Full text of Review (Federal Reserve Bank of St. Louis) : October 1971

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FEDERAL RESERVE BANK
OCTO B ER 1971
OF ST. LOUIS

Slowing in Money Growth: The Key
to Success in Curbing In flatio n ....
c i r * L I T LI

t lu r i I n

LITTLE*ROCK




Money Stock Control and Its
Implications for Monetary Policy

Slowing in Money Growth:
The Key to Success in Curbing Inflation
by KEITH M. CARLSON

T HE ROLE of monetary actions in the administra­
tion’s new economic program has received little em­
phasis. Controlling inflation is an important objective
of the program, yet a course for monetary actions has
not been proposed. Historical experience in the United
States and other countries indicates that the rate of
inflation is related very closely to the trend rate of
monetary expansion.
Inflation has been a major economic problem since
1965, but experience since 1969 has been especially
frustrating to the nation’s economic policymakers. In­
flation continued unabated in 1970, while unemploy­
ment rose sharply, and has since persisted in the face
of relatively high unemployment. Conventional stabili­
zation actions taken in the last three years to reduce
the growth of money and Federal expenditures have
had their major impact on output rather than on the
price level. This development has led some analysts to
become skeptical about the usefulness of traditional
monetary and fiscal actions in coping with the current
economic situation.
The new economic program was announced on
August 15, outlining a set of measures designed to
deal with the problem of simultaneous inflation and
relatively high unemployment.1 A temporary wageprice freeze was implemented, and a number of fiscal
actions were recommended with the objective of stim­
ulating output and employment. The second phase
of the program takes the form of Government inter­
vention in private wage and price decisions for pur­
poses of making certain that the rate of advance of
consumer prices is reduced to below a 3 per cent
annual rate by late 1972.
There are two major views prevailing with regard
to the current problem of simultaneous occurrence of
high unemployment and rapid inflation. One view
stresses the role of “market power” as a factor influ!The program also included important provisions relating to
the international system of exchange and the U. S. balance
of payments. These provisions are not discussed here.

Page 2


encing recent price level movements.- The other
view is a part of the monetarist explanation of eco­
nomic processes, where the rate of inflation is de­
termined by the trend of monetary expansion. This
latter view attributes the simultaneous occurrence of
inflation and high and/or rising unemployment to
uncertainty regarding the state of total demand and
the costs of information and adjustment involved in
making price and output decisions. These two views
relating to the current economic situation are dis­
cussed along with their policy implications. Preceding
the discussion of these two views is a brief survey
of economic developments from 1969 to the present.

Economic Developments From Late 1969
to the Present
Monetary and fiscal actions turned restrictive in
late 1968 and early 1969, and this policy stance was
maintained until early 1971. The money stock rose at
a 4 per cent average annual rate from early 1969 to
late 1970, following an 8 per cent increase in the year
ending first quarter 1969. So far this year monetary
actions have been very stimulative, with the money
stock rising at about a 9 per cent annual rate from
January to September.
Fiscal actions became less expansionary after pas­
sage of the Revenue and Expenditure Control Act of
1968, but more recently have turned stimulative. Fed­
eral expenditures rose at a 6 per cent average annual
rate from mid-1968 to late 1970, compared with a 15
per cent average rate of advance in the previous three
years. Since the fourth quarter of 1970, growth of
Federal expenditures has accelerated to more than a
10 per cent rate. The income tax surcharge was im­
plemented in mid-1968, then allowed to expire in
mid-1970.
These stabilization actions, while having limited
success in slowing inflation, have had their primary
impact in reducing output growth and increasing un2The term “market power” is ambiguous in its meaning. As
used here it is meant to encompass several views, including
“cost-push,” “administered price,” and “sellers’ ” inflation.

FED ERAL R ESER V E BANK OF ST. LOUIS

OCTOBER 1971

Fiscal Measures

Dem and and Production

{ + ) S u r p lu s ; (-)D e fic it
R a tio S c a le
T r i ll i o n s o f D o l l a r s

R c t io S c a l e
T r i ll i o n s o f D o l l a r s

Quarterly Totals at A n n u a l Rates

i.i
1.0
.9

1963
Sources: U.S. Department of Commerce, Council ol Economic Advisers, ond Federal Reserve Bonk of St. Louis
latest doto plotted: 2nd quarter

employment. The average level of prices advanced
5.7 per cent from fourth quarter 1969 to fourth quarter
1970, then slowed slightly to a 4.7 per cent annual
rate. Unemployment increased from 3.6 per cent of
the labor force in December 1969 to 6.2 per cent a
year later, and has remained near this level, averaging
6 per cent in the first nine months of 1971.
A year before unemployment started rising, unit
labor costs, which had been rising since 1965, acceler­
ated further, reflecting a slowdown in productivity.
Compensation per man-hour rose at a 7 per cent aver­
age rate from late 1968 to second quarter 1971, the same
as from late 1965 to late 1968. In contrast, output per
man-hour slowed to a 1.2 per cent rate of increase
after late 1968, well below the 2 per cent average rate
of advance from late 1965 to late 1968. As a result,




1964

1965

1966

1967

1968

i_[G NP in current dollars.
[2 G N P in 1958 dollars.
Percentages ore an nu al rates of c h o n ge for p eriod s indicated
Latest d o to plotted: 2n d quarter

1969

1970

1971

Source: U.S. Department of Commerce

unit labor costs have increased at a 5.8 per cent aver­
age rate since late 1968, compared to a 4.3 per cent
rate from late 1965 to late 1968.

