Optimal Budget Rules: Making Government Spending Sustainable through Present-Value Balance

Abstract

This article uses simple and self-contained optimal control theory and martingale methods to find optimal government expenditure consistent with present value balance and, implicitly sustainable saving, borrowing, and tax levels as well, since long-term sustainable paths are, in principle, not different from optimal paths. Our approach identifies time-consistent budget rules, where most other efforts to do so have not, because it makes the reasonable assumption that the stochastic nature of revenues is more or less given, and ignores the relationship between the level and kind of taxes employed and revenue growth. Further allowing the government to invest in risky as well as risk-free financial assets, we derive explicit formulas for optimal expenditure and the parameters of its future stochastic evolution, expected surpluses and deficits and their dependence on model parameters, and the probability of sustained long-term growth and its dependence on the initial size of the reserve account.