AK E€0fi€METEREC ENALYSES 6F SEEMS
MAJGR EXGGENBUS RE?EE§§EN§NTS
i}? NMEGRAL GEEK}?

“was Eon flu Degree of pit. D.
MICEEEGAN STATE UNEYERSKTY
Jcim Murwyn Mas-en, Jr:

2976:

LIBRARY

THFH‘IS

Michigan Sta to

University

 

This is to certify that the

thesis entitled

An Econometric Analysis of Some Major
Exogenous Determinants of National Output

presented by

John Murwyn Mason, Jr.

has been accepted towards fulfillment
of the requirements for

:) . ~
LLL degree in _g C 5'5 1’ 5’331 I 64'

Date / 1/ 2 1/ 70

0-169

 

 

ABSTRACT

AN ECONOMETRIC ANALYSIS OF SOME MAJOR EXOGENOUS
DETERMINANTS OF NATIONAL OUTPUT

BY

John Murwyn Mason, Jr.

In a stylized sense, there exist two theories of
national output determination. They are the Quantity Theory
of Money and the Income-Expenditure Theory. Each theory
places primary emphasis on different items as the major driv-
ing force behind changes in aggregate economic activity.

In the Quantity Theory, emphasis is placed upon the stock

of money, while in the Income-Expenditure approach, emphasis
is placed upon autonomous expenditures. Although it is not
necessary that the two theories be mutually exclusive, a
considerable amount of empirical testing has been completed
in recent years attempting to compare the relative stability
of the theoretical relationships implied by the two theories.
The purpose of this dissertation is to study the relation—
ships implied by these two theories within the framework of
a complete macro-econometric model.

A nine-equation macro-econometric model is constructed.
An attempt is made to incorporate recent theoretical devel-

opments into the model. For example, it is assumed that

John Murwyn Mason, Jr.

consumption expenditures are related to permanent disposable
income. Investment expenditures are related not only to an
interest rate variable, but also to an accelerator variable
and the level of aggregate economic activity. Investment
expenditures are linked to financial markets by means of the
term structure of interest rates. The short-term rate of
interest is determined by the interaction of the demand for
and supply of money. The SUpply of money is endogenously
determined.

The model shows that government eXpenditures have a
greater initial impact on the level of aggregate activity,
as measured by the level of Gross National Product, than
does the monetary base, the variable assumed to be under the
control of the monetary authorities. The model shows,
however, that the major effects of monetary policy come sev-
eral quarters after the initial change. At the end of one
year, the accumulated effect of a change in the monetary
base is greater than the accumulated effect of a change in
government expenditures. This must be interpreted cautious—
ly, however, for the average change in government eXpendi-
tures exceeds the average change in the monetary base, in
the time period used in estimation of the model. The model
also shows that whereas the impact of government eXpenditures
is direct, the impact of monetary policy must work its way

through financial markets before its impact is felt in real

John Murwyn Mason, Jr.

markets. The linkages implied by the results of the model
are not close.

The literature contributing to the recent empirical
tests is surveyed and the results obtained by the single-
equation models are evaluated. The reduced-form hypothesis
is restated and regressions are run for the time period
covered by the complete model estimated in this thesis.

An attempt is also made to re-evaluate the results obtained
in earlier studies by correcting standard errors for the

presence of autocorrelation in the residuals.

AN ECONOMETRIC ANALYSIS OF SOME MAJOR EXOGENOUS

DETERMINANTS OF NATIONAL OUTPUT

BY

John Murwyn Mason, Jr.

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1970

LCOpyright by
JOHN MURWYN MASON, JR.
1970

ACKNOWLEDGMENTS

The writer wishes to eXpress his appreciation to
Dr. John R. Moroney, chairman of his thesis committee, for
direction, encouragement, and constructive suggestions
throughout the study. Dr. Moroney's continued interest in
the study and his personal attention to many details con-
tributed greatly to the completion of the study. My thanks
are also expressed to Dr. Byron W. Brown and Dr. Bruce T.
Allen for their assistance as members of the thesis commitee.

A great deal of benefit was derived from my association
with the staff of the Federal Reserve Bank of Cleveland.
I am particularly indebted to Dr. William J. Hocter, who
provided encouragement and an atmosphere conducive to eco-
nomic research and to Dr. Eric C. Williams for assistance
on some facets of the study. I would also like to thank
Miss Alicia Janusczok and Miss Marsha Judy, who typed earlier
drafts of the manuscript and worked very industriously in
order to meet some crucial deadlines.

My greatest debt is to my wife who knows better than
anyone the sacrifices made and the work involved in the com-

pletion of this study.

 

ii

TABLE OF CONTENTS

CHAPTER Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . 1
Simplified Exposition of the Existing

Theories of Income Determination . . . 2
Purpose and Principal Hypothesis of

This Study . . . . . . . . . . . . . . 6
Major Determinants of Aggregate Activity. 7
Plan of the Study . . . . . . . . . . . . 7
II. A REVIEW OF THE LITERATURE . . . . . . . . . . 9
Introduction. . . . . . . . . . . . . . . 9
The Friedman-Meiselman Paper. . . . . . . 12
Major Points of Criticism . . . . . . . . 50
Minor Points of Discussion. . . . . . . . 57
Discussion of the time periods chosen. 37
rDiscussion of the discriminatory power
of the two models . . . . . . . . . 40
Other specifications of the models . . 41
Discussion of a more complete model. . 44
Additional WOrk . . . . . . . . . . . . . 45
Summary . . . . . . . . . . . . . . . . . 51
III. A DISCUSSION OF FURTHER TESTS. . . . . . . . . 52
Introduction. . . . . . . . . . . . . . . 52
Friedman-Meiselman Hypothesis . . . . . . 56
Hester's Developments . . . . . . . . . . 61
A Complete Econometric Model. . . . . . . 62
IV. ADDITIONAL TESTS OF VARIOUS SINGLE-EQUATION
SPECIFICATIONS. . . . . . . . . . . . . . 79
Introduction. . . . . . . . . . . . . . . 79
Tests Concerning the Friedman-Meiselman
Hypothesis . . . . . . . . . . . . . . 79
General problems . . . . . . . . . . . 79
Definitional tests . . . . . . . . . . 85
The narrow definition of the money
suPply. . . . . . . . . . . . . . . 87

iii

TABLE OF CONTENTS--continued

CHAPTER

Periods which include the Second World

war 0 O O O O O O O O O O O

0

Additional single—equation tests--1955—

1965 . . . . . . . . . . .
Autocorrelation . . . . . . .
Simultaneous equation bias. .

Summary. . . . . . . . . . . . .

V. THE COMPLETE MODEL. . . . . . . . . .

Identification . . . . . . . . .
Estimation Procedure . . . . . .
Autocorrelation. . . . . . . . .
Statistical Estimates. . . . . .
Individual Equations . . . . . .
Dynamic ASpects of the Model . .
Summary. . . . . . . . . . . . .

VI. SUMMARY AND RECOMMENDATIONS FOR FURTHER

RESEARCH O O O O O O O O O C O 0

Summary of Work Completed. . . .

Recommendations for Further Study in
Area of Single-Equation Models.

BIBLIOGRAPHY . . . . . . . . . . . . . . . .

APPENDICES . O O O O O O O O O O O O O O O O

A. RESULTS OF THE FRIEDMAN-MEISELMAN TESTS AND THE
CORRECTIONS FOR STANDARD ERROR TERMS

B. SOURCES OF DATA USED. . . . . . . . .

iv

Page

94

97
120
122
125
127
127
129
151
155
156
145
149
151
151
155
161

166

166
180

TABLE

4-1.

4-2.

4-3.

4-4.

4-7.

LIST OF TABLES

Page
Tests Using Broad Definition of Money Supply:
First Set of Friedman-Meiselman Data. . . . . . 89
Tests Using Broad Definition of Money Supply:
Second Set of Friedman-Meiselman Data . . . . . 90
Using the Narrow Definition of the Money Supply 91
Results Shown in Friedman-Meiselman Appendix
Table II-Al o o o o o o o o o o o o o o o o o o 95
Friedman-Meiselman Results During War Years:
Second Set of Data. . . . . . . . . . . . . . . 96

The Effects of Various Exogenous Variables on
Consumption Expenditures: Annual Data 1954-
1965. C O O O O O O O O O O O O O O O O O O O O 98

The Effects of Various Exogenous Variables on
Consumption EXpenditures: Quarterly Data 1955-
III to 1965-IV. . . . . . . . . . . . . . . . . 102

Marginal Multipliers Associated with Hester's
Definitions of Autonomous EXpenditures. . . . . 115

Partial Correlations Between Variables in
Nominal Terms . . . . . . . . . . . . . . . . . 114

Beta Coefficients of Various Measures of Auton—
omous Expenditures and Money Supply in Nominal
Terms 0 O O O O O O O O O O O O O O O O O O O O 116

Dynamic Multipliers for the Time Path of Gross
National Product. . . . . . . . . . . . . . . . 146

The Friedman-Meiselman Results with Corrected
and Uncorrected Standard Error Terms. . . . . . 168

CHAPTER I

INTRODUCTION

In a stylized sense, there exist two important and com-
peting theories of income determination. One theory is the
income expenditure approach that in an extreme form hypothe-
sizes that the equilibrium level of income is determined
solely by the level of autonomous eXpenditures in the econo-
my when the technological and behavioral structure is given.
Any change in autonomous expenditure will result in a change
in aggregate income that is a multiple of the initial change.
By controlling or influencing the autonomous component of
aggregate demand, any level of aggregate income consistent
with the technological constraints and factor endowments of
an economy can be attained.

The other, the Quantity Theory of Money, states that
when the technological and behavioral structure of an economy
is given, aggregate income is determined mainly by the amount
of money that exists in the economy; and any change in this
stock of money will be reflected directly in a change in the
level of money income. The conclusion one can draw from

these extreme characterizations is that vastly different

views of aggregate income determination are implied by the
two theories. In this sense, the two theories are competi-
tive, and it is clearly of the first importance to deter-

mine which is the more apprOpriate, if for no other reason

than their differing suggestions for economic policy.

Simplified Exposition of the Existing Theories
of Income Determination

The Quantity Theory of Money is the older of the two,
at least from the standpoint of presenting a hypothesis in
which a limited number of identifiable variables can be used
to examine the behavior of an economy. Although early
formulations did not receive mathematical eXpression, it is
obvious that they conform very closely with those developed
by Irving Fisher in the United States and Alfred Marshall in
England. The simplest form of Fisher's model of the Quantity
Theory is

(1.1) MXV xT

in
re

where M = nominal money supply
V = incOme velocity of circulation
P = general index of prices
T = number of final transactions that
take place in the economy.
In the crudest form of this theory it was generally
assumed that the velocity of circulation was determined by

institutional factors, such as payment habits, and only

changed slowly over time. For short-run analysis, it could
be taken as constant. The number of transactions that took
place was limited to the amount of goods that the economy
could produce. If the adjustments of wages and prices al-
lowed the economy always to Operate at full employment, the
number of transactions could be taken as a constant, limited
by the full-employment productivity of the economy. Since
prices were assumed to be perfectly flexible, any change in
the stock of money would be reflected in price changes, and
these price changes would be a constant multiple of the

change in the stock of money.

dP _ V _
dM —T_. a constant.

(1.2)

The development by Marshall was similar to that of
Fisher, except Marshall devoted primary attention to peOples'
desires to hold money, rather than the number of times a

given money supply turned over. This resulted in the so-

called "Cambridge equation."

(1.5) M = k PT

where k = -%—-. The value k represents the prOportion of

money which peOple would like to hold in cash balances rela-
tive to the total money income of the society, i.e., PT.

If one makes assumptions that are consistent with the attain-
ment of full employment such as wage and price flexibility

and if peOple desire to hold a fixed proportion of their

incomes in money balances, then Marshall's model of the
Quantity Theory gives exactly the same conclusions as

Fisher's model.

(11’ _i_._._V_=
(1.4) dM - kT T a constant.

Because accumulated experience apparently did not con—
form closely with the above theory, particularly in the
Great Depression, the income eXpenditure theory developed by
John Maynard Keynes was enthusiastically received by most of
the economics profession. Income velocity did not appear to
be constant and changed rapidly over time. In fact, it was
felt that velocity could change so rapidly and in such mag-
nitude that it could offset any changes in the stock of
money. Secondly, wages and prices did not appear to be flex-
ible, at least in the short run, so that automatic adjustment
to a full employment level of output might not be possible.
Thirdly, eXpectations of the future, particularly in a de-
pression, might be quite pessimistic and Upset normal behavior
so that it would be impossible to increase aggregate eXpendi-
tures by private means. Consequently, it was necessary to
look at the various components of these expenditures to de-
termine just what it was that affected them and how corrective
measures could be taken to increase the level of activity in
the economy. The income-eXpenditure theory in its simplest

form is as follows:

(1.5) C = f(Y) = a + bY
(1.6) A =5
(1.7) Y=C+A
(1.8) Y=0L+8'A
where C = consumption eXpenditures
Y = aggregate income (P x T)
A = autonomous expenditures

B'= the Keynesian Multiplier.

In this model, prices are assumed to be inflexible,
consequently, any change in aggregate income represents a
change in the real output of the economy. Changes in autono-
mous expenditures are the sole source of changes in aggregate
income and the increase in income is a constant multiple of

these changes.

dY

(1.9) —dA_ = 6'

l theorists

Beginning with the classic effort of Hicks,
have attempted to consolidate the two models since under
less rigid assumptions they need not be mutually exclusive.
However, much economic discussion, particularly at the ele—

mentary level, is stated in the terms of the two theories

presented above. Also, policy recommendations are often

 

1J. R. Hicks, "Mr. Keynes and the 'Classics': A Sug-
gested Interpretation," Econometrica, V, 1937, pp. 147-159.
Reprinted in Readings in the Theory of Income Distribution
(Homewood, 111.: Richard D. Irwin, Inc., 1951, pp. 461-476.

couched in terms of one theory or the other. Consequently,
it is necessary to discuss the merits of these two simple
theories and examine their strengths and weaknesses in order
to see how more complex models improve our understanding of

the world relative to these simple theories.

Purpose and Principal Hypothesis of This Study

The purpose of this study is to examine the relative
merits of the two theories in a statistical investigation.
The stimulus for the present work has been a paper by Milton
Friedman and David Meiselman prepared for the Commission on
Money and Credit.2 In this paper the two theories were
tested in their simple "crude" forms. The models were chosen
because they reflected the forms presented in elementary
textbooks. A number of subsequent articles also tested crude
forms of the two theories, although other_tests were occa-
sionally proposed but not implemented in a fully Specified
model.

The starting point of this study is that the extreme
versions of the two theories are inappropriate in the light
of current economic knowledge. In the face of recent re-

finements in macroeconomic model construction, these versions

 

2Milton Friedman and David Meiselman, "The Relative Sta—
bility of Monetary Velocity and the Investment Multiplier in
the United States, 1897-1958" in B. Fox and E. Shapiro,
Stabilization Policies (Englewood Cliffs, N. J.: Prentice-
Hall, 1963). PP..165-268.

lead to misleading conclusions and unreliable statistical
results. The theories, themselves, can hold in their crude
forms only if one ignores almost all of the develOpments in
economic science over the last 50 years. Therefore, it is
necessary to develop more complete theories that can test
not only the relative importance of the different explana—
tory variables, but also the way in which these variables

effect other important items within the economic system.

Major Determinants of Aggregate Activity

 

In this investigation the major determinants of aggre-
gate income will be those hypothesized above: the stock of
money and autonomous expenditures. However, the problem of
defining the components of these crucial variables has
emerged as one of the major obstacles in this as well as
several related studies. As will be pointed out later, the
definitions chosen can alter one's conclusions rather

dramatically.

Plan of the Study

In Chapter II the underlying model will be developed in
relation to the published research that has already been
done in this area. In this way one can isolate the crucial
issues under debate and the problems that exist in any test

of the two theories. In Chapter III models are deve10ped

that can be used to test, at various levels of aggregation,
the hypotheses presented above. Chapter IV presents the
additional empirical tests of the single-equation models
while the results of a multi-equation econometric model are
presented in Chapter V. In Chapter VI tentative conclusions

are drawn in light of the work that has been finished so far.

CHAPTER II

A REVIEW OF THE LITERATURE

Introduction

 

This chapter presents a discussion of the recent contro-
versy concerning the two theories of income determination.
The seminal work was the paper prepared by Milton Friedman
and David Meiselman for the Commission on Money and Credit.1
This was soon followed by the articles of Donald Hester,2
Albert Ando and Franco Modigliani,3 and Michael DePrano and
Thomas Mayer.4 There have been other papers that have re-
lated to the continuing discussion in this area, but only two

additional ones will be discussed in this paper.

 

1Milton Friedman and David Meiselman, "The Relative Sta-
bility of Monetary Velocity and the Investment Multiplier in
the United States, 1897-1958," in B. Fox and E. Shapiro,
Stabilization Policies (Englewood<21iffs, New Jersey:'
Prentice-Hall, 1965), pp. 165-268.

2Donald Hester, "Keynes and the Quantity Theory: A Com-
ment on the Friedman-Meiselman CMC Paper," The Review of
Economics and Statistics, XLVI (November, 1964), pp. 564-568.

 

3Albert Ando and Franco Modigliani, "The Relative Stabil-
ity ofoonetary Velocity and the Investment Multiplier,"
The American Economic Review, LV (September, 1965), pp. 695-728.

4Michael DePrano and Thomas Mayer, "Tests of the Relative
Importance of Autonomous EXpenditures.and Money,” The American
Economic Review, LV (September, 1965), pp. 729-752.

10

The empirical tests that have taken place since the
Friedman-Meiselman paper play the main role in the develOp-
ment of this discussion. Although theoretical considerations
are of the utmost importance, the original papers deal mostly
with empirical relationships. Several times Friedman and
Meiselman state that on a purely theoretical level, it is
easy to derive simple income-expenditure models or simple
Quantity Theory models. This assumes that the original sys—
tem of equations is of the form in which only autonomous
expenditures or money determinants are included. Using addi-
tional information, it is possible to reconcile the two
theories and within a more SOphisticated framework there is
little disagreemnt as to the possibility of reaching one con-
sistent theory in terms of a general equilibrium model for a
free-market economy.

At a high level of abstraction there is a rich and full
body of literature going back over many years. However, it
is not the intention of this thesis to present a full discus-
sion of the theoretical aSpects of the two theories. The
problem that Friedman and Meiselman pose is an empirical one.
They are primarily concerned with the short-run relationship
between "investment" eXpenditures and total eXpenditures and
the money stock and total expenditures. It is assumed that
the major area that separates the adherents of the divergent

theories is the stability of these two relationships within

11

a short-run framework.5 Those who accept the income—
eXpenditure approach feel that the more stable relationship
of the two is that between "investment" eXpenditures and
total eXpenditures, while those who profess the quantity-
theory approach feel that the relationship between the money
stock and total expenditures is the more stable.

Thus the recent controversy has been centered on the
statistical comparison of the two theories. A conclusion
to the argument could have important reprecussions, particu-
larly in the area of policy making. Although both relation-
ships appear to be absolutely unstable, the fact that one
is relatively more stable than the other would seem to indi-
cate that the more stable of the two would be a more trust—
worthy instrument to use in carrying out policy action.
Also, policy makers are most often interested in the short-
run behavior of the economy and not its long-run equilibrium.

The thesis will, therefore, be primarily interested in
empirical questions. The literature discussed will be
limited to those contributions that involve statistical test-
ing relevant to the question. The volume of literature on
this topic is not very extensive. The Friedman-Meiselman
paper will be discussed first, then the content of subsequent
articles will be develOped in terms of the relevant areas of

criticism. This seems to be the most efficient method of

 

5Friedman and Meiselman, op. cit., p. 169.

12

presentation because there is a great deal of overlapping
in these articles. The chapter will close with a brief dis-
cussion of other studies that relate to the tOpic under

examination.

The Friedman-Meiselman Paper

Friedman and Meiselman feel that most economists must
make empirical judgments on two important questions.6 The
first concerns the source of change in economic activity
and the effects these changes have on other economic vari-
ables. This question concerns which economic variables are
most truly exogenous and represent the autonomous "shocks"
to an economy. Closely linked to this is the problem of
determining which of these exogenous variables can be con-
trolled, or how closely they can be controlled, so as to be
of use in implementing economic policy.

This problem has been dealt with elsewhere and is not
treated to any great extent in this paper and a fairly con-
sistent effort has been made to keep this type of discussion
on the sidelines. However, the implication is always present
that this question has been answered satisfactorily.

The second empirical judgment concerns the relative
stability of different relationships. Stability, in this

case, is defined as an empirically consistent relationship.

 

BIbid.. pp. 168-169.

15

Given exogenous variables, it is desirable to know which

have the most stable relationship with certain endogenous
variables. The endogenous variables, of course, are variables
that are important either as "final" determinants of economic
activity (such as consumption expenditures) or as "intermediate"
determinants (such as interest rates) that transmit their
effects to other endogenous variables.

Friedman and Meiselman Specifically use the coefficient
of correlation as their measure of the consistency of a rela-
tionship. Their argument reduces to the fact that if two
variables appear to move more closely together, as measured
by their coefficient of correlation, than two others do, the
former relation is a relatively more stable relation than
the latter.

One should be careful to distinguish between relative
stability, as measured by the comparison of two values, and
the absolute stability. One of the major criticisms of the
naive Quantity Theory was that the income velocity of circu-
lation was not constant. At certain times, particularly in
periods of depression, velocity might change rapidly and
offset any efforts of the monetary authorities to correct the
situation. This criticism was in terms of the absolute
stability of income velocity and is accepted by almost all
contemporary economists, including Friedman and Meiselman.

-Due to this variability of the velocity of circulation,

an alternative hypothesis, the income-eXpenditure approach,

14

was developed. It gained SUpport because it proposed rela-
tionships that were supposedly more stable than the relation—
ship between money and income. In the early development of
the income-eXpenditure approach, the aggregate consumption
function was thought to be a very stable economic relation—
ship over time. The marginal propensity to consume, which
was derived from the consumption function, was important
because it was the major determinant of the income multiplier.
If the marginal propensity to consume happened to be constant
then the multiplier would be constant. Later studies of the
consumption function have indicated, however, that the con-
sumption function is not as stable over the short run as it
was first thought to be. Consequently, the multiplier rela-
tionship was not as stable over the short—run as originally
believed.

Rather than attempting to determine the absolute stabil-
ity of the two relationships, Friedman and Meiselman felt
that it would be more informative to test the stability of
the one relationship relative to the other. To do so, they
set Up simple models of the two theories. They felt that
tests had to be carried on at this level if the two theoret—
cal concepts, in the terms of their crude ancestors, were to
be compared.

The simplest form of the income-expenditure approach
states that income is directly related to autonomous expendi-

tures. This was expressed in equation (1.8) in Chapter I.

15

(2.1) Y = d + 8 'A

t t

Changes in income are assumed to be a constant multiple of

changes in autonomous expenditures.

(2.2) dY = 5' dA

t t

As mentioned above, the multiplier is directly derived from
a consumption function like that in equation (1.5) and is

of the following form:

1

(2.5) s- = 1 _ MPC

In the crude model the MPC is assumed to be constant
and this leads to the conclusion that the multiplier is a
constant. As was mentioned above, recent develOpments have
shown that the MPC is not constant, particularly in the short
run, and this leads one to question the stability of the
multiplier. It should be noted that one of the problems of
this analysis is that the consumption function used to develop
the simple multiplier model does not conform to recent de-
velopments in the field. Current advancements require that
the consumption function be specified in a more SOphisticated
manner to be better able to explain observed behavior. For
example, the permanent income hypothesis was develOped to
explain the behavior of the consumption function and to help
account for the instability of the short-run multiplier.

It would seem reasonable to expect that if the more

16

sophisticated consumption function explains observed behavior
better, the simple consumption function could be eXpected to
yield poorer results in terms of a lower coefficient of
correlation than could otherwise be obtained.

Autonomous eXpenditures constitute a major portion of
income; therefore, it was felt that the relavant test of the
income—expenditure approach would be to relate autonomous
expenditures to induced eXpenditures. Otherwise, autonomous
expenditures would appear on both sides of the equation (2.1)
and since this variable is subject to errors in measurement,

7

it would introduce spurious correlation. This equation was

altered to obtain the following:

(2.4) Ct = a + B At + u1

where B B' - 1

stochastic error term with zero

u
1
mean, constant variance and zero

covariance.

The a can be tested for significance to determine whether
the average and marginal multipliers are the same. It has
generally been assumed by economists that they are not the
same.

(Friedman and Meiselman developed the Quantity Theory in

/

the following way:

 

7Ibid., p. 175.

17

(2.5) Yt = o + y'Mt + u2
where Yt = nominal income
Mt = money Stock--coin and currency in
hands of the nonbank public plus
all commercial bank deposits.
u2 = stochastic error term with zero

In order to compare

equations, the dependent

mean, constant variance and zero

covariance.

the results of the tests on the two

variable in each must be the same.8

That is, the dependent variable of equation (2.5) must be

altered to correspond with that of equation (2.4). Friedman

and Meiselman felt that this would put the Quantity Theory

at a disadvantage and were therefore surprised that the re-

sults were so one-sided.

In particular, they found that the

money stock was closely related to consumption expenditures

and in many cases the relationship was closer than that be-

tween the money stock and aggregate income. They proceeded

to justify their empirical results in terms of the permanent

income hypothesis.9

to permanent income than

Since consumption is more closely related

to current income, it must be more

closely related to the money stock, because the demand for

money is a function of permanent income and not current

 

81bid., p. 176.

9Ibid., pp. 176-177

18

income. The revised Quantity Theory model is:

. = 5 + +
(2 6) Ct yMt 115
where Ct = induced eXpenditures
u = stochastic error term with zero

5
mean, constant variance and zero

covariance.

In the usual formulation of the Quantity Theory the
average velocity and the marginal velocity are assumed to be
equal. That is, a = 0. It was decided to test this hypothe-
sis by leaving '6' in the equation.

So far, the development of the models has been in nominal
terms. Since the income eXpenditure theory is often stated
in real terms, further tests of the two hypothesis would con-
sider prices. It was decided that instead of deflating the
two equations, (2.4) and (2.6), the price level would be
added to the equations as an independent variable. This was
done to avoid Spurious correlation caused by errors of
measurement in variables that would be included on both sides

of the equation.10

(2.7) C a + BAt + kpt + u

4

(2.8) c

6 + yMt + APt + u5

 

1°Ibid., p. 178.

