The hog-maize cycle
When economists talk about instability, they start with the hog-maize cycle, first described in 1925. What one expects is that, when hog prices are high, people eat less of them and more maize, so the price of maize should go up and the price of hogs go down; people then would switch back to eating more hogs.
The system can become unstable, though, if hogs are fed on maize. Then, an increase in the price of maize causes hog-breeders to cut costs by raising fewer hogs. This decrease in hogs increases their price. The increase in the price of hogs causes people to eat more maize, which in turn increases the price of maize again. This leads to ever-increasing prices.
Oh no! Math! (and ecology and particle physics)
This phenomenon has been described mathematically using cobweb theory, which relies upon equations first described by the ecologists Lotka and Volterra independently in 1924 and 1925, one studying competition for limited resources and the other predation.
The Lotka-Volterra equations are one specific result of a general mathematical model called the Kolmogorov Forward Equation, described in 1931. It happens to be identical to the Fokker-Planck equation, who described the movement of populations of particles without the mathematical rigor of Kolmogorov. I may be the only person who's studied all of these fields.
What the math means for budgets
All the math shows is that, if you have set a budget to balance to zero, over time the amount of surplus or deficit is dependent only upon the volatility of the elements (I'm going to use the words "volatility" "variance" and "variability" in ways that statisticians will abhor, as they each have specific meanings that I will ignore). Obviously, those things that do not change will not change the budget's balance; the more variable something's value is, the further it can move the sum of values.
Sources of variability
The Minnesota Management and Budget department (MMB) provides reports on what the values of assets and liabilities were in the state's general fund and how far they differ from what was predicted. The spreadsheet from November of last year is here.
According to the statistical models above, it is the squares of the individual deviations that are important and one can rank elements by the squares of the variances divided by the actual values. In this way, one finds that sales and excise taxes are remarkably stable; in fact, the values do not change greatly regardless of other economic factors. Property taxes as a whole also do not vary greatly, but income taxes are less predictable (in a committee meeting, one state economist, Matt Schoeppner, gave his opinion that what variability existed in income taxes were due to bonuses and stock options among the wealthiest citizens) and corporate taxes are nearly impossible to predict accurately. There are also a few small elements that vary greatly, but average out to be unimportant over time, creating "noise" in the budget system; in last February's report from the MMB, departmental earnings were an example of this. Expenses do not contribute to the variability to any appreciable extent, which leads to an interesting observation:
The Leaky Bucket
Think of the state's general fund as a water bucket with a hole in the bottom. If you do not control the flow of water into the bucket, it eventually either runs dry or overflows, which is the instability of the system. Changing the size of the hole changes how fast the system goes unstable, but does not change the fact that it will still go unstable. You cannot solve the problem only by controlling the outflow. What this means in terms of budget is:
You cannot solve the state's budget problem with spending cuts!
The next time there's a budget deficit, anyone who says "We have to cut expenses, tighten our belts and live within our means" is being dangerously naive. The situation is not like balancing a checkbook.
Budget as a process control problem
The ever-expanding fluctuations in the budget are seen commonly in process control problems.
|From an old textbook of mine.|
This is what's called an "unstable underdamped second-order" system. The Kolmogorov equation is itself a second-order differential equation:
The second-order nature of the system comes from the least stable elements, namely corporate taxes and income taxes of the very wealthy. When the budget strays far from a zero sum, changes to the tax code are made and accountants then find ways to exploit the changes for the advantage of their employers, which soon leads to new changes in the tax code, repeating the cycle.
Fortunately, there are a number of ways to tame these unruly systems, even though we don't have enough information to model them accurately.
Ways out of the quagmire
Decrease response stringency
One way to decrease both the size and frequency of budget oscillations is to balance the budget less frequently, say every 10 years; this would require legislation (and probably a constitutional amendment) and would be unlikely to pass.
