Betting on the Future with a Cloudy Crystal Ball?

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Betting on the Future with a Cloudy Crystal Ball?

• Spending, Taxing, Saving, and Borrowing
• A balanced budget
• Portfolio management
• Hedging
• Self-insurance
• Optimal spending rules

Fred Thompson Bruce Gates Atkinson Graduate
School of Management Willamette University
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Lesson

• Trying to balance budgets (match spending to
  taxing) one year at a time leads to
  manic-depressive spending and taxing patterns
• This is costly, both directly in terms of the
  expedients taken to balance budgets and
  indirectly from a macroeconomic perspective
• The problem faced by budget makers derives from
  volatility in revenue growth.

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Lesson

• Economists cannot accurately predict revenue
  growth from one year to the next or the timing of
  the business cycle, but we can make actuarial
  predictions
• Mean/variance analysis

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Example Classical Multiplicative Decomposition
Conceptual Decomposition
Trend Long-term growth/decline Cycle
Long-term slow, irregular oscillation Seasonal
Regular, periodic variation w/in calendar
year Irregular Short-term, erratic variation
Conceptual Forecast
Forecasting Model
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Example Classical Multiplicative Decomposition
Conceptual Decomposition
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Example Classical Multiplicative Decomposition
Visual Representation
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Example Classical Multiplicative Decomposition,
Model Interpretation
Model Interpretation Initial, time-zero
(1995Q4) level is 731.92 million Increasing at
18.5 million per quarter Seasonal
pattern Peak in Q4 21 over trend Trough in
Q3 11 below trend
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Example Classical Multiplicative Decomposition,
Forecasts
Forecasts
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Forecast Model Assessment

• Residual analysis
• Residual (Error) Actual Forecast
• Assessment possible for any type of forecasting
  process.

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Second section portfolio theory
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Lesson

• Most states cannot significantly reduce
  volatility in revenue growth by substituting one
  tax type for another (e.g. a broad-based foods
  and services taxes for in income tax, or vice
  versa).

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Lesson

• Unsystematic volatility in revenue growth can be
  significantly reduced via a well-designed
  portfolio of tax types.
• Diversification of tax types can reduce revenue
  volatility most states rely on a portfolio of
  tax types.
• How does diversification of tax portfolios work?
  The answer is that portfolio volatility is a
  function of the covariance or correlation, ?, of
  its component revenue sources

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Diversification of tax types

• Expected growth is the weighted average of the
  growth rates or four percent.
• The volatility of the portfolio, ??? 3.1 percent
  -- much less than the volatility of either the
  income tax (13.4 percent) or the income and
  alcohol taxes combined (8.9 percent). It is less
  even, than the volatility of the alcohol tax
  alone (4.4 percent)

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Implications of portfolio theory

• In general, tax sources have ????0.65, so adding
  taxes to the portfolio tends to reduce but not
  eliminate volatility.
• It is possible to construct an efficient growth
  frontier, showing an efficient linear combination
  of growth rates and volatilities ranging from
  zero volatility, to a states optimal volatility
  at its current growth rate and beyond
• All one needs is information on the covariance of
  the growth rates of each of the different tax
  types and designs that obtain in different
  states.
• Only if we look at efficient tax portfolios is
  there a necessary tradeoff between stability and
  growth.

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Efficient Tax Portfolios
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Lesson

• Average volatility will usually be reduced by
  adding tax sources, except where the two taxes
  are perfectly correlated, r 1.0
• A two tax portfolio could in theory be combined
  to eliminate revenue volatility completely, but
  only if r -1.0 and the two taxes were weighted
  equally

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Lesson

• Once an efficient tax-portfolio frontier has been
  identified, changes in the portfolio of tax types
  to increase tax-equity will also increase
  volatility in revenue growth

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Lesson

• Even the best-designed tax portfolio would not
  eliminate all volatility. In the absence of a
  policy of borrowing and lending at the risk free
  rate, the best tax-portfolio designers could do
  is eliminate the unsystematic or random portion
  of the variation in revenue growth.
• The systematic portion would remain. By
  systematic we mean, the portion correlated with
  some underlying variable

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Lesson

• GNP growth is the main underlying variable --
  which has two components
• Trend (mean)
• Cyclical
• Predicting the timing and amplitude of business
  cycles is no easier than predicting the growth of
  the economy from one year to the next

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Third Section Hedging and self insurance

• One way to eliminate systematic volatility in
  revenue growth is with a revenue flow of equal
  and opposite volatility. This is called hedging.
• If we could find two tax types which produced
  revenue flows of the same size that were
  perfectly, but inversely correlated with each
  other, we could eliminate all volatility in
  revenue growth. Unfortunately, there are no such
  tax types.
• Is it possible to design a hedge against the
  systematic component of revenue volatility?

