The Congress of the United States O Congressional Budget Office

CBO

The Uncertainty of Budget Projections: 

A Discussion of Data and Methods

March 2007

A

PAPER

Preface

On January 24, 2007, the Congressional Budget Office (CBO) released The Budget 

and Economic Outlook: Fiscal Years 2008 to 2017. Chapter 1 of that report discusses the 

uncertainty of CBO’s baseline projection of the total budget balance and includes a figure 

illustrating how the uncertainty increases as the projections extend into the future. This 

supplementary report describes the data and methods used to construct that figure. 

Ufuk Demiroglu and Frank Russek of CBO’s Macroeconomic Analysis Division wrote this 

report under the direction of Robert Dennis. Andrew Gisselquist provided research assistance. 

Christine Bogusz edited the report, Maureen Costantino prepared it for publication, and 

Lenny Skutnik printed the copies. Simone Thomas produced the electronic version for CBO’s 

Web site. 

Peter R. Orszag

Director

March 2007 

Contents

Stage One: Constructing the Measures of Deviations 3

Revenues 4

Outlays 6

Primary Budget Deficit or Surplus 7

Stage Two: Constructing Probability Distributions 8

The Statistical Model for Deviations from Forecasts of the 

Primary Deficit or Surplus 8

Calculating the Distribution of Deviations from the Model 9

Uncertainty of Projections of the Total Deficit or Surplus 

and of the Level of Outstanding Debt 11
VI THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Tables

1. Example: How CBO’s January 1999 Revenue Projection 

Was Adjusted for Subsequent Legislation 5

2. Inaccuracies in CBO’s Baseline Projections of Revenues That 

Are Attributable to Economic and Technical Factors 6

3. Inaccuracies in CBO’s Baseline Projections of Outlays That 

Are Attributable to Economic and Technical Factors 7

4. Inaccuracies in CBO’s Baseline Projections of the Primary 

Deficit or Surplus That Are Attributable to Economic and 

Technical Factors 8

5. Estimated Probability Distribution of Total Budget Deficits or 

Surpluses, in Billions of Dollars 16

6. Estimated Probability Distribution of Total Budget Deficits or 

Surpluses, as a Percentage of Gross Domestic Product 17

7. Estimated Probability That the Budget Will Be in Deficit 

Under CBO’s Baseline Assumptions 18

Figures

1. Uncertainty of CBO’s Projections of the Budget Deficit or 

Surplus Under Current Policies 2

2. Cyclical and Noncyclical Deviations from the Primary Surplus 

Projections 3

3. CBO’s Past Deviations in Projecting the Primary Surplus, 

Compared with the Constructed 90 Percent Confidence 

Ranges 12

4. Deviations from CBO’s Primary Surplus Projections Made 

Between 1981 and 2006 13

5. Deviations from the 1996 Primary Surplus Projection 14

6. Uncertainty of CBO’s Projections of the Level of Outstanding 

Debt Under Current Policies 15

Box

1. Regression Equation for the Analysis of Uncertainty 10
The Uncertainty of Budget Projections:

A Discussion of Data and Methods

On January 24, 2007, the Congressional Budget 

Office (CBO) released The Budget and Economic Outlook: 

Fiscal Years 2008 to 2017, which presents CBO’s latest 

projections of federal revenues and outlays for that 

period. Chapter 1 of that report includes a brief discussion of the uncertainty in CBO’s baseline projection of 

the total budget balance and shows a figure (reproduced 

here as Figure 1) illustrating how that uncertainty 

increases as the projections extend into the future. This 

supplementary report describes the data and methods 

used to construct that figure. Throughout this document, 

the word “deviation” indicates the difference between 

CBO’s projections and actual outcomes, unless specified 

otherwise. For example, the deviation from a projected 

budget balance means the difference between the actual 

budget outcome and the projected value. In brief, CBO 

calculated measures of uncertainty using the deviations 

from its past projections that arose from economic and 

technical factors. Uncertainty arising from legislation was 

not considered because baseline projections assume that 

current tax and spending policies remain in place.

Figure 1 presents CBO’s baseline projection of the budget 

balance as a fan of probabilities around the mean projection for 2007 through 2012. 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

 For example, the baseline

projection shows an improvement in the deficit over the 

projection period, but there is about a one-in-four chance 

that the deficit will be larger in 2012 than it was last year 

(both in dollar terms and as a percentage of gross domestic product, or GDP), even under the favorable baseline 

assumptions of rapidly growing tax revenues from the 

alternative minimum tax and the expiration of provisions 

originally enacted in the Economic Growth and Tax 

Relief Reconciliation Act of 2001 and the Jobs and 

Growth Tax Relief Reconciliation Act of 2003. Similarly, 

there is a chance that the level of debt will be higher in 

2012 than it was last year—about a 60 percent chance 

when that debt is measured in dollar terms and about a 

25 percent chance when that debt is measured as a percentage of GDP. (See Figure 6 on page 15.)

The shaded area in Figure 1 represents the 90 percent 

confidence range (the range within which the actual value 

for each year 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 25 

baselines spanning the period from 1981 to 2006.2

 In 

other words, the estimates of uncertainty presume that, in 

the future, budget outcomes will deviate from CBO’s

1. Technically, the probability density is highest near the baseline 

and falls off for more-distant projections.

