1 The following model allows the return to education to depend upon the total amount of both parents’ education, called
pareduc: log1wage2 5 b0 1 b1educ
1 b2educ#pareduc
1 b3exper
1 b4tenure
1
u.
(i) Show that, in decimal form, the return to another year of education in this model is
Dlog1wage2/Deduc
5 b1 1 b2
pareduc. What sign do you expect for b2? Why?
(ii) Using the data in WAGE2, the estimated equation is log1wage2 5 5.65 1 .047
educ
1 .00078
educ
#
pareduc
1 1.132 1.0102 1.000212 .019
exper
1 .010
tenure
1.0042 1.0032
n
5 722,
R2 5 .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
5 32 if both parents have a college education, or
pareduc
5 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:
log1wage2 5 4.94 1 .097
educ
1 .033
pareduc
2 .0016
educ
#
pareduc
1.382 1.0272 1.0172 1.00122 1 .020
exper
1 .010
tenure
1.0042 1.0032
n
5 722,
R2 5 .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.
Q94;
1 In Example 4.2, where the percentage of students receiving a passing score on a tenth-grade math exam (math10) is the dependent variable, does it make sense to include
sci11—the percentage of eleventh graders passing a science exam—as an additional explanatory variable?
2 When
atndrte2 and
ACT
#
atndrte
are added to the equation estimated in (6.19), the
R-squared becomes .232. Are these additional terms jointly significant at the 10% level? Would you include them in the model?