Tax Base Volatility

Thomas StinsonMatthew SchoeppnerJune 24, 2008

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

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

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

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?

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

Volatility Is the Variation Around the Trend Rate of Growth

Sometimes Shocks Move Series in Different Directions

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

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.

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

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?

Minnesota’s Individual Income Tax BasePercent of Federal Gross Income

      1960-1965 2000-2005 Change

Salaries and wages 79.3% 71.8% ↓Taxable Interest 2.1% 2.5% ↑Ordinary Dividends 3.0% 2.0% ↓Net Capital Gains 4.0% 6.6% ↑Taxable Pensions, Annuities, and IRAs 0.7% 7.1% ↑Business, Partner, S-Corp, and Farm 9.4% 7.5% ↓All Other Income 1.6% 2.6% ↑

    Total: 100.0% 100.0%  

Data Source: IRS, Statistics of Income (SOI)

3.7%

1.3%

3.7%

1.3%

2.3%

0.9%

16.9%19.2%

27.3%

16.9%19.2%21.8%

2.3%0.6%

3.3%

6.0%

12.3%

15.2%

27.3%

Wages Are Largest Portion of Tax Base and Least Volatile

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

3.0%

5.4%

3.1%3.0%

5.4%

1.4%

General Sales Tax Base Results2006-2007 Estimated Current Law Proportion of General Sales Tax Base

  2006-2007Investment in Equipment 17.7%Non-Auto Durables 15.1%Other Non-Durables 10.2%Construction Materials 9.9%Prepared / Purchased Meals and Beverages 9.8%Telephone 5.6%Gas and Electricity 5.5%Recreation 3.7%State and Local Government Consumption 3.6%Auto Parts 3.5%Alcoholic Beverages 3.2%Candy, Gum, and Soft Drinks 2.6%Motor vehicle rental, leasing, washing, parking, and other 2.5%Hotels and Motels 2.4%Other Household Operation 1.7%Investment in Software 1.6%Personal Care/Other Services 0.9%Fuel Oil and Lubricants 0.3%Tobacco 0.2%

TOTAL 100.0% Data Source: BEA, National Income and Product Accounts (NIPA)

2.7%

5.2%

2.1%

2.7%

5.2%

2.2%

Corporate Income Tax Base Results

Data Source: BEA, National Income and Product Accounts (NIPA)

12.3%14.9%

12.1%12.3%14.9%

7.4%

Other Minnesota Tax Revenues

- 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 Tax Revenue 2006 Trend Growth Rate Comparison (Nominal)

Other General Fund Total Tax Revenue 7.7%Other General Fund Total Tax Revenue - Post MVST Phase-out 11.1%Inflation 2.6%

5.9%

10.9%

3.7%

Total Minnesota Tax Base Portfolio Results

General Fund Tax Base Sources Portfolio 1. Pre MVST Phase-Out 2. Post MVST Phase-Out

Total General Fund Tax Base Portfolio (Pre MVST Phase-out)

Proportion of Total General Fund Tax Revenue

      1970-75 2000-06 Change

General Sales Tax 22.6% 30.4% ↑

Corporate Income Tax 10.6% 5.7% ↓

Individual Income Tax 42.6% 44.9% ↑

Other General Fund Taxes 24.2% 19.0% ↓

    TOTAL: 100.0% 100.0%  

Data Source: U.S. Census, State Government Finances

2.4%2.1%

5.9%

12.1%

3.1%

2005-2007 Trend Growth Rate of General Fund Tax Base

Corporate IncomeTax Base 14.9%Individual Income Tax Base 5.4%MN Sales Tax Base 5.2%Other Revenue Tax Base 7.6%Total Portfolio 6.2%Inflation 2.6%

2.0%

2.4%

2.0%

2.9% in 1983

1.9% in 1996

2.7% in 2002

Total MN General Fund (Post MVST Phase-out)

Proportion of General Fund Tax Revenue With / Without MVST

     2000-06

(w/MVST)2000-06

(w/No MVST ) Change

General Sales Tax 30.4% 31.8% ↑

Corporate Income Tax 5.7% 6.0% ↑

Individual Income Tax 44.9% 47.0% ↑

Other General Fund Taxes 19.0% 15.2% ↓

    TOTAL: 100.0% 100.0%  

Data Source: U.S. Census, State Government Finances

2.6%2.1%

10.9%

12.1%

3.1%

2.0%

2005-2007 Trend Growth Rate of General Fund Tax Base

Corporate Income Tax Base 14.9%Individual Income Tax Base 5.4%MN Sales Tax Base 5.2%Other Revenue Tax Base 11.0%Total Portfolio 6.5%Inflation 2.6%

2.6%

2.0%

2.2% in 1987

2.1% in 1996

2.8% in 2002

2.5% in 1991

2.5% in 1983

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?