2. The projections are those made in July 1981 and CBO’s winter 

projections (usually published in January) from 1983 through 

2006. Sufficient data were unavailable to use the projections made 

before 1981 or the projection made in early 1982. For the two 

years surrounding the 1981 projection, available data about the 

effects of legislation on changes in CBO’s baseline budget projections were insufficient, and discretionary spending was not 

reported separately. As discussed in the next section, those data are 

important because the measures of deviations used in this analysis 

were constructed by removing the effects of legislation, including 

discretionary spending. The baseline budget projections that 

CBO made before 1980 were not comparable with later ones, 

because the agency’s early economic assumptions represented targets rather than projections.
2 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Figure 1.

Uncertainty of CBO’s Projections of the Budget Deficit or Surplus

Under Current Policies

(Deficit or surplus as a percentage of gross domestic product)

Source: Congressional Budget Office.

Notes: This figure, calculated on the basis of CBO’s track record in forecasting, shows the estimated likelihood of alternative projections of the 

budget deficit or surplus under current policies. The baseline projections described in The Budget and Economic Outlook: Fiscal Years 

2008 to 2017 fall in the middle of the darkest area of the figure. Under the assumption that tax and spending policies do not change, 

the probability is 10 percent that actual deficits or surpluses will fall in the darkest area and 90 percent that they will fall within the 

whole shaded area.

Actual deficits or surpluses will be affected by legislation enacted in future years, including decisions about discretionary spending. 

The effects of future legislation are not reflected in this figure.

projections as they have in the past, with about the same 

probability distribution of large and small differences.

CBO’s analysis of uncertainty separates deviations correlated with the business cycle from those that are not. 

That distinction helps in estimating the probability 

distribution of the deviations, as discussed later in this 

report. Cyclical deviations are not expected to grow after 

the first few years of a projection’s horizon, whereas noncyclical deviations may persistently grow as the projection’s horizon lengthens. According to CBO’s estimates, 

cyclical deviations historically have been small for the first 

two years of a baseline projection, the period for which 

CBO incorporates its views of the business cycle in its 

forecasts. Those cyclical deviations rise in the later years 

of a projection—when CBO does not try to forecast the 

business cycle—but then flatten out (see Figure 2).

Noncyclical deviations, by contrast, continue to grow in 

the later years.3 That breakdown suggests that, on average, the deviations from CBO’s projections of the budget’s bottom line have consisted, in roughly equal parts, 

of cyclical deviations and of deviations due to economic 

trends and other noncyclical factors that underlie the 

budget. 

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

3. CBO did not begin making 10-year baseline projections until 

1996. Although the agency published supplemental 10-year projections as early as 1992, those reports did not provide information about the budgetary effects of legislation for the extended 

time periods. Before 1996, CBO’s baseline typically extended out 

five years from the current year. Because there are only one to five 

uncertainty measures for the sixth through 10th years, this analysis focuses on a five-year projection horizon.
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 3

Figure 2.

Cyclical and Noncyclical Deviations 

from the Primary Surplus Projections

(Percentage of total revenues)

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 the total deviation is equal to a value 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.

The 1981–2006 sample period is not typical of the postWorld War II period as a whole. It contains only three 

recessions (those of 1981 and 1982, 1990 and 1991, and 

2001) in the 26 years—compared with seven in the previous 31 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. If the economy over 

the past two decades had been less stable—more representative of the cyclical experience of the whole postWorld War II period—the cyclical component of the 

deviations would have been roughly one-third larger than 

the noncyclical component, on average, instead of 

roughly equal. If the greater volatility of output in the 

entire post-World War II period is taken into account, 

the width of the fan chart increases by about one-fourth, 

on average (by 14 percent to 38 percent in different years 

of the projection period).

Whether the next decade will more closely resemble the 

past 26 years 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 but generally do not 

expect a return to higher volatility in the next five years.4

Preparing the fan chart involved two stages. In the first 

stage, CBO constructed measures of past projection deviations 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 deviations that appear to stem 

from the difficulty of forecasting the business cycle and 

deviations that are not correlated with the business cycle 

and appear to stem from other causes.

Stage One: Constructing the Measures 

of Deviations

Creating measures of deviations from 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 concerning revenues or mandatory spending that were enacted after the projections were 

made. That adjustment was necessary because CBO’s

Current

Year

Budget

Year

Budget

Year+1

Budget

Year+2

Budget

Year+3

Budget

Year+4

0

5

10

15

20

Total Deviation

Noncyclical Part

Cyclical Part

4. More specifically, although there seems to be general agreement 

that the growth of output has become more stable and that the 

expansion phases of business cycles have lengthened, economists 

disagree about the causes of that increased stability. Those disagreements concern the importance of factors such as monetary 

policy, financial markets and institutions, inflation, supply shocks, 

and inventory investment. See Congressional Budget Office, The 

Economic Effects of Recent Increases in Energy Prices (July 2006); 

and Economic Volatility, statement of Peter R. Orszag, Director, 

before the Committee on Ways and Means, House of Representatives (January 31, 2007).
4 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

baseline projections are intended to show the future level 

of the budget deficit or surplus under the assumption 

that current tax and spending policies remain the same.5

Without that adjustment to take into account subsequent 

tax and spending legislation, the measures of deviations 

would reflect the effects of later policy changes, 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. In its usual 

analyses of changes in its projections since the previous 

baseline, CBO attributes a small proportion of the 

changes in assumptions about discretionary outlays to 

economic or technical changes, but legislation accounts 

for nearly all of the overall change in the form of new 

budget authority. CBO decided on its approach for several reasons. First, it permits the use of a longer historical 

record. Second, because levels of discretionary spending 

are determined anew each year through appropriation 

acts, any discrepancy between actual levels and baseline 

projections of discretionary spending is essentially attributable to legislation. Third, the economic and technical 

effects on projections of discretionary outlays are small, 

so attributing all of those deviations to legislation does 

not affect the measures of deviations very much.

