Use the data in HTV.RAW for this exercise.
(i) Run a simple OLS regression of log{wage) on educ. Without controlling for other factors, what is the 95% confidence interval for the return to another year of education?
(ii) The variable ctuit, in thousands of dollars, is the change in college tuition facing students from age 17 to age 18. Show that educ and ctuit are essentially uncorrelated. What does this say about ctuit as a possible IV for educ in a simple regression analysis?
(iii) Now, add to the simple regression model in part (i) a quadratic in experience and a full set of regional dummy variables for current residence and residence at age 18. Also include the urban indicators for current and age 18 residences. What is the estimated return to a year of education?
(iv) Again using ctuit as a potential IV for educ, estimate the reduced form for educ. [Naturally, the reduced form for educ now includes the explanatory variables in part (iii).] Show that ctuit is now statistically significant in the reduced form for educ.
(v) Estimate the model from part (iii) by IV, using ctuit as an IV for educ. How does the confidence interval for the return to education compare with the OLS CI from part (iii)?
(vi) Do you think the IV procedure from part (v) is convincing?