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 profiles, 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 heteroskedasticityrobust standard errors): LiiEar n= 6.92 -3.13 X Dage -0.019 XAge + 0.085 X (Dage XAge) , R2 = 0.20, SER = 0.721. (38.33) (0.22) (0.004) (0.005) 1. Interpret the coefficient of the interaction term: 0.085 11. Sketch both regression lines: one for the age category 39 years and under,and one for 40 and above. 111. Does it make sense to have a negative sign on the Age coefficient? 1v. Predict the In( earnings) for a 30 year old and a 50 year old. What is the percentage difference between these two