This exercise uses the data file nls_ panel.dat that was introduced in Section 15.1 and carried through as an example in Sections 15.2 to 15.6.We are interested in estimating the equation LWAGEit ¼ b1i þ b2EDUCi þ b3EXPERit þ b4EXPER2 it þ b5HOURSit

þ b6BLACKi þ eit Our primary focus is on estimating the percentage return to education f ¼ 100 b2 and the percentage return to experience for a woman with five years of experience, u ¼ 100 ð Þ b3 þ 10 b4 .

(a) Why is the percentage return to experience for a woman with five years of experience equal to 100 ð Þ b3 þ 10 b4 ?

(b) Estimate the model assuming that the intercept b1i is the same for all individuals

ð Þ b1i ¼ b1 and that the errors eit are homoskedastic and uncorrelated. Find 95%

interval estimates for f and u.

(c) Estimate the model assuming that the intercept b1i is the same for all individuals

ð Þ b1i ¼ b1 , computing standard errors consistent with the assumption cov eit ð Þ¼ ; eis cts. Find 95% interval estimates for f and u. Discuss any differences between these results and those from part (b).

(d) Estimate the model assuming that the intercept b1i is a random variable with mean b1 and variance s2 u, and the errors eit are homoskedastic and uncorrelated.

Find 95% interval estimates for f and u. Discuss any differences between these results and those from parts

(b) and (c).

(e) Are there any variables in the model that might be correlated with the b1i in part

(d)? Use t tests and an overall x2-test to test for correlation between the b1i and the variables in the model.

(f) Re-estimate the model in

(d) assuming that EDUC and HOURS are correlated with the b1i. Find 95% interval estimates for f and u. Discuss any differences between these results and those from parts (b), (c), and (d).