Multiple Choice Questions (circle one part) 1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e

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1 Economics 102: Analysis of Economic Data Cameron Fall 2005 Department of Economics, U.C.-Davis Final Exam (A) Tuesday December 16 Compulsory. Closed book. Total of 56 points and worth 40% of course grade. Read question carefully so you answer the question. Question scores Question 1a 1b 1c 1d 2a 2b 2c 2d 2e 3a 3b 3c 3d 3e 3f Points Question 4a 4b 4c 4d M ult Choice Points Multiple Choice Questions (circle one part) 1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e 6: a b c d e 7: a b c d e 8: a b c d e 9: a b c d e 10: a b c d e Short Answer Questions 1-5 These questions are based on the study by Joni Hersch, Compensating Wage Di erentials for Gender-Speci c Job Injury Risks, American Economic Review, 1998, pp The original data are from the 1994 Current Population Survey, for a sample of males age Dependent Variable wage = Hourly wage rate in dollars lnwage = Natural logarithm of wage Regressors jirate = job injury rate per 100 workers per year for the industry that the individual works in exper = years of work experience expersq = experience-squared educ = years of schooling union = 1 if union member and 0 otherwise nonwhite = 1 if nonwhite and 0 otherwise Use the two pages of output provided at the end of this exam on descriptive statistics; correlations; various TINV and FINV values; three regressions. Part of the following questions involves deciding which output to use. You can use the output that gets the correct answer in the quickest possible way. 1

2 1.(a) Which variable seems to be most symmetrically distributed - wage or lnwage? Explain your answer giving two di erent reasons. (b) Give a 90% con dence interval for the population mean wage. (c) Perform a one-sided test at signi cance level.05 of the claim that the population mean wage exceeds $12. State clearly the null and alternative hypotheses of your test, and your conclusion. (d) Which variable (other than lnwage) appears to be most highly correlated with wage? 2

3 2. In this question the regression studied is a linear regression of wage on jirate. (a) According to the regression results, by how much does the wage change in response to a one-unit increase in the job injury rate per 100 workers? (b) Is the sign of the e ect what you expect? Explain your answer. (c) Give a 95 percent con dence interval for the population slope parameter. (d) Using relevant output show that the sum of squares P n i=1 (x i x) 2 = 1625:6 where x is jirate. (e) Give a 95 percent con dence interval for expected wage given jirate, when jirate equals 3. Use the result given in part (d) (even if your answer in (d) was di erent). Give answer as an expression involving numbers only, though you need not complete all the calculations. 3

4 3. In this question focus on the multivariate regression where wage is the dependent variable. (a) Which regressors are individually statistically signi cant at signi cance level 0.01? Explain your answer. (b) Are the regressors jointly statistically signi cant at signi cance level 0.01? Explain your answer. Perform an appropriate test. State clearly the null and alternative hypotheses of your test, and your conclusion. (c) What is the e ect on the wage of being a union member? (d) What is the e ect on the wage of a one year increase in experience for the average worker? [Hint: You need to think about this]. (e) Which model explains the data better, the multivariate regression for wage or the bivariate regression for wage, on the basis of t of the model? Explain your answer. 4

5 (f) Which model explains the data better, the multivariate regression or the bivariate regression, on the basis of a formal test of statistical signi cance at 5 percent? Perform an appropriate test. State clearly the null and alternative hypotheses of your test, and your conclusion. 4. In this question consider the regression where lnwage is the dependent variable. (a) What is the e ect on the level of wages of one more year of education? (b) Test the hypothesis at signi cance level 0.05 that the union coe cient exceeds State clearly the null and alternative hypothesis in terms of population parameters and your conclusion. (c) Compute the R 2 for this regression. (d) If you wanted to calculate an estimate of the elasticity of wage with respect to education, what regression would you run? 5

