1. Measurement Error in Linear Multiple Regression Models Ulf H Olsson Professor Dep. Of Economics

2. Ulf H. Olsson The stadard linear multiple regression Model

3. Ulf H. Olsson Measurement Error/Errors-in-variables

4. Ulf H. Olsson The consequences of neglecting the measurent error

5. 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

6. Ulf H. Olsson The consequences of neglecting the measurent error Lack of orthogonality – crucial assumption underlying the use of OLS is violated !

7. Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

8. Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

9. 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.

10. Ulf H. Olsson The consequences of neglecting the measurent error In the limit we find:

11. Ulf H. Olsson The consequences of neglecting the measurent error The estimator is biased upward

12. Ulf H. Olsson The consequences of neglecting the measurent error

13. Ulf H. Olsson The consequences of neglecting the measurent error