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Solution Manual for Using Econometrics: A Practical Guide, 7th Edition

  • Economics
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    Instructor’s Manual Answers to Odd - numbered Exercises Chapter 1 1 - 3. ( a ) The coefficient of Li represents the change in the percentage chance of making a putt when the length of the putt increases by one foot. In this case, the percentage chance of making the putt decreases by 4.1 for each foot longer the putt is. ( b) The equations are identical. To convert one to the other, note that ˆ P i = P i – e i , which is true because e i = P i - ˆ P i (or more generally, e i = Y i – ˆ Y i ). ( c) 42.6 percent, yes; 79.5 percent, no (too low); - 18.9 percent, no (negative!). ( d) One problem is that the theoretical relationship between the length of the putt and the percentage of putts made is almost surely non - linear in the variables; we’ll discuss models appropriate to this problem in Chapter 7. A second problem is that the ac tual dependent variable is limited by zero and one but the regression estimate is not; we’ll discuss models appropriate to this problem in Chapter 13. 1 - 5. ( a) β ʏ is the change in S caused by a one - unit increase in Y, holding G constant and β G is the change in S caused by a one - unit increase in G, holding Y constant. (b) +, - (c) Yes. Richer states spend at least some of their extra money on education, but states with rapidly growing student populations find it difficult to increase spending at the same rate as the student population, causing spending per student to fall, espe cially if you hold the wealth of the state constant. ( d ) Ŝ i = - 183 + 0.1422Y i - 59.26G i . Note that 59.26 ∙ 10 = 5926 ∙ 0.10, so nothing in the equation has changed except the scale of the coefficient of G. 1 - 7. ( a) β 2 represents the impact on the wage of the i th worker of a one - year increase in the education of the i th worker, holding constant that worker’s experience and gender. (b) β 3 represents the impact on the wage of the i th worker of being male instead of female, holding constant that worker’s experience and education. (c) There are two ways of defining such a dummy variable. You could define COLOR i = 1 if the i th worker is a person of color and 0 otherwise, or you could define COLOR 1 = 1 if the i th worker is not a person of color and 0 otherwise. (The actual name you use for the variable doesn’t have to be “COLOR.” You could choose any variable name as long as it didn’t conflict with the other variable names in the equation.) (d) We’d favor adding a measure of the quality of the worker to this equation, and answer iv, the number of employee of the month awards won, is the best measure of quality in this group. As tempting as it might be to add the average wage in the field, it would be the same for each employee in the sample and thus wouldn’t provide any useful information.

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    2 Studenmund • Using Econometrics, Seventh Edition Chapter 2 2 - 3. ( a) The squares are “least” in the sense that they are being minimized. ( b) If R 2 = 0, then RSS = TSS, and ESS = 0. If R 2 is calculated as ESS/TSS, then it cannot be negative. If R 2 is calculated as 1 – RSS/TSS, however, then it can be negative if RSS > TSS, which can happen if ˆ Y is a worse predictor of Y than Y (possible only with a non - OLS estimator or if the constant term is omitted). (c) positive. ( d) We prefer Model T because it has estimated signs that meet expectations and also because it includes an important variable that Model A omits. A higher R 2 does not automatically mean that an equation is preferred. 2 - 5. ( a ) Even though the fit in Equation A is better, most researchers would prefer equation B because the signs of the estimated coefficients are as would be expected. In addition, X 4 is a theoretically sound variable for a campus track, while X 3 seems poorly specified because an especially hot or cold day would discourage fitness runners. ( b) The coefficient of an independent variable tells us the impact of a one - unit increase in that variable on the dependent variable holding constant the other explanatory variables in the equation. If we change the other variables in the equation, we’re ho lding different variables constant, and so the ˆ  has a different meaning. 2 - 7. ( a) Yes. We’d expect bigger colleges to get more applicants, and we’d expect colleges that used the common application to attract more applicants. It might seem at first that the rank of a college ought to have a positive coefficient, but the variable is defined a s 1 = best, so we’d expect a negative coefficient for RANK. (b) The meaning of the coefficient of SIZE is that for every increase of one in the size of the student body, we’d expect a college to generate 2.15 more applications, holding RANK and COMMONAP constant. The meaning of the coefficient of RANK is that eve ry one - rank improvement in a college’s USNews ranking should generate 32.1 more applications, holding SIZE and COMMONAP constant. These results do not allow us to conclude that a college’s ranking is 15 times more important than the size of that college b ecause the units of the variables SIZE and RANK are quite different in magnitude. On a more philosophical level, it’s risky to draw any general conclusions at all from one regression estimated on a sample of 49 colleges. (c) The meaning of the coefficient of COMMONAP is that a college that switches to using the common application can expect to generate 1222 more applications, holding constant RANK and SIZE. However, this result does not prove that a given college would i ncrease applications by 1222 by switching to the common application. Why not? First, we don’t trust this result because there may well be an omitted relevant variable (or two) and because all but three of the colleges in the sample use the common applica tion. Second, in general, econometric results are evidence that can be used to support an argument, but in and of themselves they don’t come close to “proving” anything. ( e ) If you drop COMMONAP from the equation, 2 R falls. This is evidence (but not proof) that COMMONAP belongs in the equation.

