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 + β1ezit + 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 + β1△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 β1? 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 β1?