Use the data in WAGEPAN.RAW for this exercise.
(i) Consider the unobserved effects model
Iwage it = (0 + (1d81t+ ... + (7d87t + (1educi
+ (1d81t, educi + ... + (7dx87t educi + (2 unionit + ai + uit,
Where ai is allowed to be correlated with educi and unionit, Which parameters can you estimate using first differencing?
(ii) Estimate the equation from part (i) by FD, and test the null hypothesis that the return to education has not changed over time.
(iii) Test the hypothesis from part (ii) using a fully robust test, that is, one that allows arbitrary heteroskedasticity and serial correlation in the FD errors, (uit. Does your conclusion change?
(iv) Now allow the union differential to change over time (along with education) and estimate the equation by FD. What is the estimated union differential in 1980? What about 1987? Is the difference statistically significant?
(v) Test the null hypothesis that the union differential has not changed over time, and discuss your results in light of your answer to part (iv)?