Econ 399 Chapter8a - 8. Heteroskedasticity We have already...

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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 Heteroskedasticity-Robust 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 Heteroskedasticity-Robust Inference after OLS Estimation-Because testing hypothesis is a key element of econometrics, we need to obtain accurate standard errors in the presence of heteroskedasticity-in the last few decades, econometricians have learned how to adjust standard errors when HETEROSKEDASTICITY OF UNKNOWN FORM exists-these heteroskedasticity-robust procedures are valid (in large samples) regardless of eror variance 8.2 Het Fixing 1-Given 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 1-Recall that...
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Econ 399 Chapter8a - 8. Heteroskedasticity We have already...

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