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C7D5 - HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS b OLS...

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HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 1 Heteroscedasticity causes OLS standard errors to be biased is finite samples. However it can be demonstrated that they are nevertheless consistent, provided that their variances are distributed independently of the regressors. = - - = n i i i i X X X X a 1 2 ) ( ) ( = + = n i i i u a b 1 2 OLS 2 β where
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HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 2 Even if this is not the case, it is still possible to obtain consistent estimators. We have seen that the slope coefficient in a simple OLS regression could be decomposed as above. = + = n i i i u a b 1 2 OLS 2 β ( 29 = = = = n i u i n i i i b i a u E a 1 2 2 1 2 2 2 OLS 2 σ σ = - - = n i i i i X X X X a 1 2 ) ( ) ( where
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HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 3 We have also seen that the variance of the estimator is given by the expression above if u i is distributed independently of u j for j i . = + = n i i i u a b 1 2 OLS 2 β = - - = n i i i i X X X X a 1 2 ) ( ) ( ( 29 = = = = n i u i n i i i b i a u E a 1 2 2 1 2 2 2 OLS 2 σ σ where
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HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 4
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