C7D5 - HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 1...

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Unformatted text preview: 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 where 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 ( 29 = = = = n i u i n i i i b i a u E a 1 2 2 1 2 2 2 OLS 2 =-- = n i i i i X X X X a 1 2 ) ( ) ( where 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 =-- = 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 where HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 4 White (1980) demonstrates that a consistent estimator of is obtained if the squared residual in observation i is used as an estimator of . Taking the square root, one obtains a heteroscedasticity-consistent standard error. = + = n i i i u a b 1 2 OLS 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 2 OLS 2 b 2 i u = = n i i i b e a s 1 2 2 2 OLS 2 =-- = n i i i i X X X X a 1 2 ) ( ) ( where HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS...
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This note was uploaded on 05/26/2010 for the course ECON 301 taught by Professor Öcal during the Spring '10 term at Middle East Technical University.

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C7D5 - HETEROSCEDASTICITY-CONSISTENT STANDARD ERRORS 1...

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