Deviations from projected net interest are largely a result 

of deviations from the projected level of the government’s 

publicly held debt. That debt, in turn, is the cumulation 

of past budget deficits (minus surpluses), so deviations 

from projected net interest depend on the cumulation of 

deviations from the projections of the deficit or surplus. 

The final fan-chart calculations include all those effects 

on net interest.

CBO calculated differences between projections and outcomes for each year covered by the winter baseline projections that it published from 1981 through 2006. 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 1982.6 The resulting sample is small: only 25 

current-year projections, declining to 20 five-year-ahead 

projections.7 (The sample size diminishes because projections made in the past five years can be compared with 

actual outcomes only through 2006.)

The estimated effects of legislation concerning 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 projections were made. For 

cases in which estimates were not available (as will be discussed below), substitutes were constructed.8

Revenues

The Joint Committee on Taxation (JCT) estimates the 

effects of tax legislation—bills that amend the Internal 

Revenue Code to alter income, estate and gift, excise, and 

Social Security payroll taxes—that is considered in a session of Congress and provides the estimates to the Congressional Budget Office for use during that session.9

CBO is responsible for producing estimates for all other 

legislation that affects revenues. 

Those estimated effects of tax legislation were used to 

adjust each baseline projection of revenues. For example, 

the projection made in January 1999 for total revenues in 

2004 was lowered from $2,184 billion to $1,913 billion 

(see Table 1). That adjustment reflected all tax laws 

enacted after January 1999 and through fiscal year 2004. 

5. For more information about the purpose of CBO’s baseline and 

the rules that govern its construction, see Congressional Budget 

Office, The Budget and Economic Outlook: Fiscal Years 2008 to 

2017 (January 2007), Chapter 1, and What Is a Current-Law

Economic Baseline? CBO Issue Brief (June 2005). 

6. Specifically, CBO did not have enough information in its files to 

include the estimated effects of legislation enacted between February 1982 and February 1983. More complete data were available 

for the slightly longer period of July 1981 through February 1983.

7. With the exception of 1981, CBO did not include its updated 

forecasts made in the summer, which would have doubled the 

sample size, because the deviations from those forecasts are not 

comparable to the deviations from the winter forecasts. In particular, the summer updates are published near the end of the ongoing 

fiscal year, so the accuracy for that year would be greater than that 

associated with the forecast made in the preceding winter.

8. The underlying worksheets used in computing the deviations of 

projections and a brief explanation of each one are available from 

within the electronic version of this document at www.cbo.gov.

9. See Section 201(f) of the Congressional Budget Act of 1974 (as 

amended), 2 U.S.C. 601(f).
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 5

Table 1.

Example: How CBO’s January 1999 Revenue Projection Was Adjusted for

Subsequent Legislation

(Billions of dollars)

Source: Congressional Budget Office.

Note: The three major changes in tax law enacted in the five years after CBO’s January 1999 baseline projection were in the Economic 

Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA), the Job Creation and Worker Assistance Act of 2002 (JCWAA), and the 

Jobs and Growth Tax Relief Reconciliation Act of 2003 (JGTRRA). The effects of those laws were incorporated in CBO's July 2001,

August 2002, and August 2003 baseline projections, respectively. Several other adjustments were made to account for the effects of 

other legislation, but they are relatively minor.

* = between -$500 million and $500 million.

The three laws with the largest budgetary impacts were 

the Economic Growth and Tax Relief Reconciliation Act 

of 2001 (EGTRRA), the Job Creation and Worker Assistance Act of 2002 (JCWAA), and the Jobs and Growth 

Tax Relief Reconciliation Act of 2003 (JGTRRA).

JCT and CBO estimated that EGTRRA, JCWAA, and 

JGTRRA would reduce revenues in fiscal year 2004 by 

$101 billion, $30 billion, and $135 billion, respectively.10 Similar adjustments were made for the other 

years in the baseline projections and for all of the other 

pieces of tax legislation. The differences between those 

adjusted projections and actual revenues represent the 

deviations attributable to economic and technical factors 

(see Table 2).

JCT’s and CBO’s estimates of the effects of tax legislation 

generally 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 

estimates of the budgetary impacts of tax and spending 

legislation could affect the estimates of uncertainty in 

CBO’s baseline budget projections, but the direction and 

size of that effect are unclear.

