Consequences of errors in variables:

Most of the published data or summary  information contain errors of summsrizing or misrepresenting  by informer. When these data are used, one of the assumptions of classical  least-squares method is violated.  In this case,  the classical least-squares estimator will be biased even when sample size increases, which is alternatively known as asymptotic biases or inconsistency.

Under the classical assumptions the ordinary least squares  (OLS) estimators  are best linear unbiased. One of  the major underlying  assumptions is the interdependence of regressors  from  the disturbance term. If this condition does not hold, OLS estimators are biased and inconsistent. This statement may be illustrated by simple errors in variables.

We  discuss about the consequences in the following, if the error appears in the measurement of dependent variable, independent variable or both.