Notes Unless otherwise indicated, all years referred to in this report are fiscal years. Numbers in the text and tables may not add up to totals because of rounding. A description of the five spreadsheets used to construct the fan of uncertainty presented in Chapter 5 of The Budget and Economic Outlook: Fiscal Years 2004-2013 is available by clicking here:

On January 29, 2003, the Congressional Budget Office (CBO) released The Budget and Economic Outlook: Fiscal Years 2004-2013, which presents CBO's latest projections of federal revenues and outlays for that period. Chapter 5 of that report discusses the uncertainties in CBO's baseline projection of the total budget surplus or deficit and includes a chart (reproduced here as Figure 1) illustrating how those uncertainties increase over six years. This supplementary report describes the data and methods used to construct the chart. In brief, CBO calculated measures of uncertainty using the inaccuracies in its past projections that arose from economic and technical factors. Uncertainty arising from legislation is not considered because baseline projections assume that current tax and spending policies remain the same.
 

Figure 1.

Uncertainty in CBO's Projection of the Total Budget Surplus or Deficit Under Current Policies

(In trillions of dollars)

Source: Congressional Budget Office.

Note: Calculated on the basis of CBO's forecasting track record, this figure shows the estimated likelihood of alternative projections of the total budget surplus or deficit under current policies. CBO's baseline projection falls in the middle of the darkest area. Under the assumption that tax and spending policies do not change, the probability is 10 percent that actual surpluses or deficits will fall in the darkest area and 90 percent that they will fall within the whole shaded area.

Actual surpluses or deficits will of course be affected by legislation enacted during the next five years, including decisions about discretionary spending. The effects of future legislation are not included in this figure.

Figure 1 presents CBO's baseline projection of the budget balance as a fan of probabilities around the mean projection for 2003 through 2008. The fan widens as the projection period extends. The baseline projection falls in the middle of the highest-probability area--the darkest part of the figure. But the figure makes clear that nearby projections--other paths in the darkest part of the figure--have nearly the same probability of occurring as the baseline projection does. Moreover, projections that are quite different from the baseline have a significant probability of being realized.⁽¹⁾

The shaded area in the figure represents the 90 percent confidence range (the range within which the actual value has a 90 percent chance of falling). CBO estimates that range on the basis of the uncertainty in its historical record of budget projections--a total of 21 baselines spanning the period from 1981 to 2002.⁽²⁾ In other words, the estimates of uncertainty presume that in the future, CBO will experience inaccuracies similar to those it experienced in the past, with about the same probability distribution of large and small inaccuracies.

Even when the most recent recession is included, however, the 1981-2002 sample period is not typical of the post-World War II period as a whole. It contains only three recessions (those of 1981-1982, 1990-1991, and 2001)--compared with seven in the earlier post-World War II years--and the two most recent recessions were milder than average. Moreover, the 1981-1982 recession is not well represented in the sample because only one of the baseline projections preceded it, and the January 2002 baseline forecast is the only one following the 2001 recession for which at least one inaccuracy is available.⁽³⁾ When CBO takes into account the greater volatility of output in that entire post-World War II period, the width of the fan chart increases by roughly one-third by the fifth year (see Figure 2).
 

Figure 2.

Uncertainty in CBO's Projection of the Total Budget Surplus or Deficit, Assuming Average Business-Cycle Activity Since 1947

Source: Congressional Budget Office.

Note: The narrower confidence range (the outer boundary of the fan chart in Figure 1) is based on CBO's record of budget projections since 1981. The wider range represents the uncertainty in CBO's current projection if future cyclical movements of the economy follow the average pattern since 1947 rather than the less volatile pattern that has existed since 1981. The assumption is that cyclical inaccuracies will be proportionally larger if business-cycle activity is greater but that noncyclical inaccuracies will be unaffected.

CBO's analysis of uncertainty distinguishes between inaccuracies correlated with the business cycle and those not correlated with the business cycle. That distinction is a useful one, because inaccuracies in the assessment of noncyclical changes are likely to grow as the projection horizon lengthens, whereas inaccuracies correlated with the business cycle would not be expected to increase in the same way. According to CBO's estimates, cyclical inaccuracies historically have in fact been small for the first two years of a baseline, when CBO attempts to incorporate its views of the business cycle in its forecast. Those inaccuracies rise to a higher level for the later years of a projection--when CBO does not try to forecast the business cycle--but then flatten out (see Figure 3). Noncyclical inaccuracies, by contrast, grow in the later years.⁽⁴⁾
 

Figure 3.

Cyclical and Noncyclical Inaccuracies in Projecting the Primary Surplus

Source: Congressional Budget Office.

Notes: The lines in this figure show root-mean-square errors (RMSEs), a type of average that ignores the signs of individual errors and gives greater weight to larger errors. The RMSE of total inaccuracy is calculated by squaring the RMSEs of the cyclical and noncyclical parts, adding them together, and taking the square root of the sum. Thus, the combined RMSE is smaller than the sum of the two components' RMSEs.

The primary budget surplus is the difference between federal revenues and federal outlays excluding net interest.

