7.4 Using the regression results in column (3):

a. Are there important regional differences? Use an appropriate hypothesis test to explain your answer.

b. Juan is a 32-year-old male high school graduate from the North. Ali is a 32-year-old male college graduate from the West. Mayank is a 32-year-old male college graduate from the East.

i. Construct a 95% confidence interval for the difference in expected earnings between Juan and Ali.

ii. Explain how you would construct a 95% confidence interval for the difference in expected earnings between Juan and Mayank.

(Hint: What would happen if you included West and excluded East from the regression?)

The data set consists of information on over 10000 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 40 years. The data set also contains information on the region of the country where the person lived, and the individual’s gender and age.
For the purposes of these exercises, let AWE = logarithm of average weekly earnings (in 2007 units)
High school = binary variable (1 if High school, 0 if less)
Male = binary variable (1 if male, 0 if female)
Age = age (in years)
North = binary variable (1 if Region = North, 0 otherwise)
East = binary variable (1 if Region = East, 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 2007 Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor Graduated high school (X) 1 Male (X2) Age (X3) North (X4) South (X) East (X6) Intercept F-statistic for regional effects=0 SER R n 2 3 0.352 0.373 (0.021) (0.021) 0.371 (0.021) 0.458 (0.021) 0.457 (0.020) 0.451 (0.020) 0.011 (0.001) 0.011 (0.001) 0.175 (0.37) 0.103 (0.033) -0.102 (0.043) 12.84 12.471 12.390 (0.018) (0.049) (0.057) 21.87 1.026 1.023 1.020 0.0710 0.0761 0.0814 10973 10973 10973