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FEDERAL RESERVE BANK
O F ST. L O U IS
JANUARY 1971
Current Stabilization Policy
2
The Revised M oney Stock: Explanation
and Illustrations ............................ ........ 6
•
* MEMPHIS
LITTLE ROCK
EJ
Digitized for Vol.
FRASER 53, No.
1
Expectations, Money, and the Stock Market 16
Current Stabilization Policy
I HE NATIONAL ECONOMY is confronted with
two major problems —inflation and unemployment —
and for the first time since 1957 and 1958 both
problems must be dealt with simultaneously. The
course of events which brought the economy to this
juncture includes the monetary and fiscal actions of
the past five years.
other post W orld W ar II periods when the growth of
total spending slowed. The growth rate of raw indus
trial material prices rose steadily in the last half of
1968 and 1969, reaching a peak in 1970. The growth of
wholesale industrial prices and consumer prices
reached peaks in the first half of 1970.
Until mid-1970, rising unemployment did not ap
pear to many analysts to be a major problem for the
economy. The rise of unemployment in the first half
of 1970, compared to 1969, was viewed as a temporary
effect of a moderated growth of total demand and as
a necessary cost of establishing price stability. It was
recognized that a somewhat higher and gradually ris
ing level of unemployment was to be expected for a
short time, as a result of applying more restrictive
stabilization actions in hopes of achieving a relatively
stable price level. By the autumn of 1970, however,
unemployment had risen more than most analysts
expected.
Since February 1970, the prices of raw industrial
materials have declined at an 11.7 per cent annual
rate. While these prices are highly responsive to chang
ing demand and supply conditions, their decline
should not be viewed as conclusive evidence that
substantial improvement in inflation w ill follow. The
decline reflects international as well as domestic
market conditions.
Recent Developments
Recent Price and Employment Trends
The gradual moderation of the pace of price in
creases in 1970 was similar to price trends during
Page 2
Wholesale prices of industrial commodities rose at
a 3 per cent annual rate from May to December,
down from the 3.9 per cent increase in the preceding
twelve months. Wholesale prices of farm products and
processed foods and feeds declined slightly over the
year ending in December, but these prices frequently
reflect special supply conditions, and for short periods
of time often follow trends independent of business
fluctuations in the economy. Consumer prices have
moderated since last April, rising at a 4.9 per cent
annual rate to November, compared with a 6 per cent
increase in the previous twelve months.
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
JANUARY
1971
Slower growth in total spending and a growing la
bor force resulted in a rising unemployment rate in
1970. Unemployment reached 6 per cent of the labor
force in December, compared with a 3.9 per cent rate
in January 1970. The average duration of unemploy
ment increased from approximately 7.8 weeks late in
1969 to 9.2 weeks in the last quarter of 1970.
The tax surcharge was reduced to 5 from 10 per cent
on January 1, 1970, and expired on June 30. These
actions, together with lower-than-anticipated tax re
ceipts associated with the economic slowdown, re
sulted in a swing in the national income accounts
budget from a surplus of $9.3 billion in the calendar
year 1969 to a deficit at an $11.9 billion annual rate
in the third quarter of 1970.
Monetary and Fiscal Developments
Federal budget trends and priorities of the past
decade can be seen in the accompanying chart. Total
Federal spending increased from 18 per cent of total
spending in 1965 to an average of 21 per cent for the
years 1967 to 1970. Government spending for defense
and defense-related programs increased from 7 per
The money stock rose 5.4 per cent from December
1969 to December 1970, compared with 3 per cent in
1969.1 In 1967 and 1968, when inflationary pressures
were intensifying, money expanded at about a 7.2
M o n e y Stock
Percentages a re annual rates o f change (or p e rio ds indicated.
Revised series - N ovem ber 1970.
Lotestdata p lotted: D ecem ber
per cent annual rate. Time deposits have increased
at a rapid 23 per cent rate since February, to a large
extent the result of reintermediation associated with
the substantial decline in market interest rates this
year, and relaxation of Regulation Q ceilings on the
rates banks were permitted to pay on time deposits.
Several budget actions in 1970 contributed to in
creases in disposable personal income. A 6 per cent
pay increase for Federal employees and an increase
in the Social Security benefit schedule were enacted
into law, both retroactive to the beginning of the year.
iSee “The Revised Money Stock: Explanation and Illustrations”
on pages 6-15 of this Reveiw, for a discussion of the recent
revisions of money stock data.
cent of total spending in 1965 to 9 per cent in 1968,
and then declined to slightly less than 8 per cent in
1970. Since 1968, nondefense spending as a proportion
of total spending in the economy has expanded by
an amount slightly greater than the decline in defense
spending as a proportion of total spending, so that
total Federal spending in 1970 were slightly higher
than in 1969.
Policy Dilemma
The problems facing stabilization authorities are
substantially different now than a year ago. At the
end of 1969 there was little question that inflation
was the most important problem facing economic pol
icymakers. A year later the rate of price increase (as
Page 3
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
measured by the GNP implicit price deflator) had
declined to about a 4.5 per cent annual rate,
while unemployment as a per cent of the civilian
work force had risen from 3.5 per cent to 6
per cent.
Few economic analysts would argue that the effort
to eliminate inflation should be abandoned to give full
attention to preventing further increases in unemploy
ment. Similarly, few analysts would propose that the
level of unemployment should be disregarded and that
any amount of idle work force should be allowed to
occur, while the remaining forces of inflation are
purged from the economy. The approach to economic
stabilization taken in view of these circumstances will
depend on the consensus of policymakers regarding
two questions: how long w ill it be before the rate of
inflation subsides substantially if the policies of 1970
are continued in 1971; and what will be the likely
path of the unemployment rate in the interim? If the
time span required to stem inflation is considered to
be too long, or the contemplated average level of un
employment is deemed to be too great, alternative
policies would be recommended by some. However,
an assessment of the most probable results of continu
ing recent past policies should be made, before alter
native courses are proposed.
A position which favors continuing the policies of
1970 is based to some extent upon the assumption that
people still anticipate rapid inflation, on the basis of
the last five years of inflation. Further, it is argued
that the current slowdown in business activity and the
associated rising unemployment were to be expected
and were necessary in order to eventually achieve a
continued reduction of the rate of inflation. It is prob
ably neither desirable nor necessary, according to this
view, to reduce the rate of growth of total demand
for goods and services in the future below the rate of
1970. A substantial and prolonged increase in the
growth of total spending from the present rate, ini
tiated by expansive monetary and fiscal actions, would
preclude further progress in controlling inflation.
A second position, which favors emphasizing a re
duction in unemployment as the primary objective of
stabilization policy, argues that stabilization actions to
stimulate total spending would promptly accelerate
the growth of production and employment. Since there
currently exists excess labor and capital equipment, it
is argued that such stimulation would result in little
interruption in the rate of price decline. Only when
the gap between actual and potential output is sub
Page 4
JANUARY
1971
stantially narrowed, it is contended, would there be a
danger of adding to inflationary forces.
The difference between these positions depends on
the weighting of economic objectives and the choice
of a time horizon in which to achieve the objectives.
If a decline in unemployment is the dominant, but
not the exclusive, objective of stabilization policy,
the goal of relative price stability will probably have
to be sacrificed in the near-term. If the reduction of
inflation is the dominant, but not the exclusive, ob
jective of policy, a quicker reduction in inflation
might be obtained at the expense of temporarily
higher unemployment.
There is little direct historical evidence as to the
types of actions which are best suited to deal simul
taneously with the problems of inflation and unem
ployment. Indirect evidence of the likelihood of cer
tain outcomes of various policy alternatives, however,
can be obtained from statistical studies of historical
relationships among economic magnitudes. Implica
tions from such studies indicate the most probable
response of the economy to alternative stabilization
actions.
The results of recent studies by this Bank indicate
that a growth of the money stock at a 5 per cent rate
in 1971 would imply a 7 per cent increase in nominal
GNP for the four quarters of 1971. A price rise of
about 4 per cent and an unemployment rate of about
6 per cent would be associated with this rate of growth
of total spending during 1971. Beyond 1971, a con
tinuation of a 5 per cent rate of growth of money
would be conducive to further reduction in the rate
of inflation and some improvement in the level of
unemployment.
By comparison, an 8 per cent rate of increase in the
money stock during 1971 most likely would be asso
ciated with about a 9 per cent rate of growth of
total spending, a 4.4 per cent rate of increase in prices,
and a 5.7 per cent unemployment rate. The rate of
inflation would remain high beyond 1971, even if a
slower growth in money were sought after 1971.
Strategies for Policy in 1971
Some persons who desire “full” employment within
the next year or two have suggested that it would be
desirable for real output to rise at about an 8 per cent
annual rate until full employment is achieved. It is
doubtful that this goal is attainable, given the current
state of the economy and the lagged effects of past
actions. Moreover, such a rapid expansion would
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
JANUARY
1971
probably revive expectations of rapid inflation, which
would cause substantial problems for stabilizing the
price level in the future. The course suggested to at
tain the 8 per cent real growth would be to maintain
or accelerate the growth in Federal expenditures,
which would result in a $15 to $20 billion budget
(NIA) deficit in 1971 (but a near balance on the highemployment accounts budget). The deficit might be
financed, in large part, by a more rapid monetary
expansion.
This expansive policy has appeal for those with
short time horizons for evaluation. However, when
judgment includes the effects beyond the present
year or so, the more expansionary course is not so
clearly desirable. The more moderate course, of con
tinuing through 1971 to expand the money stock at
about the same rate achieved in 1970, would be con
ducive to continued reduction in the rate of inflation
while allowing a resumption in the growth of real
product.
Inflation and inflationary expectations should con
tinue to have a bearing on stabilization policy, al
though this concern is likely to be tempered by greater
attention to unemployment than was the case only
three or four months ago. Relaxation of stabilization
policies and resulting increased growth in spending
will cause a lengthening of the waiting period neces
sary to stem inflation. If the relaxation is great, sub
stantial spending increases may cause further infla
tion, with employment benefits and increased growth
of real output only temporary.
Page 5
The Revised Money Stock:
Explanation and Illustrations1
by ALBERT E. BURGER and JERRY L. JORDAN
T h e BOARD OF GOVERNORS of the Federal
Reserve System recently revised the data for currency
held by the public, demand deposits held by the
public, and time deposits at all commercial banks. The
revision includes semi-annual adjustments for new
benchmark data on nonmember bank deposits and
vault cash, and the annual recomputation of seasonal
adjustment factors which are applied to each of the
basic deposit and currency series.
In addition to the semi-annual benchmark and an
nual seasonal adjustments, a major aspect of the pres
ent revision is the correction of a measurement error
in member bank demand deposits adjusted. This meas
urement error resulted mainly from international fi
nancial transactions flowing through U. S. agencies
and branches of foreign banks, and subsidiaries of
U. S. banks organized under the Edge Act to engage
in international banking.2
This note explains the revisions, illustrates their
effect on the level and growth rates of money, and
analyzes their significance for assessing recent mone
tary actions and their influence on the economy. In
the Appendix, a sequence of transactions involving
Edge Act corporations are presented in T-accounts to
show how the money stock series was underestimated.
■The discussion in this note regarding the effects of trans
actions involving Edge Act corporations has benefited sig
nificantly from discussions with and papers made available
by Irving Auerbach at the Federal Reserve Bank of New
York and Edward R. Fry at the Board of Governors of the
Federal Reserve System. Mr. Auerbach, Mr. Fry, and their
respective associates are absolved of any remaining errors.
For further discussion of the magnitude of the underestima
tion of the old money series, and the procedures used in
the revision to correct for these measurement errors, see
“Revision of the Money Stock,” Federal Reserve Bulletin,
December 1970, pp. 887-909.
2The Edge Act of 1919 amended the Federal Reserve Act
permitting the Federal Reserve Board to charter corporations
“for the purpose of engaging in international or foreign
banking or other international or foreign financial opera
tions . . . either directly or through the agency, ownership,
or control of local institutions in foreign countries. . . . ”
Digitized for Page
FRASER
6
Reasons for the Revision
Seasonal Factors
Most weekly, monthly, and quarterly economic
time series are subject to recurrent seasonal move
ments which are not related to broader underlying
trends. In order to analyze movements in the series
free of seasonal movements, statisticians have de
vised methods of identifying seasonal patterns and
computing factors which are used to adjust the raw
data. The seasonal pattern for a given series may
change over time for various reasons, so it is desirable
to recompute periodically the seasonal adjustment
factors. The seasonal factors for components of the
money supply and related series are recomputed
annually.
Benchmark Adjustments
Twice each year insured nonmember banks submit
their Reports of Condition (call reports) to the Fed
eral Deposit Insurance Corporation. From these re
ports the Federal Reserve obtains information on
nonmember bank deposits and vault cash. Between
such reports the nonmember bank data on vault cash
and deposits are estimated for purposes of computing
the money stock. The receipt of new call report data
provides a “benchmark” for improving the estimated
nonmember bank data. Benchmark adjustments re
vised estimated nonmember bank deposits down
ward by $300 million at the end of 1969 and by $900
million for mid-1970.
Revisions in Demand Deposit Calculations
The U. S. money supply series, as compiled and
published by the Federal Reserve System, consists of
currency in the hands of the public and demand
deposits held by the public at all commercial banks.
The currency component of the money supply is ob
tained by subtracting vault cash of all commercial
banks from total currency in circulation.3
3Data for vault cash of member banks are available on a
weekly basis to the Federal Reserve. Data for vault cash of
nonmember banks are estimated between semi-annual call
reports. Data for total currency in circulation are available
daily from Treasury and Federal Reserve statements.
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
The demand deposit component of the money
supply includes only demand deposits held by the
nonbank public, that is, demand deposits at all com
mercial banks other than those due to domestic com
mercial banks (interbank demand deposits) and the
U.S. Government. Also, “cash items in process of
collection” and Federal Reserve float are deducted, to
avoid double counting in measuring the amount of
demand deposits the nonbank public knows that it
holds (and hence influences spending decisions).
The reason for deducting cash items in process of
collection between domestic commercial banks can
be illustrated by an example:
Suppose Mr. A writes a check for $100 on his
commercial bank ( C B a ) . He then gives the check
to Mr. B who deposits it in his bank ( C B b ) . While
the check is in process of collection, that is, while
CBb is waiting to receive a transfer of reserves
from CBa, the funds involved appear as a demand
deposit on the books of both C Ba and CBb. Since
checks do not clear instantaneously, gross demand
deposits temporarily rise by $100.
