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ps9_sol

ps9_sol - Introduction to Econometrics Professor Alexei...

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Introduction to Econometrics Professor Alexei Onatski Problem Set 9 – December 7 Problem 1) [ Stock and Watson 11.1 ] (a) The t -statistic for the coefficient on Experience is 0.031/0.009 = 3.44, which is significant at the 1% level. (b) 0.712 0.031 10 1.022; (1.022) 0.847 Matthew z = + × = Φ = (c) = + × = Φ = 0.712 0.031 0 0.712; (0.712) 0.762 Christopher z (d) = + × = Φ = 0.712 0.031 80 3.192; (3.192) 0.999, Jed z this is unlikely to be accurate because the sample did not include anyone with more that 40 years of driving experience. Problem 2) [ Stock and Watson 11.6 ] (a) For a black applicant having a P/I ratio of 0.35, the probability that the application will be denied is Φ ( - 2.26 + 2.74 × 0.35 + 0.71) = Φ ( - 0.59) = 27.76%. (b) With the P/I ratio reduced to 0.30, the probability of being denied is Φ ( - 2.26 + 2.74 × 0.30 + 0.71) = Φ ( - 0.73) = 23.27%. The difference in denial probabilities compared to (a) is 4.4 percentage points lower. (c) For a white applicant having a P/I ratio of 0.35, the probability that the application will be denied is Φ ( - 2.26 + 2.74 × 0.35) = 9.7%. If the P/I ratio is reduced to 0.30, the probability of being denied is Φ ( - 2.26 + 2.74 × 0.30) = 7.5%. The difference in denial probabilities is 2.2 percentage points lower. (d) From the results in parts (a)–(c), we can see that the marginal effect of the P/I ratio on the probability of mortgage denial depends on race. In the probit regression functional form, the marginal effect depends on the level of probability which in turn depends on the race of the applicant. The coefficient on black is statistically significant at the 1% level.

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Problem 3) [ Stock and Watson 11.7 ] (a) For a black applicant having a P/I ratio of 0.35, the probability that the application will be denied is 0.9805 1 1 ( 4.13 5.37 0.35 1.27) 27.28%. e F + - + × + = = (b) With the P/I ratio reduced to 0.30, the probability of being denied is + - + × + = = 1.249 1 1 ( 4.13 5.37 0.30 1.27) 22.29%. e F The difference in denial probabilities compared to (a) is 4.99 percentage points lower. (c) For a white applicant having a P/I ratio of 0.35, the probability that the application will be denied is 2.2505 1 1 ( 4.13 5.37 0.35) 9.53%. e F + - + × = = If the P/I ratio is reduced to 0.30, the probability of being denied is 2.519 1 1 ( 4.13 5.37 0.30) 7.45%. e F + - + × = = The difference in denial probabilities is 2.08 percentage points lower.
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ps9_sol - Introduction to Econometrics Professor Alexei...

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