19

The addition of prices presents many problems. One prob-
lem has to do with the distribution of changes in nominal
income between real output and prices. Another concerns the
direction of causation. Whereas it is assumed that the
Federal Reserve System can control the nominal supply of
money, the central bank cannot determine the real money sup-
ply. .This might mean that the situation in the real sector,
i.e., the relationship of aggregate demand to aggregate
SUpply, would affect the real supply of money and not the Op-
posite way around.11

Finally, the two theories were combined into one reduced
form. This was done so as to test the relative importance
of the two independent variables. It could also be true that
some of the movement in one variable might represent the
hidden influence of the other. It was felt that the expanded
reduced form would allow this to be tested. This would, of
course, invalidate the previous tests if (2.9) and (2.10)

represented true reduced forms. The equations tested were:

(2.9)

0
II

+ + +
d 7 Mt 8 At u6

(2.10) C d + y Mt + B At + A Pt + u7

The results of these two equations were analyzed in the
following way. If the partial correlation coefficient of

one of the independent variables was nearly equal to its

 

llIbid., pp. 178-179.

20

Simple correlation coefficient, then it would be assumed
that the variable in question exhibited little or no hidden
influence of the other variable. However, if the partial
correlation coefficient were much less than the simple corre-
lation coefficient, it could be assumed that the variable
in question reflected in part the movement of the other
eXplanatory variable. Therefore, the relationship shown in
the simple regression models, (2.4) or (2.6), between the
independent variable and consumption would appear to be pri-
marily the hidden influence of the other eXplanatory variable
working through the eXplanatory variable being tested.

Friedman and Meiselman also discuss further elaboration
of the two theories. Any further elaboration would include
eXplanations of the velocity of circulation (y) and the
multiplier (8) and the determinants of the independent vari-
ables. In particular, the equations tested are true reduced
forms only within the extremely Simple models Specified above.
If the models are imprOperly Specified, one may seriously
question the validity of the results. AS will be shown later,
there are serious statistical problems that arise due to the
misspecification of a model by not using all the information
that is available to the researcher.

In regard to the results of these tests, it has been
noted that when two variables are synchronous and are closely
related to one another this does not imply that one is

"determining" the other. Friedman and Meiselman make it very

21

clear that even when they examine the equations with lagged
variables, a high correlation between a lagged variable and
a dependent variable does not necessarily imply causation.
Both variables might move together because of the influence
of a third variable. Therefore, it is necessary, when
examining lagged relationships, not to draw any hasty con-
clusions about the direction of causation.12

One of the major problems encountered in the study was
the definition of the variables. It is readily apparent
that in tests where the data are so highly aggregated, a
slight change in a definition can alter the conclusions con-
siderably. Friedman and Meiselman attempt to define the
variables in an objective way so that their definitions can
be duplicated in Similar tests by others. This, they hope,
will allow economists to get away from the reliance on
a_priori definitions or the use of intuition.

One'method of determining the apprOpriate composition
of a variable would be to regress income on the various com-
binations of the variable and accept the combination that
was most closely related to ingome in terms of the coeffi-
cient of correlation. However, Friedman and Meiselman felt
that this presented a problem, for in the case of autonomous
eXpenditureS this approach would result in regressing income
on part of itself. .Consequently, this would introduce

Spurious correlation.

 

121bid., p. 179.

22

In order to derive a different test, Friedman and
Meiselman assumed that the components of a given variable
were close substitutes. In fact, the components were
assumed to be such close substitutes that it would be better
if they were treated as one variable, or as perfect substi-
tutes, than to treat them separately. Thus, they hypothe-
size that in the case of perfect substitutes, switching a
dollar from one component to another Should not affect the
relationship of the total with income. In the case of
autonomous eXpenditureS, it would not affect the relationship
of the total of the two with the induced component of income.
Because of this, income or the induced component of income
Should move more closely with the total value of the autono-
mous variable than with the individual components of the
autonomous variable. However, in the case where components
are not good substitutes, switching a dollar from one com—
ponent to another should affect the value of income and,
therefore, the induced component of income. Consequently,
income Should move more closely with the individual compon-
ents than with the total valueg

In order to describe this test further, it is helpful
to proceed by means of an example. .This is the same one
used by Friedman and Meiselman.13 Assume that there exists

a preliminary definition of autonomous expenditures (A).

 

13Ibid., pp. 182-185.

25

The question arises whether durable consumer goods (D) should
be included in this definition of autonomous expenditures or
not. «Let N represent eXpenditureS on non-durable goods. If
D and A are perfect substitutes, then shifting $1 from D to

A or from A to D would have no effect on N. If this were
true, then the statistical relationship between N and (D+A)
should be closer in terms of a higher coefficient of correla-
tion than that between N and A and N and D alone. The test,
therefore, requires that the regressions of N on (D+A) and

N on D and N on A should Show that the correlation between

N and D or N and A alone would be lower than the correlation

with their sum. That is,

(2°11) rN(D+-A) ND

>.
and

NA

 

This might not be satisfied and so an alternative test
is developed. D might be a part of induced expenditures.
Therefore, changes in N and D could be independent of A and
changes in A might only affect their sum. Additional regres-
sions need to be run of A on (D+N) and A on D and A on N.

In this case, the following conditions need to be met.

—

(2.12) r

rA(D+N) >' AD

and

AN

 

24

Friedman and Meiselman use the following criterion to
determine whether D should be included in A or not.

Possibility Condition (2.11) Condition (2.12) Conclusion

(a) Satisfied Not Satisfied D Autonomous
(b) Not Satisfied Satisfied D Induced
(c) Satisfied Satisfied Ambiguous
(d) Not Satisfied Not Satisfied Ambiguous

The results of the test may turn out to be ambiguous.
Friedman and Meiselman state that "when the results (are)
ambiguous, (they) . . . followed the procedure that seemed
more in accord with the general presumptions in the litera-
ture about the income-expenditure relations."14

The results of the test limit the definitions of money
and autonomous expenditures to the following items:

Money = Coin and currency in the hands of the non-bank
public plus adjusted demand deposits plus
adjusted time deposits at commercial banks.

Autonomous Expenditures = Net private domestic invest-
ment plus the government deficit on income and
product account plus the net foreign balance.

The consumer price index was chosen as the second
regressor in (2.7), (2.8) and (2.10) because the dependent
variable was consumer expenditures.

For the most part, the study used annual data. This was

because of the lack of quarterly data before 1941. Annual

 

14Ibid., p. 185.

25

data were also used in testing for the definitions. In this
respect Friedman and Meiselman contend that perhaps the
final form of the definitions arrived at in this way may not
be the apprOpriate ones for a shorter time period, such as
calendar quarters. They feel that ". . . quarter-to-quarter
changes reflect very short period relationships and that for
such Short periods our definition of autonomous is not
apprOpriate, that the autonomous category should be enlarged
to include all of eXportS and not simply the foreign balance
and all of government expenditures and not Simply the
deficit."15

The period covered is from 1897 to 1958. Since the
study was more interested in the short-run stability of the
two models, it was necessary to find some way to divide the
data into shorter time periods. It was decided that sub—
periods should be based upon turning points in the business
cycle as determined by the National Bureau of Economic
Research. Also, since the velocity of circulation and the
multiplier could change decidedly over the business cycle
it was necessary to test the theories at different points
of time within the cycle. (Therefore, two additional divi-
sions were made. The first divided the data into time
periods that conformed.with the troughs of major depressions
(1897, 1907, 1921, 1955, 1958, and the end of World War II).
.The second division made the separation at peaks intermediate

between the troughs (1905, 1915, 1920, 1929, 1959, 1948, and

 

151bid., p. 204.

26

1957). This allowed for a great deal of overlapping. This
would provide some idea of how velocity and the multiplier
behave over the cycle.

The.results oftained by Friedman and Meiselman were
quite one-Sided. In all cases except the early years of
the Great Depression, consumption expenditures were more
closely related to the money supply than to autonomous ex-
penditures. If the year 1929 is dropped from the tests,
the money supply equation exhibits the more stable relation
over most of the depression years.

Tests on quarterly data from the third quarter of 1945
to the fourth quarter of 1958 give the same one-Sided results.
The results carry over when first differences are used and
also when the variables are expressed in real, rather than
in nominal values.

To a large extent, it appears that the effects of auton-
omous expenditures on consumption represent the hidden in-
fluence of the money supply. The partial correlation
coefficient between consumption and the money stock is almost
the same as the Simple correlation coefficient of consumption
and the money stock. On the other hand, the partial correla-
tion coefficient between consumption and autonomous expendi-
tures is considerably lower than the Simple correlation
coefficient between these variables.

When lagged quarterly values are introduced, consumption

seems to be most closely related to the money stock two

27

periods earlier while consumption is most highly correlated
with the contemporaneous value of autonomous expenditures.
This implies that the money stock could have a strong influ—
ence on consumption expenditures over several quarters, while
autonomous expenditures would have the greatest effect in

the quarter in which they are made.

The resultscxftests on d and o are interesting in the
light of a_priori reasoning. They both tend to conform to
what one would eXpect. The test of the multiplier hypothesis
seems to indicate that the intercept term is positive and
significantly different from zero. This would imply that
the average is greater than the marginal multiplier. The
test of the Quantity Theory shows that the intercept term is
not significantly different from.zero. This would imply that
the version of the Quantity Theory developed in Chapter I
would be the correct specification and that the average
velocity of circulation would be equal to the marginal.

The absolute stability of the multiplier and the velocity
of circulation is:also discussed briefly. "(A)lthough the
multiplier was generally highly stable between cycles for this
period the typically low intracyclical correlations between C
and A indicate that the multiplier was highly unstable."16
The results were just the opposite for velocity. "Although

average and marginal velocities were highly stable

 

laIbid., p. 206.

28

intracyclically, secular Shifts are immediately apparent."17

These two results agree with current theory. Since the
multiplier is closely related to the marginal prOpensity to
consume (MPC), a stable value for the multiplier would indi-
cate that the MPC was fairly stable. .Since the multiplier .
'is fairly stable between cycles, it would appear that the
long-run MPC is relatively stable. The variability intra-
cyclically can be explained by the Shifting of the Short-run
consumption function. This is consistent with much of the
contemporary work that has been done on the consumption
function, in particular the permanent income hypothesis.

The stability intracyclically of the velocity of circu—
lation implies that the demand function for money iS rela-
tively stable within the cycle, which is generally assumed
by quantity theorists. 'The instability between cycles can
result from institutional changes or longer run effects.
This is again consistent with the theoretical eXpectations
of the latter school.

The conclusion drawn from the study by Friedman and
Meiselman is that although the income velocity of circula-
tion is not absolutely stable, it is nevertheless more stable
in the short run than is the alternative hypothesis presented
by the income-expenditure approach. As a result, if the
money supply is controlled by the central bank and is a caus-

ative factor in income determination, then one should choose

 

17Ibid., p. 206.

29

changes in the money supply as the more reliable policy
instrument because it is more closely related to changes in
income than are changes in autonomous eXpenditures.

These results run counter to the beliefs of many econo-
mists. It is generally felt that if the Quantity Theory is
to hold, it will hold over the long run and not in the Short
run. Some of the difficulty in understanding the results
of the Friedman-Meiselman tests is caused by the failure to
consider that the tests are aimed at the relative stability
of the two relationships and not their absolute stability.
The Quantity Theory, in its more naive form, may be more
relevant in the long run than in the Short run. However,
the tests are aimed at showing that even though the relation-
ship between the stock of money and consumption is not abso-
lutely Stable in the Short run, it is a more stable relation-
ship than that proposed by the income-eXpenditure theory.

.These tests were the first attempt to compare the rela—
tive stability of the two theories. It has been implied
that there are many problems that exist in the study. It
was to be eXpected that the paper would draw a rebuttal from
the proponents of the income-eXpenditure approach. Soon
after the publication of this paper, other economists pub-
lished Similar tests. They attempted, primarily, to stay
at the same level of aggregation. Once a battleground is
chosen, it is hard to Shift the place of combat. The follow-

ing discussion represents an attempt to classify some of

50

the major points of criticism leveled at the Friedman-

Meiselman paper.

Major Points of Criticism

 

The three articles that followed the Friedman-Meiselman
paper were relatively consistent in their criticisms. There
is much overlapping in these papers, consequently, only the
main points of discussion will be presented. To some extent
De Prano and Mayer missed the point of the discussion in
their article because they seem to be unduly concerned with
the two approaches as forecasting models, whereas the aim of
the study was to determine which variable had the closer
relationships with movements in income. However, many of
their remarks are still relevant.

.All of the discussants seemed to feel that the tOpic of
greatest concern was the definition of autonomous expendi-
tures. It was felt that the choice of the components of A
seriously biased the tests against the income-eXpenditure
model.

Hester, for example, concentrates mainly on the specifi-
cation of the "Keynesian" model. By maintaining the same
level of aggregation as the previous tests he ignores models
that could reconcile the two theories. His model is one

derived in the textbook by Dernberg and McDougall, which

51

does not include a monetary sector.18

In so doing, he presents a strong argument against the
use of an empirical technique in defining variables. He
feels that if the main idea of the Friedman-Meiselman tests
are to investigate the empirical foundations of elementary
textbook models, then the definitions that are used Should
be the ones most commonly associated with the theory being
tested. Choosing any other definition would result in a
test, not of the model the researcher wants to subject to
test, but of another model and its assumptions and defini-
tions. Therefore, the results of the test cannot be used to
draw conclusions about the original conceptual model.

(Hester does criticize the FriedmaneMeiselman defini—
tional test, by stating that "their test is sensitive to the
variances and covariances of I (Investment), G (Government
Expenditures), and H (Exports). (C)omponents of autonomous
expenditures will not be reliably selected by their pro-

19 Friedman and Meiselman agree that Hester has a

cedure."
valid point, but state that he proposes no alternative.
Therefore, until an alternative method is proposed, the old

method should continue to be used.20

 

18Thomas F. Dernberg and Duncan M. McDougall, Macro-
economics, Third Edition (New YOrk: McGraw-Hill, 1968),
Chapters 5 and 6.

19Hester, “Rejoinder,” The Review of Economics and
Statistics, XLVI (November 1964), p. 577.

 

 

20Milton Friedman and David Meiselman, "Reply to Donald
Hester," The Review of Economics and Statistics, XLVI
(November 1964), p. 570.

52

Hester proposes several different definitions of auton-
omous expenditures. For example, he says that in the
Dernberg-McDougall model, all taxes are assumed to be endo-
genous. This is because a large proportion of tax collections
depend upon the amount of income economic units receive.

In the short run, these tax collections are divorced from
the corresponding eXpenditureS made by the government. The
immediate conclusion is that autonomous expenditures should
include the total of government expenditures and not just
the deficit. This gives him his first definition of auton-
omous expenditures.

Imports are a function of the level of income and,
therefore, Should be considered endogenous. There is also
a question as to the validity of the measurement of depreci-
ation. Since this figure is just an estimate and bears
little or no relation to economic depreciation, it was de—
cided to use gross investment rather than data net of
capital consumption allowances. The second definition used
by Hester included Gross Private Domestic Investment, Total
Government Expenditures, and Total EXports.

The third definition used by Hester subtracts imports
from the second definition. This is done because some of
the value of imports is double counted in consumption ex—
penditures. If imports are not subtracted, they might
introduce some Spurious correlation. A fourth definition
subtracts inventory investment because it is endogenously

determined.

55

Hester feels that in their particular choice of At’
FriedmanéMeiselman introduce a downward bias in the correla-
tion between consumption and autonomous expenditures. He
states that the coefficient of correlation must be lower
between Ct and At than between Ct and the first of Hester's
definitions unless the latter correlation is equal to one.
In this case, both coefficients of correlation will be equal
to one.21

De Prano and Mayer also find fault with the definition
of autonomous expenditure used by Friedman and Meiselman.
However, they provide little eXplanation as to the method
of choosing items they use in their definitions, but do make
some interesting comments on the problems associated with
the definition used in the previous tests.

Their first point concerns the effect of capital con-
sumption allowances Upon the values of the correlation co-
efficient. In all the time periods tested, they found that
the gross concept of investment expenditures was more
closely related to consumption expenditures than the net con-
cept. From this they conclude that errors in measurement
of capital consumption allowances are great enough to cause
considerable bias to the tests and that the gross concept

is better for statistical purposes. This conclusion is in

agreement with the results of Hester's tests.

 

21Hester, "Keynes and the Quantity Theory," op. cit.,
p. 566.

54

Their second point concerns the performance of an inter-

22 They correlate consumption with various

esting eXperiment.
components of autonomous expenditure, both in terms of levels
and in terms of first differences. Additional variables are

not added to the equation; only the definition of the regres—
sor is changed.

The inclusion of some items in a definition raise the
correlation coefficient and some lower it. It is apparent
from their results that the items that tend to lower the
correlation coefficient are those items that are considered
endogenous in many Short-run economic models.

-De Prano and Mayer make little use of this test in de-
fining their variables. Their purpose in mentioning these
tests is that definitions of autonomous expenditure that have
endogenous elements in their sum tend to lower the coeffi-
cient of correlation of autonomous expenditures with consump-

3 Since Friedman and Meiselman's

tion expenditures.2
definition of autonomous expenditures does contain induced
components, this would tend to bias their results downward
and put the income-expenditure theory at a disadvantage rela-
tive to the Quantity Theory.

Ando and Modigliani also discuss the definition of

autonomous expenditures. They, too, draw on the fact that

 

22De Prano and Mayer, op. cit., pp. 754-758.

231bid., p. 754.

55

the definition has endogenous elements in it. They contend
that the variable, therefore, is not independent of the
disturbance term and introduces simultaneous equation bias
into the results. This would explain some of the results
obtained by De Prano and Mayer. The bias in this case re-

duces the correlation between Ct and At and in the extreme

could make it a negative correlation.24

An attempt is made by Ando and Modigliani to derive a
definition of autonomous expenditures by a thorough exami-
nation of the national income accounts. Although they do
not perform the statistical test of their criterion for
separating autonomous components from induced components,
they feel that the definitions of the variables they arrive
at are independent of the disturbance term in the equation
they test. After making some Simplifying assumptions, they

arrive at the following definition.25

(2.15) A* = Net investment in plant and equipment
and in residential houses plus total
government purchases of goods and
services plus exports plus property tax
portion of indirect business taxes plus
net interest paid by government plus

government transfer payments plus

 

24Ando and Modigliani, op. cit., p. 699.

251bid., p. 702.

56

enterprises minus statistical discrep-
ancy minus excess of wage accruals over
disbursements.

Their definition differed from that used by Friedman
and Meiselman because A* and consumption eXpenditureS (C)
do not aggregate to the total value of income. They felt it
was necessary to alter the test somewhat, so they decided
to run.A* against the rest of income. This latter component
of income was called induced eXpenditures and labeled Cf.

It becomes apparent in going through this debate that
one major point about the appropriate definition for the
model boils down to a discussion of time periods. Certain
items should be considered autonomous if the time period
under examination is of a certain length. If a shorter time
period is chosen the item is induced. For example, Friedman
and Meiselman feel that the deficit is autonomous for a
period as long as one year. The government accounts must
be balanced in this time period in terms of paying for its
expenditures. (In tests over shorter periods, they feel
that perhaps the deficit is not autonomous because the govern-
ment does not need to concern itself with balancing its
accounts. Over this shorter length of time the level of
government eXpenditures might be the autonomous component.
Thus, the debate is reduced to the question of appropriate
time periods. That is, over what time periods must tax

collections be reconciled with eXpenditures? If one year

57

is the correct time period, the Friedman-Meiselman concept

is correct.

Minor Points of Discussion

 

Discussion of the time periods chosen

The different definitions of autonomous eXpenditures
were tested in the three articles under review over the
period 1929-1958 and 1929-1965. Hester used five subperiods
in his testing, while the Ando-Modigliani and De Prano—Mayer
tests were over the whole period. Ando and Modigliani also
excluded the war years.

Hester found that, excluding the war years, the income-
expenditure approach performed about as well as the quantity
theory model in terms of the coefficient of correlation.

In almost every case the variables defined by Hester did
better than the one develOped by Friedman and Meiselman.
The same results were apparent when first differences were
used.

De Prano and Mayer arrived at very similar results.
Their tests included more postwar years and seem preferable
to Hester's for that reason. From their tests excluding
the war years, they conclude that since there is little dif-
ference between the income-expenditure model using their
definitions and the quantity theory model, that both models

do equally well in eXplaining movements in consumption.

58

In their tests, Ando and Modigliani found that A* per-
formed better than A in terms of a higher coefficient of
correlation. In reply, Friedman and Meiselman tested A*
over shorter periods of time. However, the correlation co-
efficient between M and C was still larger than between A*
and C, although the difference was negligible.

Friedman and Meiselman criticize all three papers for
testing over a shorter time period than they did.26 They
feel that the data are available to all and that the tests
should have been carried back further. Hester, and others,
argue that 1929 is the earliest date in which one can ob-
tain consistent government data. All other series are not
consistent with these government estimates.

The problem of using such a short time period can be
brought into focus by using Hester's tests. If one excludes
the subperiods that include World War II, there exists only
three samples and two of these include the depression, the
time period in which the income-eXpenditure approach was
formulated. This period has also shown the worst results
for the Quantity Theory.

This problem of excluding the war years seems to be
quite serious. It raises a question about changes in the
structure of the economy. That is, did the war cause a shift

in the structure or should the results obtained during the

 

26For example, Friedman and Meiselman, "Reply to Donald
Hester," op. cit., p. 569.

59

war years be consistent with those obtained in peacetime?
This has been a frequent topic of discussion in econometric
textbooks in reference to the Specification of the consump-
tion function. It seems very likely that the intercept or
the slope of the consumption function, or both would change
during the war years.

However, Friedman and Meiselman found that "(t)he
results turned out to be so consistent, . . . that we had no
occasion to discuss the results for other subperiods in
detail: the peacetime subperiods alone gave the same re-
sults as did the subperiods including some war years."27
That is, the Quantity Theory showed the same close relation-
ship in wartime as it did in peacetime.

A failure to detect shifts in the structure of an

economy has been found in other studies where a money supply

model is used.28 Although it might be eXpected on an

 

27Friedman and Meiselman, "Reply to Ando and Modigliani
and to DePrano and Mayer," The American Economic Review, LV
(September 1965), p. 761.

28Leonall Anderson and Jerry Jordan, Appendix, "Mone-
tary and Fiscal Actions: A Test of Their Relative Importance
in Economic Stabilization," Review, Federal Reserve Bank 6f
‘St. Louis, 50 (November'1968), p. 24. Tests of a simple fore-
‘casting model based-upon a reduced form derived from the
Quantity Theory show that the hypothesis that there was no
structural shifts in the economy from 1947-1968 could not be
rejected. ~See also, Edgar Feige, The Demand for Liquid Assets:
A Tempppgl Cross-Section Analysis (Englewood Cliffs, New
Jersey: Prentice-Hall, 1964). -Feige states that he could
find no evidence that would reject the hypothesis of a con-
sistent structural relationship in the demand for demand de-
posits over the time period of 1949-1959, p. 24.

40

p priori basis that the structure of the economy has changed,
the simple quantity theory model has failed to pick up this
Shift. This should lead one to question the theoretical
constructs of the model. It is possible that the statistical
properties inherent in the Quantity Theory model make it im-
possible to identify these Shifts.
Qiscussion of the discrimina—
tory power of the two models

Ando and Modigliani discuss this problem in the Appendix

29 In order to test the discriminatory

to their article.
power of the two models they set up a complete model and
attempt to determine the conditions necessary for the "money
only" theory to hold, and for the "effective demand" theory
to hold. Also, they determine the conditions that need to
be fulfilled for both theories to hold Simultaneously. These
conditions were then compared with the possible outcomes of
the Single equation test. They condluded that the two single
equation models had no power of discrimination between the
two theories. If one model turned out relatively more stable
than the other, no real conclusion could be drawn because
the results could be consistent with either the Quantity
Theory approach or the income-eXpenditure approach.

Friedman and Meiselman concur with the discriminatory

power of the tests, but still feel that comparing the rela-

tive stability of the two relations provides the answers to

 

29Ando and Modigliani, op. cit., pp. 716-725.

41

the questions they are posing. However, if the results are
consistent with either of the two theories, then the rela-

tive tests point to little if anything at all.

Other Specifications of the models

Ando and Modigliani feel that the consumption function
has been miSSpecified.30 They feel that very few economists
use the consumption function proposed by Friedman and Meisel-
man, particularly Friedman himself. Consequently, they
introduce a consumption function that incorporates a
"permanent income" Specification in the Spirit of Friedman's
earlier theoretical work. Thus, they feel the consumption
equation should have the lagged endogenous variable, Ct—1'
included. This, of course, violates the rules set up by
Friedman and Meiselman.

Secondly, Ando and Modigliani develop a demand for money
equation similar to that used by Friedman in earlier work.31
This, of course, introduces a more complicated equation and
leads to some change in the results. Ando and Modigliani
contend fundamentally and prOperly that the CMC paper of
Friedman and Meiselman fails to be consistent with previous

theoretical knowledge and does not incorporate theoretical

developments by the authors themselves.

 

30Ibid., p. 696 and p. 704.

31Ibid., pp. 707-710.

42

A third point concerns the exogeniety of the money
SUpply. Friedman and Meiselman contend that the direction
of causation could be from income to the money supply.
However, they draw upon earlier studies of monetary reforms
and devaluations to imply that causation apparently runs
the opposite way. Also, recent empirical work indicates
that the money supply has a very low income elasticity.

Hester discusses this point in his paper but fails to
perform any tests of the hypothesis. Ando and Modigliani
also raise the point, and do make an attempt to test the

possibility.32

They specify a new variable, M*, which is
the maximum amount of money that could be created by the
commercial banking sector, given the amount of reserves
supplied by the central banking system. This will always
be larger than the actual money SUpply. They feel that it
is this variable that should be entered into the quantity
theory model because it represents the behavior of the
monetary authorities.

This raises once again the question of the apprOpriate
time period in defining the extent to which variables are
exogenous or endogenous. Certainly in the short—run the
money supply should be considered an endogenous variable

and some other variable should be used to represent the

behavior of the monetary authorities. Over a longer period

 

32Ibid., pp. 711-714.