The money supply series measures the currency
and demand deposits which the public knows it
holds. Mr. A knows that he has $100 less in his
checking account. Therefore, the cash item in process
of collection (the $100 check of Mr. A) is deducted
to get a more accurate measurement of the money
supply series.
“Cash items” (which appear as asset items in the
balance sheets of banks waiting to receive payment)
are also generated by certain international transac
tions. To the extent that the cash items resulting from
the collection of funds relating to an international
transaction (for example, the borrowing and repay
ment of Eurodollars)4 are matched by a liability such
as a demand deposit of a foreign corporation, the
computation of the demand deposit component of the
money supply is the same as for cash items arising
from purely domestic clearings.
JANUARY
1971
domestic commercial banks’ balance sheet.5 A deposit
of an Edge Act corporation or similar institution is
treated by a U. S. bank as an interbank deposit and
is therefore not included in the demand deposit com
ponent of the money supply.6 However, the cash items
generated by the Edge Act transactions are included
in the bank’s total cash items, which are deducted
from gross demand deposits.
The following example illustrates the effect of this
treatment of Edge Act deposits on the money supply.
When a U. S. bank receives a check to be credited
to the account of an Edge Act corporation, the bank
enters the amount of the check in a liability account
“due to bank” and also adds the amount to cash
items in process of collection. When computing the
money supply data, both the cash item and the “due
to” account are deducted from gross demand deposits.
The deduction of cash items is only appropriate when
there is a counterpart deposit in the money supply
data. Hence, it is double subtracting to include the
cash item temporarily created by this transaction in
the total cash items in process of collection to be de
ducted from gross demand deposits.
The volume of international transactions which
creates these particular “due to” or interbank deposit
accounts has been increasing rapidly in recent years.
Thus, the old money supply series was subject to an
increasing underestimation.
To correct for this measurement error in the de
mand deposit component of the money stock, data
were collected from U. S. agencies and branches of
foreign banks, and from Edge Act corporations, and
added to gross member bank demand deposits.7 As a
result, the deduction of total cash items in process of
5The discussion in this article will emphasize transactions
involving Edge Act corporations, but the reader should be
aware that the discussion applies to certain other types of in
ternational institutions as well.
However, certain other international transactions —
involving Edge Act corporations and U. S. agencies
and branches of foreign banks — may not give rise to
deposit liabilities on domestic commercial banks to
offset the international cash items generated on the
6This is the same as the liability account “due to domestic
commercial banks” that appears on the balance sheet of a
large correspondent bank with which another bank main
tains deposits for clearing purposes (see Table I). These
transactions do not affect the required reserves of the com
mercial bank. The “due to” account increases the bank’s
demand deposits subject to reserve requirements, but the
corresponding “cash item” is subtracted, thus demand de
posits subject to reserve requirements are not affected.
4See Albert E. Burger, “Revision of the Money Supply
Series,” this Review, October 1969, pp. 6-9, and “Revision
of the Money Supply Series,” Federal Reserve Bulletin,
October 1969, pp. 787-803, for discussions of the effects of
Eurodollar transactions on the money supply prior to mid1969, and a description of changes in Regulation D to
require certain transactions to be treated the same as other
deposits subject to reserve requirements.
7According to the article, “Revision of the Money Stock,” Fed
eral Reserve Bulletin, December 1970, p. 891: “The figures
for deposits of Edge Act corporations are readily available
from weekly reports submitted to the Federal Reserve Bank of
New York in accordance with Regulation K. For agencies
and branches of foreign banks, end-of-month deposit figures
are available from reports submitted to the New York State
Commissioner of Banking. However, it was necessary to
Page 7
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
collection ( including those created by
both domestic and international trans
actions) now provides a more accurate
measure of “member bank demand
deposits adjusted.”8
JANUARY
Table 1
Com putation o f D em and Deposit Com ponent o f M o ney Supply1
G ross dem and deposits (member banks)
Computation of the demand deposit
component of the money supply for
a sample week is illustrated in Table
I. Although the data in the table are
approximations of the actual dollar
changes, they reflect accurately the
relative sizes of the revisions resulting
from international transactions rela
tive to benchmark adjustments. In the
sample week, the addition of gross
deposit liabilities of Edge Act corpo
rations and other international bank
ing institutions raised demand de
posits adjusted by $7.9 billion. Data
for nonmember bank deposits, based
on new benchmark data, were revised
downward by $1.2 billion. The net of
these two corrections raised the de
mand deposit component of the money
supply (before seasonal adjustment)
by $6.7 billion in the sample week.
O ld
Series
Revised
Series
$179.1
same
3.0
same
PLUS:
Demand deposits due to
mutual savings banks and
foreign institutions
Liabilities of specialized
banking institutions2
— 0—
7.9
23.8
5.9
31.5
same
same
same
$ 1 2 0 .9
$ 1 2 8 .8
38.3
37.1
0.4
same
LESS:
Demand deposits due to banks3
U.S. Government dem and deposits
Cash items in process of collection
Demand deposits adjusted (member banks]
PLUS:
Nonm ember bank
dem and deposits adjusted
Foreign and international
deposits at Federal Reserve
LESS:
Federal Reserve float
Total demand deposit component
3.0
same
$ 1 5 6 .6
$ 1 6 3 .3
Effective
C hange
* f 7.9
+ $ 7 .9
-
1.24
+ $ 6 .7
*D ata a r e in b illio n s o f d o lla rs, n o t s e a so n a lly a d ju s te d .
R e p r e s e n t s lia b ilitie s o f E d g e A c t c o r p o r a t io n s a n d f o r e ig n a g e n c ie s . T h e se lia
b ilitie s a r e c o u n t e r p a r t s t o c e r ta in cash ite m s o n th e b o o k s o f d o m e s tic c o m m e r
cia l b a n k s . T h e y a r e in clu d e d t o n e u tra liz e the d o w n w a r d e ffe c t in m o n e y s u p p ly
ca lcu la tio n s o f a n e q u iv a le n t a m o u n t o f cash item s o n th e b o o k s o f co m m e r c ia l
b a n k s, w h ic h a r e s u b tra cte d f r o m g r o s s d e m a n d d e p o s its . B e ca u se f o r e ig n a g e n c ie s
an d E d g e A c t c o r p o r a t io n s a r e n o w tre a te d as p a r t o f th e c o m m e r c ia l b a n k in g
system , a sm all a m o u n t o f d e p o s its held m o r e o r less p e r m a n e n tly b y t h e ir cu s
t o m e rs is a ls o a d d e d to th e d e m a n d d e p o s it c o m p o n e n t o f th e m o n e y s u p p ly .
3C o n sists o f a ll in te rb a n k d ep osits
t io n s a n d fo r e ig n a g e n cie s .
in c lu d in g dep osits d u e to E d g e A c t
corpora-
4B e n ch m a rk a d ju s tm e n t.
Magnitude of the Revisions:
Levels and Growth Rates of Money
The accompanying chart of monthly data for the
“revised” and the “old” money supply series from 1967
to the present illustrates the effects of the recent
revisions.9 Underestimation of the old money supply
series has been building up since mid-1968, and has
widened more rapidly since mid-1969. However, com
parison of the levels of the old and revised money
supply data would not provide an accurate assessment
of the effects of the recent revision on the influence of
monetary actions in the past few years. Empirical
obtain additional data from agencies and branches to allow
for checks written by them that were making for inappropri
ate cash items as a result of the intermediary role of these
institutions in international transfers. Such data have been
reported daily since October 1 and will be available on a
continuing basis.”
8Two other much smaller sources of understatement of
demand deposits resulting from banks’ practices in account
ing for Eurodollar repayments were identified and eliminated
by a change in accounting practices of certain banks.
9The ^recently revised money supply data are referred to as
the “revised money supply series,” and the former data are
referred to as the “old money supply series” only as an aid to
exposition in this article.
Digitized forPage
FRASER
8
1971
M o n e y Stock
Ratio Scale
Billions of Dollars
230
225
220
Ratio Scale
Billions of Dollars
230
M o n t h ly A v e r a g e * o f D a i l y F ig u r e s
1
K
1
*
C
c
o
* 225
“
l>-
o
U
220
215
215
210
6210
+0.6%
R e v is e d S e rie S kJ
+5.1% ^ — > — f l
205
____ 2 0 6
/
200
200
195
195
O ld S e r i e s 21
190
190
185
185
180
180
175
175
170
170
165
165
160
■ 1111
i 1 1 1 1 1 ,X I . L
1967
u l . u
lu
1968
. 11 1 i i
1 11 1 11.
1 1 1 1 1 i 1 1 1 11
1969
1970
a j S e r ie s p u b li s h e d p r io r to N o v e m b e r 1 9 7 0 .
bjT h e r e v is e d s e r ie s r e fle c t s a n n u a l r e v i s i o n s o f s e a s o n a l f a c t o rs a n d b e n c h m a r k
a d ju st m e n ts , a s w e ll a s m a j o r a d j u s t m e n t s f o r a n u n d e r e s t im a t io n o f the o ld
s e r ie s a r i s i n g fro m in t e r n a t io n a l t ra n s a c tio n s .
P e r c e n t a g e s a r e a n n u a l ra t e s o f c h a n g e fo r p e r i o d s in d i c a t e d .
L a te st d a t a p lo tte d : R e v i s e d S e r i e s - D e c e m b e r ; O l d S e r i e s - O c t o b e r
160
F E D E R A L R E S E R V E B A NK OF ST. LO UIS
T a b le
JANUARY
1971
REVISED MONEY SUPPLY
CO MP O U N D E D ANNUAL RATES OF CHANGE
TERMINAL
BILLIONS OF
DOLLARS
INITIAL MONTH
M O N TH
5-69
6-69
7-69
8-69
9-69 10-69 11-69 12-69
1-70
2-70
3-70
4-70
5-70
6- 70
7- 70
8-70
9-70 10-70 11-70
4-70
5-70
6-70
7-70
OLD MONEY SUPPLY
C O MP OU ND ED ANNUAL RATES OF CHANGE
TERMINAL
MONTH
3-69
4-69
5-69
8.2
5-69
4.7
1.2
6-69
4.5
2.8
4.3
8-69
i
7-69
8-69
INITIAL MONTH
DOLLARS
9-69 10-69 11-69 12-69
1-70
BI LL IO NS OF
2-70
3-70
8-70
9-70
198.1
4-69
7-69
6-69
198.3
199.0
3.9
2.4
3. 1
1.8
2-7
1.4
1.4
0.0
-1.8
199.3
199.0
9-69
2.2
1.1
1.1
0.0
-0 .9
0.0
10-69
2.0
1.0
1.0
0.2
-0.4
0.3
0.6
11-69
1.9
1.0
1.0
0.4
0.0
0.6
0.9
199.0
199.1
199.3
1.2
12-69
1.9
1.1
1.1
0.6
0.4
0.9
1.2
1.5
1.8
1-70
2.6
2.0
2.1
1.8
1.8
2.6
3.2
4.1
5.5
199.6
2-70
1.4
0.7
C.7
0.2
0.0
0.3
0.4
0.3
0.0
3-70
2.4
1.9
1.9
1.7
1.7
2.2
2.5
2.9
3.3
3.9
1.2
14.1
4-70
3.0
2.6
2.8
2.6
2.7
3.3
3.7
4.3
4.9
5.7
4.4
12.7
11.3
5-70
3.1
2.7
2.8
2.7
2.8
3.3
3.7
4.2
4.7
5.2
1 4,2
9.6
7.4
3.6
6-70
2.8
2.4
2.5
2.3
2.4
2.8
3.1
3.4
3.7
4.0
3.0
6.6
4.2
0.9
-1 . 8
7-70
2.8
2.5
2.6
2.5
2.5
2.9
3.2
3.5
3.8
4.1
3.2
6.1
4.2
2.0
1.2
4.2
9.4
201.1
-0.9 -10.2
199.3
201.5
203.3
203.9
203.6
204.3
8-70
3.3
3.0
3.1
3.0
3.1
3.5
3.8
4.2
4.5
4.8
4.2
6.8
5.4
4.0
4.2
7.3
10.5
9-70
3.2
2.9
3.0
2.9
3.0
3.3
3.6
3.9
4.2
4.4
3.8
6.0
4.7
3.5
3.4
5.2
5.7
1.2
10-70
2.9
2.6
2.7
2.6
2.7
3.0
3.2
3.5
3.7
3.9
3.3
5.1
3.9
2.7
2.5
3.6
3.4
0.0
-1 .2
8 -6 9 — 9 -6 9
1 0 -6 9
1 1 -6 9
1 -7 0
Z -T O
6 -7 0 — 7=70— 8=70
9 -7 0
3=59
4 -6 9 —
5=59— 6=& T
T -6 9
1 2 -6 9 —
3 -7 0 —
4 -7 0 — 5 -7 0
206.0
206.2
206.0
INITIAL MONTH
Page 9
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
studies provide evidence that, for purposes of assess
ing the impact of monetary developments on the econ
omy, it is appropriate to look at the changes in the
rate of growth of money over the past twelve or more
months.
The growth rates of money indicated by the revised
series for 1968 and 1969 are not sufficiently greater
than the respective growth rates indicated by the old
series to warrant reassessment of the influence of
monetary actions during those two years. The growth
of money in 1968 (from IV/67 to IV/68) was at a
7.4 per cent annual rate for the revised series, com
pared with a 6.8 per cent rate in the same period
for the old series. Similarly, the revised money series
rose at a 3.8 per cent rate from IV/68 to IV/69, not
much faster than the 3.1 per cent rate of increase
of the old series in that period.
The significance of the recent money supply revi
sions depends upon the impact of the revisions on
the rates of change of money during 1969 and 1970.
Table II contains two “rate-of-change triangles” show
ing the growth rates of the revised and the old money
supply series from various initial months to various
terminal months in 1969 and 1970. To read the tri
angles, observe that the rate of change of the revised
money supply series from December 1969 (on top
and bottom horizontal axis) to May 1970 (on left
vertical axis) was 6.7 per cent. The rate of change of
the old money series in the same period was 5.2 per
cent. W ith the aid of these triangles, the reader can
choose any beginning and ending month he considers
relevant, and compare the impact of the recent revi
sions on the growth rates of money.
