Use the data set in AIRFARE to answer this question. The estimates can be compared with those in Computer Exercise 10, in this Chapter.

(i) Compute the time averages of the variable concen; call these concenbar. How many different time averages can there be? Report the smallest and the largest.

(ii) Estimate the equation lfareit 5 b0 1 d1y98t 1 d2y99t 1 d3y00t 1 b1concenit 1 b2ldisti 1 b3ldistsqi 1 g1concenbari 1 ai 1 uit by random effects. Verify that b^

1 is identical to the FE estimate computed in C10.

(iii) If you drop ldist and ldistsq from the estimation in part (i) but still include concenbari

, what happens to the estimate of b^

1? What happens to the estimate of g1?

(iv) Using the equation in part (ii) and the usual RE standard error, test H0: g1 5 0 against the twosided alternative. Report the p-value. What do you conclude about RE versus FE for estimating b1 in this application?

(v) If possible, for the test in part (iv) obtain a t-statistic (and, therefore, p-value) that is robust to arbitrary serial correlation and heteroskedasticity. Does this change the conclusion reached in part (iv)?