Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 10

In Example 13.8, we used the unemployment claims data from Papke (1994) to estimate the effect of enterprise zones on unemployment claims. Papke also uses a model that allows each city to have its own time trend.
log(uclmst) = ai + cit + 1ezit + uit ,
where ai and ci are both unobserved effects. This allows for more heterogeneity across cities.
(i) Show that, when the previous equation is first differenced, we obtain
log(uclmsit) = ci + 1 ezit + uit, t = 2,..., T.
Notice that the differenced equation contains a fixed effect, ci.
(ii) Estimate the differenced equation by fixed effects. What is the estimate of 1 Is it very different from the estimate obtained in Example 13.8 Is the effect of enterprise zones still statistically significant
(iii) Add a full set of year dummies to the estimation in part (ii). What happens to the estimate of 1