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HW8_sol

# HW8_sol - ECON 414 SOLUTION TO HOMEWORK 8 Spring 2011 7.2(i...

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ECON 414 SOLUTION TO HOMEWORK 8 Spring 2011 7.2 (i) If cigs = 10 then · log( ) bwght = - .0044(10) = - .044, which means about a 4.4% lower birth weight. (ii) A white child is estimated to weigh about 5.5% more, other factors in the first equation fixed. Further, t white 4.23, which is well above any commonly used critical value. Thus, the difference between white and nonwhite babies is also statistically significant. (iii) If the mother has one more year of education, the child’s birth weight is estimated to be . 3% higher. This is not a huge effect, and the t statistic is only one, so it is not statistically significant. (iv) The two regressions use different sets of observations. The second regression uses fewer observations because motheduc or fatheduc are missing for some observations. We would have to reestimate the first equation (and obtain the R -squared) using the same observations used to estimate the second equation. 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 β + 1 log( sales ) + 2 roe + 1 δ 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 .

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C7.4 (i) The two signs that are pretty clear are 3 β < 0 (because hsperc is defined so that the smaller the number the better the student) and 4 > 0. The effect of size of graduating class is not clear. It is also unclear whether males and females have systematically different GPAs. We may think that 6 < 0, that is, athletes do worse than other students with comparable characteristics. But remember, we are controlling for ability to some degree with hsperc and sat . (ii) The estimated equation is · colgpa = 1.241 - .0569 hsize + .00468 hsize 2 - .0132 hsperc (0.079) (.0164) (.00225) (.0006) + .00165 sat + .155 female + .169 athlete (.00007) (.018) (.042) n = 4,137, R 2 = .293. Holding other factors fixed, an athlete is predicted to have a GPA about .169 points
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HW8_sol - ECON 414 SOLUTION TO HOMEWORK 8 Spring 2011 7.2(i...

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