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FEDERAL RESERVE B A N K
O F S T. L O U IS
JUNE 1975

Two Stages to the Current Recession ............... 2
A M onetary M odel of N om inal Income
Determ ination ...................................... ................ 9

V ol. 5 7, No. 6

Two Stages to the Current Recession
NORMAN N. BOWSHER

T HE pattern of economic developments since the
X

R ea l Product*

fall of 1973 has seemed baffling to many. It has been
a period of prolonged and deep economic recession
combined with intensified inflation for a year. The re
cession has had substantially different characteristics
from the four previous recessions since 1950, including
two distinct periods within the current contraction.

S e a s o n a lly A d ju s t e d

P e a k s -1 0 0

A v e r a g e o f 1968-71, 1 9 5 9 -6 , 1 9 5 6 -5 8 ,
a n d 1 9 5 2 -5 4

/
✓

In terms of causal forces, the recent downturn also
differs from earlier contractions. All previous reces
sions in the past twenty-five years were preceded by
periods of pronounced monetary restraint. The current
downturn, by contrast, was preceded, and accom
panied for a time, by stimulative policy actions. As
the downturn progressed, however, the growth of the
money stock did slow markedly. In addition, develop
ments which have hampered production — such as
the higher price of oil, unfavorable weather condi
tions, and the effects of price controls — have played
a much greater role in the current downturn than in
earlier recessions.
This article reviews economic developments since
the fall of 1973 and finds that some of the confusion
concerning the current recession is eliminated if the
period is divided into two stages. The first stage,
which began in the late fall of 1973, was largely a
response to constraints placed on aggregate supply.
The second stage, which began in the early fall of
1974, reflected, in addition, a reduction in the growth
of demand for goods and services.
For this study, November 1973 is used as a tenta
tive peak for the past expansion.1 It was the month of
greatest industrial production, and in the following
three months production declined. The second stage
of the recession is postulated to have begun after Sep
tember 1974. Industrial production and employment,
1There are, of course, differences of opinion with respect to
the dating of the cyclical peak.
Page 2

J *

✓

V -/

t f

1 9 7 2 -7 5 \
3 R D C)TR 5 3
3RD C)TR 5 7

\
\

4 TH Q T R 6 9
1
4 TH Q T R 73

-4

-3

-2

-1

QUARTERS TO A N D FR O M PEAK
* G r o s s n a t i o n a l p r o d u c t in c o n s ta n t d o ll a r s .
L a te s t d a t a p lo t t e d : 1st q u a r t e r
S o u rc e : U.S. D e p a rtm e n t o f C o m m e rc e

which had risen, on balance, in the previous seven
months, declined sharply after September. Compari
sons are made with averages of periods just before
and after the four preceding cyclical peaks, as se
lected by the National Bureau of Economic Research.
They are November 1969, May 1960, July 1957, and
July 1953.

COURSE OF THE RECESSION
Production
Total real output of goods and services has declined
markedly throughout the recent economic contrac
tion. In the first five quarters following the peak ( end
ing first quarter 1975), real output decreased at a 6
percent annual rate, and available data indicate that

FEDERAL RESERVE BANK OF ST. LOUIS

the contraction probably has continued into the cur
rent quarter. By comparison, in the four previous
recessions, real output declined for only two quarters,
on average, and by the fifth quarter output typically
exceeded the previous cyclical high.
Industrial production declined for three months
after the 1973 cyclical peak, then increased slightly
for the seven months from February to September
1974. During this period, production was bolstered by
increased inventory demand as a result of anticipated
shortages of many items and by anticipations of in
ventory profits as prices jumped. However, from
September 1974 to April 1975 industrial production
again fell sharply at a 21 percent annual rate.

JU N E

1975

ten-month period of earlier recessions, employment
declined at an average 2 percent rate.
Reflecting a marked rise in employment since mid1971, 65.2 percent of the non-institutional population
of working force age (16 through 64) were employed
in the third quarter of the current contraction (III/
1974). On average, 62.7 percent held jobs at the four
earlier cyclical highs. As the recession intensified in
the period from last September to March, total em
ployment decreased at a rapid 6 percent rate. Never
theless, 63 percent of the noninstitutional population
of working force age were employed in the first quar
ter of 1975, or slightly more than had been employed
at the peaks of the four earlier cycles.
Total Em ploym ent

M O N T H S TO A N D F R O M PEAK
L a te s t d a t a p lo t t e d : A p r i l
S o u rc e : U.S. D e p a r tm e n t o f L a b o r

In the four previous recessions the pattern was for
industrial production to contract for about nine or ten
months. Thereafter, production turned up and rose,
on average, at an 11 percent annual rate from the
tenth to the seventeenth month, the stage comparable
to the period of marked drop in the current cycle.

Employment
A distinctive feature of the current cycle has been
the relatively high level of employment throughout
much of the contraction. Total employment, which
had risen a rapid 4 percent in the year preceding
November 1973, continued to increase, but at a slower
1 percent annual rate during the first stage of the eco
nomic downturn. By contrast, in the corresponding

The unemployment rate remained relatively low
until early last fall, but has risen abruptly since then.
In the first two months after the peak in economic
activity, the unemployment rate rose. Then, from the
second to the ninth month after the turn (January to
August 1974) the unemployment rate changed little,
in marked contrast to pronounced increases in com
parable periods of the earlier recessions. Since the
ninth month, the trends have been reversed; the rate
has risen sharply in recent months at a time when it
usually remained on a high plateau. At the seven
teenth month after the turning point (April 1975),
the unemployment rate, at 8.9 percent, was higher
than in any of the four previous recessions.
The combination of high unemployment and a rela
tively large percentage of the working age population
Page 3

JU N E

FED ER AL RESERVE BANK OF ST. LOUIS

U n em p lo y m en t Rate
P e o k s -1 0 0

Pea k s= 1 0 0

S e a s o n a lly A d ju s t e d

go 1 i I I I i I I l 1 I l 1 I 1 1 1
-12

-9

-6

-3

l l 1 1 i 1 I 1 1 gO
6

M O N T H S TO A N D FR O M PEAK
L a te s t d a t a p lo t t e d : A p r il
S o u r c e : U .S . D e p a r tm e n t o f L a b o r

employed reflects a rise in the participation rate in the
labor force. A larger share of women have entered the
labor force in the last several years, and more recently,
second and third members of many households have
sought jobs to meet the higher cost of living or to
maintain income when another member loses a job.
G e n e r a l Prices*
P eaks= 1 0 0

120 r

S e a s o n a lly A d ju s t e d

P eaks= 1 0 0

---------- 120

1975

average, during the final year of the four earlier eco
nomic expansions and the first two quarters of re
trenchment, general prices, as measured by the im
plicit GNP deflator, rose at a 3 percent annual rate.
From the second to the fifth quarters after the earlier
cyclical peaks, overall prices increased at a slower 2
percent average rate.
Despite the sharp and prolonged contraction, the
rate of inflation in the most recent downturn did not
behave as in previous recessions. For the period from
four quarters before to two quarters after the most
recent peak, general prices advanced at an 8.5 percent
annual rate. From the second to the fifth quarter of
the recession, the pace of inflation accelerated to 12
percent. In the fifth quarter, however, prices rose at a
slower 8.5 percent pace, and preliminary indications
are that the slowing has continued into the sixth
quarter (11/1975).

FIRST STAGE - NOVEMBER 1973
TO SEPTEMBER 1974
The contraction in production in the current reces
sion, as noted above, has come in two distinct waves
— the first from the November 1973 peak to Septem
ber 1974 and the second from September 1974 to the
present. The two periods of decline displayed sub
stantially different characteristics and resulted from
different causes. Therefore, in examining the recession
it is useful to analyze the two periods separately, even
though there is obviously an overlap of causes and
effects.

Demand

Q U A R TE R S T O A N D F R O M PEAK
* G r o s s n a t i o n a l p r o d u c t i m p l i c i t p r ic e d e f l a t o r .