1999 2000 2001 2002 2003 2004

Baseline Projection of Revenues 1,815 1,870 1,930 2,015 2,091 2,184

Subsequent Legislation 

January 1999 to July 1999 0 * 0 0 0 0

July 1999 to January 2000 0 3 -6 -8 -2 -2

January 2000 to August 2000 * -1 -1 -1 -1

August 2000 to January 2001 0 -2 -2 -3 -3

January 2001 to August 2001 -70 -31 -84 -101

August 2001 to January 2002 1 * -2 -2

January 2002 to August 2002 -43 -40 -30

August 2002 to January 2003 0 * *

January 2003 to August 2003 -53 -135

August 2003 to January 2004 0 *

January 2004 to September 2004 3

September 2004 to January 2005 0

Total 0 3 -77 -86 -185 -271

Adjusted Baseline Projection of Revenues 1,815 1,873 1,853 1,929 1,906 1,913

Fiscal Year

10. See Congressional Budget Office, The Budget and Economic Outlook: An Update (August 2001), Table 1-4, p. 8; An Analysis of the 

President’s Budgetary Proposals for Fiscal Year 2003 (March 2002), 

Box 1, p. 2; and The Budget and Economic Outlook: An Update 

(August 2003), Table 1-8, p. 18.
6 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Table 2.

Inaccuracies in CBO’s Baseline Projections of Revenues That Are Attributable to 

Economic and Technical Factors

(Percentage of actual revenues)

Source: Congressional Budget Office.

Note: Forecast inaccuracies are actual revenues minus projected revenues, adjusted for the effects of legislation.

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 adjustments to that information were 

necessary. 

Baseline Projections of Discretionary Spending. As 

noted previously, 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.11

Insufficient Details About Legislation. In some cases, the 

estimated effects of legislation were not reported 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 

Date the Projection 

Was Published

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 -13.0

February 1987 2.4 -0.1 1.2 -3.9 -11.5 -15.3

February 1988 1.4 3.8 -0.7 -7.3 -10.5 -12.4

February 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 -12.3

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 17.2

May 1996 1.7 5.9 10.9 12.3 17.9 16.8

January 1997 4.4 9.5 10.9 16.7 15.7 5.3

January 1998 3.3 5.3 11.9 11.2 0.6 -2.2

January 1999 0.7 7.5 7.0 -4.1 -6.9 -1.8

January 2000 4.0 2.3 -8.9 -11.9 -6.1 0.4

January 2001 -3.8 -16.6 -21.4 -16.4 -9.5 -3.9

January 2002 -4.7 -10.9 -8.7 -3.7 0.9

January 2003 -4.8 -2.2 1.5 4.7

January 2004 3.2 6.1 8.6

January 2005 4.5 8.6

January 2006 4.1

Fiscal Year for Which the Projection Was Made

Budget Budget

Year + 2

Budget

Year + 3

Current 

Year

Budget

Year + 1

Budget

Year Year + 4

11. See Congressional Budget Office, Baseline Budget Projections: 

Fiscal Years 1982–1986 (July 1981), p. 38.
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 7

Table 3.

Inaccuracies in CBO’s Baseline Projections of Outlays That Are Attributable to 

Economic and Technical Factors

(Percentage of actual revenues)

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.

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 changes attributable to 

economic and technical factors (see Table 3).

Primary Budget Deficit or Surplus

The difference between revenues and outlays excluding 

net interest is known as the primary budget surplus (or 

deficit when negative). Correspondingly, the deviations 

from CBO’s projections of revenues, minus the deviations from its projections of noninterest outlays, equal 

the deviations from its projections of the primary deficit 

or surplus (see Table 4). As described previously, that calculation excludes legislative changes. In stage two of the 

fan-chart preparation, the deviations from the projected 

primary budget deficits or surpluses were cumulated into 

deviations from the projected level of the publicly held 

Date the Projection 

Was Published

July 1981 -2.4 -1.6 -0.7 -4.1 -3.5 -3.4

February 1983 -1.3 -2.1 -0.8 0.1 -0.1 0.2

February 1984 -0.9 * -0.2 -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

February 1987 -1.1 0.8 -0.4 6.3 6.4 7.2

February 1988 0.7 -0.5 5.6 5.8 6.8 4.6

February 1989 -1.1 5.6 5.2 6.2 4.1 5.4

January 1990 4.4 3.9 4.8 2.6 3.9 2.2

January 1991 -7.2 -7.4 -3.7 -0.8 3.3 2.8

January 1992 -5.6 -7.6 -3.4 -0.9 1.3 -1.9

January 1993 -3.2 -2.8 -4.3 -2.6 -3.4 -3.8

January 1994 -1.0 -1.3 -1.2 -3.5 -4.0 -4.7

January 1995 -1.0 -2.1 -3.9 -4.2 -4.9 -5.5

May 1996 -0.8 -2.6 -3.7 -4.0 -4.5 -5.7

January 1997 -1.7 -1.7 -2.7 -3.6 -4.2 -2.3

January 1998 -0.5 -1.2 -2.2 -2.5 -0.3 -2.2

January 1999 * -0.8 -0.8 1.3 0.1 -0.3

January 2000 -0.2 * 2.3 1.8 1.2 1.4

January 2001 -0.3 1.3 1.2 0.3 * -0.1

January 2002 -0.2 -0.3 1.0 1.7 1.0

January 2003 -0.4 -0.3 1.1 0.9

January 2004 -0.3 0.9 1.4

January 2005 0.1 0.6

January 2006 -0.7

Fiscal Year for Which the Projection Was Made

Current Budget Budget Budget Budget Budget

Year Year Year + 1 Year + 2 Year + 3 Year + 4
8 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Table 4.

