Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 7

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?

Step 1 of 4

Consider the unobserved effects model is given by:

(i)

At time, the unobserved effects model is given by:

At time, the unobserved effects model is given by:

On taking the difference fromto , the result is:

The first-differenced equation contain a fixed effect