Revision of Money and Assessment of the
Influence of Monetary Actions on GNP
An Analytical Approach
It is useful to employ a consistent analytic frame
work to analyze the implications of the revised money
supply series on the implied course of total spending.
Such an analytic framework is available in which
changes in gross national product are statistically re
lated to current and lagged changes in the money sup
ply and high-employment Government expenditures.10
After obtaining a historical relation between
changes in GNP on the one hand, and changes
10See Leonall Andersen and Keith Carlson, “A Monetarist
Model for Economic Stabilization,” this Review, April 1970,
pp. 7-25, for discussion of a procedure whereby alternative
constant rates of growth of money are used to simulate the
relative impacts on projections of various measures of eco
nomic activity.
Digitized forPage
FRASER
10
JANUARY
1971
in money and Government expenditures on the other,
it is possible to estimate the changes in GNP which
are implied for the future under alternative assumed
growth rates of money. The same assumptions about
future Government expenditures are employed in each
case, and it is assumed that there is no difference in
other factors that influence GNP. In such illustrations,
the relative sizes of the projected changes in GNP
under various assumptions concerning the future
growth rate of money are important. The absolute
level and the changes in the projected values for GNP
are naturally subject to many factors not provided for
in this procedure, such as the duration of an automo
bile industry strike.
Monetary Actions in 1970
As noted above, the growth rates of money for
1968 and 1969, according to the revised series, were
not much greater than the rates indicated by the old
series. Consequentiy, assessment of the thrust of mon
etary actions during those two years is little affected
by availability of the revised series as opposed to the
old series.
The effect of one’s assessment of the thrust of
monetary actions in 1970 bears closer analysis. From
IV/69 to 111/70 the growth of money was indicated
by the old series to have been at a 4.2 per cent
annual rate, and is now shown to have been at a
5.5 per cent rate by the revised series. A relevant
question to pose at this point is whether one’s conclu
sion about the influence of monetary actions on the
future growth of total spending, and hence prices and
unemployment, would be much affected by the avail
ability of the revised series.
By employing this approach, it is possible to test
whether the growth rate of money for 1970 that ap
peared most likely to achieve a given growth rate of
total spending would have been different at the end
of 1969, if the revised money series had been avail
able at that time. Using statistical relations estimated
from data available through the end of 1969, projec
tions were made of the growth paths of GNP for the
four quarters of 1970 based on alternative assumed
(constant) growth rates of the revised money series.
These projections were then compared with similar
projections based on the same assumed growth rates
of the old money supply series.11
"Specifically, data for quarter-to-quarter changes in the old
series from 1953 through 1969 were used to estimate a
statistical relationship with quarter-to-quarter changes in
GNP in the same period. Next, alternative assumptions
about the growth rate of money during 1970 were used to
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
The results were very close between each growth
rate for the two series, indicating that the availability
of the revised series at the end of 1969 would not
have influenced substantially the selection of the de
sired growth of money for 1970. For example, based
on the actual growth of the revised series during
1969 and an assumed constant 5 per cent rate of
growth of this series during 1970, the growth of GNP
was indicated to be 6.1 per cent from IV/69 to
IV/70. This compares with a 5.8 per cent growth
of GNP for the same period as indicated by the
actual growth of the old series in 1969 and an ex
trapolation of that series at a 5 per cent rate for 1970.
It now appears that the actual growth of GNP
during 1970 was somewhat less than 5 per cent. A
5 per cent rate of growth of either money series
indicated a faster GNP growth during 1970. However,
it should not be surprising that the actual growth of
GNP fell short of the projections based on 5 per
cent growth of money. The actual growth of GNP in
the second half of 1970 was substantially dampened
by the automobile industry strike, but, since there is
no provision for the effects of a strike in this proce
dure, the actual should be less than the projected.
Furthermore, the procedure is based on historic aver
age relationships between changes in GNP and
changes in money and Government expenditures
during a period (from 1953) in which there have
been several “business cycles” of varying lengths
and degrees of severity.
Monetary Actions in 1971
Table III shows the projected quarterly changes in
GNP from IV/1970 to IV/1971 as calculated for the
revised money series and for the old series (based on
data available through III/70). A 5 per cent annual
obtain quarter-to-quarter changes in money for 1970, be
ginning from the actual level of money (old series) in the
fourth quarter of 1969. These assumed changes in money in
1970 were then used, together with actual changes for
money in 1969, to compute the projections of GNP for 1970
implied by each alternative growth rate of the old money
series during 1970. Finally, the entire procedure was re
peated using actual changes in the revised money through
1969 to estimate a statistical relation with changes in GNP
for the period, and to make projections for 1970.
JANUARY
1971
Table III
PROJECTED CHANG ES IN G N P
Using the Revised M oney Supply Series
and the O ld Series1
A nnual Rates of Change
Revised Series
111/70 (A c tu a l)
IV /70
1/71
11/71
111/71
IV/71
O ld Series
(6 .1 % )
6 .4 %
6.3
6.3
8.9
6.0
5 .4 %
5.9
6.4
9.2
6.3
Dollar C hange from Previous Quarter^
Revised Series
111/70 (Actual)
IV /70
1/71
11/71
111/71
IV/71
O ld Series
($ 1 4 .4 )
$1 5 .4
15.4
15.5
22.2
15.4
$1 2 .9
14.3
15.7
23.0
16.1
'P r o je c t e d u s in g firs t d iffe r e n c e s o f m o n e y a n d h ig h e m p lo y m e n t
G o v e rn m e n t e x p e n d itu r e s . T h e a n n u a l g r o w t h o f m o n e y is assum ed
to be 5 p e r c e n t f r o m 111/70 t o I V /7 1 . E x p e n d itu r e s a r e estim a ted
t h r o u g h 11/71, a n d t h e r e a fte r a r e p r o je c t e d a t a 6 p e r c e n t rate.
2B illio n s o f d o lla rs a t a n n u a l rates.
rate of increase was assumed in the respective money
supply series from 111/70 to IV/71.
The table shows that GNP projections for IV/70
and 1/71, obtained using the revised money supply
series, are higher than those obtained using the old
money supply series. The GNP projections based on
the old series for these two quarters are strongly
influenced by the relatively slower growth of money
in 1970 indicated by the old series. The GNP projec
tions for the period from the fourth quarter of 1970
through the end of 1971, using a 5 per cent growth
rate of either money supply series, are approximately
the same.
The revision of the money supply data has per
mitted a reassessment of the predicted strength of
economic activity in the near future. However, the
revision has not had a noticeable influence on pre
dictions of the effects of monetary growth on economic
activity over the coming year. On balance, if the
goals of policy have remained unchanged, the com
parisons presented here do not support any conjecture
that monetary actions in the near future should be
altered substantially from actions that were deemed
appropriate based on the old series.
This article is available as Reprint No. 62.
The Appendix to this article begins on the next page.
Page 11
APPENDIX
The following Appendix provides a technical analysis of how transactions involving
Edge A ct corporations caused an underestimation o f the money stock series prior to
the N ovem ber 1970 revision. The example transactions used in this analysis should be
view ed as a typical sequence of entries which would affect the measurement of the
money stock.
The examples used draw heavily on a paper by Irving Auerbach of the Federal
Reserve Bank of N ew York: “Edge A ct Corporations: Some Problems For U.S. Bank
ing and Monetary Statistics.”
The purpose of this Appendix is to illustrate, through
the use of “T - accounts,” the type of transactions involv
ing Edge Act corporations which have resulted in an
understatement of the money stock. A key to under
standing the examples used is to remember that one
asset account of commercial banks (Cash Items in the
Process of Collection) and one liability account (Due
to Banks) are both deducted from the banks’ gross
(total) demand deposits in order to obtain the demand
deposit component of the money stock. Also, demand
deposits of foreigners at U.S. commercial banks, whether
foreign individuals, banks, corporations, or governments,
are included in the demand deposit component of the
money stock.
In the illustration, a Chicago bank will borrow Euro
dollars for one day from a German bank, using the
services of an Edge Act corporation, and then repay the
amount through the Edge Act corporation (hereafter
abbreviated to Edge Act). The Edge Act is located in
New York City, but performs services for banks elsewhere
in the United States as well as for European banks.
First Day
A Chicago bank desires to borrow funds for a day,
say $1000, from a European bank (possibly a branch of
a U.S. bank in Europe), and instructs its foreign branch
bank (say in London or Paris) to borrow Eurodollars
and have the funds paid to the Edge Act which will
transfer the amount to Chicago. The foreign branch of
the Chicago bank arranges the loan from a German
bank, which notifies its New York correspondent bank
to draw a check on its account payable to the Edge Act.
The initial transaction for the first day is by the New York
correspondent of the German bank, which issues an
Officers Check1 payable to the Edge Act (and is deliv
ered immediately to the Edge Act). This New York bank
increases Officers Checks Outstanding and decreases the
demand deposit account of the German bank, denoted
as the Deposit of Foreigner account.
New York Correspondent of German Bank
Deposit of
Foreigner — $1000
Officers Checks
Outstanding + $1000
(payable to Edge
Act)
No Net
Effect on
Demand
Deposits
For the illustration, it will be necessary to report the
transactions of two New York banks. One New York
bank is the “correspondent” of the German bank which
is lending funds to the Chicago bank. The other New
York bank is used by the Edge Act to clear funds, that
is, to receive transfers from the account of foreign lend
ing banks and to repay borrowed funds to the account
of foreign banks. In other words, the Edge Act maintains
a checking (demand deposit) account at the New York
(clearing) bank for purposes of conducting international
transactions as a service to U.S. and foreign banks.
The Edge Act immediately takes the Officers Check
to its clearing bank in New York and deposits the check
to its own account. On its own books the Edge Act
increases an asset account, Due from Bank (the New
York correspondent) waiting for the check to clear, and
also increases a liability account, Due to Bank (the
Chicago bank).
The effects on the money stock when a U.S. bank
borrows Eurodollars for one day using an Edge Act
corporation will be illustrated by T-account entries for
three successive days.
'A change in the Federal Reserve Regulation D, effective
July 31, 1969, requires that issuing banks include such items
as “Officers Checks,” used in the borrowing and repayment
of Eurodollars, in gross demand deposits.
Page 12
JANUARY
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
Edge Act Corporation
Due from
Bank
-I- $1000
(from N.Y. corre
spondent of lender)
Due to Bank + $1000
( to borrower in
Chicago)
No Net
Effect on
Demand
Deposits
At the same time the Edge Act’s clearing bank in
creases an asset account, Cash Items in Process of Col
lection, and increases a liability, Due to Bank (Edge
Act).
New York Clearing Bank of
Edge Act Corporation
Cash Items in Process
of Collection + $1000
Due to Bank + $1000
(to Edge Act)
Demand
Deposits
Decrease
In the meantime, the Edge Act notifies the Chicago
bank that it has borrowed $1000 for one day from the
German bank, and that collection of the funds is in
progress, so the Chicago bank records an asset entry,
Due from Bank (the Edge Act), and increases a non
deposit liability, Due to Foreign Branch.
Due to Foreign
Branch
+ $1000
(own overseas
branch)
No Net
Effect on
Demand
Deposits
At the close of business on the first day the entries
recorded in the above T - Accounts show that the money
supply has decreased by $1000. To see this, note that
there is no effect on the net deposits of the New York cor
respondent of the German bank, since both Officers
Checks and Deposits of Foreigners are included in the
demand deposit component of money. Also, the deposits
of the Chicago bank are not affected, since the liability
account, Due to Foreign Branch, is not a deposit ac
count and therefore does not enter into the computation
of the money supply series, and the asset account, Due
from Bank, does not affect the deposit component of
money.- Furthermore, prior to the November 1970 re
vision of the money supply data, the transactions of
Edge Act corporations were not considered in comput
ing private demand deposits.
Finally, the clearing bank of the Edge Act has two
entries that affect deposits. An increase in the liability
account, Due to Bank, causes gross demand deposits to
rise but, since these “interbank deposits” are subtracted
from gross deposits to derive the demand deposit com
ponent of money, there is no net increase in demand
deposits from this entry. Furthermore, the increase in
the asset account, Cash Items in Process of Collection,
liabilities due to its own foreign branches are not considered
deposits by the parent bank. The parent is not required to
hold reserve balances against these liabilities (as they are
against “due to domestic commercial banks”), and these
deposits are not considered to be a part of the “private de
mand deposits in the hands of the public.”
causes a reduction of demand deposits of $1000, since
“Cash Items” are also deducted from gross deposits to
obtain the money component. The decrease in deposits
occurs because there was no offsetting rise in net deposits.
Stated simply, since the increases in both the asset and
the liability accounts of the clearing bank are deducted
from gross deposits, and since no other bank closed on
the first day with a net increase in demand deposits, the
demand deposit component of money has fallen $1000.
Second Day
On the second day the Officers Check will clear, re
serves will be transferred first from the New York cor
respondent bank to the clearing bank, and then to the
Chicago bank. Meanwhile, the Chicago bank will initiate
repayment of the loan through the Edge Act. At the end
of the second day the demand deposits will still be re
duced by $1000. The day’s transactions are shown in
steps.
First, when the Officers Check clears, the New York
correspondent loses reserves of $1000 and reduces its
liability account, Officers Checks Outstanding.
New York Correspondent of German Bank
Chicago Bank
Due from
Bank
+ $1000
(from Edge Act)
1971
Reserves
-$ 10 0 0
Officers Checks
Outstanding —SI 000
Demand
Deposits
Decrease
At the same time, the clearing bank gains the re
serves and reduces its Cash Items in Process of Collec
tion by $1000.
New York Clearing Bank of
Edge Act Corporation
Reserves
+ $1000
Cash Items in Process
of Collection —$1000
Demand
Deposits
Increase
Upon receiving the reserves, the clearing bank in
itiates a transfer of funds to the Chicago bank, so the
former bank loses the reserves it just received and re
duces a liability, Due to Bank.
New York Clearing Bank of
Edge Act Corporation
Reserves
—$1000
Due to Bank —$1000
(due to Edge Act)
No Net
Effect on
Demand
Deposits
As this transfer occurs, the Chicago bank reduces an
asset, Due from Bank, to match the increase in reserves,
and the Edge Act clears the transaction from its books.