45

of time, however, the money supply can be controlled within
limits. The variable which has a large measure of influence
over the money supply and which is considered to be under
the control of the central bank, would be the monetary base.
Preliminary estimates indicate that the lag in the influence
of the monetary base on the money supply is approximately
six months and that the elasticity of the money supply with
reSpect to the monetary base, adjusted for member bank bor-
rowings, is about 0.75. .This covers the period from the
third quarter of 1955 to the fourth quarter of 1965. This
implies that on a yearly basis the money supply can be suf-
ficiently controlled by the monetary authorities so that it
can be considered exogenous to the economic system. If one
were to consider a quarterly model, the money supply Should
probably be considered to be endogenous because over this
shorter time period the money supply is determined by the
interaction of economic forces.

The introduction of M* lowers the correlation of a money
supply measure with consumption expenditures when tested in
the original model. However, when the more SOphisticated
demand for money model is used, the coefficient of correla-
tion is the same as when the other measure is used, but the
error variance is lowered. Ando and Modigliani conclude
from this result that a large component of the money supply
is induced and that it therefore introduces an upward bias

in the correlation coefficient of the Quantity Theory model.

44

This upward bias is a result of the positive correlation of
the money supply with monetary Gross National Product. An
increase in this latter measure will increase the money
supply (M) and also will increase consumption expenditures.

M* need not change to arrive at this increase in M.

Discussion of a more complete model

DePrano and Mayer, and Ando and Modigliani both discuss
the need for a more complete model. They both feel that the
confines of the single-equation models are too restrictive.
However, the strong evidence presented by Friedman and
Meiselman had to be answered according to the ground rules
set up in the original article. The overwhelming results
had to be matched, bettered, or discredited.

.It is particularly evident in the Ando-Modigliani arti—
cle that the authors feel that the single-equation models
are misrepresentations of the real world and in many respects
are a waste of time. DePrano and Mayer also question whether
the two single—equation models are even comparable. This
presents the problem that if they are not then what two
would be.

These two articles imply that more complete models
represent a truer picture of the world. In such models the
stock of money and autonomous expenditures are both important
and they should both be included in attempts to explain in-
come determination. Also, a more complete model allows one

to look for more complex transmission processes, which are

45

simply not identifiable in Single—equation models.

Finally, the Single-equation models do not include
some recent theoretical developments. As has been mentioned
above, neither the permanent income hypothesis nor recent
advancements in the area of the demand for money have been

included in the simple formulations.

Additional Work

Two additional papers will be discussed in this section.
These are papers by Pesek33 and by Kmenta and Smith.34 They
are later papers than the ones discussed above and they
approach the subject in slightly different ways.

The article by Pesek is primarily concerned with the
quality of the evidence used in the test of the two theories.
Specifically, Pesek thinks the Friedman-Meiselman test sets
up the Quantity Theory so it is difficult to reject, while
DePrano and Mayer do the same thing for the income-expenditure
approach.

In the case of Friedman and Meiselman, the method of

regressing induced expenditures (consumption expenditures

 

33Boris Pesek, "Money vs. Autonomous Expenditures:
~The Quality of the Evidence," Business Economics, III
(Spring, 1968). pp. 27-34.

34Jan Kmenta and Paul Smith, "Autonomous Expenditures
vs. Money Supply: An Application of Dynamic Multipliers,"
Econometrics WOrkShop Paper No. 6604, Michigan State Univer-
sity, February, 1967.

46

above) on money will not only compete favorably with the
income-eXpenditure approach, but will Show better results
the higher the correlation between induced and antonomous
expenditures. To see this, one may examine the two coeffi-

cients of correlation:

2 cov (YJM)2
(2°14) rY,M var Y var M

 

where Y Friedman-Meiselman concept of

 

income
M =Inoney stock
2
2 = cov (C+I,M)
(2°15) rc+I,M var (C+I) var M
where C+I = induced expenditures
A = autonomous expenditures.

If cov (M, A) = 0, then cov (Y, M) = cov (C+I, M)2 so that
(2.14) and (2.15) have like numerators. Now, var Y = var
(C+I) + var (A) + 2 cov (C+I, A) and var Y > var (C+I) if
var (A) + 2 cov (C+I, A)> O, which implies that 2 cov

_ 2 2
(C+I,A) > var (A). If cov (C+I,A) > 0 then rY’M < rC+I,M°

The higher cov (C+I, A) the greater r; M will be. This is

exactly what would happen if the income-eXpenditure approach

obtains good results. It should be noted that Friedman and

2 2
Y,M < rc+1,m‘

However, they use the permanent income theory to explain

Meiselman report that results confirm r

what has occurred.

47

DePrano and Mayer, on the other hand, Specify their
model so that a part of investment eXpenditures is induced.
That is, they assume net private domestic investment is
composed of fixed investment and inventory investment.
Inventory investment is endogenous and thus is eliminated
from the definition of autonomous expenditures. This vior
lates the test because DePrano and Mayer now relate their
measure of autonomous expenditures to just the consumption
component. To be consistent, autonomous expenditures Should
be related to all of the induced component. This means that
DePrano and Mayer are trying to relate autonomous expendi-
tures with a smaller item than do Friedman and Meiselman.

Friedman and Meiselman avoid this pitfall because they
use all of net private domestic investment in their defini—
tion. ~They are left only with consumption expenditures in
the induced component. Inventory investment, therefore, is
included in autonomous expenditures.

A second point of Pesek's concerns the theoretical
problem of defining autonomous expenditures. He feels that
induced expenditures are a theoretically sound concept, but
that perhaps autonomous component should be divided into two
parts. One part would consist of private eXpenditures such
as business investment, while the other part would be made
up of public expenditures, such as government expenditures.
This latter concept is the only one that would be directly

comparable to a theoretical policy variable such as the money

supply.

48

Two additional points are raised concerning the defini-
tion of the money supply. The first of these implies a bias
introduced into the tests by the definition of M chosen by
Friedman and Meiselman. The measure chosen to represent
the money supply is relatively interest inelastic. By using
this measure they have arrived at a value that will cause the
LM curve of the familiar Hicks—Hansen IS-LM function to be
almost vertical. This means that the only way income could
change is by a monetary policy that Shifted the LM function.

Since this is true, then any correlation between this
measure of the money supply and income will be quite high.
Therefore, defining variables empirically, as Friedman and
Meiselman do, would lead them to choose this particular
measure. Consequently, their conclusions are preordained.

The theoretical definition of the money supply also is
questioned by Pesek. "Close substitutes" are defined in
terms of cross-elasticities. In attempting to test defini-
tions the way Friedman and Meiselman do, the more economically
valid test is ignored.

Thus, Pesek concludes that the definitions and tests
bias the results against the income-expenditure approach in
favor of the Quantity Theory approach. But this is really
secondary because he feels that these single-equation tests
are out of date and that more attention should be paid to
more complete theories in which both monetary and fiscal

policies are important. In this way economists can learn

49

more about the behavior of the economy and prOper policy
mixes.

The final paper discussed here takes the controversy
into a full econometric model. Kmenta and Smith feel that
it is necessary to combine the two theories and attempt to
discover their relative importance in terms of the impact
they have in the current time period and also the effect
they have on an economy over time. They attempt to do this
in a quarterly econometric model.

This is a very desirable direction in which to take
the discussion. Since the paper is only a beginning attempt
to assess the relative importance of the money supply and
autonomous expenditures, this thesis will discuss only the
important features of the model and some of the conclusions
that were drawn from the work.

The money supply and government expenditures were taken
as the exogenous elements or policy variables. Kmenta and
Smith discussed the possibility that these might not be
truly exogenous, but decided that, at the present stage of
the investigation, they would assume them to be under the
complete control of the prOper authorities.

They engage in no discussion whatsoever of the proper
definitions. One reason why so little attention was paid
to the definition problem is that the more disaggregated a
model becomes, the smaller the definitional problem becomes.

Two developments should be noted, however. First,

government eXpenditures include net foreign investment.

50

Consequently, this variable is not completely under the con-
trol of the government. Also, some parts of government
eXpenditures might be considered endogenous in a quarterly
model. Secondly, taxes are excluded altogether. Autonomous
expenditures are government eXpenditureS plus the net foreign
balance. The deficit problem is eliminated because taxes

are eliminated. Net private domestic investment, in a larger
model, such as this, becomes determined within the system.

Estimates were obtained for the whole system using two-
stage least squares. Variables whose coefficients were not
Significantly different from zero were retained. This has
been fairly common practice as can be noted in the litera-
ture of the field and it occurs because econometricians are
generally interested.in the behavior of the whole system
over time. Even though these variables are not Significant
in a statistical sense, they do contribute to the understand-
ing of this system.

.The tentative conclusions drawn by Kmenta and Smith were
that there is little to differentiate between the effects of
autonomous expenditures and the money supply. This is not
inconsistent with the battery of tests performed by Ando
and Modigliani, DePrano and Mayer, and Hester. Also, the
"long-run" multipliers of the two policy variables are lower
than usually obtained in tests on static models such as the

ones mentioned above.

51

Summary

A few things are implied in all of the above discussion.
Firstly, a great deal depends on the definitions one chooses
for the relevant variables. Secondly, most researchers are
uncomfortable using the simple one—equation models. Thirdly,
most feel that both the money supply and autonomous expendi-
tures are important in determining aggregate income, but
there is a Significant area of theoretical disagreement and
empirical ignorance concerning which of the two may be the
more important. Consequently, in the following chapter a
macroeconometric model that is theoretically more completely
specified then those used in previous investigations will be
develoPed. This model will subsequently be implemented in an
effort to shed new evidence on the question of the relative
importance of autonomous expenditures versus the money supply

as determinants of aggregate economic activity.

CHAPTER III

A DISCUSSION OF FURTHER TESTS

Introduction

.Friedman and Meiselman set out to test two simple models
of income-determination. The explicit purpose of their test
was to determine which variable, the money stock or autonomous
expenditures, was more closely related to movements in income.
They were not specifically concerned about causation;
nevertheless, inferences were drawn, linking this study with
other studies that have been completed, particularly those
of Friedman.

The two models tested were supposed to represent the
simplest forms of the two theories. However, there is a great
deal of ambiguity in the point of view that one theory is as
simple as another, and that the results obtained in testing
them are comparable. Be that as it may, these models were
felt to be a desirable starting place for testing which vari-
able moves more clésely with some measure of income.

The two simple models do represent testable hypotheses
about the structure of the economy. However, it is possible

that the two models are so highly aggregated and simplified

52

55

that they might actually offer little power for discriminat-
ing among alternative hypotheses concerning the structure

of the economy. Simple models such as these depend quite
heavily upon the definitions of the several variables. AS
was mentioned in Chapter II, much of the earlier debate
centered on the definitional specification of the models.
One could therefore question the validity of the results,
because quite different conclusions might be reached by only
a Slight change in the definition of any of the variables
used.

This thesis will rely primarily on definitions that
result from g_priori theory. There are certain elements of
arbitrariness in this method, but there are also elements of
arbitrariness in defining varibles empirically. By contrast,
Friedman and Meiselman contend that the use of intuition or
§_priori guessing is not a scientifically valid method.

They contend that the empirical method is the only "objective
way" to define variables consistently.l

Deriving definitions theoretically, however, is a valid
method. All scientific researchers must use their intuition
to some extent in order to establish theoretical concepts.
These concepts can be used to construct theoretical structures

that can be tested. The scientific method requires only that

 

1Friedman and Meiselman, "Reply to Ando and Modigliani
and to DePrano and Mayer," The American Economic Review, LV
(September, 1965), p. 764.

54

the researcher set up his assumptions (which also include
his definitions), state his hypothesis (which is possible to
refute) and then follow procedures which can be duplicated.
The ability of a test to be duplicated is the backbone of
experimental science. How the assumptions are determined in
many cases is arbitrary--one set is unacceptable only in the
face of an alternative body of assumptions that are more
acceptable in terms of framing a hypothesis.

The effort of Friedman and Meiselman to define variables
empirically appears to set back the formulation of assump-
tions and tests one step. They still proceed along the same
lines as others, using their intuition and/or theory, but one
step removed from defining the variables, theoretically.
Consequently, it is argued that one method is as valid as the
other.

It would also appear that if economic analysis is to have
any relevance as a "science" that an analyst should be capable
of defining variables by the logical application of its
methods. This must assume, of course, a given level of aggre—
gation. In the following, the definitions developed by
Friedman and Meiselman and by Hester will be used in retest-
ing their own models. Further develOpmentS, however, will be
made along the lines discussed above. The various functional
forms have been developed using the tools of analysis avail-
able. The variables have been defined in a manner that

enables the two theories to be tested.

55

In the second section of this Chapter, the Friedman-
Meiselman models will be Specified again in order to rerun
the original data and also to perhaps correct it for some
statistical deficiencies. In the third section, Hester's
model will be develoPed so that it can be used as an alterna—
tive hypothesis when testing the two F-M models over a more
current period. In the fourth section, a complete model
will be Specified. This is necessary for three reasons.

It is readily apparent that the more one aggregates an eco—
nometric model, the greater the problem of definition becomes,
and hence the greater is the need for careful Specification.
The second reason is that much of the disagreement between
the two schools of economic thought is caused by the failure
of many monetary economists to Specify or to derive the trans—
mission process by which changes in the financial sector are
transferred to the real sector. Ando and Modigliani make
Specific reference to this matter2 while Harry G. Johnson has
stated that the results of Friedman and Meiselman

. . . pose an important theoretical problem since they

imply that a change in the quantity of money that has

no wealth-effect nevertheless will have an effect on

consumption even though it has no effect on interest

rates. The difficulty of understanding how this can be
prompted the dissatisfaction of Keynes, Wicksell and
other income-eXpenditure theorists with the quantity

theory, and provides the hard core of contemporary re-
sistance to it.3

2Albert Ando and Franco Modigliani, "The Relative Stabil-
ity of Monetary Velocity and the Investment Multiplier,"
The American Economic Review, LV (September, 1965), p. 716.

3Harry G. Johnson, "Monetary Theory and Policy," The
Amepican Economic Review, LII (June, 1962), p. 557.

56

In the complete model deve10ped here, the transmission pro-
cesses are eXplicitly articulated and are consequently
susceptable to empirical test. Finally, the model introduces
dynamic elements. Modern economic models have shown that

the impact effects of changes in exogenous variables are con-
siderably different than the total effects achieved over time.
These modern methods might Shed some additional light on the

relative importance of the two theories.

Friedman-Meiselman Hypothesis

Friedman and Meiselman develop their "reduced form"
models from very rudimentary examples of the income-eXpenditure
and quantity-theory models.

The development of the income—eXpenditure model is as

follows:
. = +
(5 1) Yt ct At
where Yt = income in current dollars
Ct = all induced expenditures in current
dollars
At = all autonomous expenditures in
current dollars
(5.2) Ct = a + bYt + 1.11
(3.5) At = At

from which the following is obtained:

(5.4) Ct = d + BAt + u2
_ a
where a — 1—b
_ b
and B - 1-b

ul and u2 are normal stochastic error terms with zero
mean, constant variance, and zero covariance.

The Quantity Theory model is develOped along Similar

lines:
(5.5) Ct = a + bYt + u1
(5.6) Yt - VM
from which the following is obtained:
(5.7) Ct = a + VMt + US
where a = a
and V = V'b
Mt = money stock (defined by F-M as

coin and currency in hands of
nonbank public and all commercial
bank deposits).
u3 = normal stochastic error term with
zero mean, constant variance and
zero covariance.
Each equation allegedly represents the reduced form of
a system of simultaneous equations. In addition, they are
identified and can be estimated by the method of ordinary

least squares. The estimates will be unbiased, consistent

58

and most efficient among all unbiased estimators. The test
of Significance will therefore be statistically valid, given
the stringent assumptions of the models.

It has been mentioned before that the systems of equa-
tions chosen are ambiguous from several points of view. In
the first place the two sets of equations are not mutually
exclusive.4 In constructing them in this way, part of our
knowledge is not utilized because other important theoretical
and empirical relationships are ignored or passed over. The
influence of the monetary variables on the various components
of autonomous expenditures are left out, for instance.
Secondly, they are deceptively and, in fact undesirably Simple.
For example, the consumption function in (5.2) and (5.5) is
used by very few economists in the face of recent advances in
the science, particularly those of Friedman and Dusenberry.5
Thirdly, there are probably some endogenous components on
the right hand Side of the equations that tend to bias the
estimated regression coefficients, upward for the Quantity
Theory equation and downwards for the income-eXpenditure model.

In this sense the equations (5.4) and (5.7) cannot prOperly

 

4See Appendix to Albert Ando and Franco Modigliani, "The
Relative Stability of Monetary Velocity and the Investment
Multiplier," The American Economic Review, LV (September,

1965), pp. 716-722.

 

5Milton Friedman, A Theory of the Consumption Functigp
(Princeton University Press, 1957), and James-Duesenberry,
Incomey_Saving and the Theory of Consumer Behavior (Harvard
University Press, 1949).

 

59

be regarded as reduced forms. Finally, in the face of the
additional knowledge available in the field, each model is
misspecified. Hence, there are some difficulties in statis-
tical estimation. These last two points will be discussed
more thoroughly in Chapter IV, where empirical tests are
reported.

In testing these versions of the two theories, two defi-
nitions of the money supply will be used. The first is coin
and currency in the hands of the nonbank public and demand
deposits at commercial banks; the second is the definition
of the money stock presented above, which was used by
Friedman and Meiselman.

The definition of autonomous expenditures (A) is de-

veloped in the following way:

(5.8) GNPt = ct + GPDIt + Gt + Et - ot

where GNPt = Gross National Product in
current dollars
C = consumption eXpenditures in
current dollars
GPDI = gross private domestic invest-
ment in current dollars

G = government eXpenditures on

goods and services in current

dollars
Et = exports in current dollars
0 = imports in current dollars

60

Equation (5.8) is altered in the following way:

(5-9) GNPt — Dt — Tt = ct + GPDIt e Dt + Gt - Tt + Et — 0t
= ct + NPDIt + (Gt - Tt) + (Et — 0t)
= ct + At

where Dt = depreciation in current dollars
Tt = net taxes and transfers in current
dollars
NPDIt = net private domestic investment in
current dollars
Gt-Tt = government deficit in current dollars
Et-Ot = net foreign balance in current

dollars

The income total used by Friedman and Meiselman is that
value on the left hand side of (5.9). It is the sum of in-
comes on an accrued basis and not those actually received.

In order to compare the simple income-eXpenditure approach
with the simple quantity theory approach both equations tested
must have the same dependent variable. Consequently, the

Quantity Theory equation is altered in the following way:

(5.10) GNPt — Dt - Tt = a + VMt

It should be noted that the velocity and multiplier re—
lations derived here are marginal values, whereas most
derivations of the Quantity Theory work with average values,
because it is assumed that the marginal and average are the

same.

61

In order to present tests of the possibility of hidden
influence (or joint explanation by A and M) as discussed in

Chapter II it will be necessary to also test

= +
(5.11) ct a + BAt + VMt u4

Hester's Developments

 

Hester develOped his model in a way that is very similar
to that of Friedman and Meiselman. He does not quarrel with
the Quantity Theory approach used, and therefore deals solely
with the income-expenditure approach. Using the symbols of the

second section of this chapter, Hester defines income as:

o — = _. + _
(5 12) GNPt Dt ct + (GPDIt Dt) + ct Et Ot
= +
Ct Lt
where Lt = autonomous expenditures and in this instance include

net private domestic investment, total government expendi-
tures, and the net foreign balance. Alterations are made in
this definition as Hester varies the items he considers to
be endogenous and that should not be included in the total of

autonomous eXpenditures. In particular, L; is the same as

L only imports (0t) are eliminated and depreciation (Dt) is

tl
added back into the total. L3, is the same as Lé but imports

(0t) are taken out and depreciation is left in. Lé" is the

same as Lé except that inventory investment is removed.

The definition of consumption Should be adjusted to take into

62

account the various changes in the definition of autonomous
eXpenditures. Using one of these four definitions, Hester

tested the following equation:

(5.15) ct = a1 + 51 Lt + u5

where u5 = normal stochastic error term
satisfying all the normal
assumptions of zero mean, con-
stant variance, and zero
covariance.
The reduced form for consumption will be tested over
recent data and compared directly with the result of the
test of the Friedman-Meiselman model over the same time
period. One of the primary purposes of testing the two formu-

lations over the same time period is to Show the effects of

the differences in the definitions of autonomous expenditures.

A Complete Econometric Model

In order to perform additional tests concerning the rela-
tive stability of the multiplier and the velocity of circula-
tion, it is necessary to develop a more complex model. A less
aggregated model will encounter fewer difficulties with prob-
lems of definition. An attempt can also be made with a more
complete model to identify the transmission processes from
the financial sector to the real sector and from the real

sector back to the financial sector. Also, dynamic elements

65

can be introduced into the model which can lead to a study
of the behavior of the system over time. The more complete
model can also provide additional information concerning
shifts in the structure of the economy. As Friedman and
Meiselman have noted, a reduced form cannot take account of
such shifts that occur within the complete model. These
represent just a few directions a researcher can follow in
order to test the two theoretical models more thoroughly.

In the following model, use will be made of the defini-

tions listed below:

Yt = Gross National Product

Ct = consumption eXpenditures

It = gross private domestic investment

Gt = total government eXpenditures on goods and services

Et = exports

0t = imports

Y3 = disposable income

Mt = money stock (coin and currency in the hands of the
nonbank public plus adjusted demand deposits in
commercial banks)

r: = interest rate on three-month U. S. Treasury bills

r: = interest rate on U. S. Treasury bonds

Bt = adjusted monetary base

r: = rediscount rate

t = time trend, guarterly, t = 1 on 1955-III

64

All data are quarterly, current dollar and seasonally

adjusted. »The subscript t, refers to the current quarter.

The data cover the period from the third quarter of 1955 to

the fourth quarter of 1965.

(5.14)

(5.15)

(5.16)

(5.17)

(5.18)

(5.19)

(5.20)

(5.21)

(5.22)

The exogenous variables are G

Yt

+ _
+ It Gt + Et 0t
+ a Yd + a + a M - a M + u
1 t 2 t-1 5 t 4 t-1 1t
+ 8 (c - c ) + 8 Y + 8 r1 +
1 t-1 t-2 2 t 5 t
B4t + u2t
+
71 Yt + u5t
+ T‘1_Yt + u4t
+ e r8 + 6 Y + u
1 t 2 t 5t
+ A Y + A Md + u
1 t 2 t 6t
5 d
+ 01 rt + 02 rt + 03 Bt + u7t
=Mt
E rd d B Th
t’ t' t’ an t' e uit

represent disturbance terms that are assumed to have a normal

distribution,

zero mean,

constant variance and zero covariance.

The consumption function (5.19) is derived from the

permanent income hypothesis in which consumption expenditures
)

are based upon the eXpected permanent disposable income of

the individual rather than upon current disposable income.

65

This seems to be an improvement over the one used in (5.2)
and (5.5) for it takes account of the whole Spectrum of a
consumer's horizon and can account for shifts in the short—
run consumption function that cannot be accounted for in the
simpler model of income determination.6 Money balances are
included as an argument in the consumption function.

The following is the original form of the consumption

function:

(5.25) Ct = a0 + alYEt)d + a2Mt
where YEdis permanent disposable income, which is estimated
as:

(5.24) rid = bYE + bzyf_l + . . . + bnYS_n_1 + . . .

where 0 < b < 1. Substituting this into (5.25) and applying
Koyck's transformation and then adding a disturbance term,
we get equation (5.15).

Some economists have found liquid assets or money bal-
ances to be significant in the specification of a consump-

7

tion function. Since the model is formulated in terms of

 

6Shifts in the simple consumption function generally
come from autonomous movements in the intercept term a. In
the more SOphisticated consumption function there can be
changes in the expected flow of income, which would offset
the whole consumption function, even though the relationship
with current income is not changed.

7For example, see A. Zellner, D. S. Huang and L. C. Chau,
"Further Analysis of the Short-run Consumption Function with
Emphasis on the Role of Liquid Assets," Econometrica, Vol. 55
(July, 1965), pp. 571-581.

 

66

nominal values, this is not quite the same as a real balance
effect. A statistically Significant coefficient for M would
indicate the importance of this variable but this result may
or may not be a result of the real balance effect. Some
economists do not consider an increase in money as an increase
in monetary wealth.8 They do, however, regard it as an in—
crease in the liquidity of the economy, which would have some
effect on consumer eXpenditureS. Therefore, the money stock
will serve as a proxy for liquid assets. Other economists
feel that the money supply is a component of wealth and changes
in this variable result in direct changes in monetary wealth.9
In any event, the inclusion of liquid assets can be justified
using several theoretical approaches.

Changes in the money stock could affect expenditure
decisions in two ways. First, an increase could increase the
wealth of the economic unit and, with interest rates held
constant, could increase imputed income, and, therefore, con-
sumption. 'Secondly, the increase could cause a portfolio
effect because, assuming equilibrium in the consumer's balance
sheet before the change in money balances, there would be

more money now relative to other assets. This would imply

 

8For example, see James Tobin, "An Essay on Principles
of Debt Management," in B. Fox and E. Shapiro, Fiscal and
Debt Management Policies (Englewood Cliffs, New Jersey:
Prentice-Hall, 1965), p. 148.

9Boris P. Pesek and Thomas R. Saving, Money, Wealth, and
Economic Theory_(New York: The Macmillan Co., 1967).

(tr

he

0;

,.
.-

(D

"r1

(f

'r_1

l' 1..

(I)

67

that other uses of the unit's assets would provide the con—
sumer with a greater return. If one or both of these

effects were to occur it would tend to alter behavior leading
to an adjustment of the portfolio and a purchase of alterna—
tive assets. The economic unit would tend to buy more
financial assets, more durable goods, and more nondurable
goods, in an effort to return to an equilibrium position.
This would be achieved when the rate of return on each type
of asset, for a given risk class, is the same. A change in
wealth, although it is not included eXplicitly here, which
caused a wealth effect, could take place with no change in
interest rates or it could take place with a change in inter-
est rates and no change in expected income.

In light of the quotation made by H. G. Johnson above,
the testing of an equation such as this could help to deter-
mine whether the wealth effect, as supported by Milton
Friedman,.does actually occur and whether the transmission
from monetary variables to real variables can take place in
the consumer sectors. However, it is doubtful whether this
particular form of the consumption function can discriminate
between the quantity theorists and the economists who ad—
vance the liquidity preference theory. If as and/or d4 are
significant and possess the correct signs, then this is
actually consistent with both theories.

Investment eXpenditures, in this model, are determined

by the level of income, the level of interest rates, and the

68

change in consumption eXpenditures. The level of income acts
as an inducement to invest. It would be eXpected that busi-
nessmen would be influenced not only by how fast sales are
increasing but also by the level of income and output.
Whereas business firms base their planned expenditures on the
expected future level of receipts, investment demand would be
influenced by the level of economic activity. The level of
income is thus expected to help eXplain aggregate investment
demand.