That breakdown suggests that by the end of five years, CBO's inaccuracies in projecting the budget's bottom line have consisted, in roughly equal parts, of cyclical inaccuracies and inaccuracies in assessing economic trends and noncyclical factors that underlie the budget.

The analysis also suggests that if CBO had been confronted over the past two decades with a less stable economy--one more representative of the cyclical experience of the whole post-World War II period--the cyclical component would have been roughly twice as large as the noncyclical component by the end of five years (see Figure 4).
 

Figure 4.

Cyclical and Noncyclical Inaccuracies in Projecting the Primary Surplus, Assuming Average Business-Cycle Activity Since 1947

Source: Congressional Budget Office.

Notes: The lines in this figure show root-mean-square errors (RMSEs), a type of average that ignores the signs of individual errors and gives greater weight to larger errors. The RMSE of total inaccuracy is calculated by squaring the RMSEs of the cyclical and noncyclical parts, adding them together, and taking the square root of the sum. Thus, the combined RMSE is smaller than the sum of the two components' RMSEs.

This figure represents the inaccuracies in CBO's projections assuming that future cyclical movements of the economy follow the average pattern since 1947 rather than the less volatile pattern that has existed since 1981. The assumption is that cyclical inaccuracies will be proportionally larger if business-cycle activity is greater but that noncyclical inaccuracies will be unaffected.

The primary budget surplus is the difference between federal revenues and federal outlays excluding net interest.

Whether the next decade will more closely resemble the past two decades or the entire postwar period cannot be determined in advance. However, recent research suggests that fundamental changes in the economy that occurred in the early 1980s may have resulted in fewer and milder cyclical movements in the past two decades and may presage a relatively stable economy in the future. Analysts differ on the nature of those changes.⁽⁵⁾ But if they persist in the form of relatively less volatility, Figure 1 may portray the uncertainties in CBO's projection of the surplus or deficit better than the wider range in Figure 2 does.

Preparing the fan chart involved two stages. In the first stage, CBO constructed measures of its past projection inaccuracies that remove the effects of changes in legislation and other factors. In the second stage, CBO constructed probability distributions at six time horizons, beginning with the current fiscal year (the one in which the projection was made) and covering the next five years. The probability distributions were derived from a model that distinguishes between inaccuracies that appear to stem from the difficulty of forecasting the business cycle and inaccuracies that are not correlated with the business cycle and appear to stem from other causes.
 

Stage One: Constructing the Measures of Inaccuracies

Creating measures of inaccuracies in CBO's past budget projections involved adjusting those projections for two factors: legislation (including laws that affect discretionary spending) and net interest on the federal debt.

CBO added to its projections of revenues and outlays the estimated effects of laws dealing with revenues or mandatory spending that were enacted after the projections were made. That adjustment was necessary because CBO's baseline projections are intended to show the expected level of the budget surplus or deficit under the assumption that current tax and spending policies remain the same.⁽⁶⁾ Without that adjustment, the measures of inaccuracies would include the effects of later legislation, which would run counter to the purpose of the baseline.

CBO excluded discretionary spending from both the baseline projections and actual outlays. The effect of omitting discretionary spending is to treat all discrepancies between actual discretionary spending and baseline projections of such spending in the same way as differences resulting from other budget legislation.⁽⁷⁾ CBO decided on that treatment for two reasons: because levels of discretionary spending are determined anew each year through appropriation acts and because that treatment permits the use of a longer historical record. Moreover, inaccuracies in projecting discretionary outlays tend to be quite small, so the omission does not affect the measure of inaccuracy very much.

Inaccuracies in projecting net interest largely depend on inaccuracies in projecting the government's publicly held debt. That debt, in turn, is the cumulation of annual budget deficits (minus surpluses), so inaccuracies in projecting net interest depend on the cumulation of other inaccuracies in projecting the deficit or surplus. CBO therefore excluded net interest from its initial calculations of projection inaccuracies. However, the final fan-chart calculations reflect the effects of other misestimates on net interest.

CBO calculated inaccuracies for each year covered by the winter baseline projections that it published from 1981 through 2002. In most years, those projections were issued in January or February, although in 1996, publication was delayed until May. For reasons involving the availability of data, CBO used its July 1981 projection in place of the one published in February 1982.⁽⁸⁾ The resulting sample was small: only 21 current-year projections, declining to 16 five-year-ahead projections.⁽⁹⁾ (The sample size diminishes because projections made in the past five years can be compared with actual outcomes only through 2002.)

The estimated effects of legislation dealing with revenues or mandatory spending were taken primarily from information published in CBO's twice-yearly reports on the budget and economic outlook. Most of those reports show the multiyear budgetary effects of legislation enacted since the previous projection. For cases in which estimates were not available (as will be discussed below), substitutes were constructed. The underlying worksheets used in computing the inaccuracies and a brief explanation of each one are available by clicking here:

Revenues

As required by the Congressional Budget Act of 1974, the Joint Committee on Taxation (JCT) estimates the effects of tax legislation--bills that alter income, estate and gift, excise, or payroll taxes--at the time that the legislation is being considered by the Congress.⁽¹⁰⁾ CBO produces estimates for legislation that affects customs duties and miscellaneous receipts.