Simultaneous Occurrence of Inflation
and Unemployment: Two Views
Inflation is a common economic problem, but infla­
tion in conjunction with high and/or rising unemploy­
ment is not so common. In the United States since
Prices
R a t io S c a le

R a tio S c a le

Source: U.S. Department of Labor
Percentages are annual rotes of chan ge for p eriod s indicated.
Latest d ata plotted:Consum er • August;
W h o le sa le - September

Page 3

OCTOBER 1971

FED ERA L R ESER V E BANK OF ST. LOUIS

World War II, there have been few instances when
rapid inflation and high unemployment have per­
sisted together for a significant period of time. Any
such experiences lead some observers to develop the
opinion that conventional monetary and fiscal actions
are not adequate for the task of achieving what seem
to be conflicting social goals.
Explanations of the simultaneous occurrence of high
unemployment and inflation can be divided into two
categories. One attributes the source of the dilemma
to an “excess of market power” among certain eco­
nomic units, and advocates Government intervention
in market pricing to supplement conventional mone­
tary and fiscal policies. The other views the inflationunemployment dilemma as a result of rational eco­
nomic behavior in the face of uncertainty, and stresses
monetary and fiscal actions as the means of restoring
high employment and relative price stability.3

Market Power View
According to the “market power” view, economic
units, most commonly labor or businesses, are said to
have excess market power when the prices of the
goods or services they sell can be pushed up despite
stable or falling demand. For example, because of
substantial bargaining power, union wages may be
pushed up faster than productivity advances. Firms
respond to the increase in unit labor costs by increas­
ing their prices so as to protect their profit margins.
According to this illustration, possession of market
power by either labor or firms (or both) causes prices
to increase in the face of stable or declining demand.
Little evidence has been offered to support the
market power view as it applies to the conjuncture of
inflation and unemployment. For inflation to occur
( not just a once-and-for-all increase in the price level)
when demand is stable, market power must be grow­
ing, or the use of existing market power must be in­
creasing. The existence of market power, however
defined, probably means only that the price level is
higher than it would be if no such market power
prevailed. If one is to argue consistently within this
view, a continuing rise in the price level can persevere
despite stable demand only if market power or its use
continues to grow.
3Those who demonstrate impatience with conventional mone­
tary and fiscal actions are not prepared to abandon such
policies. Rather, these analysts feel that conventional stabili­
zation actions need to be supplemented at certain times to
improve their effectiveness. On the other hand, those who
oppose a supplement in the form of Government interven­
tion do so because they feel that the effectiveness of tradi­
tional actions would be hindered by such intervention.

Page 4


Cost of Information View
The cost of information view concerning the simul­
taneous occurrence of inflation and unemployment
emphasizes the lags in adjustment of prices to an
excess of total demand relative to total supply.4 A
slowing of growth in total demand following a long
period of excess demand and inflation, according to
this view, can produce continuing inflation along with
declining output and rising unemployment. Such a
situation occurs, and is to be expected, because in­
formation about changes in total demand is not avail­
able without cost to decision-making units.
Information about demand can be acquired only at
a cost, and that cost varies with the speed at which it
is obtained. Firms and households must incur a high
cost per unit of information if they are to determine
quickly that a change in total demand has taken place.
There are also costs involved in adjusting prices and
output, so prices can be expected to respond only
slowly to a change in total demand. Under such cir­
cumstances of uncertainty, past price and demand
changes frequently are used to form expectations
about most likely future changes, and these expecta­
tions about demand will lag behind the actual facts
of the demand situation. Thus, following a period of
accelerating inflation, as from 1965 to 1969, there is a
tendency for inflation to continue until changed econ­
omic facts are recognized and eventually lead to ex­
pectations of a slowing in inflation.

Policy Implications of the Two Views
Evidence that clearly supports one view as opposed
to the other is difficult to develop. Nevertheless, the
implications of the two views for monetary policy are
of great significance and require further discussion.

