4i e i jxi 0 e lecture 7 heteroscedasticity pi

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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 Heteroscedasticity-robust 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 heteroscedasticity-robust 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 heteroscedastic-robust standard error Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 31 / 34 r dβ Var bj Using these formulas, the usual t-test is valid asymptotically The usual F-statistic does not work under heteroscedast...
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