Full text of The CBO Multipliers Project : A Methodology for Analyzing the Effects of Alternative Economic Policies

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

THE CBO MULTIPLIERS PROJECT:
A METHODOLOGY FOR ANALYZING
THE EFFECTS OF
ALTERNATIVE ECONOMIC POLICIES

A CBO Technical Analysis Paper
August 1977




CONGRESSIONAL BUDGET OFFICE
U.S. CONGRESS
WASHINGTON, D.C.

THE CBO MULTIPLIERS PROJECT:
A Methodology for Analyzing the Effects of Alternative
Economic Policies

The Congress of the United States
Congressional Budget Office

For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C. 20402
Stock No. 052-070-04180-3







PREFACE

This study presents some of the technical material used by
the Congressional Budget Office in analyzing the impact of alternative economic policies. It was written by Mary Kay Plantes and
Frank de Leeuw. Nancy Morawetz and Michael Owen performed many of
the model simulations. The paper was typed by Dorothy J. Kornegay
and edited by Patricia H. Johnston




Alice M. Rivlin
Director

iii




CONTENTS
Preface

iii

Summary
Chapter I*

•

•

Introduction

ix
1

Chapter II. Factoring Fiscal Policy Multipliers
Basic Multipliers Model
Key Components of Fiscal Policy
Multipliers
The Fiscal Multiplier Formula

5
12

Chapter III. Some Extensions of the Multipliers
Model
Monetary Policy
Corporate Tax Changes

15
15
20

Chapter IV. Price Changes Versus Real Changes

23

Chapter V. Other Relationships Used in Measuring
Policy Impacts

25




3
4




TABLES

1.

Quarterly Values of a,

6

2.

Quarterly Values of b

7

3.

Estimated Values of b , b_, c , and c
Basic Multipliers Model

Used In the
T

9

4.

Quarterly Values of a~

10

5.
6.

Quarterly Values of a~
Change in GNP Resulting From A Permanent Increment in Policy Instruments

11

K

8.

9.

10.

11.

12.

14

Changes in 3-month Treasury Bill Rate and GNP Resulting from a Permanent Increment in Federal
Government Purchases and a Permanent Increment
in Unborrowed Reserves

16

Quarterly Values of d , d 2 , and d , and b. for
Unborrowed Reserve Changes

19

Changes in GNP Resulting From a Permanent Increment in Unborrowed Reserves

20

Corporate Tax Cut Parameters Used in the Basic
Multipliers Model

21

Changes in GNP Resulting From a Permanent Increment in Corporate Tax Payments

22

Division of Government Purchases GNP$ Multiplier,
a., and a« Into Real and Nominal Effects for Four
Econometric Models

24

Measuring Policy Impacts

26

FIGURE

1.




VII




SUMMARY

At the peak of the budget season, CBO is called upon
several times a week to estimate the impact on the economy
of a change in the federal budget•
These estimates are quite
sensitive to which macroeconomic model or other procedure is used
to prepare them.
The multipliers project is an attempt to
understand and deal with the diversity of results that various
models may produce*
The project consists of (a) systematic comparison of
econometric model estimates of the impact of changes in fiscal
policies, and (b) selection of a uniform set of procedures fcr
calculating policy impacts.
The systematic comparison involves
the factoring of an overall GNP multiplier—the amount of GNP
generated per dollar of a spending increase or a tax cut—into a
number of key components, including:
o

the ratio of the change in consumption
in disposable income;

o

the ratio of the change in investment
plant, and equipment to the change in GNP;

o

the ratio of the change in "other GNP" (inventories,
state and local purchases, net exports) to the change
in GNP;

o

the fraction of a change in GNP going into wages and
salaries and other labor income and nonwage income;

o

the fraction of a change in GNP serving
transfer payments; and

o

the fraction of a change in wages and salaries and other
labor income and nonwage income going into personal
tax payments.

ix
94-329 O - 77 - 2




to the change

in housing,

to reduce

With th§ aid of this factoring, differences in policy
multipliers among models can be traced back to differences
in one or more of these key ratios.
The selection of a uniform set of procedures begins with
choosing a value (or, more precisely, a set of quarterly values)
for each of these key ratios on the basis of reasonableness,
other empirical studies, and, when necessary, simply averaging
across models.
The values of the key ratios determine CBO's
overall GNP multipliers.
To go beyond GNP to real and price
effects, employment impacts, etc., CBO makes use of a number of
simple relationships, including Okun's law and a two-equation,
wage-price model. This paper focuses largely on the first step
in the multipliers project, the factoring of GNP multipliers into
their major components. The final section discusses briefly the
other relationships used by CBO.




CHAPTER I.

