Tax Base Volatility

1. Tax Base Volatility Thomas Stinson Matthew Schoeppner June 24, 2008

2. Tax Base Volatility • What is volatility? • A measure of the variation between normal (trend) growth and actual changes • How do we measure volatility? • The standard deviation (σ)is the standard measure of volatility

3. What is a Standard Deviation? • A measure of dispersion or central tendency • In a normal distribution 68.2 percent of the values will fall within one σ of the mean and 95.4 percent of the values will fall within 2 σ’s of the mean • A distribution with σ = 1 will have a narrower concentration of values than a distribution with σ = 2

4. Why Is Volatility Important? • More volatile (higher σ) tax systems will have larger surpluses and deficits • The volatility of a tax system helps determine how large a reserve is needed • Tax system volatility can be adjusted by changing either the proportion of revenue derived from each tax or the volatility of the individual taxes

5. Questions • How volatile is Minnesota’s tax system? • Has its volatility changed over time? • Is Minnesota’s tax base more volatile than the economy? • How large a budget reserve is needed? • Could we produce the same revenue with less volatility?

6. How We Measure Volatility • Focus first on tax base, not revenues • Analyze growth rates, not dollar amounts • Find annual growth rates for detailed items in the tax base • Find yearly deviations from trend growth • Convert tax base to revenues • Combine volatilities of each separate segment of the tax base to produce an estimate of the system-wide volatility

7. Volatility Is the Variation Around the Trend Rate of Growth

8. Sometimes Shocks Move Series in Different Directions

9. U.S. Capital Gains 1960-2006(Annual Percent Change)

10. Hodrick Prescott Filter uses a trend component and a cyclical component to obtain a smoothed non-linear representation of the long term trend growth rate of a data-series.

13. Volatility Calculation Summary • Method • Hodrick-Prescott filter gives trend growth rate • ARCH, GARCH, and EGARCH models used to estimate volatility (σ) from trend growth rate over time • Data • National data from SOI, NIPA accounts • Income tax: 7 income types • Sales tax: 19 purchase categories • Corporate tax: domestic profits • Other tax and non tax revenue

14. Questions • How volatile is Minnesota’s revenue system? • Has the volatility changed over time? • Are Minnesota’s revenues more volatile than the economy? • Could Minnesota’s tax system produce the same revenue with less volatility? • How large a reserve should we have?

15. Minnesota’s Individual Income Tax Base Data Source: IRS, Statistics of Income (SOI)

16. 3.7% 1.3%

17. 3.7% 2.3% 1.3% 0.9%

18. 19.2% 16.9%

19. 27.3% 21.8% 19.2% 16.9%

20. 27.3% 15.2% 12.3% 6.0% 3.3% 2.3% 0.6%

21. Wages Are Largest Portion of Tax Base and Least Volatile

22. Estimating the Volatility of a System of Taxes • Markowitz’s modern portfolio theory used as a guide: • The expected growth rate in revenues is the weighted sum of the individual growth rates • Portfolio volatility is the square root of the weighted sum of the variances and covariances of the individual components

23. 5.4% 3.0%

24. 5.4% 3.1% 3.0% 1.4%

25. General Sales Tax Base Results

26. 5.2% 2.7%

27. 5.2% 2.7% 2.2% 2.1%

28. Corporate Income Tax Base Results Data Source: BEA, National Income and Product Accounts (NIPA)

29. 14.9% 12.3%

30. 14.9% 12.3% 12.1% 7.4%

31. - Motor Fuels Excise Tax (Non-General Fund Revenue) • - State General Property Tax • Motor Vehicle Sales Tax (Phasing-out of General Fund)- Motor Vehicle License Fee (Non-General Fund Revenue) • MinnesotaCare Tax (Non-General Fund Revenue) • Insurance Premiums Tax- Deed and Mortgage Tax • Health Care Provider Surcharge- Cigarette/Tobacco Tax- Liquor/Wine/Beer Tax • Estate Tax Other Minnesota Tax Revenues