Monetary Policy and the Market Power View
Since the problem of inflation in conjunction with
unemployment is viewed by some observers as one of
excessive market power, the natural policy implica­
tion is to curb the growth of such power or the exer­
cise of existing power. A policy of Government inter­
vention to guide prices and wages in line with pro­
ductivity would supposedly lower the rate of inflation
sooner than otherwise.5 Furthermore, the implication
is that with prices and wages directly controlled in
4This view does not deny the existence of market power, but
it does deny the growth or growing use of that power as
a major factor explaining inflation.
5Note that attention is focused on the inflation aspect of the
problem. There is no disagreement between the two views
on improving the operation of free markets.

FED ER A L R ESER V E BANK OF ST. LOUIS

OCTOBER 1971

this way, monetary and fiscal actions can properly be
conducted towards stimulating total demand. An in­
crease in total demand with prices “directly” con­
trolled would be reflected in increased output and
employment.

Monetary Policy and the Cost of
Information View
The information-cost view of the inflation-unemployment dilemma is that the current situation is
“temporary.” Following four years of accelerating in­
flation, the length of this period of adjustment to
slower growth in total demand is probably quite sub­
stantial. However, according to this view, it is desir­
able for the economic system to complete the adjust­
ment without direct Government intervention in the
price and wage policies of private economic units.
Direct intervention in the form of wage-price-productivity formulae runs the risk of being viewed as a
substitute for anti-inflationary monetary and fiscal
actions; the return of monetary growth to a sustain­
able noninflationary rate consequently may be delayed.
Wage-price standards, when accompanied by sus­
tained rates of monetary expansion in excess of the
growth rate of potential output, will not prevent the
creation of pressures which eventually result in the
abandonment of any system of guidelines.“ Further­
more, controls hamper the operation of free markets,
which are required to allocate resources according to
consumer wants.

Conclusions
Given that the new economic program is concerned
ultimately with achieving high employment with rela­
tively stable prices, historical experience indicates that
monetary expansion should be maintained at a rate
6The experience with wage-price guideposts during the
1962-66 period is a case in point. See the 1970 Annual
Report o f the Council o f Econom ic Advisers (Washington,
D.C.: U. S. Government Printing Office, February 1970),
pp. 23-25.




about equal to the growth of the economy’s produc­
tive potential, or about 4 per cent per year under
present circumstances. Whether a policy of moderate
monetary growth supplemented with Government in­
tervention in private wage and price policy can re­
store high employment with price stability more
quickly than without s u c h a supplement is
problematical.
Recent monetary developments, if continued,
would provide the underlying basis for the control of
inflation. After increasing at a 12.5 per cent annual
rate from January to June, the money stock has slowed
to about a 3 per cent annual rate of increase from June
to September. If monetary actions are to contribute
towards the battle against inflation, moderate mone­
tary expansion must be continued until a trend rate
of money growth is established more in line with the
growth of productive potential.

Page 5

Money Stock Control and Its
Implications for Monetary Policy
by ALBERT E. BURGER, LIONEL KALISH III, and CHRISTOPHER T. BABB

In the last two years there has been an increased concern within the F ederal Reserve Sys­
tem about the role of monetary aggregates in policy, and about the operating procedures impli­
cit in the policy directive o f the F ederal Open M arket Com mittee. A collection o f studies on
these subjects, O p e n M a r k e t P o l i c i e s a n d O p e r a t i n g P r o c e d u r e s - S t a f f S t u d i e s , was pu b­
lished by the Board of Governors in 1971. Other economists have presented m ethods for analyz­
ing the effects of different growth rates o f m oney on policy objectives. An equally important
subject is the controllability of different aggregates and the effect this controllability would
have on the ability o f policym akers to achieve policy objectives.
This article presents a procedure that could be used by the F ederal Reserve System to con­
trol the growth o f the money stock and a m ethod for evaluating the effect o f this control pro­
cedure on the ability o f policym akers to achieve their policy objectives.

growing volume of research has demonstrated
that changes in the money stock are a reliable sum­
mary measure of the effect of monetary policy actions
on economic activity. One result of this research has
been the suggestion that the monetary authorities
could best achieve ultimate policy objectives, such as
full employment and stable prices, by controlling the
growth rate of the money stock. Such a suggestion re­
quires (1 ) an operational procedure for controlling
money, and (2 ) a means of assessing the implica­
tions of such a procedure for the ability of policy­
makers to achieve their policy objectives.
A possible procedure for monetary policy includes:
( 1 ) T h e Federal Open M arket Committee (F O M C )
decides upon the ultimate objectives of monetary
policy, such as desired growth rates for real output
and prices, and a desired level of employment.
( 2 ) These ultim ate objectives are related to a growth
rate of money, and the FO M C issues a “direc­
°The authors wish to express their thanks to the many people
who read earlier drafts of this article. A special obligation
is due the following economists who, in working sessions or
otherwise, offered specific comments: Professors Milton
Friedman, Arnold Zellner, Robert Gordon, Richard Zecher,
Stanley Fisher, Allan Meltzer, Michele Fratianni, William
Yohe, David Fand, and Messrs. Paul Meek and Wolfgang
Gebauer. As always, we benefited from comments and criti­
cism of the research staff at the Federal Reserve Bank of
St. Louis. The procedures and conclusions are the responsi­
bility of the authors and do not necessarily reflect the views
of any of the commentators on the article or the Federal
Reserve System.

