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Measurement Error in Linear Multiple Regression Models

Explore the impact of neglecting measurement error in linear multiple regression models. Learn about biases and inconsistencies arising from errors in variables.

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Measurement Error in Linear Multiple Regression Models

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

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

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

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

  5. 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

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

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

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

  9. 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

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

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

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

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

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