INTRODUCTION

At the peak of the budget season, CBO is called on several
times a week to evaluate the impact on the economy of a change in
the federal budget.
Occasionally clients ask for a specific
econometric model, but usually the choice of methodology is left
to CBO. Most clients are not aware of how sensitive the results
can be to the model chosen. For example, one well-known econometric model says a $10 billion annual sustained increase in
government purchases causes a decrease in prices lasting for one
and one-half years under current conditions; another says that
the same policy action causes a 0.3 percentage point increase in
the rate of inflation during the same interval.
While continually reminding users of the uncertainty of policy impact estimates, CBO also strives to make sense out of the diverse estimates.
This diversity of results is the basic reason for the
multipliers project.
Not only does CBO need a uniform set of
procedures for measuring policy impacts, but it ought to understand why models now widely used on Capitol Hill differ so much
in their policy implications.
Furthermore, CBO is frequently
called on to deal with quite specialized fiscal instruments, such
as public service employment and countercyclical revenue sharing,
that are not incorporated in most models. It is highly useful to
have a procedure that enables CBO to standardize the treatment of
the rate of fiscal displacement in public service employment, the
average salary paid to public employees, and other matters
relevant to these instruments.
The multipliers project consists of (a) systematic comparison of econometric model results for step changes in fiscal
policies, and (b) selection of a uniform set of procedures for
calculating policy impacts.
The systematic comparison involves
factoring an overall Gross National Product (GNP) multiplier into
a number of key components—for example, the ratio of investment
change to GNP change or the ratio of consumption change to a
change in disposable income.
(The relation of overall multipliers to these key ratios is shown in equation (8) on page
12).
With the aid of this factoring, differences in policy
multipliers among models can be traced back to differences in one
or more of these key ratios.




The selection of a uniform set of procedures begins with
choosing a value (or, more precisely, a set of quarterly values)
of each of these key ratios on the basis of reasonableness, other
empirical studies, and when necessary, simple averaging across
models. The values of the key ratios determine the size of the
overall GNP multipliers.
To go beyond current-dollar GNP to
output price effects, employment impacts, etc., CBO uses a number
of simple relationships, including Okun's law and a two-equation,
wage-price model.
Most of the remainder of this paper describes the first
step in the multipliers project, the factoring of GNP multipliers
into their major components and comparing these components across
models. The final section discusses briefly the other relationships that are used in addition to the GNP multipliers in
measuring policy impacts.
The model simulation results that have been used as the
starting point of this analysis depend on initial conditions.
They depend, for example, on whether interest rate levels
are high or low and whether there is a lot of excess capacity
in the economy or not. The multipliers presented in this paper
refer to the conditions of the U.S. economy as of early 1977.
The analysis needs to be redone whenever there is a substantial
change in initial conditions. CBO's tentative plan is to redo it
once a year.




CHAPTER II.

FACTORING FISCAL POLICY MULTIPLIERS

A simple income-expenditure model is the starting point
for factoring GNP multipliers into key components. This chapter
presents the simple model; the following chapter presents a
number of extensions.
The basic model, which is shown on the following page,
consists of an identity expressing GNP identity as the sum of
five components and six additional equations relating changes in
the components of GNP to their determinants. The parameter
estimates for the income-expenditure model are derived from
simulating step changes in fiscal policy in full-scale econometric models. While the basic multiplier model itself is simple
in structure, each of its coefficients summarizes a wide range
of price and wealth responses as well as income-expenditure
relationships incorporated in the full-scale models.
For example, one of the coefficients in the simple model
(a2) is the ratio of a change in fixed investment to a change
in GNP.
The value of this ratio in a particular model is not
simply a naive accelerator coefficient but rather reflects the
net outcome of all the investment determinants in that model,
including accelerator-type forces, cost of capital components,
and a range of other influences (all as of early 1977).
The
ratio could
be less than zero in a model with very strong
"crowding-out" forces, or it could be greater than zero in a
model with strong accelerator-type forces.
The same is true
of the other coefficients in the simple income-expenditure
model; they too summarize net outcomes of complex influences
represented in the actual models CBO has used.
The coefficients of the basic model are thus reduced-form
rather than structural relationships.
While they are reducedform relationships, they are, however, much closer to observable
economic magnitudes—for example, the share of personal income in
GNP—than are the fiscal policy multipliers of which they are
components.
It is scarcely possible to develop any a^ priori
judgments to which to compare policy multipliers, but it is
possible to form judgments about some of the ratios investigated
in this study.

94-329 O - 77 - 3




BASIC MULTIPLIERS MODEL




(1)

AGNP$(t) = AC$(t) + AFI$(t) + AGG$(t) + AGE$(t) + AX$(t)

(2)

AC$(t) = a u ( A I N C $ ( t ) + A T R $ ( t ) - ATP$(t))

(3)

AINC$(t) = b l t AGNP$(t) + c u A G E $ ( t )

(4)

ATR$(t) = ~ b 2 t A G N P $ ( t ) - c 2 t AGE$(t) + ATRO$(t)

(5)

ATP$(t) = b 3 t A I N C $ ( t ) - c 3 t AGE$(t) + ATPO$(t)

(6)

AFI$(t) = a 2t [AGNP$(t) - AGE$(t)]

(7)

AX$(t) =a 3 t AGNP$(t) +AXO$(t)
(all variables are in current dollars)

where
GNP$

=

Gross National Product

C$

=

Consumption

Fl$

=

Fixed investment (business and residential)

GG$

=

Federal government purchases except public employment

GE$

=

Public employment spending net of displacement, federal and
state and local (displaced funds used for tax reduction or general
state and local spending enter as TP$ or GG$)

X$

=

Rest of GNP$: inventory investment, net exports, state and local
spending other than public service employment

INC$

=

Wages and salaries and other labor income and nonwage income

TR$

=

Federal transfer payments

TP$

=

Federal personal tax revenues (including employee payroll taxes)

