s04pre2a - Economics 321: Applied Econometrics Spring 2004...

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Economics 321: Applied Econometrics Spring 2004 G. Jakubson PRELIMINARY EXAM #2: Answer Key 1. (10 points) a. 20% poor, and ¼ of the poor are head start, so 5% are head start, so P(head start) = .05 b. 77 = (.8)(85) + (.15)(40) + (.05)x => average score of head start group = 60 2. (10 points) a. E(test) = 77. E(test 2 ) = (85) 2 (.80) + (40) 2 (.15) + (60) 2 (.05) = 6200. V(test) = E(test 2 ) - (E(test)) 2 = 6200 - (77)(77) = 6200 - 5929 = 271. b. among the poor, P(HS) =.05/.2=.25 So E(test|poor) = (.25)(60) + (.75)(40) = 45 3. (35 points) a. Would expect Jones not to find HS effective. He will look at HS vs. non-HS for the whole population, not just the poor children. Since most non-HS kids are not poor and they do better in school, on average the HS kids will do worse than the non-HS kids. b. test = β 0 + β 1 H + u . β 0 = mean for nonHS kids. β 0 + β 1 = mean for HS kids, so β 1 = mean for HS kids minus mean for non-HS kids. c. test = β 0 + β 1 H + β 2 P + u. β 0 = mean for non-poor kids. β 0 + β 2 = mean for poor non-HS kids. ( β 0 + β 1 + β 2 )= mean for poor HS kids, so β 1 = mean for poor HS kids minus mean for poor non-HS kids while β 2 = mean for poor non-HS kids minus mean for nonpoor nonHS kids. 4. (20 points) a. You are asked to find β 1 , which is the mean score for HS kids minus the mean score for non-HS kids. We already have the mean score for HS kids, which is 60. Must figure out the mean for the non-HS: E(test|not HS) = (85)(.80)/(.80+.15) + (40)(.15)/(.80+.15) = 77.9. So coeff on HS is (60 - 77.9) = -17.9 b.
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s04pre2a - Economics 321: Applied Econometrics Spring 2004...

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