IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES

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 li...

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Bibliographic Details
Published inEconometric theory Vol. 37; no. 4; pp. 633 - 663
Main Author Ben-Moshe, Dan
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.08.2021
Subjects
Econometrics
Economic theory
Generalized method of moments
Measurement
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ISSN0266-4666
1469-4360
DOI10.1017/S0266466620000250

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Summary: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.
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ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466620000250