4 The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc: log(wage -Bo Bieduc B2educ pare duc B3exper B4tenure u. (i) Show that, in decimal form, the return to another year of education in this model is Alog(wage)/Aeduc Bit Bnpareduc. What sign do you expect for B2? Why? (ii Using the data in WAGE2.RAW, the estimated equation is log(wage) 5.65 .047 educ .00078 educ pareduc t (13) (010) 00021) .019 exper .010 tenure (004) 003) 722, R 69 (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 (.0012) (38) (027) (017) .020 exper .010 tenure (003) 00 n 722, R 174. 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