Inaccuracies in CBO’s Baseline Projections of the Primary Deficit or Surplus That 

Are Attributable to Economic and Technical Factors

(Percentage of actual revenues)

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).

 debt, which were used to estimate the uncertainty of 

CBO’s projections of net interest.

Stage Two: Constructing Probability 

Distributions

The historical record of deviations from CBO’s projections of the primary deficit or surplus (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 is taken from a period that 

contains fewer and less frequent business cycles than 

occurred historically). 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 deviations from its 

budget projections.

The Statistical Model for Deviations from Forecasts 

of the Primary Deficit or Surplus

With the effects of legislation removed, differences 

between CBO’s past projections and actual budget outDate the Projection 

Was Published

July 1981 0.3 -6.8 -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 -4.0 -2.9 -5.7 -3.5 -15.8

February 1986 -3.2 -2.7 -5.3 -2.8 -14.5 -21.7

February 1987 3.5 -1.0 1.6 -10.1 -17.9 -22.6

February 1988 0.7 4.3 -6.3 -13.2 -17.3 -17.1

February 1989 1.9 -9.2 -14.7 -18.7 -17.5 -18.2

January 1990 -7.8 -13.3 -17.0 -15.9 -16.4 -14.5

January 1991 3.6 1.3 -4.5 -7.0 -11.2 -9.1

January 1992 6.0 5.6 1.0 -1.5 -2.0 3.8

January 1993 4.2 4.2 5.6 5.9 10.1 15.1

January 1994 1.6 2.3 4.2 10.0 14.4 16.1

January 1995 0.8 4.6 10.5 15.1 16.8 22.7

May 1996 2.5 8.5 14.6 16.3 22.4 22.5

January 1997 6.1 11.3 13.6 20.3 19.9 7.6

January 1998 3.8 6.5 14.1 13.7 0.9 0

January 1999 0.7 8.3 7.8 -5.4 -7.0 -1.4

January 2000 4.2 2.3 -11.2 -13.7 -7.3 -1.0

January 2001 -3.5 -17.9 -22.5 -16.6 -9.5 -3.8

January 2002 -4.5 -10.6 -9.7 -5.4 -0.1

January 2003 -4.4 -1.9 0.4 3.8

January 2004 3.4 5.2 7.2

January 2005 4.4 8.0

January 2006 4.8

Year Year Year + 1 Year + 2 Year + 3 Year + 4

Fiscal Year for Which the Projection Was Made

Current Budget Budget Budget Budget Budget
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 9

comes are closely related to the agency’s accuracy in projecting the business cycle. Forecasting the course of a 

business cycle more than two years ahead is virtually 

impossible, so CBO has traditionally tried to incorporate 

the business cycle in its economic projections explicitly 

for only the current year and the budget year.12 In its projections for longer horizons, CBO simply assumes that 

GDP will, on average, adhere to its trend (or “potential”) 

path.13 That assumption recognizes that, in fact, GDP 

will sometimes be above and sometimes below its potential level, but CBO does not attempt to forecast those 

boom or recession periods more than a couple of years 

ahead.

As long as CBO continues to do a reasonably good job of 

forecasting the business cycle for the current year, that 

cycle should have only a small impact on the accuracy of 

current-year budget projections. For the budget year, its 

contribution should be larger (because accuracy in forecasting diminishes as the horizon lengthens) but still 

modest. For later years, however, cyclical factors should 

loom larger. For the last two years of the five-year projection period, CBO assumes that GDP is the same as or 

close to its potential level. Thus, any actual difference 

between GDP and its potential level will not be reflected 

in those budget projections. Consequently, as the projection horizon extends, the deviations from budget estimates that result from unexpected changes in the business 

cycle should, on average, grow in importance, until they 

reach their maximum level in the last two years of the 

five-year period.

The portion of deviations attributable to the business 

cycle may be estimated by using the correlation between 

those deviations 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 may be a better indicator of cyclical surprises 

than the level, because the approaching levels of the gap 

can 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 past deviations was 

attributable to business cycles (see Box 1). Restrictions on 

the regression incorporate the view 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.

The portion of the overall deviations explained by the 

two business-cycle variables in the regression is called the 

cyclical part. The rest, the noncyclical part, represents the 

deviations 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.14

CBO does not expect its projections to display a negative 

or positive bias—otherwise it would change them. 

Accordingly, CBO assumed that the probability distribution of deviations from its projections was centered 

around an average of zero. The data do not contradict 

that assumption; the average of past deviations for each 

horizon is not statistically significantly different from 

zero.

Calculating the Distribution of Deviations from the 

Model

The regression model produces coefficients that relate 

deviations from the primary deficit or surplus (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 deviations that might 

be expected to occur simply because of the business cycle. 

One way to describe that distribution is through the rootmean-square error (RMSE), a measure of the average size 

of the errors that ignores the signs of individual errors

12. In relation to CBO’s baseline, the current year is the fiscal year in 

which the projection is made and the budget year is the following 

fiscal year (the one for which the budget is under consideration). 

Years beyond the budget year are referred to as out-years. 

13. See Congressional Budget Office, CBO’s Method for Estimating 

Potential Output: An Update (August 2001); and A Summary of 

Alternative Methods for Estimating Potential GDP (March 2004).