Chicago Bank
Reserves
Due from
Bank
4- $1000
-$ 10 0 0
No Net
Effect on
Demand
Deposits
Page 13
FEDERAL. R E S E R V E B A N K OF ST. LOUIS
JANUARY
Edge Act Corporation
Due from
Bank
Due to Bank —$1000
—$1000
No Net
Effect on
Demand
Deposits
To initiate repayment of the borrowing of the previous
day, the Chicago bank tells the Edge Act to make a de
posit to the account of the German bank (at the latter’s
New York correspondent bank). As a provision for this
repayment, the Chicago bank increases one liability ac
count, Due to Bank (to the Edge Act), and decreases
another liability, Due to Foreign Branch.
Chicago Bank
Due to Bank + $1000
(due to Edge Act)
Due to Foreign
Branch
—$1000
No Net
Effect on
Demand
Deposits
The Edge Act writes an Officers Check drawn on its
account at its clearing bank and increases an asset, Due
from Bank (Chicago).
deposits were reduced at the end of Day 1, they remain
at the lower level at the end of Day 2.3
Third Day
As repayment of the Day 1 loan is cleared on the third
day, the money stock will be restored to its original $1000
greater level, assuming no new transactions through
Edge Act corporations have occurred in the meantime.
To cover the Officers Check written by the Edge Act,
the Chicago bank makes a transfer of funds to the ac
count of the clearing bank of the Edge Act. The Chicago
bank loses reserves and reduces its Due to Bank (Edge
Act) liability account. The Edge Act reverses its prior
entries to clear the transaction from its books, and the
clearing bank of the Edge Act gains reserves and
increases a liability account, Due to Bank (to New York
correspondent of German bank).
Chicago Bank
Reserves
—$1000
Due to Bank - $ 1 0 0 0
(Edge Act)
Edge Act Corporation
Due from Bank
(Chicago) + $1000
Officers Checks
Outstanding + $ 1 0 0 0
(payable to German
bank)
No Net
Effect on
Demand
Deposits
Due from
Bank
No Net
Effect on
Demand
Deposits
At the end of the second day, the New York corres
pondent has had an offsetting increase and decrease in
deposits, with an increase in cash items, resulting in a
decrease in the demand deposit component of money.
The clearing bank of the Edge Act reduced its cash
items, which caused the deposit component of money
to rise at that bank, since there was no corresponding
decrease in deposits (again, a change in the Due to
Bank liability does not, by itself, result in a change
in the deposit component of money). The entries
of the Chicago bank are a reduction in the nondeposit
account, Due to Foreign Branch, which has no effect
at all, and an increase in the Due to Bank liability
account, which increases this bank’s gross demand
deposits, then, it is subtracted out once again to compute
the deposit component of money, resulting in no net ef
fect. Again, the Edge Act entries did not enter into the
computation of money.
On balance the above transactions for the second day
do not result in a change in the demand deposit com
ponent of money compared to the first day. Since demand
14
Digitized forPage
FRASER
—$1000
Officers Checks
Outstanding —$1000
No Net
Effect on
Demand
Deposits
New York Clearing Bank of
Edge Act Corporation
New York Correspondent of German Bank
Deposit of
Foreigner + $ 1 0 0 0
(Geiman bank)
No Net
Effect on
Demand
Deposits
Edge Act Corporation
The check is delivered to the New York correspondent
which increases the German bank’s account (Deposit
of Foreigner) and increases its Cash Item in Process of
Collection account.
Cash Items in Process
of Collection + $1000
1971
Reserves
+ $1000
Due to Bank + $1000
(New York
correspondent)
No Net
Effect on
Demand
Deposits
Upon receiving the reserves from the Chicago bank,
the clearing bank makes a transfer of funds to the New
York correspondent. The entries for the clearing bank
are a decrease in reserves and a reduction of the account,
Due to Bank. The entries for the New York correspond
ent of the German bank are an increase in reserves and
a reduction of Cash Items in Process of Collection.
New York Clearing Bank of
Edge Act Corporation
Reserves
—$1000
Due to Bank —$1000
(New York
correspondent)
No Net
Effect on
Demand
Deposits
3The reader may note that if the Chicago bank had borrowed
another $1,000 on the second day all of the entries for the
first day would be repeated in addition to the above entries
for Day 2, and the deposit component of money would be
understated an additional $1,000. This point will be discussed
again at the end of this Appendix.
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
JANUARY
New York Correspondent of German Bank
1971
Possibility of “Double Underestimation”
dollar borrowings of the example (Chicago) bank, if the
bank were to borrow the same amount every day, for
one day. In the illustration used, the original amount bor
rowed from the example German bank was already in
cluded in the private demand deposit component of
money. If the original $1000 had been, for instance, a
deposit at a foreign branch of the New York correspond
ent bank, and the amount was transferred from the
branch to its New York parent when the loan was made,
then the deposit component of money would not have
been reduced on the first day. The fall in deposits at
the clearing bank would have been matched by a tem
porary rise in deposits at the New York correspondent.
The demand deposit component of money would then
fall on the second day, as the amount is both cleared to
Chicago and repayment is initiated through the Edge Act.
As indicated in footnote three of this Appendix, the
example transactions involving an Edge Act corpora
tion, which illustrate how an understatement of private
demand deposits can occur, could result in deposits
being understated by twice the amount of the Euro
Similarly, if the
bank had been a
respondent bank,
money would not
day.
Reserves
+ $ 10 0 0
Cash Items in Process
of Collection —$1000
Demand
Deposits
Increase
It should be clear that the deposit component of
money rises at the New York correspondent bank, since
the asset it deducts from gross demand deposits, Cash
Items in Process of Collection, is reduced while there is
no corresponding decrease in deposits. The entries for
the Edge Act and the other banks have no effect. The
demand deposit component of money is returned to the
level at the beginning of the first day.
original amount held by the German
time deposit at its New York cor
the demand deposit component of
have been reduced until the second
Page 15
Expectations, Money, and the Stock Market*
by MICHAEL W . RERAN
In recent years, increasing attention has been given to analyzing influences of expecta
tions and monetary actions on the course of economic activity. This article examines the re
sponse of the general level of stock market prices (measured by the quarterly average of the
Standard and Poors 500 Daily Index) to these two influences. Attention is given exclusively
to explaining the general movement of stock prices rather than to explaining very short-run
movements in the level of stock prices or changes in the prices of individual stocks.
The standard theory of stock price determination —discounting to the present the value of
expected future earnings —is used to extend the St. Louis model to include relationships which
influence the level of stock prices. The discounting procedure involves the use of an interest
rate to determine the present value of expected corporate earnings over some future time
horizon.
The statistical estimates of the stock market relationships lead to the conclusion that the gen
eral level of stock prices is influenced mainly by expected corporate earnings and expectations
of inflation. An increase in expected corporate earnings leads to a higher level of stock prices.
Expectations of increasing inflation were found to lower the level of stock prices and not to raise
it as is commonly argued. Inflationary expectations increase both expected corporate earn
ings and the interest rate at which these earnings are discounted. Evidence is presented in
this study, however, that changes in inflation expectations exert a much greater influence on
the rate of discount than on expected corporate earnings. This explains the negative relation
ship found between the general level of stock prices and expectations of inflation.
Expectations are formed on the basis of current and past events. Corporate earnings expecta
tions, according to this study, are formed on the basis of actual earnings over the preceding
five years. Inflation expectations are formed on the basis of actual rates of inflation over the
past four years. Since these formation periods are quite long, fundamental changes in ex
pectations occur slowly.
According to the St. Louis model (this R e v i e w , April 1970), monetary actions, measured
by changes in the money stock, exercise an important influence on gross national product,
the price level, and real output. Since movements in these three economic magnitudes are
basic factors in the formation of expectations in the stock market, the expanded model de
veloped in this article is used to examine the response of the general level of stock prices to
changes in the rate of monetary expansion. The major influence of changes in money on the level
of stock prices was found to be indirect — operating through induced changes in expectations.
Page
16
FEDERAL. R E S E R V E B A N K OF ST. LOUIS
1
HE STOCK MARKET is perhaps the most talked
about and the least understood of all major economic
phenomena. The primary reason for this is the major
influence which expectations play in determining
stock market prices. The lack of knowledge about
how expectations are formed and how they operate
on the stock market has been the major impediment
to empirical research in this area.
In a pioneering work in 1964, Beryl Sprinkle
handled this problem by essentially leapfrogging the
expectations issue and analyzing the relationship di
rectly between changes in the money stock and move
ments in the aggregate stock price index.1 Sprinkle
observed that at least since W orld W ar I the stock
price index has moved systematically with changes in
the money stock. He explained this phenomenon as
an element in the quantity theory of money.
In a recent article, Malkiel and Cragg have ex
plicitly introduced expectations into the determina
tion of stock prices of individual corporations.2 They
surveyed a cross section of security analysts with
respect to their forecasts for corporate earnings and
compared these forecasts with the actual stock price
at the time of the forecast. They concluded that
earnings expectations were an important influence on
the stock price of a corporation. Clearly, investors put
their money where their expectations are.
It is the intention of this article to integrate the
money supply and expectations approaches to de
termination of the aggregate stock price index. In the
first part of the article, a very simple stock market
model is developed which incorporates a method of
measuring corporate earnings expectations. The em
pirical estimation of this model indicates that the
earnings expectations variable and the long-term
interest rate are the dominant factors in stock price
formation. Next, the article considers the factors which
determine interest rates and corporate earnings. Using
the factors' which were found to determine interest
“This article has benefited substantially from comments on
earlier drafts by Lewis Drake, Otto Eckstein, Harry John
son, Thomas Mayer, David Meiselman, Robert Rasche, Fred
Renwick, and William White. In addition, the author owes a
special thanks to his colleagues, Leonall Andersen, Christopher
Babb and Jerry Jordan. Any errors in the analysis are, of
course, the responsibility of the author.
'See Beryl Sprinkle, Money and Stock Price (Homewood,
Illinois, Richard D. Irwin Co., 1964). James Meigs investi
gates the Money-Stock Price issue with more sophisticated
statistical methods in his manuscript in preparation.
2Burton Malkiel and John Cragg, “Expectations and the Structure
of Share Prices,” American Economic Review, September 1970.
This article also includes an extensive and up-to-date bibliog
raphy on the stock market.
JANUARY
1971
rates (which includes changes in money), the stock
price equation is re-estimated in a “semi-reduced
form” specification. Using this alternative stock price
equation and the “St. Louis” econometric model, a
number of dynamic ex post and ex ante simulation
experiments are performed. The results of these ex
periments conform closely to the actual stock price
movement in most time periods tested.
The Stock Market Model
The Theory —The theory of stock price determi
nation has always been clear in concept but weak in
application. Conceptually, the price an individual is
willing to pay for an equity share is equal to the
discount to present value of both expected future
dividends and the discount to present value of the
expected stock price at the time of sale. In its simplest
form, this relationship can be represented by the
following equation
x
( 1 ) SPt —
De
tj1
(1+ R )
De
t-{-2
_)- , t . -(-
(1+ R )2
De
f SPe
1
t-j-n -)- I____t-(-n I
(1+ R )n l ( l + R ) nJ
w here:
SPt
SPe
t-fn
De
R
= Stock Price today —as valued by the individual
investor.
= Stock Price expected at time of sale
= Dividends expected
= Interest Rate expressed in decimal form (8.1% is
written as .081)
The value which an individual will place on equities
today will rise if dividends are expected to rise or if
the stock price is expected to be higher at the date of
sale ( so-called capital gains). The value an individual
attaches to equities today will fall if the interest
rate increases, because the rate at which one dis
counts expected future dividends and capital gains has
risen, and consequently the present value is lower.4
:iThis formulization asserts that each investor has an explicit
time horizon which is equivalent to the date he expects to
sell his stock. It is not necessary that the investor actually
sell the stock in period t+n. It is possible that his expecta
tions about the future stock price and dividends are not
realized, which would cause the actual sale date to change.
A simplifying assumption is that the attitudes about risk
are unchanged, or are accurately incorporated into the inter
est rate. In addition, some individual’s opportunity cost may
not be adequately measured by market interest rates. The
interested reader is referred to Eugene M. Lerner and Wil
lard T. Carleton, A Theory of Financial Analysis (New
York: Harcourt, Brace & World, 1966), especially chapters
7-9, and Fred B. Renwick, Introduction to Investment and
Finance; Theory and Analysis, (New York: McMillan, Jan
uary 1971) for a more complete and formal analysis of stock
price determination.
4There are a number of important factors which are common
in their effects on the interest rate and the stock price. Thus,
any statistical analysis (such as presented in this article)
Page 17
F E D E R A L R E S E R V E B A NK OF ST
LOUIS
JANUARY
1971
An economic decision-making unit w ill wish to in
vest its portfolio in such a w ay as to maximize the
discounted value of returns from alternative invest
ments. This implies that the last dollar invested in
the equity market should give the same expected
rate of return as the last dollar invested in alternative
markets. If the price of bonds falls because of a
shift in the supply schedule, interest rates have risen,
and some investors will find it to their advantage to
switch out of the stock market and into the bond or
other markets. Other things equal, this switching will
have a depressing effect on stock prices.
For the individual investor it is reasonable to as
sume that investment decisions are made on the basis
of an explicit or implicit time horizon, t+ n . For
average investor behavior, one must assume some
thing approaching an infinite time horizon, because
the longest time horizon of the individual investor
will dominate the time horizon of the average in
vestor, (where the average investor is merely the
weighted sum of the individual investors).6 Thus, we
can re-write the average investor equation with re
spect to the stock price as:
Aggregation Issues — W hen one moves from a
description of individual investor behavior to a de
scription of aggregate or average investor behavior,
the formulation of the discount to present value theory
is somewhat modified.5 In the case of the individual
investor, the price of the stock is given and the in
vestor w ill either buy or sell, depending upon whether
his individual evaluation of expected return (dis
counted to present value) is greater or less than the
market price of the stock. In the case of aggregate
investor behavior, it is the current quantity of equities
outstanding which is relatively fixed in the short run
and the stock price which must move to clear the
market. Therefore, the average investor evaluation
of expected returns (discounted to present value) will
determine the price of the stock.