Since future receipts are unknown, particularly for the
economy as a.whole, a variable is needed to reflect the di—
rection of these future receipts and also the rate at which
they are changing. The change in consumption eXpenditures
provides a proxy. Changes in sales also provide some informa-
tion on the unintended accumulation or depletion of inven—
tories. Changes in consumption expenditures seem to be a
better indicator of future receipts than changes in physical
output. .This is because changes in consumption eXpenditures
are more closely linked to the future receipts of final sales
and through them exert a pull on future receipts of all other
types of expenditures.

The level of interest rates represents to some extent
the cost of capital to business and thus is a vital figure in
investment decisions. The time trend, t, is included in the
investment function to allow for induced technological

progress.

69

Government expenditures are assumed to be exogenous
inasmuch as the level of these expenditures is determined
outside of the system. There appears to be little or no
induced component in government expenditures, for these are
based more upon political considerations than the current
level of activity in the economy.

Tax collections and transfer payments present a differ-
ent situation. In the long run, these items could be con-
sidered exogenous to the system. Theoretically any level of
the collections of payments could be obtained if the politi-
cal units that had responsibility for levying taxes maneu—
vered tax rates which are totally exogenous so as to achieve
their desired goal. This would imply that the political
unit possessed the necessary information about the economy in
order to adjust tax rates instantaneously to obtain the de—
sired tax aggregates. In turn this would imply that the
political unit had sufficient knowledge of the structure of
the economy. That is, they have an adequate model which
represents the economy and have knowledge of the structural
parameters so that any adjustment they make would have the
predicted effect. It is generally believed that these con—
ditions are not met. The political units seem to possess
fairly wide latitude to set tax rates and to determine the
structure of tax collections, but they do not have the neces-
sary information concerning present and future changes in the

economy, nor the knowledge of the structure of the economy,

70

nor the capability of adjusting the tax structure instan-
taneously. Once a given tax structure is determined, actual
tax collections clearly depend upon the level of economic
activity, at least in the short run: as the level of
activity rises, tax collections rise.

A related problem is that the government has a budget
restraint in the longer run.10 That is, it must finance a
deficit in one of three ways. It must collect taxes, make
additions to the monetary base by either the printing press
or selling bonds to the central banks, or by selling bonds
to the private sector of the economy. This can be formu-

lated as follows:

(5.25) Gt = Tt + A Bt + xt
where Tt = taxes collected
ABt = change in the monetary base
X = new Government issues sold to

private sector

Only three of these are independent. The fourth must be
endogenous. Consequently, in the longer run, it might be

necessary to consider the financing of the Government's

 

10Carl F. Christ, "A Short-run Aggregate-demand Model
of the Interdependence and Effects of Monetary and Fiscal
Policies with Keynesian and Classical Interest Elasticities,"
The American.Economic Review, Vol. LVII (May 1967), pp.
454-445 and Carl F. Christ, "A Simple Macroeconomic Model
with a Government Budget Restraint," The Journal of Political
Economy, Vol. 76 (January-February .1968), pp. 55-67.

71

deficit. This is the conclusion drawn by Friedman and
Meiselman for a period as long as one year.

In the short run, however, this is not a necessary con—
dition. That is, several of the decisions are determined
endogenously. For example, tax payments are made at the
initiative of the tax payer, if he pays before a given tax
date. Whereas, over the whole year taxes may be exogenously
determined, in one quarter they are not. Also, the distribu-
tion of the deficit between B and X may not be eXplicitly
determined in any one quarter, whereas over the full year it
must be.

Therefore, in a quarterly model, such as the present
one, it will be assumed that only Government eXpenditures
are exogenous. This is consistent with the belief Friedman
and Meiselman have eXpressed that Government eXpenditures
and not the Government deficit is the relevant variable for
a short-run model.11

The development of equation (5.17) is as follows:

d _
(5.26) Yt — Yt TX + Tr D CP SI -IV

where TX = taxes

T

r transfer payments

 

11Milton Friedman and David Meiselman, "The Relative
Stability of Monetary Velocity and the Investment Multiplier
in the United.States, 1897-1958," in B. Fox and E. Shapiro,
Stabilization Policies (Englewood Cliffs, New Jersey:
Prentice—Hall, 1965), p. 204.

72

‘D = depreciation
CP = corporate profits

social insurance collections

SI

IV inventory evaluation

Since all these variables are taken to be endogenously de—
termined in the short run, they can be assumed to be a func-
tion of the current level of Gross National Product.

Consequently, (5.26) can be reduced to (5.17) by

(5.27) Y

d
t t

= Y + f(Yt) = 70 + 71 Yt

Exports are considered to be exogenous because the de-
cision to purchase goods from the economic system under con-
sideration are based upon variables that are determined
primarily outside of this system. Imports, in the short run,
are determined within the system. Over time imports must
equal exports. That is, a country must pay, in terms of
eXports, for the goods it purchases from other countries.
.In the short run this is not necessary. Therefore, it is
generally considered that in a quarterly model, increases in
income will lead to increases in imports.

Equation (5.19) represents the term structure of inter-
est rates. As expressed, the long—term rate, in this
.instance the rate on long-term U. S. Treasury bonds, is a
function of the three-month U. S. Treasury bill rate and the

current level of GNP. The short-term rate is partially

75

determined in the money demand and supply equations to be
discussed below. The primary movements in the short-term
rate represent changes in monetary variables. The current
level of GNP also affects the long-term interest rate posi-
tively. An increase in economic activity will increase the
demand for loanable funds, which will cause upward pressure
on the long-term interest rate. In a rough way, current
dollar GNP is a proxy for the influence of productivity on
interest rates as espoused by neoclassical economists.

Money consists of coin and currency in the hands of
the nonbank public and adjusted demand deposits at commercial
banks. The primary function of money is to serve as a medium
of exchange. No other asset, at the present time, fulfills

this function.12

Money can serve as a store of value, and
certainly does provide this service to economic units holding
assets in this form. However, money derives its function
as a store of value by virtue of its function as a medium of
exchange. Any broader definition of money obtained by
§_priori reasoning or by empirical tests can result only in
an arbitrary listing of assets, which could be extended in—
definitely.

It is also true that any other listing of assets would

give money the prOperty of being relatively more interest

inelastic. Any variation in interest rates would lead to

 

12Pesek and Saving feel that Traveler's checks should
be included in this category. See op. cit., p. 255.

74

relatively smaller changes in individuals' demand for money.
Such a definition of money would bias empirical results in
favor of a theory which favored the use of the quantity of
money in circulation.13 In the familiar Hicks-Hansen IS-LM
formulation, it would result in the LM curve being fixed at
one level of income. Changes in the money supply would be
the only way for an economy to alter its level of activity.

.The demand for money (in this instance the interest
rate determination function) is taken as a function of cur-
rent income and the current level of interest rates. The
form presented in (5.20) is necessary for testing purposes
and can be interpreted in either of two ways. Representing
the demand for money as an asset the equation shows interest
rates as the Opportunity cost of holding money. The higher
the rate of interest, the greater the cost of holding any
given amount of money. The level of current income affects
the transactions that individuals wish to undertake. A rise
in income will increase the demand for money at each inter-
est rate.

A second way of interpreting equation (5.20) is to show
that the level of interest rates is determined by influences
from both the real sector and the financial sector. Whereas,
an increase in the money supply would increase loanable funds,

for a given level of income and consequently lower interest

 

13Boris P. Pesek, "Money versus Autonomous Expenditures:
The Quality of the Evidence," Business Economics, III
(Spring.1968), pp. 29-50.

75

rates, and increase in income, for a given level of the money
stock, would raise interest rates by increasing the demand
for loanable funds.

The money supply represents a problem Similar to that
of tax collections and transfer payments. Theoretically, it
could be set at any desired level by the central banking
authorities, and thus could be considered an exogenous vari-
able. Yet for pure exogeniety, the central banking authority
must have knowledge of the economic structure and of the way
in which the policy variables over which it has control work
through the structure. .The banking authority must also be
able to predict what will occur as changes in these variables
take place. These conditions, as in the case of tax collec-
tions, are generally not met.

A useful way to develOp a money SUpply model is as

follows. The money supply is defined as:

(5.28) M =c +D

S
s
m
H
m
0
ll

coin and currency in the hands

of the nonbank public

U
ll

adjusted demand deposits at
commercial banks

The adjusted monetary base is:

(5.29) B =c +R

where Rt = total bank reserves less member

bank borrowing

76

'Dividing (5.28) by (5.29) and rearranging, we get:

 

(5.50) Mt = Ct R

 

where Ct/Dt is called the currency-deposit ratio and Rt/Dt
is called the reserve-deposit ratio. As it now stands (5.50)
is an identity. However, behavioral relations can be intro-
duced that can transfer the equation into a stochastic
equation.

Ct/Dt can be affected by many things. As yet, however,
it has been difficult to quantify the determinants of this
behavioral relationship. One could assume, for instance,
that this ratio will tend to be lower when the economy is
very active. ~Since interest rates usually rise in periods of
high activity, interest rates could be used as an explanatory
variable in a behavioral equation. This is a tenuous conclu-
sion and, therefore, will not be relied upon. A closer rela-
tionship can be derived in the case of the reserve-deposit
ratio.

The reserve-deposit ratio tends to fall as interest
rates rise. Teigen feels that the relevant variable in a
money supply function is the difference between some interest

4

rate and the rediscount rate.1 As the Spread increases,

 

‘14Ronald L. Teigen, "The Demand for and Supply of Money,"
in W. L. Smith and R. L. Teigen, Readings in Money, National
Income, and Stabilization Poligy (Homewood, 111.: Richard D.

Irwin, 1965), p.'62.

77

banks squeeze their excess reserves, and so for a given level
of the adjusted monetary base the money supply will be larger.
Since the interest rate may also affect the currency-deposit
ratio the equation tested will use the level of an interest
rate and the level of the rediscount rate, rather than their
difference. The hypothesis that the difference matters
rather than the level can be tested from the form of equation
(5.21). If 01 and 02 are not significantly different from
one another in absolute value but do possess opposite signs,
this would tend to support the hypothesis that the difference
could be used rather than levels. Three-month Treasury bills
are used as a proxy fOr other interest rates because, being
Short-term and generally risk free, they represent the anchor
of the whole spectrum of interest rates.

The adjusted monetary base is assumed to be the variable
truly under the control of the central banking authorities.
Member bank borrowings are excluded from the base because
they are undertaken at the initiative of commercial banks
and not at the initiative of the central bank. Consequently,
since commercial banks supposedly have a reluctance to borrow
at the central bank, they will adjust their behavior to non-
borrowed reserves rather than total reserves. The rest of
the base is determined at the will of the monetary authori-
ties. They determine how the base is used even though the

source of the base represents some endogenous components.15

 

lsKarl Brunner and Allan H. Meltzer, "Rejoinder to Chase
and Hendershott," in G. Horwich, Monetarerrocess and Policy:
A Symposium (Homewood, Ill.: Richard D. Irwin, 1967), p. 577.

78

Therefore, the adjusted monetary base and the rediscount
rate will be taken as the variables that are truly exogenous

and representative of monetary policy in the short run.

CHAPTER IV

ADDITIONAL TESTS OF VARIOUS SINGLE-
EQUATION SPECIFICATIONS

Introduction

Although the discussion of the Friedman-Meiselman work
has covered a wide range of topics, several additional
areas need to be eXplored in greater depth. This chapter
attempts to go into these areas. Also, a few topics, which
have been discussed earlier, such as the problem of simul-
taneous equation bias, will be brought up again. Most,
however, have either been ignored or forgotten, such as the
problem of autocorrelation and the use of the narrow measure
of the money supply.

Results are presented which provide tests for the same
period used in computing the complete model develOped in
Chapter III. This can allow for the comparison of the re—

sults of the full model with the naive models.

Tests Concerning the Friedman-Meiselman Hypothesis

Generalgproblems
In the process of recalculating regressions using the

Friedman-Meiselman data, two omissions on their part became

79

80

quite evident. The first pertains to the reporting of the
data, while the second pertains to the data itself.

.In the first place standard errors are reported for
exogenous variables only in equations where more than one
variable is being tested. This would seem to imply that
the variable in question always had a coefficient that was
significantly different than zero. However, this is not
quite the case.

In discussing this point, the autonomous expenditures
variable will be examined. Thirteen regressions are run
.where consumption expenditures (C) is regressed just on
autonomous eXpenditures (A), using annual data. Of these,
the coefficient of autonomous expenditures is not signifi-
cantly different from zero at a 5% level of significance in
four instances. Therefore the coefficient for autonomous
expenditures is not significantly different from zero roughly
one-third of the time.

A frequently encountered problem which relates to the
value of the standard error is autocorrelation. If autocorre-
lation is present in any equation, the use of ordinary least
squares will provide estimates that are inefficient, and in
addition the computed standard errors will be biased down-
ward. All thirteen equations show evidence of autocorrelation
at the 5% level of significance. This means that the true
standard errors are underestimated. If this is the case,

there exists strong possibility that several more coefficients

81

are insignificant. Results presented in Appendix A Show the
effects of one method of correction for autocorrelation in
these regressions. From these results it appears that in
over half of the equations tested, the coefficient of the
Friedman-Meiselman definition of autonomous expenditures,
where used as an eXplanatory variable for consumption expendi-
tures, is not Significant. The failure to publish standard
errors certainly leads to a false impression as to the impor—
tance of the autonomous variable. It also leads to some ques-
tion concerning the definition used and also the ability of
the definitional test proposed by Friedman and Meiselman to
discriminate correctly the relevant components of a variable.
(These results, however, carry over to all the regres-
sions. In total, fifty-two regressions are run in which
autonomous expenditures is a regressor, either separately or
combined with other explanatory variables. In thirty-three
of these fifty-two runs the coefficient of autonomous expendi-
tures has either the wrong Sign or has a coefficient that is
not significantly different from zero or both. Again, auto-
correlation is present in most cases and if the equations
are corrected for its presence there is strong possibility
that several more coefficients will be insignificant. This
would mean that the Friedman-Meiselman concept would either
be not significantly different from zero or possess the
wrong sign in about seventy-five per cent of the time periods
tested. It is questionable whether this equation is capable

of being compared with the money supply equation.

82

In the case of the money supply, the coefficient is not
significantly different from zero only ten times out of the
seventy-eight periods tested. The standard error was cor-
rected for autocorrelation in these equations also. The
results are presented in Appendix A. The number of insignifi—
cant coefficients increase somewhat but are still approxi-
mately only 15 per cent of the cases. Thus, it appears that
Friedman and Meiselman test a variable that is of significant
value most of the time against a variable that is insignifi-
cant most of the time.

The other difficulty is that different data were used
over the time period of the study. The regressions up to
and including 1929 use a different set of data than those
used in the regressions from 1929 to 1958. In the former,
consumption outlays were taken from unpublished figures
develOped by Kuznets for the National Bureau of Economic
Research. Autonomous expenditures were computed from Raymond

Goldsmith's A Studyyof Saving_(Vol. I). Data for the 1946-

 

55 period came from the Survey of Current Business (July
1959). The money supply figures came from data develOped by
Friedman and Schwartz for the National Bureau of Economic
Research. The implicit price deflator for consumer outlays
came from.Kuznets.

For the regressions covering the period from 1929-1958
a different set of data were used. Consumption eXpenditureS

came from the Survey of Current Business (July 1959).

85

Autonomous expenditures came from the 1954 edition of
National Income and also the Survey_of Current Business
(July 1959). .Money supply data came from Friedman and
Schwartz. The implicit price deflator of personal consump-
tion expenditures for the Department of Commerce came from
the 1958 edition of U. S. Income and Output supplemented by
the Survey of Current Business (July 1959).

It is understandable that more than one source of data
would be used in compiling a long time series such as the
one under review here. It would appear more appropriate,
however, if tests had been reported for the complete series
of 1897 to 1958 and the Commerce series of 1929-1958.
Although this may cause only little difference in the re-
ported regressions, Friedman and Meiselman give no indica-
tion that the results have been derived from two sets of

data.

Definitional tests

 

The test used by Friedman and Meiselman to determine
the composition of the money supply and autonomous expendi-
tures has caused a considerable amount of discussion. This
test appears to be of doubtful validity. It was assumed
(see above pages 21-24), that if an item was autonomous,
that a shift of one dollar between this item and other auton-
omous items would not affect consumer eXpenditures (or induced
eXpenditures). If this were true, Friedman and Meiselman

hypothesize that the correlation between the sum of the two

84

autonomous components and induced expenditures should be
greater than the correlation between each component indi—
vidually and induced expenditures. In terms of the example
used in Chapter II,

r

(4.1) rN(D + A) >. ND

and

NA

 

where N is eXpenditures on nondurable consumer goods. D is
expenditures on durable consumer goods and A is what has
already been determined as autonomous. To examine this re-

sult further we need to examine the correlation coefficients.

= cov N(D + A)

(4.2) r
N(D + A) Jvar N Jvar D+A

cov N (D + A)
Jvar N Jvar D+ var A+ 2 cov DA

 

if D and A are both autonomous and independent, then cov
DA = 0. If not, then it would be expected, on an §_priori

basis, that this value would be positive, i.e., cov DA:>0.

 

Also,
(4.5) rN A = cov N,A
’ Jvar N’ 4var A
and
(4.4) r = CO" N1”

 

N’D Jvar N ~/var D

85

Taking one of the possible cases, any of the following

conditions might hold:

 

 

 

(4 5) cov N (D + A) >/< cov N,D
Jvar N Jvar (D+A) Jvar N Jvar D

The necessary condition for (4.1) to be satisfied is
that cov N (D+A) > cov N,D. It is not sufficient, however,
because var (D+A) > var D. This is true whether D and A are
autonomous and independent or not. Thus, it can be seen,
COV’N (D+A) might be greater than cov ND but condition (4.1)
would not be satisfied.

If var A is small and either cov DA is zero or small
then this might not be too serious a problem. However,
autonomous expenditures are presumed to be quite erratic and
would therefore have a relatively large variance. If this
were so then the cov N (D+A) would have to exceed cov ND
by a considerable amount in order for the condition (4.1)
to be satisfied. Thus, it would appear that the test prOposed
by Friedman and Meiselman has very little power to discrimi—
nate between autonomous and induced expenditures.

Looking at the second case, the necessary condition
that must be satisfied is cov N (D+A)‘>>cov NA. The same
conclusions hold here as in the former case. Carrying this

even further, it can easily be shown that cov N (D+A) =

86

cov ND + cov NA.1 We would expect on an §_priori basis

that cov NA > 0. An increase in autonomous eXpenditures
would lead to an increase in income, which would bring forth
an increase in expenditures on nondurable consumer eXpendi-

tures. Thus,

(4.6) cov N (D+A) = cov ND + cov NA >/< cov ND
which implies

(4.7) cov N(D+A) > cov ND

since cov ND and cov NA are always positive. If D is auton-
omous then it would be expected that cov ND ) 0 and the
necessary condition would be satisfied. If D is induced,

the Sign will also be positive. Also,

(4.8) cov N(D+A) = cov ND + cov NA >/< cov NA
which implies

(4.9) cov N(D+A) > cov NA

since cov ND and cov NA are always positive.

 

1The covariance of two variables x and y is equal to
E [x-E(x)] [y-E(y)] where E is the expected value. Assume
that y = a + b. Then
Elx-E(x)] [y-E(y)] E[x-E(x)] [a+b - E (a+b)]
E [x-E (x)] [a+b - E (a) - E (b) ]
E [x-E (x)] [(a-E (a) ) + (b-E (b) )]
E{ [x-E (x)] [a-E (a) ]+ [x-E (x)] [b—E (b) J}
E [x-E (x)] [a-E (a) ]+E [x-E (x)] [b—E (b) ]
covariance (x,a) + covariance (x,b)

87

If there is an increase in autonomous expenditures then
induced expenditures will increase, via the multiplier.
.Since, in this case, both nondurable goods and durable goods
are induced, both will rise. Hence, cov ND > 0. If auton-
omous expenditures decline, then eXpenditures on both non-
durable goods and durable goods will fall. As a result,
cov ND will again be positive.

The necessary condition will always be satisfied.
However, it still will not be possible to tell whether dur-
able expenditures are induced or autonomous. Thus, the
Friedman-Meiselman test fails to discriminate between various
components of a variable. A similar analysis can be made of

the determination of the money supply variable.

The narrow defipition of the money supply

Since the Friedman-Meiselman test resulted in the se-
lection of the broad definition of the money supply, no
computations were made with the narrow definition of the
money supply. .Many economists feel that the narrow defini-
tion is the one to be preferred on both theoretical and
empirical grounds.2 However, time series data are not avail-
’able for this variable going back as far as 1897. The

longest series of annualdata is that prepared by Friedman

 

2Boris P. Pesek and Thomas R. Saving, Mongy, Wealth
and Economic Theory (New York: The Macmillan Co., 1967)
and Edgar L. Feige, The Demand for Liquid Assets: A Temp-
ppgl Cross-Secpion Analysi§_(Englewood Cliffs, N.J.:
Prentice-Hall, Inc., 1964).

 

88

andewartz for the National Bureau of Economic Research.3

The series begins in 1915 and continues to 1946. This series
is consistent with the series published by the Federal
Reserve which begins in 1947 and continues to the present.
Computations were made with the available data, substituting
the narrow measure of the money supply for the broad defini-
tion. .This would allow for a direct comparison of the two
measures of the money supply. These results are presented

in Tables 4-1, 4-2, and 4-5.

The results of the regressions Show that if consumption
is the dependent variable, the broad measure of the money
supply is the more stable relation in seven periods of the
eight tested. However, in five of the seven, there was a
difference of less than .017 in the coefficient of correla-
tion in any one period. If current dollar Gross National
Product is used as the dependent variable then the broad
measure has the higher coefficient of correlation in only
four of the eight cases. Five times out of the eight periods
tested, the coefficients are within .012 of each other.

It would appear to be a tenuous conclusion that one measure
of the money supply bears a closer relation with either
consumption expenditures or current dollar Gross National

Product than the other.

 

3U. S. Department of Commerce, Long Term Economic
Growth: .1860—1965 (Washington, D. C.: U. S. Government
Printing Office, 1966), pp. 208—8.

89

 

 

 

 

TABLE 4—1. Test Using Broad Definition of Money SUpply:
First Set of Friedman—Meiselman Data*
' d C t t T M R
Perio one an erm 2t D.W.
A. Ct - n + 7M2t
1920-1929 - 15290.2 1.557 .968
( .124) 2.199
1921-1955 527.952 1.665 .897
' ( .248) .605
1929-1959 - 2496.75 1.596 .920
( .226) .704
1955-1958 5051.56 1.594 .991
( .095) 2.995
1958-1955 - 1455.14 1.280 .959
( .101) .256
1959-1948 18165.6 .996 .964
( .097) .667
1929-1958 - 591.400 1.567 .976
( .058) .157
1948-1957 -151920. 2.201 .990
( .112) 1.026
B. Yt - n + 7M2t
1920-1929 15505.6 1.618 .955
( .220) 2.265
1921-1955 - 20522.8 2.525 .810
( .508) .596
1929-1959 - 55187.5 2.572 .906
( .570) .705
1955-1958 - 19582.4 2.006 .988
( .155) 2.552
1958-1955 7800.81 1.585 .964
( .102) .504
1929-1948 50921.7 1.089 .958
( .116) 1.047
1929—1958 - 2410.52 1.545 .982
( .056) .565
1948-1957 -142404. 2.418 .987
( .140) 1.202

 

*Standard errors are listed below estimated coefficients.

R is the coefficient of correlation.
‘D.W..is the Durbin-Watson statistic which is listed

directly below the coefficient of correlation for every

time period considered.

90

TABLE 4-2. Tests Using Broad Definition of Money Supply:
Second Set of Friedman-MeiselmanwData*

 

 

 

. R
Period Constant Term M2t D.W.
A. Ct - n + yMZt

1929-1959 - 945.465 1.527 .912
( .229) .629

1955—1958 7256.61 1.505 .990
( .090) 2.959

1958-1955 - 2457.40 1.262 .958
( .101) .255

1959-1948 17458.1 .976 .964
( .096) .668

1929-1958 - 1198.28 1.551 .974
( .059) .152

1948-1957 -140040. 2.250 .990
( .115) .986

B. Yt = n + yMZt

1929-1959 - 22251.5 2.080 .915
' ( .506) .766

1955-1958 - 10104.7 1.765 .984
( .158) 2.060

1958-1955 4818.41 1.402 .966
( .101) .427

1959—1948 28995.8 1.092 .967
( .102) 1.054

1929-1958 - 5650.20 1.545 .985
( .054) .524

1948-1957 -159876. 2.599 .986
‘ ( .144) 1.128

 

*

Standard errors are listed below estimated coefficients.
R is the coefficient of correlation.
.D.W. is the Durbin—Watson statistic which is listed
directly below the coefficient of correlation for every
time period considered.

91

 

 

 

TABLE 4—5. Using the Narrow Definition of the Money Supply*
Period Constant Term M R
1t D.W.
A. Ct n + yMlt
1920-1929 - 16825.1 5.552 .945
( .440) 1.767
1921-1955 - 50988.9 4.085 .958
(5.67 ) 1.291
1929-1959 20711.5 1.624 .706
( .545) .550
1955-1958 11955.8 1.856 .989
( .155) 2.844
1958-1955 5552.90 1.589 .950
( .159) .256
1959-1948 25598.6 1.225 .955
( .155) .604
1929—1958 9822.54 1.710 .958
( .096) .120
1948-1957 -215486. 5.555 .978
( .267) .825
B. Yt — n + yMlt
1920—1929 - 28742.0 4.575 .945
( .558) 1.902
1921-1955 - 72295.8 6.045 .917
( .795) .627
1929-1959 1559.0' 2.405 .692
( .855) .572
1955-1958 9559.82 2.645 .988
( .205) 2.842
1958—1955 15790.5 1.755 .964
( .129) .482
1959-1948 54645.2 1.566 .968
( .126) 1.150
1929-1958 8280.29 1.942 .971
( .091) .220
1948-1957 -254592. 5.924 .980
( .281) 1.026

 

*Standard errors are listed below estimated coefficients.

R is the coefficient of correlation.
D.W. is the Durbin-Watson statistic which is listed

directly below the coefficient of correlation for every

time period considered.