Growth in demand for goods and services, as indi
cated by nominal gross national product, moderated
after the 1973 peak, but remained rapid by historical
standards for the first three quarters of the recession.
From the fourth quarter of 1973 to the third quarter
of 1974, total spending rose at a 7 percent annual rate.
By comparison, even in the final year of economic
expansion preceding the four earlier economic con
tractions, total spending rose at only a 5.5 percent
rate on average; then, in the first three quarters of
recession the rise in spending slowed to a 0.3 percent
rate.

L a te s t d a t a p l o t t e d : 1 st q u a r t e r
S o u rc e : U.S. D e p a r tm e n t o f C o m m e r c e

Prices
The rate of inflation has typically moderated after
about two quarters of economic sluggishness. On
Page 4

Policy Actions
The unusual demand growth during the first three
quarters of the current recession is partially explained
by monetary developments. Monetary actions, as

JU N E

FEDERAL RESERVE BANK OF ST. LOUIS

Total Spending on G o o d s an d Services*

M o n e y Stock

Q UARTERS TO A N D FR O M PEAK
‘ G ro s s n a t io n a l p r o d u c t in c u r r e n t d o lla r s .

1975

QUARTERS T O A N D FR O M PEAK
L a te s t d a t a p l o t t e d : 1st q u a r t e r

L a te s t d a t a p l o t t e d : 1st q u a r te r
S o u rc e : U.S. D e p a r tm e n t o f C o m m e rc e

measured by the growth rate of the money stock, were
restrictive prior to each of the four earlier business
cycle peaks. In each case the rate of money growth
fell substantially below its trend rate of growth. This
has been cited as a prominent causal factor in the
cyclical changes in demand and subsequent reces
sions. In the year preceding the current recession, the
rate of monetary expansion slowed, but fell only
slightly below its pre-1973 trend rate of 6 percent in
the second half of the year. From the fourth quarter
of 1972 to the fourth quarter of 1973, the money stock
rose 6.3 percent.
In the last two quarters of the most recent economic
expansion (11/1973 - IV/1973) money growth did slow
to a 5.3 percent annual rate. This break in the pace of
money expansion probably contributed to the moder
ation in the growth rate of total spending after the
fourth quarter of 1973.
After the recession began, demand growth con
tinued for a time to be stimulated by monetary ex
pansion. In the first two quarters of the current re
cession (IV/1973 -11/1974), the money stock grew at
a 6.7 percent annual rate, slightly above the trend rate
of growth.
Fiscal developments were also more expansive in
the first stage of the current recession than in the cor
responding periods of earlier recessions. In the year
ending third quarter 1974, Federal Government ex

penditures, on a national income accounts basis,
jumped 16 percent. In the corresponding spans of the
four earlier cycles, Federal spending rose an average
of 4 percent.
Even though tax receipts, bolstered by rising nomi
nal incomes, rose sharply, Government expenditures
exceeded receipts by a substantial margin in 1973 and
1974. The deficit in the national income accounts
budget was $14 billion in these two years, compared
with an average deficit of $6 billion in the correspond
ing periods of the earlier cycles.

Production
Despite the relatively rapid growth in demand for
goods and services in the first stage of the current
recession, output declined. Total real output de
creased at a 3.5 percent annual rate from the fourth
quarter of 1973 to the third quarter of 1974. In the
corresponding periods of the four earlier recessions,
output declined at a 2.4 percent rate.
The apparent paradox of substantial production cut
backs in the face of rapidly expanding demand during
the first three quarters of the current recession re
flects a number of supply constraints which sharply
increased production costs. In 1973, rates of produc
tion were very high in many industries, and marginal
costs rose rapidly with increased output. Then, the
economy was struck by a number of adverse factors
which reduced resource availability and raised costs.
Page 5

FED ER AL RESERVE BANK OF ST. LOUIS

Through monopolistic actions of producing nations
and domestic price (and, therefore, production) con
trols, oil supplies were cut back and energy costs
increased sharply. Adverse weather conditions, both
here and abroad, resulted in widespread crop failures
and increased food prices. Depreciation of the dollar
relative to other currencies raised domestic produc
tion costs by increasing the dollar prices of imported
goods, and caused significant shifts in demand for re
sources. Compliance with environmental and safety
laws consumed resources and added further to costs,
while making adjustment to all the other changing
forces much more difficult and costly.
In addition, output was inhibited by marked
changes in consumer spending and by price controls.
The rapidly rising prices of certain items prompted
consumers to shift consumption patterns, causing
abrupt contractions in the demand for some items
(such as autos) while intensifying upward pressures
on prices of other commodities. Price controls, still in
effect in early 1974, prevented firms from adjusting
to increasing production costs. With fixed selling
prices, production of many goods was no longer prof
itable; some marginal facilities were closed, and plant
expansions were postponed. As a result, production
in related industries was hampered further by short
ages for a time, and later by higher prices for inputs.
These interferences in the productive process made
the country poorer by reducing output capabilities.
The adverse effects of these constraints were dis
tributed through the economy by higher prices, a
chief factor in the intensification of inflation during a
period of recession.

JU N E

1975

The money stock, after rising at a 6.7 percent an
nual rate in the first two quarters of the recession,
slowed abruptly to a 3 percent pace in the following
three quarters (ending March 1975). In the earlier
recessions money typically increased at an accelerated
rate in the third through fifth quarters. A few months
after money began accelerating in previous recessions,
growth in demand also accelerated. A few months
after money growth began decelerating during the
current recession, growth in demand also decelerated.
The first stage of the current recession, being caused
in large part by constraints on supply, was unlike any
of the earlier recessions, which were largely demand
induced. However, the second stage, which has been
fostered by a slowing in the growth of demand, is
similar to the earlier experiences. Hence, for certain
studies, comparisons of the period since last Septem
ber with the periods immediately following the pre
vious cyclical peaks have more relevance than com
parisons which use the entire span of the current
recession.
At this second stage turning point, the growth rate
in total demand for goods and services fell precipi
tously from the aforementioned 7 percent rate in the
first stage to the virtual plateau in the first two quar
ters of the second stage. Between the comparable
periods before and after the four earlier cyclical

R e a l Product*
Second Stag* of Current Decline Compared w itk Previous Recessions
S e a s o n a lly A d ju s te d

SECOND STAGE - SEPTEMBER 1974
TO DATE

A v erag e of 1969-70, 1960-61, 1957-58,
and 1953-54
i
/

Demand
As the effects of some of the supply interferences
were diminishing last fall, production was severely
hampered a second time by a marked slowing in de
mand for goods and services. Total spending, which
had risen at a 7 percent annual rate in the first three
quarters of the recession, decelerated sharply last fall
and declined in the first quarter of this year. By com
parison, in the four previous recessions spending rose
at an average 0.3 percent rate in the first three quar
ters, but at an accelerated 9 percent rate in the fourth
and fifth quarters. With the reduction in demand
growth, it was not feasible to maintain existing pro
duction levels, and sharp cutbacks occurred.
6
Digitized forPage
FRASER

V -/'
\

1974-75

3RD
TR.53
3 R D G T R .5 7
4TH QTR '69

1
3 R D QTR. 74

QUARTERS FROM TURN
*G ro ss n a tio n a l product in constant d o lla rs.
Source: U.S. Department of C o m m erce

FEDERAL. RESERVE BANK OF ST. LOUIS

JU N E

In d u stria l Production

Total E m p lo y m e n t

Second Stage of Current Decline Compared w ith Previous Recessions
Peaks= 100
105 r

Peaks= 100
105

S e a s o n a lly A d ju s t e d

100

1975

Second Stage of Current Decline Compared w ith Previous Recessions

^ A v e r a g e o f 1 9 6 9 -7 0 , 1 9 6 0 -6 1 , 1 9 5 7 -5 8 , 100
V
and 1 9 5 3 -5 4
\v
\ N
\ \
\
\
\
\
\
\
95

' N

' '

\ 1 9 7 4 -7 5

90
JU L 5 3
JU L ' 5 7
M A r-6 0
NOV 69

\
\

SEP

. . . ---- -------- .....................
0

85
12

M O N T H S FR O M TURN

peaks, demand growth decelerated nearly the same
amount, averaging a drop of 6 percentage points.