14. For a discussion of various factors affecting budget revenues and 

outlays, see Congressional Budget Office, The Budget and Economic Outlook: Fiscal Years 2008 to 2017, Chapters 3 and 4.
10 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

and gives extra weight to large errors.15 The model 

assumes that the RMSE of the cyclical part of deviations 

will rise to a plateau (see Figure 2 on page 3). 

That model does not account for all of the deviation from 

a given projection, 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 deviation has an RMSE that rises as the projection horizon 

lengthens, but it does not plateau (see Figure 2). For simplicity, CBO assumed that the noncyclical influences captured in the residual from the regression were independent of the cyclical component at each horizon.16 That 

assumption is not contradicted by the data, and using 

the sample correlations makes little difference to the 

results.17

Box 1.

Regression Equation for the Analysis of Uncertainty

To estimate the effect of the business cycle on the 

deviations of its past budget projections from actual 

outcomes, the Congressional Budget Office (CBO) 

used the following regression equation:

et,h = ß1whdt+h + ß2(1 - wh)gt+h + residualt,h

where: 

et,h = the deviation in projecting the primary deficit 

or surplus (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, and

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)—that restrict their effect at different projection horizons. The weights are chosen so 

that, for the four- and five-year-ahead projections, 

the forecast deviation depends only on gt+h, and for 

the current year, the deviation 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 deviations (different ß1

and ß2) because, although gt+h is completely unforeseen (for out-years), dt+h can be partly forecast, 

especially for the current budget year. ß1 and ß2 are 

estimated at 1.8 and 6.7, respectively, with a standard 

error of 0.5 and 0.6, respectively.

15. The RMSE is calculated by squaring the deviation from each projection, averaging the squares, and taking the square root of the 

result. (For distributions with a mean of zero, the RMSE is equal 

to the standard deviation.) The RMSE forms the basis for CBO’s 

calculation of the fan chart. Roughly speaking, a band of plus or 

minus one RMSE from a projection encompasses about twothirds of the likely variation—that is, the outcome is likely to be 

within one RMSE of the estimate about two-thirds of the time. 

Other confidence intervals in the fan chart are also calculated 

from RMSEs.

16. The fitted part and the residual from the regression are taken, 

respectively, to be the cyclical and noncyclical parts of the deviations. By construction, those two parts are uncorrelated for the 

whole regression sample, which pools the deviations for the six 

different horizons, but the two parts have sample correlations different from zero at individual forecast horizons. 

17. Because the sample of projections is small, CBO, to estimate the 

distribution of deviations with any confidence, assumed that the 

deviations shown in Table 4 were generated by a normal distribution. The kurtosis (a measure of how thick the tails of the probability distribution are) and skewness of the deviations in the 

sample are consistent with that assumption. The kurtosis and 

skewness were not statistically different from those of a normal 

distribution at a 5 percent significance level at any of the

horizons. 
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 11

The estimated RMSEs for the cyclical and noncyclical 

parts can be combined to form an estimate of the RMSE 

for the total budget deviation. Two RMSEs are combined 

by squaring each of them, adding those squares together, 

and taking the square root of the sum. While each deviation is the sum of its cyclical and noncyclical parts, the 

RMSE is less than the sum of the RMSEs of the two parts 

because the two parts sometimes offset each other (see 

Figure 2 on page 3). For example, when the cyclical part 

is positive, the noncyclical part could be negative, resulting in a total deviation that is smaller in size than the sum 

of the absolute size of the two parts. 

The estimated RMSEs for a given year were formulated 

as a percentage of that year’s actual revenues. For the 

projection of the total primary deficit or surplus, those 

RMSEs can be converted into dollars or expressed as a 

percentage of GDP using CBO’s current baseline projections of total revenues and GDP. 

The model’s estimate of the distribution of differences 

between CBO’s projections and budget outcomes appears 

generally consistent with CBO’s past record. Out of 135 

past deviations from projections of the primary deficit or 

surplus made in the 1981–2006 period, 5 percent fell 

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 3 on page 12).

Figure 4 on page 13 shows the 90 percent confidence 

bands for the primary surplus projections together with 

the deviations from the individual baselines from 1981 

through 2006. The figure shows that the five-year projections made in 1991 and before tended to be too optimistic, while the projections made between 1993 and 1998 

were too pessimistic. Those were followed by the 1999 

and 2000 projections, which were too pessimistic for the 

early years and too optimistic for the later years. The 

record for the last five years of projections is not complete. So far, however, the projections made in 2001 and 

2002 have proved to be too optimistic. The primary 

source of deviations from the baselines between 1993 and 

1998 was the unforeseen economic boom of the late 

1990s and the associated rapid rise in revenues. For the 

earlier baseline projections, the primary sources of deviations were the unexpected continuation of the productivity slowdown that started in the 1970s and the recessions 

of 1981–1982 and 1990–1991. The primary sources of 

deviations from the projections made between 2001 and 

2003 were the 2001 recession, a slower-than-expected 

recovery from that recession, and a fall in taxable income 

shares in GDP. The primary source of deviations after 

2003 has been the unexpected surge in corporate profits. 

CBO computes the uncertainty range for only the first 

five years, although the projections have covered a period 

of 10 years beginning with the 1996 baseline. The fan 

does not extend to the second five years because the 

record of deviations beyond the first five years is too small 

to make reliable inferences about the uncertainty range 

for those years, and such estimates could be misleading. 

