Two assumptions motivate our model for presidential targeting of LFEs. The first is that the President's targeting decisions are based on forecasts of the support he (or his party's successor candidate) will receive in each area in the next election. The second is that those forecasts are strongly informed by the support the President received from each area in the most recent election. Even if the President is not running for reelection, he and his administration ought to support a targeting plan to try to maintain party control of the White House.
Suppose each individual voter i in local area s in year t decides whether to vote for the incumbent based on a continuous index , according to the rule if , if , where indicates a vote for the incumbent and indicates a vote against the incumbent. Specifically,
where is a row vector of variables, is a row vector of variables measuring the LFEs supplied to the local area, is a scalar and and are column vectors of constant coefficients, is a vector of coefficients constant for each individual, and is a stochastic disturbance identically and independently across individuals, local areas and time.
The President cares about the aggregate distribution of the vote in each area. Given the Electoral College, the President's direct interest is in winning half or more of the electoral votes. Because a direct model of the President's choice among all the possible electoral vote majority patterns would be unwieldy, we simplify by assuming that the President is interested in the aggregate vote in each local area. Specifically, we assume that the President cares about the mean value of in area s at the time of the upcoming election, i.e., about , where denotes the set and denotes the number of voters in area s at .
The President targets LFEs to each area to increase his expected support there, according to some strategy. The strategy is a function of the information that the President has at time t about , and is tailored to each type of expenditure. We use to denote the targeting function the President uses for the kth type of LFE. For each value of , this function indicates how much of the kth type of LFE ought to be supplied to area s. The set of possible strategies for each kind of LFE includes the null possibility that the President does no targeting related to at all. In this case is a constant.
We allow the targeting function to differ between the first two years and the last two years of the President's term. Our specification for the amount of the kth type of LFE going to area s in year t is
where during the first two years and during the second two years, and denote targeting functions for early and late in the term, is a fixed vector of observed exogenous variables, is a scalar and is a vector of constant coefficients, and and are respectively area-specific and time-specific fixed effects. The area-specific effects would capture any adjustment in the level of the LFE done throughout whole States pursuant to a plan to build a majority in the Electoral College. The disturbance has expectation and variance . We use the exponential form in equation (2) because virtually all observed local aggregations of LFEs are nonnegative. An additive disturbance with the specified form of heteroscedasticity is frequently appropriate for models with loglinear expectations (McCullagh and Nelder 1989:193ff). The disturbances and are assumed to be uncorrelated for all k, i, s and t.