The first four exercises refer to the table of estimated regressions below, computed using data for 2012 from the CPS. The data set consists of information on 7440 full-time, full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The workers' ages ranged from 25 to 34 years. The data set also contains information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let AHE average hourly earnings (in 2012 dollars) College = binary variable (1 if college, 0 if high school) Female = binary variable (1 if female, O if male) = Age age (in years) Ntheast = binary variable (1 if Region = Northeast, 0 otherwise) Midwest = binary variable (1 if Region = Midwest, 0 otherwise) South = binary variable (1 if Region = South, 0 otherwise) West = binary variable (1 if Region = West, 0 otherwise) Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using 2012 Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). = Regressor College (X1) Female (X2) Age (X3) (1) (2) (3) 8.31 8.32 (0.23) (0.22) 8.34 (0.22) -3.85 -3.81 (0.23) (0.22) 0.51 (0.04) Northeast (X4) -3.80 (0.22) 0.52 (0.04) 0.18 (0.36) Midwest (X5) -1.23 South (X6) Intercept 17.02 (0.17) (1.18) 2.05 (1.18) 1.87 (0.31) -0.43 (0.30) Summary Statistics and Joint Tests F-statistic for regional effects = 0 7.38 SER 9.79 9.68 9.67 R 0.162 0.180 0.182 n 7440 7440 7440 * 1. Add (5%) and ** (1%) to the table to indicate the statistical significance of the coefficients. 2 Using the regression results in column (1): a. Is the college-high school earnings difference estimated from this regression statistically significant at the 5% level? Construct a 95% confidence interval of the difference. b. Is the male-female earnings difference estimated from this regression statistically significant at the 5% level? Construct a 95% confidence interval for the difference. 3 Using the regression results in column (3): a. Do there appear to be important regional differences? Use an appropriate hypothesis test to explain your answer. b. Juanita is a 28-year-old female college graduate from the South. Molly is a 28- year-old female college graduate from the West. Jennifer is a 28-year-old female college graduate from the Midwest. i. Construct a 95% confidence interval for the difference in expected earnings between Juanita and Molly. ii. Explain how you would construct a 95% confidence interval for the difference in expected earnings between Juanita and Jennifer. (Hint: What would happen if you included West and excluded Midwest from the regression?) 4. Evaluate the following statement: "In all of the regressions, the coefficient on Female is negative, large, and statistically significant. This provides strong statistical evidence of gender discrimination in the U.S. labor market." 5. Consider the regression model Yi = Bo + BX1; + B2X2; + Uj. Use Approach #2 from Section 7.3 to transform the regression so that you can use a t-statistic to test a. 1 = 2. b. 1+2 2 = 0. c. 1 + 2 = 1. (Hint: You must redefine the dependent variable in the regression.)