Production, Employment, and Prices
Total real output of goods and services fell at a 10
percent annual rate from the third quarter of 1974 to
the first quarter of 1975. In the first two quarters of the
four earlier recessions, real output declined at an
average 4 percent rate. Industrial production dropped
at a 21 percent rate from September 1974 to April
1975, compared with an average 11 percent rate in
the first seven months of the earlier recessions. Total
employment declined at a 6 percent rate from Sep
tember to April, whereas it decreased at an average
2 percent rate in the comparable earlier periods.
Prices continued to rise rapidly for a time after the
second stage of the recession began, the rate of in
crease has now slowed. From September to November
1974, consumer prices rose at a rapid 12 percent an
nual rate, about the same pace as in the first stage.
Then, from November to April 1975 prices rose at a
reduced 7 percent rate. In the earlier recessions, in
creases in consumer prices decelerated less than two
percentage points at the seventh month, on average.
The greater and quicker reduction in the rate of infla
tion in the second stage than in earlier recessions
reflects the greater severity of the current economic
decline, some dampening price effects from the first
stage recession, and a dissipation of the short-run
price effects resulting from removal of wage-price

S o u rc e : U.S. D e p a r tm e n t o f L a b o r

controls, the dollar devaluation, and the markup of
oil prices.

SUMMARY AND CONCLUSIONS
The current recession has been severe by post
World War II standards, with output contracting by a
greater magnitude and for a longer period than in any
of the four previous recessions experienced since
1950. Not only has the current contraction been deep
and prolonged, but it has been, in effect, two reces
sions. The first, induced largely by constraints on sup
ply, had characteristics which differ strikingly from
prior experience.
Previous recessions were preceded, and accom
panied for a time, by a slow ( relative to trend) rate of
money growth. By contrast, money expansion in the
current cycle continued to be rapid, except for a brief
period, through the first two quarters of the recession.
However, from the second quarter of 1974 to the first
quarter of this year, the rate of money growth slowed
markedly. Fiscal actions, on the other hand, have
been expansive since a quarter before the current
cyclical peak.
Total spending for goods and services rose substan
tially during the first three quarters of the current
recession, pausing only moderately after the cyclical
peak. However, spending growth slowed significantly
Page 7

FEDERAL RESERVE BANK OF ST. LOUIS

after the third quarter of the contraction, causing the
recession to enter the second stage.
Until last fall, the chief cause of the downturn came
from the supply side. The nation’s ability to produce
was reduced by increased energy costs, unfavorable
weather, costs of environmental and safety programs,
the impact of dollar devaluation, and the effects of
price controls. The quantity of goods and services
available for consumption thus declined. Much of the
current recession and the persistence of inflation have
reflected the process of adjustment that the economy
has been making to the constraints placed on
production.
Recovery from the current recession depends on
the overcoming or removal of constraints on supply.
Elimination of wage and price controls was a signi
ficant step in attaining greater output, since produc

Digitized forPage
FRASER
8

JU N E

1975

tion tends to expand when profits are enhanced. With
normal weather, agricultural production should in
crease, placing downward pressures on the price of
food. While some adjustment to the higher cost of
fuel has taken place, a full adjustment will take addi
tional time.
Economic recovery is also dependent on a pick-up
in demand growth. In view of the projected sizable
Federal deficits, and the probable monetary creation
that will occur in financing them, total demand is
likely to receive a substantial boost from fiscal and
monetary developments in the near future. Since Jan
uary the money stock has again risen sharply. Expan
sionary developments are now welcome, because
demand is inadequate. Yet, a stimulation of demand
in excess of the ability of the economy to produce
would likely result in a re-intensification of inflationary
pressures at a later date.

A Monetary Model
of Nominal Income Determination
LEONALL C. ANDERSEN

D u RING the past several years the Federal Re
serve Bank of St. Louis has presented a number of
empirical studies demonstrating a strong and pre
dictable response of nominal gross national product
( GNP) to changes in the nation’s money stock. These
studies found that changes in the secular trend of
the money stock are the prime determinant of
changes in the secular trend of GNP. They also found
that short-run changes in GNP are related to similar
changes in the money stock. On the other hand,
changes in Government spending were found to have
only a temporary short-run influence on changes in
GNP. A number of other studies, using variations of
the approach of the St. Louis studies, have yielded
similar empirical relationships.
The St. Louis studies related changes in nominal
GNP directly to current and past changes in the
money stock and in high-employment Government
expenditures. No underlying set of relationships was
specified. Instead, the empirical relationship was pre
sented as the reduced-form of an unspecified struc
ture of the economy.
This article sets forth a theoretical model consist
ing of a set of postulated relationships which form a
basis for the relationship of nominal income (GNP)
to the money stock and Government expenditures.
The theoretical properties of this model are similar to
the empirical relationships found in the St. Louis
studies. The parameters of the model are estimated
for the period from first quarter 1955 to fourth quarter
1973. Empirical tests fail to reject the theory as an
explanation of nominal income determination in the
sample period.

THEORETICAL MODEL
This section develops a model of nominal income
determination which is based primarily on a prominent
NOTE: This presentation was given as part of the Lawrence
H. Seltzer Memorial Lecture Series at Wayne State Univer
sity, Detroit, Michigan, May 21, 1975.

theory of the influence of changes in the money stock
on income.1 At times, however, assertions different
from those in the prominent theory are made. It is
also asserted that the responses of holders of money
balances to changes in the dependent variables are in
relative terms; that is, rates of change or percent
discrepancies. The model, therefore, is expressed in
log-linear form.

Desired Nominal Money Balances
The theory underlying this study is based on the
assertion that households and business firms desire
nominal money balances to conduct market transac
tions and to hold as a store of value. Specifically, the
desired amount of nominal money balances, in the
aggregate, depends on the perceived price of newly
produced final goods and services, perceived nominal
income, the expected rate of inflation, yields on alter
native financial assets, and the technical efficiency of
the economy’s system of making money payments.2
Since holders of money balances do not have perfect
information regarding market opportunities, and since
there exist costs of both collecting information and
conducting market transactions, the desire to hold
money balances depends on the perceived, instead
1For statements of this theory, see Milton Friedman, “The
Demand for Money: Some Theoretical and Empirical Re
sults,” Journal o f Political Econom y (August 1959), pp.
327-351; “A Theoretical Framework for Monetary Analysis,”
Journal o f Political Econom y (March/April 1970), pp. 193238; and “A Monetary Theory of Nominal Income,” Journal
o f Political Econom y ( March/April 1971), pp. 323-337.
2For various asserted forms of the money demand function,
see David E. W. Laidler, The D emand For M oney: T he
ories and E vidence (Scranton: International Textbook Com
pany, 1969). For an excellent statement of the “conventional
view” of the money demand function, see Stephen M.
Goldfeld, “The Demand For Money Revisited,” Brookings
Papers on Econom ic Activity —■3 (1 9 7 3 ), pp. 577-638. Also
see John T. Boorman, “The Evidence on the Demand for
Money: Theoretical Formulations and Empirical Results,” in
John T. Boorman and Thomas M. Havrilesky, Money Sup
ply, Money Demand, and M acroeconomic M odels (Boston:
Allyn and Bacon, Inc., 1972), pp. 248-291, and Stephen
Rousseas, Monetary Theory (New York: Alfred A. Knopf,
1972).
Page 9

JU N E

FED ER AL RESERVE BANK OF ST. LOUIS

of the actual, price of goods and services and nominal
income. Given the influences of the other factors, the
amount of nominal money balances demanded is posi
tively related to the perceived price of newly pro
duced final goods and services. Given the influences
of both perceived price and the other factors, the
amount of money balances demanded is positively re
lated to the amount of goods and services that per
ceived nominal income can purchase.
It is asserted that the response of holders of money
balances is of the same magnitude with regard to both
perceived price and the amount of goods and services
that perceived nominal income can purchase. The
desire for nominal money balances, therefore, is form
ulated in terms of perceived nominal income only
(Equation l ) . 3
A continuing rise in the price of goods and services
results in a given amount of nominal money balances
held as a store of value commanding, over time, a
decreasing amount of goods and services. Given the
influences of the other factors, the amount of money
demanded is negatively related to the rate of inflation
expected to prevail in the future (Equation l ) . 4
Other financial assets are substitutes for money bal
ances as a store of value, and they yield a rate of
return. These rates of return, with constant, per
ceived prices for goods and services, are measured in
terms of real rates of interest. To the holder of a
financial asset, the real rate of interest is the annual
percent increase in the amount of goods and services,
at current prices, that a given dollar value of a finan
cial asset will command over the term to maturity.
With the influence of other factors held constant, the
amount of money demanded is negatively related to
real rates of return on alternative financial assets.
It is asserted that the dominant substitutes for
money as a store of value are short-term financial
^Ignoring the other factors,
In M° = a i In Pp + «2 In

= a i In Pp + <*2 ln Yp - a 2 In Pp.