A second way is to remove the demand for a completely balanced budget. The simplest way to do this is to create a reserve, the amount of which should be quite large compared to what has been tried in the past. During the Ventura administration, the budget surplus was returned to taxpayers, but holding that amount in reserve might, at that time, kept the following deficit from occurring. Another way of doing this are "accounting shifts," moving items from one budget cycle to another; this, however, tends to exacerbate the problem in the long term.
Shift burden from unstable to stable elements
This is the "conservative" approach. The most unstable elements are corporate taxes and income taxes of the very wealthy; if the tax rates on these are lowered with a concomitant increase in property and sales/excise taxes, the stability of the system improves. The problem with this approach is that it rewards those who are exploiting the system and regressively increases the burden upon those least able to afford it.
"Tune" tax rates
It is possible with most systems to stabilize control by adjusting rates and measurements: if you are getting too little or too much from one source, you adjust the rate from which you take from that source to compensate. Unfortunately, this only works if the system itself is not changing. With the state budget being balanced every two years with new taxes, new ways of measuring taxation and elaborate accounting changes, there is no way to reign in the chaos by simple rate changes.
If a moratorium on these changes in the methods of taxation could be enforced and enough time could elapse to study the system made constant, these rates could be adjusted by empirical methods that have been known for 50 years. Because the budget must be balanced every two years, this is unlikely to ever happen.
Have everyone play by the same simple rules
This is the "libertarian" approach. It is not the corner dry cleaner that's causing instability in corporate taxes. Even restaurants, which are renowned for their failure rates, are not a problem, because they exist in such numbers that their overall contribution to the tax base remains relatively constant. It is the largest businesses, which have their own lobbyists to push for changes that will help them at the capitol that cause instability. [The example of Medtronic buying a foreign company for billions and changing their incorporation is a current example.]
Everyone, conservatives and liberals alike, agree that the tax code should be simplified. Every change that has ever been made has been to lessen someone's taxes. Because those with the most to gain have influenced the most, we currently live in a corporate plutocracy. Making changes to simplify the tax code, however, runs counter to the moratorium mentioned two paragraphs earlier.
Alter the method of control
As the integral feedback control of balancing the budget is necessary for instability, lessening it and switching to a different kind of control will stabilize.
1) Proportional control. If a budget reserve is created, it can be maintained within a certain range by simply adjusting tax rates in proportion to the change in the reserve between budget cycles. This is a simple elegant solution, but requires that no other changes be made.
2) Derivative control. Rather than trying to completely control the total perturbation to the ystem over time (integral control), one can add a control based upon the rate of change of the perturbation. This is anticipatory and decreases the time it takes to bring the system to a steady state. [If you actually read the Wikipedia link on the hog cycle, you'll find that some say anticipation is the problem, that over-reacting to expected future changes leads to instability. In closed loop systems with integral control, adding derivative control has been shown to be stabilizing.] This method is difficult to employ in complex budgets and works best with frequent adjustments, the opposite of the "reduced stringency" approach outlined earlier.
3) Feedforward control. Another necessity of instability is feedback control, i.e. responding to a change in the system after it has been quantified. Controlling perturbations before they enter the system, called feedforward control, does not lead to instability and adding it should increase stability in a system with feedback control. In the case of the state budget, I would suggest an alternative minimum tax for corporations that are large ("large" being defined by state economists), with the incentive of returning a portion of this collection to those businesses whose taxable income is closest to predictions. This would encourage businesses to stop trying to "game" the system. Support for this would be garnered by promising lower overall corporate tax rates.
Breaking the system's back
This is the "conspiracy theorist" approach. The instability of integral feedback control can be halted if the system itself can be changed so that it reacts differently to control. If, as I believe, corporations are exploiting the legislative system for their own gain, it becomes necessary to identify the manipulation and make it public. It appears that a record number of bills will be introduced this session and among these are ones designed to help large businesses at the expense of the state, it people and small businesses. These need to be stopped politically and could very slowly bring the budget fluctuations under control. We probably don't have enough time for this to work.