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INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

Published online by Cambridge University Press:  13 March 2020

Takuya Ura
Takuya Ura*
Affiliation:
University of California, Davis
*
Address correspondence to Takuya Ura, Department of Economics, University of California, Davis, One Shields Avenue, Davis, CA 95616-5270, USA; e-mail: [email protected].
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Abstract

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This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 1 , February 2021 , pp. 169 - 204
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2020

Footnotes

First version: October, 2016. I am grateful to Peter C.B. Phillips, Arthur Lewbel, and four anonymous referees for comments and suggestions that have significantly improved this article. I would like to thank Alexandre Belloni, Stéphane Bonhomme, Federico A. Bugni, A. Colin Cameron, V. Joseph Hotz, Shakeeb Khan, Jia Li, Matthew A. Masten, Arnaud Maurel, Adam M. Rosen, and seminar participants at Duke, UC Berkeley, Shanghai University of Finance and Economics, Hakodate Conference in Econometrics, IAAE Annual Conference, Econometric Society North American Summer Meeting, and Econometric Society Asian Meeting for very helpful comments. The usual disclaimer applies.

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