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SPECIFICATION TESTING IN NONPARAMETRIC INSTRUMENTAL QUANTILE REGRESSION

Published online by Cambridge University Press:  07 January 2020

Christoph Breunig
Christoph Breunig*
Affiliation:
Emory University
*
Address correspondence to Christoph Breunig, Department of Economics, Emory University, Rich Memorial Building, Atlanta, GA30322, USA; e-mail: christoph.breunig@emory.edu.
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Abstract

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There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This article develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 4 , August 2020 , pp. 583 - 625
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
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

Parts of this article derive from my doctoral dissertation, completed under the guidance of Enno Mammen. I would like to thank Liangjun Su and four anonymous referees for excellent comments and suggestions that greatly improved the article. I also thank seminar participants at Boston College, Bristol, Mannheim, Toulouse School of Economics, University College London, WIAS Berlin, and Yale. I am also grateful for the support and hospitality of the Cowles Foundation.

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