By assertion ft 1 =
therefore, ln M° = a j ln Yp. Friedman
in “A Monetary Theory of Nominal Income” asserts that for
all practical purposes <*1 = c*2 = 1. In this study the only
assertion made is that « i = a.%. The validity of this assertion
is tested later in the study and the hypothesis that the two
responses are identical cannot be rejected. Friedman’s asser
tion that they both equal unity is also tested and is rejected.
4It is important to note that there are two different influences
on the amount of money balances demanded related to the
price of newly produced final goods and services. One is the
positive influence of the perceived price level for the current
period, and the other is the negative influence of the ex
pected rate of change in the price level over the relevant
future.

Page 10

1975

assets and that the time horizon upon which expecta
tions of the rate of inflation are based is the same
for money balances as for these assets. It is generally
accepted that the nominal rate of interest on a finan
cial asset is the sum of the real rate of return and the
rate of inflation expected over the term of the financial
asset. The nominal short-term interest rate, therefore,
is presumed to capture the negative influence on the
amount of money demanded of both the real short
term interest rate and the expected rate of inflation
(Equation 1).
The technical efficiency of the system of making
money payments is defined as the average amount of
money balances required to be held to conduct a given
nominal volume of transactions. With the influences
of other factors held constant, the amount of money
demanded is negatively related to the technical ef
ficiency of the system of making money payments
( Equation 1). In other words, the smaller the amount
of money balances technically required to be held to
conduct a given dollar volume of transactions, the
smaller is the amount of money demanded.
(1) In M* (t) = <*o In E(t) + <*i ln Yp (t) + (*2 ln r(t).
<*0 < 0, <*1 > 0, and <*2 < 0.
M° = desired nominal money balances.
E = technical efficiency of the payments system.
Yp = perceived level of nominal income.
r = nominal short-term interest rate.

Adjustment of Spending by
Households and Business Firms
The nominal stock of money is assumed to be ex
ogenous, determined by the monetary authorities.
Therefore, holders of money balances, in the aggre
gate, cannot adjust their holdings when a discrepancy
occurs between actual and desired money balances.
Instead, it is asserted that individual holders of money
balances attempt to add to (reduce) money balances
by reducing (increasing) their rate of spending on
goods and services. Such an adjustment continues un
til desired money balances are brought into equality
with actual money balances.
It is assumed that the rate of change in the dollar
volume of spending by households and firms on newly
produced final goods and services from both domestic
and foreign sources is proportional to the percent dis
crepancy between actual and desired money bal
ances.5 It is also assumed that the response of spend
ing is distributed over time (Equation 2 ).
5This specification of the adjustment process is a marked de
parture from that specified in other studies. Some specify

FED ER AL RESERVE BANK OF ST. LOUIS

(2) d l " Yd = X [In M(t) - In M* (t)].
dt
M = actual nominal money balances.
d In
dt

= rate of change in spending by households and
business firms for newly produced, final goods
and services.
X = speed of adjustment. 0 < X ^ o°. The larger is X ,
the faster is the speed of adjustment. X = 00 is
instantaneous adjustment.

Combining Desired Money
Balances and Adjustment Process
The preceding assertions regarding the demand
for nominal money balances and the adjustment proc
ess are now combined by substituting equation (1)
into equation (2 ). The result is that the rate of change
of nominal spending by households and business firms
is related to the level of actual nominal money bal
ances, the technical efficiency of the payments sys
tem, the level of the nominal short-term interest rate,
and the perceived level of nominal income.
(3) d ln Yd = \ [In M(t) - a 0 In E(t)
dt

<*1 ln Yp(t) - <*2 ln r(t)].

Definition of Nominal Income
Nominal income is defined as total value added
(that is, factor payments) in the domestic production
of new final goods and services. Total nominal spend
ing on domestic product is also equal, by definition, to
value added. Nominal income, accordingly, is equal
to nominal spending for both domestic and foreign
product by domestic households, business firms, and
all units of government, plus nominal spending by
foreigners for domestic product, less domestic nomi
nal spending for foreign produced goods and services.
(4) Y(t) = Yd(t) + G(t) + X(t) - IM(t).
Y = nominal income.
Yd = spending by household and business firms for both
domestic and foreign product.
G = spending by all units of government for both domestic
and foreign product.
X = spending by foreigners for domestic product.
IM = domestic spending for foreign product.
that the actual money stock changes in response to a dis
crepancy between actual and desired money balances; others
specify that “real” money balances change; and others spe
cify that the short-term interest rate changes. See references
in fn. 2 for specific examples of these other specifications.
For discussion of the importance of the specification of the
adjustment process in empirical research, see; A. A. Walters,
“The Demand for Money — The Dynamic Properties of the
Multiplier,” Journal o f Political Economy (June 1967), pp.
293-298, and D. R. Starleaf, “The Specification of Money
Demand — Supply Models Which Involve the Use of Dis
tributed Lags,” Journal o f Finance (September 1970), pp.
743-760.

JU N E

1975

Domestic Spending for Foreign Product
Domestic nominal spending for foreign product is
assumed to be a constant proportion of total nominal
spending in the economy.
(5)6 (t) =

IM(t)
= 6.
Yd (t) + G(t) + X(t)

Dynamic Form of the Model
The model, up to this point, involves the change
in the level of income in response to changes in the
level of the money stock, or in Government spending,
or in foreign spending on domestic product, or in the
short-term interest rate, or in the technical efficiency
of the payments system. All of these variables, how
ever, are continuously changing over time. The model
is differentiated with respect to time to reflect the
response of households and business firms to those
variables which are continuously changing.
In its dynamic form, the rate of change in desired
money balances is related to the rates of change in
the technical efficiency of the payments system, in the
short-term interest rate, and in perceived income.
d in M"
dt

d ln E
dt

d ln YP

d in r

(1 ) ---- ----- = ag--- ---- + <*! ----------+ a2

The change in the rate of change in nominal spend
ing by households and business firms is proportional
to the discrepancy between the rate of change in
actual money balances and the rate of change in de
sired money balances.
(2 ')

d2 ln Yd
dt2

d ln M
dt

d in M*
dt

The statement combining the adjustment process
and the factors influencing desired money balances is
accordingly modified.
/0,\ d2 ln Yd
dt2

^ r d ln M
dt

(3 /--------- —AI

- «2-

d In E
dt

a i ■d In

«o -

d ln
Z-l
dt

Substituting equation (5 ) into (4) and differentiat
ing with respect to time, the rate of change in nominal
income is equal to the weighted sum of the rates of
change of spending for product by domestic house
holds and business firms, domestic units of govern
ment, and foreigners.
(4,) d J n Y = W l(t)_d
dt
dt

/ % d In G
+ W2(t)
---- ;---- + W3(t). d ln X
dt

Wi(t) = [1 - 6 ] J ^ L ;W 2 (t) = [ l - B] ^ > ;
Y (t)
Y(t)
and W3(t) = [ 1 - 6 ]

Y(t)
Page 11

FED ER AL RESERVE BANK OF ST. LOUIS

JU N E

19 75

Summary of Variables

Dynamic Equilibrium State

The endogenous variables of the model are the
change in the rate of change in nominal spending by
households and business firms, the rate of change in
desired money balances, and the rate of change in
nominal income. It will also be developed in sub
sequent analyses that the rate of change in the per
ceived level of nominal income is an endogenous
variable related to past rates of change in nominal
income. The exogenous variables are the rates of
change in actual money balances, in the short-term
interest rate, in the technical efficiency of the pay
ments system, in Government spending on goods and
services, and in foreign spending on domestic product.

