Identification of linear regressions with errors in all variables

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)633-663
Number of pages31
JournalEconometric Theory
Issue number4
StatePublished - 1 Aug 2021
Externally publishedYes

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


Dive into the research topics of 'Identification of linear regressions with errors in all variables'. Together they form a unique fingerprint.

Cite this