# ie_Slide08 - Introductory Econometrics ECON2206/ECON3209...

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Introductory Econometrics ECON2206/ECON3209 Slides08 Rachida Ouysse ie_Slides08 School of Economics, UNSW 1

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8. Heteroskedasticity (Ch8) 8. Heteroskedasticity • Lecture plan onsequences of eteroskedasticity r OLS Consequences of heteroskedasticity for OLS estimation Heteroskedasticity-robust inference y – Testing for heteroskedasticity eighted least squares estimation Weighted least squares estimation – Linear probability model revisited ie_Slides08 School of Economics, UNSW 2
8. Heteroskedasticity (Ch8) • Consequences of heteroskedasticity – Recall MLR1-5 • MLR1: linear (in parameter) model; • MLR2: random sample; The OLS estimators are unbiased and onsistent under • MLR3: no perfect-collinearity; • MLR4: zero conditional mean; LR5: omoskedasticity ar = r all consistent under MLR1-4. • MLR5: homoskedasticity, Var ( u i | x i ) = σ 2 for all i . –Why MLR5 LR5 is required for using the formula of the variance of the ) ( ˆ ) ˆ r( a ˆ v 2 2 1 j j j R SST • 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. ithout MLR5, the OLS is no longer asymptotically efficient. Without MLR5, the OLS is no longer asymptotically efficient. ie_Slides08 School of Economics, UNSW 3

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8. Heteroskedasticity (Ch8) • Homoskedasticity and heteroskedasticity ie_Slides08 School of Economics, UNSW 4
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 heteroskedasticityof unknown form. – The adjustment is called heteroskedasticity-robust procedure. – The procedure is “robust” because the adjusted t-stat r F tat) is valid regardless of the type of (or F-stat) is valid regardless of the type of heteroskedasticity in the population (even if there is no heteroskedasticity). y) ie_Slides08 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 , ,..., 1 , 0 , ) ˆ r( a ˆ v of diagnal the ) ˆ ( . th k j B j se r j , ) ' ( ' ˆ ) ' ( 1 ) ˆ ( ˆ v 1 1 2 1 X X u X X k n n B r a n i i i i x x where u i - hat is the i- th residual from OLS and ˆ ˆ k x x 0 1 11 1 1 . ˆ ˆ , , i i k k B x x x x x x X 1 1 2 21 1 1 x ie_Slides08 School of Economics, UNSW 6 k ik nk n 1
8. Heteroskedasticity (Ch8) • Heteroskedasticity-robust inference – Robust standard errors • The het.-robust t-stat is given by ˆ tat - j j a  • The het.-robust F-stat must be computed using a , ) ˆ ( .

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ie_Slide08 - Introductory Econometrics ECON2206/ECON3209...

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