6 Multiple choice questions (1 point each) 1. Which of the following types of data include observations across di erent individuals a. cross-section data b. longitudinal (or panel) data c. both of the above d. neither of the above. 2. In statistical inference the goal is to a. infer population behavior from sample data b. infer sample behavior from population data c. both of the above d. neither of the above. 3. For variables y and x the sample correlation coe cient conveys a. more information than the R 2 from regression of y on x b. the same amount of information as the R 2 from regression of y on x c. less information than the R 2 from regression of y on x: 4. If we regress y on x and the slope coe cient is 2 then without further information, an increase of one unit in x on average a. causes a 2 unit change in y b. is associated with a 2 unit change in y c. neither a. nor b. 5. To obtain the probability that a distributed random variable with 25 degrees of freedom is less than -1, one uses the Excel command a. TDIST(-1, 25, 1) b. TDIST(-1, 25, 2) c. TDIST(1, 25, 1) d. TDIST(1, 25, 2) 6

7 6. Let by i = b 1 x 1i + b 2 x 2i + + b k x ki : Then the ordinary least squares estimator minimizes a. P n i=1 (by i y) 2 b. P n i=1 (y i y) 2 c. P n i=1 (y i by i ) 2 d. None of the above. 7. Suppose we regress annual earnings on age, gender and education and nd that the standard error of the regression is 10,000. For a woman aged 30 with 14 years of schooling the model predicts annual earnings to be $40,000. It follows that a 95% con dence interval for actual earnings of this person a. is at least as wide as (20,000, 60,000) b. is no wider than (20,000, 60,000) c. could be either - more information is needed. 8. One lesson from analysis of the augmented Phillips curve is that a. omission of a key regressor does not lead to a change in the sign of the other regressors b. omission of a key regressor can lead to a change in the sign of the other regressors 9. The paper by Krueger investigates the relationship between wages and computer use in the U.S. a. without any controls for other factors that may e ect wages b. with many controls but not including education or ability c. with many controls including education but not ability d. with many controls including education and ability. 10. Some of the assumptions underlying statistical inference are easier to relax than others. Which of the following is hardest to relax? a. the errors have mean zero and are uncorrelated with the regressors b. the errors are homoskedastic c. the errors are independent of each other d. the errors are normally distributed. 7

8 Cameron: Department of Economics, U.C.-Davis SOME USEFUL FORMULAS Univariate Data P x = 1 n n i=1 x P i and s 2 x = 1 n n 1 i=1 (x i x) 2 x t =2;n 1 (s= p n) t = x 0 s= p n TDIST(t; df; 1) = Pr[T > t] and TDIST(t; df; 2) = Pr[jT j > t] t =2 such that Pr[jT j > t =2 ] = is calculated using TINV(; df): Bivariate Data P n i=1 r xy = (x i x)(y i y) pp n i=1 (x i x) 2 P n i=1 (y i y) = s xy p 2 sxx s P yy n i=1 by = b 1 + b 2 x i b 2 = (x i x)(y i y) P n i=1 (x b i x) 2 1 = y bx TSS = P n i=1 (y i y i ) 2 ErrorSS= P n i=1 (y i by i ) 2 RegSS = TSS - ErrorSS R 2 = 1 ErrorSS/TSS b 2 t =2;n 2 s b2 t = b 2 20 s b2 s 2 b 2 = yjx = x 2 b 1 + b 2 x t =2;n E[yjx = x ] 2 b 1 + b 2 x t =2;n Multivariate Data s 2 e P P n i=1 (x s 2 i x) 2 e = 1 n n 2 i=1 (y i by i ) 2 2 s e 2 s e q 1 n + (x x) 2 Pi (x i x) q 1 + P (x x) 2 n i (x i x) 2 by = b 1 + b 2 x 2i + + b k x ki R 2 = 1 ErrorSS/TSS R 2 = R 2 k 1 n k (1 R2 ) b j t =2;n k s bj t = b j F = s bj j0 R 2 =(k 1) (1 R 2 )=(n k) and F = (SSE r SSE u )=(k g) SSE u =(n k) 8

9 Figure 1 Excel output: page 1 of 2 9

10 Figure 2 Excel output: page 2 of 2 10

1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e. 6: a b c d e 7: a b c d e 8: a b c d e 9: a b c d e 10: a b c d e

1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e. 6: a b c d e 7: a b c d e 8: a b c d e 9: a b c d e 10: a b c d e Economics 102: Analysis of Economic Data Cameron Spring 2016 Department of Economics, U.C.-Davis Final Exam (A) Tuesday June 7 Compulsory. Closed book. Total of 58 points and worth 45% of course grade.