Those estimated effects of tax legislation were used to adjust each baseline projection of revenues. For example, the projection made in January 1994 for fiscal year 1999 was lowered from $1,630 billion to $1,619 billion (see Table 1). That adjustment reflected all tax laws enacted after January 1994 and through fiscal year 1999. The law with the largest budgetary impact was the Taxpayer Relief Act of 1997, which JCT estimated would reduce revenues in 1999 by $7 billion.⁽¹¹⁾ Similar adjustments were made for the other years in the baseline projections. The differences between those adjusted projections and actual revenues represent the inaccuracies attributable to economic and technical factors (see Table 2).

Table 1.
How CBO's January 1994 Revenue Projection Was Adjusted for Subsequent Legislation
(In billions of dollars)
			Fiscal Years
			1994	1995	1996	1997	1998	1999
Baseline Projection of Revenues			1,251	1,338	1,411	1,479	1,556	1,630
Subsequent Legislation
	January 1994 to August 1994		0	0	0	0	0	0
	August 1994 to January 1995		0	1	-1	-1	-3	-3
	January 1995 to August 1995			*	*	*	*	*
	August 1995 to May 1996			0	*	*	*	*
	May 1996 to August 1996				-1	-3	-2	-2
	August 1996 to January 1997				*	1	*	*
	January 1997 to September 1997					2	-10	-7
	September 1997 to January 1998					*	*	*
	January 1998 to August 1998						1	1
	August 1998 to January 1999						0	*
	January 1999 to July 1999							*
	July 1999 to January 2000							0
		Total	0	*	-2	-1	-14	-11
Adjusted Baseline Projection of Revenues			1,251	1,338	1,409	1,478	1,542	1,619
Source: Congressional Budget Office.
Notes: The only major changes in tax law enacted after CBO's January 1994 baseline projection were made in the Taxpayer Relief Act of 1997. Its effects were incorporated in CBO's September 1997 baseline projection. Two other adjustments are notable but relatively minor. The January 1995 baseline reflected various reductions in tariff rates, primarily those in the Generalized System of Preferences. The downward adjustment in the August 1996 baseline projection reflected two pieces of legislation: the Health Insurance Portability Act of 1996 and the Small Business Job Protection Act of 1996.
* = between -$500 million and $500 million.

Table 2.
Inaccuracies in CBO's Baseline Projections of Revenues That Are Attributable to Economic and Technical Factors
(As a percentage of actual revenues)
	Fiscal Year for Which the Projection Was Made
Date the Projection Was Published	Current Year		Budget Year		Budget Year + 1		Budget Year + 2		Budget Year + 3		Budget Year + 4
July 1981	-2.1		-8.5		-22.1		-22.2		-23.1		-28.4
February 1983	-0.9		1.3		0.3		-3.2		-2.3		-3.8
February 1984	0.4		-1.2		-5.7		-5.9		-8.7		-7.0
February 1985	-0.1		-2.6		-2.4		-4.8		-3.2		-8.3
February 1986	-1.2		-1.1		-3.4		-1.7		-6.2		-13.1
January 1987	2.4		-0.1		1.2		-3.9		-11.5		-15.3
February 1988	1.4		3.8		-0.7		-7.4		-10.5		-12.4
January 1989	0.8		-3.5		-9.5		-12.5		-13.4		-12.9
January 1990	-3.4		-9.4		-12.2		-13.3		-12.6		-12.4
January 1991	-3.6		-6.1		-8.2		-7.8		-7.9		-6.3
January 1992	0.4		-2.0		-2.4		-2.4		-0.7		1.8
January 1993	1.0		1.4		1.3		3.3		6.7		11.3
January 1994	0.6		1.0		3.0		6.4		10.5		11.4
January 1995	-0.2		2.5		6.6		10.9		11.9		17.1
May 1996	1.7		5.9		10.9		12.3		17.8		16.8
January 1997	4.4		9.5		10.9		16.7		15.6		5.3
January 1998	3.3		5.3		11.9		11.1		0.6
January 1999	0.7		7.5		6.9		-4.1
January 2000	4.0		2.3		-8.9
January 2001	-3.8		-16.6
January 2002	-4.7
Source: Congressional Budget Office.
Note: Forecast inaccuracies are actual revenues minus projected revenues, adjusted for the effects of legislation.

CBO's and JCT's estimates of the effects of tax legislation are not revised after their initial publication, even though later economic and technical information might permit better estimates. (For instance, knowledge about an actual tax base, such as wages or corporate profits, in a given year would improve estimates of how a change in tax law would affect revenues.) Using unrevised data on the effects of legislation may overstate the true uncertainty of CBO's budget projections, all other things being equal.

Outlays

The estimated effects of legislation on outlays (excluding net interest) were also taken largely from CBO's reports on the budget and economic outlook. However, as with revenues, some adjustment to that information was necessary.