1
where:
which is designed to explain the stock price with interest rates
as one of the important arguments, must consider the simul
taneous interaction among certain variables. For example, in
flation expectations can lead to both higher earnings
expectations and to higher interest rates. Or, an increase in
the real growth rate can also lead to both higher interest
rates and higher earnings expectations.
In the former case, the problem can be handled by dis
tinguishing between real and nominal interest rates and ex
pected earnings. This is done later in the article, especially
in equation (16). In the latter case, no explicit separation can
be made. However, given the way in which real earnings ex
pectations are developed in this article, it is implicitly ac
counted for.
There are, of course, other ways of separating the common
elements in the interest rate and the stock price than those
employed here. The test, however, of the appropriateness of
any procedure is its degree of success in explaining the past
and forecasting the future movement in the stock price.
5The determination of stock prices on the basis of discounting
expected future returns would be generally accepted by
most economists. However, there is considerable professional
controversy with respect to the proper interpretation of this
theory. To a large extent, the debate is over the factors
which affect behavior of the individual investor or individual
firm share price. This article is concerned with the factors
which affect aggregate investor behavior and the average stock
jrice of all fiims. While there is obviously a substantial overap, there are a number of factors that are important in the in
dividual case but tend to average out in the aggregate, such
as the quality of management, the ratio of debt to equity,
and the time horizon of the individual investor. As long as
these basic factors are unchanged on average, they would
not be expected to cause changes in the aggregate stock
price index.
f
Page 18
(2 ) SP = <De+ ASpe)t+i + (De+ASP«)t+2
(1+R)
ASP®
ASPe
t+ i
ASPe
t+ 2
(1+ R )2
= expected change in the stock price in each time
period;
= SPe - SP
t+ i
= SP6
t+ 2
t
- SPe
t+ 1
etc.
A shift in emphasis also occurs when one moves
from determination of the stock price for one firm to
determination of the average stock price of all firms.
The primary factor in investor expectations of in
creases in the stock price, (A SP e> 0 ) in the case
of the single firm, is the relative competence of man
agement in productively employing new capital. This
is irrespective of whether the new capital is financed
by retained earnings or by debt issues. In the case
of the average stock price of all firms, however, the
differential management factor tends to remain con
stant. In this case it is not unreasonable to postulate
that the major factor in expected capital gains is the
rate at which retained earnings are plowed back into
the firm.7 If (k) is defined as the ratio of dividends
to earnings ( the expected payout ratio), then (1 —k ) is
the expected retained earnings ratio, and the ag(iThere are a whole range of interest rates representing ma
turities at different points in time. Discounting the present
value of the expected flow one time period in the future
should be at the interest rate for instruments which mature
one time period in the future. Discounting the expected flow
“n” time periods in the future should be at the interest rate
for bonds which mature in the nth time period. Discounting
with one “representative” interest rate introduces a potential
bias into the stock price estimate, because the term structure
of interest rates is not flat. However, the least bias will occur
if a long rate is used. According to Meiselman, the long rate
is the weighted average of expected short-term rates. For
example, the current rate on a 10-year bond is a function of
the current rate on a 1-year bond and the expected rate on
one-year bonds in the second through tenth years. See David
Meiselman, The Term Structure of Interest Rates (Chicago:
University of Chicago Press, 1963).
'The return on investment financed with debt instruments
can, as a first approximation, be considered as equal to the
average interest rate paid on these instruments when all
firms are aggregated. This assumption allows us to ignore the
source of financing new capital equipment.
F E D E R A L R E S E R V E B A NK OF ST. LO UIS
gregate stock price, equation (2) can be re-written
as follows:
(3 )
SP
=
[k E e +
'
( l - k ) E e ]
t+i
+
(1+R)
[kEe + ( 1 —k) Ee ] t+2. . . .
(1+R)2
which simplifies to
—
E e
t—
|—1
E e
t+ 2
(1+R)
(1+R)2
• • • •
or
=
00
2
i= l
E e
t+ i
(1+R)1
where Ee stands for expected future corporate eam8This formulation is in terms of nominal expected earnings.
An alternative formulation would separate this into expecta
tions of real earnings and expectations of inflation. This latter
formulation would also require the interest rate to be sep
arated into real and inflation expectation components. In this
case, the stock price formulation would look as follows:
(1+ R #)i (l+ P 6)*
where Pe represents inflation expectations, E°'‘ represents
expected real earnings, and R* is the real interest rate today.
If inflation expectations are the same for earnings and interest
rates, then the inflation effect on stock prices will be zero.
That is, the numerator and denominator will rise by the same
proportion, and the ratio (which determines the stock price)
will be unchanged.
This would be the case in tjie long-run steady state solu
tion when expected inflation (P®) equals actual inflation (P)
for a sufficiently long period that all decision-making units
had completely adjusted. Short of this steady state solution,
however, the “gap” between real and nominal values could
be achieved in systematically different ways in earnings and
interest rates. Then the stock price would not be invariant to
inflation expectations. For example, if the gap between real
and nominal earnings is achieved by a fall in real earnings
and a constant level of nominal earnings, while the gap be
tween real and nominal interest rates is realized by constant
real interest rates and rising nominal rates, then the stock
price will fall.
Another factor which could affect the stock price is a
once-and-for-all increase in goods prices. This would not
affect inflation expectations because the rise in prices is not
expected to' continue. Such an event would lead to an in
crease in nominal earnings and therefore to an increase in
earnings expectations, but would not lead to an increase in
the interest rate. In this circumstance, the stock price formu
lation in equation 3-A would tend to understate the actual
stock price.
This conceptually possible event is not probable in the real
world, short of a major war or natural disaster which would
make any analysis of stock prices redundant. If the change in
goods prices is in relatively small increments, and the in
crease in factor prices occurs with a lag (both plausible
statements), then the practical bias in equation 3-A can be
considered negligible.
For an interesting discussion of how to diminish the market
distortions related to strong inflation expectations, see David
Meiselman, “Institutional Reforms to Moderate the Effects of
Variable Price Levels,” Journal of Economic Issues, June/
September 1970, pp. 77-86.
JANUARY
1971
ings.8 This formulation allows us to omit explicit
consideration of expected capital gains. Expected
earnings will be used either to pay expected dividends
(k) or to add to expected capital growth (1—k ).9
Estimation Issues — One of the major problems in
applying the stock price theory described in equation
(3) to an analysis of actual stock price movement is
to determine how earnings expectations are formed.
There are two approaches to analyzing expectations.
If the future is expected to be roughly similar to the
recent past, then the “adaptive expectations hypoth
esis” is used. This hypothesis asserts that in forming
expectations about the future, decision-making units
are strongly influenced by current and recent past
experience. As time goes on and new facts become
available, expectations are adapted to accommodate
them.
If, however, the future is expected to be sharply
different from the recent past, then expectations will
be formed on the basis of some similar historic period
rather than on the most recent past. For example,
when the United States economy switched from war
to peacetime conditions in early 1946, expectations
were formed more on the basis of what happened
before W orld W ar II than on what was occurring
during W orld W ar II.10
In most “normal” periods it is reasonable to postu
late that the adaptive expectations hypothesis is the
most plausible description of expectations behavior.
On this basis w e will assert that expected corporate
earnings, and through this the stock price, are sig
nificantly dependent upon the actual level of current
and past corporate earnings. The Almon distributed
lag approach is used to estimate expectations.
To put the stock price theory into a form which
separates the earnings expectations hypothesis from
the interest rate effect, it is specified as follow s:11
9The individual tax rate on expected dividends (kEe) will
be higher than on expected capital gains ( 1 —kEe) in the
United States. Thus, even if expected earnings are un
changed, a decrease in the dividend rate (k) would shift
earnings into a form in which the tax rate is lower, which
would tend to raise the stock price. The formulation in
equation (3) implies that the expectations about k at any one
point in time (t) is stable for the time horizon of the typical
investor. This implication is reasonable, given that k in the
period 1947-70 has had no secular trend.
10See Thomas Sargent, “Some New Evidence on Anticipated
Inflation and Asset Yields” (Unpublished Manuscript),
National Bureau of Economic Research, August 1970.
1'The equation was also estimated in a nonlinear additive
form, and the results were virtually the same, except that
the R2 and S.E. were somewhat better in the linear form
used in die text.
Page 19
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
JANUARY
1971
1
( 4 ) SPt = a o +
2 ai Rt—i + a2 Ee
i= 0
STOCK PRICE EQUATION
t
Sample Period: 1/1956 -11/ 1970
(Summary Results)
Equation (4) states that the stock price in the
current time period (SP t ) is a function of interest
rates in the current and one lagged time period,
and current expectations about future corporate earn
ings (Ee). The one-quarter lag in (R) is designed to
capture the possible lag in investor awareness of, and
response to, changes in rates. W e postulate that the
value ai is negatively related to the stock price, and
that the value a2 is positively related to the stock
price.
Equation (5) states that expectations of future cor
porate earnings after taxes are a weighted sum (2)
of current and past corporate earnings after taxes.
The value w ( represents the weights applied in form
ing earnings expectations at various periods in the
past, and “n” indicates how many periods in the past
are relevant in forming earnings expectations.
Substituting equation (5) into equation (4 ) yields
a form of the equation which can be estimated
empirically:12
(6 ) SPt = ao +
| J
2
ai
R t-i + | 2
a 2 Wi| E t- i
The stock price equation was estimated with
quarterly data for time periods as short as 1960-70 to
as long as 1952-70. The longest time period which
gave statistically significant results was 1956-70.13
That result is presented in equation (7).
12In this aggregate formulation of stock price determination,
earnings expectations ( Ee) do not take into account the
degree of confidence or risk the average investor has with
respect to how accurately his expectations will be realized.
If this basic risk factor should change, then this adaptive
expectation approach would not be sufficient to determine
the stock price.
It would be desirable to include another variable in this
equation to indicate the degree of confidence the average
investor has about his earnings expectations. Experimenta
tion with a number of proxies for investor confidence were
tried, without success. Thus, the usefulness of this stock
price formulation is dependent upon the absence of a ma
jor change in the average investors confidence in his expec
tations of future earnings. By the same token, the length of
time for which this equation explains the stock price indi
cates the period for which the confidence or risk factor of
the average investor remained unchanged.
13The stock price equation with data from 1/1952 to 11/1970
predicts the stock price index as well as equation (7),
when a dummy variable is added. The dummy variable
assumes a value of 1 from 1/1952 to 11/1955, and zero
thereafter. This result implies that the specified behavior
was the same in both periods, but that some other factor
(roughly measured by the dummy variable) was also im
portant. This additional behavioral factor is most likely re
lated to a change in attitude about risk. Stock price esti
mates could not be made prior to 1/1952 because of data
limitations. Specifically, earnings data (which has a 19quarter lagged effect) were available quarterly since 1947.
Page 20
1
19
(7) SPt = 1 2 . 3 3 - 2 16.27 R t-i+ 2 4.44 Et-i
(3.08) i=°( 4.48)
i=o (8.69)
R2 = .94
S.E. = 4.70
D-W = .74
(Detailed Results)
Ro
Ri
2Ri =
Eo =
Ei =
-19.30
(4.04)
3.03
-1 6 .2 7
( .60)
(4.48)
1.65
(7 .4 2 )
Eu =
.14
(2.15)
.32
(3 .6 7 )
El2 =
.05
( .91)
E?
— .30
(2 .4 8 )
El3 =
.01
(
E3 =
— .46
(5 .1 0 )
El4 =
.05
( .73)
E4
-.3 6
(5.92)
El5 =
.17
(2.25)
Es
— .15
(2.35)
El6 =
.36
(4.5 4 )
.06
(
Ee
-
21)
9 2)
El7 =
.57
(5 .8 4 )
E7 =
Es‘ =
.23
(3.90)
E is =
.69
(5 .2 4 )
.31
(6 .1 3 )
El9 ---
.58
(4 .3 7 )
E9 =
.30
(5.3 1 )
.24
(3.58)
4.44
Eio =
(8.69)
2Ei
=
C o n s t r a in t s : 6th D e g re e P o ly n o m ia l f o r E
2n d D e g re e P o ly n o m ia l f o r R
E t + 1 # 0 : E t_ n = 0
R t+ 1 ^
0 : R t —n — 0
Note: “t” statistics appear w ill each regression coefficient,
enclosed by parentheses. An estimated coefficient is
considered statistically significant if its accompanying
“t” statistic is 1.95 or larger. R2 is the per cent of varia
tion in the dependent variable which is explained by
variations in the independent variables. S.E. is the stand
ard error of the estimate. D-W is the Durbin-Watson
statistic.
The stock price (SP) is measured by Standard
and Poor’s 500 Index.14 The interest rate (R ) is
measured by the corporate Aaa bond yield on sea
soned issues.15 Earnings (E) are measured as cor
porate profits after taxes in billions of dollars from
the national income accounts.
This specification explains 94 per cent of the vari
ance in the level of the stock price index.16 Both
"Standard and Poor’s Stock Price Index is defined as follows:
IndeX =
(10)
where Po and Qo are the stock price and quantity in the
base years 1941-43, Pi is average price in the current pe
riod, and Qi is the volume of stock outstanding in the cur
rent period. The index is also adjusted for stock splits.
15A stock price equation with a roughly similar interest rate
specification can be found in the MIT-FRB model. See Frank
de Leeuw and Edward Gramlich, “The Federal Reserve
MIT Econometric Model,” Federal Reserve Bulletin, Janu
ary 1968, pp. 11-40.
16A11 equations in this article are estimated by the Almon
distribution lag technique. By constraining the distribution
of coefficients to fit a polynomial curve of n degree, it is
designed to avoid the bias in estimating distributed lag co
efficients which may arise from multicollinearity in the lag
values of the independent variables. The theoretical justi
fication for this procedure is that the Almon constrained
JANUARY
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
the expected corporate earnings variable (E) and
the interest rate variable (R) have the expected
sign and are statistically significant. Expectations
about future earnings are based on the actual level
of reported earnings in the current and 19 lagged
quarters. The earnings expectations coefficient has a
high degree of statistical significance and explains a
major share of the movement in stock prices from
1956 to 1970.17
One weakness of the stock price specification in
equation (7) is the low Durbin-Watson (D- W) statis
tic. This implies that the estimated value of the stock
price is systematically above or below the actual
stock price. This problem will be dealt with later in
the article.
