulations and considering application to Engel curves.

Suggested Citation

  • Babii, Andrii, 2017. "Honest confidence sets in nonparametric IV regression and other ill-posed models," TSE Working Papers 17-803, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:31687
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    Cited by:

    1. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    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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    More about this item

    Keywords

    nonparametric instrumental regression; functional linear regression; density deconvolution; honest uniform confidence sets; non-asymptotic inference; ill-posed models; Tikhonov regularization;
    All these keywords.

    JEL classification:

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

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