Use the following table of estimated regressions, computed using data for 2015 from the Current Population Survey (CPS). The data set consists of information on 7178 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
3. Use the following table of estimated regressions, computed using data for 2015 from the Current Population Survey (CPS). The data set consists of information on 7178 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 College = binary variable (1 if college, 0 if high school) Female = binary variable (1 if female, 0 if male) Age = age (in years) Northeast = 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 Sex and Education Binary Variables and Other Characteristics, Using 2015 Data from the Current Population Survey. Dependent variable: average hourly earnings (AHE). Regressor (1) (2) (3) College (X1) 10.47 10.44 10.42 (0.29) (0.29) (0.29) Female (X2) -4.69 -4.56 4.57 (0.29) (0.29) (0.29) Age (X3) 0.61 0.61 (0.05) (0.05) Northeast (X4) 0.74 (0.47) Midwest (Xs) -1.54 (0.40 South (X6) -0.44 (0.37) Intercept 18.15 0.11 0.33 (0.19) (1.46) (1.47) Summary Statistics F-Statistic testing regional effects = 0 9.32 SER 12.15 12.03 12.01 R2 0.165 0.18 0.185 0.165 0.182 0.184 7178 7178 7178 a. Using the regression results in column (1): i. 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. ii. Is the male-female earnings difference estimated from this regression statistically significant at the 5% level? Construct a 95% confidence interval for the difference. b. Using the regression results in column (2): i. Is age an important determinant of earnings? Use an appropriate statistical test and/or confidence interval to explain your answer. ii. Sally is a 29-year-old female college graduate. Betsy is a 34-year-old female college graduate. Construct a 95% confidence interval for the expected difference between their earnings. c. Using the regression results in column (3): i. Do there appear to be important regional differences? Use an appropriate hypothesis test to explain your answer. ii. 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. aa. Construct a 95% confidence interval for the difference in expected earnings between Juanita and Molly. ab. 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?) d. The regression shown in column (2) was estimated again, this time using data from 1992 (4000 observations selected at random from the March 1993 Current Population Survey, converted into 2015 dollars using the Consumer Price Index). The results are AHE = 1.30 + 8.94College - 4.38Female + 0.67Age, SER = 9.88, R2 = 0.21 (1.65) (0.34) (0.30) (0.05) Comparing this regression to the regression for 2016 shown in column (2), was there a statistically significant change in the coefficient on College? e. 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 sex discrimination in the US labor market."