The Stock Market and the Economy
If we wish to understand how the stock market
fits into the larger economic picture, we must con
sider the factors which explain long-term interest rates
(R ) and corporate earnings (E).
Interest Rates18 —An analysis of the price of
bonds will not only be of value because it is an
important argument in the stock price equation, but
because it is important for its own sake. In perpetuity
(like British consols), the price of bonds can be
represented as the reciprocal of the interest rate,
(8) BP = -g-
1971
will be explicitly in terms of long-term interest rates.
However, because of the direct transformation illus
trated in equation (8), we can also interpret the
results in terms of the effect on bond prices.
The explanation of interest rates can be illustrated
with three equations:
(9) R = R° + Pe
t
t
t
(10) R °= co + ci M‘ + c2 | 2
t
t
1 i=0
Ul|x
J t—i
(11) Pe = [ 2 Zil P
t I i=0 J t—i
Equation (9) states that the observed market
long-term interest rate ( R t ) is equal to the real rate
of interest (Rt) and the expected rate of change in
prices (Pf). Equation (10) says that the real rate of
interest is a function of a short-run liquidity effect
and a real growth component. The real growth com
ponent is measured as _a weighted average rate of
change in real GNP, ( X ) : u ; indicates the weights
applied to past time periods, and “n” indicates how
many time periods are relevant in determining the
real growth rate. The coefficient c2 indicates the effect
of the real growth rate on the interest rate; c2 is postu
lated to be positive.
The short-run liquidity effect is measured by the
current rate of change in the real money stock ( M°) .
The real money stock is defined as the nominal money
stock (M ) divided by the price index (P):
where BP represents the current bond price and R
the current rate of interest. The following analysis
estimate is superior to the unconstrained estimate, because
it will create a distribution of coefficients which more closely
approximates the distribution derived from a sample of in
finite size. In order to minimize the severity of the Almon
constraint, the maximum degree of the polynomial was used
in each case. The maximum degree is equal to one more
than the number of lags of the independent variables
up to five lags. This follows the convention estab
lished by Shirley Almon, “The Distributed Lag Between
Capital Appropriations and Expenditures,” Econometrica,
January 1965. The lag on earnings (E) was selected on the
basis of minimum standard error (S.E.) of estimate.
17The coefficient 4.44 on the earnings expectations variable
consists of two components; wi, the weights applied to cur
rent and past actual earnings to generate expected earnings,
and a2, the effect on stock prices of a given level of ex
pected earnings. There is no reason to assume that 2 W i = 1 .
Therefore, we cannot separate ( a.-> • wi) into its component
parts. Fortunately for purposes of estimating the stock price
index, such separation is not necessary. This observation also
applies to equation (16), where other expectation variables
are used.
18The discussion in this section relies heavily on the work of
Yohe and Karnosky, “Interest Rates and Price Level
Changes, 1952-69” this^ Review (December 1969), and
Anderson and Carlson, “A Monetarist Model for Economic
Stabilization” this Review (April 1970).
This liquidity effect results from current investment
being temporarily financed from sources other than
intended savings, which is possible as a consequence
of the creation of new money. This should have a
negative effect on the rate of interest, and is some
times referred to as the “Wicksell effect.”
Equation ( 1 1 ) says that the expected rate of
change in prices (P®) is a function of past price
changes, where z t is the weight or importance at
tached to each past time period in the formation of
price expectations, and “n” is the number of past
time periods that are relevant in forming price ex
pectations. Actual price changes are measured by
the GNP implicit price deflator.18
19The effect of price expectations on interest rates has had a
long history in economic literature. As early as 1910, Irving
Fisher published a study relating the impact of price ex
pectations on interest rates. Because of his pioneering work
in this area, such price expectation effects on interest rates
are referred to as the “Fisher effect.”
Page 21
F E D E R A L R E S E R V E B A NK OF ST
LOUIS
JANUARY
Substituting equations (10) and ( 1 1 ) into equa
tion (9) yields the form of the equation which was
estimated:
(12) R = co + c i M * + [ 2 cam X
t
L
®
J
t— *
+ 1 2 vi I ?
L
®
J
t— i
Equation (1 2) asserts that the interest rate in the
bond market is influenced by three factors. Expecta
tions of inflation (P) is measured by the adaptive
expectations approach, and should be positively re
lated to interest rates. The real growth of the economy
(X ) should be positively related to the interest rate.
The liquidity effect ( M ° ) , on the other hand, is
postulated to be negatively related to interest rates.
To test the various elements of the hypothesis con
tained in equation (1 2), it was estimated using
quarterly data from 1/1955 to 11/1970. R is measured
by the Corporate Aaa bond rate on seasoned issues.
LONG-TERM INTEREST RATE EQUATION
Sample Period: 1/ 1955 - 11/1970
(Summary Results)
16
(13) R t = 1.22 - .06 M t ° + 2
.15 Xt-i
(4.63) (3.55)
i=o(2.11)
16
R2 = .94
+ 2
1.00 Pt-i + 1.60 Zt
S.E. = .30
i=o (20.31)
(12.56)
D-W = .74
Results)
=
.01
(1 .8 7 )
Xl
=
.02
(3.5 5 )
X7
=
.01
(1 .5 7 )
x2 =
.02
(3.5 8 )
X8
=
.01
(1 3 4 )
x3 =
.01
(3 .2 4 )
x* =
.01
(2 .7 3 )
X 10
x5
.01
(2.2 5)
X l! =
( -79)
(
-70)
II
b
o
X
II
o
.01
(1 .0 1 )
X 16 =
.00
( .52)
.01
(
2Xi =
.15
(2 .1 1 )
.08
(1 7 .8 1 )
P l2 =
.07
( 9.24)
o
00
to
o
=
(1 4 .6 8 )
P l3 =
06
( 8.85)
.09
(1 2 .6 6 )
P l4 =
.05
(
8.53)
.03
(
8.28)
(
8.06)
89)
Po =
.01
(
Pi
=
.03
( 2.20)
?2
=
.04
( 4.95)
P8 =
P3
=
.05
(
P0
=
.08
(1 1 .3 3 )
Pl5
k
=
.07
(1 7 .6 8 )
PlO
=
.08
(1 0 .4 1 )
P l6 =
.02
P5
=
.07 (2 1 .1 7 )
Pu
=
.08
(
2 Pj =
1.00
9.85)
II
P6 =
13 •
(
(1 .1 5 )
m
.53)
( -6 3 )
o
II
=
• X
•
•
X6
O o
o
o
II n
(3.2 0 )
eo
•X
.02
•X
©
•X
=
X
(Detailed
—
.57)
1971
The equation as specified explains 94 per cent of
the variance in long-term interest rates (R). All co
efficients are statistically significant and have the
theoretically expected sign. The estimated coefficients
indicate that for every 1 per cent annual rate accelera
tion in the real money stock, interest rates will de
crease by 6 basis points; for every 1 per cent ac
celeration in the real growth rate of the economy, the
interest rate w ill increase 15 basis points; and for
every 1 per cent acceleration in expected prices,
interest rates will increase 100 basis points.20
A dummy variable, Zt, assumes the value of “0”
from 1955 to 1960, and the value of “1” from 1961
to 1970. This variable is intended to partially account
for an apparent shift in the financial market relation
ships which distinguished the 1950’s from the 1960’s.
Corporate Earnings — Corporate earnings can be
thought of as the return to risk-taking capital. For
any one corporation, the competence of the manage
ment, the costs of factor inputs, and the demand for
the product are the key variables in explaining
earnings. However, for the economy as a whole, the
management factor tends to change only slowly, and
the major dynamic factors are the strength of total
demand and factor costs. Because total demand and
costs move systematically with each other, and be
cause the monetarist model, discussed below, does not
have an explicit supply equation, we will only consider
total demand factors.
In the short run, earnings are a residual after other
costs of production have been accounted for, and
therefore are sensitive to both changes in total de
mand and to the level of total demand. The most
comprehensive measure of total demand is nominal
GNP: it is the- most important explanatory variable
in our earnings equation. W e w ill assert that the
current level of total demand (Yt ), and changes in
total demand in the current and past quarters
(
2 AY
i— 0
Y have distinct and positive influences on
t—i /
(2 0 .3 1 )
earnings in the current period ( E t ). If total demand
is rising, but at a declining rate, then earnings may
fall, as in the first half of 1970. This roughly captures
cost-push effects on earnings.
Note: “t” statistics appear with each regression coefficient,
20Following Andersen and Carlson, the current and lagged
values or the price variable have been divided by the un
employment rate, on the assumption that price expectations
are influenced not only by past movements in prices but by
the relative slack of economic activity measured by the un
employment rate. In contrast to Andersen and Carlson,
changes in real money rather than nominal money are used
to measure the liquidity effect.
9 .75)
C o n s tr a in t s : 2n d D e g re e P o ly n o m ia l f o r X , P,
*t+l ^ 0 • ^t—n = 0
Pt+ 1
# 0 ; P t_ n = 0
enclosed by parentheses. An estimated coefficient is
considered statistically significant if its accompanying
“t” statistic is 1.95 or larger. R2 is the per cent of varia
tion in the dependent variable which is explained by
variations in the independent variables. S.E. is the stand
ard error of the estimate. D-W is the Durbin-Watson
statistic.
Page 22
F E D E R A L R E S E R V E B A N K OF ST. LO UIS
J A N U A R Y 1971
A c tu a l & Predicted V a lu e s of C o r p o r a te E a r n in g s A fte r T a x e s
J _ P r e d ic t e d v a lu e s a r e fro m e q u a t io n 15 in the text. P r e d ic t e d v a l u e s in 111/1970 a r e b a s e d o n c o e ffic ie n ts e s tim a t e d t h r o u g h 11/1970 a n d o n a c t u a l v a l u e s o f the
in d e p e n d e n t v a r i a b l e s in 111/1970.
S o u r c e : U.S. D e p a r t m e n t o f C o m m e r c e
The other explanatory variable in the corporate
earnings equation is the corporate tax rate (tx), which
is mainly dependent upon Congressional legislation.
A rise in the tax rate will lead to a fall in after-tax
earnings, and vice versa.
The corporate after-tax earnings equation is speci
fied in general terms as follows:
CORPORATE AFTER-TAX EARNINGS
EQUATION
Sample Period: 1/1953 - II/1970
(Summary Results)
(15) Et = 63.04 1.12 txt + .013 Yt + 2
1.59 AYt-i
(19.53) (16.50)
(4.79)
i=o (13.23)
R2 = .99
S.E. = 1.11
D -W = .98
(Detailed Results)
(14) Et = bo + bi txt + b2 Yt + b3 2
i= 0
AYt-i
where
E
= Corporate earnings after taxes (billions of dollars)
tx
= Corporate tax rate
Y
= Nominal GNP (billions of dollars)
AY = Change in nominal GNP (billions of dollars)
W e postulate that (bi) is negative and that (b2 )
and (b3 ) are positive.
AYo = .26 (1 3 .3 5 )
AY7 =
.10
( 7.25)
AYi =
.27
(1 5 .9 5 )
AYg
=
.07
( 5.7 8 )
AY2 =
.20
(1 2 .9 3 )
AY9 =
.04
( 3.33)
AY3 = .1 4
( 9.3 8 )
A Y io =
.03
( 2.59)
AY4 = .1 2
( 8.52)
AY u
.05
( 3.65)
A Y 5 := .1 2
( 8.10)
A Y 12 =
A y6 =
( 7.6 3 )
SAYi =
.12
=
.07 ( 3.8 7 )
1.59
(1 3 .2 3 )
C o n s tr a in t s : 6th D e g re e P o ly n o m ia l
, A Y t + 1 = 0 ; A Y t_ n = 0
Note-, “t” statistics appear with each regression coefficient,
enclosed by parentheses. An estimated coefficient is
considered statistically significant if its accompanying
“t” statistic is 1.95 or larger. R2 is the per cent of varia
tion in the dependent variable which is explained by
variations in the independent variables. S.E. is the stand
ard error of the estimate. D-W is the Durbin-Watson
statistic.
Page 23
F E D E R A L R E S E R V E B A N K OF ST. LO U IS
This equation explains 99 per cent of the variance
in after-tax corporate earnings.21 All of the coeffi
cients are statistically significant and have the theoret
ically expected signs. As illustrated in the preceding
chart, the estimated values of corporate earnings after
taxes are very close to the actual values. Every cyclical
turning point in corporate earnings, as well as most
of the magnitude, is accounted for.
JANUARY
1971
This is because the interest rate in equation (7 ) is
negatively related to the stock price.
In a later section of this article we w ill be inter
ested in real corporate earnings (E*). Real cor
porate earnings can be defined as nominal corporate
earnings (E) divided by the price index (P):
W hen we move to a semi-reduced form estimate,
one issue which had been considered only in a foot
note in the previous discussion must now be given
explicit consideration. As mentioned in footnote (8),
inflation expectations not only will affect the current
level of interest rates but w ill also affect current ex
pectations of future nominal earnings. In a sense, one
can consider expectations of nominal earnings to con
sist of two components: an expectation of future real
earnings, and an expectation of future inflation.
To estimate real corporate earnings, it is only neces
sary to estimate nominal earnings as described in
equation (15) and to divide this value by an estimate
of the price index. (The method of estimating the
price index is described later in the article when the
stock market model is linked to the “St. Louis” econo
metric model.)
If inflation expectations raise current nominal in
terest rates and expected nominal earnings by the
same proportion, then they w ill have no effect on the
stock price. Put in a slightly different way, if inflation
expectations, operating through nominal earnings,
raise the stock price and, operating through current
interest rates, lower the stock price by the same
proportion, then the net impact on the stock price
is zero.
Direct Measures of Expectation Effects
W hat insights into the stock market can be ac
quired from the theoretical and empirical evidence
developed above? It can be said with some confidence
that the stock price is strongly influenced by ex
pectations, and that these expectations are both ra
tional and quantifiable. This should not be confused
with the vague and random expectations typically
associated with day-to-day movements in stock prices.
