IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES

2020/06/29 by Dan Ben-Moshe · 1 citation
Economics, Econometrics and Finance · Decision Sciences · Mathematics · #Monetary Policy and Economic Impact #Forecasting Techniques and Applications #Advanced Statistical Methods and Models

paper · doi:10.1017/s0266466620000250

openalex publication_date 2020/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Higher moment estimators for linear regression models with errors in the variables
• Tobin's Marginal q and Average q: A Neoclassical Interpretation
• A General Equilibrium Approach To Monetary Theory
• Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models
• TWO-STEP GMM ESTIMATION OF THE ERRORS-IN-VARIABLES MODEL USING HIGH-ORDER MOMENTS
• Robust and consistent estimation of nonlinear errors-in-variables models
• The effect of measurement error
• Estimation of Nonlinear Models with Measurement Error
• Identifiability of a Linear Relation between Variables Which Are Subject to Error

Cited by

• Errors-in-variables model [wikipedia]

Related

• Errors-in-variables models: a generalized functions approach
• Identification of Multivariate Measurement Error Models
• Uniform Inference in Linear Error-in-Variables Models: Divide-and-Conquer
• Simple Estimation of Semiparametric Models with Measurement Errors
• Nonparametric Identification and Estimation with Non-Classical Errors-in-Variables