Variability of the unobserved influences does not

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Unformatted text preview: lity of the unobserved influences does not dependent on the value of the explanatory variable Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 7 / 34 An example for heteroskedasticity: Wage and education The variance of the unobserved determinants of wages increases with the level of education Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 8 / 34 Consequences of heteroscedasticity for OLS Some things do not change: OLS still unbiased and consistent under heteroscedasticty! Also, interpretation of R-squared is not changed R2 t 1 σ2 ε σ2 y σ2 Unconditional error variance is una¤ected by heteroscedasticity ε (which refers to the conditional error variance) However, some things do change: Heteroscedasticity invalidates variance formulas for OLS estimators The usual F-tests and t-tests are not valid under heteroscedasticity Under heteroscedasticity, OLS is no longer the best linear unbiased estimator (BLUE); there may be more e¢ cient linear estimators Lecture 7 (heteroscedasticity) EMET2007/6007 24 th April 2013 9 / 34 How can I tell if I have it? Anecdotal evidence There are a number of graphical ways of observing whether we have heteroscedasticity We could plot the bi or b2 against yi or against yi or against any of ε εi b the xji If εt s N 0, σ2 then E (jεi j) = σ. So the absolute value of the ε residuals jbi j should resemble the standard deviation at each point i We could plot the jbi j against yi or against any of the xji ε Note that the relationship may not be linea...
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This note was uploaded on 06/15/2013 for the course EMET 2007 taught by Professor Strachan during the Two '13 term at Australian National University.

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