The Uncertainty of Budget Projections: A Discussion of Data and Methods |
April 2003 |
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:
|
Tables |
|
|
1. |
How CBO's January 1994 Revenue Projection Was Adjusted for Subsequent
Legislation |
2. |
Inaccuracies in CBO's Baseline Projections of Revenues That Are
Attributable to Economic and Technical Factors |
3. |
Inaccuracies in CBO's Baseline Projections of Outlays That Are Attributable
to Economic and Technical Factors |
4. |
Inaccuracies in CBO's Baseline Projections of the Primary Surplus
or Deficit |
5. |
The Historical Record of CBO's Baseline Budget Projections |
6. |
Estimated Probability Distribution of Total Budget Surpluses |
|
|
Figures |
|
|
1. |
Uncertainty in CBO's Projection of the Total Budget Surplus or Deficit
Under Current Policies |
2. |
Uncertainty in CBO's Projection of the Total Budget Surplus or Deficit,
Assuming Average Business-Cycle Activity Since 1947 |
3. |
Cyclical and Noncyclical Inaccuracies in Projecting the Primary
Surplus |
4. |
Cyclical and Noncyclical Inaccuracies in Projecting the Primary
Surplus, Assuming Average Business-Cycle Activity Since 1947 |
5. |
CBO's Past Inaccuracies in Projecting the Primary Surplus, Compared
with the Constructed 90 Percent Confidence Range |
6. |
Misestimates in CBO's Projections Made from 1981 to 1997 |
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|
Box |
|
|
1. |
Regression Equation for the Analysis of Uncertainty |
The Uncertainty of Budget Projections: A Discussion of Data and Methods |
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) |
|
|
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 |
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|
|
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 |
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|
|
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 |
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|
|
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).
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|
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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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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).
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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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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.
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|
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|
|
|
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|
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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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 |
|
|
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 |
|
|
|
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) |
|
|
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.
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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 |
|
|
CBO will continue its efforts to refine these calculations. It welcomes
suggestions for improving the methodology.
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 2001. Insufficient data were available to use either projections made before 1981 or the projection made in early 1982. In the cases of 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 following section, those data are important because the measures of inaccuracy used in this analysis were constructed by removing the effects of legislation, including discretionary spending (along with interest payments). The baseline budget projections that CBO made before 1980 were not comparable with later
ones, because the early economic assumptions represented targets rather
than projections. |
3. |
The end of the most recent recession than began in March 2001 has not yet been determined by the National Bureau of Economic Research, the organization charged with that duty. For now, CBO has assumed that the recession concluded at the end of calendar year 2001. |
4. |
CBO did not begin making 10-year baseline projections until 1996. Although supplemental 10-year projections were published as early as 1992, those earlier reports did not provide information about the budgetary effects of legislation for the extended time periods. Before 1996, CBO's baseline typically extended for five years after the current year. Because there are not yet any uncertainty measures for the seventh through tenth years, and only one for the sixth year, this analysis focuses on a five-year projection horizon. |
5. |
Although there seems to be general agreement in the recent economics literature that the growth of output has become more stable and that the expansion phases of business cycles are likely to be longer in the future than in the past, 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 the behavior of inventory investment. For discussions of those and other points, see Margaret M. McConnell and Gabriel
Perez Quiros, "Output Fluctuations in the United States: What Has Changed
Since the Early 1980s?" American Economic Review, vol. 90, no. 5
(December 2000), pp. 1464-1476; Olivier Blanchard and John Simon, "The
Long and Large Decline in U.S. Output Volatility," Brookings Papers
on Economic Activity, no. 1 (2001), pp. 135-174; and Marcelle Chauvet
and Simon Potter, "Recent Changes in the U.S. Business Cycle," The Manchester
School, vol. 69, no. 5 (special issue 2001), pp. 481-508. |
6. |
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 2004-2013 (January 2003), Chapter 1. |
7. |
In CBO's usual analyses of changes in its projections since the previous baseline, CBO allocates a small proportion of any changes in assumptions about discretionary outlays to the categories of economic or technical revisions (ibid., Box 5-1). In CBO's classifications, economic revisions are ones that stem from changes in the agency's economic forecast, and technical revisions are ones that cannot be attributed to new legislation or to changes in the components of the economic forecast. |
8. |
Specifically, CBO did not have enough information in its files to include the estimated effects of legislation enacted between February 1982 and February 1983. Much better data were available for the slightly longer period of July 1981 through February 1983. |
9. |
The sample size could have been doubled by including the updated projections that CBO typically publishes in the summer, but those updates are closely related to the winter baselines and do not really offer additional information useful for calculating inaccuracies. |
10. |
See Section 201(f) of the Congressional Budget Act of 1974 (as amended), 2 U.S.C. 601(f). |
11. |
See Congressional Budget Office, The Economic and Budget Outlook: An Update (September 1997), p. 36. |
12. |
See Congressional Budget Office, Baseline Budget Projections: Fiscal Years 1982-1986 (July 1981), p. 38. |
13. |
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. |
14. |
See Congressional Budget Office, CBO's Method for Estimating Potential Output: An Update (August 2001). |
15. |
See Congressional Budget Office, The Budget and Economic Outlook: Fiscal Years 2004-2013, Chapters 3 and 4. |
16. |
The RMSE is calculated by squaring each projection inaccuracy, 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 two-thirds 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. |
17. |
The fitted part and the residual from the regression are taken, respectively, to be the cyclical and noncyclical parts of the projection inaccuracies. By construction, those two parts are uncorrelated for the whole regression sample, which pools the inaccuracies for the six different horizons, but they have sample correlations different from zero at individual forecast horizons. |
18. |
Because the sample of projections is small, CBO, to estimate the distribution of inaccuracies with any confidence, assumed that the inaccuracies shown in Table 4 were generated by a normal distribution. The sample kurtosis and skewness of the inaccuracies are consistent with that assumption. The assumption of a normal distribution is not rejected at any conventional significance level at any of the horizons for skewness, and for most of the horizons for kurtosis. For the four- and five-year-ahead projections, kurtosis is not rejected at the 5 percent significance level. |
19. |
The uncertainty of net interest payments increases the RMSE of the probability distribution of projection inaccuracies. However, it does not alter the assumption that inaccuracies are normally distributed, because the changes in debt-service costs are a linear function of the current and past changes in the primary budget balance. The RMSE of the total surplus, in fact, is computed using that linear relationship. |
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