TRO$

=

Intercept, transfer payments

TP0$

-

Intercept, personal tax revenues

XO$

=

Intercept, other spending

t

=

Time, in quarters

Simulations of fiscal policy in full-scale models are used
to derive coefficients for the simple model.
Each econometric
model simulation yields a specific set of values for the key
components that together capture the total change in GNP implied
by that model.
The GNP multiplier is an algebraic function of
the coefficients of the basic model, called "key components11 of
the multiplier.
As the tables below show, wide disparities sometimes
exist between different estimates of the key components.
Frequently, an unusually high or low estimate can be traced
to an unreasonable structural specification in the underlying
model. Values of key components chosen for this policy simulation work were based on what CBO felt were the more reliable
model estimates. In cases where CBO had little insight into the
reliability of values derived from the econometric models,
simple averaging across models was necessary.
The key components depend on the period of time over
which relationships between components of GNP and their determinants are measured.
The (approximate) marginal propensity to
consume, aj_, for example, can refer to consumption changes
divided by income changes during the first quarter of a sustained change in fiscal policy, during the second quarter, or
during a later quarter. CBO's procedure has been to derive
quarterly values for each of the coefficients for the first
through the tenth quarter. In effect, the model is 10 different
models, which together measure the dynamic adjustment path
accompanying a policy change.
KEY COMPONENTS OF FISCAL POLICY MULTIPLIERS
Equation 1, the GNP identity, expresses changes in GNP
as the sum of changes in consumption, fixed investment, government spending on goods and services other than public employment
programs, government spending on public employment programs, and
"other GNP" (namely, inventory investment, net exports, and state
and local spending other than federally financed public service
employment).
The next block of four equations relate to consumption
and its determinants.
The first, (2) expresses changes in
consumption as a fraction of changes in disposable income.
Changes in disposable income include changes in wages and salaries, plus other labor income plus nonwage income, changes in




personal transfer receipts minus changes in personal tax payments. Values of the parameter of this equation, a^, are shown
quarter by quarter for five econometric models—Data Resources,
Inc., (DRI), Wharton, Chase, MIT-Penn (MPS), and Fair-—and for
the multipliers model in Table 1. jL/ The latter values can be
adjusted if the policy change is targeted on population groups
whose (approximate) marginal propensities to spend are significantly different from the average values reported here.

TABLE 1.

QUARTERLY VALUES OF ax

Mo d e 1 s
Quarter

1

2

1
2
3
4
5

.41
.63

.26
.26
.28
.30
.39

6
7
8
9
10

.73
.73
.71
.71
.71

1/




.68
.71
.73

3

4

5

.55

.25
.37

.68
.80
.95
.97

Basic Multipliers
Model

.56
.65
.68

.44
.51
.58

1.02

.35
.45
.51
.55
.60

.49

.67

.69
.83
.75
.67

.69
.70
.70
.70

.62
.65
.70
.72
.76

.96
.97
.98
.95
.90

.62
.67
.70
.71
.71

.47

Parameter values from econometric models reported in Tables
1, 2, 4, and 5 were derived by simulating a change in
federal government purchases, holding the path of unborrowed
reserves constant.
For a number of models, results vary
significantly with the monetary variable selected as exogenous.
Selecting unborrowed reserves implies that both
interest rates and the money supply rise moderately in
response to an expansionary fiscal move.

The quarterly values of a^ are considerably lower than the
average ratio of total consumption to total disposable personal
income*
This difference arises from the existence of wealthinduced consumption flows that are relatively insensitive to
changes in disposable income and, therefore, not measured by
a^*
The ratio of total consumption, which includes wealthinduced consumption, to disposable income averaged over 0.9 for
both the past five- and ten-year periods*
The next equation in the consumption block,(3), relates
changes in wages and salaries and other labor income and nonwage
income to changes in GNP and changes in public service employment
outlays*
The first parameter of this equation, b^, is estimated on the basis of econometric model results that are shown in
Table 2.

TABLE 2.

QUARTERLY VALUES OF

Mod

els

Basic Multipliers
Model

Quarter

1

2

3

4

5

1
2
3

.78
.77
.80
.82
.83

.33
.41
.45
.50
.54

.27
.45
.55
.57
.61

.40
.59
.62
.65
.67

.28
.39
.44
.46
.49

.42
.54
.60
.63
.66

.84
.85
.87
.88
.89

.54
.48
.46
.55
.71

.68
.71

.71
.73

.74
.77
.79

.74

.55
.56
.59
.61
.65

.69
.71
.73
.75
.78

4
5
6

7
8
9
10




.76
.76

The share of wages and salaries, other labor income, and
nonwage income in GNP has averaged about .75 over the past fiveand ten-year periods. Quarterly values of bj used in the multipliers model are initially lower than the average share due
to the disproportionate rise in profits immediately following a
policy-induced income change. In later quarters, nonprofit
income shares rise above their average value.
This occurs
because depreciation, which is subtracted from GNP to obtain
national income levels, is very slow to change in response to
changes in GNP.
Nonprofit income shares will return to their
average value after the depreciation adjustment is complete.
The second parameter in the income equation, c j , reflects
the difference between the fraction of public employment programs
going into wage i n c o m (more precisely, wages and salaries plus
other labor income plu* Honwage income), and the fraction of
other components of GNP that goes into wage income. Its value is
not estimated from econometric models but rather is estimated on
the basis of experience under public employment programs and
legislative provisions of such programs.
The next equation, (4), in the consumption block relates
changes in transfer payments to changes in GNP and outlays on
public employment programs. Estimates of the first parameter in
this equation, b£, were derived from econometric model results
and empirical studies of transfer payments. The second parameter
in this equation, C2f represents the difference between the
transfer reduction rate of public employment programs and that of
other changes in GNP. Like c^, it is estimated on the basis of
experience under public service employment and program design
considerations.
A public employment program targeted at youth,
for example, would have a lower value of C£ than one targeted
at adults. The final term in the equation, ATRO$, measures
policy-induced changes in transfer payments.
The final equation in the consumption block, (5), relates
changes in personal tax payments to changes in GNP and outlays on
public employment programs.
Its specification is analogous to
that discussed above for transfer payments and its parameters
were estimated in an identical fashion. Table 3 lists the values
of equation (4) and (5) parameters used in the basic multipliers
model.




