Error-in-the-variables model

Representing regression mitigation through a series of regression estimates in error-in-variables models. Two regression lines (red) delimited the search space from pontential regression functions.

In statistics  , error-in-variables models , also called measurement error models , are regression models for regression with stochastic regressors , in which either the response variable or some explanatory variables are measured with errors .

Classic error-in-variables model

In the simplest case, a simple linear regression model is given :

${\displaystyle Y_{i}=\beta _{0}+\beta _{1}x_{i}+\varepsilon _{i};\ i=1,\dots ,n}$.

In the classic error-in-variables model it is assumed that observations can only be made with random errors , i.e. H. you then have the stochastic regressor . It is assumed for the measurement errors that they are independent and independent and distributed with zero expected value and variance , uncorrelated with and uncorrelated with the disturbance variable . ${\displaystyle x_{i}}$ ${\displaystyle u_{i}}$ ${\displaystyle z_{i}=x_{i}+u_{i}}$ ${\displaystyle u_{i}}$ ${\displaystyle \sigma _{u}^{2}}$ ${\displaystyle x_{i}}$ ${\displaystyle \varepsilon _{i}}$

Consequences of errors in the variables

Measurement errors in the explanatory variables mean that the ordinary least squares estimate is inconsistent .

Individual evidence

1. ↑ Jeffrey Marc Wooldridge : Introductory econometrics: A modern approach. 4th edition. Nelson Education, 2015, p. 848.
2. ↑ Schneeweiß, H .: Ökonometrie , Physica Verlag 1990 (4th edition) Chapter 7 (3rd edition 1978)