EMET2007 Lecture 9 for Wattle

515 78355 4 8178 ssru n k 1 78355 366 7 1 the

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Unformatted text preview: st with F-statistic 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 test-statistic 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 Chow-Test 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…eld-Quandt 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.

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