We build a model of electoral campaigning in which two office-motivated candidates each allocate a budget over time to affect their relative popularity, which evolves as a mean-reverting stochastic process. In equilibrium the ratio of spending by each candidate equals the ratio of their available budgets in every period. This result holds under a wide range of specifications of the model. We characterize the path of spending over time as a function of the parameters of the popularity process. We then use this relationship to recover estimates of the decay rate in the popularity process for U.S. elections from 2000-2014 and find substantial weekly decay rates well above 50%, consistent with the estimates obtained using different approaches by the literature on political advertising.