92

These results actually coincide with those reported
by Friedman and Meiselman. A part of their Appendix, Table
II-A-1 is reported in Table 4-4.4 Three points, however,
should be noted. First, except for the 1929-1959 period,
their dates do not conform to those used in this thesis.
Second, the data for M1 are taken from Federal Reserve
Statistics whereas the ones used in this study are those
computed by Friedman and Swartz for the period 1915-1946.
Third, Friedman and Meiselman also use quarterly data to
support their conclusions. The reported differences are
very small except for the 1929-1959 period. It has been
shown, however, that there are some periods whenM1 per-
formed considerably better than M2' Even the regressions of
(M2 - M1) on Y2 do not conclusively support the use of M2
as Friedman and Meiselman claim they do.

One additional result can be obtained from these data
that was not expected. In Table 4-5, the marginal velocity
for the narrow definition of the money supply in both parts
A and B are relatively high in the 1920-1929 period and the
1921-1955 period. This value decreased tremendously after
that time period. Economists eXplain this fall in the mar-

ginal velocity as a shift in the demand curve for money.

 

4Milton Friedman and David Meiselman, "The Relative
Stability of Monetary Velocity and the Investment Multiplier
in the United States, 1897-1958," in B. Fox and E. Shapiro,
Stabilization Policies (Englewood Cliffs, N. J.: Prentice-
Hall, 1965), p. 244.

95

TABLE 4-4. Results Shown in Friedman-Meiselman Appendix
Table II-Aél. Coefficient of Determination is
Shown.

 

 

I. Annual Data 1929-1959

1 2
Y2 .512 .855
II. Annual Data .1940-1952
M1 M2
Y2 .882 .886
III. Annual Data 1929-1952
M1 M2
Y2 .955 .958

IV. Quarterly Data 1946—1958

M1 M2

YZ .956 .957
V. Quarterly Data .1946-1950

M1 M2

Y2 .654 .779
VI. Quarterly Data 1951-1958

M1 M2

Y .899 .950

 

94

Some feel that it was this shift in individual preferences
that helped account fOr the depression of the 1950's. Any
action on the part of the monetary authorities would have
to more than compensate for this, if the central bank were
to stimulate economic activity.

Observing the results using M2 in Tables 4-1 and 4-2,
however, it is apparent that the large decline in the mar-
ginal velocity did not take place. There was a decline
that took place over the whole decade of the thirties, but
this appears to be more of a longer—term nature. Therefore,
if one used M2 as the measure of the money supply, and if
the Quantity Theory represents a "valid" view of economic
activity, then the decline in economic activity in the
1950's occurred primarily as a result of Federal Reserve
activity and not as a result of a Shift in individual pref-
erences.

One can conclude from the results presented in this
section that there is little reason to say that the broad
measure of the money supply moves more closely with either
consumption expenditures and/or current dollar Gross National
Product than does the narrow definition of the money supply.
However, the measure one chooses can drastically alter the

conclusions one can infer from the data.

Periods which include the Second World War
It has been noted above that Friedman and Meiselman

felt that the years of the Second World War should not be

95

excluded from the tests. Although values of individual
coefficients did change during the war period, Friedman

and Meiselman contend that the results were consistent with
pre- and post-war results. This is especially true of the
money supply equations. However, the number of items that
become insignificant during this period raises a question
as to the validity of including these data.

For example, in the two periods that closely Span the
Second World War only the consumer price index is consis-
tently significant at a 5% level of significance. This is
Shown in Table 4-5. The Friedman—Meiselman definition of
autonomous expenditures is never significant in these two
periods. The broad measure of the money supply is signifi-
cant only when it is the single regressor or when it appears
with autonomous expenditures only. Any time the consumer
price index appears, it dominates the other two variables
and is the only variable that possesses a coefficient sig-
nificantly different from zero.

It would seem that during World War II there definitely
was a change in the structure of the economy. It is cor-
rect to imply that the results obtained during this time
period are consistent with the results obtained either be-

fore or after the war.

96

TABLE 4‘5- Friedman-Meiselman Results During War Years.

Second Set of Data*

 

 

 

 

Constant R
Dependent Term At M2t PCt D.W.
A. 1958—1955
(1) ct 1257.18 - .509 1.555/ .965
( .407) ( .114) .515
(ii) ct 96779.7 1.865 .598
( 1.151). .140
(iii) ct - 2457.40 1.262/ .958
( .101) .255
(iv) ct -105819. - .555 -.199 5714.40/ .966
( .181) ( .215) ( 502.44) .427
(V) et - 95482.5 - .576 2558.77/ .995
( .175) ( 118.252) .895
(vi) ct -111687. -.295 5855.01/ .995
( .225) ( 542.615) .628
(vii) Yt 4818.41 1.402/ .992
( .101) .025
(viii) Yt — 94185.4 —.009 5475.27/ .988
( .290) ( 697.025) .550
B. 1959—1948
(1) ct 22696.6 - .425 1.029/ .975
( .255) ( .090) .969
(ii) ct 102058. .494 .175
( .994) .156
(iii) ct 17458.1 .976/ .964
( .096) .668
(iv) ct - 56647.2 - .415 .156 2491.67/ .967
( .067) ( .095) ( 257.252)1.054
(v) ct - 67558.1 - .599 2848.61/ .999
( .071) ( 68.871)2.020
(vi) ct - 64675.7 .052 2594.57/ .998
( .256) ( 642.407)1.959
(vii) Yt 28995.7 1.092/ .989
( .102) .865
(viii) Yt - 45227.0 .257 2545.51/ .984
( .525) ( 881.878) .755

 

*-
Standard errors are listed below estimated coefficients.

R is the coefficient of correlation.
D.W. is the Durbin-Watson statistic which is listed directly
below the coefficient of correlation for every time period

considered.

,7

the five percent level.

The regression coefficient is statistically significant at

97

Additiongl;single equation tests-—1955-1965

In order to have results of the single-equation tests
that are comparable to the results obtained in the complete
model, regressions were run over the same time period as
the complete model using the definitions of Friedman and
Meiselman and those of Hester. The regressions were run
using both annual data and quarterly data. The regressions
using quarterly data were divided Up into five subperiods
that correSpond to the criteria for dating set up by Friedman
and Meiselman. That is, subperiods were obtained by using
turning points in the business cycle as determined by the
National Bureau of Economic Research. The dates of troughs
relevant for this study are the third quarter of 1954, the
second quarter of 1958 and the first quarter of 1961. Peaks
intermittent between these dates are the third quarter 1955,
the third quarter 1957 and the second quarter 1960.

The simple least squares estimates of the equations us-
ing annual data are presented in Table 4-6. Data are in
current dollars.

Once again the Friedman-Meiselman definition of auton-
omous eXpenditure performs worse in terms of its correlation
with consumption eXpenditures than does the money supply.

In this case, the results can be compared with either the
narrow definition of the money supply (M1) or the broad
definition (M2). ~When the consumer price index is included,

the regression that includes the money supply is more closely

98

TABLE 4-6. The Effects of Various Exogenous Variables on
Consumption EXpenditures: Annual Data 1954—1965*

 

 

A. Friedman-Meiselman Variables

ct = 18.020 + 8.009 At R = .874
(1.411) D.W. = .805
(2.819)
ct = -570.521 + 5.175 At + 7.654 p t R = .994
( .491) ( .576) C D.W. = 2.181
ct = -18.562 + 1.545 M2t R = .985
(0.86) D.W. = .526
( .259)
ct = -527.555 + .967 M2t + 4.512 Pct R = .998
(.092) (.628) D.W. = 1.894
B. Narrow Definition of the Money Supply
ct = -579.475 + 6.295 M1t R = .984
(.556) D.W. = .955
(.584)
ct = -678.507 + 5.942 M1t + 4.511 Pct R = .997
(.415) (.694) 0.w = 1.578
(.562) (.945)
C. Hester's Definitions
ct = 17.469 + 2.201 L1t R = .991
(.095) D.W. = 1.056
(.150)
ct = -247.998 + 1.517 L1t + 5.562 Pct R = .999
(.104) (.505) D.W. = 1.056
ct = 25.156 + 1.451 L R = .996
(.042) 2t D.W. = 1.567
(.057)
ct = -159.029 + 1.155 L2t + 2.460 Pct R = .999
(.080) (.592) D.W. = 1.575
ct = 26.949 + 1.625 L5t R = .995
(.049) D.W. =. 1.200
(.074)
ct = -168.984 + 1.251 L3t + 2.610 Pct R = .999
(.090) (.594) D.W. = 1.457

continued

99

TABLE 4-6-wcontinued

 

 

C.

Hester's Definitions (cont'd)

C

C

t

t

= 15.514 + 1.724 L4t R = .997
(.042) D.W. = 1.120

(.066)
= -108.569 + 1.466 L4t + 1.682 Pct R = .998
(.124) (.769) D.W. = 1.545

 

*

Standard errors are listed below estimated coefficients.
R is the coefficient of correlation.

-D.W.
ly below the coefficient of correlation for every time
period considered.

Second figure in parenthesis under estimated coefficient is
the standard error of the coefficient corrected for autos
correlation as described in Section F of this chapter.

Ct

At

Pct
1t

3

2

2t
1t

fl

2t

t
4t

is the Durbin-Watson statistic which is listed direct-

Consumption expenditures.

Net private domestic investment plus the government
deficit on income and product account plus the net
foreign balance.

Consumer price index.

Currency in public circulation plus adjusted demand
deposits.

M1t + time deposits in commercial banks.

Net private domestic investment plus total government
eXpenditures plus net foreign balance.

Gross private domestic investment plus total govern-
ment expenditures plus eXports.

L2t minus imports.

L minus inventory investment.

2t

100

correlated with consumption than the regression that utilizes
autonomous expenditures, although the differences are only
marginal.

The results are somewhat different when the money supply
equations are compared with the equations that contain
Hester's definitions of autonomous expenditures. In every
case, Hester's definitions are more closely correlated with
consumption than is either the narrow or broad definition of
the money supply. This remains true when the consumer price
index is added. It should be noted, however, that the dif-
ferences are not large.

In the fourteen equations tested, six show positive
signs of autocorrelation at a 5% level of significance accord-
ing to the Von Neuman-Hart statistic: All the parameters
have coefficients that are at least four times their standard
error. When the standard errors are corrected in the manner
described below,all parameters remain significantly different
from zero.

On the basis of looking at the single-equation tests on
annual data one could conclude that the definition of
"autonomous" was again quite important. If an economist took
the Friedman-Meiselman definitions, he would conclude that
the money supply formulation was the relatively more stable
relationship. If Hester's definitions were used, the conclu-
sions reached would differ, since both relationships were of

about the same stability.

101

In Table 4—7, least squares estimates using quarterly
data are presented. Once again the variables are measured
in current dollars. In all periods examined, the Friedman-
Meiselman definition of autonomous is out-performed by
either measure of the money supply in terms of how-closely
these variables are correlated with consumption expenditures.
It is interesting to note that in all subperiods, using the
criterion of the highest coefficient of correlation, the
broad measure of the money supply performs better than the
narrowly defined money supply.

The comparison of Hester's measures of autonomous ex-

penditures with the broad measure of the money supply re-
veals little difference in the stability of the two different
relationships. The results, must be interpreted with care,
for the dependent variable is, in all cases, the same.
This is the only way the coefficients of correlation can be
compared. However, Friedman and Meiselman felt that auton-
omous expenditures should explain all induced expenditures.
Therefore, if the autonomous component varies then the in-
duced component should vary, too.

Excluding the test over the whole period, M2 performed
considerably better than Hester's L1 in three cases and in
two cases there was little difference. M2 performed better
than L2 in only one case, with little difference in the other
four cases. M2 did better than L5 in two cases, with mar-

ginal difference in two other cases. M2 performed better

”.381

TABLE 4-7.

102

The Effects of Various Exogenous Variables on
Consumption EXpenditures:
III to 1965 IV.*

Quarterly Data 1955

 

 

A. Friedman-Meiselman Variables

A.1.

(i)

(ii)
(iii)
(iv)
(v)

(vi)

(1)
(ii)
(iii)
(iv)

(v)

(vi)

 

 

 

 

C = d + 8A
t t Constant A
Period Term t
1955 III - 1965 IV 55.555 7.514
.687)
(2.008)
1954 III - 1958 II 225.015 1.258
(2.178)
1955 III - 1957 III - 52.055 8.577
(1.629)
1958 II - 1961 I 596.459 - 2.455
(1.257)
1957 III - 1960 II 294.952 .200
‘ (1.477)
1960 II - 1965 IV 178.252 4.622
.410)
.798)
C d + 8A + 0P
t t Ct Constant A
Period Term t
1955 III - 1965 IV —588.95 2.655
.285)
.606)
1954 III - 1958 II ~554.275 1.825
.576)
(1.252)
1955 III - 1957 III -455.279 2.906
(1.704)
1958 II - 1961 I -822.117 .525
.545)
1957 III - 1960 II -755.660 .281
.494)
1960 II - 1965 IV -1,455.64 .592
.507)

 

 

 

R
D.W.
.845
569
.150
.055
.805
.807
.526
.478
.045
.092
.926
.815
R
W_Pct BTW;
8.022 .989
( .540) .687
5.662 .968
( .412) .751
6.512 .922
(1.455) .565
10.976 .961
( 1.246) .759
10.221 .948
( 1.140) .787
17.120 .994
( 1.144) 1.114

continued

105

TABLE 4-7--continued

 

 

A.5. c = a + 7M

 

 

 

 

 

 

 

 

t 2t Constant M R
Period Term 2t D.W.
(i) 1955 III - 1965 IV - 19.400 1.542 .985
( .042) .072
( .267)
(ii) 1954 III — 1958 II -258.815 2.691 .962
( .206) .515
( .557)
(iii) 1955 III - 1957 III -248.156 2.749 .985
( .155) .502
(iv) 1958 II - 1961 I -289.801 2.887 .846
( .574) .541
(1.545)
(v) 1957 III - 1960 II - 97.425 1.959 .858
( .570) .295
( .811)
(vi) 1960 II - 1965 Iv 72.4505 1.192 .998
( .017) .946
( .050)
A.4. C = d + yM + 0P
t at CtConstant R
Period ' Term M2t Pct D.W.
(i) 1955 III - 1965 Iv —558.550 .959 4.477 .997
( .042) ( .289) .572
( .129)
(ii) 1954 III - 1958 II —251.146 2.100 1.294 .965
* ( .786) (1.659) .451
(1.556)
(iii) 1955 III - 1957 III -550.591 2.162 2.256 .991
( .187) ( .606) .489
(iv) 1958 II - 1961 I —695.182 .627 8.618 .965
( .556) (1.680) .575
(v) 1957 III - 1960 II -664.169 .285 9.028 .948
( .501) (2.567) .719
(vi) 1960 II - 1965 Iv 759.248 1.685 — 7.659 .998
( .220) (5.417) 1.174
( .552)

continued

104

TABLE 4-7-—continued

 

 

B. Narrow Definition of the Money Supply

 

 

 

 

 

 

 

B.1. Ct - d + yMlt
Constant M R
Period Term 1t D.W.
(i) 1955 III - 1965 IV -574.69 6.262 .985
( .167) .169
( .554)
(ii) 1954 III - 1958 II -781.759 7.745 .918
( .089) .407
( .272)
(iii) 1955 III - 1957 III —480.958 5.508 .965
( .584) .227
(iv) 1958 II - 1961 I -275.745 4.154 .480
(2.598) .159
(v) 1957 III - 1960 II -559.559 4.581 .805
(1.074) .552
(1.994)
(vi) 1960 II - 1965 IV -550.656 4.812 .997
( .087) 1.040
( .142)
B.2. Ct = d + yMlt + éPct
Constant - M P R
Period Term 1t ct D.W.
(i) 1955 III - 1965 IV -675.468 5.851 4.595 .997
( .195) ( .527) .568
( .597)
(ii) 1954 III - 1958 II -606.114 4.058 5.420 .995
( .455) ( .505) 1.298
( .527)
(iii) 1955 III - 1957 III -584.749 5.768 5.581 .997
( .169) ( .268) 1.142
(iv) 1958 II - 1961 I -928.517 1.910 9.548 .980
( .587) ( .725) .962
( .884)
(v) 1957 III - 1960 II —721.206 1.208 8.492 .956
" ( .858) (1.586) .697
(vi) 1960 II - 1965 IV -550.656 5.278 5.954 .997
( .596) (2.294) 1.250
( .864)

continued

TABLE 4-7--continued

105

 

 

C. Hester's Definitions

Ct = A + T“‘11:

C.1.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(1)
(ii)
(iii)
(iv)

(v)

(vi)

1954

1955

1958

1957

1960

Period

1955 III - 1965 IV

= A + nth + 0P

Period

1955 III - 1965 IV

1954 III - 1958 II

1955 III - 1957 III
1958 II - 1961 I
1957 III - 1960 II

III - 1958 II

III - 1957 III

II - 1961 I

III - 1960 II

II - 1965 IV

Constant
Term

 

15.745

84.695

44.825

110.969

120.171

71.777

ct

Constant
Term

-502.22

—252.078

-180.182
-606.775

-555.864

1960 II - 1965 IV -1,060.59

L1t
2.208
( .058)
( .150)
1.581
( .595)
(1.021)
1.872
( .160)
1.552
( .402)
( .695)
1.440
( .294)
( .406)
1.875
( .065)
( .129)
L1t
1.575
( .075)
( .145)
.741
( .108)
( .259)
1.295
( .269)
.615
( .150)
.625
( .144)
.607
( .224)
( .564)

 

 

 

R
D.W.
.984
486
.751
.164
.950
.496
.774
.785
.840
1.058
.988
.778
R
Pct D.W.
4.289 .996
( .556) .752
4.545 .988
( .295) .690
5.085 .965
(1.257) .555
8.251 .988
( .690) 1.786
7.529 .985
( .907) 1.511
12.621 .995
(2-191) 1.021

continued

106

TABLE 4-7--continued

 

 

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(1)
(ii)
(iii)
(iv)

(v)

(vi)

 

 

 

 

Ct - A + nLZt
Constant L
Period Term 2t
1955 III - 1965 IV 24.054 1.454
( .025)
( .060)
1954 III - 1958 II 59.219 1.252
( .164)
( .592)
1955 III — 1957 III 56.815 1.222
( .069)
1958 II - 1961 I 67.751 1.261
( .245)
( .598)
1957 III - 1960 II 80.909 1-171
( .165)
( .174)
1960 II — 1965 IV 64.162 1.294
( .059)
( .085)
Ct - A + nLZt + 0Pct
Constant L
Period Term 2t
1955 III - 1965 IV -199.191 1.066
( .049)
( .097)
1954 III - 1958 II -185.645 .618
( .068)
( .151)
1955 III - 1957 III - 67.545 1.017
( .142)
1958 II - 1961 I -559.590 .554
( .087)
1957 III - 1960 II —451.011 .577
( .109)
1960 II - 1965 IV -928.259

( .252)

 

.995
.594

.895
.225

.977
.455
.852
.856

.915
1.525

.991
.705

P

ct

2.996
( .557)

5.652
( .290)

1.676
(1.028)
7.552

R

 

D.W.

.997
.778

.995
.802

.980
.562
.992

( .626)2.255

6.404

.987

( .920)1.799
.524 11.112
( .157)( 2.229)1.042

.996

continued

107

TABLE 4—7-—continued

C.5.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(1)
(ii)
(iii)
(iv)

(v)

(vi)

 

 

 

 

 

Ct - A + nL5t
Constant L R
Period Term 5t D.W.
1955 III - 1965 IV 26.055 1.629 .991
( .052) .615
( .076)
1954 III - 1958 II 55.901 1.415 .878
( .206) .228
( .487)
1955 III - 1957 III 52.575 1.406 .977
( .080) .491
1958 II — 1961 I 85.151 1.541 .807
( .510) .918
( .516)
1957 III - 1960 II 85.779 1.298 .897
( .202) 1.295
( .257)
1960 II - 1965 IV 69.002 1.454 .986
( .052) .699
( .109)
Ct — A + nL5t + 0PC
. Constant L P
Period Term 5t ct
1955 III - 1965 IV —220.718 . 1.151 5.502
( .057) ( .572)
( .110)
1954 III - 1958 II —198.608 .692 5.796
( .080) ( .295)
( .158)
1955 III - 1957 III — 75.045 1.165 1.751
( .160) (1.006)
1958 II - 1961 I -595.194 .541 7.995
( .105) ( .679)
1957 III - 1960 II -478.721 .610 6.752
( .127) ( .945)
1960 II - 1965 IV -1,105.15 .428 15.088
. ( .169) (2.165)
( .288)

R
D.W.

 

 

.997
.802

.992
.745

.981
.585
.989
2.056
.985
1.708
.995
.942

continued

TABLE 4-7--continued

108

 

 

(i)

(ii)

(iii)
(iv)

(v)

(vi)

(1)

(ii)

(iii)

(iv)

(v)

(vi)

 

 

 

 

 

 

Ct - A + nL4t
Constant L R
Period Term 4t D.W.

1955 III - 1965 IV 11.565 1.745 .994
( .027) .550
( .097)

1954 III - 1958 II 48.595 1.486 .977
( .087) .514
( .172)

1955 III - 1957 III 28.551 1.601 .945
( .146) .552

1958 II - 1961 I -44.914 2.120 .962
( .189) 1.792

1957 III - 1960 II ~85.054 2.557 .970
( .188) 1.085
( .298)

1960 II - 1965 IV 45.198 1.594 .992
( .045) .655
( .098)

ct — A + nL4t + 0PCt

Constant L P R
Period Term 4t ct D.W.

1955 III - 1965 IV -158.554 1.581 2.520 .997
( .070) ( .428) .408
( .207)

1954 III - 1958 II - 67.058 1.044 1.891 .986
( .167) ( .647) .619
( .585)

1955 III - 1957 III - 17.162 1.482 .665 .945
( .495) (2.652) .298

1958 II - 1961 I -596.159 1.170 5.026 .980
( .562) (1.756) 1.099
( .449)

1957 III - 1960 II -404.507 1.456 4.648 .994
( .171) ( .760) 1.495
( .220)

1960 II - 1965 IV —951.528 .646 11.065 .995
( .271) (5.159) .844
( .505)

 

*Standard errors are listed below estimated coefficients.
R is the coefficient of correlation.
D.W. is the Durbin-Watson statistic which is listed directly

continued

109

TABLE 4—7--continued

 

 

below the coefficient of correlation for every time period
considered.

Second figure in parenthesis under estimated coefficient is
the standard error of the coefficient corrected for auto-
correlation as described in Section F of this chapter.

t

At

Pct
1t

3

2t
1t

2t

fl

5t

fl

4t

Consumption eXpenditures.

Net private domestic investment plus the government
deficit on income and product account plus the net
foreign balance.

Consumer price index.

Currency in public circulation plus adjusted demand
deposits.

M1t + time deposits in commercial banks.
Net private domestic investment plus total government
expenditures plus net foreign balance.

Gross private domestic investment plus total govern-
ment expenditures plus exports.

L minus imports.

2t

L minus inventory investment.

2t

110

than L4 in only one case with just one case showing little
difference.

The narrow definition of the money supply, however, did
not do so well. In fact, Hester's measures consistently
outperform M1.

When real values are considered, both measures of the
money SUpply do worse than the measures posed by Hester.
There is only a marginal difference between the money supply
measures and the Friedman-Meiselman definition of autonomous
expenditure.

There is also a noticeable difference in the behavior
of the marginal velocity of circulation of the two money
supply measures. If the broad measure of the money supply
is used, the marginal velocity is of similar magnitude in
three of the periods under review, but declines seriously in
the periods from 1957-III to 1960-II and from 1960-II to
1965‘IV. Both of these periods represent measures from peak-
to-peak, reflecting a.growth in consumption expenditures
which exceeds the growth of the money supply measure. In
other words, there was a decline in the demand for money,
broadly defined, during these time periods. The latter de—
cline was of considerable magnitude.

An examination of the marginal velocity of circulation
of the narrow measure of the money supply Shows that in the
earliest two periods under review this value decreased quite

rapidly. However, a review of the latter three periods Show

111

that the marginal velocity remained relatively constant.

If M1 is used as a measure of the money supply, it would be
inferred that there was an increase in the demand for money
in the trough-to-trough period from 1954-III to 1958-II but
a decline in the demand for money occurred in the peak-to-
peak time period covering from 1957-III to 1960-II. After
this latter shift took place, the demand for money remained
relatively stable up to the end of the period discussed in
this thesis.

Stability of the demand for money in real terms seems
to be nonexistent. The problem of comparison is difficult
in this instance because several of the coefficients of M1
and M2 are not Significantly different from zero. Of those
values of M2 that are significantly different from zero,
there does appear to be greater stability than exists between
the nominal measures of the variables. The marginal velocity
of real money balances, in forms of M1 or M2 shows a general
decline. This would indicate that there was a secular de-
cline in the demand for real money balances.

The values of the marginal multiplier show varied
results. The Friedman-Meiselman multiplier shows little
stability. One problem here is that in the five periods
reviewed, this value is insignificant in two and possesses a
wrong sign in the third. In terms of real values, their
measure is insignificant in four out of the five cases tested.

When the standard error is corrected for the presence of

autocorrelation, all five are insignificant.

112

The measures devised by Hester Show an entirely differ-
ent pattern. The stability of the marginal multiplier is

quite remarkable for all variables except L This is shown

4.
in Table 4-8. It Should be noted, however, that L4 performed
better than the others in terms of its correlation with
consumption expenditures. This stability is still quite
evident in real terms, as can be seen from Table 4-7.

The final comparison of the different measures is con-
ducted in terms of the partial correlation coefficients.
This is the same test performed by Friedman and Meiselman
in which they attempted to determine the relative importance
of two measures in a multiple regression equation. This ex—
amination will be carried one step further by including Beta
coefficients. This latter value measures the relative im-
portance of the individual regressors by weighting the
regression coefficients with the ratio of the standard error
of the variable in question to the standard error of the

5 Partial correlation coefficients are

dependent variable.
shown in Table 4-9 while Beta coefficients are shown in
Table 4—10.