32. 10.9% 5.9% 3.7%

33. Total Minnesota Tax Base Portfolio Results General Fund Tax Base Sources Portfolio 1. Pre MVST Phase-Out 2. Post MVST Phase-Out

34. Total General Fund Tax Base Portfolio (Pre MVST Phase-out) Data Source: U.S. Census, State Government Finances

35. 12.1% 5.9% 3.1% 2.4% 2.0% 2.1%

36. 2.9% in 1983 2.7% in 2002 2.4% 1.9% in 1996 2.0%

37. Total MN General Fund (Post MVST Phase-out) Data Source: U.S. Census, State Government Finances

38. 12.1% 10.9% 3.1% 2.6% 2.0% 2.1%

39. 2.8% in 2002 2.5% in 1983 2.6% 2.5% in 1991 2.2% in 1987 2.1% in 1996 2.0%

40. Questions • How volatile is Minnesota’s revenue system? • Has the volatility changed over time? • Are Minnesota’s revenues more volatile than the U.S. economy? • How large a reserve should we have? • Could Minnesota’s tax system produce the same revenue with less volatility?

41. How Does the Volatility of MN’s Tax Base Compare with the National Economy? • Measure the “income elasticity of taxes” • Provides information concerning: • How MN’s Tax Base grows relative to GDP Long Run Elasticity: ln(TAXt) = α + β ln(GDPt) + εt • How MN’s major Tax Base fluctuates over the business cycle Short Run Elasticity: Δln(TAXt) = α + β Δln(GDPt) + εt

42. How Does the Volatility of MN’s Tax Base Compare with the National Economy? • Over the long run (1970-2005) MN’s tax base growth was statistically the same as nominal GDP growth • Personal Income Tax Base -- same as GDP • Corporate Income Tax Base -- 92% of the rate of GDP • Sales Tax Base -- 10% faster than the rate of GDP* • “Other” Taxes -- 82% of the rate of GDP • Over the business cycle there is no statistically significant difference between MN’s tax base volatility and nominal GDP • Personal Income Tax Base -- same as GDP • Corporate Income Tax Base -- more volatile • Sales Tax Base -- nearly the same as GDP • “Other” Taxes -- volatility not statistically different from zero, (unaffected by the business cycle) * MN’s Sales Tax Base growth has slowed to below the rate of GDP since 2002

43. Questions • How volatile is Minnesota’s revenue system? • Has the volatility changed over time? • Are Minnesota’s revenues more volatile than the economy? • How large a reserve should we have? • Could Minnesota’s tax system produce the same revenue with less volatility?

44. Calculating the Appropriate Size for Minnesota’s Budget Reserve • Convert estimated tax base volatility to total GF revenue volatility (3.03% post MVST) • Choose how often it is acceptable for the budget shortfall to exceed the budget reserve (1 in 20, 5%) • Multiply the revenue volatility estimate by the critical failure rate value to obtain the percent shortfall exceeded 1 in every 20 times (3.03*1.645 = 4.98%) (critical value for a 5% one tail z test = 1.645)

45. Appropriate Budget Reserve for General FundPost-MVST Phase-Out

46. Appropriate Budget Reserve for General FundPre-MVST Phase-Out

47. Questions • How volatile is Minnesota’s revenue system? • Has the volatility changed over time? • Are Minnesota’s revenues more volatile than the economy? • How large a reserve should we have? • Could Minnesota’s tax system produce the same revenue with less volatility?

48. Portfolio Theory Suggests Using a Tax System that Minimizes Volatility for a Given Growth Rate • Given the trend growth rate, variance and covariance of each major tax, an Efficiency Frontier Line (EFL) can be estimated • The EFL shows combinations of taxes that provide the lowest volatility for each growth rate • Points below the frontier are suboptimal. • The EFL is determined using quadratic programming to minimize state tax revenue volatility, σ2T, given growth rates gT • Minimize • Subject to: and and where ω is the weight of each tax.

50. Actual vs. Efficient MN One-Year Tax-Mix Given the Current Trend Growth Rate