• Baseline Projections of Discretionary Spending. As noted above, differences between actual and projected levels of discretionary spending were assumed to be attributable to legislation. But the July 1981 baseline projection did not include a separate category for discretionary spending. For that baseline only, discretionary spending was approximated by adding the projections for defense, other grants to state and local governments, and other federal operations.⁽¹²⁾



• Insufficient Details About Legislation. In some cases, the estimated effects of legislation were not published in enough detail to separate out the effects of legislation on mandatory spending. In other cases, the information was published for some but not all of the six years in the baseline budget projection. One or both of those problems applied to the following periods: August 1986 to January 1987, August 1987 to February 1988, August 1994 to January 1995, and January 1998 to August 1998. In those cases, supplemental information from CBO's files was used to estimate the needed numbers.

As with revenues, the estimated effects of legislation on outlays were used to adjust each baseline projection of outlays. After removing interest payments and discretionary outlays, the differences between those adjusted projections and actual outlays are the inaccuracies attributable to economic and technical factors (see Table 3).

Table 3.
Inaccuracies in CBO's Baseline Projections of Outlays That Are Attributable to Economic and Technical Factors
(As a percentage of actual revenues)
	Fiscal Year for Which the Projection Was Made
Date the Projection Was Published	Current Year		Budget Year		Budget Year + 1		Budget Year + 2		Budget Year + 3		Budget Year + 4
July 1981	-2.4		-1.6		-0.7		-3.7		-3.3		-3.1
February 1983	-1.3		-2.0		-0.8		0.1		-0.2		0.2
February 1984	-0.8		*		-0.1		-0.6		-0.8		-1.4
February 1985	0.3		1.4		0.6		0.8		0.3		7.5
February 1986	2.0		1.6		1.9		1.1		8.3		8.7
January 1987	-1.1		0.8		-0.5		6.3		6.4		7.2
February 1988	0.7		-0.5		5.6		5.8		6.7		4.5
January 1989	-1.1		5.7		5.2		6.1		4.0		5.2
January 1990	4.4		3.9		4.7		2.5		3.7		2.1
January 1991	-7.1		-7.4		-3.8		-1.0		3.3		2.7
January 1992	-5.7		-7.7		-3.6		-0.9		1.1		-2.0
January 1993	-3.3		-3.0		-4.4		-2.7		-3.5		-4.0
January 1994	-1.2		-1.4		-1.3		-3.6		-4.1		-4.8
January 1995	-1.0		-2.3		-4.0		-4.3		-5.0		-5.7
May 1996	-0.9		-2.7		-3.9		-4.1		-4.7		-5.7
January 1997	-1.8		-1.9		-2.8		-3.8		-4.2		-2.2
January 1998	-0.7		-1.3		-2.4		-2.5		-0.3
January 1999	-0.1		-1.0		-0.8		1.3
January 2000	-0.4		*		2.3
January 2001	-0.3		1.3
January 2002	-0.2
Source: Congressional Budget Office.
Notes: Forecast inaccuracies are actual outlays minus projected outlays, adjusted for the effects of legislation. They exclude inaccuracies in the baseline projections of discretionary spending (which are assumed to be attributable solely to legislation) and in the baseline projections of net interest (which depend on the inaccuracies in the surplus excluding interest).
* = between -0.05 percent and 0.05 percent.

Primary Budget Surplus or Deficit

The difference between revenues and outlays excluding net interest is known as the primary budget surplus (or deficit when negative). Correspondingly, CBO's inaccuracies in projecting revenues, minus its inaccuracies in projecting noninterest outlays, equal its inaccuracies in projecting the primary surplus or deficit (see Tables 4 and 5). As described above, that calculation excludes legislative changes. In stage two of the fan-chart preparation, the inaccuracies in projecting the primary budget surplus or deficit were cumulated into inaccuracies in projecting publicly held debt, which were used to estimate the uncertainty of CBO's projections of net interest.

Table 4.
Inaccuracies in CBO's Baseline Projections of the Primary Surplus or Deficit
(As a percentage of actual revenues)
	Fiscal Year for Which the Projection Was Made
Date the Projection Was Published	Current Year		Budget Year		Budget Year + 1		Budget Year + 2		Budget Year + 3		Budget Year + 4
July 1981	0.3		-6.9		-21.3		-18.1		-19.6		-25.0
February 1983	0.4		3.3		1.1		-3.3		-2.1		-4.0
February 1984	1.2		-1.3		-5.5		-5.3		-7.9		-5.6
February 1985	-0.4		-4.1		-2.9		-5.7		-3.5		-15.8
February 1986	-3.2		-2.7		-5.3		-2.8		-14.5		-21.7
January 1987	3.5		-1.0		1.7		-10.2		-17.9		-22.5
February 1988	0.7		4.3		-6.3		-13.2		-17.2		-16.9
January 1989	1.9		-9.2		-14.7		-18.7		-17.4		-18.1
January 1990	-7.8		-13.3		-17.0		-15.8		-16.2		-14.4
January 1991	3.5		1.4		-4.4		-6.8		-11.1		-9.0
January 1992	6.1		5.7		1.2		-1.5		-1.9		3.9
January 1993	4.3		4.4		5.6		6.0		10.2		15.3
January 1994	1.8		2.4		4.3		10.1		14.6		16.2
January 1995	0.8		4.7		10.6		15.2		16.9		22.9
May 1996	2.6		8.6		14.7		16.4		22.5		22.4
January 1997	6.2		11.4		13.7		20.5		19.9		7.6
January 1998	3.9		6.6		14.3		13.6		0.9
January 1999	0.8		8.5		7.8		-5.4
January 2000	4.3		2.3		-11.2
January 2001	-3.5		-17.9
January 2002	-4.5
Source: Congressional Budget Office.
Note: Forecast inaccuracies are actual surpluses minus projected surpluses, adjusted for the effects of legislation. They exclude inaccuracies in the baseline projections of discretionary spending (which are assumed to be attributable solely to legislation) and in the baseline projections of net interest (which depend on the inaccuracies in the surplus excluding interest).

