# HW3 Answers - Answer keys for HW3 7.4 (i) The approximate...

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62 Answer keys for HW3 7.4 (i) The approximate difference is just the coefficient on utility times 100, or –28.3%. The t statistic is .283/.099 2.86, which is very statistically significant. (ii) 100 [exp( .283) – 1) 24.7%, and so the estimate is somewhat smaller in magnitude. (iii) The proportionate difference is .181 .158 = .023, or about 2.3%. One equation that can be estimated to obtain the standard error of this difference is log( salary ) = 0 + 1 log( sales ) + 2 roe + 1 consprod + 2 utility + 3 trans + u , where trans is a dummy variable for the transportation industry. Now, the base group is finance , and so the coefficient 1 directly measures the difference between the consumer products and finance industries, and we can use the t statistic on consprod . C7.8 (i) If the appropriate factors have been controlled for, 1 > 0 signals discrimination against minorities: a white person has a greater chance of having a loan approved, other relevant factors fixed. (ii) The simple regression results are ± approve = .708 + .201 white (.018) (.020) n = 1,989, R 2 = .049. The coefficient on white means that, in the sample of 1,989 loan applications, an application submitted by a white application was 20.1% more likely to be approved than that of a nonwhite applicant. This is a practically large difference and the t statistic is about 10. (We have a large sample size, so standard errors are pretty small.) (iii) When we add the other explanatory variables as controls, we obtain 1 ˆ .129, se( 1 ˆ ) .020. The coefficient has fallen by some margin because we are now controlling for factors that should affect loan approval rates, and some of these clearly differ by race. (On average, white people have financial characteristics – such as higher incomes and stronger credit histories – that make them better loan risks.) But the race effect is still strong and very significant ( t statistic 6.45). (iv) When we add the interaction white obrat to the regression, its coefficient and t statistic are about .0081 and 3.53, respectively. Therefore, there is an interactive effect: a white

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63 applicant is penalized less than a nonwhite applicant for having other obligations as a larger percent of income. (v) The trick should be familiar by now. Replace white obrat with white ( obrat – 32); the coefficient on white is now the race differential when obrat = 32. We obtain about .113 and se .020. So the 95% confidence interval is about .113 1.96(.020) or about .074 to .152. Clearly, this interval excludes zero, so at the average obrat there is evidence of discrimination (or, at least loan approval rates that differ by race for some other reason that is not captured by the control variables).
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