Abstract

Feenberg et al. (1989) apply a simple regression-based method to test the rationality of state revenue forecasts. Using the same regression-based methodology, we test the rationality of federal revenue forecasts for fiscal year 1802 through 2001. We find that Treasury forecasts of federal revenues satisfy the conditions of weak rationality.

"It is hardly necessary to point out that estimates are at best approximate. ... Congressional appropriations, extraordinary in character, or failures to realize fully estimated revenues, are ... influences which may operate seriously to derange all calculations. A conservative margin should, therefore, be reserved in forecasting definite results based on hypothetical calculations."

L. J. Gage

Secretary of the Treasury

December 4, 1900

Introduction

The effective conduct of fiscal policy critically depends upon the properties of the revenue forecasts used to implement these policies. More specifically, fiscal policy is frequently used to promote macroeconomic stability, allocative efficiency, and distributional fairness. In order to conduct fiscal policy in support of these goals, officials require accurate revenue forecasts. Suppose, for example, that budget deficits (surpluses) are unexpectedly large due, in part, to inaccurate revenue forecasts. The resulting fiscal posture of the country may be inappropriate for the circumstances and may even exacerbate the conditions that fiscal policy is intended to help alleviate.

Likewise, the ability of officials to use tax policy to promote allocative efficiency requires accurate revenue forecasts. For example, tax policy experts frequently recommend broadening the tax base and reducing marginal tax rates to encourage work, savings, investment, and entrepreneurial risk-taking. In order to implement such policy prescriptions, however, officials require accurate forecasts of their revenue consequences. Finally, officials also use tax policy to distribute tax burdens according to notions of fairness, such as the ability to pay principle. Designing tax policy to achieve distributional goals without jeopardizing other policy goals, particularly revenue adequacy, also requires accurate revenue forecasts. In short, accurate revenue forecasts play an important role in the development of sound fiscal policies.

The purpose of this study is to evaluate the quality of U.S. Treasury revenue forecasts; however, quality, like beauty, is in the eye of the beholder. For example, the preamble of this study suggests that a "conservative margin should be reserved in forecasting." This statement seems to argue for downwardly biased forecasts. But, forecasts that are consistently biased in one direction or another may lack credibility. In addition to unbiased estimates, there may be other properties that may be desirable in revenue forecasts.

Accordingly, we propose the following three properties of revenue forecasts. First, the average forecast error should equal zero; otherwise, the forecast is biased. A forecast that is consistently biased in one direction or another will not be credible to officials and the public in the long run. Second, the variance of the revenue forecasts should be less than the variance of actual revenues. A forecast of revenues that is more volatile that actual revenues will not provide a good guide to fiscal policy, particularly stabilization policy. Third, the forecast errors should be uncorrelated with the forecast itself; otherwise, the forecast is not using all available information and could be improved.

We proceed as follows. In the next section, we discuss a regression-based test of forecast accuracy and describe the data employed in this study. Then, we assess the rationality of U.S. Treasury revenue forecasts for the period 1802 to 2001 and for three sub-periods thereof that correspond to major changes in U.S. fiscal policy. We conclude with a summary of our findings and offer suggestions for further research.

Assessing the Rationality of Revenue Forecasts

Future revenues are uncertain for a number of reasons: unanticipated fluctuations in business investment and consumer spending, the future state of business and consumer confidence, war and peace, and political events at home and abroad. Additional uncertainty arises because the federal tax structure may change in the future. These difficulties are illustrated by the following passage:

It may be useful to add a few general illustrations of the reasons for some of the small estimates now submitted, and of the intrinsic difficulties in attaining much certainty concerning them during crises of overaction and revulsions like the past and the present. ... During the two years before the revulsions in commerce in 1819, and including that year, the sales of public land exceeded the unusual amount of nearly thirty millions of dollars, while in the following years they fell to only about four millions, or less than one-seventh. The system being changed from credit to cash may have cooperated in producing this result; though at the same time, the minimum price per acre was reduced, in order, in some degree, to counteract the effect of that change. Levi Woodbury

Secretary of the Treasury

September 5, 1837

Reports of the Finances, vol. IV

(pp. 99-100)

Methodology

Since forecasts can only be approximate, we propose the following three properties with which to evaluate the rationality of revenue forecasts.

(i.) Unbiasedness: The expected value of the forecast errors equal zero.

(ii.) Efficiency: The variance of the forecast is less than the variance of actual revenues.

(iii.) Independence: The forecast errors are independent of the forecast itself.

We say that a forecast is strongly rational if it exhibits properties (i), (ii), and (iii), and weakly rational if it exhibits properties (i) and (ii). (1) While we believe that these three properties are desirable and consistent with generally agreed upon notions of rationality, we concede that an optimal forecast need not be "rational" in the sense described here. A more analytical approach to identifying the properties of optimal revenue forecasts would be to define a loss function in terms of the errors of the revenue forecasts. The optimal properties of the optimal revenue forecasts would those that minimize the loss function. In addition to economic objectives, the loss function could be extended to include political objectives as well. Although this approach has merit, it is beyond the scope of the present study.

Following Feenberg et al. (1989), we use a simple regression-based method to evaluate the rationality of a set of revenue forecasts. More specifically, first we estimate

Ra,t = a0 + a1Re,t-f + ut (1)

where Ra,t is the actual revenues in fiscal year t, and Re,t-f is the forecast of Ra,t made f periods ago. Then, we use appropriate statistical methods to test the joint hypothesis that a0 = 0 and a1= 1.

Now, we intend to show that the joint test of a0 = 0 and a1 = 1 provides a valid statistical test of weak rationality, as defined above. Greene (1990) shows that a0 = E(Re,t)--a1E(Ra,t-f); therefore, it follows that a forecast is unbiased if and only if a0 = 0 and a1 = 1. Also, assuming var(ut,Re,t-f)=0, it follows from (1) that var(Ra,t)=(a1).sup.2]var(Re,t-f) + var(ut). Since variances cannot be negative, if a1 [greater than or equal to] 1, then var(Re,t-f) [less than or equal to] var(Ra,t). In other words, if the slope coefficient is less than 1.0, the variance of the forecasts is less than the variance of actual revenues. Finally, we note that least squares estimation of (1) imposes property (iii). In summary, the joint test of a0 = 0 and a1=1 is a valid statistical test of unbiasedness and efficiency of the forecasts or weak rationality.

The Data

We collected U.S. Treasury revenue forecasts from annual budget reports for fiscal years 1802 to 2001. During this period, the government employs three different definitions of a fiscal year. Consequently, it is necessary to use a variety of sources to get a series of actual revenues that is consistent with the forecasts. Specifically, actual revenues for fiscal years 1802 to 1842 are obtained from the Report on Finances, 1929; the FY 1976 Budget for 1843 to 1976; and the FY 2003 Budget for 1977 to 2001. The data used in this study are reported in a Data Appendix. Finally, the reader should be aware that the series of actual revenues reported in the Historical Tables of the FY 2003 Budget are adjusted to...