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Unformatted text preview: st with Fstatistic
F= (SSRr SSRu ) /q
(85.515 78.355) /4
=
= 8.178
SSRu / (n k 1)
78.355/ (366 7 1) The null hypothesis is rejected Pr (F4,358 > 8.178) = 0.000 Alternative way to compute teststatistic in the given case
Run separate regressions for men and for women; the SSRu is given by
the sum of the SSR of these two regressions
Run regression for the restricted model and store SSRr
If the test is computed in this way it is called the ChowTest
Important: Test assumes a constant error variance across groups Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 32 / 53 The Chow Test assumed that the variance for the women, σ2 , was
w
the same as the variance of the men, σ2 .
m
That is, the Chow test assumes the regressions for the two groups A
and B are of the form
y
y
and σ2
A = βA + βA x + ε
0
1
=
= βB
0
σ2
B βB x
1
2 +
=σ ε s N 0, σ2
A for group A 0, σ2
B for group B +ε εsN It is not always reasonable to assume the variance is the same across
groups Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 33 / 53 To check if this test is appropriate we test
H0 : σ 2 = σ 2
w
m
This is a special case of the Gold…eldQuandt test To do the test
Let nw denote the number of women and nm the number of men in the
sample
2
Let sw be the estimate of σ2 for the regression using the data for the
women and
2
Let sm be the estimate of σ2 for the regression using the data for the
men The test statistic is then
2
sm
s Fn w
2
sw Lecture 9 (qualitative variables) k 1 ,n m k 1 EMET2007/6007 8 st May 2013 34 / 53 Regression with everyone, n = 4137 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 35 / 53 2
Regression with only women, nw = 1860 and sw = (0.52889)2 = 0.27972 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 36 / 53 2
Regression with only men, nm = 2277 and sm = (0.57251)2 = 0.32777 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 37 / 53 We now test the hypotheses
H0 : σ 2 = σ 2
w
m H1 : σ 2 6 = σ 2
w
m The decision r...
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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
 strachan

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