Page 6


tive” to the Trading Desk to obtain this growth
rate for money.1
( 3 ) T he Trading Desk uses open market operations
to achieve the growth rate of money which is
consistent with the policymaker’s objectives.

This article is concerned with the actual implemen­
tation of policy decisions. It is not concerned with
how the policymakers decide upon their ultimate ob­
jectives, or with the specific way in which these ob­
jectives are related to a growth rate for money. The
policy objectives are taken as given. Converting policy
objectives into a desired growth rate of money re­
quires information on the linkage between changes in
the growth rate of the money stock and the ultimate
objectives. Such information can be derived from com­
peting models of income or spending determination.
This article presents a procedure the Federal Re­
serve could use to control money and a method for
evaluating the effect of this control on the policy­
maker’s ability to achieve GNP objectives. The money
stock control procedure requires only that the Federal
Reserve has information about the previous three
'The FOMC issues a policy directive to the New York Fed­
eral Reserve Bank. The Trading Desk at the New York Bank
carries out day-to-day open market transactions (purchase
and sale of Government securities) for the System. The text
of each policy directive issued by the FOMC is made public
about 90 days after each FOMC meeting and published in
the Federal Reserve Bulletin.

FED ER A L R ESER V E BANK OF ST. LOUIS

month’s values of the money multiplier and the effect
of reserve requirement changes on member bank re­
serves. Using a simulation technique, some empirical
evidence is presented on the control the Federal Re­
serve could expect to exercise, using this procedure,
over the growth of the money stock, and the effect of
such control on the Federal Reserve’s ability to attain
its policy objectives. The technical details of the
money stock control procedure, the simulation proced­
ure, and the development of the statistic for assess­
ing the influence of money stock control on achieving
policy objectives, are discussed in the Appendix to
the article and in a working paper of technical ap­
pendices available upon request from this Bank.-

Money Stock Control Procedure
There are two major ways in which the Federal
Reserve might operate to control the growth of money.
One way is to estimate the money market conditions
that would be consistent with the growth rate of
money stated in the directive, and then operate to
achieve these conditions in the money market. This
approach might involve choosing bounds for the Fed­
eral funds rate and free reserves and then operating
on a day-to-day basis to maintain money market con­
ditions within these bounds. A second method of
money stock control, the one discussed in this article,
involves estimating the changes in the source base ( or
some other reserve aggregate) required to achieve
the policy determined growth path for money. The
Federal Reserve would then operate on a day-to-day
basis to determine the growth of the source base.:!
The money stock control procedure used in this
article is developed from a multiplier-base framework,
within which the money stock (M ) is expressed as:
M = mB.

In this expression B denotes the net source base and
m represents the money multiplier. An increase in
Federal Reserve holdings of securities, float, the gold
stock, and Treasury currency outstanding will increase
the net source base. An increase in Treasury deposits
2Albert E. Burger, Lionel Kalish III, and Christopher T.
Babb, “Money Stock Control and Its Implications for Mone­
tary Policy: Technical Appendices,” Working Paper No. 14,
Federal Reserve Bank of St. Louis, October 1971.
3These two methods of money stock control are not inde­
pendent of each other. Open market actions taken to deter­
mine money market conditions will influence the growth of
the base, and actions taken to influence the base will affect
short-term money market conditions. See, Albert E. Burger,
“The Implementation Problem of Monetary Policy,” this
Review (March 1971).



