Michael U. Dothan, Ph.D, Guy F. Atkinson Professor of Economics & Finance, Willamette University, Guy F. Atkinson Professor of Economics & Finance, Atkinson 210, Salem, OR 97301 and Fred Thompson, Ph.D., Atkinson Graduate School of Management, Willamette University, Willamette University, Salem, OR 97301.
Since time immemorial, prudent polities have established self-denying ordinances governing their behavior. Among the most important of these are fiscal rules designed to constrain inter-temporal transfers. These include debt limits, interest coverage ratios, one-period-at-a-time balanced budget requirements, pay-as-you go rules, and tax and expenditure limits. Unfortunately, there are no free lunches. These are not costless expedients. There is considerable evidence that the least costly as well as the most efficacious of these rules focus directly on the rate of spending growth. The problem with budget rules aimed at stabilizing the rate of spending growth, is that, although they seem to work fairly well, they are little more than arbitrary rules of thumb. What is needed is a non-arbitrary spending rule that would yield numerical targets, which would allow us to assess a government's spending (and implicitly its taxing, saving, and borrowing) policies in booms as well as in busts, thereby providing early warning signs to policy makers, bond raters, and the market. Moreover, if we had such a rule, it could be also used to assess the effectiveness of simpler budget rules. In this essay we provide just such a non-arbitrary rule. That is: we show how to identify the maximum rate of spending growth that is consistent with present value balance, given existing revenue processes and volatilities. Under this formulation public officials would use savings and/or borrowing to smooth the growth rate (not the level) of consumption over time. This is desirable because decision costs make high frequency adjustment excessively expensive. Our numerical specifications of maximum sustainable rate of spending growth are calculated using optimal control theory and martingale methods, where revenue and savings growth are treated as continuous-time, continuous-state stochastic processes. This approach identifies time-consistent spending rules, where most efforts to do so have not, because it takes a jurisdiction's revenue processes as given. This means that the solution to the problem of calculating the maximum sustainable rate of spending growth depends only upon current state variables (known in the period of budget formulation) and can be used to say whether a proposed rate of spending growth (spending in the year of execution) is sustainable or not.