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    An Additional Interactive Regression Learning Exercise 3 Chapter 3 3 - 3. ( a) A male professor in this sample earns $817 more than a female professor, holding constant the other independent variables in the equation. ( b) Most students will expect a negative coefficient, so they will call this an unexpected sign. Most professors and administrators will expect a positive sign because of the growing competition among colleges for African - American professors, so they will c all this an expected sign. A key point here is not to change expectations based solely on this result. ( c) R is not a dummy variable because it takes on more than two values. For each additional year in rank, the ith professor’s salary will rise by $406, holding constant the other independent variables in the equation. ( d) Yes. The coefficient is large and, as we’ll learn in Chapter 5, statistically significantly greater than zero. (In addition, it’s quite robust.) ( e) There’s no measure of the quality of the professor in the equation as it stands, so good suggestions might the number of articles published by the i th professor or the average teaching evaluation (on a standard scale) of the i th professor. 3 - 5. ( a) A male student’s GRE subject score in Economics is likely to be 39.7 points higher than a female’s, holding constant their GPA and SATs. (b) This result is evidence of, but not proof of, bias. If we were sure that we had the best possible specification (the topic of Chapter 6) and if this result turned out to be statistically significant (the topic of Chapter 5), and if we were able to re produce this result in other samples, we’d be much closer to a “proof.” Even then, there still would be a possibility that some factor other than bias was the cause of these results. (c) Possible variables include the number of upper divi s ion economics courses taken, the number of mathematics classes taken, and dummy variables measuring whether the student had taken econometrics or international economics (two fields frequently covered in the test). It’s vital that any suggested variable be cross - sectional by student. (d) The equation would become i GRE = 212.1 – 39.7G i + 78.9GPA i + 0.203SATM i + 0.110SATV i. . 3 - 7. ( a ) The best way to handle three discrete conditions is to specify two dummy variables. For example, one dummy variable could =1 if the iPod is new (and 0 otherwise) and the other dummy variable could =1 if the iPod is used but unblemished (and 0 otherwise). The omitted condition, that the iPod is used and scratched, would be represented by both dummy variables equaling zero. ( b ) Positive, negative, positive ( c ) In theory, the narrower the time spread of the observations, the better the sample, but three weeks probably is a short enough time period to ensure that the observations are from the same population. If the three weeks included a major shock to the iPod market, however, then the friend would be right , and the sample should be split into “before the shock” and “after the shock” subsamples. ( d ) Yes, they match with the answer to part b.

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    4 Studenmund • Using Econometrics, Seventh Edition ( e ) 2 R is missing! ( f ) 2 R is .431. Chapter 4 4 - 3. Pair “ c ” clearly violates Assumption VI, and pair “ a ” probably violates it for most samples. 4 - 5. ( a ) Yes, Yes. In particular, there’s no measure of prices in the equation. ( b ) Yes ( c ) Yes, Very unlikely ( d ) No ( e ) No ( f ) No ( g ) The nightclub should hire a dancer because the estimated coefficient is higher. Chapter 5 5 - 3. (a) H 0 :β 1  0, H A :β 1 > 0 (b) H 0 :β 1 ≥ 0, H A :β 1 < 0; H 0 :β 2 ≤ 0, H A :β 2 > 0; H 0 :β 3 ≤ 0, H A :β 3 > 0 (The hypothesis for β 3 assumes that it is never too hot to go jogging.) (c) H 0 :β 1  0, H A :β 1 > 0; H 0 :β 2 ≤ 0, H A :β 2 > 0; H 0 :β 3 ≥ 0, H A :β 3 < 0; (The hypothesis for β 3 assumes you’re not breaking the speed limit. ) (d) H 0 :β G = 0; H A :β G  0 (G for grunt.) 5 - 5. (a) t 2 = (200 – 160)/25.0 = 1.6; t c = 2.052; therefore cannot reject H 0 . (Notice the violation of the principle that the null hypothesis contains that which we do not expect.) (b) t 3 = 2.37; t c = 2.756; therefore cannot reject the null hypothesis. (c) t 2 = 5.6; t c = 2.447; therefore reject H 0 if it is formulated as in the exercise, but this poses a problem because the original hypothesized sign of the coefficient was negative. Thus, the alternative hypothesis ought to have been stated: H A : β 2 < 0, and H 0 cannot be rejected because the sign of t 2 doesn’t agree with the sign in the alternative hypothesis . 5 - 7. (a) For both, H 0 : β ≤ 0 and H A : β > 0. For WIN, we cannot reject H 0 , even though the sign agrees with the sign implied by H A , because |+1.00| < 1.697, the 5 percent one - sided critical t - value for 30 degrees of freedom. For FREE, we can reject H 0 at the 5 percent level of significance because |2.00|> 1.697 and because 2.00 has the sign implied by H A .

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