OCTOBER 1971

at the Federal Reserve, Treasury cash holdings, and
other deposits and other Federal Reserve accounts
will decrease the net source base. A complete listing
of the sources and uses of base money and the rela­
tionships between the net source base, source base,
and monetary base are given in Table I.
The net source base is taken as the control variable
for the process , 4 From the sources side, the major
component of the net source base ( about 75 per cent)
is Federal Reserve holdings of Government securities.
The Federal Reserve is assumed to be able to accur­
ately measure and determine the magnitude of the
base within a monthly period. Evidence on the accu­
racy with which the Federal Reserve has been able to
forecast and measure the net source base is presented
in the working paper of technical appendices.5
The money multiplier (m ) summarizes all other
factors involved in the money supply process. The
money multiplier responds to portfolio decisions by
the commercial banks, the Treasury, and the public.
Also included in this formulation of the multiplier are
the influences of reserve requirement changes, the
discount rate, and Regulation Q.°
In our money stock control procedure the Federal
Reserve decides upon the desired growth rate of
!The data requirements for controlling the net source base are
as small or smaller than any of the other major aggregates
commonly suggested as operating targets for the Federal
Reserve. Richard Davis has shown that out of a wide range
of possible aggregate targets the nonborrowed base and
nonborrowed reserves would be the easiest targets for the
Desk to hit. These two targets are entirely exogeneous with
respect to open market operations. Contrary to other pro­
posed targets, success in hitting these two targets does not
depend upon the Desk offsetting items whose movements are
functionally related to open market operations. See Richard
G. Davis, “Short-Run Targets For Open Market Operations,”
Open M arket Policies and Operating Procedures-Staff Studies,
Board of Governors of the Federal Reserve System, July
1971, pp. 37-70.
5Burger, Kalish, Babb, Working Paper No. 14.
BThe money multiplier associated with the net source base is:
1+ k
“
( r - b ) (1 + t+ d ) + k
where k and d, respectively, are the ratios of currency held
by the public and U.S. Government deposits at commercial
banks to the demand deposit component of the money
stock.
r, b, and t, respectively, are the ratios of bank reserves,
member bank borrowings, and time deposits to commercial
bank deposit liabilities (excluding interbank deposits).
The reserve ratio (through the dependence of banks’ de­
sired excess reserves), the borrowing ratio and the time
deposit ratio are all dependent upon credit market interest
rates.
This formulation of the money multiplier is taken from the
Brunner-Meltzer nonlinear money supply hypothesis. Karl
Brunner and Allan H. Meltzer, “Liquidity Traps for Money,
Bank Credit and Interest Rates,” Journal o f Political E co­
nomy (January/February 1968), pp. 1-37.
Page 7

O CTOBER 1971

FED ER AL R ESE R V E BANK OF ST. LOUIS

Table I

Sources and Uses o f the N et Source Base,
the Source Base,
and the M o n etary Base, January 1971
(millions of dollars)
Uses

Sources
Federal Reserve holdings of
Governm ent securities
Federal Reserve float
G old stock plus special
draw ing rights
Treasury currency outstanding
O ther Federal Reserve Assets
Less:
Treasury cash holdings
Treasury deposits at Fed­
eral Reserve Banks
Foreign deposits at Fed­
eral Reserve Banks
O ther deposits at F.R.
plus F.R. liabilities and
capital
Equals:
Net source base
Plus:
Federal Reserve discounts
and advances
Equals:
Source base
Plus:
Reserve adjustment
Equals:
M onetary base

$62,1 41
3,6 3 6
1 1,132
7 ,1 5 7
1,216

M em ber bank deposits at
Federal Reserve Banks less
discounts and advances
Currency held by banks
Currency held by the public

445
1,028

Forecasting the Money
Multiplier

155

2,894
$ 8 0 ,7 6 0

370
$ 8 1 ,1 3 0
3 ,8 2 6
$ 8 4 ,9 5 6

Equals:
Net source base
Plus:
Federal Reserve dis­
counts and advances
Equals:
Source base
Plus:
Reserve adjustment
Equals:
M onetary base

♦ D ata n o t seasonally ad ju sted .

money, converts this growth rate into desired money
stock levels for the control periods, and forecasts the
money multiplier (m ) for the control periods. Then
during the control periods, the Federal Reserve uses
open market operations to attain the net source base
( B ) such that the product ( m B) equals the desired
money stock levels. Implementing monetary policy
under such a money stock control procedure requires
three considerations: (1 ) the length of the control
period; (2 ) a procedure for forecasting the money
multiplier; and (3 ) the response to previous errors in
money stock control.

Control Period
The maximum acceptable time period for forecasts
of the multiplier depends upon the relationship be­
tween changes in money and changes in economic
activity. Empirical evidence indicates that quarter-toquarter changes in the growth rate of money influ­
ence economic activity. Therefore, the maximum time
period over which the Federal Reserve would aim to
control the money stock would be a quarterly period.
Such an assumption, however, leaves open the possi­
bility of sharp fluctuations in the growth of money
over the quarter. Therefore, it is further assumed that
as an operating strategy, it is preferable to minimize

Page 8


$ 2 4 ,5 6 8
7,092
4 9 ,1 0 0

the expected squared deviation of the
monthly value of money from its de­
sired growth path. The net source base
is assumed to be controllable on a dailyaverage monthly basis; therefore, with­
in our control procedure monthly aver­
age multipliers are forecast. Having
predicted the value for the month’s
money multiplier, and given the desired
level for the money stock in that month,
the average monthly value for the net
source base necessary to achieve the
desired growth of money is determined.