If the Friedman-Meiselman measure of autonomous expendi—

tures is used the results are very one-sided. In all periods

 

5Mordechai Ezekiel and Karl A. Fox, Methods of Correla-
tion and Regression Analysis (New York: John Wiley and Sons,
Inc.,.1959), pp. 147-48. Arthur S. Goldberger,.Econometric
Theory (New York:' John Wiley and Sons, Inc., 1964), pp. 197-
98. »

115

 

 

 

 

TABLE 4-8. Marginal Multipliers Associated with Hester's
Definitions of Autonomous Expenditures.
Marginal Multiplier of:
Period L1 L2 L3 L4
1954 III - 1958 II 1.58 1.25 1.41 1.49
1955 III - 1957 III 1.87 1.22 1.41 1.60
1958 II - 1961 I 1.55 1.26 1.54 2.12
1957 III - 1960 II 1.44 1.17 1.50 2.56
1960 II - 1965 IV 1.88 1.29 1.45 1.59

 

 

 

 

 

#mm. wmm. mom.
«mm. mmm. NdN.
mmm. mfim. mHN.
mmm. mmm. wan.
mmm. Nmm. hmfi.
N .N N N .H
4 SUM SUM 4 EU
mam. mam. wmm.
new. mmm. mm¢.
Nam. mwm. mmo.
mmm. mmm. flow.
0mm. Nmm. 0mm.
M“ HQ.NZU NEU HQ.HZU
4.. .H .H
mmm. mmm. mmm.
00m. mmm. mhm.
How. New. Hmw.
aha. mmm. ONm.
mhm. Nwm. mmm.
.N N .d
fl SUM SUN 4 ZUH

 

 

was. and. mam. Ham.
now. New. «we. mam.
owe. amp. New. mmm.
mmm. -mmm. New. hem.
mam. Nam. mad. mam.
H m .m a .m m
SUM E AUH E GUM AUH
saw. 840. mam. mam.
mom. mmm. New. 045.
owe. dam. map. as».
mom. mam. amp. omm.
mam. mom. mmm.- an».
a .5 a .a 5
EUR 2 AUH Z HUM QUH
ham. emo. mmo. 6mm.
mom. amp.) mam.) meow
owe. mam.) 40>.) mmm.
mmm. mmm. «we. mom.
mam. omm. ems.) one.
a . a .

SUM 2 dUH Z <UH ¢UH

 

 

 

 

>H mmma I HH owmd
HH Omma I HHH hmmd
H ammd I HH wmmd
HHH smmd I HHH mmmd
HH mmmfi I HHH emmd
poflumm
>H mmma HH Omma
HH Coma I HHH emma
H «mad I HH mmma
HHH emmd I HHH mmma
HH mmmd I HHH emma
pofluom
>H mwmd I HH owma
HH Omma I HHH bmma
H Hmma I HH mmma
HHH hmma I HHH mmma
HH mmma I HHH emmfi
pofluom

E
3.3
:2:
:3

Age

.U
A>V
A>HV
AHHAV
AHHV

AHV

.m
13
A>HV
AHHHV
AHHV

AHV

 

 

mEHmB HmcflEoz CH mmaflmflum> cmeDmm mcoflumamuuou Hmfiuumm

.mlfi mqmfifi

115

 

 

 

 

 

4mm. moo. new.
mo4. omo. mod.
mao. o4o. moo.
ooo. moo. m4m.
moo. moo. own.

4 .m N 4 .4

a 20 son A son
mmm. moo. 40o.
Oem. moo. mmm.
4mm. o4o. ooo.I
o4o. mom. woo.
duo. moo. mom.

m .N .4

A Son «209 a son

 

 

pom. 44o.I moo. moo. >H moofi I HH oooa
poo. poo. mam. ohm. HH oooa I HHH smma
oo4. ooo. 4mm. moo. H 4854 I .HH omma
moo. omm. odo. m4o. HHH Amma I HHH mmoH
mam. omm. ooo. who. HH omoa I HHH 4554
4 N .4 4 .4 4

son 2 nos 2 qua non eoAumm

smo. mmo.I 84m. ooo. >H mooa I HH ooma
moo. ooh. 44>. poo. HH ooma I HHH smoa
oo4. mom. N44. poo. H 4oo4 I HH omoa
moo. woo. woo. who. HHH smma I HHH mmoa
o4o. ooo. 4o4. oeo. HH omoa I HHH 4mo4
4 m .n .4 .m m

son 2 guy 2 qua non panama

A>V
A>flv
AHMAD
Aflflv

AHV

A>V
A>Hv
AAHHV
Aaav

AHV

116

 

 

 

 

 

 

 

 

 

 

mmm. 484. 4N4. mom. 444 smm4 I 444 mmm4 A4445
moo. mom. moo. mmm. 44 mmm4 I 444 4mm4 x44v
>H mmm4 I 444 mmm4 A45
ms 44 42 mg 604404
umza + umqm + o u no 442% + umqn + o u no .0
who. omo. ems. 4mm. >4 mom4 I 44 oom4 14>o
mmm. mm4. oem. o4m. 44 ooo4 I 444 4mo4 A>V
mom. ohm. 440. I now. 4 4om4 I 44 mmm4 A>4V
moo. own. mom. 4N4. 444 smm4 I 444 mmm4 A444L
moo. mom. 444.4 4mm.I 44 mmm4 I 444 4mo4 A44V
>4 mom4 I 444 mmm4 14V
42 44 4s 44 604444
umzr + 44am + 8 u po 54:» + p44o + 8 u 40 .m
mom. moo. mom. moo. >4 mom4 I 44 oom4 14>v
mmm. mmN.I moo. osm.I 44 com4 I 444 4mm4 A>v
ooe. mmm.I mom. smo.I 4 4om4 I 44 omo4 A>4v
mom. me4. 0mm. om4. 444 >mm4 I 444 mmm4 A444v
mom. 4m4. mmo.4 Amm.I 44 mmm4 I 444 4mm4 A44V
>4 moo4 I 444 mmm4 141
N2 4 2 m ©0440m
umza + pen + o u no 442» + pen + o u U.o .<
manna 4mc4Eoz c4 >4mmsm wocoz
pom m04544pcomxm msoaocoDsg mo monommmz m5044m> mo muc0404mmmoo ouwm .oaIe mqmmB

 

117

 

 

oeo. 4mm.
84o. eoo.
moo.I 4mm.
mom. 844.
m44. o4o.
H2 fig

 

 

 

 

 

umza + umqm + 8

mhh. NNN.
o4m. mo».
®©O.I 0mm.
o44. mom.
how. mad.
42 ma
u4z> + undo + 8 u 40
06>. OmN.
mmd. fish.
844. I 4mm.

>4 mmm4 I HH ommd
HH ommd I HHH >mm4
H 4mm4 I 44 mmma
HHH >mm4 I HHH mmmfi
HH mmm4 I HHH 4mm4
>4 mmmd I 444 mmma
p0440m
>H mmmfi I 44 Omm4
HH ommfi I 444 smma
H 4wm4 I HH mmma
HHH >mm4 I 444 mmma
HH mmm4 I HHH 4mm4
>4 mmm4 I HHH mmma
oowuom
>4 mmm4 I HH omm4
HH omma I HHH hmma
H dead I HH mmmd

a:
E
A>4V
:4:
A44v

A4V

.m
A4>v
A>v
A>4v
A4445
A44V

A4v

.o
A4>V

A>v

A>4V

118

tested, the partial correlation coefficient of either measure
of the money supply holding autonomous eXpenditures con-
stant, is relatively close to the simple correlation coeffi—
cient obtained in the earlier tests. The partial correlation
coefficient of autonomous expenditures, holding either
measure of the money supply constant, is considerably lower
than the simple correlation coefficient. Also, the Sign of
autonomous expenditures is negative in many cases. The Beta
coefficients reflect the same general impression. In all
cases the Beta coefficients of either measure of the money
supply are larger. It could be inferred from these tests,
that if this measure of autonomous expenditures is correct,
then either measure of the money supply is relatively more
important and most of the observed influence of autonomous
expenditures on consumption eXpenditures represent the hidden
influence of the money supply.

When Hester's measures of autonomous expenditures are
used the results are mixed. Also, there is a considerable
difference in the results depending upon which definition
of the money supply is used. The measure L1, does not com-
pare well with the narrow definition of the money supply.

Its partial correlation coefficient, holding M1 constant,
is much lower than its simple correlation coefficient in the
majority of cases. The Beta coefficients, however, are

larger for M1 than for L in every case. This is also true

1
if the broad measure of the money SUpply is used rather than

the narrow one.

119

The use of one of the other three measures instead of

L1 reverses the situation relative to M1. The partial cor-

relation coefficients of L2, L3 or L4 holding M1 constant

are closer to their simple correlation coefficients than

1 2' L5 °r L4

five cases tested. The Beta coefficients of L2, L:5 or L4

those of M holding L constant, in three of the

are also larger than those of M1 in three of the five cases
tested. It is interesting to note that the cases that favor
different measures of autonomous eXpenditures are not the
same in all instances.

These results, although they would not reverse the con-
clusions obtained with the first two measures of autonomous
expenditures, would at least show that in the case of M1,
the money supply is not relatively more important than some
measures of autonomous eXpenditures. The problem again re-
duces to that of choosing the most appropriate definition of
the variables in question.

If M2 is the appr0priate measure of the money supply,
L4 is the only measure of autonomous eXpenditure that per-
forms better than this money supply measure. M2 performs
marginally better than L2 and quite a bit better than L3.
The results, however, are not so one-sided as to allow for
a definite conclusion to be reached. M2 apparently performs

better than M relative to these latter three measures of

1

autonomous expenditure, but again the difference is not over-

whelming.

120

Unless one makes a definite selection of either A or L,
as the correct measure of autonomous expenditure, it is im-
possible, at this stage, to draw any conclusion as to the
most important variable or the one that possesses the
greatest relative stability. Additional problems associated
with single-equation tests also indicate that perhaps it is
not possible to reach any firm conclusion within the frame—

work of these simple models. This will be discussed next.

Autocorrelation

The problem of autocorrelation was mentioned earlier
in this chapter. This problem is common in time series
analysis and two reasons are given for its possible cause.
First, trend may be a very important element in the observa-
tions on the dependent variable under examination. If this
is true, then the residuals of successive time periods cannot
be considered to be random. Second, both the regressor and
the regressand may be influenced by a third variable which
also moves in the same direction. This third variable may
be autocorrelated with both of the former.

If the technique of simple least squares is used in
estimating a relationship between two variables the presence
of autocorrelation has two main consequences on the estimates.
Although the estimates themselves are unbiased, they are
inefficient. However, the use of the least-square method
will bias the standard errors downward so as to cover up the

inefficiency of the estimates.

121

Several methods exist of correcting for the presence
of autocorrelation. The one that will be used in this
thesis is that developed by WOld6 to correct the standard
error for its downward bias. weld makes the basic assump—
tion that the observed residual, S, is a function of all
past and present values of the true error term, 8. The

relationship is assumed to be linear.

(4.1) gt = Et + a16t_1 + a26t_2 + . . .
(p
where Z a.2 <00
. 1
i=1
and E(€t) = O

E(8 8 )_=0 (v =41, :2, . . .)

If p1 is the autocorrelation coefficient between successive
residuals and p2 is that between residuals lagged two periods,

then the standard errors can be multiplied by

 

41 +2p1 +2p2 + . . . to correct for the autocorrelation
present. It can be assumed that p2 = p12, p3 = p13, and so
on. The correlation exhibited between terms beyond..p1 will,
therefore, be very slight. A good approximation can be ob—
tained with knowledge of just p1.

This correction has been made on both the Friedman-

Meiselman data and the data presented in previous subsections

 

6Herman Wold, Demand Analysis (New York: John Wiley and
Sons, Inc., 1951), pp. 210—11. Also see Ezekiel and Fox,

op. cit., pp. 555.

122

of this chapter. Some results of this correction appear in
Tables 4-6 and 4-7. Results concerning the Friedman—Meiselman

data are presented in Appendix A.

Simultaneous equation bias

 

This problem has been advanced in most of the discussions
of the Friedman-Meiselman paper. Essentially, the difficulty
is that in single-equation models, such as the ones that have
been tested so far, the independent variable is not exogenous
to the economic system in a statistical sense because it is
not independent of the error term in the equation. This means
that simple least square estimates of the coefficient of the
regressor will be biased. Also, the coefficient of correla-
tion will be biased; in some cases upward, and in some cases
downward. The lack of independence of certain variables can
be explained by demonstration.

As an example, assume that the two specified "independent"
variables are the Federal Government's deficit and the money
supply. Generally, it is felt that the tax collections of
the Federal Government are endogenous to the system. That is,
they are affected by other economic magnitudes. In the case
of tax collections, the level of income is assumed to influ-
ence the amount of taxes collected. The larger the level
of income received in a society, the greater are the taxes
its citizens have to pay. The money supply is also considered

by many to be endogenous. In the development of the more

125

complex model of Chapter III, the level of interest rates

was included as a determinant of the money supply. It could
be argued that a rise in incomes would lead to an increase in
the demand for loanable funds. This, holding all other
things constant, would cause commercial bankers to squeeze
their reserves further and increase the amounts of their
loans outstanding. Thus, by allowing demand deposits to in-
crease, the money supply would increase.

Suppose the equation being tested includes the govern-
ment deficit and current dollar Gross National Product. If
it is assumed that the money supply is increased during the
time period under review and it is also assumed that the
money supply can influence the level of income in society
this increase would raise the level of income of the society
and, consequently, would increase the taxes paid by the in-
dividuals of a society. This would mean the government de-
ficit would be smaller than it otherwise would be. It might
even result in a surplus (which would result in a negative
correlation with Gross National Product). Thus, a given
level of Gross National Product would be associated with a
smaller deficit than in the case of no increase in the money
supply or it might even be associated with a surplus. Either
result would affect the coefficient of the government deficit
and might even reverse its Sign. This, of course, would
tend to reduce the coefficient of correlation.

Assume now that Gross-National Product is regressed upon

the money suPply. Also, assume that the deficit is

124

positively related to this latter figure. If the deficit
increases, this would raise current dollar Gross National
Product. As discussed above, this movement will tend to
raise interest rates, which will result in an increase in
the money supply. Similar to the previous case, the coef-
fient of the money supply would be affected. Also, the
coefficient of correlation would be altered, but since the
two variables move in the same direction, its value would
generally not be reduced.

If the independent variables are not truly exogenous
to the equation, then the equation is miSSpecified and the
regressor is not independent of the disturbance term. In
the example given, the result would be that the correlation
between the government deficit and current dollar Gross
National Product would be weaker relative to the correlation
between the money supply and current dollar Gross National
Product.

This helps to eXplain some of the results obtained in
Tables 4-9 and 4-10. The coefficient of autonomous expendi-
tures as defined by Friedman and Meiselman is negative in
only one case in Table 4-7, Part A, and it is negative in
three cases in Table 4-9, Part A, when multiple regression
techniques are used and M1 is the second regressor. One would
expect this coefficient to always be positive. Apparently,
the effect of other variables has been so gréat as to reverse

the Sign from positive to negative. How greatly the value of

125

the other coefficients have been affected or the extent to
which the coefficient of correlation has been affected is
unknown. From these results, however, it is very likely
that they have been affected in the direction indicated
above.

The major justification for the use of the classical
least-squares technique is that the estimates possess the
minimum variance prOperty. Thus, even though the estimates
are biased, they have a smaller variance than those obtained
by other estimation methods, as for example, the two-stage
least-squares method. This becomes quite important in small
samples, because if the variance is sufficiently small, it
can compensate for the bias of the estimate.7 Classical
least squares would give results that would not vary sig-
nificantly from the results obtained by other methods. In
large samples, however, the variances of both classical
least squares and two-stage least squares go to zero. However,

the bias of classical least squares remains.

Summary

There exists several problems that single-equation esti-
mation techniques cannot handle. Theoretically, the problem
of simultaneous equation bias requires the use of a complete

model.

 

7Arthur S. Goldberger, op. cit., p. 560.

126

Empirically, the results of many of the tests performed
in this chapter indicate that the conclusion one draws de-
pends, to a great extent, upon the definition of the
variables used. As in the case of Hester's measures of
autonomous expenditure, the results concerning the relative
stability of either model allow for no definite conclusion,
whereas the use of the Friedman-Meiselman measure results
in the formidable support of the Quantity Theory model.

Also, the transmission process is hidden in a single-
equation model, and attempts to identify it can be achieved
only through the use of the larger model. A more complete
model can reduce this problem to some extent. That is, a
greater degree of disaggregation can be achieved with a more
complete model.

Thus, the only possible path open to a researcher in-
terested in the relative effects of selected exogenous com-
ponents of aggregate demand upon important endogenous
variables is that of more complete and complex econometric
models. This eliminates the simple concepts of "the multi—
plier" and "the income velocity of circulation." The
indicated trade off between simplicity and increased infor-
mation, in this case, seems to favor the use of the more
complex models. Therefore, this is the direction taken in

Chapter V.

CHAPTER V

THE COMPLETE MODEL

This chapter presents the results of estimation of the
complete model and various experiments designed to assess
the relative importance of monetary and fiscal policy.
Initially, however, there is a discussion of some statistical
problems associated with the estimation of the complete

econometric model.

Identification

One problem faced prior to the estimation of an economic
model is that of identification. Basically, the problem of
parameter identification reduces the question of whether or
not the parameters of an equation that is part of a system
of equations can be uniquely determined from the estimated
parameters of a system of reduced form equations. If.it is
possible to estimate all of the parameters in each of the
structural equations from a complete system, then it is said
that the system is identified. If all of the parameters in
the set of equations cannot be uniquely estimated, the system

is said to be not identified.

127

128

The condition of identification is usually derived in
terms of the rank of the matrix of reduced form parameters.
Since the rank of this matrix cannot exceed the number of

rows, it is common practice to use the order condition of

 

identifiabilitijhich is derived from the rank condition of

 

identifiability. The order condition is a necessary, though
not sufficient, condition for identifiability. And, it is
much easier to apply than the rank condition. The order con-
dition :flnr identifiability states that if an equation is to
be identified, the number of predetermined variables excluded
from the equation must be at least as great as one less than
the number of dependent variables included in the equation.1
The complete model to be tested is a system of nine equa-
tions with nine endogenous variables. For convenience the

complete model is reproduced again.

(5.1) Y c + I + G + E - O

t t t t t t

_ d
(5.2) Ct — do + Gth + GZCt—l + dth + a4Mt-1

_ _ 1
(5.5) It — 90 + 61(Ct_1 ct_2) + BZYt + fisrt-2 + 54It—1

d _

(5.4) Yt — let

(5.5) 0t = no + n1Yt .
l _ s

(5.6) rt - 60 + sirt + EZYt

 

J'Arthur S. Goldberger, Econometric Theory (New York:
John Wiley & Sons, Inc., 1964), p. 516. Also, J. Johnston,
Econometric Methods (New York: McGraw Hill, 1965), pp. 250-
252.

 

129

_ d
(5.7) r — A + AlYt + AZMt

(5.8) Ms=0+0rs+0rf+0B

t 0 1 t 2 5 t
s _ d =
(5.9) Mt - Mt Mt

The stochastic error terms are not reproduced at this time.

. d s d
The endogenous variables are. Ct' It' Ot' Yt, Mt' Mt’ Yt'
1 Q I C
ri, rt. There are also eight predetermined variables:
d

condition can be applied to the nine equations of the model.
It can be seen that all.the equations meet the order condi-

tion of identifiability.

Estimation Procedure

The test of identification provides some insight into
the method that Should be used to estimate the structural
parameters. In this case, since the model is overidentified,
it is best to use a simultaneous equation method for estima-
tion purposes instead of the ordinary least—squares procedure.
In a simultaneous system it is well known that even though
the ordinary least—squares method has the prOperty of minimum
variance, all the classical conditions for estimation are not
satisfied. To be exact, in some equations the variables
that serve as regressors are jointly determined with the
regressand. Therefore, these regressors cannot be said to

be independent of the contemporaneous disturbance term and

150

the ordinary least-squares procedure will lead to incon-
sistent estimates. Reliance cannot be placed upon reduced—
form estimates either, for in the general case of over-
identification, unique estimates of structural coefficients
cannot be obtained from the values of the reduced-form
estimates.

A structural method of estimation, therefore, was more
desirable to use than the ordinary least-squares method.
Also, it was felt that because additional refinements were
to be made in estimation, one desirable prOperty of the
estimation procedure chosen should be the efficiency of the
estimators. The three-stage least-squares procedure was
chosen primarily for this reason. This procedure yields
estimates that are asymptotically normal, and asymptotically
more efficient than the two—stage least-squares estimators.2

The three—stage least-squares estimator is considered
to be a full-information estimator because it takes into
account all parameters in computing the structural equations.
It is for this reason that the estimates are more efficient
than two-stage least-squares estimates that do not take
account of all the parameters in the system.

Some objections have been raised about the use of full-
information methods. One such problem is miSSpecification.

However, these objections have usually been based upon

 

2Carl F. Christ, EcOnometric Models and Methods (New York:
John Wiley & Sons, Inc., 1966), p. 449.

151

Monte Carlo studies of the small sample properties of the

various estimators.3

Since the time period used in this
thesis contains 50 sample points, these objections were not
considered to be as serious as they might be in a smaller
sample.

The three steps of the three-stage least—squares pro-
cedure are as follows. First, the full reduced-form system
is estimated. Second, the two-stage least-squares estimates
are computed and the residuals are estimated. These residuals
are then used to compute the variance—covariance matrix of
the structural equations of the system. Finally, this
variance-covariance matrix is used to obtain the generalized

least-squares estimates of the structural parameters.4

Autocorrelation

In early tests of the model it was apparent that all of
the structural equations exhibited a significant amount of
autocorrelation as shown by the Durbin—Watson statistic.
This is a very common phenomenon when quarterly data are
used. A desirable refinement of the estimation procedure
would be to correct the estimates for the presence of auto-

correlation.5

 

3J. Johnston, op. cit., pp. 275-295.
4Arthur S. Goldberger, op. cit., pp. 546—552.

5There exists a problem in this reSpect, however, in
that very little is known about the joint presence of auto-
correlation and simultaneous-equation complications. See,
for example, J. Johnston, op. cit., pp. 294-295.

152

The general method of correction uses the assumption
of a first-order autoregressive scheme. That is, the

postulated relationship is

(5.10) Yt = d + Emi + ut

where Yt and Xt are two sets of time series data and ut is
a stochastic disturbance term. In this case, the disturbance

term follows the first-order scheme
(5.11) ut = (Mt-1 + 8t

where p is the coefficient of correlation between successive
disturbance terms and St is a stochastic disturbance term

satisfying the classical assumptions:

(5.12) E(et) = 0

0)
V
II

E(€t 0: if s = 0

t+s
0 if s # O.

Lagging (5.10) one period and multiplying by p gives the

following relationship.

(5.15) th_1 = pa + Bpxt_1 + put_1

If (5.15) is subtracted from (5.10) we get

(5.14) Yt - th_1 = 0L(1 - p) + 8(Xt — pxtyl) + 8t .

Since at satisfies the properties of the classical model,

estimation can proceed along the usual lines with (Yt - th 1)

155

and (Xt - pxt_1) serving as the dependent and independent
variable, respectively.

In the three-stage procedure, least-squares estimates
were made of the individual structural equations to obtain
an estimate of p for each equation. The variables were then
transformed as in (5.14) for use in the three—stage process.
After this transformation was made, in all cases except one,
the hypothesis that significant autocorrelation existed in
the various structural equations could be rejected at a 5%
level of significance according to the Durbin—Watson statis-
tic. One should note, however, that several equations con-
tain lagged dependent variables. Under classical conditions

this tends to bias the Durbin-Watson statistic towards two.6

Statistical Estimates

The three—stage least-squareSvestimates of the structural
equations are presented below. The data used in computing
these estimates are quarterly and seasonally adjusted cover-
ing the time period from the third quarter of 1955 to the
fourth quarter of 1965. This period begins at the close of

the Korean conflict and ends with the large expansion of

 

6Marc Nerlove and Kenneth F. Walis, TUse of the Durbin-
Watson Statistic in Inappropriate Situations," Econometrig§_
Vol. 54 (January 1966), p. 255. This applies, of course, to
a situation where the ordinary least-squares technique is
used. As was noted in footnote 5, little is known of the
prOperties of these statistics when more than one problem
exists.

154

defense expenditures for the Vietnam War. Data are expressed
in current dollars. The sources of the data appear in

Appendix B.

(5.15) Yt = Ct + It + Gt + Et - 0t
(5.16) ct = -57.449 + .242 YE + .702 Ct—1 + .515 Mt
(.007) (.007) (.104)
+ .046 M
(.119) t'1
R2 = .9469 D.W. = 1.950
(5.17) I = 6.166 + .060 Y + .502 (C - C )
t (-018) t (.249) t‘1 t'2
1
- 5.501 r + .665 I
(1.815) t'2 (.097) t'1
R2 = .9469 D.W. = 1.950
(5 18) Yd = 67 Y
. t . t
(5.19) 0t = -1.205 + .048 Yt
(.000008)
R2 = .8655 D.W. = 2.282
(5.20) r: = 1.650 + .201 r: + .005 Yt
(.001) (.000002)
R2 = .5451 D.W. = 2.065
(5.21) r: = 15.569 + .040 Yt - .250 mi
(.00004) (.015)
R2 = .4559 D.W. = 1.578
(5.22) M: = 45.219 + .890 r: + .208 r: + 1.852 Bt
(.082) (.159) (.007)

R2 = .9520 D.W. = 1.507

155

s _ d
(5.25) Mt - Mt

Figures in parenthesis directly below the estimated coeffi-
cients of the various parameters are the (asymptotic)
standard errors of the coefficients. R2 is the coefficient
of determination and D. W. is the Durbin—Watson statistic
relating to a given structural equation. In all equations
except (5.22) it appears that autocorrelation has been re—
moved by the use of the transformation described in the pre—
ceding section.

Several alterations were made in computation to adjust
for difficulties that arose during the estimation procedure.
For example, in equation (5.18) disposable personal income
was taken to be two-thirds of Gross National Product. In
earlier testing, in every case results indicated that the
coefficient of Yt was 0.67 and the intercept term was not
significantly different from zero. However, p, the coeffi-
cient of correlation between successive disturbance terms,
was estimated to be very close to 1.00. Since the estimated
intercept term is equal to the true estimate of the intercept
term multiplied by (1 - p), as shown in equation (5.14)
above, when the intercept term is corrected, the true esti-
mate becomes very large, approaching infinity as p approaches
one. Consequently, the identity in (5.18) was used in place
of the actual estimate.

Further alterations were made in the investment func—

tion, here shown as equation (5.17). The long-term rate of

156

interest, lagged two quarters, was used rather than the con—
temporaneous value. In several trial estimates of the
model, the coefficient for the long-term rate Carried the
wrong Sign and/or was not significantly different from zero
when either the current value or a one-quarter lag was used.
As presented in (5.17) the coefficient has the appropriate
Sign and is significantly different from zero at the 10%
level of significance. These results are consistent with
the evidence in other papers that investment has a lagged
response with respect to the rate of interest.

