4 The following model allows the return to education to depend upon the total am

Question

4 The following model allows the return to education to depend upon the total amount of both parents' education, called pareduc: log(wage) = 0+ ,educ + 2educ.pareduc + Aexper + 4tenure + u. (i) Show that, in decimal form, the return to another year of education in this model is What sign do you expect for A? Why? (ii) Using the data in WAGE2.RAW, the estimated equation is log(wage) = 5.65 + .047 educ + .00078 educ-pare duc + (.13) (010) .00021) 9 exper .010 tenure 019 .004) (.003) n = 722, = .169 ghts Reserved. May not be copied, scanned, or duplicated, in whole or in part De to electronic rights, some third party content may be suppressed from the eBook andfor eChapeis Edinorial review has CHAPTER 6 Multiple Regression Analysis: Further Issues 219 (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 pareauc-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: 0016 educ.pareduc (.0012) log(wage) 4.94 + .097 educ + .033 pareduc .017) +.02 0 exper .010 tenure .004) n = 722, R-.174. 003) 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.

Explanation / Answer

(i) Here the equation implies that each of the terms(apart from b0 and u) vary with the variable associated when other variables are cnstant. It means that, if we vary exper with other variables constant, log(wage) will be increase by b3

Hence, when we vary educ, keeping others as constant, then, b0, b1, b2*pareduc, b3*exper and b4*tenor are all constants.

Hence, d(log(wage))/d(educ) = b1+b2*pareduc (proved)

(ii) The interaction term is b2*educ*pareduc, where b2 =0.00078.

So, in this case,if both Parents have College Education, then pareduc=32.

Hence coef of educ = b1+b2*pareduc where b1 = 0.047, b2 =0.00078

=0.047+0.00078*32 = 0.07196 (Answer)

(iii) Here the coef of pareduc = 0.33-0.0016*educ, where specific values of educ are not given.

Hence The dependency will be positive as long as

0.33-0.0016*educ > 0

or, educ < 206.25

At educ = 206.25, parents education will not effect wage. And when education level >206.25, Parents education will negatively impact wage.

Since the p value for parents education = 0.017 < 0.05, we fail to reject the null hypothesis, and conclude that parents education affect the final outcome.

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