# It is not the same type of heteroscedasticity as we

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PN = β1 NREC + β2 + β3 N + v EXPN = δ1 + δ2 N + δ3 NREC + v (3) (4) (5) (6) RSS of the above regression using 19 smallest (N ) schools is 900,000. On the other hand, RSS of the above regression using 19 largest (N ) schools is 600,000. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)i) What is heteroscedasticity and what are its consequences? Heteroscedasticity means that the variance of disturbance terms is not equal across all observations. Homoscedasticity means that variances differ. 2 2 Mathematically σui = σu is homoscedasticity. Consequences are: 1 2 3 OLS inefﬁcient. OLS not biased. s.e.’s of estimators invalid (also the t and F tests). Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)ii) Describe Goldfeld-Quandt test and why under certain conditions it may detect heteroscedasticity? Observe that the subpart has 6 points assigned. This means, provide a detailed description of the test. Important point (relating to 2nd part) is that G-Q test assumes heteroscedasticity of a particular form. The alternative hypothesis of heteroscedasticity that is tested assumes: σui , the s.d. of disturbance term (!) is proportional (or inversely proportional) to one of the regressors. Don’t forget that this is a particular type of heteroscedasticity! Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)iii) Perform Goldfeld-Quandt test on both speciﬁcations For ﬁrst speciﬁcation: EXP = β1 + β2 N + β3 NSQ + u H0 = Homoscedasticity (σui = σu ) H1 = Heteroscedasticity (Here we test whether σui is increasing with N ) F (16, 16) = 64/16 =8 8/16 Why 16? For second speciﬁcation: EXPN = δ1 + δ2 N + δ3 NREC + v H0 = Homoscedasticity (σvi = σv ) H1 = Heteroscedasticity (Here we test whether σvi is increasing with N ) F (16, 16) = 900/16 = 1.5 600/16 Critical values of F (16, 16) at 5% and 1% signiﬁcance level are 2.33 and 5.20 → Reject H0 of homoscedasticity for 1st regression at 0.1% → Fail to reject H0 of homoscedasticity for 2st regression even at 5% Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)iv) Explain why researcher ran 2nd regression In light of part iii), argue how disturbance term becomes homoscedastic. s.d. of disturbance term is proportional to N ; i.e. σui = λNi What happens when divide by N ? EXP /N = β1 /N + β2 N /N + β3 NSQ /N + u /N EXPN = δ3 NREC + δ1 + δ2 N + v N.B. (8) is 2nd regression with different order of terms. Looking at disturbance term v of new speciﬁcation: var ( 1 1 ui ) = 2 var (ui ) = 2 (λ2 Ni2 ) = λ2 Ni Ni Ni → It is clearly homoscedastic. (7) (8) Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)v) R 2 is lower in 2nd regression. Does this mean 1st is better? Trick question! R 2 ’s are not comparable as dependent variables differ in two specications. Fundamental answer: Prefer second. Why? Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)a)v) R 2 is lower in 2nd regression....
View Full Document

## This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).

Ask a homework question - tutors are online