Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 12

VOTE2.RAW includes panel data on House of Representative elections in 1988 and 1990. Only winners from 1988 who are also running in 1990 appear in the sample; these are the incumbents. An unobserved effects model explaining the share of the incumbent's vote in terms of expenditures by both candidates is
vote.t = 0 + 0 d90 t + l og(inexp it ) + log(chexpi it ) + 3incshr it + a i + u it ,
where incshrtt is the incumbent's share of total campaign spending (in percentage form). The unobserved effect a. contains characteristics of the incumbent-such as "quality"-as well as things about the district that are constant. The incumbent's gender and party are constant over time, so these are subsumed in a i. We are interested in the effect of campaign expenditures on election outcomes.
(i) Difference the given equation across the two years and estimate the differenced equation by OLS. Which variables are individually significant at the 5% level against a two-sided alternative
(ii) In the equation from part (i), test for joint significance of Alog(inexp) and Alog(chexp). Report the p-value.
(iii) Reestimate the equation from part (i) using Aincshr as the only independent variable. Interpret the coefficient on Aincshr. For example, if the incumbent's share of spending increases by 10 percentage points, how is this predicted to affect the incumbent's share of the vote
(iv) Redo part (iii), but now use only the pairs that have repeat challengers. [This allows us to control for characteristics of the challengers as well, which would be in ai. Levitt (1994) conducts a much more extensive analysis.]