s04fin1a - CORNELL UNIVERSITY Economics 321: Applied...

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CORNELL UNIVERSITY Economics 321: Applied Econometrics Spring 2004 G. Jakubson FINAL EXAM ANSWERS 1. Low Productivity Eligible High Productivity Not Eligible Margin s Participate .15=.6*.25 0 .15 Not Participate .10 .75 .85 Margins .25 .75 1.0 a. P(participate) = .15 b. Average output = 16.95 = (18)(.75) + (12)(.1) + (X)(.05) solve for X = 15 c. Average output among the low productivity = (12)(.1/.25) + (15)(.15/.25) = 13.8 d. Y = output. Y = β 0 + β 1 T + u mean for nonparticipants = β 0 ; mean for participants = β 0 + β 1 so β 1 = mean for participants minus mean for nonparticipants e. mean for trainees = (16.95 – (.1)(12) _ (.75)(18))/(.15) = 15 mean for nontrainees = ((.75)(19) + (.1)(12))/(.85) = 17.3 trainee mean minus nontrainee mean =15 – 17.3 = -2.3 f. let group1 be nontrainees and group 2 be trainees. For group j, let j x be the sample mean, be the sample variance, and n 2 j s j be the sample size. Since the samples are big, we have (approximately) that ) n / s , (( N ) n / , ( N x j 2 j j j 2 j j j µ σ µ confidence interval takes the form θ where ) sd )( ˆ m ( ± 2 1 x x ˆ = θ , m = 1.96 (since we want a 95% confidence interval and we're using the standard normal approximation in large sample, and 2 2 2 1 2 1 n s n s sd + = No covariance term since we assume the groups are independent. Now substitute the sample values and away you go. g. y = u C T 2 1 0 + β + β + β ; β 0 = mean for nonprogram; β 0 + β 2 = mean for eligible nonparticipants; ( β 0 + β 1 + β 2 )= mean for eligible participants, so β 1 = mean for participants minus mean for eligible nonparticipants, while β 2 = mean for eligible nonparticipants minus mean for nonprogram. Economics 321, Applied Econometrics Page 1 of 6 Final Exam Answers, Spring 2004 c:\…\s04fin1a.doc
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h. β 0 + β 1 + β 2 =15 β 0 + β 2 =12 β 0 =18 β 2 =12 – 18 = -6 β 1 =15 – 12 = 3 i. Simple regression: output = α 0 + α 1 T + u 1 Multiple regression: output = β 0 + β 1 T + β 2 A + u 2 Auxiliary regression: A = δ 0 + δ 1 T + u 3 The relationship between simple and multiple regression says: α 1 = β 1 + ( β 2 δ 1 ). We have β 2 > 0 . The key is δ 1 . If you take the phrase in the question " Worker’s with “good” attitudes are selected into the training program " then δ 1 > 0, so α 1 = β 1 “+
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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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s04fin1a - CORNELL UNIVERSITY Economics 321: Applied...

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