Unformatted text preview: εi jxi ) = 0
Assumption MLR.4(i )
E (ε) = 0 and Cov (xj , ε) = 0 WLS is consistent under MLR.4 but not necessarily under MLR.4(i )
E (εi jxi ) = 0 ) E
Lecture 7 (heteroscedasticity) ε
pi jxi
hi EMET2007/6007 =0
24 th April 2013 28 / 34 If OLS and WLS produce very di¤erent estimates, this typically indicates
that some other assumptions (e.g. MLR.4) are wrong
If there is strong heteroscedasticity, it is still often better to use a wrong
form of heteroscedasticity in order to increase e¢ ciency Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 29 / 34 What can I do about it (II)? Adjust the variances to account for it
Adjust the variance estimates such that they are robust to
heteroscedasticity
This results in heteroscedastic robust standard errors Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 30 / 34 Heteroscedasticityrobust inference after OLS
Formulas for OLS standard errors and related statistics have been
developed that are robust to heteroscedasticity of unknown form
All formulas are only valid in large samples
Formula for heteroscedasticityrobust OLS standard error
2 dβ
Var bj r = r 2ε
∑n=1 bij bi
i
SSRj2 bij is the i th residual from regressing xj on all other independent
r
variables
SSRj is the sum of squared residuals from this regression dβ
Var bj is the heteroscedasticrobust standard error Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 31 / 34 r dβ
Var bj Using these formulas, the usual ttest is valid asymptotically
The usual Fstatistic does not work under heteroscedast...
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 Two '13
 strachan
 Normal Distribution, Regression Analysis, Variance, Heteroscedasticity

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