ie_Slide08 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides08 Lecturer: Minxian Yang ie_Slides08 my, School of Economics, UNSW 1
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8. Heteroskedasticity (Ch8) 8. Heteroskedasticity • Lecture plan – Consequences of heteroskedasticity for OLS estimation – Heteroskedasticity-robust inference – Testing for heteroskedasticity – Weighted least squares estimation – Linear probability model revisited ie_Slides08 my, School of Economics, UNSW 2
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8. Heteroskedasticity (Ch8) • Consequences of heteroskedasticity – Recall MLR1-5 • MLR1: linear (in parameter) model; • MLR2: random sample; • MLR3: no perfect-collinearity; • MLR4: zero conditional mean; • MLR5: homoskedasticity, Var ( u i | x i ) = σ 2 for all i . – Why MLR5 • MLR5 is required for using the formula of the variance of the OLS estimator, which is important for inference. • Without MLR5, the usual standard errors are incorrect and the t-stat (or F-stat) does not follow the t (or F) distribution and may lead to wrong conclusions. • Without MLR5, the OLS is no longer asymptotically efficient. ie_Slides08 my, School of Economics, UNSW 3 The OLS estimators are unbiased and consistent under MLR1-4. ) ( ˆ ) ˆ r( a ˆ v 2 2 1 j j j R SST
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8. Heteroskedasticity (Ch8) • Homoskedasticity and heteroskedasticity ie_Slides08 my, School of Economics, UNSW 4
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8. Heteroskedasticity (Ch8) • Heteroskedasticity-robust inference – It is possible to adjust the OLS standard errors to make the t-stat (or F-stat) valid in the presence of heteroskedasticity of unknown form. – The adjustment is called heteroskedasticity-robust procedure. – The procedure is “robust” because the adjusted t-stat (or F-stat) is valid regardless of the type of heteroskedasticity in the population (even if there is no heteroskedasticity). ie_Slides08 my, School of Economics, UNSW 5
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8. Heteroskedasticity (Ch8) • Heteroskedasticity-robust inference – Robust standard errors • Assume MLR1-4 for y = β 0 + β 1 x 1 +...+ β k x k + u . • Allow heteroskedasticity (drop MLR5). • Robust standard errors where u i - hat is the i- th residual from OLS and ie_Slides08 my, School of Economics, UNSW 6 , ) ' ( ' ˆ ) ' ( ) ˆ ( ˆ v , ,..., , , ) ˆ r( a ˆ v of diagnal the ) ˆ ( . th 1 1 2 1 1 1 0 X X u X X k n n B r a k j B j β se r n i i i i j x x . ˆ ˆ ˆ ˆ , , k ik i i nk k k n B x x x x x x x x X 1 0 1 2 1 1 21 11 1 1 1 1 x
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8. Heteroskedasticity (Ch8) • Heteroskedasticity-robust inference – Robust standard errors • The het.-robust t-stat is given by • The het.-robust F-stat must be computed using a
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This note was uploaded on 06/12/2011 for the course ECONOMICS 3291 taught by Professor Professorsnamespublishedtheyarethesoleowners during the Three '11 term at University of New South Wales.

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ie_Slide08 - Introductory Econometrics ECON2206/ECON3209...

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