The relationships of the model (Equations 3', 4',
and the weights) together with the three dynamic
equilibrium conditions (Equations E -l through E-3)
are used to solve for the dynamic equilibrium state of
the endogenous variables.7 In the dynamic equili
brium state, taking into consideration the postulated
signs of the coefficients, the rate of change in nominal
spending by households and business firms is posi
tively related to the rates of change in actual money
balances, in the technical efficiency of the payments
system, and in the nominal short-term interest rate,
and is negatively related to the rates of change in
government spending and exports (Equation ES-1).
The rate of change in nominal income is positively
related to the rates of change in actual money bal
ances, in the technical efficiency of the payments
system, and in the nominal short-term interest rate
(Equation ES-2).

The model is one of partial analysis, inasmuch as
the nominal short-term interest rate is an exogenous
variable. There is no provision for feed-back effects
on the rate of change in nominal income. These effects
would emanate from changes in exogenous variables
which change the rate of change in the short-term
interest rate, either by induced changes in the real
interest rate or in the expected rate of inflation.

Conditions for Dynamic Equilibrium
Dynamic equilibrium is defined as the state in
which all of the variables are changing at constant
rates.6 This occurs when the rates of change in actual
and desired money balances are equal. Three condi
tions are required for this equality to be fulfilled —
changes in the rates of change in nominal spending
by households and business firms and in nominal in
come equal zero (E - l and E -2), and the rates of
change in nominal income and in the perceived level
of nominal income are equal ( E -3 ).
(E -l)

rl2 I n Y<i

- - ■- = 0.
dt-

(E-2) d2 1---Y- = 0.
dt2
d In YP
d In Y
(E-3)
dt
dt

BThe definition of equilibrium as constant rates o f change is
a marked departure from the standard literature in monetary
economics, other than some growth models. The standard
analysis defines equilibrium as constant levels of the endo
genous variables. The equilibrium conditions for the standard
analysis would be that desired and actual levels of money
balances are equal, that the rates of change in spending by
households and business firms and in nominal income equal
zero, and that the perceived level of nominal income equals
the actual level. Thus, in the standard analysis there is both
stock and flow equilibrium. In the dynamic form in this
study, however, equilibrium is defined as constant rates of
change in both stock and flow variables.
Page
12

1
d In M
d In E
d In i
«0---:------ «2
dt
dt
Wi(t)<*i
dt
dt
d In G
d ln X ,
- W2(t)
W3(t)
dt
dt
d In Y
d In M
d In E
d In r ,
(ES-2)
«o ■
«2 ---:--- 1dt
<*l ~ d t
dt
dt

(ES-1)

d In Yd

A Change in Dynamic Equilibrium State
An existing dynamic equilibrium state is disturbed,
in this model, by two types of events. One type is the
initial creation of a discrepancy between the rates of
change in actual and desired money balances. Factors
initiating such a discrepancy are changes in the rate
of change in actual money balances or changes in the
rate of change in desired money balances. This latter
change can result from changes in the rate of change
in either the technical efficiency of the payments
system or in the short-term interest rate. The other
type of equilibrium disturbance is a change in the
rate of change in government spending or in foreign
spending for domestic product, which initiates a
change in the rate of change in nominal income. Fol
lowing both types of disturbance, a new equilibrium
state is achieved when the rate of change in nominal
income has changed to the extent that the rate of
change in desired money balances is brought into
equality with the rate of change in actual money
balances.
7This analysis and the one immediately following is for partial
equilibrium only inasmuch as the interest rate is exogenous.
The model only considers the influence of exogenous shocks
on the choice between money and new production and not
on the choice between money and existing assets.

JU N E

FEDERAL RESERVE BANK OF ST. LOUIS

For example, starting from dynamic equilibrium
(that is, all variables changing at constant rates) as
sume there is a maintained increase in the rate of
change in actual money balances, with the rates of
change in the other independent variables remaining
as they were. First, there occurs a positive discrep
ancy between the rates of change in actual and de
sired money balances, resulting in an increase in the
rate of change in nominal spending by households
and business firms. As a result, there is an increase in
the rate of change in nominal income. This latter in
crease, in turn, results in an increase in the rate of
change in perceived nominal income and thereby in
the rate of change in desired money balances.
As a result, the discrepancy between the rates of
change in actual and desired money balances is nar
rowed and the rate of change in spending by house
holds and business firms decreases. This decrease
reduces the rate of change in nominal income from
what it was initially. This process continues until
there is equality between the rates of change in actual
and desired money balances. In the new dynamic
equilibrium state, the rates of change in spending by
households and business firms and in nominal income
are higher than their starting equilibrium values (ES-1
and ES-2).
In another example, starting from equilibrium, as
sume there is a maintained increase in the rate of
change in government spending, with rates of change
in the other independent variables remaining the
same. The first response is an increase in the rate of
change in nominal income which produces an increase
in the rate of change in perceived nominal income.
This results in an increase in the rate of change in
desired money balances.
As a consequence, there is a negative discrepancy
between the rates of change in actual and desired
money balances, resulting in a subsequent decrease in
the rate of change in spending by households and
business firms. This is accompanied by a decrease in
the rates of change in nominal income and in per
ceived nominal income, which, in turn decreases the
rate of change in desired money balances. This
process continues until the rate of change in desired
money balances equals that of actual money balances.
In the new dynamic equilibrium state the rate of
change in nominal income is the same as it was be
fore the increase in the rate of change in government
spending (E S-2). The rate of change in spending by
households and business firms has been permanently
decreased (E S-1), offsetting fully the initial increase

1975

in the rate of change in nominal income generated by
the increase in the rate of change in government
spending.
The length of time required for achieving the new
equilibrium state depends on (1 ) the speed of re
sponse of the rate of change in spending by house
holds and business firms to a discrepancy between the
rates of change in actual and desired money balances
and (2 ) on the length of time required for the rate
of change in perceived nominal income to respond
fully to past rates of change in actual nominal income.
The time path to a new equilibrium — whether it
oscillates or moves only in one direction — depends
on the response characteristics of the relationships
comprising the model.

EMPIRICAL FORM OF THE
THEORETICAL MODEL
The theoretical model consists of three relation
ships. One is for the change in the rate of change in
spending by households and business firms ( Equation
3 '). The other two are the identity for the rate of
change in nominal income (Equation 4 '), and the
weights involved in this identity. The theoretical
model is next given an empirical form which pro
vides the basis for testing whether or not the theory
can be accepted. This section presents the empirical
model and the following section uses it to test the
theory.

Data Problems
A major data problem is involved in developing
the empirical form of the model — the theory is in
terms of changes in time which are infinitesimally
small while data on the variables are available only
for discrete points in time separated by a month or a
quarter of a year. A linear approximation in discrete
time is used — the first difference of natural loga
rithms of a variable between two discrete points in
time is presumed to approximate its rate of change
(Appendix).
Another data problem exists inasmuch as there are
no measurements of the technical efficiency of the
payments system or of the perceived level of nominal
income. It is assumed that, on average, the technical
efficiency of the payments system increases at a con
stant rate (Appendix).8 The second problem is solved
8Examples of developments which are usually presumed to
have increased the efficiency of the payments system ( a
reduced amount of money balances required to carry out a
given volume of money payments) over the sample period
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FED ER AL RESERVE BANK OF ST. LOUIS

by em ploying a procedure presented by Philip C agan.9
According to this procedure, the rate of change in
perceived nom inal incom e can be approxim ated by
a w eighted average of past rates of change in actual
nominal incom e (A p p end ix). In this procedure, the
w eights sum to unity.

