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IDENTIFICATION OF REGRESSION MODELS WITH A MISCLASSIFIED AND ENDOGENOUS BINARY REGRESSOR

Published online by Cambridge University Press:  08 October 2021

Hiroyuki Kasahara  and
Katsumi Shimotsu
Hiroyuki Kasahara
Affiliation:
University of British Columbia
Katsumi Shimotsu*
Affiliation:
University of Tokyo
*
Address for correspondence: Katsumi Shimotsu, Faculty of Economics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; e-mail: shimotsu@e.u-tokyo.ac.jp
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Abstract

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We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 6: YALE 2018 CONFERENCE IN HONOR OF PETER C. B. PHILLIPS: PART II , December 2022 , pp. 1117 - 1139
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 (https://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), 2021. Published by Cambridge University Press

Footnotes

The authors are grateful to the co-editor, two anonymous referees, and participants of A Celebration of Peter Phillips’ Forty Years at Yale Conference whose comments greatly improved the paper. This research is support by the Natural Science and Engineering Research Council of Canada and JSPS Grant-in-Aid for Scientific Research (C) No. 26380267.

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