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Lesson

• It is theoretically possible to do so using
  forwards, futures, or options

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Lesson

• It is theoretically possible to do so using
  forwards, futures, or options
• It is not practically feasible to do so at this
  time

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Lesson

• It may never be politically feasible to do so

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Hedging with options futures contracts

• Futures
• Options

See C. Hinkelmann Steve Swidler, Macroeconomic
Hedging with Existing Futures Contracts, Risk
Letters, forthcoming State Government Hedging
with Financial Derivatives, State and Local
Government Review, volume 372, 2005 Using
Futures Contracts to Hedge Macroeconomic Risks in
the Public Sector, Trading and Regulation,
volume 10, number 1, 2004.
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Self insurance?

• Rainy day fund
• Cooperative cash pool

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Lesson

• Self insurance and risk pooling
• Insurance is like a put option.
• A rainy-day fund is simply a form of self
  insurance.
• A rainy day fund large enough to prevent all
  revenue shortfalls would be very costly
• Risk pooling would dramatically reduce those costs

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Fourth Section Optimal Spending
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Lesson

• States can use savings and/or borrowing to smooth
  out consumption over the business cycle
• Consumption smoothing implies present value
  balance
• PV future revenue net assets PV future
  outlays
• Goal should be to balance budgets in a
  present-value sense, using savings and debt to
  smooth spending
• Hence, the problem faced by budgeters is to
  identify the maximum rate of growth in the
  spending level from one year to the next that is
  consistent with present value balance, given the
  states existing revenue structure and
  volatility.
• where PV future revenues net assets lt PV future
  outlays, permanent reductions in spending or
  permanent increases in taxes are necessary

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Lesson

• This can be done by treating revenue growth as a
  random walk. In which case, the problem faced by
  budget makers can be solved mathematically by
  optimal control theory.

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The basic question

• How much should we spend next year?
• State and local governments have few degrees of
  freedom but can focus on issues of solvency and
  liquidity

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Managing spending

• Schunk and Woodwards (SW) spending rule
• Increase spending no faster than the rate of
  inflation plus the long-term real growth rate of
  the underlying economy (put aside the remainder
  for a rainy day)

Donald Schunk and Douglas P. Woodward. Spending
Stabilization Rules A Solution to Recurring
State Budget Crises? 2005. Public Budgeting
Finance 5(4) 105-124.
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Managing spending 2
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Revenue growth is a random walk

• Revenue growth can be modeled as a Wiener
  process
• a continuous-time, continuous-state stochastic
  process in which the distribution of future
  values conditional on current and past values is
  identical to the distribution of future values
  conditional on the current value alone, and
• the variance of the change in the process grows
  linearly with the time horizon.

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Monte Carlo simulation of Oregons future
spending and revenues, given the adoption of
SWs spending rule
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An optimal spending rule

• Given that we can model revenue growth as a
  Wiener process, it is possible to calculate a
  spending rule directly using optimal control
  theory.
• By comparing proposed spending levels (including
  tax expenditures and debt service) against the
  optimum spending level calculated using this
  rule, one can say whether or not the specified
  spending level is sustainable and implicitly
  assess a states saving and borrowing policies as
  well.

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Indexes of Revenue, Asset Portfolio Value, and
ExpenditureThe blue line shows an index of
revenue, the beige line shows an index of
portfolio value, and the red line shows an index
of optimal expenditure. All indexes are
normalized to 100 in year 1.
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Practical Implications

• Oregon cannot significantly reduce volatility in
  revenue growth by tinkering with its tax
  structure -- at least not without also
  reducing progressivity
• Hedging -- probably not practical
• Oregon could rely on a rainy day fund of
  sufficient size to mitigate the adverse
  consequences of cyclical revenue shortfalls (if
  it had one) or meliorate them via a program of
  countercyclical borrowing
• Other things equal, Oregons revenue growth trend
  is faster than outlay growth under the SW rule
• Oregon doesnt need to increase taxes to offset a
  structural budget deficit -- it could adopt an
  optimal spending rule that would allow it to
  smooth consumption