Estimated Parameters of the Model
Only the param eters of the relationship explaining
the change in the rate of change in spending for
product by households and business firms are esti
m ated; the other relationships are identities. Tw o ver
sions of this relationship are estim ated. O ne is based
on the assertion th at desired money balances are posi
tively related to perceived price and the amount of
goods and services that perceived nominal incom e
can purchase, w ith no assertions regarding the m agni
tudes of response. T h e other one is based on the
assertion th at the m agnitude of response of desired
m oney balances is the same w ith regard to perceived
price as w ith regard to the am ount of goods and
services th at perceived nom inal incom e can purchase
— the perceived incom e form ulation used in the
theoretical discussion. T h e general forms of these two
relationships are as follow s:
(A) A in Yjl — A in Y ^

+a 3 2

i = 1

(B) Ain Y

= ao + a i A in Mt + a.2 A in rt

, _

Wi Ain Pt-i + a4 1 Wi Ain Qt-i + £ t.
i = 1

— Ain Y j! j =bo + bi Ain Mt + b£ Ain rt

+ b 3 £ W i Ain Yt-i + 8 t.
i =1
Ain Yf1 —Ain Y td_[ = change in the rate of change in spending
by households and business firms for
product.
a,, and bo
= response to the average rate of change in
the technical efficiency of the payments
system.
Ain Mt
= rate of change in nominal money balances.
Ain rt
= rate of change in nominal short-term
interest rate.
X wi Ain Pt-i
= weighted sum of past rates of change in
*=1
price.
X W i Ain Qt-i
= weighted sum of past rates of change in
1= 1
the amount of goods and services that
nominal income can purchase.
X

1= 1

Ain Yt-i

= weighted sum of past rates of change in
nominal income.

a random error term.

are the introduction of faster means of transferring funds
and the adoption of improved methods of managing money
balances. See George Garvy and Martin R. Blyn, The V eloc
ity o f Money (New York: Federal Reserve Bank of New
York, 1969), pp. 207-218, for further discussion of this point.
!'Phillip Cagan, “The Monetary Dynamics of Hyperinflation,”
Studies in the Quantity Theory o f Money, ed. Milton Fried
man (Chicago: University of Chicago Press, 1956), pp. 31-41.

Page 14

JU N E

1975

Ordinary least-squares regressions, using quarterly
data from first quarter 1955 to fourth quarter 1973,
are used to estimate the parameters of equations A
and B. Spending by households and business firms is
measured by the sum of consumption plus investment
in the national income accounts. Nominal income is
measured by nominal GNP.10 The price level is
measured by the GNP deflator, and the amount of
goods and services that nominal income can purchase
is measured by nominal GNP divided by the price
deflator. Two definitions of money are used. One
(M j) is the sum of demand deposits and currency
held by the nonbank public. The other one (M 2) is
Mt plus time and savings deposits at commercial
banks, other than large, negotiable certificates of de
posit. The short-term interest rate is measured by the
4- to 6- month commercial paper rate. Two zero-one
dummy variables are included for the average influ
ence of major strikes on income, with D j equaling one
for the quarter of a strike and D2 equaling one for
the quarter following a strike.11
A test was performed for a structural change in the
model (Appendix). For M! such a change is alleged
by some analysts to have occurred after the fourth
quarter of 1966 when a change in the trend growth
of the ratio of GNP to Mx is observed. A similar
change in the trend growth of the ratio of GNP to M2
occurred after the fourth quarter of 1961. In both
cases the structural change hypothesis was rejected.
A statistical procedure (Appendix) was next used to
select the appropriate number of lagged changes in
the price level, nominal income, and in the amount
of goods and services that nominal income can pur
chase; four lagged terms were deemed appropriate.
The estimated parameters of equations A and B are
reported in Tables I and II.

EMPIRICAL MODEL AS A TEST
OF THE THEORY
The empirical model is used to test whether or not
the theory of nominal income determination advanced
earlier can be accepted. The part of this theory re
garding the determination of nominal spending by
households and business firms carries specific implica10In national income terms, the definition of nominal income
used in this study is the sum of consumption, investment,
government expenditures, and exports less imports. This
sum should be adjusted for depreciation and indirect busi
ness taxes, to be identical to value added. It is assumed that
variations in these two magnitudes will have little influence
on the outcome of this study.
1'The major strikes in the sample period were: steel III/1959,
autos 1V/1964, and autos IV/1970.

FEDERAL RESERVE BANK OF ST. LOUIS

JU N E

Table I

1975

Table II

Regression Results*
Equation
Independent
V a riab le

Regression Results*

(A )

Equation
m2

- 1 .9 9 6
(- 3 .7 6 5 )

- 1 .9 4 7
(- 3 .6 3 7 )

2 .2 5 9
(3 .9 7 8 )

A in Mt

.6 8 5
(4 .0 0 3 )

- 1 .9 3 0
( - 3 .7 4 4 )

2 .3 8 0
(4 .3 2 6 )

- 1 .8 8 6
( - 3 .6 1 6 )
2.041
(3 .6 3 0 )

A in Mt

.701
(4 .5 2 7 )

.5 7 2
(4 .3 0 9 )

V a ria b le

(2 .2 5 7 )

1.921
(3 .3 2 1 )
.5 3 4
(3 .8 1 4 )
.0 3 2
(3 .0 9 6 )

A in Q t- i

- .7 9 7
( - 5 .2 5 0 )

- .7 9 9
(- 5 .1 8 2 )

A in Y t _ i

c
<

M l,

- .2 4 9
( - 1 .9 0 5 )

- .2 0 8
( - 1 .5 8 0 )

A in Yt -2

A in Qt _3

.2 6 3
( 2 .0 5 1 )

.2 3 8
(1 .8 4 2 )

A in Q t _4

- .2 7 8
( - 2 .3 4 1 )

- .301
( - 2 .5 1 8 )

A in P t-i

- .91 8
(- 2 .1 0 5 )

A in Pt-2

- .5 5 8
( - 1 .1 9 3 )

- .811
( - 1 .8 5 5 )
- .5 9 2
( - 1 .2 5 4 )

A in Pt-3

.1 4 3
( .2 9 8 )

.0 2 2

A in rt

A in Pt_4

.251
( .6 0 6 )

.2 3 2
( .4 7 9 )
.2 7 4
( .6 5 7 )

Constant

1 .0 7 4
(3 .0 7 8 )

.7 7 2
(2 .1 3 5 )

.5 6 9

.561

SEE

.8 7 5

.8 8 3

2 .0 0 9

2 .0 3 7

♦Numbers in parentheses are t-values.

tions regarding the estimated coefficients reported in
Tables I and II. If the estimated coefficients are con
sistent with the implied coefficients, at the five per
cent level of statistical significance, this part of the
theory is accepted.
The model as a whole constitutes the theory of
nominal income determination. This theory is tested
by the ability of the empirical model to forecast
nominal income.12
Relatively small root mean
squared errors in forecasting nominal income are
taken as evidence that the theory of nominal income
determination can be accepted.

Testing Implications of Theory Regarding the
Responses of Households and Business Firms
It was asserted in the theoretical section that the
response of holders of money balances is of the same
12A more appropriate test would be to solve for the reducedform of the model, and then to test whether the estimated
coefficients of this equation are consistent with those implied
by the theory. The reduced-form is a nonlinear equation
with variable coefficients, which poses some very difficult
problems of estimation. The forecasting test was therefore
selected.

