April 7, 2010

LEVELING OREGON GENERAL FUND REVENUES

by

John H. Detweiler

Introduction and Summary

The revenue for the Oregon general fund is composed of personal income tax, corporate income tax and other revenues which fluctuate depending on the economic situation. The Legislature tends to ignore this variability and not save during good times so that we would have money in bad times. We keep ending up in a situation where we have started programs during good times and have to make severe reductions in bad times. What we need to do is estimate a steady-state funding level for each biennium and, in bad times, use money in the "general fund reservoir" -- aka rainy day and educational stability funds -- to bring us up to the steady-state level, if the reservoir is full enough. In good times, we need to restrict our general fund spending to the steady-state level and put the funds over the steady-state level in the reservoir. If we don't do this, we are just going to keep starting and reducing programs in time with the business cycles.

Using the general fund history, which can be downloaded from the Oregon Office of Economic Analysis, and assuming that general fund revenue is a function of Oregon's population, inflation, and the business cycles, I estimated a steady-state level for the 2009-2011 biennium. The population data can be obtained from Portland State University Population Center. Inflation data can be obtained from the Bureau of Labor Statistics. I adjusted the general fund history, which is in then-year dollars, to constant 2010 dollars using the consumer price index (CPI) for all items for all urban consumers. I then adjusted the constant dollar general fund history to a constant 2010 population using the population numbers as if they were an index like the CPI. Presumably the only thing left in the data are the business cycles.The ups and down of the business cycles can be converted to annuities in the same way that any uneven set of cash flows can be converted to an annuity -- compute the net present value of the cash flows over the period of the business cycle and divide that by the annuity factor.

Using data that was current in March 2009, the expected general fund revenue was $13,050.0 million. I found that the steady state level of funds that should come from the general fund and reservoir to be about $13.75 billion for the 2009-2011 biennium. Looking at the budget press briefing of December 2009, the total general fund resources are $13,393.1 million, the triggered withdrawals are only $4.7 million, the beginning balance of the rainy day fund was $112.5 million, and the beginning balance of the educational stability fund is as $0.1 million. Obviously we are not ready for a steady-state solution; but when the good times come again, we need to start putting sufficient money into the reservoir or we will keep dancing to the business cycles.

The section below contains the details of my analysis for the 2009-2011 biennium. This analysis should be done before each biennium because the numbers will change. We will have inflation, population, and general fund data for two additional years as each biennium passes. Not only will the parameters change a little, the periods of the business cycles may change too.

Analysis

Again, assuming that general fund revenue is a function of Oregon's population, inflation, and the business cycle, I adjusted the nominal general fund data from FY 1978 to FY 2008 with the CPI and the population index to constant 2010 dollars with the 2010 population. I then ran a simple linear regression analysis with time as the independent variable. To determine the more important business cycles I conducted a fast fourier transform on the residuals adding sine-cosine terms, one at a time for each business cycle adding the most important cycle to the regression each time. The final regression analysis is shown below.

Valid cases:                    31      Dependent variable:              GFREAL 
Missing cases:                   0      Deletion method:                   None
Total SS:             20891974.742      Degrees of freedom:                  24
R-squared:                   0.871      Rbar-squared:                     0.838
Residual SS:           2702326.056      Std error of est:               335.555
F(6,24):                    26.924      Probability of F:                 0.000
Durbin-Watson:               1.853

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONST     6838.692675  135.238576   50.567618     0.000    ---         ---      
TIME        66.787786    7.054221    9.467776     0.000    0.727668    0.822631 
COS(W2)   -160.704434   60.365807   -2.662177     0.014   -0.195656   -0.198179 
SIN(W5)     46.447775   86.407852    0.537541     0.596    0.039793    0.088317 
COS(W5)    122.677724   85.307789    1.438060     0.163    0.106121    0.083077 
SIN(W24)  -252.178627   84.268057   -2.992577     0.006   -0.220716   -0.248662 
COS(W24)  -402.213341   94.117540   -4.273522     0.000   -0.326943   -0.507920

The zero year is FY 2010. The most important and significant business cycles have periods of two and twenty-four years. The cycle with a period of five years appears be important on the spectral estimate -- intensity vs. radian frequency -- graph but the coefficients are not statistically significant. The change with time is significant; general fund revenue is increasing at the rate of $66.8 million per year in 2010 dollars after accounting for the changes in population.

The graph below shows the general fund nominal history, the nominal history adjusted for inflation and population, and the projection of the inflation and population adjusted general fund with the results of the regression analysis.

Computing the net present value of the cash flows over the period of the business cycle -- 0 to T -- and dividing that by the annuity factor involves solving equation one for the constant "C" in terms of the constants "A" and "B", the radian frequency, omega, and the real interest rate, r. A and B are the estimates of the sine and cosine regression coefficients respectively. Solving equation one and rearranging terms results in equation two.

Substituting the coefficients of A and B into the regression equation gives an equation to project the general fund for 2010 and 2011 where there are three constants in place of the three sine-cosine business cycle waves. The 2011 projection is then adjusted for inflation and population and added to the 2010 projection to get the steady-state biennium projection. A graph showing the biennium projection vs the real interest rate is shown below

The steady-state biennium projection is a function of the real interest rate. The most important cycle is the long term cycle of twenty-four years; therefore, the real interest rate should be relatively high -- say 4% -- which gives a steady-state biennium projection of about $13.75 billion.

Notes:

• The CPI obtained from the BLS stopped at March 2009. Therefore I projected the CPI to 2011 with exponential smoothing.
• The population estimates stopped at July 2008. Therefore I projected the population estimates to 2011 with ARIMA.
• Some computations were done with Excel; most were done with Gauss Mathematical & Statistical System Version 8.0. All graphics were done with Gauss, a product of Aptech Systems, Inc.
• The reason for the difference between the time the data was current and the date at the top of this web page is that it took me a while to figure out how to do this and this web page has been revised several times.
• The real problem with leveling the general fund revenue is not methodology. Had it been methodology, the Legislative Revenue Office or the Department of Administrative Services Economic Section would have developed a methodology years ago. The real problem is a legislature that won't live within Oregon's means.