Unformatted text preview: ui is proportional to size of Xi .
Above is an important point as the test exploits exactly that assumption’s
implications.
H0 : Homoscedasticity (σui =σu )
H1 : Heteroscedasticity (σui is proportional to size of Xi )
Relationship is between s.d. of disturbance term σui and Xi
Mechanics:
1 Order n observations by magnitude of Xi 2 Run separate regression ﬁrst n and last n obs. to get RSS1 and RSS2 3 Recommended optimal choice of n to be
RSS2
RSS1 3
8 of total sample size n. ∼ Fn −k ,n −k . 4 Under H0 , 5 Intuition: if H1 holds, probably RSS2 > RSS1 and test statistic large
→ we reject H0 Introduction Heteroscedasticity Past Exam Practice Question Detection GoldfeldQuandt Test Important points:
This test assumes s.d. changes proportionally to size of Xi . Moving Forward: Model B Introduction Heteroscedasticity Past Exam Practice Question Detection GoldfeldQuandt Test Important points:
This test assumes s.d. changes proportionally to size of Xi .
It tests this assumption particularly. Moving Forward: Model B Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Detection GoldfeldQuandt Test Important points:
This test assumes s.d. changes proportionally to size of Xi .
It tests this assumption particularly.
Alternatively also possible to test inverse proportionality (that σui is
decreasing in Xi ). Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Detection GoldfeldQuandt Test Important points:
This test assumes s.d. changes proportionally to size of Xi .
It tests this assumption particularly.
Alternatively also possible to test inverse proportionality (that σui is
decreasing in Xi ).
Mechanically change H1 and the test statistic by switching RSS2 and
RSS1 in the fraction. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Detection GoldfeldQuandt Test Important points:
This test assumes s.d. changes proportionally to size of Xi .
It tests this assumption particularly.
Alternatively also possible to test inverse proportionality (that σui is
decreasing in Xi ).
Mechanically change H1 and the test statistic by switching RSS2 and
RSS1 in the fraction.
Here intuition is also adapted: If heteroscedasticity then RSS1 > RSS2
(or H1 is correct). Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Detection White Test
This test is much more general.
It looks for evidence of an association between variance of disturbance term
and regressors.
H0 : Homoscedasticity (σui =σu )
H1 : Heteroscedasticity (σui changes with X’s) Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Detection White Test
This test is much more general.
It looks for evidence of an association between variance of disturbance term
and regressors.
H0 : Homoscedasticity (σui =σu )
H1 : Heteroscedasticity (σui changes with X’s)
Mechanics:
1 Run OLS and save residuals. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward:...
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 Spring '13
 ChristopherDougherty
 Econometrics, Regression Analysis, β2 Xi, Exam Practice Question, Past Exam Practice

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