(B )

Independent

A in rt

.0 2 0

(2 .1 8 3 )

.0 3 0
(2 .9 7 4 )

- .7 8 2
( - 5 .2 4 2 )
- .2 7 4
(- 2 .1 6 4 )

- .781
( - 5 .1 5 7 )

A in Yt - 3

.2 2 6
(1 .8 4 6 )

.1 9 7
( 1 .5 9 2 )

A in Yt -4

- .3 0 9
( - 2 .7 3 9 )

- .3 1 5
( - 2 .7 6 5 )

Constant

1 .1 5 2
(3 .7 8 5 )

.911
(2 .7 9 2 )

- .2 2 5
(- 1 .7 5 9 )

.5 8 0

SEE

.8 6 4

.8 7 4

2 .0 3 6

2 .0 4 9

.5 7 0

♦Numbers in parentheses are t-values.

magnitude with regard to perceived price as with re
gard to the amount of goods and services that per
ceived nominal income can purchase. Therefore, the
theoretical formulation was in terms of perceived
nominal income. This assertion implies in Equations
A and B that for each lag the coefficients for the
rates of change in price, in the amount of goods and
services that nominal income can purchase, and in
nominal income are equal. This implication was tested
and could not be rejected at the five percent level
of statistical significance (Appendix).13 As a result of
this test, estimates of the coefficients of Equation B
are used for the balance of this study (Table II).
The theory of determination of nominal spending
by households and business firms implies that all of
the coefficients in Equation B are statistically signifi
cant from zero at the five percent level and that they
have the following signs: b0, bi, and b2 are positive
and b3 is negative.14 All of the estimated coefficients
in Table II are statistically significant from zero at
the five percent level and have the implied signs. The
13The proposition that the elasticity of desired money bal
ances with respect to the perceived level of nominal income
equals unity was tested and rejected ( Appendix). The
proposition that this elasticity is greater than unity was
accepted.
14These implied signs are derived by applying the postulated
signs for Equations 1' and 2' to Equation 3'. The magni
tude of b3 is derived by adding the coefficients on the
lagged income terms.
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FED ER AL RESERVE BAN K OF ST. LOUIS

empirical evidence is consistent with the implications
of this part of the theory, which is, therefore, accepted.

Testing Theory of Nominal
Income Determination
A test of the theory of nominal income determina
tion is the ability of the empirical form of the model
to forecast nominal income with relatively small
root mean squared errors. This forecasting ability of
the model is determined by dynamic simulations. In
a dynamic simulation actual values of the quarterly
rates of change in money balances, in government
spending plus exports, and in the nominal short-term
interest rate are used. At the start of the simulation,
actual lagged rates of change in nominal income are
used, but, subsequently, simulated rates of change are
incorporated. Two types of simulations are performed
— ex post for the sample period and a number of
ex ante simulations beyond various sample periods.
The simulation model consists of Equation B (Table
I I ), Equation (4 '), and the definition of the weights.
Using the discrete-time linear approximation to rates
of change in Equation (4 '):
Ain Yt = Wt Ain Y td + (1-W,) Ain Z,.
W ,= (1-6)

Y ^

Yt-i
Z = government spending plus exports.
5 = ratio of imports to total spending on product. The ratio
is held constant at its average value in the sample
period.

Ex post simulations are used to ascertain the ability
of the model to capture movements in nominal in
come over the sample period. The root-mean-squarederror (R M SE ) for the quarterly rates of change of
nominal income (expressed as annual rates) is 2.85
percentage points using M2 and 2.95 using M2. Al
though the errors in the quarterly rates of change
( expressed as annual rates) are quite large, the errors
tend to be offsetting over the sample period. In the
fourth quarter of 1973, the error in the level of nomi
nal income was 0.36 percent using M, and 0.33 per
cent using M2. Over the sample period, the RMSE
for the quarterly levels of nominal income is 1.57
percent using Mx and 2.07 percent using M2.
Ex ante simulations are used to determine the abil
ity of the model to forecast nominal income beyond
a sample period, with known values of the exogenous
variables. The coefficients of Equation B are estimated
for the sample period from first quarter 1955 to fourth
quarter 1961. The coefficients are then re-estimated
for the sample period from first quarter 1955 to fourth
quarter 1962. This procedure of lengthening the sam
Page 16

JU N E

1975

ple period by four quarters is continued until fourth
quarter 1973, the terminal date.
Dynamic simulations are then performed for the
eight quarters following each sample period. The
simulated annual rate of change in nominal income
over the first four quarters and over the entire eight
quarters are calculated. For the set of first four
quarters, using all the post sample periods, the
RM SE’s of the annual rate of change in nominal in
come are 1.59 percentage points using Mx and 1.40
using M2. For the set of eight quarter periods, the
RM SE’s are 0.99 percentage points using Mx and
0.82 using M2.
For each post sample period, the simulated level of
nominal income is calculated for the fourth quarter
and the eighth quarter. The RM SE’s are then cal
culated for the set of all post sample periods. Using
M1; the RMSE in the fourth quarter level of nominal
income is 1.59 percent and using M2 is 1.40 percent.
For the eighth quarter level, the RMSE is 1.98 per
cent using Mx and 1.64 percent using M2.
The ex ante simulation results indicate that the
empirical model forecasts the level of nominal income
with relatively small RM SE’s, compared with fore
casts from nine major econometric models of the U.S.
economy. Carl F. Christ, in reviewing the ex ante
forecasting performance of these models, concluded,
“All have RM SE’s for real and nominal GNP that are
1 percent or less for one quarter ahead, and 3 percent
or less for five or six quarters ahead.”15 The model
presented in this study, which is based on a markedly
different theory than eight of these nine models, fore
casts nominal GNP with smaller RM SE’s than several
of the large scale econometric models of the U.S. This
forecasting evidence thus leads to acceptance of the
theoretical model of nominal income determination.

CONCLUSIONS
A theoretical model of nominal income determina
tion was developed, based on a set of postulates re
garding the behavior of households and business firms.
The central postulate is that the rate of change in
nominal spending by households and business firms
for newly produced final goods and services responds
to a discrepancy between the rates of change in actual
and desired nominal money balances.
On the basis of the empirical tests, the theoretical
model was accepted as representing the determination
15Carl F. Christ, “Judging the Performance of Econometric
Models of the U.S. Economy,” International Econom ic R e
view (February 1975), p. 64.

FEDERAL RESERVE BANK OF ST. LOUIS

JU N E

of nominal income in the period 1955 -1973. The
estimated coefficients of the empirical model have the
signs implied by the theory. In addition, ex post
and ex ante dynamic simulations indicate that it fore
casts nominal income with relatively small errors.
The empirical results mentioned in the introduction
of the St. Louis reduced-form equation relating changes
in GNP to changes in money and government spend
ing are consistent with the theoretical properties of
the model presented in this study. These theoretical
properties are developed in the section which dis
cusses the changes in the dynamic equilibrium state.
A theoretical property of the model is that a change
in the trend growth of nominal money balances
changes the trend growth of nominal income. An
other theoretical property is that short-run changes
in the growth of nominal balances result in short-run

1975

changes in the growth of nominal income. A third
theoretical property ( based on partial analysis) is that
changes in the growth of government spending exert
a short-run, but not a long-run, influence on growth
of nominal income. Thus, there is “crowding-out” of
spending by households and business firms, but only
in partial equilibrium analysis. Since the desire to
hold money balances is negatively related to the
short-term interest rate, the financing of the growth
of government expenditures by issuing debt may have
a positive influence on growth on nominal income.
The estimated interest elasticity of desired'money
balances is very small (about .03); therefore, for debt
financing to have much of an influence on growth of
nominal income, the elasticity of the interest rate with
respect to government debt must be very large or the
increase in debt outstanding must be exceedingly
large.

APPENDIX
Data Problems
The linear approximation of rates of change in dis
crete time is given by the following:
d In Y
1 dY
v
. v
-------- = ---------- --- In Yt - ln Yt-l.
dt

The technical efficiency of the payments system is
assumed, on average, to increase at a constant rate given
by the following exponential growth function:
E(t) = aebt; or ln E(t) = ln a + bt.
e = the base of natural logarithms,
b = constant rate of growth,
a = beginning level of E.

of change in nominal income and the rate of change in
the perceived level of nominal income.
d2 ln YP =
dt-

——--------

dt'

d ln
dt

_ d ln YP ,
dt

= th e c h a n g e in th e ra te o f c h a n g e in th e p e r c e iv e d

level of nominal income.
f3 = the adjustment coefficient. O < 0 =s
The larger
is A. the faster is the speed of adjustment.

According to Cagan’s procedure, the rate of change in
the perceived level of nominal income can be approxi
mated in discrete time by the following:
A in

Ytp = d -e-'3 ) I

i = 0

(l-e-0) I

A in

Yt-ie’^

e -& = l.

i = o

t = an index of time.

