Section 8

# 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 ε i is constant for all i = 1 ,...,N . That is, V ar ( ε i ) = σ 2 I . • Heteroskedasticity : variance of the error term ε i is NOT constant for all i = 1 ,...,N . That is, V ar ( ε i ) = σ 2 Ω . • Serial correlation : covariance of each two di erent error terms ε i and ε j is NOT zero. That is, V ar ( ε i ) = σ 2 Ω . • Remark : Ω is a positive de nite matrix. Remember that Ω is symmetric. 1.2 Consequences • OLS estimators remain unbiased and consistent E [ ˆ β ] = β + E [( X X )- 1 X ε ] = β + ( X X )- 1 X E [ ε ] = β • OLS estimators are not BLUE anymore ⇒ inferences invalid V ar [ ˆ β ] = V ar [ β + ( X X )- 1 X ε ] = V ar [( X X )- 1 X ε ] = ( X X )- 1 X V ar ( ε ) X ( X X )- 1 = ( X X )- 1 X σ 2 Ω X ( X X )- 1 = σ 2 ( X X )- 1 X Ω X ( X X )- 1 ≥ σ 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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