8

TABLE 3.

ESTIMATED VALUES OF b 2 , b 3 , c 2 , a/ and c 3 a./ USED IN
THE BASIC MULTIPLIERS MODEL

P a r a m e t e r s
Quarter

b2

b3

1
2 - 10

.03
.07

.167
.167

a./

c2

c3

.19
.19

.05
.05

c 2 and c 3 vary according to program design. Values reported in Table 3 are used for public employment programs
that are directed at long-term unemployed adults.

Equation (6) expresses changes in fixed investment (business
and residential) as a fraction of changes in GNP other than
government employment spending. Quarterly values of this ratio,
a 2 , are shown for five econometric models and the basic multipliers model in Table 4. Historically, the share of fixed
investment in GNP has averaged 0.14 in the past five- and tenyear periods.
Quarterly values of a 2 may be expected to approach the average shared after accelerator influences, which
raise the value of a 2 above the average share, cease operating.




TABLE 4.

QUARTERLY VALUES OF a 2

M o d

3

4

5

.02

.07

.03
.04

.03
.05
.07

.04
.10
.14

.05
.06

.12
.18
.21
.22

.09
.08

.16
.18

.08
.14
.17
.21
.22

.06
.11
.17
.19
.20

.06
.05
.05
.03
.03

.23
.23
.22
.16
.06

.06
.04
.03
.01
.01

.18
.18
.17
.16
.16

.25
.24
.24
.24
.24

.20
.19

1

1
2
3

4
5
6
7
10

Basic Multipliers
Model

2

Quarter

8
9

els

.18
.16
.14

The final equation, (7), in the basic multipliers model
relates changes in the remaining GNP components—inventory
investment, net exports, and state and local spending other than
federally financed public service employment—to changes in GNP.
The intercept-change term reflects exogenous changes in net
exports and state and local spending.
Table 5 lists quarterly
values of the parameter of this equation, 33, for five econometric models and the basic multipliers model*
The models yield different values for key parameters
when the policy simulated is a change in federal government
purchases rather than when the policy is a change in personal tax
receipts.
The differences are significant,. however, only
with respect to a3«
This is due to the more rapid change
in import spending that occurs following an exogenous change in
personal taxes.
The estimated values of a 3 used in the multipliers model differ, therefore, depending on whether the policy
being considered is similar to a tax change or similar to a
purchase change.
Table 5 reports only values of a3 based on a




10

purchase change for the five models, but presents both sets of
values for the multipliers model.
The share of the remaining GNP components in GNP has
averaged 0.144 over the past five years and 0.138 over the
past ten years, These ratios are significantly higher than
quarterly values of a3 reported in Table 5, principally because
of the relative insensitivity of state and local spending to
changes in GNP.
The marginal response of these components to
changes in GNP, in other words, has been much smaller than the
average response.

TABLE 5.

QUARTERLY VALUES OF a 3 a./

M o d e l s
Quarter

1
2
3

-.07

.09
.11
.10
.09

4
5
6
7

.08
.08
.08
.09
.09

8
9
10

a/

1

2

4

3

.00
.01
.03
.02
.01

-.03

-.04

.00

.13
.17
.14
.03

-.01
-.03
-.04
-.05

.08
.07
.06
.06
.06

-.16
-.08
-.05
-.02
-.01

.03
.07
.08
.09

5

-.23
-.02
-.02
-.01

Basic Multipliers Model
Purchase
Tax
Change
Change

-.08

-.07

.01

.01
.05
.05
.06

.00
.04
.04
.04

-.06
-.03
-.05
-.05
-.05

.07
.08
.07
.06
.05

.05
.05
.05
.03
.02

Values reported for models 1 through 5 are based on simulations of a change in federal purchases.




11

THE FISCAL MULTIPLIER FORMULA
The seven equations listed in the basic multipliers model on
page 4 can be combined through simple algebra to yield the
following multiplier expression for standard changes in fiscal
policy:

JAGG$(t)

x

(8)

AGNP$(t) =

AX0$(t) + a l t [ATRO$(t)-ATPO$(t)]

U ^ c ^ (1b

)

" °2t + C 3t } " a 2t l A G B $ ( t ) }
The first expression on the right-hand side of the equation
is the multiplier for changes in government purchases other than
public employment programs. It depends on six of the parameters
of the model, namely:




a^,

the ratio of a change in consumption to a change
in disposable income

a£,

the ratio of a change in investment
in GNP

a3,

the ratio of a change in "other GNP" to a change
in GNP

bi»

the fraction of a change in GNP going into wages
and salaries and other labor income and nonwage
income

b2,

the fraction of a change in GNP serving to reduce
transfer payments

b3,

the fraction of a change in wages and salaries
and other labor income and nonwage income going
into personal tax payments