As estimated in equation (7), earnings expecta
tions Ee play a key direct role in forming stock
prices. Inflation expectations play an important in
direct role in forming stock prices through their
effect on interest rates. These expectations effects on
stock prices, along with changes in real money and
real growth (which are also important arguments in
the interest rate equation), can be made explicit by
going to a “semi-reduced form” equation which di
rectly relates the rates of change in real money, real
output, and price variables to stock prices. However,
we would expect these variables ( M s , X, P) to have
signs with respect to the stock price ( S P ) that are the
reverse of those with respect to interest rates (R).
21Equation (15) is designed only as a method of estimating
current earnings. This equation should not be considered an
attempt to measure the behavior of the major decision
making units which affect corporate earnings. That objective
would require a more sophisticated model than that pre
sented here.
Page 24
It is not necessary, however, that inflation expecta
tions should just offset each other with respect to the
stock price except in the long-run equilibrium case
when actual and expected inflation are equal.
First, it is consistent with economic theory that the
average investor in the bond market may evaluate
inflation expectations differently than the average
investor in the stock market, because of a different
time horizon. This would imply that the gap be
tween real and nominal interest rates and real and
nominal expected earnings would be different. Sec
ond, even if expectations of the average investor in
the stock market and the bond market were identical,
it is possible that inflation may have a systematic
effect on the spread between real interest rates and
expected real earnings. This would be the case if
inflation led to expectations of cost increases in excess
of price increases, so that real earnings expectations
would be lowered relative to real interest rates. With
these considerations in mind, the reduced form stock
price equation should be estimated with the follow
ing variables:
1) Changes in the real money stock (M*), because
this is an argument in the interest rate equation;
2) Changes in real growth measured by changes in
current and lagged real GNP (X), because this is also
an argument in the interest rate equation;
3) Changes in expected inflation measured by
changes in current and lagged prices (P).22 This is
22For reasons discussed in footnote (15), P is divided by the
unemployment rate.
F E D E R A L R E S E R V E B A NK OF ST. LO UIS
both an argument in the interest rate equation and an
element in the nominal earnings expectations variable.
Thus, its net impact on the stock price could be plus,
minus, or zero, for the reasons discussed above;
4) Expected real corporate earnings (E°e) are
measured as current and lagged values of real cor
porate earnings. W e use real earnings expectations in
this equation because that element of expected nominal
earnings associated with inflation expectations should
be captured by the inflation variable.
JANUARY
ALTERNATIVE STOCK PRICE EQUATION
Sample Period: 1/1956 -11/1970
( Summary Results)
2
. «
7
(16) S Pt = -3 0 .6 8 + 2 1.31 Mt - i - 2 5.37 Xt - i
(9.84) i=o (4.14)
i=o (5.67)
16
-2
24The R2, SE, and D-W of equation (16) should be viewed in
the light of comparable values when the stock price is re
gressed only with respect to a time trend. In this case
R2 = .87, SE = 6.77 and D-W = .30.
.98
2.49
D-W = 1.71
— 0.48
1.84)
— 0.37
1.73)
-0 .2 2
1.39)
— 0.29
1.29)
— 0.61
2.18)
P5 =
— 1.07
3.75)
P6 =
-1 .5 2
5.58)
=
II
Pi
II
P3 =
P7 =
-1 .8 4
6.80)
Ps
=
-1 .9 0
7.06)
Eo
*
El
*
E2
*
E3
*
Et
*
E5
*
Eo
*
E7
*
E8
*
E9
=
1.17
9.36)
=
1.16
9.25)
=
0.64
8.00)
=
0.05
0.84)
=
-0 .4 0
5.53)
=
-0 .6 0
7.08)
=
-0 .5 6
6.99)
=
-0 .3 4
5.24)
=
-0 .0 4
0.79)
=
0.25
4.72)
=
0.48
8.19)
E ll =
0.58
9.73)
0.69)
E^2 =
0.56
9.46)
El3 =
0.44
7.26)
4.43)
Pe =
— 1.69
6.62)
PlO =
— 1.25
5.38)
e!o
P ii =
— 0.69
3.11)
Pl2 =
-0 .1 6
Pl3 =
0.18
0.74)
Pl4 =
0.22
0.87)
ii
23The lags in equation (16) are not exactly those derived
from equatipn (7) and (13). The major difference is with
respect to X. The longer lags on X in equation (13) had
small and statistically insignificant coefficients and have been
eliminated from equation (16).
R2 =
S.E. =
(Detailed Results)
UJ
This result is contrary to much popular thinking
which asserts that inflation will help the stock price.
The difference arises from the confusion between ex
pected inflation and actual inflation. W hen inflation
occurs, but is not expected to continue, there may be
some increase in observed earnings of corporations,
which would tend to raise earnings expectations and
the stock price. However, when inflation is expected
to continue, real earnings expectations are apparently
not significantly influenced. This can be seen from
comparing the sum coefficient for real corporate earn
ings expectations in equation (16) with the sum
4.80 E* t - i
i=0 (20.00)
*
Equation 16 explains 98 per cent of the variance
in the level of the stock price index over the last
fifteen years.24 Each of the sum coefficients is statis
tically significant and has the expected sign. In this
reduced form estimate of the stock price, all of the
expectation variables are explicitly accounted for.
Changes in real money ( M ° ) and expected real
earnings ( E ° ) have a positive effect on the stock
price, while real growth (X ) has a negative effect on
the stock price. Inflation expectations (P ) have a
negative effect on the stock price.
* 1 9
1 1 . 96 P t-i + 2
i=» (7.93)
Po =
W e would expect the coefficients associated with
the rate of change in the real money stock (M*)
and level of expected real earnings ( E ° ) to be posi
tive, and the coefficient associated with real growth
(X ) to be negative. The coefficient measuring expecta
tions of inflation (P ) could be either positive or nega
tive. The equation is estimated with quarterly data for
the same time period as equation (7).23
1971
0.29
Pl5 =
-0 .0 1
0.02)
El5 =
0.16
2.46)
Pl6 =
-0 .2 7
0.98)
El 6 =
0.11
2.04)
2P i =
-1 1 .9 6
(7.93)
E17 =
0.18
3.28)
E l8 =
0.31
4.28)
El9 =
0.36
4.74)
ZEt* =
4.80
20.00)
X0 =
-
.60
4.13)
Xl
—
.89
5.96)
X2 =
-1 .0 5
6.55)
_*
0.57
3.62)
0.52
4.14)
0.21
1.30)
1.31
4.14)
=
x3 =
-1 .0 8
6.46)
x4 =
-0 .9 3
5.96)
X6 =
— 0.61
4.60)
M0 =
# *
Mi =
. *
M2 =
X6 =
-0 .2 3
1.88)
2Mi =
x7 =
0.04
0.29)
2Xi =
-5 .3 7
5.67)
C o n s tr a in t s : 6th D e g re e P o ly n o m ia l f o r E *, P , X
3 r d D e g re e P o ly n o m ia l f o r M *
X t+ i = o;
x t_ n — o
Pt+ 1 = 0 ;
P t_ n = 0
Et +1 = 0 ■
Et-n = 0
Mt+1 = 0 = M*-n = 0
Note: “t” statistics appear with each regression coefficient,
enclosed by parentheses. An estimated coefficient is
considered statistically significant if its accompanying
“t” statistic is 1.95 or larger. R2 is the per cent of varia
tion in the dependent variable which is explained by
variations in the independent variables. S.E. is the
standard error of the estimate. D-W is the DurbinWatson statistic.
Page 25
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
JANUARY
1971
There are, however, important in
direct influences of money on stock
prices which clearly exceed the direct
influence. Money, as will be described
in the next section, has an impor
tant influence on real output, prices,
and earnings. Through this process,
changes in money are the dominant
factor, both direct and indirect, in
fluencing stock prices.
The actual stock price, and values
predicted by equation (1 6 ), are
shown in the adjacent chart. This
shows how closely equation (16) has
been able to track major movements
in the stock price from 1/1956 through
IV/1970.
coefficient for nominal corporate earnings expectations
in equation (7). These values are not significantly
different in a statistical sense. But, as indicated in
equation (13), inflation expectations increase the
interest rate which tends to depress the stock price.
Thus, it is possible in the early stages of an inflation,
when expectations have not become strong, for the
stock price to rise. But when inflation continues long
enough that the major decision-making units in the
economy expect further inflation, the stock price
will fall.
It is interesting to note the role of money in this
reduced form stock price equation. A 1 per cent
acceleration in real money will lead to a 1.31 point
increase in the stock price index. This indicates a
significant, but relatively small, direct influence on
stock prices. If growth in real money moved from a
zero to 5 per cent annual rate, the stock price index
would increase by about 7 points over several quar
ters and have no further direct effect.
The relatively modest direct role of money can be
seen by comparing it with real earnings expectations,
which has an eight times larger impact on the stock
price, and with inflation expectations, which has a
4% times greater impact than money.25
25These relationships are derived from the beta coefficients of
the respective variables: M° = .20, E* = 1.65, P = -.90.
Page 26
The largest “miss” in the chart
occurred in 11/1970 and III/1970,
when the estimated stock price was 7
and 8 points above the actual stock
price index. The actual and estimated
stock prices in IV/1970 returned to
their normal close relation.28 This
event implies that an important but basically random
shock pushed the stock price down temporarily in
11/1970, which was not reversed until IV/1970.
The inability of the stock price equation to capture
the major decline in 11/1970 should caution the reader
about applying this model to forecasting. No matter
how w ell the model has explained past stock price
movements, the emergence of essentially noneconomic
events, such as the Cambodian incursion and the
campus riots of May 1970, may at least temporarily
affect stock prices.27 The major utility of the model
lies in its use in systematically analyzing the basic
factors which history has shown to determine the
long-term trend in stock prices.
Experiments with the Stock Market Model
If the stock market model described above is inte
grated into a larger econometric model of the United
States, it w ill provide some insights into the inter
relationships between the stock market and the rest
of the economy. The econometric model, which is
26The stock price estimates in III/1970 and IV/1970 were
derived from the coefficients estimated through 11/1970.
27The ability of stock price equation (16) to pick the major
quarterly movements from 1/1956 to 1/1970 would indicate
that other “famous” random shocks to the stock market have
tended to average out over a quarter.
F E D E R A L R E S E R V E B A NK OF ST. LO UIS
JANUARY
1971
E x h ib it I
Flow D ia g r a m of Stock Price Determ ination
Exogenous
Variables
Endogenous
Variables
CORPORATE
TAX RATE
tx
Changes in
GOVERNMENT SPENDING L i :
Changes in
TOTAL SPENDING
AY
N o te : For o c o m p le te H o w d ia g r a m o f the St. L o u is m o d e l, se e
NOMINAL
CORPORATE EARNINGS
REAL
CORPORATE EARNINGS
A M o n e t a rist M o d e l lo r E c o n o m ic S t a b iliz a t io n ,
EXPECTED REAL
CORPORATE EARNINGS
this R e v ie w (April 1970), p .10. In the flow d ia g r a m a b o v e , c h a n g e s in re o l
o u tp u t (AX), the p ric e le ve l lAP). a n d real m o n e y ( A M * ) a ffe ct the interest rate (R), w hich then offects the sto c k p ric e (SP). T h is flow se q u e n c e is d e s ig n e d io s h o w the lo g ic o f the
re la t io n sh ip s ra th e r t h a n the a c t u a l m e th o d o f sim ulation . The sim u la tio n e x p e rim e n t s d e s c r ib e d in the text a re b a s e d o n the sto c k p ric e e q u a t io n 16, w h e re the interest rate v a r i a b l e is
not in c lu d e d d ir e c t ly in stock p ric e form ation. C h a n g e s in X, P, a n d M * affe ct the stock p rice directly rather than in d ire c t ly t h r o u g h the interest rate. It m ust b e re m e m b e re d , how e ver,
that these v a r i a b l e s o p e r a te c o n c e p t u a lly t h ro u g h the interest rate, a s s h o w n in the flo w d ia g ra m .
used to link the stock market to the rest of the
economy, is the one developed by Andersen and
Carlson and published in this Review in April 1970.
It is small by the standards of most econometric
models, containing only eight equations. However,
it includes all of the variables that are necessary to
experiment with our stock market “sub-model.”
Linking with St. Louis Model — Before describing
the simulation experiments relating the stock market
submodel to the econometric model, it would be use
ful to consider the linkages implied by tying the
models together. Schematically, the link with the
econometric model is illustrated in the Exhibit above.28
There are three independent or exogenous policy
variables in the combined model: monetary policy
measured by changes in nominal money ( A M ) , and
fiscal policy measured by changes in government ex
penditures (A G) , and the tax rate on corporate
profits (tx). There is one nonpolicy exogenous vari
able, the capacity of the economy ( Y 8 ), which is
estimated by the Council of Economic Advisors to
grow at about a 4 per cent annual rate. All the other
variables are determined within the model and are
called dependent or endogenous variables.
^For a complete description of the model see Andersen and
Carlson, pp. 7-25. Each equation in this article was reestimated using the November 1970 revision of the money
stock series.
There are two channels by which the exogenous
policy variables (A M and A G ) affect stock prices.
First, changes in money and Government expendi
tures will affect total spending ( A Y ). The current
level and lagged changes in total spending plus the
current corporate tax rate (tx) determine nominal
corporate earnings (E). Real earnings ( E ° ) are de
rived by deflating nominal earnings by the price
index ( P ). Current and lagged values of real earnings
generate expected real earnings ( E oe) which, in turn,
will have a positive influence on the stock price (SP).
The other influence of the policy variables ( AM
and A G ) operates through interest rates. The change
in total spending ( A Y ) induced by the change in
money and government spending, combined with the
initial conditions with respect to capacity of the econ
omy (Y °) and past changes in prices, w ill determine
current changes in prices ( A P) . The difference be
tween current changes in total spending (AY) and
current changes in prices (AP) will determine cur
rent changes in real output (AX). Current and past
changes in real output and prices w ill generate ex
pectations about inflation and real growth, which will
in turn influence the current rate of interest ( R ). The
interest rate is also influenced by current changes in
real money ( A M * ) . Finally, interest rates will have
a negative influence on the stock price (SP).
Page 27
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
In the following experiments we will be interested
to see whether, by merely manipulating the exogenous
policy variables in the model, nominal money, gov
ernment spending, and the corporate tax rate, com
bined with the initial conditions at the beginning of
each experiment, we can simulate the actual move
ments in the stock price index over an extended
time period.
