Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 10

In a study of the effect on earnings of education using panel data on annual earnings for a large number of workers, a researcher regresses earnings in a given year on age, education, union status, and the worker's earnings in the previous year using fixed effects regression. Will this regression give reliable estimates of the effects of the regressors (age, education, union status, and previous year's earnings) on earnings Explain.
10.11 Let
denote the entity-demeaned estimator given in Equation (10.22), and let denote the "before and after" estimator without an intercept, so that Show that, if
.