For example, CBO’s 1996 forecast, which is the first that 

covered a 10-year period (and which contains five of the 

15 data points beyond the fifth year of the projections), 

generally had larger deviations in the first five years than 

in the second five years of that projection (see Figure 5 on 

page 14). Generally, though, deviations for years beyond 

the five-year forecast would be larger (not smaller) than 

those for the first five years. In the particular case of the 

1996 forecast, the deviations in the first five years, which 

resulted from the unexpected strength of the economy 

and the rise in taxable income shares, were reduced significantly in the sixth through tenth years by the unforeseen 

effects of the 2001 recession and the fall in taxable 

income shares.

Uncertainty of Projections of the Total Deficit or 

Surplus and of the Level of Outstanding Debt

Determining the uncertainty range for CBO’s current 

baseline projection of the total deficit or surplus (shown 

in Figure 1 on page 2) requires information about how 

the deviations from the primary budget (the budget 

excluding net interest) will affect the government’s debtservice costs. Those deviations from budget outcomes are 

run through a simple debt-service model that tracks how 

they translate into deviations from the projected debt service; 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 deviations from interest 

rate projections are not considered because their contribution to deviations from overall budget projections is 

not expected to be substantial.

The extent to which the deviations from projections of 

the primary deficit or surplus are correlated across horizons is important for the computation of debt-service 

costs. When those deviations are highly correlated, they
12 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Figure 3.

CBO’s Past Deviations in Projecting the Primary Surplus, Compared with the 

Constructed 90 Percent Confidence Ranges

(Percentage of GDP)

Source: Congressional Budget Office. 

Note: Each thin line represents the actual deviations from 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 deviations. That range encompasses most of CBO’s past record. 

have a larger accumulated effect on outstanding debt, and 

the associated change in the government’s interest burden 

is larger. In calculating the probability distribution of 

deviations from projections of the total deficit or surplus 

(including net interest), CBO assumed that the cyclical 

and noncyclical parts would continue to have the same 

correlation structure as in the past.18 The uncertainty 

range for outstanding debt under that assumption is 

shown in Figure 6 on page 15. (Reasonable alternative 

assumptions about the extent to which deviations are 

correlated do not produce a very different picture.) 

The percentiles for the total deficit or 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 deficit or surplus 

at different horizons. Those percentiles are shown in 

Table 5 on page 16 in billions of dollars and in Table 6 on 

page 17 as percentages of GDP. Those estimates permit 

the construction of probability statements about the 

future path of the total budget deficit or surplus. For 

example, although CBO’s baseline forecast for 2008 is a 

budget deficit, there is a 31 percent chance of a surplus. 

Similarly, although the baseline forecast for 2012 is a 

budget surplus, there is a 37 percent chance that it will 

instead be a deficit (see Table 7 on page 18).

CBO will continue its efforts to refine these calculations and welcomes suggestions for improving the 

methodology. 

Current

Year

Budget

Year

Budget

Year+1

Budget

Year+2

Budget

Year+3

Budget

Year+4

-6

-4

-2

0

2

4

6

18. Interest payments increase the RMSE of the probability distribution of deviations. However, they do not alter the assumption that 

deviations are normally distributed, because the changes in debtservice costs are a linear function of the current and past changes 

in the primary budget balance. The RMSE of the total deficit or 

surplus, in fact, is computed using that linear relationship.
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 13

Figure 4.

Deviations from CBO’s Primary Surplus Projections 

Made Between 1981 and 2006 

(Percentage of gross domestic product)

Source: Congressional Budget Office. 

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

This figure shows the deviations from CBO’s projections of the primary deficit or surplus—the total deficit or surplus excluding net 

interest—made at different times. Plotted points that lie below the center line reflect instances in which CBO underestimated the 

primary deficit or overestimated the primary surplus, whereas points above the center line reflect the opposite. In each panel, the 

shaded cone indicates the estimated 90 percent confidence band; that is, there was a 90 percent chance that CBO's projection would 

be within the shaded area. CBO estimated that confidence band on the basis of its forecasting record since 1981 (excluding 1982, 

because of insufficient data).

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

-6

-4

-2

0

2

4

6

1981 1983 1984 1985 1986

1987 1988 1989 1990 1991

1992 1993

-6

-4

-2

0

2

4

6

1994 1995 1996

1997

-6

-4

-2

0

2

4

6

1998

CY BY +1 +2 +3 +4

-6

-4

-2

0

2

4

6

1999 2000 2001

CY BY +1 +2 +3 +4 CY BY +1 +2 +3 +4 CY BY +1 +2 +3 +4

-6

-4

-2

0

2

4

6

2002 2003 2004 2005 2006

CY BY +1 +2 +3 +4
14 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Figure 5.

Deviations from the 1996 Primary Surplus Projection

(Percentage of gross domestic product)

Source: Congressional Budget Office. 

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

This figure shows the deviations from CBO’s projection of the primary deficit or surplus—the total deficit or surplus excluding net 

interest—made in 1996. The plotted points, all of which lie above the center line, reflect instances in which CBO overestimated the 

primary deficit or underestimated the primary surplus. The outside cone indicates the estimated 90 percent confidence band; that is, 

there was a 90 percent chance that CBO’s projection would be within the area of the cone. CBO estimated that confidence band on the 

basis of its forecasting record since 1981 (excluding 1982, because of insufficient data). 

