Which of the following is true of measurement error?
A)If measurement error in a dependent variable has zero mean, the ordinary least squares estimators for the intercept are biased and inconsistent.
B)If measurement error in an independent variable is uncorrelated with the variable, the ordinary least squares estimators are unbiased.
C)If measurement error in an independent variable is uncorrelated with other independent variables, all estimators are biased.
D)If measurement error in a dependent variable is correlated with the independent variables, the ordinary least squares estimators are unbiased.

Question

Quizplus · Accepted Answer

When measurement error in an independent variable is uncorrelated with the variable, the ordinary least squares estimators are unbiased. This is because the error is random and does not have a systematic relationship with the independent variable, so the OLS estimators still have a consistent structure. However, if measurement error in a dependent variable has zero mean, the ordinary least squares estimators for the intercept are biased and inconsistent (A), if measurement error in an independent variable is uncorrelated with other independent variables, all estimators are biased (C), and if measurement error in a dependent variable is correlated with the independent variables, the ordinary least squares estimators are biased (D).

Which of the Following Is True of Measurement Error