4 The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc: = log(wage) Bo+ Beduc + Beduc-pareduc + Bexper + Batenure + u. (i) Show that, in decimal form, the return to another year of education in this model is Alog(wage)/Aeduc = B + Bpareduc. What sign do you expect for B2? Why? (ii) Using the data in WAGE2, the estimated equation is log(wage) = 5.65 + .047 educ+.00078 educ-pareduc + (.13) (.010) (.00021) .019 exper + .010 tenure (.004) (.003) n = 722, R2 = .169. (Only 722 observations contain full information on parents' education.) Interpret the coefficient on the interaction term. It might help to choose two specific values for pareduc-for example, pareduc 32 if both parents have a college education, or pareduc 24 if both parents have a high school education-and to compare the estimated return to educ. (iii) When pareduc is added as a separate variable to the equation, we get: log(wage) = = 4.94 + .097 educ + .033 pareduc - .0016 educ-pareduc (.38) (.027) (.017) + .020 exper+ .010 tenure (.004) (.003) n = 722, R = .174. (.0012) Does the estimated return to education now depend positively on parent education? Test the null hypothesis that the return to education does not depend on parent education.