$ 8 0 ,7 6 0

Next period’s multiplier might be
forecast by any one of the following
methods:

370

(1 )

D efin ition al m e th o d
multiplier-base
framework
is
treated as an accounting iden­
3,826
tity. Some of the ratios of the
$ 8 4 ,9 5 6
multiplier are forecast using in­
formation about the various
components (for example, Treas­
ury deposits) acquired by the
Desk in its daily operations. O ther elements of
the ratios are treated as being equal to their
previous values with some adjustment for trend
or seasonal variation.7

$ 8 1 ,1 3 0

( 2 ) R eg ression m e th o d — T he money multiplier is
expressed as a function of variables that are
known or are under the policy control of the
Federal Reserve at the time each forecast is
made. This relationship is estimated each period
by multiple regression analysis.
( 3 ) B eh a v io ra l m e th o d — E a ch of the ratios of the
multiplier is expressed as being dependent upon
other variables such as interest rates, policy
instruments, and other factors influencing the
deposit behavior of the banks and the public.
This procedure requires predicting these other
variables.

In this article, the second method is used. Each
month’s multiplier is forecast using the three-month
moving average of past values of the multiplier, re­
serve adjustment magnitude in the forecast month,
7See Leonall C. Andersen, “A Study of Factors Affecting the
Money Stock: Phase I,” Federal Reserve Bulletin (October
1965), p. 1379; and William G. DeWald, “Monetary Control
and the Distribution of Money,” unpublished Ph.D. thesis,
University of Minnesota, 1963.

—

T

FED ER A L R ESE R V E BANK OF ST. LOUIS

dummy variables to account for seasonal factors, and
an adjustment for autocorrelation. The values of these
independent variables are known to the Federal
Reserve.8

OCTOBER 1971

M oney Stock Control Process
G R O W T H RATE OF M O N E Y
CO N SISTEN T W IT H THE
P O LIC Y O B JEC T IV E S OF
THE FEDERAL RESERVE

Response to Previous Errors in
Money Stock Control
If there are errors in the forecasts of the money
multiplier, the desired growth of money and the con­
trolled growth of money will not be the same in every
period. Under these conditions, further information is
required to determine the optimal setting for the net
source base. Suppose in period tj the money man­
agers over-predict the money multiplier. Consequently,
the achieved growth of money is less than the desired
growth rate. What is the optimal setting for the net
source base in period t2? Should the money managers
ignore the shortfall of money in t 3? Should they try
and make up the shortfall of money in t, by setting
the net source base in t2 so that the growth of money
is above the desired growth path? If they try and
make up the shortfall, should they operate to make
up all of the gap in t2, or only part of the gap in t2
and the remainder in succeeding periods?
There are many possible error-response mecha­
nisms. Our procedure assumes that the money man­
agers assign proportionally more weight to large errors
in money stock control than small errors. Therefore,
the error-response mechanism is designed to minimize
the expected value of the squared deviations of con­
trolled money from its policy chosen growth path.9
At the end of each control period, the money man­
agers compute their error in money stock control.
During the next control period the net source base is
set approximately to make up last period’s error.10
The money stock control procedure is illustrated in
the following exhibit.
8The Federal Reserve sets member bank reserve require­
ments. Since, under the current lagged reserve requirement
procedure the effect on member bank required reserves of
a change in reserve requirements effective this week depends
upon member bank deposits subject to reserve requirements
two weeks earlier, the Federal Reserve can accurately de­
termine the effect of a change in reserve requirements on
the reserve adjustment magnitude.
9This error-response mechanism assumes a quadratic loss
function for the money managers. The control periods’ base
values are determined by minimizing the expected value of
the loss function with respect to B. For a discussion of this
procedure see the Appendix at the end of this article.
10If only the growth rate of money mattered, then the money
managers would not attempt to make up last period’s
error in the level of money. Each period the money man­
gers would try to move along the desired growth path from
where they were last period.



G R O W T H RATE FOR M O N E Y
CONVERTED TO M ON TH LY
M O N E Y S T O C K LEVELS
M O N EY STOCK
-------- ^ 7 --------

E R R O R -R E S P O N S E
Com pute the difference
betw een the desired
level of m o ney and
actual m oney achieved
by the control process
in the p re v io u s month
M o n th ly ch an ge in b a se
e q u a ls am o un t necessary
to achieve current m o n th 's
d e sire d m o n e y sto ck level,
takin g into account the
error in last m onth’s
money stock level

C O N VERTED TO M O N T H LY
D A IL Y -A V E R A G E BASE LEVEL
BY FOR EC A ST IN G THE
M ON TH LY M O N EY M U LT IP LIER
<3>

B A SE TARGET EQUALS
A M O U N T OF B A SE
N ECESSA RY
TO ACH IEV E
DESIRED
M O N EY ST O C K LEVEL
O

NET SO U R C E BASE
CONVERTED TO O PEN M A R K E T
O PERA TIO N S B Y CO M PU T IN G
THE P R E V IO U S D A Y ’S BASE
A N D FORECASTING THE
U N C ON TRO LLED CO M PONENTS
OF THE BASE FOR EACH D A Y
O
O PEN M A R K E T O P ER A T IO N S

