1 Use the data in HTV to answer this question. The data set includes information on wages, education, parents’ education, and several other variables for 1,230 working men in 1991.
(i) What is the range of the
educ
variable in the sample? What percentage of men completed
twelfth grade but no higher grade? Do the men or their parents have, on average, higher levels
of education?
(ii) Estimate the regression model
educ
5 b0 1 b1motheduc
1 b2fatheduc
1
u
by OLS and report the results in the usual form. How much sample variation in
educ
is explained
by parents’ education? Interpret the coefficient on
motheduc.
(iii) Add the variable
abil
(a measure of cognitive ability) to the regression from part (ii), and report the results in equation form. Does “ability” help to explain variations in education, even after controlling for parents’ education? Explain.
(iv) (Requires calculus) Now estimate an equation where
abil
appears in quadratic form:
educ
5 b0 1 b1motheduc
1 b2fatheduc
1 b3abil
1 b4abil2 1
u. Using the estimates b^ 3 and b^ 4, use calculus to find the value of
abil, call it
abil*, where
educ
is minimized. (The other coefficients and values of parents’ education variables have no effect; we are holding parents’ education fixed.) Notice that
abil
is measured so that negative values are permissible. You might also verify that the second derivative is positive so that you do indeed
have a minimum.
(v) Argue that only a small fraction of men in the sample have “ability” less than the value calculated in part (iv). Why is this important?
(vi) If you have access to a statistical program that includes graphing capabilities, use the estimates in part (iv) to graph the relationship between the predicted education and
abil. Set
motheduc
and
fatheduc
at their average values in the sample, 12.18 and 12.45, respectively.