130 likes | 162 Views
Measurement Error in Linear Multiple Regression Models. Ulf H Olsson Professor Dep. Of Economics. The stadard linear multiple regression Model. Measurement Error/Errors-in-variables. The consequences of neglecting the measurent error. The consequences of neglecting the measurent error.
E N D
Measurement Error in Linear Multiple Regression Models Ulf H Olsson Professor Dep. Of Economics
The stadard linear multiple regression Model Ulf H. Olsson
Measurement Error/Errors-in-variables Ulf H. Olsson
The consequences of neglecting the measurent error Ulf H. Olsson
The consequences of neglecting the measurent error • The probability limits of the two estimators when there is measurement error present: The disturbance term shares a stochastic term (V) with the regressor matrix => u is correlated with X and hence E(u|X)0 Ulf H. Olsson
The consequences of neglecting the measurent error • Lack of orthogonality – crucial assumption underlying the use of OLS is violated ! Ulf H. Olsson
The consequences of neglecting the measurent error • The inconsistency of b Ulf H. Olsson
The consequences of neglecting the measurent error • The inconsistency of b Ulf H. Olsson
The consequences of neglecting the measurent error • The inconsistency of b • Bias towards zero (attenuation) for g=1 • In multiple regression context things are less clear cut. Not all estimates are necessarilly biased towards zero, but there is an overall attenuation effect. Ulf H. Olsson
The consequences of neglecting the measurent error In the limit we find: Ulf H. Olsson
The consequences of neglecting the measurent error The estimator is biased upward Ulf H. Olsson
The consequences of neglecting the measurent error Ulf H. Olsson
The consequences of neglecting the measurent error Ulf H. Olsson