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## Betting on the Future with a Cloudy Crystal Ball?

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**Spending, Taxing, Saving, and Borrowing**A balanced budget Portfolio management Hedging Self-insurance Optimal spending rules Betting on the Future with aCloudy Crystal Ball? Fred Thompson & Bruce Gates Atkinson Graduate School of Management Willamette University**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.**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**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:**Example: Classical Multiplicative Decomposition**Conceptual Decomposition:**Example: Classical Multiplicative Decomposition**Visual Representation**Example: Classical Multiplicative Decomposition, Model**Interpretation Model Interpretation Initial, time-zero (1995:Q4) 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**Example: Classical Multiplicative Decomposition, Forecasts**Forecasts**Forecast Model Assessment**Residual analysis: Residual (Error) = Actual – Forecast Assessment possible for any type of forecasting process.**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).**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**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)**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 state’s 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.**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**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**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**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**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? Third Section: Hedging and self insurance**Lesson**• It is theoretically possible to do so using forwards, futures, or options**Lesson**• It is theoretically possible to do so using forwards, futures, or options • It is not practically feasible to do so at this time**Lesson**• It may never be politically feasible to do so**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 37:2, 2005; “Using Futures Contracts to Hedge Macroeconomic Risks in the Public Sector,” Trading and Regulation, volume 10, number 1, 2004.**Self insurance?**• Rainy day fund • Cooperative cash pool**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**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 tobalance 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 state’s existing revenue structure and volatility. • where PV future revenues + net assets < PV future outlays, permanent reductions in spendingor permanent increases in taxes are necessary**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.**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**Managing spending**• Schunk and Woodward’s (S&W) 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.**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.**Monte Carlo simulation of Oregon’s future spending and**revenues, given the adoption of S&W’s spending rule**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 state’s saving and borrowing policies as well.**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.**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, Oregon’s revenue growth trend is faster than outlay growth under the S&W rule • Oregon doesn’t need to increase taxes to offset a structural budget deficit -- it could adopt an optimal spending rule that would allow it to smooth consumption