Electoral Campaigns as Dynamic Contests

We develop a model of electoral campaigns in which two office-motivated candidates allocate their budgets over time to affect their odds of winning. We measure the candidates' evolving odds of winning using a state variable that tends to decay over time, and we refer to it as the candidates' "relative popularity." In our baseline model, the equilibrium ratio of spending by each candidate equals the ratio of their initial budgets; spending is independent of past realizations of relative popularity; and there is a positive relationship between the strength of decay in the popularity process and the rate at which candidates increase their spending over time as election day approaches. We use this relationship to recover estimates of the perceived decay rate in popularity leads in U.S. subnational elections.