1. You have learned that earnings functions are one of the most investigated relationships in economics. These typically relate the logarithm of earnings to a series of explanatory variables such as education, work experience, gender, race, etc. (a) Why do you think that researchers have preferred a log-linear specification over a linear specification? (b) You decide, given your knowledge of age-earning proles, to allow the regression line to differ for the below and above 40 years age category. Accordingly you create a binary variable, Dage, that takes the value one for age 39 and below, and is zero otherwise. Estimating the earnings equation results in the following output (using heteroskedasticity-robust standard errors): LWn: 6.92 - 3.13 x Dage - 0.019 x Age + 0.085 X (Dage x Age), R2 = 0.20, SER = 0.721. (38.33) (0.22) (0.004) (0.005) i. Interpret the coefficient of the interaction term: 0.085 ii. Sketch both regression lines: one for the age category 39 years and under, and one for 40 and above. iii. Does it make sense to have a negative sign on the Age coefficient? iv. Predict the |n(earnings) for a 30 year old and a 50 year old. What is the percentage difference between these two