Table 5.
The Historical Record of CBO's Baseline Budget Projections
(In billions of dollars)
		1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992
Actual
Budget Surplus or Deficit (-)		-79	-128	-208	-185	-212	-221	-150	-155	-153	-221	-269	-290
Net Interest		69	85	90	111	130	136	139	152	169	184	195	199
Primary Surplus or Deficit (-)		-10	-43	-118	-74	-83	-85	-11	-3	17	-37	-75	-91
Projections
July 1981 Baseline
	Primary surplus or deficit (-)	18	43	87	143	201	268
	Inaccuracy	-28	-86	-205	-218	-283	-353
	Effect of legislation	-30	-43	-77	-97	-140	-161
	Inaccuracy excluding legislation	2	-42	-128	-121	-144	-192
February 1983 Baseline
	Primary surplus or deficit (-)			-123	-116	-124	-133	-142	-151
	Inaccuracy			5	42	41	48	131	148
	Effect of legislation			3	19	33	73	149	184
	Inaccuracy excluding legislation			2	22	8	-26	-18	-36
February 1984 Baseline
	Primary surplus or deficit (-)				-95	-81	-85	-94	-101	-120
	Inaccuracy				21	-2	*	83	98	137
	Effect of legislation				12	7	42	128	170	192
	Inaccuracy excluding legislation				8	-9	-43	-45	-72	-55
February 1985 Baseline
	Primary surplus or deficit (-)					-84	-69	-70	-63	-65	-66
	Inaccuracy					1	-16	59	60	82	29
	Effect of legislation					4	15	84	111	116	192
	Inaccuracy excluding legislation					-3	-31	-25	-51	-34	-163
February 1986 Baseline
	Primary surplus or deficit (-)						-70	-36	-11	14	39	56
	Inaccuracy						-16	25	7	3	-76	-131
	Effect of legislation						9	48	55	30	74	98
	Inaccuracy excluding legislation						-25	-23	-48	-28	-150	-229
January 1987 Baseline
	Primary surplus or deficit (-)							-39	-28	-15	18	46	69
	Inaccuracy							28	25	32	-55	-121	-160
	Effect of legislation							-2	33	15	50	68	86
	Inaccuracy excluding legislation							30	-9	16	-105	-189	-246
			1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998
Actual
Budget Surplus or Deficit (-)			-155	-153	-221	-269	-290	-255	-203	-164	-108	-22	69
Net Interest			152	169	184	195	199	199	203	232	241	244	241
Primary Surplus or Deficit (-)			-3	17	-37	-75	-91	-56	*	68	134	222	310
Projections
February 1988 Baseline
	Primary surplus or deficit (-)		-7	-10	17	39	50	72
	Inaccuracy		4	27	-54	-114	-141	-128
	Effect of legislation		-2	-16	11	25	47	67
	Inaccuracy excluding legislation		6	43	-65	-139	-188	-195
January 1989 Baseline
	Primary surplus or deficit (-)			14	42	52	63	73	85
	Inaccuracy			3	-79	-127	-154	-129	-85
	Effect of legislation			-16	16	28	50	71	142
	Inaccuracy excluding legislation			19	-95	-155	-204	-201	-227
January 1990 Baseline
	Primary surplus or deficit (-)				42	47	57	58	76	92
	Inaccuracy				-79	-122	-148	-114	-76	-24
	Effect of legislation				2	19	37	67	128	171
	Inaccuracy excluding legislation				-80	-140	-185	-182	-204	-195
January 1991 Baseline
	Primary surplus or deficit (-)					-99	-77	4	67	173	176
	Inaccuracy					24	-14	-60	-67	-105	-42
	Effect of legislation					-13	-29	-9	18	46	89
	Inaccuracy excluding legislation					37	15	-51	-85	-150	-131
January 1992 Baseline
	Primary surplus or deficit (-)						-151	-113	-29	51	82	52
	Inaccuracy						60	57	29	17	52	170
	Effect of legislation						-6	-9	14	37	79	109
	Inaccuracy excluding legislation						66	66	15	-20	-27	61
January 1993 Baseline
	Primary surplus or deficit (-)							-112	-81	-53	-37	-49	-65
	Inaccuracy							56	81	121	171	271	375
	Effect of legislation							6	26	45	83	110	113
	Inaccuracy excluding legislation							50	55	76	87	161	263
					1994	1995	1996	1997	1998	1999	2000	2001	2002
Actual
Budget Surplus or Deficit (-)					-203	-164	-108	-22	69	125	237	127	-158
Net Interest					203	232	241	244	241	230	223	206	171
Primary Surplus or Deficit (-)					*	68	134	222	310	354	460	333	13
Projections
January 1994 Baseline
	Primary surplus or deficit (-)				-22	41	62	57	69	57
	Inaccuracy				22	27	72	165	241	297
	Effect of legislation				-1	-4	8	7	-10	1
	Inaccuracy excluding legislation				23	32	63	159	251	296
January 1995 Baseline
	Primary surplus or deficit (-)					59	53	46	56	40	26
	Inaccuracy					9	81	176	254	314	434
	Effect of legislation					-2	12	8	-8	6	-29
	Inaccuracy excluding legislation					11	69	167	262	308	463
May 1996 Baseline
	Primary surplus or deficit (-)						96	75	64	52	39	38	26
	Inaccuracy						38	147	246	302	421	295	-13
	Effect of legislation						*	11	-7	3	-35	-151	-197
	Inaccuracy excluding legislation						38	135	254	299	456	446	184
January 1997 Baseline
	Primary surplus or deficit (-)							123	133	114	95	105	90
	Inaccuracy							99	177	240	365	228	-77
	Effect of legislation							1	-19	-11	-50	-167	-217
	Inaccuracy excluding legislation							98	196	251	415	395	140
January 1998 Baseline
	Primary surplus or deficit (-)								239	246	241	252	301
	Inaccuracy								71	108	219	81	-288
	Effect of legislation								4	-13	-69	-190	-305
	Inaccuracy excluding legislation								67	121	289	271	17
January 1999 Baseline
	Primary surplus or deficit (-)									339	349	358	404
	Inaccuracy									15	111	-25	-391
	Effect of legislation									*	-60	-179	-291
	Inaccuracy excluding legislation									15	172	154	-100
											2000	2001	2002
Actual
Budget Surplus or Deficit (-)											237	127	-158
Net Interest											223	206	171
Primary Surplus or Deficit (-)											460	333	13
Projections
January 2000 Baseline
	Primary surplus or deficit (-)										400	395	417
	Inaccuracy										60	-62	-404
	Effect of legislation										-28	-107	-196
	Inaccuracy excluding legislation										88	46	-208
January 2001 Baseline
	Primary surplus or deficit (-)											487	492
	Inaccuracy											-154	-479
	Effect of legislation											-84	-147
	Inaccuracy excluding legislation											-70	-332
January 2002 Baseline
	Primary surplus or deficit (-)												150
	Inaccuracy												-137
	Effect of legislation												-54
	Inaccuracy excluding legislation												-83
Source: Congressional Budget Office.
Notes: Inaccuracies in projections of discretionary spending are assumed to be attributable solely to legislation and are included in the rows labeled "effect of legislation."
The underlying worksheets used in computing the inaccuracies and a brief explanation of each one are available by clicking here:
* = between -$500 million and $500 million.

