Use the data in TWOYEAR.RAW for this exercise.
(i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and standard deviation of stotal.
(ii) Run simple regressions of jc and univ on stotal. Are both college education variables statistically related to stotal? Explain.
(iii) Add stotal to equation (4.17) and test the hypothesis that the returns to two- and four-year colleges are the same against the alternative that the return to four-year colleges is greater. How do your findings compare with those from Section 4.4?
(iv) Add stotal2 to the equation estimated in part (iii). Does a quadratic in the test score variable seem necessary?
(v) Add the interaction terms stotal-jc and stotal-univ to the equation from part (iii). Are these terms jointly significant?
(vi) What would be your final model that controls for ability through the use of stotal? Justify your answer.