12

to a change

The government spending multiplier also applies to AXO$,
changes in the intercept term of "other GNP;11 that is, to
exogenous changes in exports, inventory investment, or state and
local spending*
The multiplier for shifts in personal taxes and transfers is
equal to a^ times the GNP multiplier, a common result in incomeexpenditure models.
The multiplier for nondisplaced changes in government
employment program spending is a bit more complex*
It is equal
to the basic government spending multiplier times
l+a l t (c l t (l-b 3 t ) - c 2 t+c 3 t ) -a 2 t
If cj « c.2 = C3 = 0, then the expression for the government
employment multiplier is slightly less than that for the government purchases multiplier due to the absence of any direct
inducement to fixed investment from public employment spending.
The two multipliers differ further to the extent that (a) a
higher fraction of spending on government employment (higher by
C].) goes into compensation than is the case for changes in the
rest of GNP; (b) a higher fraction of spending on government
employment (higher by c 2 ) is offset by a reduction in transfer
payments than is the case for other components of GNP; and (c) a
lower marginal personal tax rate (lower by C3) is applicable to
government employment income than is the case for the rest of
GNP* These deviations can have offsetting effects on the public
employment multiplier*
A high fraction of spending devoted to
compensation, for example, could increase it while targeting at
the long-term unemployed could increase the transfer-reduction
rate and thereby reduce the size of the multiplier*
Table 6 presents the GNP multipliers
basic multipliers model*




13

derived

from

the

TABLE 6.

CHANGE IN GNP RESULTING FROM A PERMANENT INCREMENT IN
POLICY INSTRUMENT: IN BILLIONS OF CURRENT DOLLARS FOR
EACH BILLION DOLLAR PERMANENT INCREMENT

Quarter

Federal Government
Purchases of Goods

1
2
3

1.10
1.42
1.79

1.15
1.34
1.57

-.40
-.63
-1.09

4
5
6

2.00
2.22
2.41

1.66
1.78
1.90

-1.07
-1.27
-1.43

7
8
9

2.62
2.71
2.66

2.04
2.12
2.01

-1.64
-1.77
-1.74

10
11
12

2.53
2.44
2.44

1.96
1.89
1.89

-1.64
-1.57
-1.57




14

Public Service
Federal Taxes or
Employment
(With Opposite Sign)
Transfers

CHAPTER III.

SOME EXTENSIONS OF THE MULTIPLIERS MODEL

The preceding chapter covered standard fiscal policies.
The basic model presented there is in fact the one CBO has
used for nearly all its policy simulation work.
This chapter
adds two policy instruments to the basic model—monetary policy
and corporate tax rates.
MONETARY POLICY
Parameter estimates used in the basic model are based
on policy simulations in which the Federal Reserve Board holds
the path of unborrowed reserves constant. The monetary response
to an expansionary fiscal move, therefore, cannot include any
change in unborrowed reserves, but it can include an increase in
the money supply and some (at least temporary) increase in
interest rates.
Econometric models differ considerably in their specification of the monetary sector. To highlight these differences,
Table 7 presents changes in three-month Treasury bill rates and
in GNP occurring in five econometric models as a result of a step
increase in unborrowed reserves.
An increase in unborrowed reserves also expands the money
supply but (at least temporarily) reduces interest rates.
Its
effects are, therefore, not a simple multiple of fiscal policy
effects, and additional parameters are needed to capture them.
This is accomplished by adding an unborrowed reserve term to
equations (2), (6), and (7), changing them to:
(2)'

AC$(t) = a lt (AINC$(t) + ATR$(t) - ATP$(t))
+d lt ARU$(t)
AFI$(t) = a 2t AGNP$(t) + d 2t ARU$(t)

(7)'
where

AX$(t) = a 3t AGNP$(t) + AXO$(t) + d 3 t ARU$(t).

RU$ = unborrowed reserves.




-

15

TABLE 7:

Quarter

CHANGES IN THREE-MONTH TREASURY BILL RATE AND GNP$ IN
T-l RESULTING FROM A STEP INCREASE IN UNBORROWED
RESERVES a/

Model 1
Rate
GNP

Model 2
Rate
GNP

1
2
3
4
5

-.98
-1.06
-1.08
-1.05
-.96

13.3
19.8
25.5

-.45
-.45
-.44

6
7
8
9
10

-.83
-.73
-.61
-.51
-.45

30.0
33.2
34.8
35.2
34.2

-.42
-.39
-.35
-.33
-.32

a./

3.4 -.60
5.4 -.42

.3
.9
1.9
3.3
,•5.0

6.9
9.4
12.5
13.7
13.0

Model 3
GNP
Rate

Model 4
GNP
Rate

Model 5
GNP
Rate

-.13
-.13
-.12
-.12
-.11

0
2.5
4.8
4.9
5.5

-.6
.5 -1.26
.1
-.8 1.8 -1.24
3.7
-.8 4.2 -.97
6.8
-.8 7.4 -.97 10.0
-.7 11.4 -.83 14.2

-.09
-.08
-.08
-.09
-.10

4.2
4.2
4.3
4.1
3.7

-.7
-.6
-.5
-.5
-.4

15.8
20.9
26.9
33.6
40.9

-.65
-.54
-.33
-.29
-.17

16.4
20.8
24.9
28.2
31.3

All models were simulated for a $1 billion step increase in
unborrowed reserves. Bill rate differences from baseline
are reported in percentage points. GNP differences from
baseline are reported in billions of dollars.