 

Stage Two: Constructing Probability Distributions

The historical record of inaccuracies in projecting the primary surplus or deficit (adjusted for legislation) presented in Table 4 forms the basis for the statistical calculations that CBO used to derive the probability distributions underlying the fan chart.

As noted above, CBO's record of projections is both short and possibly unrepresentative (in that it contains fewer and less frequent business cycles than occurred previously). In the absence of a large sample, estimates may be improved if additional information can be brought to bear. In this case, CBO used its knowledge of its forecasting procedures and of business cycles, as well as its historical record, to draw more-reliable conclusions about the probability distribution of inaccuracies in its budget projections.

The Statistical Model for Inaccuracies in the Primary Surplus or Deficit

With the effects of legislation removed, CBO's past inaccuracies are closely related to inaccuracies in forecasting economic variables. Thus, they should be affected by errors in the projection of the business cycle. Forecasting the course of a business cycle over more than two years is virtually impossible, so CBO has traditionally tried to incorporate the business cycle in its economic projections explicitly only for the current year and the budget year.⁽¹³⁾ In its projections for longer horizons, CBO simply assumes that gross domestic product (GDP) will, on average, adhere to its trend (or "potential") path.⁽¹⁴⁾ That assumption recognizes that, in fact, GDP will sometimes be above and sometimes below its potential level, but CBO cannot forecast those boom or recession periods more than a couple of years ahead.

Given the way in which CBO makes its economic projections, its budget projections can be expected to show a certain pattern of inaccuracies. As long as CBO continues to do a reasonably good job of projecting the business cycle, that cycle should not contribute much to the inaccuracy of budget projections for the current year. For the budget year, its contribution should be larger (because errors in forecasting increase as the horizon lengthens) but still modest. For later years, however, cyclical factors should loom larger. CBO assumes that by the last two years of the five-year projection horizon, GDP will be at or close to its potential level. Thus, any difference between actual and potential levels will not be reflected in those budget projections. Consequently, as the projection horizon extends, the budget misestimates that result from miscalculating the business cycle should grow in importance, until they reach their maximum level in the last two years of the five-year period.

