Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 4

The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc: log(wage) = 0 + 1 educ + 2 educ.pareduc + 3 exper + 4 tenure + u.
(i) Show that, in decimal form, the return to another year of education in this model is log(wage)/ educ = 1 + 2 pareduc. What sign do you expect for _2 Why
(ii) Using the data in WAGE2.RAW, the estimated equation is
(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: 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.