s07pre2a - CORNELL UNIVERSITY Economics 321: Applied...

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CORNELL UNIVERSITY Economics 321: Applied Econometrics, Spring 2007, G. Jakubson PRELIMINARY EXAM #2 ANSWER KEY 1. (10 points) 30% poor and 40%of the poor are program, so P(program) = P(program | poor)P(poor) = (.4)(.3) = 12% in program. Wealthy Poor, not in Poor, participate Prob .7 .18 .12 mean income 800 450 x E(income) = 700 = (.7)(800) + (.18)(450) + (.12)(x) => x = 491.67 2. (15 points) a. V(income) = E(income - E(income)) 2 = (.7)(800-700) 2 + (.18)(450-700) 2 + (.12)(491.67-700) 2 b. E(income | poor) = (450)(.18/.3) + (491.67)(.12/.3) = 466.67 (use conditional distribution - probability weights must add to one) c. V(income | poor) = E[income - E(income | poor) | poor] 2 = (.6)(450-466.67) 2 + (.4)(491.67-466.67) 2 (For parts a and c could also use V(x) = E(x 2 ) - (E(x)) 2 form) 3. (35 points) a. No. Harleyson says to compare the mean incomes for nonparticipants vs. participants without regard to whether a country is wealthy or poor. The mean income for nonparticipating counties is (800)(.7/.88) + (450)(.18/.88) = 728.41> the mean income for participating counties (all poor) = 491.67. Most nonparticipators are not poor. b. y = per capita income. y = ββ ; β 01 ++ Du 0 = mean of nonparticipating; β 0 + β 1 = mean for participating; β 1 = mean of participating minus mean of nonparticipating < 0 ; c. y = ; β β 2 +++ DC u 0 = mean for nonpoor nonprogram; β 0 + β 2 = mean for poor nonprogram; ( β 0 + β 1 + β 2 )= mean for poor program, so β 1 = mean for poor program minus mean for poor nonprogram, while β 2 = mean for poor nonprogram minus mean for nonpoor nonprogram. 4. (20 points) a. Using the above calculations and parameter interpretations, we want β 1 from the simple regression = mean of participating minus mean of nonparticipating = 491.67-728.41 = -236.74 b. Again using the above information, we want β 1 from the multiple regression = mean for poor program minus mean for poor nonprogram 491.67- 450 = 41.67. When we control for whether or not a nation is poor, we see that the program is effective. 5. (40 points) a. Simple regression: y = α 0 + α 1 D + u 1 Multiple regression: y = β 0 + β 1 D + β 2 A + u 2 Auxiliary regression: A = δ 0 + δ 1 D + u 3 The relationship between simple and multiple regression says: α 1 = β 1 + ( β

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This note was uploaded on 05/26/2008 for the course ECON 3210 taught by Professor Molinari during the Spring '07 term at Cornell University (Engineering School).

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s07pre2a - CORNELL UNIVERSITY Economics 321: Applied...

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