The stock price equation has been estimated with
two different specifications. In equation (7) it is
estimated on the basis of interest rates and expected
corporate earnings. An equivalent specification is given
in equation (16) as a semi-reduced form. In this
case, rather than directly employing interest rates to
determine stock prices, the factors which affect inter
est rates, as specified in equation (13), are used to
estimate the stock price.
The stock price specification in equation (16) has
a number of desirable statistical properties which are
not present in the stock price estimate in equation
(7). The Durbin-Watson ( D- W) statistic in equation
(16) indicates the absence of autocorrelation in the
error term. The D -W statistic in equation (7) implies
the existence of autocorrelation. This means that the
estimated value of stock prices in equation (16) does
not deviate consistently on one side or the other
from the actual value of stock prices, while in equa
tion (7), such a deviation does exist.
In addition, the standard error of equation (16) is
only about half as large as the standard error of equa
tion (7) ; 2.49 versus 4.70. This means that 64 per cent
of the time (one standard deviation), the estimated
value of the stock price is within 2.49 points of the
actual value of the stock price in equation (16). By
contrast, in equation (7), in 64 per cent of the
observations the estimated value of the stock price is
within 4.70 points of the actual value.
JANUARY
1971
“detailed results”), simulated values of endogenous
variables are generated in the same sequence of
cause and effect as described in Exhibit I. A com
parison of the simulated values for the stock price
with actual values enables one to judge how
well the complete model performs as an integrated
unit.
The time spans selected to conduct the dynamic
ex post simulations were designed to represent diverse
periods in the United States economy. The first
dynamic ex post simulation was III/1961 through,
IV/1965, and the second from 1/1966 through
1/1970. During die first time span, the economy went
from early stages of economic recovery with relatively
high unemployment and stable prices, to a period of
economic boom and a decline in the unemployment
rate below 4 per cent. In the second time span, the
economy w ent from the stage of economic boom with
low unemployment and relatively stable prices to the
early stages of a recession with a high degree of
inflation.
During both of these time spans there were major
rises and falls in the stock price. A good test of
the relevance of our model with respect to the stock
market would be its ability to “track” the movement
in the stock price index against the background of
such diverse general economic conditions.
Botn ex post simulations are illustrated in the chart
below. The simulation starting with III/1961 tracks the
last stages of the rising bull market, picks the peak in
the first quarter of 1962, and the decline in stock
D y n a m ic Ex Post Sim u la tio n s of Stock Price In d e x *
For these reasons the ex post and ex ante simula
tions presented below will be conducted using the
coefficients estimated in equation (16).
Dynamic Ex Post Simulations — Ex post simulation
experiments are conducted within the data period
used to estimate the equations. For example, in the
model used here (and illustrated in Exhibit I), the
shortest data period is for the stock price equation
(1/1956 through 11/1970). Therefore, the ex post
simulations are conducted within this time span. The
variable we wish to simulate is the stock price. Only the
actual values of the policy variables (AM, AG, and
tx) are fed into the computer and, when combined
with the estimated coefficients (which are given as
Page 28
I960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
•S ton da rd & Poor's In dex 500 Stocks, 1941-43=10
These sim ulations are based on equations 15 o n d 16. de scrib ed in the text, as w ell os on updated
estimates o f the St. Louis M odel de scrib ed in the text and published in this Review, A p ril 1970.
Source: Standard & Poor's Security Price In dex Record, 1970 Edition; S tandard & Poor's
Current Statistics, monthly.
JANUARY
F E D E R A L R E S E R V E B A N K OF ST. LOUIS
prices in the second and third quarters of 1962. How
ever, it overstates the stock price index at both the
peak and trough. The simulation does a good job of
measuring the rising market from early 1963 through
1965.
The second dynamic ex post simulation starts with
the first quarter of 1966 and continues through the
first quarter of 1970. It accurately tracks the decline
in the stock price through the fourth quarter of 1966
and its recovery during 1967. However, it does not
capture the rise in the stock price which occurred af
ter the first quarter of 1968. Again, it does a reasonable
job of tracking the moderate decline in the stock mar
ket in the last half of 1969 and the first quarter of 1970.
In general, we can see that these dynamic ex post
simulations tended to track the major turning points
in the stock market rather well, and were moderately
successful in indicating the size of movements in the
stock price after each turning point.29 Moreover, it is
only two years after the beginning of a simulation
that errors tend to become large.
Dynamic Ex Ante Simulation —The acid test of
any economic model is its ability to forecast the future.
This test can be performed experimentally by what
is called a dynamic ex ante simulation. This operates
in much the same w ay as a dynamic ex post simula
tion, with one significant difference. The ex ante simu
lation predicts values of the stock price index beyond
the time period in which the model was statistically
estimated.
1971
Four dynamic ex ante simulations are performed.
For each ex ante simulation all of the coefficients in
the model were re-estimated with data through four
different terminal dates, IV/1966, IV/1967, IV/1968
and 11/1970. W ith these different sets of model es
timates, four alternative ex ante simulations of the
stock price index were made:
1)
2)
3)
4)
ex
ex
ex
ex
ante
ante
ante
ante
simulation
simulation
simulation
simulation
from 1/1967
from 1/1968
from 1/1969
from 1/1970
to 1/1970.
to 1/1970.
to 1/1970.
to IV/1970.
The results of these ex ante simulations are pre
sented in the chart below. Simulation 1 ( which is based
on coefficients estimated with data through IV/1966
and simulates the stock price from 1/1967) accurately
measures the rapidly rising market in the four quar
ters of 1967. It picks the small decline in first quarter
of 1968 and the rise for the rest of the year. For 1969
and 1970, however, this first simulation trails upward
while the actual stock price falls substantially. The
accuracy of this dynamic ex ante simulation diminishes
Dynam ic Ex Ante Sim ulations of Stock Price Index*
1941 -43—10
Q u a r terly A v e r a g e s
of D a i l y
F ig u re s
1941-43 ^10
Simulations ^
------ 1) 1/1967-1/1970
------ 2) 1/1968-1/1970
- 3) 1/1969-1/1970
■“ ■— -4) I/1970-IV/1970
The statistical estimates of the model presented in
this article were performed with data through 11/1970.
To perform dynamic ex ante simulations, therefore, it
was necessary to re-estimate all of the equations in
the stock market model and in the larger St. Louis
econometric model with data through shorter time pe
riods. In this way it would be possible to compare the
ex ante simulation with the actual movements in the
stock price index.
29More technically, this can be seen from the fact that the
standard error of equation (16) was 2.49, while the standard
error of dynamic ex post simulations are higher. The first
simulation (III/1961 through IV/1965) had a standard
error of 3.9, and the second simulation (1/1966 through
1/1970) had a standard error of 4.7. This indicates that
the simulated value of the stock price (which uses the
simulated values for all the variables in the stock price
equation, equation 16) gives a less accurate measure of the
stock price than the estimated equation, using the actual
variables. This result, of course, is not surprising. It reminds
us that simulations of this type are of use in picking turning
points in the stock price, but are less reliable in measuring
the quarter-by-quarter movement in stock prices.
1966
1967
1968
1969
1970
’ S t a n d a r d & P o o r 's I n d e x 5 0 0 S t o c k s , 1 9 4 1 - 4 3 = 1 0
T h e s e s i m u l a t i o n s a r e b a s e d o n r e - e s t i m a t e s o f e q u a t i o n 1 5 a n d 1 6 in t h e te xt:
s im u l a t io n 1 is b a s e d o n c o e f fic ie n t s e s t im a t e d w ith d a t a t h r o u g h IV / 1 9 6 6 ; s im u la t io n
2 t h r o u g h IV / 1 9 6 7 ; sim u la t io n 3 t h r o u g h IV / 1 9 6 8 ; a n d s i m u la t io n 4 t h r o u g h IV / 1 9 6 9 .
C o m p a r a b l e re -e s t im a t e s o f the St. L o u is M o d e l w e re a l s o u s e d fo r t h e se sim u la t io n s .
S o u r c e : S t a n d a r d & P o o r s S e c u r it y P ric e In d e x R e c o rd , 1 9 7 0 E d it io n ; S t a n d a r d & P o o r s
C u r r e n t S ta tistic s , m o n th ly .
Page 29
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
as we move more than eight quarters away from the
initial point of the simulation.
In simulation 2 all of the coefficients of the model
were estimated with data through IV/1967, and the
simulation was commenced in 1/1968. This second
simulation tracks the stock price rise during 1968 and,
contrary to simulation 1, it also tracks the decline in
1969; however, it tended to understate the magni
tude of the fall.
In simulation 3, all of the coefficients in the model
are estimated with data through IV/1968, and the
simulation starts with 1/1969. This simulation indicates
a decline in the stock price during the four quarters
of 1969. It measures the magnitude of the decline
better than simulation 2, but still understates it.
In simulation 4, all of the coefficients are estimated
through 11/1970 and the simulation runs from 1/1970
through IV/1970. It differs from other simulations in
that it is a combination ex post and ex ante simulation.
The simulation is reasonably accurate at forecasting
1/1970 and IV/1970, but overstates 11/1970 and
III/1970 by a substantial margin. The cause of this
discrepancy has already been discussed. It appears
that investor behavior (estimated in equation 16),
which dominated stock price movements since the
middle 1950’s, broke down in 11/1970 and III/1970,
but apparently resumed its previous pattern in IV/1970.
In general, these ex ante simulations tend to per
form well in the first four to eight quarters after they are
started, but then gradually drift away from the actual
value of the stock price. Considering that the periods
used for the simulations were those in which stock
prices reached highs not observed in the data period
used to estimate the coefficients, the simulations per
formed relatively well.
A final dynamic ex ante simulation is conducted
using coefficients estimated with data through 11/1970.
Simulations are conducted for the period IV/1970
through IV/1972. Because the actual value of the
policy variables is unknown, the following assump
tions are made:
(1) The corporate tax rate is assumed to be un
changed from the level of the third quarter of 1970.
(At this printing, depreciation allowances have been
liberalized, effective January 1, 1971. This reduction
in the effective tax rate is not incorporated in the
accompanying stock price simulations;)
(2) The growth in Government spending through
the second quarter of 1971 is estimated from the Gov
ernment budget. Thereafter, it is assumed to grow at
a 6 per cent annual rate;
Page 30
JANUARY
1971
(3) The money stock is assumed to grow at four
alternative rates: 0 per cent, 3 per cent, 6 per cent,
and 9 per cent.
Because changes in the nominal money stock is the
most significant policy variable in the model, it is the
only one which is postulated at alternative growth
rates.
These ex ante simulations should not be treated as
exact forecasts of stock prices. There are some im
portant factors which would make the actual stock
price movement substantially different from any
one of the simulated stock price movements.
First, all of these results are based on quarterly
averages of the stock price, and movements in the
stock price in any one week or month can deviate
significantly from a quarterly average value. For
example, on a monthly basis the most recent trough
in the stock index was May 1970. However, on a
quarterly average basis, the trough occurred in
III/1970.
Second, the simulations are based on assumed con
stant rates of growth in the major policy variable
(money). However, there in fact can be substantial
variance in the growth of money, either because
economic policy may change, or because of random
factors which may influence the quarter-to-quarter
pattern of money growth. If money should grow at
a steady 3 per cent annual rate from 1/1971 to
IV/1972, the simulated stock price is as predicted in
the table below. However, if money growth should
vary between 6 per cent and 0 per cent, with an
average of 3 per cent, the simulated stock price
movement would be substantially different.
Third, the ex ante simulation is based on the
assumption that the average economic behavior of the
D Y N A M IC EX ANTE SIM ULATIO NS OF
STOCK PRICE IN D E X 1
Alternative Rates of M o n e y Growth
Quarter
0%
3%
6%
9%
1 9 7 0 / IV
84.3
85.9
87.5
89.1
1971/1
82.2
85.5
88.7
9 1.9
II
79.9
84.2
88.4
92.6
III
76.1
80.9
IV
75.5
80.6
85.6
85.6
90.3
90.5
1 972/1
II
78.6
83.4
88.1
92.7
81.4
85.5
89.5
9 3.4
III
84.1
87.5
90.8
94.0
IV
85.5
88.3
91.1
93.5
1L e v e ls o f S ta n d a r d & P o o r ’ s I n d e x 500 S to ck s, 1941-43 = 10.
N o te : P r o je c tio n s a r e based on e q u a tio n s ( 1 5 ) a n d (1 6 ) in th e te x t , an d
o n th e S t. L o u is M odel.
F E D E R A L R E S E R V E B A NK OF ST. LOUIS
past fifteen years w ill continue into the future. If
there is a major structural shift in investor behavior
from that implied in equation (1 6) (as temporarily
occurred in II-III/1970), then these ex ante simula
tions will provide misleading predictions.
Finally, simulations are generally better at picking
the timing of a turning point in the stock price than
indicating the size of the movement after the turning
point.
C o n c lu sio n
The intent of this article is threefold. First, it seeks
a rational explanation for movements in stock prices
which is consistent with standard economic price
theory, and which can be tested against historical
observations. It is shown that the standard theory of
stock price determination, that is, discounting to pres
ent value expected future earnings, provides a solid
theoretical base for a reasonably good empirical ex
planation of stock price movements in the past fifteen
years. The major factors determining stock prices
are shown to be expected corporate earnings and
current interest rates. The interest rate in turn is
determined by expectations of inflation, the real growth
rate, and the change in real money. Increased
earnings expectations tend to increase the stock price,
JANUARY
1971
while increased interest rates tend to depress the
stock price. According to this analysis, changes in the
nominal money stock have little direct impact on
the stock price, but a major indirect influence on
stock prices through their effect on inflation and
corporate earnings expectations.
The second objective of this article is to test the
interrelationships between the stock price hypothesis
and a monetarist econometric model of the United
States. By integrating the stock price submodel into
the monetarist model to obtain a combined model,
it is possible to better understand the link between
Federal Reserve actions (measured by changes in the
nominal money supply) and the resulting effect on
the stock and bond markets.
A final objective is to illustrate how a small mone
tarist econometric model can be used to analyze sub
sectors of the economy. In this regard, the article can
be viewed as an application of a monetarist model
to issues with which the model was not originally
intended to deal. The fact that it has worked with
relative success provides further evidence on the
usefulness of the monetarist model and its potential
for further application in explaining other subsectors
of the economy.
This article is available as Reprint No. 63.
Page 31
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