The lagged value of investment was also substituted
for the trend variable. It was hypothesized above that
trend would help to account for induced technological change.
The presence of trend influenced the sign of accelerator

variable (Ct - Ct-2)' That is, the sign of this coeffi-

-1
cient became negative. It was found that with this coeffi-
cient negative and the interest rate coefficient positive,

the estimated model was not dynamically stable. Consequently,

the lagged value of investment expenditures was used to pick

up the effect of induced technological Change.

Individual Equationg

The complete model will be examined later in regard to
the relative strengths and stability relationships of the
various policy parameters. It is interesting at the present

time to consider the relative strengths and stability

157

relationships of the individual equations. This can lead
to some knowledge of the transmission process.

It is possible for monetary policy to affect aggregate
activity in two ways. One path-is through consumption
eXpenditures as exhibited in equation (5.16), while a second
one is through investment eXpenditures. This latter path
can be achieved either indirectly in terms of the effect
on consumption expenditures and hence through the accelerator,
or directly through the influence on interest rates. In
either case, monetary policy seems to work primarily with a
lag.

According to the estimates of the model, monetary policy
can affect consumption eXpenditures directly through changes
in the money SUpply. The contemporaneous value of the money
supply possesses a regression coefficient significantly dif—
ferent from zero, while the lagged value does not. It is
apparent that the money supply is not as important an explana-
tory variable as either disposable personal income or lagged
consumption expenditures in terms of the t-values of their
coefficients. Particularly because of the importance of
the lagged consumption variable, it would seem that consump-
tion eXpenditures adapt fairly slowly to changing economic
conditions. This is what is postulated by the permanent
income hypothesis. However, it does appear that monetary
policy does have some significant contemporaneous influence

on these Spending decisions.

158

The influence of monetary policy can be carried to
other variables through consumption expenditures. These
expenditures affect final sales which are relevant for in-
vestment decisions. It has been postulated in this thesis
that the change in final sales can be represented in the
accelerator variable (Ct—1 - Ct-2)' This channel Of influ-
ence Operates with a lag.

The second means of influencing investment expenditures
is through variations in the long-term interest rate. It is
the long-term rate that is most important for business
investment decisions. However, the only way the monetary
authorities can alter this rate is through the term structure,
that is, by altering short-term rates first. The relationship
between long-term rates and short-term rates is highly sig-
nificant. However, equation (5.20) shows that movements in
short-term rates or the level of aggregate economic activity
do not explain all of the variation in long—term rates.
Another loose link from the standpoint of policy seems to be
the control of the short-term rate. As can be seen in equa-
tion (5.21), the relationship between the money supply and
short-term interest rate is not exceptionally Close. This

7

result coincides with findings elsewhere. Consequently, the

 

7Note has been made on previous occasions concerning the
absence of a relationship between the money supply and the
rate of interest if the demand fOr money equation is inverted.
See, Gregory C. Chow, "Multiplier, Accelerator, and Liquidity
Preference in the Determination of National Income in the
United States," The Review of Economicg and Statistipp, XLIX
(February 1967), p. 4.

159

transmission path of influence running through interest rates
seems to be somewhat weak. Even if the monetary authorities
can affect the long—term rate, the first significant effect
on investment spending seems to be after a two-quarter lag.

One final point should be made concerning monetary policy.
In the model under discussion, the money supply represents
the relevant variable for economic decisions. However, equa—
tion (5.22) shows that it is reasonable to treat the money
supply as an endogenously determined variable. Much of the
movement in the money supply is a result of the monetary
authorities who alter the level of the adjusted monetary base.
However, the short-term interest rate also enters into the
money supply equation significantly; and since the level of
short-term rates is influenced by the level of economic activ-
ity (as is shown in equation (5.21)), it is very apparent that
the control of the mOney supply by the monetary authorities
is far from complete.

Government expenditures enter the economy by directly
influencing incomes or the production of goods and services.
The total effect of these expenditures, however, is felt
through the multiplier process. In terms of consumption ex-
penditures, the multiplier will be dampened by income taxes.
Taxes enter into the model in an implicit way as described
by the relationship of Gross National Product to disposable
personal income (equation (5.18)). That is, a dollar increase

in government expenditures will result in a dollar increase

140

in Gross National Product, but will only result in a $.67
increase in disposable personal income.

Government expenditures will also have a multiplier
effect on investment expenditures. First, the level of
economic activity will affect investment expenditures directly
as Gross National Product enters into the investment function.
Secondly, government eXpenditures also influence consumption
eXpenditures and, consequently, the accelerator.

There are two repercussions which tend to lower the
total government multiplier over time. An increase in govern-
ment expenditures which raises Gross National Product also
increases imports. This has a negative effect on Gross
National Product and, consequently, on consumption and invest-
ment expenditures. Aggregate activity, as represented by
Gross National Product, also affects the level of interest
rates so that some feedback will be registered on investment
expenditures.

It might be noted that by influencing the level of
interest rates, government eXpenditures will also influence
the money SUpply in the same direction. (This has one direct
implication in that these changes in the money supply will
have effects on Spending decisions that reinforce the effect
of the government expenditures. A second, less apparent
implication is that if the monetary authorities attempt to
maintain stable credit markets, changes in interest rates,

caused by Changes in government expenditures, could induce

141

the monetary authorities to change the monetary base. An un-
stable market in this case would be one that experienced
large fluctuations in market rates of interest. Consequently,
there could be no Change in interest rates, but a change in
the monetary base which would result in a Change in the money
supply. In this case, the monetary base would not be an
exogenous variable.8

The estimated structural equations can be solved for the
level of Gross National Product, giving a reduced—form
equation. The coefficients of this equation are called
"impact multipliers" because they measure the immediate impact
of exogenous and lagged endogenous variables on the current

value of Gross National Product. The reduced form is:

d

(5.24) Yt = —18.556 + .860 Ct—1 + .067 rt + .586 at
1'
+ .056 Mt_1 + .614 (Ct_1 - Ct_2) - 4.059 rt_2
+ .812 I

t_1 + 1.225 Gt + 1.225 Et.

In this case, a $1 billion increase in the adjusted
monetary base would result in a $586 million increase in Gross
National Product in the same quarter the base increased.

A $1 billion increase in government eXpenditures would result

 

8See, John H. Wood, "A Model of Federal Reserve Behavior,"
in George Horwich, Monetary Process and Poligy: A Symposium
(Homewood, 111., Richard D. Irwin, 1967), pp. 155-166, for an
interesting study of endogenous policy variables.

142

in a $1.225 billion increase in Gross National Product the
same quarter the increase in government expenditures took
place.

To put things on a somewhat comparable basis, a $1
billion quarterly increase in Gross National Product would
require approximately a $800 million increase in government
expenditures or approximately a $1.7 billion increase in the
adjusted monetary base.

In terms of the relative stability of the transmission
process, it is hard to arrive at any strong conclusions.

Due to the weakness of the path through interest rates and
the sluggishness of Changes in consumption expenditures in
reSponse to changes in the money supply it would appear that
as a first approximation, monetary policy may be the weaker
of the two relationships.

In terms of the impact multipliers, fiscal policy
clearly merges as the stronger short-run instrument. .During
the time period under review, the adjusted monetary base did
not increase in any quarter by $1.7 billion. In fact, it
increased by $1 billion only once in the entire period, and
that was in the fourth quarter of 1965.

By contrast, the necessary growth of government expendi-
tures necessary to alter the GNP by $1 billion could be con—
sidered moderate in terms of the actual changes that took
place in the time period under review. In fact, quarterly

Changes of at least $800 million occurred quite frequently.

145
Dynamic Aspects of the Model

It is hard to draw conclusions about the relative ef—
fects of monetary and fiscal policy when the model we have
estimated covers the whole period of time under review.

It is desirable, therefore, to investigate the dynamic
properties of the model and to Observe its short-run prOper-
ties and multipliers.

The reduced form of the model, presented above as
equation (5.24), can be altered to Obtain the final form9
of the equation or what has also been called the fundamental

O This equation is derived by successive

dynamic equation.l
substitutions for the lagged endogenous variables in the
reduced-form equation. The final result will Show the cur—
rent endogenous variable of interest as a function of its
own lagged values and current and lagged values of the exo-

genous variables. The final form for Gross National Product

is presented as:

(5.25) Y = -9.145 + 1.668 Yt__1 - 0.745 Yt_2 + 0.028 Yt_3

t
+ 0.586 Bt - 0.009 Bt_1 - 0.024 Bt_2
- 0.242 Bt_5 + 1.225 (Gt + Et)

- 1.671 (Gt_1 + Et_1) + 0.570 (Gt_2 + E ).

t-2

 

9Arthur S. Goldberger, op. cit., p. 574.

10Jan Kmenta and Paul E. Smith, "Autonomous Expenditures
vs. Money Supply: An Application of Dynamic Multipliers,"
Econometrics Workshop Paper No. 6604, Michigan State Univer-
sity, February 1967, p. 15.

144

The coefficients of the various policy variables are called
"delay multipliers." They Show the effect on the expecta—
tion of current Gross National Product of a Change in any
variable in a particular period. For example, a $1 billion
increase in government expenditures two quarters in the
past will result in a $570 million increase in the expecta-
tion of Gross National Product in the current quarter.

The final form can also be used to determine the in-
herent stability of the model. In this case, an "auxiliary
equation" is obtained by putting all terms that involve
Gross National Product (Y) on the leftehand side of the equa-
tion and setting the right-hand side equal to zero. The
resulting difference equation is then solved and the largest
root of the equation determines whether the system is stable

or not. In the present case, the auxiliary equation becomes:

(5.26) Y - 1.668 Yt_

t + 0.745 Yt_

- 0.028 Yt_ = 0.

1 2 5

This is solved for the following roots:

A1 = 0.058
A2 = 0.815 + 0.118 i
A5 = 0.815 - 0.118 i.

It appears that the model is stable since the largest real
root and the modulus of the conjugate complex roots are less
than unity in absolute value. Because of the presence of
complex roots the system will oscillate toward its equie

librium value. Consequently, the sources of instability in

145

the system appear to be either from random disturbances or
from Changes in the exogenous policy variables.

The final form can be put to a second use. From this
equation dynamic multipliers can be derived for the time path
of Gross National Product. These multipliers are obtained
by establishing the initial conditions of the reduced form
and then substituting in the value for lagged components of
Gross National Product. Once this is done, the time period
is increased by one and substitution takes place again.

This can be carried on for as long as the investigator feels
it is desirable. The coefficients attached to the various
current and lagged exogenous variables are the "dynamic
multipliers." The sum of these for any particular variable
gives the intermediate- or long-run multiplier for that
variable.

The dynamic multipliers have been computed for the ad-
justed monetary base and government expenditures. These are
presented in Table 5-1. The values were not computed for
the discount rate. In the first place, the coefficient for
the current value of the discount rate has the "wrong" Sign.
It should be emphasized, however, that this coefficient was
not significantly different from zero. .Thus the information
in the sample suggests that there is not a significant
current-quarter reSponse in the money SUpply to Changes in
the discount rate.

.Since this thesis is primarily concerned with short-run

behavior the values of the multipliers were computed only up

146

 

 

 

 

TABLE 5-1. .Dynamic Multipliers for the Time Path of Gross
~National Product
Coefficient of

Lag s Bt-s Gt-s
0 + 0.586 + 1.225
1 0.968 0.571
2 1.156 0.279
5 0.982 0.224
4 0.807 0.176

' 5 0.649 — 0.075
6 0.510 - 0.246
7 0.591 - 0.552
8 0.291 - 0.405

 

147

to an eight-quarter lag. Also, if monetary and fiscal policy
are carried out each quarter, the long-run effects are not
too significant if the system is stable, for the multipliers
should tend either to oscillate or to follow a monotonic

path towards zero. However, the intermediate-term multipliers
can be quite significant for the fulfillment of policy. If,
for example, the multipliers oscillate widely, future policy
might be more difficult to implement because of the reper-
cussions of present policy. If the multipliers change in a
relatively smooth way or oscillate only mildly, future policy
will be easier to implement and its effects will be more
easily projected.

As shown in Table 5—1, the dynamic multipliers of both
policy variables tend to change in a relatively moderate way
over time. The multipliers for the adjusted monetary base
rise to a peak after a two-quarter lag and then decline in
a smooth fashion. Because of the adjustments in the multi—
pliers, it would appear that future policy could take into
account past policy and be implemented without any problem
of offsetting or irregular movements in the economy due to
these previous policy decisions. It is obvious, however,
that a decision to reverse policy quickly would require a
greater than normal change in the policy variable under
discussion.

The dynamic multipliers of government expenditures show

that the greatest impact is felt in the quarter in which

148

these expenditures are undertaken. After this period the
value of the multiplier declines considerably. The multi-
plier tends to oscillate around zero if their values are
estimated for more than eight quarters.

The major implication to be derived from these figures
is that government expenditures have relatively little ef-
fect on the economy after the quarter they are undertaken.
This can imply two things. First, the total impact of
government expenditures can be felt rather quickly. Second,
policymakers face very little difficulty in implementing
future policy because of the cumulative effect of past fiscal
policy. Therefore, fiscal policy, in terms only of its
effect on the economy, can be reversed quickly and does not
encounter, to any great extent, the problem of offsetting
past policy decisions.11

In terms of relative effects, the impact of a $1
billion increase in government expenditures is greater than

a $1 billion increase in the adjusted monetary base. The

effect is still greater one quarter after the initial

 

11It should be noted that these results concerning the
lagged effects of monetary and fiscal policy are similar to
the results obtained by Friedman and Meiselman. They found
that autonomous expenditures were most highly correlated
with induced expenditures in the time period in which they
were undertaken. The money supply, however, was most highly
correlated with induced expenditures when it was lagged two
quarters. Milton Friedman and David Meiselman, "The Relative
Stability of Monetary Velocity and the Investment Multiplier
in the United States, 1897-1958," in B. Fox and E. Shapiro,
Stabilization Policies (Englewood Cliffs, N. J.: Prentice-
Hall, 1965), pp. 209-210. This coincides, to some extent,
with these policy variables having the greatest influence
on Gross National Produce in any one quarter.

149

changes. After that, however, the cumulative strength of
changes in the adjusted monetary base becomes much larger
than that of government expenditures. At the end of a year
the cumulative multiplier for the adjusted monetary base is
4.499, while it is 2.274 for government expenditures. After
two years the cumulative multipliers are 6.540 for the ad—
justed monetary base and 1.198 for government expenditures.
In judging the influence of these multipliers on aggre—
gate demand, the relative Size of changes in the two policy
variables must be taken into consideration. During the time
period under review, the adjusted monetary base did not
change by more than $1 billion in any one quarter. As was
mentioned above, the largest change was $1 billion in the
fourth quarter of 1965. If the monetary base Changed by
$500 million, this would have the effect of Changing Gross
National Product by only $2225 billion at the end of a year's
time. On the other hand, government expenditures changed by

more than $1 billion in one quarter quite frequently.

Summary

Assuming that the estimated model is a reasonable Short-
run specification of aggregate demand, several conclusions
can be drawn from the above results:

(i) The linkages between monetary variables and Gross
National Product are somewhat loose. Monetary policy works

through both consumption expenditures and investment

150

expenditures. However, the relationship with consumption

is not very strong and that with investment occurs only with
some passage of time. The current-period transmission process
Operating through interest rate variables is very weak.

(ii) Government expenditures work quickly on consumption
and investment expenditures through direct increases in the
demand for goods and services and wages and salaries. Govern-
ment eXpenditures exert repercussions on these expenditures
through feedbacks that occur in imports and interest rates.

(iii) Government expenditures appear to have the greater
impact on Gross National Product in the short run, while the
monetary variables may have the greater overall long-run
influence. However, this conclusion must be carefully in-
terpreted in terms of the relative size of changes in the
two variables.

(iv) Monetary and fiscal policy both seem to work them-
selves out in fairly regular patterns. However, because of
the more substantial long-run influence of monetary policy,
it would seem to be more difficult to reverse the direction

of its impact on aggregate demand.

CHAPTER VI

SUMMARY AND RECOMMENDATIONS FOR FURTHER RESEARCH

Summary of WOrk Coppleted

The main purpose of this study is to investigate the
relative effects of various exogenous variables on national
income. Whereas, the original research into this area
postulated simple linear reduced-form models, this thesis
attempts to carry the discussion into the more complete
framework of a nine-equation econometric model. In so doing,
it is hOped that a greater understanding of the relative
importance of the exogenous variables can be achieved.

The major conclusion of the thesis is that there is
still no clear—cut answer to the question concerning the
most important policy variable or the most stable functional
relationship. As a result, one should probably adopt the
more moderate position that both monetary and fiscal policy
are important and that more research needs to be devoted to
observing their combined effects on the economy rather than
in trying to isolate their individual effects. Some tenta-

tive conclusions, however, can be drawn from the above

151

152

discussion that will at least arrange the primary points
in some coherent form.

(i) Aggregation. Extreme care must be used in inter—
preting the results of single-equation tests derived from
very elementary models, due to the heroic aggregation neces-
sary for such models. This seems to have been the major
problem encountered in the early work done in this area.

For example, no discussant seemed to agree on the appropriate
definition of autonomous eXpenditures. The conclusion drawn
from the tests, therefore, depended heavily upon which defi-
nition was used. As a result, the early discussions led to
no verdict. However, they did clarify some of the problems
involved in such a research effort.

(ii) Stability, Both relationships, the income velocity
of Circulation and the investment multiplier are unstable
in an absolute sense. In fact, the single-equation models
would terrify any decision maker who might use them for
policy considerations.

(iii) Control of Exogenous Variables. Friedman and
Meiselman draw satisfaction from the fact that the money
supply is easily controlled by the monetary authorities,
whereas any of the measures of autonomous expenditures are
not under the control of Federal authorities. There is, of
course, some question as to the degree of control the mone-
tary authorities have over the money supply. As to auton-

omous expenditures, there is no question about the absence

155

of direct control the‘Féderal Government has over net private
domestic investment and the net eXport balance. More will be
said on this point in the second section of this chapter.

(iv) Transmission Process. This point brings in the use
of the complete model. It is in this context that some of
the linkages between policy variables and endogenous variables
can be discussed. As pointed out in Chapter V, the transmis-
sion of shocks from fiscal policy variables to aggregate
activity seems to be more direct than those of monetary
policy. Also, the immediate impact is greater. In fact, it
would appear that there is a great deal of room for variation
in the final relationship between the adjusted monetary base
and Gross National Product. Hence, one could eXpect con-
siderable variation in the velocity of circulation.1

(v) Relative Strengths of the Two Policy Variablgg.
In terms of the initial impact on the economy, government
expenditures seem to have a greater force initially and for
one quarter thereafter. The adjusted monetary base surpasses
the total influence of government eXpenditures in the second
quarter and its effect remains larger.

Care should be taken in interpreting these effects,

because the quarter-to-quarter change in government

 

1The velocity of circulation is here defined as Gross
National Product/Adjusted Monetary Base. If the money supply
is closely related to the adjusted monetary base, then What
is true for this value will also be true for Gross National
Product/money supply. If the money supply is not closely re-
lated to the adjusted monetary base, then the velocity of
circulation loses its importance for monetary actions.

154

expenditures usually exceeds the quarter—to—quarter change
in the adjusted monetary base. A $1 billion change in
government expenditures is not the average equivalent policy
of a $1 billion Change in the adjusted monetary base.

(vi) Reversibility of Policy. It is apparent in judg-
ing the dynamic effects of monetary and fiscal policy that
it is much easier to reverse the effects of fiscal policy
than to reverse those of monetary policy. The effect of
fiscal policy is felt primarily in the quarter in which it
is undertaken. The effects of monetary policy build up to
a peak and then decline slowly. .Consequently, a reversal
of the effects of monetary policy must overcome the influ-
ences of past policy. This problem presents possibilities
for further study into the lag in effect of monetary policy.

(vii) Relation of Money to Gross National Product Over
Tlpp, The conclusion reached in (vi) above can be used to
account for some of the observed relationship between the
money supply and Gross National Product. Because the effects
of monetary policy work over time, this would mean that a
growing money supply would provide a growing effect on Gross
National Product, independent of the current monetary policy.
.What changes is the income velocity of money. In this case
it would increase. This is just what Friedman has found.
Income velocity increases in the boom time of a cycle and

2

falls in the contraction. He explains this result in

 

2Milton Friedman, "The Demand for Money: Some Theoreti-
cal and Empirical Results," The Journal of Political Edonomy,
Vol. 67 (August 1959), p. 529.

155

terms of the permanent income hypothesis. However, it can
easily be eXplained in terms of'the past effects of a grow-
ing money supply. That is, a relatively constant growth in
the monetary variable has a cumulative effect on the growth
of Gross National Product.

It also appears that one could eXpect that after a
change took place in policy, fOr example, from a positive
growth rate to a negative growth rate, and after the past
influence of monetary policy is finally overcome, there would
be a drastic Change in the current relationship between the
money supply and Gross National Product. The velocity of
circulation would in this case fall, leading to the conclu—
sion that there had been a shift in the demand for money when
there actually had not been. This certainly is an interest-

ing hypothesis and worthy of further study.

Recommendations for Further Studyyip the
Area of Single-Equation Models

The simple linear, reduced-form model, however, is not
completely without use. In the early work done in this area,
the reduced forms were derived from the very simplest models
that exemplified the characteristics of the theories under
discussion. The linear models suffer from many deficiencies,
such as simultaneous equation bias. However, the use of
these simple models represents the only way, at present, to

test short-period movements of data over many different time

156

periods. .More expanded models take up degrees of freedom
that are very vital in computing the annual data when only
ten sample points are used. Also, the larger models appear
to be quite susceptible to misspecification of the model
when small samples are used.3 Because of this, the minimum
variance prOperty of the ordinary least—squares method of
estimation becomes quite important. It would seem that
additional research could continue in several profitable
directions using only the single-equation procedure. These
are listed below.

(i) Autonomous Variable. It has been suggested by
Pesek4 that autonomous expenditures should be divided into
two components. One component, "private" autonomous expendi-
tures are outside the control of the Federal Government.
This is true, at least at the very simple level of aggrega-
tion used in these single—equation models. .The second com-
ponent would be a component that could truly be compared with
the money SUpply (or some other monetary variable). This
would be "public" eXpenditures, and preferably those public
expenditures undertaken by the Federal Government. This
autonomous variable could be either the total of Federal
Government expenditures or the Federal Government deficit.

The particular form could be as follows:

I
l

 

3J. Johnston, Econometric Methods (New York: McGraw-
Hill, 1965). pp. 295-294.

4BorisP. Pesek, "Money vs. Autonomous Expenditures:
The Quality of the Evidence," Business Economics, III
(Spring.1968), p. 29.

157

(6.1) ct = a + K'Ai + k"AE
where Ct is induced expenditures
Ai is private autonomous expenditures
A: is public antonomoquexpenditures.

This could be tested in the following form:

2
= . I.
(6.2) Ct a + KAt + ut
. _ . 1
where a — a + K At

and ut is the normal stochastic error term with zero mean,

constant variance and zero covariance. Because of the nature

of Ai,

the intercept term.

it would still be independent of u even as a part of

t’

It would be desirable to test (6.2) and compare the
results with the velocity of circulation models. This would
reduce the test to a comparison of two variables felt by many
to be under the control of policymakers.

(ii) The Interest Rate and the Demand for Money. In most
studies of the demand for money, other factors are felt to be
highly influential. The most commonly used variable in this
respect is some measure of "the" interest rate. .Many studies
have found an interest rate to be highly important in the

demand for money,5 although Friedman has not found this to be

 

5Henry A. Latané: "Cash Balances and the Interest Rate--
A Pragmatic Approach," The Review Of_§conomics and Statistics,
Vol. 56 (November 1954). PP. 456-460 and also "Income Velocity
and Interest Rates: A Pragmatic Approach," The Review of
Egonomicp and Statistics, V01. 42 (November 1960). PP. 445-
449. (See also, Allan H. Meltzer, "The Demand for Money:

158

true in his work.6 These former studies have shown that
movements in the income velocity of circulation seem to be
closely related to movements in interest rates.

This is perhaps where the concern of Friedman and Meisel—
man for the relative stability of the income velocity of
Circulation can be misleading. There is no doubt that when
one looks at the computed values of income velocity (as shown
in Appendix A), it Changes considerably. In fact, jumps of
approximately 10% appear to be quite frequent.7 It is appar-
ent that something else is needed to help explain these
jumps.

This supposedly was one of the main developments of the
"Keynesian revolution." The Keynesian approach attempted to
explain variations that took place in the velocity Of circu-
lation. This is why Keynes himself placed so much emphasis

on the rate of interest in the demand for money equation.8

 

The Evidence from the Time Series," The Journal of Political
Economy, Vol. 71 (June 1965), pp. 219-246.

6Milton Friedman, "The Demand for Money," Op. cit.,
p. 545.

7Tobin has called special attention to the fact that
velocity changed up to 10% on a year-to—year basis in the
vast majority of cases over the 91 years incorporated into
Friedman and Swartz'S'Monetary_Histogy of the United States.
Therefore, the fact that velocity changes 10% or more over
longer periods of time should not be surprising. See, James
Tobin, “The Monetary Interpretation of History," The American
Economic Review, LV (June 1965), pp. 479-480.

8John Maynard Keynes, "The Theory of the Rate of Inter-
est," in W. Feller and B. F. Haley, Readings in the Theogy
of Income Distribution (Homewood, Ill.: Richard D. Irwin,

1

Inc., 1951), p. 422.

159

Tobin has postulated that classical economists felt that
the interest rate was not needed in the demand for money

9 This was because "the" rate of interest was the

equation.
marginal productivity of Capital. In the Classical system,
with flexible wages and prices, the system would always re-
turn to full employment. Given the technological and
behavioral structure, the full employment value of the marginal
product of capital was always the same. "The" rate of inter—
est was a constant. Keynes unlocked this problem in attempt-
ing to discuss periods of less than full employment.
Consequently, "the" rate of interest became a variable again

in the demand for money equation.

Most studies of the demand for money have covered an ex-
tended period of time. It might prove instructive to include
an interest rate variable in the reduced-form quantity theory
equation, as tested above, to see if this could help explain
some of the short-run variations found in the velocity of
circulation.

