Revenue cycles and the distribution of shortfalls in U.S. states: implications for an "optimal" rainy day fund.

INTRODUCTION

Slowdowns in economic activity often leave state policymakers facing budget shortfalls and the prospects of reducing services. For example, as a result of the 2001 recession, the National Governors Association reported that 21 states enacted negative growth budgets in FY2003 and further reduced budgeted spending during the year by an additional $12 billion. (1)

Despite the attention given to state fiscal problems during slowdowns, few studies have attempted to quantify the "fiscal stress" that states experience due to recessions. This is important because, unlike the federal government, the options available for mitigating recessions at the subnational level are limited by various institutional constraints such as balanced budget rules, borrowing restrictions, and tax limitation laws (Poterba, 1994). As a result, the number of states utilizing a rainy day fund to help accumulate savings has grown from fewer than ten in 1980 to more than 45 by the start of the 2001 recession.

In this paper we make use of a Markov switching regression model, popularized by Hamilton (1989), to empirically describe the distribution of state expansions and contractions using monthly data and extend the fiscal stress literature along multiple dimensions. First, while previous authors have modeled the distribution of shortfalls a state is likely to face in a single fiscal year, our approach permits the duration of downturns to exist for an arbitrary number of periods to explore the likely impact of multi-year recessions on state revenue.

Next, if policymakers wish to save during periods of growth to hedge against downturns, then knowledge of an expected shortfall is of limited value because the duration of expansions is uncertain. In other words, if two states are expected to experience identical fiscal stress during a normal downturn (say ten percent of the budget), then the amount policymakers would need to save during each expansion period to offset the downturn will be different depending on the expansions that are likely to prevail. Using the estimated distribution of state expansions and contractions, we demonstrate how a distribution of savings rates may be constructed so that policymakers can determine the necessary amount to save during expansions to hedge all of the possible expansion-contraction combinations that may occur with a given level of certainty. The determination of savings rates has been overlooked in the literature and if policymakers wish to use savings as a means of insuring against fiscal shocks, then knowledge of a savings rate is arguably more valuable than knowledge of an expected shortfall.

Finally, our approach is very general with regard to the measurement of shortfalls and, therefore, can easily be modified to cover a variety of fiscal objectives. We present estimates of the distributions of state shortfalls and savings rates using two different shortfall measures that reflect a reasonable range of objectives that policymakers may wish to consider.

In the following sections of the paper we review previous research, outline our empirical methodology and findings, and offer concluding remarks.

PREVIOUS RESEARCH AND THE MEASUREMENT OF STATE FISCAL STRESS

Literature Review

Previous studies have addressed the issue of measuring fiscal stress from the perspective of an "optimal" rainy day fund (or budget stabilization fund) because if policymakers wish to guard against recessions via a savings instrument, then knowledge of the fiscal stress they are expected to encounter is essential. (2)

The information that is perhaps the most valuable to policymakers regarding fiscal stress is how likely a state will be to face a future shortfall of a given size, and what savings rate they need to follow during expansions in order to accumulate their target level of funds before the next downturn. Given that economic cycles are not perfectly predictable, a methodology describing the distribution of shortfalls and savings rates is more informative than an approach that generates a point-estimate. Modeling the distribution of shortfalls requires focusing on the contraction phase of state economic cycles, while modeling the distribution of savings rates requires examining both expansions and contractions.

Multiple strategies could be pursued to empirically model state expansions and contractions in order to construct distributions of shortfalls and savings rates. A Markov regime switching regression is well suited for this task because the model's parameters explicitly describe the distribution of multiple "regimes" (such as an expansion and a contraction) and estimation of the model jointly determines the parameter values describing each regime that best fit the observed data. These parameters include the mean growth rate of each regime, as well as the probabilities that a given observation came from either an expansion or contraction regime, which are known as transition probabilities. The expected duration of each regime can be computed from the transition probabilities.

Previous research has ignored the calculation of savings rates, focusing instead on measuring shortfalls using approaches that are based on the deviation from a linear trend and value-at-risk (VaR), which is a common technique used to model portfolio risk in the finance literature. The linear-trend method, followed by Pollock and Suyderhoud (1986), Sobel and Holcombe (1996), and Navin and Navin (1997), has generated a point-estimate that is equal to the cumulative deviation from trend. For example, Sobel and Holcombe (1996) sum the cumulative shortfalls in expenditures and revenues from their respective trends from 1989 to 1992 and find that the average state would have needed reserves equal to 30 percent of expenditures in order to maintain trend expenditures and revenues during the 1990-91 recession. Examining individual states over a longer time period, Pollock and Suyderhoud (1986) and Navin and Navin (1997) find that savings equal to 11 and 13 percent of the budget in Indiana and Ohio would be sufficient to offset a normal downturn.

Although the aforementioned studies provide only point-estimates, it is possible (but not optimal) to use the linear-trend method to model the distribution of shortfalls and savings rates. Designating observations that are above and below trend as expansions and contractions, respectively, one could then compute the average expansion growth rate, the average contraction growth rate, and the transition probabilities using the observations that fall into each classification. (3) The major problem with this approach is that there is no reason to believe that the expansion and contraction periods that one identifies will coincide at all with actual business-cycle movements. This is because a linear-trend model optimizes over the choice of the intercept and slope parameters to minimize the deviation from trend rather than optimizing over the parameters that best describe the distribution of expansions and contractions. In other words, a linear-trend approach estimates the parameters that are needed to form the distributions of shortfalls and savings rates as a secondary step, whereas a Markov switching regression directly optimizes over the choice of these parameters. (4) In addition, given that Pollock and Suyderhoud (1986), Sobel and Holcombe (1996), and Navin and Navin (1997) classify contractions as observations below trend, the soundness of their point-estimates depends on how closely their expansion-contraction classifications coincide with actual business-cycle movements.

In contrast, Cornia and Nelson (2003) model the distribution of budget deficits in Utah using value-at-risk and estimate that there is a 95 percent chance that Utah's deficit will be no worse than $135 million in a single fiscal year. (5) Even though Cornia and Nelson limit the time horizon to one year, VaR may be extended to multiple periods to incorporate downturns lasting longer than one year, which is important considering that Owyang, Piger, and Wall (2005) find that state-level recessions last on average for 16 months. However, because standard VaR analysis assumes that the data are being generated from a single probability distribution, it is incapable of modeling the distribution of savings rates because they are a function of the distribution of both expansions and contractions. (6)

Measuring State Fiscal Stress

The measurement of state fiscal stress, at least conceptually, merely involves quantifying how downturns force revenues and expenditures to deviate from the "norm." Since tax bases are procyclical and tend to be more volatile than state economies, holding tax rates constant over the business cycle and assessing the decline in revenue would capture the revenue side. Given Dye and McGuire's (1999) finding that several components of spending, such as public welfare and Aid to Families with Dependent Children (AFDC), tend to increase during down turns, expenditure-side fiscal stress could be evaluated by allowing social assistance spending to increase holding non-welfare spending constant. A natural measure of state fiscal stress would, therefore, be the state's cyclical surplus/deficit because it would capture the response of both revenues and expenditures to downturns.