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

CY BY BY+1 BY+2 BY+3 BY+4 BY+5 BY+6 BY+7 BY+8 BY+9

-6

-4

-2

0

2

4

6
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 15

Figure 6.

Uncertainty of CBO’s Projections of the Level of Outstanding Debt Under

Current Policies

(Percentage of gross domestic product)

Source: Congressional Budget Office.

Notes: This figure, calculated on the basis of CBO’s track record in forecasting, shows the estimated likelihood of alternative projections of the 

level of outstanding debt under current policies. The baseline projections described in The Budget and Economic Outlook: Fiscal Years 

2008 to 2017 fall in the middle of the darkest area of the figure. Under the assumption that tax and spending policies do not change, 

the probability is 10 percent that the actual level of debt will fall in the darkest area and 90 percent that it will fall within the whole 

shaded area.

The actual level of debt will be affected by legislation enacted in future years, including decisions about discretionary spending. The 

effects of future legislation are not reflected in this figure.

1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011

0

5

10

15

20

25

30

35

40

45

50

55
16 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Table 5.

Estimated Probability Distribution of Total Budget Deficits or Surpluses, 

in Billions of Dollars

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—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 deficit.

These estimates permit the construction of probability statements about CBO’s baseline projection of the total budget deficit or 

surplus. For example, the table indicates that there is a 90 percent chance that the budget’s balance in 2008 (the budget year) will 

be somewhere between a $442 billion deficit and a $246 billion surplus, and a 50 percent chance that the deficit or surplus in 2012 

(the budget year + 4) will be within $382 billion of the baseline projection. (That last calculation takes the range from the 25th to the 

75th percentiles and halves it.)

Percentile 2007 2008 2009 2010 2011 2012

5 -362 -442 -613 -724 -765 -762

10 -320 -366 -504 -594 -599 -556

15 -292 -315 -430 -507 -487 -417

20 -269 -274 -371 -437 -397 -307

25 -250 -239 -320 -378 -321 -212

30 -233 -208 -275 -324 -252 -127

35 -217 -179 -233 -274 -189 -48

40 -201 -151 -193 -227 -128 27

45 -187 -124 -154 -182 -70 99

50 -172 -98 -116 -137 -12 170

55 -158 -72 -78 -92 45 242

60 -143 -45 -40 -47 103 314

65 -128 -18 0 1 164 389

70 -112 11 42 50 227 468

75 -94 43 87 104 296 553

80 -75 78 138 163 373 647

85 -52 118 197 233 462 758

90 -24 170 271 320 574 897

95 18 246 381 450 740 1,103
THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS 17

Table 6.

Estimated Probability Distribution of Total Budget Deficits or Surpluses,

as a Percentage of Gross Domestic Product

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—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 deficit as a percentage of GDP.

These estimates permit the construction of probability statements about CBO’s baseline projection of the total budget deficit or 

surplus. For example, the table indicates that there is a 90 percent chance that the budget’s balance in 2008 (the budget year) will 

be somewhere between a deficit of 3.1 percent of GDP and a surplus of 1.7 percent of GDP, and a 50 percent chance that the deficit or 

surplus in 2012 (the budget year + 4) will be within 2.2 percent of GDP of the baseline projection (or half of the range from the 25th 

to the 75th percentiles).

Percentile 2007 2008 2009 2010 2011 2012

5 -2.7 -3.1 -4.1 -4.6 -4.6 -4.4

10 -2.3 -2.6 -3.4 -3.8 -3.6 -3.2

15 -2.1 -2.2 -2.9 -3.2 -3.0 -2.4

20 -2.0 -1.9 -2.5 -2.8 -2.4 -1.8

25 -1.8 -1.7 -2.1 -2.4 -1.9 -1.2

30 -1.7 -1.5 -1.8 -2.1 -1.5 -0.7

35 -1.6 -1.2 -1.6 -1.7 -1.1 -0.3

40 -1.5 -1.1 -1.3 -1.4 -0.8 0.2

45 -1.4 -0.9 -1.0 -1.2 -0.4 0.6

50 -1.3 -0.7 -0.8 -0.9 -0.1 1.0

55 -1.2 -0.5 -0.5 -0.6 0.3 1.4

60 -1.0 -0.3 -0.3 -0.3 0.6 1.8

65 -0.9 -0.1 0 0 1.0 2.3

70 -0.8 0.1 0.3 0.3 1.4 2.7

75 -0.7 0.3 0.6 0.7 1.8 3.2

80 -0.5 0.5 0.9 1.0 2.3 3.8

85 -0.4 0.8 1.3 1.5 2.8 4.4

90 -0.2 1.2 1.8 2.0 3.5 5.2

95 0.1 1.7 2.5 2.9 4.5 6.4
18 THE UNCERTAINTY OF BUDGET PROJECTIONS: A DISCUSSION OF DATA AND METHODS

Table 7.

Estimated Probability That the Budget 

Will Be in Deficit Under CBO’s Baseline 

Assumptions

(Percent)

Source: Congressional Budget Office.

2007 2008 2009 2010 2011 2012

Probability

of a Deficit 94 69 66 66 51 37
CBO
CBO