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Unformatted text preview: 8. Heteroskedasticity We have already seen that homoskedasticity exists when the error terms variance, conditional on all x variables, is constant: 2 )  ( = X u Var Homoskedasticity fails if the variance of the error term varies in the sample (ie: varies with the x variables)We used Homoskedasticity for t tests, F test, and confidence intervals, even with large samples 8. Heteroskedasticity 8.1 Consequences of Heteroskedasticity for OLS 8.2 HeteroskedasticityRobust Inference after OLS Estimation 8.3 Testing for Heteroskedasticity 8.4 Weighted Least Squares Estimation 8.5 The Linear Probability Model Revisited 8.1 Consequences of Heteroskedasticity We have already seen that Heteroskedasticity: 1) Does not cause bias or inconsistency (this depends on MLR. 1 through MLR. 4) 2) Does not affect R 2 or adjusted R 2 (since these estimate the POPULATION variances which are not conditional on X) Heteroskedasticity does: 1) Make Var(B j hat) biased, and therefore invalidate typical OLS standard errors (and therefore tests) 2) Make OLS no longer BLUE (a better estimator may exist) 8.2 HeteroskedasticityRobust Inference after OLS EstimationBecause testing hypothesis is a key element of econometrics, we need to obtain accurate standard errors in the presence of heteroskedasticityin the last few decades, econometricians have learned how to adjust standard errors when HETEROSKEDASTICITY OF UNKNOWN FORM existsthese heteroskedasticityrobust procedures are valid (in large samples) regardless of eror variance 8.2 Het Fixing 1Given a typical single independent variable model, heteroskedasticity implies a varying variance: 2 1 )  ( i i i i i i x u Var u x y = + + =Rewriting the OLS slope estimator, we can obtain a formula for its variance: 2 2 2 1 2 1 1 ) ( ) ( ) ( ) ( x i i i i i SST x x Var x x u x x  = + = 8.2 Het Fixing 1Recall that...
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 Spring '09
 Priemaza
 Econometrics

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