Refer to the example used in Section 4.4. You will use the data set TWOYEAR.RAW.
(i) The variable phsrank is the person's high school percentile. (A higher number is better. For example, 90 means you are ranked better than 90 percent of your graduating class.) Find the smallest, largest, and average phsrank in the sample.
(ii) Add phsrank to equation (4.26) and report the OLS estimates in the usual form. Is phsrank statistically significant? How much is 10 percentage points of high school rank worth in terms of wage?
(iii) Does adding phsrank to (4.26) substantively change the conclusions on the returns to two- and four-year colleges? Explain.
(iv) The data set contains a variable called id. Explain why if you add id to equation (4.17) or (4.26) you expect it to be statistically insignificant. What is the two-sided p-value?