Introduction heteroscedasticity past exam practice

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 Goldfeld-Quandt 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 Goldfeld-Quandt 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 Goldfeld-Quandt 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 Goldfeld-Quandt 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 Goldfeld-Quandt 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:...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online