Question 1 [8 points] - Do earnings differ by race? Using the Labor Force Participation 2011 data, we run the following regression: EARNINGS B1+B2S+B3ETHWHITE +u, where EARNINGS is the hourly earnings in dollar, S is years of schooling, and ETHWHITE is a dummy variable which equals to 1 if the individual is white and equals to 0 if the individual is non-white. Please use the following regression output to answer the questions. Source | SS df MS 2 23391.6615 Model | 46783.3229 Residual | 731501.896 3592 203.647521 Total | 778285.219 3594 216.551257 Number of obs = F( 2, 3592) Prob F R-squared Adj R-squared Root MSE 3595 114.86 = 0.0000 = 0.0601 = 0.0596 = 14.271 EARNINGS Coef. Std. Err. t P>|t| [95% Conf. Interval] S | 1.176888 ETHWHITE | 2.079192 _ cons | .1950893 .0851246 .5414326 1.231892 1. (4 points) Interpret the coefficients of S and ETHWHITE. 2. (4 points) Do earnings differ by race? Perform the relevant test and conclude. Use 5% significance level. Question 2 [6 points] The coefficient of S in the wage regression in Question 1 measures the return to education. When we include race dummy (ETHWHITE) in the regression without any interactive term, we 1 assume that the return to education (slope) is the same for white and non-white. Is it true? We can test it by adding a slope dummy variable which is the product of S and the race dummy variable. The slope dummy variable is: SETHWHITE=S× ETHWHITE. Add this slope dummy variable to the regression: EARNINGS = ß₁+ẞ₂S+BETHWHITE+ B₁SETHWHITE + u. Use the following regression output to answer the questions. Source | _SS df MS Number of obs = 3595 F( 3, 3591) = 76.80 Model | 46923.4437 3 15641.1479 Residual 731361.775 3591 203.665212 Prob > F = 0.0000 R-squared == 0.0603 Total 778285.219 3594 216.551257 Adj R-squared Root MSE = 0.0595 = 14.271 EARNINGS | Coef. Std. Err. t P> t [95% Conf. Interval] S | 1.294296 .1651741 ETHWHITE | 4.273759 2.70063 SETHWHITE -.1598729 .1927446 _cons | -1.383757 2.267356 1. (2 points) Interpret the coefficient of SETHWHITE. 2. (4 points) Does the return to education differ by race? Perform the relevant test and conclude. Use 5% significance level.