The portion of budget inaccuracies attributable to the business cycle may be estimated by using the correlation between those inaccuracies and the GDP gap (the percentage difference between actual GDP and its potential value). According to the above analysis, for projections several years ahead, the level of the GDP gap is a good indicator of unexpected cyclical conditions. For projections only one or two years ahead, by contrast, the change in the GDP gap is a better indicator than the level, because the approaching levels of the gap are likely to be quite similar to the recent level.

Using the GDP gap and its change to measure unforeseen changes in cyclical conditions, CBO estimated by means of a linear regression what portion of its past inaccuracies was attributable to business cycles (see Box 1). Restrictions on the regression incorporate the exogenous information that, of the two variables, the change in the GDP gap is the main source of uncertainty over shorter horizons and the level of the gap over longer ones. For the intermediate year (the first year after the two-year forecast), both the level of the GDP gap and its change are taken to be important indicators of unexpected cyclical changes.
 

Box 1. Regression Equation for the Analysis of Uncertainty To estimate the effect of the business cycle on the inaccuracy of its past budget projections, the Congressional Budget Office (CBO) used the following regression equation: et,h = 1 wh dt+h + 2 (1 - wh) gt+h + residualt,h   where     et,h =     the inaccuracy in projecting the primary surplus or deficit (as a percentage of actual revenues) for the h-year-out forecast published in fiscal year t         gt+h =     the GDP gap in year t+h         dt+h =     the change in the GDP gap between the level known at the time of the projection and the level in the year for which the projection was made (in other words, dt+h = gt+h-gt-1) (Note that gt is not known at the time of the projection published in January of year t.) The projection horizon h runs from the current year (h = 0) through the budget year (h = 1) to the fourth year after the budget year (h = 5). The variables dt+h and gt+h are multiplied by weights wh and (1 - wh), which restrict their effect at different projection horizons. The weights are chosen so that, for the four- and five-year-ahead projections, the forecast inaccuracy depends only on gt+h, and for the current year, the inaccuracy depends only on dt+h. In other words, w4 = w5 = 0 and w0 = 1. The weights at other horizons are w1 = 0.8, w2 = 0.5, and w3 = 0.1. Those weights are not determined statistically but represent a reasonable transition from CBO's near-term forecast to its medium-term projection. The two measures gt+h and dt+h are assumed to have different impacts on forecast inaccuracies (different 1and 2) because, although gt+h is completely unforeseen (for out-years), dt+h can be partly forecast, especially for the current budget year. 1 and 2 are estimated at 1.2 and 7.3, respectively, with standard errors of 0.5 and 0.6.

The portion of the overall inaccuracies explained by the two business-cycle variables in the regression is called the cyclical part. The rest, the noncyclical part, represents the inaccuracies that result from such factors as noncyclical changes in average tax rates, capital gains realizations, the share of GDP that goes to taxpayers in high tax brackets, and federal spending for Medicare and Medicaid.⁽¹⁵⁾

CBO does not expect its projection inaccuracies to display a negative or positive bias--otherwise it would change its projections. Accordingly, CBO assumed that the probability distribution of its projection inaccuracies was centered around a zero average. The data do not contradict that assumption.

Calculating the Distribution of Inaccuracies from the Model

The statistical model computes coefficients that relate misestimates of the primary surplus or deficit (shown in Table 4) to the business-cycle variables. Given the historical pattern of the business cycle, those coefficients can be used to describe the distribution of inaccuracies that might be expected to occur simply because of the business cycle. One way to describe that distribution is through the root-mean-square error (RMSE), a kind of average error that ignores the signs of individual errors and gives extra weight to large errors.⁽¹⁶⁾ The model assumes that the RMSE of the cyclical part of misestimates will rise to a plateau (see Figure 3).

That model does not account for all of a given projection inaccuracy, however. What is left, the noncyclical part, also has a distribution that can be summarized by its RMSE. Like the cyclical component, that part of a misestimate rises as the projection horizon lengthens, but it does not plateau (see Figure 3). For simplicity, CBO assumes that the noncyclical influences captured in the residual from the regression are independent of the cyclical component at each horizon.⁽¹⁷⁾ That assumption is not contradicted by the data, and using the sample correlations makes little difference to the results.⁽¹⁸⁾

The estimated RMSEs for the cyclical and noncyclical parts can be combined to form an estimate of the RMSE for overall budget misestimates. Two RMSEs are combined by squaring each of them, adding those squares together, and taking the square root of the sum. That calculation yields a combined RMSE that is less than the sum of the two component RMSEs (see Figure 3).

The estimated RMSEs for a given year have been formulated thus far as a percentage of that year's actual revenues. For the projection of the total surplus or deficit, those RMSEs can be converted into dollars or expressed as a percentage of GDP using CBO's current baseline projection of total revenues and GDP.

