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HONEST CONFIDENCE SETS IN NONPARAMETRIC IV REGRESSION AND OTHER ILL-POSED MODELS

Published online by Cambridge University Press:  05 March 2020

Andrii Babii
Andrii Babii*
Affiliation:
University of North Carolina at Chapel Hill
*
Address correspondence to Andrii Babii, University of North Carolina at Chapel Hill, Gardner Hall, CB 3305 Chapel Hill, NC 27599-3305, USA; babii.andrii@gmail.com
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Abstract

This article 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 et al. (2011, Econometrica 79, 1541–1565). 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, that is, 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.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 4 , August 2020 , pp. 658 - 706
Copyright
© Cambridge University Press 2020

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Footnotes

First draft: March 2016. This article is a revised first chapter of my Ph.D. thesis. I’m grateful to the Co-Editor and valuable referees for constructive criticism and suggestions of how to improve the article. I’m deeply indebted to my advisor Jean-Pierre Florens and other members of my Ph.D. committee: Eric Gautier, Ingrid Van Keilegom, and Timothy Christensen for helpful suggestions and insightful conversations. This article also benefited from discussions with Christian Bontemps, Samuele Centorrino, Jasmin Fliegner, Emanuele Guerre, Vitalijs Jascisens, Jihyun Kim, Rohit Kumar, Elia Lapenta, Pascal Lavergne, Thierry Magnac, André Mas, Nour Meddahi, Markus Reiss, and Shruti Sinha.

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