Simulation of Money Stock Control and GNP
How would the money stock control achieved by
this procedure affect the ability of the Federal Re­
serve to achieve policy objectives? To gain some in­
formation on this question, the money stock control
procedure was simulated over two sample periods,
Page 9

OCTOBER 1971

FED ER AL R ESE R V E BANK OF ST. LOUIS

and the effects of these simulation re­
sults on GNP were analyzed. First, the
method and results of simulating the
money stock control procedure are pre­
sented. Then, the method of relating
changes in money to GNP is discussed,
and the results of simulating GNP
when money is controlled without er­
ror are compared to the case where
money is controlled by our procedure.

Table II

Exam ple of M o n e y Stock Control
Desired
M o ne y

Actual
Multiplier

Con­
trolled
M o ne y
$ 2 0 0 .0

$8 0 .00

2.50

January

201

2.50

$.40

80.40

2.50

201.0

February

202

2.50

.40

80.80

2.50

202.0

March

203

2.51

.08

80.88

2.50

202.2

April

204

2.50

.72

9 1.6 0

2.50

204 .0

December

The following method was used to simulate money
stock control:
( 1 ) It was assumed that the policymakers choose
a constant 4 per cent seasonally adjusted annual
growth rate for money over the control
period.11
(2 ) The Federal Reserve adjusts the net
base in the current month to minimize
pected value of the squared deviation
achieved monthly stock level from the
4 per cent growth line.12

$200

the one that actually prevailed in that month,
the achieved level of money is different from
the desired.

Simulation of the Money Stock
Control Procedure

source
the ex­
of the
original

( 3 ) Two control periods were chosen, 1962 through
1965 and 1966 through 1969. The base periods
were chosen as fourth quarter 1961 and fourth
quarter 1965.
( 4 ) E ach month, the money stock achieved by the
control process (controlled money) is computed
by taking the level of the net source base de­
termined by our operating strategy and multi­
plying it by the value of the multiplier that
actually prevailed in that m onth.13 To the ex­
tent that the forecast multiplier is different from
n The desired growth rate of money was converted into
desired monthly levels in the following manner: (1 ) the
averages of money in IV/61 and IV/65 were taken as the
base period; (2 ) these base values were placed on Decem­
ber of 1961 and December 1965; (3 ) to compute the con­
version factor for a 4 per cent growth rate we divided .04
by 12 to yield .00333; and (4 ) each month’s desired
money stock level was equal to (base month) + (base
month) X (number of months out from base month) X
(.00333). For example, December 1966 desired level equals
(167.0999) + (167.0999) (1 2 ) (.00333) = $173.78 bil­
lion, where 167.0999 equals the average of the last three
months of 1965.
This procedure yields a simple 4 per cent growth rate
of money that appears as a straight line on an arithmetic
scale. When computing quarter-to-quarter growth rates of
money, however, the desired rate will be below 4 per cent
near the end of the period. The results of our procedure
would not have been altered if we had used a compounded
annual rate for money.
12This implies the Desk aims slightly below the desired
growth path. See the Appendix at the end of this article.

http://fraser.stlouisfed.org/
Page 10
Federal Reserve Bank of St. Louis

Control
Forecast C hange in
Actual
Multiplier
Base
Base level

The example in Table II, which may be used to
illustrate this procedure, should be taken only as an
illustration. For the technical aspects of the proce­
dure, especially die error-response mechanism, con­
sult the Appendix at the end of this article. The first
column in Table II gives the monthly money stock
levels consistent with the growth rate of money that
the policymakers are advised will give them their de­
sired policy objectives. The second column gives the
forecast of the multiplier and the fifth column gives
the money multiplier that actually prevailed in each
month. It is assumed that the control procedure be­
gins in January. For the first two months the Federal
Reserve forecasts the multiplier with complete ac­
curacy, the net source base is changed by $.4 billion,
and the money stock achieved by the control proce­
dure equals the desired.
In March, however, there is an error in the forecast
of the multiplier. The multiplier is forecast to be 2.51,
when it actually (the historical value) is 2.50. Conse­
quently, the net source base is increased by only $.08
billion. Based on a forecast of 2.51 for the multiplier,
the Federal Reserve expects that it would only have
to supply $.08 billion of base, compared to $.40 bil­
lion in the previous two months. The result is an error
in money stock control, controlled money is less than
desired ($202.2 billion compared with a desired level
of $203 billion). In April, the Federal Reserve again
forecasts the multiplier correctly. In this month the
net source base is increased enough to make up last
month’s money stock error, and to hit the target of
$204 billion.14
13This procedure assumes the independence of changes in
the net source base and the multiplier. If m and B are not
independent, then the actual multiplier might not be the
one that prevailed, given a different change in B. For a
discussion of this condition see Lionel Kalish, “A Study of
Money Stock Control,” Journal o f Finance (September
1970), pp. 761-776.
i^This example uses an absolute loss function. To minimize
the expected value of the squared deviations of money, the

