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IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES

Published online by Cambridge University Press:  29 June 2020

Dan Ben-Moshe
Dan Ben-Moshe*
Affiliation:
The Hebrew University of Jerusalem
*
Address correspondence to Dan Ben-Moshe, The Hebrew University of Jerusalem, Jerusalem, Israel; e-mail: [email protected].
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Abstract

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not identified if and only if an independent normally distributed linear combination of regressors can be transferred from the regressors to the errors. Second, we introduce a new estimator for the coefficients using a continuum of moments that are based on second derivatives of the log characteristic function of the observables. In Monte Carlo simulations, the estimator performs well and is robust to the amount of measurement error and number of mismeasured regressors. In an application to firm investment decisions, the estimates are similar to those produced by a generalized method of moments estimator based on third to fifth moments.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 633 - 663
Copyright
© Cambridge University Press 2020

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Footnotes

The paper is loosely based on the second chapter of my PhD thesis. I am grateful to Rosa Matzkin and Jinyong Hahn for their generous support, advice, and guidance. I thank the editor Liangjun Su as well as Xavier D’Haultfœuille, Jinyong Hahn, Allyn Jackson, Arthur Lewbel, Rosa Matzkin, Yannay Spitzer, and Elie Tamer for reading various parts of drafts and providing feedback. I benefited from comments at Aarhus, Boston College, CREST, Harvard, Hebrew University of Jerusalem, and Penn State, and discussions with David Genesove, Patrik Guggenberger, Kei Hirano, Stefan Hoderlein, Max Kasy, Saul Lach, Áureo de Paula, Anna Simoni, James Stock, Daniel Wilhelm, and Martin Weidner.

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