The parameters d^, d£> and d3 measure the direct spending changes that result from a change in unborroved reserves,
holding government spending and transfer and tax rates constant.
In equation (2)', dj represents the ratio of additional consumption spending (above the fiscal policy-derived response to disposable income) to changes in unborroved reserves. This additional
consumption arises from wealth and interest rate effects. Similarly, d£ and d3—the ratio of changes in fixed investment and




16

"other GNP," respectively, to changes in unborrowed reserves—
reflect the effects on capital spending, inventory investment, and
state and local spending of wealth and interest rate changes. 1/

jL/

A simple model may clarify the relation of equations
(2)', (6)', and (7)' to business and household behavior.
Suppose that investment (I) depends on income (Y) and an
interest rate (R),
I • ai + a£ Y - a3 R

a 2 , a$ > 0

that money (M) demanded also depends on income and interest
rates,

M - bxY-b2R

bi» b 2 > 0

and that money supplied depends on unborrowed reserves (RU)
and interest rates.
M

•

Eliminating M and solving for R by combining the second and
third equations gives

•

•

(^)

•

-

Substituting this expression for R into the first equation
gives
I

= a, -i- la. - :

1 Y +

I

=_=

1 RU

Equation (6)' above resembles this equation.
The coefficient of income reflects both accelerator effects and
crowding-out or interest rate effects, while the coefficient
of unborrowed reserves reflects interest rate effects and
the money-supply and money-demand linkages between unborrowed reserves and interest rates.




17

To estimate dj,, d£> and d3 the values of the a's from
fiscal policy simulations are used to deduct from total changes
in C, FI, or X the amounts due to income or GNP changes.
Substituting (2)', (6)', and (7)' into the basic multipliers
model yields the following unborrowed reserve GNP multiplier:
[ ( d j + d ^ ) ARU$ (t) ]
(9)

AGNP$(t) =

Cl-(a l t (b l t (l.b 3 t )-b 2 t ) + a 2 t + a 3 t )]

[Fiscal
+

Multiplier]

The denominator on the right-hand side of equation (9) is the
same as the denominator of a simple government purchases multiplier. The numerator represents the total direct GNP increment
originating from a change in unborrowed reserves.
Estimates of d^, d£> and d$ vary significantly across
econometric models. Differences exist not only in the level of
each parameter (d£ in the tenth quarter is 13.4 in one model
and 0.32 in another) but also in the relative size of d^, d£»
and d3 (in one model d£ is greatest and d^ is smallest whereas in another the reverse occurs). Not having any prior information on the size of these parameters, CBO used a simple averaging
procedure to estimate d]_f d2> and d^ for the multipliers model.
Table 8 presents these estimates as well as the range of each
parameter provided by the five econometric models.
Estimates of b^ also differed between an unborrowed reserve simulation and a fiscal policy simulation. This difference arises from the contrasting interest rate paths in the two
simulations, a contrast which affects corporate profits and
personal interest income. The parameter values for b^ used in
simulating monetary policy changes are presented in Table 8, and
Table 9 presents the resulting unborrowed reserve multiplier
values•
Unborrowed reserve multiplier values grow from 1.0 in the
initial quarter to over 25 by the end of three years, as shown in
Table 9. Even 25, however, is only % about half of the average
ratio of GNP to unborrowed reserves. GNP in recent quarters has
been 5 to 6 times as large as the narrowly defined money supply,
which in turn has been about 9 times as large as unborrowed
reserves. The multiplier estimates in Table 9 imply that a
step increase in unborrowed reserves above a baseline path lowers
the velocity of money relative to its baseline path.




18

TABLE 8.

QUARTERLY VALUES OF d

d

and b

d

i

Rangei Provided by
Econometric
Models
Low High

d

2

Range Providedl by
Econometric
Models
Low High

Multipliers
Model

b

3

Range Provided by
Econometric
Models
Low High

Multipliers
Model

i

Range Provided by
Econometric
Models
Low High

Quarter/
Parameter

Multipliers
Model

1
2
3

.17
.82
.54

.03
1.06
.28

.74
2,31
3.38

.33
1.11
1.95

.00
.87
1.49

1.18
2.84
4.40

.00
.15
.55

-.33
-.84
-.43

1.41
.80
1.31

.36
.51
.53

-.96
.00
.05

.68
.70
.70

4
5
6

1.05
1.30
1.70

.55
.76
1.01

4.48
5.97
6.76

2.73
3.42
4.18

1.43
1.15
1.15

6.00
7.50
9.23

.87
1.20
1.26

-.26
-.24
-.33

2.85
4.02
4.90

.60
.62
.68

.15
.24
.26

.72
.74
.74

7
8
9

2.05
2.38
2.64

1.05
1.04
1.20

7.74
8.98
9.67

4.83
5.56
6.01

.86
.62
.37

10.54
12.11
12.95

1.53
1.79
2.17

-.12
.03
.07

5.47
5.83
6.46

.70
.70
.71

.26
.26
.28

.76
.77
.78

10
11
12

2.85
3.00
3.00

1.25
—

10.48
—

6.43
6.60
6.60

.32
—

13.42
—

2.26
2.45
2.45

.04
—

6.26
—

.73
.73
.73

.29
—

.78
—




Multipliers
Model

TABLE 9.