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 cycleShort Run Elasticity: Δln(TAXt) = α + β Δln(GDPt) + εt

• 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)

How Does the Volatility of MN’s Tax Base Compare with the National Economy?

* MN’s Sales Tax Base growth has slowed to below the rate of GDP since 2002

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?

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)

Appropriate Budget Reserve for General FundPost-MVST Phase-Out

Tax Source

FY 2005-2007 Share

of GF Total Revenue

Trend Growth Rate

Volatility (σ)

       

General Sales 28.64% 5.23% 2.06%Corporate Income 6.83% 14.94% 12.03%Individual Income 44.25% 7.25% 3.88%Other Revenues 20.29% 8.55% 5.24%

   Total GF Portfolio 100.00% 7.46% 3.03%

   

Final Results:  

   

With 95% Confidence (one tail or z = 1.645) an appropriate...

One-Year Budget Reserve: 5.0% (of Year 1 Current Resources)

Two-Year Budget Reserve: 7.1% (of Year 1 Current Resources)

Biennium Budget Reserve: 3.7% (of Biennial Current Resources)       

For Example, in FY06-07(Thousands $)

FY06 Resources

FY07 Resources

FY06-07 Resources

$17,355,445 $18,192,177 $33,734,477      

With 95% Confidence an appropriate FY06-07...

One Year Budget Reserve: $868,000

Two Year Budget Reserve: $1,232,000

Biennium Budget Reserve: $1,248,000

Actual FY06-07

Budget Reserve: $653,000

Cash Flow Account: $350,000

Appropriate Budget Reserve for General FundPre-MVST Phase-Out

Tax Source

FY 2005-2007 Share

of GF Total Revenue

Trend Growth Rate

Volatility (σ)

       

General Sales 28.17% 5.23% 2.06%Corporate Income 6.72% 14.94% 12.03%Individual Income 43.53% 7.25% 3.88%Other Revenues 21.58% 6.75% 3.61%

   Total GF Portfolio 100.00% 7.09% 2.83%

   

Final Results:  

   

With 95% Confidence (one tail or z = 1.645) an appropriate...

One-Year Budget Reserve: 4.7% (of Year 1 Current Resources)

Two-Year Budget Reserve: 6.6% (of Year 1 Current Resources)

Biennium Budget Reserve: 3.4% (of Biennial Current Resources)       

For Example, in FY06-07 (Thousands $)

FY06 Resources

FY07 Resources

FY06-07 Resources

$17,355,445 $18,192,177 $33,734,477      

With 95% Confidence an appropriate FY06-07...

One Year Budget Reserve: $809,000

Two Year Budget Reserve: $1,144,000

Biennium Budget Reserve: $1,147,000

Actual FY06-07

Budget Reserve: $653,000

Cash Flow Account: $350,000

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?

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, σ2

T, given growth rates gT

– Minimize

– Subject to:

and and

where ω is the weight of each tax.

Actual FY 2005-2007

Portfolio

Efficient Tax Mix

Portfolio

Difference: (Efficient Less Actual)

     

Trend Growth Rate 7.70% 7.70% 0.00%Volatility (Standard Deviation)

3.26% 3.09% -0.17%       

Share of Total Tax Revenue         

General Sales 31.2% 60.3% +29.2%

Corporate Income 7.4% 13.1% +5.6%

Individual Income 48.1% 9.2% -39.0%

Other Revenues 13.3% 17.4% +4.2%       

Total 100.0% 100.0%

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

Summary• Minnesota’s tax base has grown more volatile • The volatility of MN’s current tax base appears to

increase during recessions• MN’s tax base is about as volatile as the national

economy (measured by GDP)• At current levels of volatility MN’s biennial budget

reserve should equal approximately 3.7 percent of biennial revenues

• The necessary budget reserve can be reduced by relying more on less volatile revenue sources

Other Considerations

• Volatility is not the only criterion that should be used in determining a state revenue system

• Good tax systems are also– Equitable– Efficient– Simple– Administratively convenient

Thank You