The model's estimate of the distribution of budget misestimates appears generally consistent with CBO's past record. Out of 111 past projection inaccuracies for the primary surplus or deficit in 1981 through 2002, only 7 percent fall outside the calculated 90 percent confidence range--a range that ought, in a large enough sample, to encompass 90 percent of the observations (see Figure 5).
 

Figure 5.

CBO's Past Inaccuracies in Projecting the Primary Surplus, Compared with the Constructed 90 Percent Confidence Range

Source: Congressional Budget Office.

Note: Each thin line represents the actual inaccuracies of the set of projections made in a given year. The thick lines represent the 90 percent confidence range constructed from CBO's statistical model for inaccuracies. That range encompasses most of CBO's past record.

Figure 6 compares the 90 percent confidence band for primary surplus projections with the inaccuracy of individual baselines from 1981 through 1997, the only baselines for which the full record is available. The figure shows that the five-year projections made between 1993 and 1997 tended to be too pessimistic, and those made earlier tended to be too optimistic. The primary source of inaccuracy for the baselines between 1993 and 1997 was the unforeseen productivity acceleration of the 1990s and the associated rapid rise in revenues. For the earlier baseline projections, the primary sources of inaccuracy were the unexpected continuation of the productivity slowdown that started in the 1970s and the recessions of 1980, 1981-1982, and 1990-1991.
 

Figure 6.

Misestimates in CBO's Projections Made from 1981 to 1997

(Percentage of GDP)

Source: Congressional Budget Office.

Notes: CY = current year; BY = budget year.

This figure shows misestimates in CBO's projections of the primary surplus--the total surplus excluding net interest--made at different times. Plotted points that lie below the center line reflect instances in which CBO overestimated the primary surplus, and points above the center line reflect underestimates. In each panel, the shaded cone indicates the estimated 90 percent confidence band; that is, each projection point had a 90 percent chance of falling within the shaded area. CBO estimated that confidence band on the basis of its track record since 1981 (excluding 1982, because of insufficient data).

The figure excludes the effects of legislation enacted after the projections were made.

Uncertainty in Projections of the Total Surplus or Deficit

The uncertainty range for CBO's projection of the total surplus or deficit (shown in Figure 1) requires information about how the predicted inaccuracies in the primary budget (the budget excluding net interest) will affect the government's debt-service costs. Those inaccuracies are run through a simple debt-service model that tracks how inaccuracies in projecting surpluses or deficits translate into inaccuracies in projecting debt; the model applies an interest rate that is a weighted average of CBO's current baseline projections of rates on three-month Treasury bills and 10-year Treasury notes. That model is an approximation of the model CBO uses for its budget projections.

The extent to which projection inaccuracies for the primary surplus are correlated across horizons is important for the computation of debt-service costs. When those inaccuracies are highly correlated, they have a large accumulated effect on outstanding debt, and the associated change in the government's interest burden is large. In calculating the probability distribution of projection inaccuracies for the total surplus (including net interest), CBO assumed that the cyclical and noncyclical parts would continue to have the same correlation structure as in the past.⁽¹⁹⁾

The percentiles for the total surplus that are used to draw the fan chart are computed by multiplying the values associated with the various percentiles for the standard normal distribution by the calculated RMSE of the probability distribution of the total surplus at different horizons. Those percentiles are shown in Table 6.

Table 6.
Estimated Probability Distribution of Total Budget Surpluses
(In billions of dollars)
Percentile	2003	2004	2005	2006	2007	2008
5	-328	-408	-478	-531	-616	-692
10	-299	-350	-389	-417	-474	-525
15	-280	-310	-328	-341	-378	-412
20	-265	-279	-280	-280	-302	-322
25	-252	-253	-239	-227	-237	-246
30	-240	-229	-202	-181	-178	-176
35	-229	-207	-168	-137	-124	-112
40	-219	-185	-135	-96	-73	-52
45	-209	-165	-104	-56	-23	7
50	-199	-145	-73	-16	26	65
55	-189	-125	-42	23	75	123
60	-179	-105	-11	63	125	182
65	-169	-83	22	104	176	242
70	-158	-61	56	148	231	306
75	-146	-37	93	194	289	375
80	-133	-11	134	247	354	452
85	-118	20	182	308	430	542
90	-99	60	243	384	526	655
95	-71	118	332	498	668	822
Source: Congressional Budget Office.
Notes: These numbers--constructed using the percentiles of the standard normal distribution and a simple probability model based on CBO's track record--are the estimated data that underlie the fan chart presented as Figure 1. The row in the table corresponding to the 50th percentile is CBO's current baseline projection of the surplus.
These estimates permit the construction of probability statements about CBO's baseline projection of the total budget surplus. For example, the table indicates that there is a 90 percent chance that the budget's balance in 2004 (the budget year) will be somewhere between a deficit of $408 billion and a surplus of $118 billion, and a 50 percent chance that the surplus in 2008 (the budget year + 4) will be within about $310 billion of the baseline projection. (That last calculation takes the range from the 25th to the 75th percentiles and halves it.)

CBO will continue its efforts to refine these calculations. It welcomes suggestions for improving the methodology.