CHANGES IN GNP RESULTING FROM A PERMANENT INCREMENT IN UNBOBROWED RESERVES: IN BILLIONS OF CURRENT
DOLLARS FOR EACH BILLION DOLLAR PERMANENT INCREMENT

Quarter

Multiplier

1
2
3
4
5
6

1.00
2.86
5.12
8.77
12.10
16.17

7
8
9
10
11
12

20.29
23.80
24.83
24.88
26.15
26.15

CORPORATE TAX CHANGES
The extensions needed to measure corporate tax change
effects on GNP are procedurally similar to those discussed
above for monetary policy.
The basic multipliers model does
not include dividends, corporate cash flow, or the corporate
tax rate as separate determinants of consumption and investment spending and, therefore, cannot account for the effect of
changes in corporate taxes on spending. The effect of corporate
taxes can be incorporated into the basic model by changing
equations (2), (3), (5), and (6) to:
(2)" AC$(t)

a lt (AINC$(t) + ATR$(t) - ATP$(t)) + dltA
RU$(t) + g lt ABUSTAX$(t)

(3)" AlNC$(t)

bltAGNP$(t) + cltAGE$(t)-g2tABUSTAX$(t)

(5)" ATP$(t)

b3tAINC$(t) - c3tAGE$(t) + ATPO$(t)
- c 4t ABUSTAX$(t)

(6)" AFI(t)

a 2t AGNP$(t) + d 2
- g 3t ABUSTAX$(t).




20

In equation (2)", gi t is the proportion of the business
tax change going into consumption.
Equations (3)", (5)", and
(6)" allow for departures from the standard fiscal-policyinduced relationships explaining personal income, personal
taxes, and fixed investment.
Parameter values from econometric models were reasonably similar for simulations in which the corporate tax equation
intercept was changed. The models varied dramatically, however,
in their estimates for a change in corporate tax rate. (A rate
change that provides a $10 billion change in corporate taxes
leads to a $54 billion addition to GNP in one model and a $5.8
billion reduction in GNP in another.) The econometric models and
empirical tax studies were, therefore, used to derive g^, g£f
g3, and C4 only for a lump-sum change in corporate taxes.
Results are reported in Table 10.
Estimating parameters for
changes in corporate tax rates will be undertaken at a later date
after CBO studies the differences in the econometric models'
simulations more carefully.

TABLE

10.

CORPORATE TAX CUT PARAMETERS
MULTIPLIERS MODEL

USED IN THE BASIC

P a r a m e t e r s
Quarter

g^

g2

1
2
3
4
5

00
04
03
02
02

6
7
8
9
10

02
01
02
03
03




21

g3

C4

.02
.05
.10
.13
.14

.00
.02
.03
.08
.09

.00
.02
.02
.03
.04

.14
.14
.14
.14
.08

.13
.15

.04
.04
.05
.05
.05

.17
.21

.24

Substituting these equations into the basic multipliers
model generates the following multiplier expression for changes
in corporate taxes:

GNP$(t)

=

" [g it +a it (g 2t (1 " b 3t ) " C 4t )+g 3t ]
_
,
,. ~ , r-r r7- TT
r

The denominator of this equation is the denominator of the
simple government purchases multiplier* The numerator represents
the direct spending induced by a change in corporate taxes. This
multiplier is useful in analyzing fiscal policies that directly
change corporate cash flow (for example, employment tax credits,
and training programs implemented in the private sector). Table
11 presents the multiplier values.

TABLE 11.




CHANGES IN GNP RESULTING FROM A PERMANENT INCREMENT
IN CORPORATE TAX PAYMENTS:
IN BILLIONS OF CURRENT
DOLLARS FOR EACH BILLION DOLLAR PERMANENT INCREMENT

Quarter

Multiplier

1
2
3
4
5
6

-.01
-.09
-.16
-.27
-.35
-.48

7
8
9
10
11
12

-.56
-.62
-.76
-.70
-.65
-.65

22

CHAPTER IV.

PRICE CHANGES VERSUS REAL OUTPUT CHANGES

Although CBO uses a two-equation, wage-price model to divide
changes in nominal GNP between prices and real output, it is easy
and interesting to compare a number of models with respect to
their output and price effects.
The differences among models
arise in large part from differences in labor market specifications and productivity behavior.
Table 12 shows the division of two key components, a^ (the
ratio of changes in consumption to changes in GNP) and a2 (the
ratio of changes in fixed investment to changes in GNP) into
quantity and price effects implied by each econometric model.
The division is based on the formula

where q is a quantity (or constant-dollar value) and p is a price
index (or deflator). The first term on the right-hand side shows
the contributions of quantity change to the total dollar change,
while the second shows the contribution of price change.
To
factor a ratio such as a^ into quantity and price effects, each
term in the formula is divided by the dollar change in the
denominator of the ratio; thus, for factoring a^, q in the
formula refers to constant-dollar consumption, p to the consumption deflator, and each term is divided by the current-dollar
change in disposable income.




23

TABLE 12.

AND a 2 INTO REAL
DIVISION OF GOVERNMENT PURCHASES GNP$ MULTIPLIER,
AND NOMINAL PRICE EFFECTS FOR SELECTED QUARTERS FOR FOUR ECONOMETRIC MODELS