Differentiating with regard to time yields:
d In E

A variation of Phillip Cagan’s procedure is used for ap
proximating the rate of change in the perceived level of
nominal income. It is assumed that changes in the rate of
change in the perceived level of nominal income are
proportional to the discrepancy between the actual rate

In the discrete time form of the model, it is asserted
that the rate of change in perceived nominal income is
that at the beginning of the period. The index (i), there
fore, runs from 1 to T. Instead of assuming, as Cagan did,
various values of P and then using their implied values
for Ain Y [ directly in the regression equation and se
lecting the one which has the largest R2, the coefficients
for each lagged income term were estimated directly.
Four lagged changes in nominal income (the lag struc
ture used in this study) implies that (5 = 1.15, with the
Page 17

FEDERAL RESERVE BANK OF ST. LOUIS

JU N E

implied weights ( 0.68, 0.22, 0.07, and 0.02) summing to
0.99. The estimated coefficients for the four lagged income
terms, given their standard errors of estimate, are approxi
mately consistent with those implied by these weights.

Test for Structural Change
A test of the hypothesis of a structural change in the
coefficients of the model is performed by introducing a
zero-one dummy variable into equation (A ) of the text.
This equation is used rather than Equation B, which
incorporates a special assumption regarding the param
eters on perceived price and the amount of goods and
services that perceived nominal income can purchase.
The dummy variable has the value of zero in the M,
equation from first quarter 1955 to fourth quarter 1966,
and then a value of one to fourth quarter 1973. It has a
zero value in the M2 equation from first quarter 1955 to
fourth quarter 1961, and then a value of one to fourth
quarter 1973.
Two forms of equation (A ) are estimated. One is the
original specification. The second one has all the original
variables, but adds the dummy variable itself (to meas
ure a change in the constant) and the product of the
dummy and each of the original variables (to measure
a change in the regression coefficients).1
If the estimated coefficients for these added varia
bles are not statistically significant from zero, the struc
tural change hypothesis is rejected. An F test is con
ducted to test the null hypothesis that all the regression
coefficients of the added set of variables are equal to
zero. If the calculated F value is less than the critical F
value, at the five percent level of significance, the null
hypothesis is not rejected.
Since the number of lagged AlnQ and AlnP terms
have not been specified at this point, the test for
structural change was conducted for lag specifications
from one quarter to ten quarters (Table A ). For every
length of lag, the calculated F value is less than the
critical value. As a result, the hypothesis of a structural
change in both the M j and M2 equations is rejected for
each of the lag structures examined.
Table A

Test For Structural C h a n g e
Equation

Calculated F
Mj

1.6 4

1 .6 7

2 .3 6

1.45

1.34

2 .1 7

C ritical
F ( .0 5 )

2.05

1.58

1 .54

1.05

1.42

1.98

.9 9

.8 7

1 .1 7
.91

1.93
1 .90

.8 2

.9 3

1.89

.7 5

.98

1 .89

.7 5

1.21

1.91

.83

1 .1 2

1.91

18
Digitized forPage
FRASER

Determination of Lag Structure
A statistical procedure is used to determine the ap
propriate number of lagged AlnQ and AlnP terms in
equation (A ). Each equation (M , and M2) is estimated
eleven times, first with no lags and then increasing the
length of lag for AlnQ and AlnP by one quarter until ten
sets of the two lagged terms are included. The F test is
used to test the null hypothesis that the two estimated
coefficients for each a d d e d lag are zero. If the cal
culated F value is greater than the critical value, at the
five percent level of significance, the null hypothesis is
rejected. Table B shows that the null hypothesis is re
jected when lags one and four are added, but not when
any of the other lags are added.
Table B

Test of Lag Structure
Equation
Each Added
Lag

(A )

Calculated F

C ritical
F (.0 5 )

1 6 .8 8

16.92

4 .0 0

1 .1 9

.8 9

4 .0 0
4 .0 0

.4 5

.1 6

4.11

4 .8 3

4 .0 0

.2 0

4 .0 0

1 .0 2

1.00

4 .0 0

.2 4

1 .24

.2 6
1.41

.3 9
2 .3 0

.3 0

4 .0 0
4 .0 4

2.78

4 .0 4

Lags
1-4
5 -10

6 .3 7
.91

4 .0 0

6 .0 9

2 .5 3

1.01

2 .2 9

The F test is next used to test the null hypothesis that
as a set all the coefficients for lags one to four are equal
to zero. This test, at the five percent level, rejects the
null hypothesis (Table B ). A similar test is conducted
for the coefficients as a set for lags five to ten, when
lags one to four are included in the regression. In this
second test the null hypothesis cannot be rejected (Table
B ). On the basis of these results, four lagged AlnQ and
AlnP terms are considered to be appropriate. Table I in
the text presents the estimated coefficients for this speci
fication, equation (A ).

(A )

Number
of Lags

1Except D i and Do.

19 75

Test of Equal Response Hypothesis
The hypothesis that the response of desired nominal
money balances is the same with regard to both per
ceived price and the amount of goods and services that
nominal income can purchase is tested by imposing a
linear constraint on equation (A ). An F test is used to
test this constraint. If the calculated F value for the con
straint is less than the critical value, at the five percent
level of significance, the proposition is accepted.
Assuming that the weights in forming Ain Q d and
Ain Pp are equal for each lag, the equal response hypo
thesis implies that for each lag the estimated coefficients
for AlnQ and AlnP are equal. Since by definition

FEDERAL RESERVE BAN K OF ST. LOUIS

JU N E

Table C

Test of U nitary Elasticity Hypothesis
Regression Results
Mi

- 2 .0 3 5
(- 3 .8 6 4 )

- 2 .0 2 2
(- 3 .7 0 8 )

2 .4 8 6
(4 .4 2 4 )

2 .0 9 5
(3 .5 5 0 )

A in rt

.0 1 5
(1 .6 7 2 )

.0 2 5
(2 .4 3 8 )

A in Y t _ i - A in Mt

- .6 9 6
(- 4 .7 2 3 )

- .6 4 5
( - 4 .2 7 6 )

A in Y u 2 - A in Mt

- .2 3 0
( - 1 .7 9 7 )
.2 6 4
(2 .1 1 8 )

- .1 4 8
( - 1 .1 2 9 )

- .2 1 3
(- 2 .0 0 7 )

- .1 8 4
( - 1 .6 8 0 )

.571
(4 .0 6 3 )

.0 4 0
(.3 5 6 )

A in Yt -3 - A in Mt
A in Yt -4 - A in Mt
Constant

.2 4 0
(1 .8 5 9 )

.5 5 8

.5 2 6

SEE

.8 8 7
2 .0 4 5

.9 1 8

2 .0 2 7

♦Numbers in parentheses are t-values.

Ain Q t + AlnPt = Ain Yt, the coefficients on each set of
lagged AlnQ and AlnP terms are constrained to be equal

1975

by specifying AlnY terms (Equation B ). Table II of the
text presents the estimated coefficients for equation B.
Regression results for this equation are tested against
those for equation (A ). The calculated F value are .58
for
and .64 for M2. The critical F value is 2.53, there
fore, the equal response hypothesis is accepted in both
cases. These results also lead to the acceptance of the
assumptions made regarding the equality of weights in
forming Ain Qp and Ain Pp.
A frequent hypothesis in monetary economics is that
the elasticity of desired money balances with regard to
nominal income is unity. Since the weights sum to unity,
the hypothesis implies that the coefficient an money in
equation (B ) is equal to, but opposite in sign, the sum
of the coefficients on the lagged AlnY terms. This con
straint is imposed on equation (B ) by dropping the
AlnMt term and subtracting AlnMt from each of the
lagged AlnY terms. The regression results are reported in
Table C and are tested against the results for equation
( B ) . The calculated F value for M j is 4.57 and for M„ is
7.99. The critical value of F is 4.00; therefore, the propo
sition that the elasticity equals unity is rejected in both
cases. The estimated elasticity of desired money balances
with regard to perceived nominal income — 1.62 for M x
and 1.97 for M ,, — is derived by dividing the sum of the
coefficients on the lagged income terms by the coefficient
on money and changing the sign.

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