Question 1 A The data set oducat ion. dt a contains data on the years of education of a random sample of 718 Americans. as well as the same information for both of their parents. It is likely that parents' achievements have some predictive power for their children's outcomes. as a result of both a hereditary component of intelligence and the possibility that higher educated parents stimulate their children more to do well at school. Thus, we consider the model educ, $i + djmeduc; +03feduci + sr.
(a) We will ignore any heteroskedasticity and autocorrelation problems in the remainder of this question. However. discuss whether it is likely that these problems are present in our modal.
(b) Estimate this model. and provide interpretations for the three estimated coefficients.
(c) Give 95% confidence inlervats for both the conditional mean and the actual value of education for people whose mother has 16 years of education, while the father has 12.
(d) Explain what the restriction A2 = means, in economic terms.
(e) Test the restriction in part (d), and show that it cannot be rejected. (Note: I want to see that you have estimated both the restricted and the unrestricted model. Feel free to use Stata's test command to check your result, but using only that would be too easy.)
(r) Use the restricted model from part (e) to repeat the prediction exercise in part (c). !Mu-
ifively, why are the resulting confidence intervals narrower this time?
(g) Go back to the original model, where ,62 and $3 are allowed to be different Now, what would the restriction $ + /Is = I mean, in economic terms?
(h) Test the restriction in part (g). (The same note as in part (e) applies.)