AGNP$(t)/AGG$(t)
Model 2

Model 1

Model 4

Model 3

Quarter

Real

Price

Multiplier

Real

Price

Multiplier

Real

Price

Multiplier

Real

Price

Multiplier

1
4
7
10

1.2
2.1
1.9
1.6

0.0
0.2
0.4
0.8

1.2
2.3
2.4
2.4

0.9
1.4
1.1
0.3

0.0
0.0
1.4
1.5

1.0
1.4
2.5
1.8

1.1
1.5
1.3
1.0

0.1
0.2
0.4
0.6

1.2
1.6
1.7
1.6

1.0
1.6
1.9
1.7

0.1
0.5
1.1
1.9

1.1
2.1
3.0
3.6

AC$(t)/ADisposable Income
Model 2

Model 1
to




Quarter

Real

Price

1
4
7
10

.42
.66
.58
.45

-.02
.05
.15
.26

a

l

.41
.71
.73
.71

Real

Price

.24
.32
-.02
-.18

.02
-.02
.71
.85

Model 4

Model 3
a

l
.26
.30
.69
.67

Real
.50
.60
.47
.29

Price

a

.05
.05
.22
.42

i
.55
.65
.69
.70

Real
.17
.21
.21
.16

Price

a

.08
,30
.44
.60

l
.25
.51
.65
.'76

AFI$(t)/AGNP$(t)
Model 1
Quarter
1
4
7
10

NOTE:

Real

Price

.01
.04
.02
-.03

.00
.01
.03
.05

Model 2
a

2

.02
.05
.05
.03

Real
.08
.21
.10
-.11

Price
.00
.00
.14
.18

Model 4

Model 3
a

2

.07
.21
.23
.06

Real

Price

.02
.07
.01
-.06

.00
.02
.03
.06

a

2

.03
.09
.04
-.01

Real
.05
.17
.16
.12

Price
-.02
-.01
.02
.04

a

2

.04
.16
.18
.16

R e a l a n d nominal d o not necessarily s u m to actual p a r a m e t e r v a l u e d u e t o r o u n d i n g
e r r o r s . Both a a n d a a r e estimated from a government p u r c h a s e s p o l i c y simulation.

CHAPTER V.

OTHER RELATIONSHIPS USED IN MEASURING POLICY IMPACTS

The multipliers model described above provides nominal
GNP changes resulting from changes in fiscal and monetary
policies. Additional relationships are used to measure the
impact of policy changes on real GNP, prices, employment, and
other economic variables of interest.
While this paper is
concerned primarily with nominal GNP multipliers, a brief description of the other relationships used by CBO may be helpful.
Figure 1 presents a flow diagram of the relationships
used to translate a change in economic policy into a change
in nominal GNP and other economic variables.
The first step
is the conversion of policy changes into nominal GNP changes,
using the multipliers described in this paper.
Next, employment and unemployment changes resulting from a
policy change are derived from an Okun's law type of relationship
between unemployment and the real GNP gap, lagged one quarter.
If a policy has a direct impact on employment beyond that implied
by Okun's law, a procedure is used (described in the next paragraph) that accounts for this differential.
A two-equation,
wage-price jL/ model and a CPI-GNP deflator relationship are then
used to derive a GNP deflator consistent with the unemployment
rate.
The deflator, together with the level of nominal GNP,
determines real GNP.
The new real GNP gap determines the next
period's unemployment.
Direct employment programs can (but do not necessarily)
create more jobs per dollar spent than conventional fiscal
policy changes.
The reasons are twofold: (1) direct employment programs may entail less "slippage" in restoring productivity and profits and increasing the average hours of existing
jobholders; and (2) direct employment programs may pay a relatively low average wage. The first step in CBO's procedure

1/

See "A Simplified Wage-Price Model," available from the
Fiscal Analysis Division, Congressional Budget Office
(September 1975).




25

Figure 1.

MEASURING POLICY IMPACTS




EXOGENOUS AND
OTHER PREDETERMINED
VARIABLES
Fiscal and
Monetary
Policy

Potential
Real GNP

Lagged
Real GNP

ENDOGENOUS VARIABLES

(multipliers model)

-•(

Nominal GNP

(special
employment
effects)

Unemployment
Rate
|(Okun's>
law)

Employment, \
Labor Force J

Wage Rate
(lag)
/
I

Food and
Fuel Prices

(wage-price
^ model)

Consumer \
A
Price Index
j ^

Federal
Pay Increases
GNP Deflator

Real GNP

7

(lag)

26

for estimating the job impact of a direct employment program
reflecting these special features is to estimate the nondisplaced
outlays quarter by quarter, and divide these outlays by an
estimate of average cost per job. This provides an estimate of
the direct jobs created by a public employment program.
The next step is to calculate an estimate of the indirect
unemployment and employment impact of the policy using GNP
multipliers and Okun's law. The indirect impact arises from two
sources:
additional spending induced by- the nondisplaced
outlays, and the use of displaced funds for tax reduction and/or
increased purchases. The/"indirect" GNP multiplier for the first
source, nondisplaced outlays, is equivalent to the overall public
employment multiplier, dealt with explicitly in this paper, less
one.
The GNP multiplier for displaced outlays is a weighted
combination of the government purchases multiplier and the
personal tax multiplier. The weights CBO used are based on the
views of experts about how state and local governments use
general revenue sharing funds. The overall multiplier of a
direct employment program is thus a combination of the multipliers described in this paper.
The final step in calculating overall job impacts is to
add the direct effects from step one to the indirect effects
from step two.
As the example of direct employment programs makes clear, it
is possible to use the multipliers framework to introduce explicitly a wide range of special assumptions about fiscal policy
changes, including assumptions about the timing of outlays,
fiscal substitution, average cost per job, proportions of grantsin-aid going to tax relief, and others.
Typically it is much
more difficult to incorporate many of these assumptions in
large-scale econometric models.
The multipliers model thus has
the advantage of introducing clear links between program details
and economic effects.

27

U.S. GOVERNMENT PRINTING OFFICE : 1977 O - 94-329