**Simulating the CBO’s Budget**

Projection Scenarios

George H. Blackford © 1/31/2014

The
Congressional Budget Office (CBO) publishes an
annual report that provides projections for the federal budget under two
scenarios: an *extended baseline scenario* and an *extended
alternative fiscal scenario*. According to the CBO:

The extended baseline scenario generally adheres
closely to current law. . . .

Under . . . the extended alternative fiscal scenario,
certain policies that are now in place but that are scheduled to change
under current law would continue instead, and some provisions of current law
that might be difficult to sustain for a long period would be modified. . .
.
*The 2013 Long-Term Budget Outlook*.

Given these scenarios, the CBO projects federal
spending and revenue over specific periods of time to show how these
projected levels of revenues and spending can be expected to affect federal
debt in the future.

## Simulating the CBO’s Projection Models

The simplest way to construct a model that simulates
the underlying models that generate the CBO’s projections is to assume that
federal debt at the end of the current year (D_{i}) will be equal to
a) the debt at the end of the previous year (D_{i-1}) plus b) the
interest paid out during the current year (I_{i}) plus c) the
non-interest expenditures paid out during the current year (NIS_{i})
less d) the revenues collected during the year (R_{i}):

1) D_{i} = D_{i-1} + I_{i} +
NIS_{i} - R_{i}.

This relationship is not exact in that it does not
take into account changes in the cash holdings of the federal government,
the accumulation or sale of assets, or the way in which other factors affect
federal borrowing that are not included in the budget. Nevertheless,
equation 3) can be used to define a model that approximates the effects of
changes in the OMB's revenue and spending projections by specifying:

2) I_{i}
= r_{i}D_{i-1} + r_{i}(R_{i} - NIS_{i})/2

_{ } =
r_{i} / (D_{i-1} + (R_{i} - NIS_{i})/2),

where r_{i} is, in effect, the average rate of
interest paid on the federal government’s debt and borrowings during the
year; (R_{i} - NIS_{i}) is the amount of money during the
current year that the government may have to borrow to fund its expenditures
or that is available to the government to pay back debt (dividing by 2
presumes that money is borrowed or paid back at a constant rate throughout
the year); and the other variables are as defined in equation 1).

The significance of 2) is that it can be solved for r_{i},

3) r_{i} = I_{i} / (D_{i-1} +
(R_{i} - NIS_{i})/2),

and, given the values for D_{i}, R_{i},
and I_{i} in the
Supplementary Data Excel workbook that is
published with the CBO's reports,* *equation* *3) can be used to
estimate the values of r_{i} that are implicit in the CBO's
projection models. These estimates can, in turn, be used with equation 2)
to estimate the value for I_{i} for any set of values for D_{i-1},
R_{i}, and NIS_{i}. These estimated values for I_{i}
can then be substitute into 1) to obtain the corresponding values for D_{i}.
Thus, equations 1) through 3) allow us to approximate how changes in the
values of non-interest spending and revenues will affect the CBO’s
projections.

## Using Excel to Simulate the CBO’s Projection Models

I have incorporated the simulation model specified in
1) through 3) above in an Excel workbook that can be downloaded by
clicking on this link. This workbook contains five
spreadsheets: *Baseline Data, Alternative Data, Baseline Simulation,
Alternative Simulation*, and *Historical Data*. These spreadsheets
are saved in a protected mode without a password so they can be unprotected
to play with the formulas at your discretion.

#### Baseline Data Spreadsheet

The first N Columns of the *Baseline Data*
spreadsheet are copied from the *1. Summary Extended Baseline*
spreadsheet in the
Supplementary Data workbook. The **Real GDP
2013 Prices** and **Nominal GDP** variables in Column P and Column Q
are copied from the *2. Economic Vars and Population* spreadsheet in
the
Supplementary Data workbook that accompanied
the CBO’s 2013 report. These last two variables are used to calculate the
**Implicit GDP Deflator** in Column R by dividing Column Q by Column P.
(You’ll have to ask the CBO why the result equals 0.99 in 2013 rather than
1.00.)

