C13.2 Use the data in CPS78_85.RAW for this exercise. (i) How do you interpret the coefficient on y85 in equation (13.2)? Does it have an interesting interpretation? (Be careful here; you must account for the interaction terms y85educ and y85female.) (ii) Holding other factors fixed, what is the estimated percent increase in nominal wage for a male with 12 years of education? Propose a regression to obtain a confidence interval for this estimate. [Hint: To get the confidence interval, replace y85educ with y85(educ  12); refer to Example 6.3.] (iii) Reestimate equation (13.2) but let all wages be measured in 1978 dollars. In particular, define the real wage as rwage
wage for 1978 and as rwage
wage/1.65 for 1985. Now, use log(rwage) in place of log(wage) in estimating (13.2). Which coefficients differ from those in equation (13.2)?

(iv) Explain why the R-squared from your regression in part (iii) is not the same as in equation (13.2). (Hint: The residuals, and therefore the sum of squared residuals, from the two regressions are identical.) (v) Describe how union participation changed from 1978 to 1985. (vi) Starting with equation (13.2), test whether the union wage differential changed over time. (This should be a simple t test.) (vii) Do your findings in parts (v) and (vi) conflict? Explain.