Section 8 - Section 8 - Econ 140 GSI: Edson Severnini 1...

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Unformatted text preview: Section 8 - Econ 140 GSI: Edson Severnini 1 Violation of Homoskedasticity 1.1 De nitions Homoskedasticity : variance of the error term i is constant for all i = 1 ,...,N . That is, V ar ( i ) = 2 I . Heteroskedasticity : variance of the error term i is NOT constant for all i = 1 ,...,N . That is, V ar ( i ) = 2 . Serial correlation : covariance of each two di erent error terms i and j is NOT zero. That is, V ar ( i ) = 2 . Remark : is a positive de nite matrix. Remember that is symmetric. 1.2 Consequences OLS estimators remain unbiased and consistent E [ ] = + E [( X X )- 1 X ] = + ( X X )- 1 X E [ ] = OLS estimators are not BLUE anymore inferences invalid V ar [ ] = V ar [ + ( X X )- 1 X ] = V ar [( X X )- 1 X ] = ( X X )- 1 X V ar ( ) X ( X X )- 1 = ( X X )- 1 X 2 X ( X X )- 1 = 2 ( X X )- 1 X X ( X X )- 1 2 ( X X )- 1 1.3 What to do when homoskedasticity is violated?What to do when homoskedasticity is violated?...
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Section 8 - Section 8 - Econ 140 GSI: Edson Severnini 1...

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