Equation 3) is used to estimate the **Average
Rate of Interest** parameters (r_{i})
in Column T of the *Baseline Data *spreadsheet using the values for
Revenues (R_{i})
in Column B, Net Interest (I_{i})
in Column H, and the **Calculated Debt/GDP **(D_{i-1})
in Column V where D_{i}
is calculated using equation 1) and the ith values of the independent
variables in 1). The value for D_{2012}
is obtained from Column C of the *Historical Tables* spreadsheet in
this workbook. The value for total non-interest spending (NIS_{i})
in 1) through 3) is calculated from the sum of Columns C through F, rather
than being obtained directly from Total Noninterest Spending in Column G, to
keep the calculation of the r_{i}
parameters consistent with the way in which these parameters are used in the
*Baseline Simulation *spreadsheet, thereby, minimizing the rounding
error in the calculations.

The CBO does not provide projections for defense
expenditures, the second largest component of the federal budget after
Social Security, but because of its importance in the federal budget I have
attempted to separate out **Defense** in Column S in this spreadsheet
from the Other category in Column F in the CBO’s data base. In doing this I
have used the
Office of Management and Budget's estimates
for defense expenditures in its
Table 3.1 for the years 2013 through 2018 and
have assumed that defense expenditures remain a constant proportion of the
CBO's projections for all Other non-interest spending thereafter. This
treatment of defense seems to be in accord with the CBO's discussion of
discretionary spending of which defense expenditures are the largest
component.

Finally, it should be noted that since the CBO
reports all of its projections as a percent of GDP (Gross Domestic Product),
almost all of the calculations in this spreadsheet (and throughout the rest
of this workbook) require that the various percentages be multiplied by the
corresponding value of GDP in Column Q to obtain their absolute magnitudes
before the calculations in 1) through 3) can be made and then divided by the
corresponding values of GDP to convert the results back to percentages of
GDP.

#### Alternative Data Spreadsheet

The *Alternative Data* spreadsheet is identical
to the *Baseline Data* spreadsheet explained above except that the
first N columns of the *Alternative Data* spreadsheet are copied from
the *6. Summary Ext Alt Fiscal Scen *spreadsheet in the
Supplementary Data workbook
rather than from the
*1. Summary Extended Baseline*
spreadsheet.

#### Baseline Simulation Spreadsheet

As is shown in **Figure 1**, the *Baseline
Simulation *spreadsheet is broken down into two sections: **Independent
Variables** and **Calculated Variables**.

**Figure 1: Baseline Simulation Spreadsheet**

The subsection at the top of the **Independent
Variables **section allows you to enter values in the **Additive Factor
**(AF), **Multiplicative Factor **(MF), **Growth Factor **(GF),**
Maximum **(Max), and **Minimum **(Min)** **rows that** **are used
to transform the variables (Var_{i}) (all of which are taken from
the various columns of the *Baseline Data* spreadsheet) in the
corresponding columns below this subsection. These transformations are
calculated according to the formula:

4) Var_{i}* = Min < AF + MF×Var_{i}
+ (GF≠0)×Var_{i}×(1+GF)^{(Current
Year-2013)}* *< Max.

The transformed variables (Var_{i}*) are then
used in conjunction with equations 1) through 3) above and the r_{i}
parameters calculated in the *Baseline Data* spreadsheet to calculate
the variables in the **Calculated Variables** section of the spreadsheet,
beginning in 2014, to show how the transformed independent variables will
affect the projections of **Nominal GDP**, **Net-Interest**, **
Federal Debt Held by the Public**, **Total Spending**, **Revenues
Minus** **Total Spending**, and **Other Minus Defense **in the CBO’s
extended baseline scenario projection model.

#### Alternative Simulation

The *Alternative Simulation* spreadsheet is
identical to the *Baseline Simulation* spreadsheet except the
independent variables in the *Alternative Simulation* spreadsheet are
taken from the *Alternative Data *spreadsheet
rather than from the *Baseline Data*
spreadsheet.

#### Historical Data

The *Historical Data*** **spreadsheet combines
the projection and transformed data from 2013 through 2088 in the other
spreadsheets in this workbook with the historical data from 1950 through
2012 for these data. The locked cells in this spreadsheet can be copied and
passed into other programs.

As is shown in **Figure 2**, at the top of this
spreadsheet is a selection box.

