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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
y σ2 Unconditional error variance is una¤ected by heteroscedasticity
(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
We could plot the bi or b2 against yi or against yi or against any of
the xji If εt s N 0, σ2 then E (jεi j) = σ. So the absolute value of the
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.
- Two '13