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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 GoldfeldQuandt 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 GQ 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 GoldfeldQuandt 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....
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This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).
 Spring '13
 ChristopherDougherty
 Econometrics

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