**Figure 2: Historical Data Spreadsheet.**

This box is used to select whether the projection data
from the baseline scenario or the alternative fiscal scenario spreadsheets
are to be combined with the historical data. Entering a **
1** in this box will
combine the historical data with the data in the *Baseline Data *and
the *Baseline Simulation *spreadsheets; entering a **
2** in this box will
combine the historical data with the data in the *Alternate Data *and
*Alternate Simulation* spreadsheets.

The *Historical Data *spreadsheet is broken down
into four sections: **Reference Data**, **Independent Variables**, **
Calculated Variables**, and **Summary Table**.

The **Reference Data** section combines historical
data with the untransformed projection data from the *Data *spreadsheet
of the scenario that has been selected.

The **Independent Variables** section combines
historical data with the transformed independent variable data from *
Simulation* spreadsheet of the scenario that has been selected.

The **Calculated Variables **section combines the
historical data with the calculated variable data from the scenario that has
been selected and also calculates a number of additional variables that are
projected in the CBO’s projection models that are not calculated in the
simulation spreadsheets: **Revenues Minus Total Noninterest Spending**,
**Total Spending**, **Revenues Minus Total Spending**, **Social
Security Plus Medicare**, **Social Security Plus Healthcare**,** Other
Excluding Defense**,** **and** Total Healthcare**.

The **Summary Table** section displays the
transformation parameters entered in the *Simulation* spreadsheet of
the scenario that has been selected and also summarizes the changes in the
most important projected variables between 2013 and 2038, 2049, and 2088
which are reference points used in the CBO’s 2013 report. These changes are
also displayed at the bottom of the other three sections of the *
Historical Data* spreadsheet (and at the bottom of the tables in the *
Baseline Simulation*** **and *Alt*ernative *Simulation*
spreadsheets as well) for all of the variables in this spreadsheet.

## Model Accuracy

There is not enough data in the CBO’s
Supplementary Data workbook to check the
accuracy of this model directly, but there are two ways to evaluate its
accuracy indirectly. The first is to see how well the estimates produced by
the model forecast the data from which the r_{i}
parameters of the model are derived.

**Figure 3**
plots the original values of the CBO’s 2013 baseline and alternative fiscal
scenario projections and the model’s estimates of these projections.

**Figure 3: Comparing Baseline and Alternative
Fiscal **

Projections and Forecasted Values.

The fit is quite good, though there is some
autocorrelation indicated by the way in which the forecasts seem to lag the
changes. The mean error is -0.98 percentage points in the baseline
forecasts with a standard deviation of 1.02, while the mean error is -1.24
percentage points for the alternative forecasts with a standard deviation of
0.77. The mean absolute error for the baseline forecasts is 1.09 percentage
points with a standard deviation of 0.91, and is 1.27 percentage points for
the alternative fiscal forecasts with a standard deviation of 0.77.

These numbers suggest that the model works quite
well within the data on which it was estimated, but this does not tell us
very much about its accuracy outside this data.

The second way we can evaluate the accuracy of
this model is to look at the accuracy with which it forecasts the fiscal
gaps that the CBO publishes in its reports:

The fiscal gap is a measure of the difference between
projected federal noninterest spending and revenues over a given period. It
represents the extent to which the government would need to immediately and
permanently raise tax revenues or cut spending—or do both, to some degree—to
make the government’s debt the same size (relative to gross domestic
product) at the end of the period that it is at the end of 2013.
The 2013 Long-Term Budget Outlook

The CBO specifies three fiscal gaps for its
baseline scenario in its 2013 report for the periods: 2013-2038, 2013-63,
and 2013-2088. In its 2012 report also specifies fiscal gaps under its
baseline scenario for the periods 2012-2037, 2012-2062, and 2012-2087 along
with a fiscal gap under its alternative fiscal scenario for the period
2012-2037.

Each of these gaps can be converted to a revenue
gap and a spending gap—that is, the amount by which revenue or spending must
permanently increase or decrease in order to eliminate the fiscal gap—by
dividing the CBO’s fiscal gap, which is expressed as a percent of GDP, by
the CBO’s projected levels of revenue and spending in the second year of the
period, which is also expressed as a percent of GDP. This is done in **
Table 1** which shows the CBO’s fiscal, revenue, and spending gaps from
the CBO’s 2013 and 2012 reports.