(iii) Determinants of the MonenyuppTy, A great deal of
work has been done in recent years in the area of the supply

of money.10 Friedman himself has contributed to this

 

9James Tobin, "Money, Capital and Other Stores of Value,"
The American Economic Review, Papers and Proceedings, Vol. 51
(May, 1961), p. 51.

l°Karl Brunner, "A Schema fOr the Supply Theory of Money,"
Tpternational Economic Review, Vol. 2 (January 1961), pp. 79-
109 and Karl Brunner and Allan H. Meltzer, "Some Further
Investigations of Demand and SUpply Functions for Money," 122
Journal of Finance, Vol. XIX (May 1964), pp. 240-285.

160

development.ll

Reference has already been made to this work
in the derivation of the money supply equation of the com—
plete model used in this thesis. As was mentioned above,
the control of this variable by the monetary authorities is
not absolute. This presents another desirable path that
could be taken in future research. The data are available
for the period that has been studied by Friedman and Meisel-
man.12 It would be interesting to see if the authorities
have as much short-run control over the money supply as is
hypothesized by those who consider this variable to be rele-
vant for economic decision making. The evidence from

quarterly data in this thesis suggests that the degree of

control is not eSpecially great.

 

11Milton Friedman, A Program for Monetary Stabilipy
(New York: Fordham University Press, 1959), pp. 105-106 and
Milton Friedman and Anna Jacobson Swartz, A Monetary History
of the United States, T867-1960 (Princeton, N. J.: Princeton
UniVersity Press, 1965), pp. 776-798. 7‘

12Milton Friedman and Anna Jacobson Swartz, op. cit.,
pp. 799-808.

BIBLIOGRAPHY

BIBLIOGRAPHY

Adelman, Irma and Adelman, Frank L. "The Dynamic PrOperties
of the Klein-Goldberger Model," Econometrica, October
1959.

Andersen, Leonall and Jordan, Jerry. "Monetary and Fiscal
Actions: Their Relative Importance in Economic Stabili-
zation," Review, Federal Reserve Bank of St. Louis, 50,
November 1968.

Ando, Albert and Modigliani, Franco. "The Relative Stability
of Monetary Velocity and the Investment Multiplier,"
The American Economic Review, LV, September 1965.

. "Rejoinder," The American Economic Review, LV,
September 1965.

Board of Governors of the Federal Reserve System. Federal
Reserve Bulletin. Board of Governors of the Federal
Reserve System, Washington, D. C., 1952.

Brunner, Karl. "A Schema for the Supply Theory of Money,"
The International Economic Review, Vol. 2, January 1961.

Brunner, Karl and Meltzer, Allan H. "Liquidity Traps for
Money, Bank Credit, and Interest Rates," The Journal of
Political Economy, Vol. 76, January/February 1968.

. "Rejoinder to Chase and Hendershott," in G.
Horwich, Monetary Process and Policy: A Symposium.
Homewood, Ill.: Richard D. Irwin, Inc., 1967.

 

. “Some Further Investigations of Demand and Supply
Functions for Money," The Journal of Finance, XIX, May
1964.

Cagan, Phillip. Determinants and Effects of Changes in the
Stock of Money, 1875-1960. New York: Columbia University
Press, 1965.

Chow, Gregory C. "Multiplier, Accelerator, and Liquidity
Preference in the Determination of National Income in
the United States," The Review of Economics and
Statistics, XLIX, February 1967.

161

162

Christ, Carl F. "A Short—run.Aggregate-demand Model of the
Interdependence and Effects of Monetary and Fiscal
Policies with Keynesian and Classical Interest Elas-
ticities," The American Economic Review, LVII, May 1967.

. "A Simple Macroeconomic Model with a Government
Budget Restraint," The Journal of Political Economy,
Vol. 76, January/February 1968.

. Econometric Models and Methods. New York: John
Wiley and Sons, Inc., 1966.

De Prano, Michael and Mayer, Thomas. "Tests of the Relative
Importance of Autonomous EXpenditures and Money,"
The American Economic Review, LV, September 1965.

"Rejoinder," The American Economic Review, LV,
September 1965.

Dernberg, Thomas F. and McDougall, Duncan M. Macroeconomics,
Third Edition, New YOrk: McGraw-Hill.

Duesenberry, James. Income, Savings andkthe Theory of
Consumer Behavior. Harvard University Press, 1949.

Ezekiel, Mordechai and Fox, Karl A. .Methods of Correlation
'and RegreSSion Analysis. New York: John Wiley and Sons,
Inc., 1959.

Feige, Edgar. The Demand for Liquid Assets: A Temporal
Cross-Section Analysis. Englewood Cliffs, N. J.:
Prentice—Hall, 1964.

Friedman, Milton. A Program for Monetary Stabilipy. New York:
Fordham University Press, 1960.

. A Theory of the Consumption Function. Princeton
University Press, 1957.

. "The Demand for Money: Some Theoretical and Empiri—
cal Results," The Journal of Political Economy, Vol. 67,
August 1959.

Friedman, Milton and Meiselman, David. "Reply to Ando and
Modigliani and De Prano and Mayer," The American Economic
Review, LV, September 1965.

. ”Reply to Donald Hester," The Review of Economics
and Statisticp, XLVI, November 1964.

. "The Relative Stability of Monetary Velocity and
the Investment Multiplier in the United States, 1897-
1958," in B. Fox and E. Shapiro, Stabilization Policies.
Englewood Cliffs, N./J.: Prentice-Hall, 1965.

165

Friedman, Milton and Swartz, Anna Jacobson. A Monetary
History of the United States, 1867-1960. Princeton,
N, J.: Princeton University Press, 1965.

 

Fromm, Gary and Taubman, Paul. Policy Simulations with an
Econometric Model. Washington, D. C.: The Brookings
Institution, 1968.

Goldberger, Arthur S. Econometric Theory. New York: John
Wiley and Sons, Inc., 1964.

. Impact Multipliers and Dynamic PrOpertiep_of the
Klein-Goldberger Model. Amsterdam: North-Holland
Publishing Co., 1959.

Hester, Donald. "Keynes and the Quantity Theory: A Comment
on the Friedman-Meiselman CMC Paper," The Review of
Economics and Statistics, XLVI, November 1964.

 

"Rejoinder," The Review or Economics and Statis-
tics, XLVI, November 1964.

Hicks, J. R. "Mr. Keynes and the 'Classics': A Suggested
Interpretation," Econometrica, V, 1959. Reprinted in
Readings in the Theory of Income Distribution. Home-
wood, Ill.: Richard D. Irwin, Inc., 1951.

Johnson, Harry G. "Monetary Theory and Policy," The American
Economic Review, LII, June 1962.

Johnston, J. Econometric Methods. New York: McGraw-Hill,
1965.

Keynes, John Maynard. A Treatise on Money, 2 Vols.
New York: Harcourt, Brace and Company, 1950.

. The General Theory of Employment Interest and
Money. New York: Harcourt, Brace and Company, 1956.

. "The Theory of the Rate of Interest," in W. Feller
and B. F. Haley, Readings in the Theory of Income
Distribution. Homewood, Ill.: Richard D. Irwin, Inc.,
1951.

Klein, L. R. Economic Fluctuations in the United States.
New York: John Wiley and Sons, Inc., 1950.

Klein, L. R. and Goldberger, A. S. An Econometric Model of
the United Statesy 1929-1952. Amsterdam: North-Holland
Publishing Co., 1955.

164

Kmenta, Jan and Smith, Paul.

"Autonomous Expenditures vs.
Money Supply: '

An Application of Dynamic Multipliers,
Econometrics Workshop Paper No. 6604, Michigan State
University, February 1967.

Latané, Henry A.

"Cash Balances and the Interest Rate-—
A Pragmatic Approach," The Review of Economics and
Statistics, Vol. 56, November 1954.

"Income Velocity and Inrerest Rates: A Pragmatic

Approach," The Review of Economics and Statistics, Vol

42, Novemben 1960.

Meltzer, Allan H. "The Demand for Money: The Evidence of
the Time Series," The Journal of Political Economy

Vol. 71, June 1965.

Nerlove, Marc and walis, Kenneth F. "Use of the Durbin-
Watson Statistic in Inappropriate Situations,
Econometrica Vol. 54, January 1966.
Pesek, Boris P. "Money vs. Autonomous Expenditures: The
Quality of the Evidence," Business Economics,

III,
September 1968.

Pesek, Boris P. and Saving, Thomas R. Moneyy_Wealth and
Economic Theory. ,New YOrk:

Macmillan Co., 1967.
Teigen, Ronald.

"The Demand for and Supply of Money,' in
W. L. Smith and R. L. Teigen, Readings in Money,
National Incomeyyand Stabilization Policy. Homewood,
Ill.: Richard D. Irwin, Inc., 1965.
Theil, H. and Boot,

J. C. G. "The Final Form of Econometric
Equation Systems," Review of the International Statis-
tical Institute, Vol. 50, 1962.

Tobin, James.

"An Essay on Principles of Debt Management,"
in B. Fox and E. Shapiro, Fiscal and Debt Management
Policies. Englewood Cliffs,

1965.

N. J.: Prentice-Hall,

"Money, Capital and Other Stores of Value,
The American Economic Review,

Papers and Proceedings,
Vol. 51, May 1961.

"The Monetary Interpretation of History,
The American Economic Review,

LV, June 1965.
United States Department of Commerce. Business Statistics,
16th Biennial Edition.

United States Department of
Commerce, Washington, D C., 1967.

165

United States Department of Commerce. Longfitermpgconomgg
Growth: 1860-1965. Washington, D. C.: U. S. Govern-
ment Printing Office, 1966.

 

. The National Income and Product Accounts of the
United States, 1929-1965, Statistical Tables. United
States Department of Commerce, Washington, D. C., 1966.

Wold, Herman and Jureen, Lars. Demand Analysis. New York:
John Wiley and Sons, Inc., 1951.

 

WOod, John H. "A Model of Federal Reserve Behavior," in
G. Horwich, Monetary Process andFPolipy: A Symposium.
Homewood, Ill.: Richard D. Irwin, Inc., 1967.

Zellner, A., Huang, D. S., and Chau, L. C. "Further Analy—
sis of the Short-run Consumption Function with Emphasis
on the Role of Liquid Assets," Econometrica, Vol. 55,
July 1965.

 

APPENDICES

APPENDIX A

RESULTS OF THE FRIEDMAN-MEISELMAN TESTS AND THE
CORRECTIONS FOR STANDARD ERROR TERMS

This appendix presents the results of the Friedman-
Meiselman tests and the corrections for standard error
terms mentioned earlier in the text in Chapter IV. It was
also stated that autocorrelation caused the standard errors
of the coefficients to be underestimated. Therefore, the
prOper correction of the standard errors would raise their
numerical value and reduce the significance level of the
various coefficients.

Since the major interest of this thesis is in the vari-
ables that possess the correct sign and are significantly
different from zero, the only standard errors corrected were
those that related to the coefficients of the policy variables
whose estimates had the proper Sign; were significantly dif—
ferent from zero at the 5% level of significance; and where
there was significant autocorrelation present in the esti-
mated equation. If the estimated coefficient had the wrong
sign or was not Significantly different from zero, the cor-
rection of its standard error was not performed because it

would not change any of the conclusions already reached.

166

167

In Table A—1, only the estimated coefficients for the
policy variables are presented for each equation and for
each time period. The results from both sets of data are
also presented. The uncorrected standard error terms are in
parenthesis directly below the estimated coefficient. Those
corrected standard error terms are shown directly below the
uncorrected values in those cases where the correction has

been performed.

TABLE A-1. The
and

168

Friedman-Meiselman Results with Corrected
Uncorrected Standard.Error Terms

 

 

C = a + kA + VM

Annual Figures

1897-1958

1897-1908
1905-1915
1908-1921
1915-1920
1920-1929
1921-1955

1929-1959

1955-1958

1958-1955

1959-1948

1948-1957

1929-1958

2
First Set of Data Second Set of Data

A M2 A M2

- .425 + 1.58
( .245)* ( .047)
( .178)
— .259 1.690
( .158)* ( .052)

- .057 + 1.91
( .159)* ( .061)

+ .181 1.750
( .126) ( .064)
+ .287 1.749
( .274)* ( .158)
+ .258 1.295,
( .500)* ( .149)
+ .794 1.157
( .155) ( .150)
+ 1.422 .495 + 1.585 .655
( .184) ( .165) ( .590) ( .571)
(1.191)/
+ .457 1.127 + .585 + 1.126
( .559)* ( .544) ( .486)* ( .245)
( .495) ( .408)
- .468 1.529 — .509 + 1.555
( .585)* ( .107) ( .407)* ( .114)
( .289) ( .508)
- .576 + 1.051 - .455 1.029
( .257)* ( .094) ( .255)* ( .090)
( .155) ( .124)
- .645 + 1.480 + .665 + 2.114
( .559)* ( .082) ( .697)* ( .166)
( .284) ( .249)
+ .455 + 2.105 - .862 + 1.519
( .670) ( .186) ( .557)* ( .089)
( .267) ( .279)

 

* Coefficients
the 5% level
error terms.

/ Coefficients
the 5% level
error terms.

are not significantly different from zero at
of significance using uncorrected standard

are not significantly different from zero at
of significance using corrected standard

169

TABLE A—1--continued

 

 

 

C = a + KA
Annual Figures First Set of Data Second Set of Data
A A
1897-1958 + 5.162
( .578)
(1.814)
1897-1908 + 2.562
(1.121)
(1.985)/
1905-1915 + 2.427
(1.459)*
1908-1921 + 2.407
( .765)
(1.424)/
1915-1920 + 2.606
( .822)
(1.082)
1920-1929 1.602
( .818)*
1921-1955 + 1.585
( .266)
( .641)
1929-1959 + 1.898 + 2.498
( .126) ( .512)
( .174) ( .555)
1955—1958 + 2.154 + 2.455
( .285) ( .467)
( .560) ( .644)
1958-1955 + 1.525 + 1.865
(1.226)* (1.151)*
1959-1948 + .554 + .494
( .990) ( .994)
1948-1957 + 5.848 _+ 7.151
( .825) ‘ (2.187)
(2.585)/ (5.875)/
1929-1958 + 6.590 + 5.946
(1.716) ( .748)
(2.565) (2.547)/

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard
error terms.

% Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard
error terms.

TABLE A-1--continued

170

 

 

C = a + VMZ

Annual Figures

First Set of Data

M

Second Set of Data

M

 

2 2
1897-1958 + 1.515
( .050)
( .114)
1897—1908 + 1.654
( .044)
1905-1915 + 1.900
( .050)
1908-1921 + 1.809.
( .051)
1915-1920 + 1.875
( .105)
1920-1929 + 1.557
( .124)
1921-1955 + 1.665
( .248)
( .540)
1929-1959 + 1.596 + 1.527
( .226) ( .229)
( .456) ( .552)
1955-1958 + 1.594 + 1.505
( .095) ( .090)
( .188) ( 1196)
1958-1955 + 1.280 + 1.262
( .101) ( .101)
( .517) ( 1517)
1959-1948 + .996 + .976
( .097) ( .096)
( .165) ( .161)
1948-1957 + 1.567 + 2.250
( .058) ( .115)
( .220) ( .170)
1929-1958 + 2.201 + 1.551
( .112) ( .059)
( .168) ( .225)

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard
error terms.

/ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard
error terms.

TABLE A-1--continued

171

 

 

= I
Y a + V M2

Annual Figures

First Set of Data

Second Set of Data

 

M2 M2
1897-1958 + 1.469
( .050)
( .094)
1897-1908 + 1.867
( .081)
1905-1915 + 2.089
( .115)
1908-1921 + 2.157
( .140)
( .201)
1915-1920 + 2.512
( .217)
1920-1929 + 1.618
( .220)
1921-1955 + 2.525
( .508)
(1.571)/
1929-1959 + 2.572 + 2.080
( .570) ( .506)
( .805) ( .618)
1955—1958 + 2.006 + 1.765
( .155) ( .158)
( .557) ( .257)
1958-1955 + 1.585 + 1.402
( .102) ( .101)
( .246) ( .244)
1959-1948 1.089 + 1.092
( .116) ( .102)
( .174) ( .155)
1948-1957 + 1.545 + 2.599
( .056) ( .144)
( .176) ( .206)
1929-1958 + 2.418 + 1.545
( .140) ( .054)
( .195) ( .169)

 

* Coefficients are not Significantly different from zero at
the 5% level of significance using uncorrected standard

error terms.

{ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard
error terms.

TABLE A-1--continued

172

 

 

C = a + kA + VM + BP

 

 

Annual Figures First Set of Data Second Set of Data
A M2 A M
2
1897-1958 - .551 1.096
( .211) ( .075)
( .260)
1897-1908 - .502 1.928
( .154) ( .258)
1905-1915 - .050 1.751
( .167)* ( .287)
1908-1921 - .159 .967
( .100)* ( .165)
1915-1920 - .225 + .618
( .127)* ( .195)
1920-1929 + .155 1.560
( .527)* ( .175)
( .241)
1921-1955 + .565 1.219
( .290)* ( .147)
1929-1959 + .957 .659 .821 .654'
( .264) ( .154) ( .227) ( .128)
( .264) ( .149)
1955-1958 - 1.009 1.256 + .056 .955
( .715)* ( .226 ( .458)* ( .259)
( .515)
1958-1955 - .547 - .255 - .555 .199
( .168)* ( .216)* ( .181)* ( .215)*
1959-1948 - .594 + .045 - .415 .156
( .061) ( .094) ( .067)* ( .095)*
1948-1957 - .478 + .510 + .557 .060
( .275)* ( .255) (1.446)* ( .657)
( .876)/ ( .986)
1929-1958 - .054 + 1.79 - .562 .515
( .985)* ( .495) ( .297)* ( .262)*
( .740)

 

* Coefficients
the 5% level
error terms.

/ Coefficients
the 5% level
error terms.

are not significantly different from zero at
of significance using uncorrected standard

are not significantly different from zero at
of significance using corrected standard

175

TABLE A-1--continued

 

C=a+kA+BP

 

Annual Figures First Set of Data Second Set of Data
A A
1897-1958 + .524
( .428)*
1897-1908 + .516
( .547)*
1905—1915 + .158
( .585)*
1908-1921 - .498
(..164)
1915-1920 - 2.196
( .189)
1920-1929 + 1.66
( .815)
(1.440)/
1921—1955 + 1.658
( .679)
(1.570))!
1929—1959 + 1.875 + 1.759
( .265) ( .281)
( .562) ( .498)
1955-1958 + 1.621 + .844
(1.767)* ( .985)*
1958-1955 — .581 - .576
( .168)* ( .175)*
1959-1948 - .592 - .599
( .058) ( .071)*
1948-1957 — .295 - 2.698
( .274)* (1.514)*
1929-1958 - 1.580 - .501
(1.464)* ( .278)*

 

* Coefficients
the 5% level
error terms.

/ Coefficients
the 5% level
error terms.

are not significantly different from zero at
of significance using uncorrected standard

are not significantly different from zero at
of significance using corrected standard

174

TABLE A-1—-continued

 

= =7—

C = d + vM + BP

 

 

2
Annual Figures First Set of Data Second Set of Data
M2 M2
1897-1958 + 1.052
( .075)
( .277)
1897-1908 + 1.658
( .250)
1905-1915 + 1.755
( .266)
1908-1921 1.118
( .144)
( .291)
1915-1920 + .779
( .204)
1920—1929 + 1.41
( .155)
1921-1955 + 1.519
( .128)
1929-1959 + 1.112 + 1.022
( .155) ( .124)
( .194) ( .165)
1955-1958 + 1.044 + .946
( .196) ( .176)
( .245)
1958—1955 - .555 - .295
( .258)* ( .225)*
1959-1948 + .025 + .052
( .244)* ( .256)*
1948-1957 + .564 + 1.879
( .247)* ( .429)
( .615)
1929—1958 + 1.795 + .289
( .411) ( .245)*
( .617)

 

* Coefficients are not significantly different from zero at
the 5% level of Significance using uncorrected standard
error terms.

/ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard
error terms.

175

TABLE A-1-—continued

 

 

 

 

Y = a + V' M2 + BP
Annual Figures First Set of Data Second Set of Data
M M
2 2__
1897-1958 + 1.152
( .072)
( .226)
1897-1908 + 2.554
( .587)
1905-1915 + 2.055
( .628)
1908-1921 + .168
( .564)*
1915-1920 + .065
( .49)*
1920—1929 + 1.724
( .229)
1921-1955 + 1.595
1929-1959 + 1.595 + 1.471
( .257) ( .254)
1955-1958 + 1.254 + 1.176
( .158) ( .556)
1958—1955 - .107 - .009
( .508)* ( .290)*
1959-1948 .077 + .257
( .562)* ( .525)*
1948-1957 + .669 + 1.526
( .249) ( .462)
( .781)/ ( .587)
1929—1958 + 1.575 + .687
( .445) ( .259)
( .565) ( .750)/
*Coefficients are not significantly different from zero at

the 5% level
error terms.

/Coefficients
the 5% level
error terms.

of significance using uncorrected standard

are not significantly different from zero at
of signigicance using corrected standard

TABLE A—1--Continued

 

 

C = d + VM1

Annual Figures

1920-1929
1921-1955
1929-1959
1955-1958

1958-1955
1959-1948_
1948-1957

1929-1958

M1

+ 5.552
( .440)

+ 4.085
( .567)
( .506)

+ 1.624
( .545)
(1.011)/

+ 1.856
( .155)
( .227)

+ 1.589
( .159)
( .456)

+ 1.225
( .155)
( .259)

+ 1.710
( .096)
( .158)

+ 5.555
( .267)
(1.011)

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard

error terms.

/ Coefficients are not significantly different from zero at
the 5% level of Significance using corrected standard

error terms.

TABLE A-1—-Continued

177

 

 

C = a + VM1 + BP

 

Annual Figures M1

1920-1929 + 5.459

( .427)
1921-1955 + 5.456

( .569)
1929—1959 + 1.257

( .075)
1955-1958 + 1.547

( .294)
1958-1955 - .557

( .255)*
1959-1948 - .168

( .295)*
1948-1957 + .062

( .262)*
1929-1958 + 2.565

(1.185)

(1.895)/

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard

error terms.

/ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard

error terms.

TABLE A-1--continued

 

 

Y = d + V'

Annual Figures

1920-1929

1921-1955

1929-1959

1955-1958

1958-1955

1959-1948

1948-1957

1929-1958

M1

+ 4.575
( .558)

+ 6.045
( .795)
(1.751)

+ 5.405
( .855)
(1.479)/

+ 2.645
( .205)
( .489)

+ 1.755
( .129)
( .511)

+ 1.566
( .126)
( .174)

+ 1.942
( .091)
( .116)

+ 5.924
( .281)
( .882)

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard

error terms.

/ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard

error terms.

.179

TABLE A-1--Continued

 

 

Y = a + V' M + BP

 

1
Annual Figures M1

1920-1929 + 4.550

( .566)
1921-1955 + 4.265

( .541)
1929-1959 + 1.809

( .152)
1955-1958 + 1.655

( .155)
1958-1955 + .011

( .558)*
1959-1948 + .564

( .425)*
1948-1957 + .481

( .271)*
1929-1958 + 2.272

(1.148)

(1.582)/

 

* Coefficients are not significantly different from zero at
the 5% level of significance using uncorrected standard
error terms.

/ Coefficients are not significantly different from zero at
the 5% level of significance using corrected standard
error terms.

APPENDIX B

SOURCES-OF DATA USED

This appendix describes the sources of the data used
for computation of the complete model presented in Chapter
V. The three major sources will be abbreviated. These
three sources are:

.(1) United States Department of Commerce, Business
Statistics, 16th Biennial Edition (United States
Department Of Commerce, Washington, D. C., 1967).
Abbreviation: Business Statistics

(2) , The National Income and Product Accounts
of the United Statepy 1929-1965. \Statistical
Tables (United States Department of Commerce,
Washington, D. C., 1966).

Abbreviation: Nationalngcome Accounts

(5) Board of Governors of the Federal Reserve System,
Federal Reserve Bulletin (Board of Governors of
the Federal Reserve System, Washington, D. C.).
Abbreviation: Federal Reserve Bulletin

Personal Consumption Expenditures: 1955-1965, quarterly
seasonally adjusted data taken from Table 1.1, pp. 2-5, line
2 of National Income Accounts.

Gross Private Domestic Investment: 1955-1965, quarterly
seasonally adjusted data taken from Table 1.1, pp. 2-5, line
6 of National Income Accounts.

Total Government Purchases of Goods and Services: 1955-

1965, quarterly, seasonally adjusted data taken from Table
1.1, pp. 2-5, line 20 of National Income Accounts.

180

181

Exports: 1955-1965, quarterly, seasonally adjusted data
taken from Table 1.1, pp. 2-5, line 18 of National Income
Accounts.

Imports: 1955-1965, quarterly, seasonally adjusted data
taken from Table 1.1, pp. 2-5, line 19 of National Income
Accounts.

Disposable Personal Income: 1955-1965, quarterly,
seasonally adjusted data taken from Table 2.1, pp. 54-55,
line 22 of National Income Accounts.

Money Stock: 1955-1965, monthly data are taken from p.
100 and p. 240 of Business StatistTgp. Quarterly averages
of the data were taken and then seasonally adjusted at the
Federal Reserve Bank of Cleveland using the X-11 variant of
the Census II Method, United States Department of Commerce,
Bureau of the Census.

Short-Term Interest Rate: New issue rate on three-
month Treasury bills, 1955-1965 monthly data from p. 90 and
p. 257 of Business Statistics. Quarterly averages of the
data were taken and then seasonally adjusted at the Federal
Reserve Bank of Cleveland using the X-11 variant of the
Census II Method, United States Department of Commerce,
Bureau of the Census.

Long-Term Interest Rate: U. S. Treasury bonds, taxable,
1955-1965 monthly data taken from p. 105 and p. 242 of
Business Statistics. Quarterly averages of the data were
taken and then seasonally adjusted at the Federal Reserve
Bank of Cleveland using the X-11 variant of the Census II
Method, United States Department of Commerce, Bureau of the
Census.

Rediscount Rate: .1955-1965 data are taken from p. A-9
in Federal Reserve Bulletin, January 1968. The rate taken
for the quarter was that rate at the Federal Reserve Bank of
New York which was prevalent for the greater part of the
quarter.

Adjusted Monetary Base: Monthly data for 1955-1965 on
the Source Base are supplied by the Federal Reserve Bank of
St. Louis. Monthly figures for Discounts and Advances at
the Federal Reserve are from various issues of the Federal
Reserve Bulletin. These latter figures were then subtracted
from the Source Base. Quarterly averages of the data were
taken and then seasonally adjusted at the Federal Reserve
Bank of Cleveland using the X-11 variant of the Census II
Method, United States Department of Commerce, Bureau of the
Census.