FED ER A L RESERV E BANK OF ST. LOUIS

There are two prevalent views among economists
concerning the constancy of the desired rate of change
of the money stock.1-' One view is that the desired
rate of change should never be altered ( seasonally or
cyclically). An alternative view holds that the mone­
tary authorities have enough knowledge to alter the
monetary growth rate seasonally and cyclically so that
economic goals can be achieved better than if the
rate were held constant. This particular issue does not
affect our control procedure. The choice of a constant
4 per cent growth rate for money does not necessarily
imply that a 4 per cent rate was a desirable monetary
growth path for this period. Different desired rates of
change mean only that the monetary authorities aim
for different money stock levels, and combined with
the same forecasted multiplier, the only difference in
the operating strategy would be a different change
in the net source base.
Com parison of the sam ple periods —In order to
gain information about the stability and robustness of
the money stock control procedure, it was simulated
during two historical periods which were markedly
different with respect to the stability of the money
multiplier. A change in any of the ratios appearing
in the money multiplier ( see footnote 6) can alter the
value of the multiplier. These ratios are influenced by
a number of factors such as market interest rates, the
relationship between Regulation Q ceiling rates and
market rates, Treasury deposit decisions and chang­
ing patterns of tax payment dates, and introduction
of changes in reserve requirements such as lagged
requirements in September of 1968.
Therefore, in periods where there are sharp or er­
ratic changes in the factors influencing the multiplier,
one might expect the errors in predicting the multi­
plier to be larger than in periods where these factors
remain constant or follow a steady trend.10 The fol­
actual change in base would be slightly less than $.72
billion.
15See Milton Friedman, A Program For Monetary Stability
(New York: Fordham University Press, 1959), and Franco
Modigliani, “Some Empirical Tests of Monetary Manage­
ment and of Rules Versus Discretion,” Journal o f Political
Economy, June 1964, pp. 211-245.
1,:The three interest rate series, commercial paper rates, mar­
ket yields on Treasury bills, and long-term corporate bond
rates, all exhibited much greater variation in the 1966-69
period. Examination of the t, k, and r-ratios also reveals a
pattern of increased variability and sharp erratic move­
ments in these ratios in the latter period. Of special interest
is the behavior of the t-ratio (time deposits/demand de­
posits of money) in the two periods. In the 1962-65 period
the t-ratio follows a steady upward trend with only a
small amount of variation about the trend. In contrast, the
t-ratio during the 1966-69 period exhibits wide and erratic
fluctuations about its trend line. In the 1966-69 period the
contribution of the t-ratio to the month-to-month percentage
change in the historical money stock had a mean of —.57 per



OCTOBER 1971

lowing chart shows the variation of the money multi­
plier about its trend during both sample periods. Com­
paring the behavior of the historical money multi­
plier, it can be seen that it exhibited much greater
variability in the 1966-69 sample period than in the
1962-65 period.
Em pirical results —The results of simulating money
stock control over the two sample periods are illus­
trated in the following chart.17 Table III presents
several alternative ways of evaluating the results of
our control procedure. This table presents controlled
and desired levels, controlled and desired growth
rates, and includes the mean, variance, mean square,
and median of the errors.
Although the underlying conditions for money stock
control are quite different in the two sample periods,
the mean value of differences between controlled and
desired growth rates is approximately the same in
both periods. The mean value of deviations of con­
trolled and desired levels is somewhat larger in the
1966-69 period. However, relative to the levels in­
volved, the average percentage errors these devia­
tions represent is approximately the same for the
1966-69 period as for the 1962-65 period.
The major difference between the results of the
control procedure in the two periods is the occurrence
of somewhat more frequent large deviations in the
1966-69 period. One indication of this difference is
that the mean squared error for differences in the
levels for the latter sample period is $.62 billion, com­
pared to $.36 billion in the earlier period. Also, the
average for the five largest percentage errors in the
levels is 0.68 per cent in the latter period, compared
to 0.58 per cent in the earlier period.

Projections of GNP
Policymakers are primarily concerned with attain­
ing ultimate policy objectives, not just with controlling
the growth of money. Controlling money is a means
to an end, not the end in itself. In this section, the
growth of GNP implied by a constant 4 per cent
growth rate of money is chosen as the policy objec­
tive. This policy objective path for GNP (desired
GNP) is then compared to the growth of GNP atcent and a variance of 4.48, compared to a mean of —2.29
per cent and a variance of .76 in the 1962-65 period. There
are pronounced changes in the pattern of the t-ratio in the
last half of 1966, in 1968, and during 1969. These changes
reflect primarily the constraint of Regulation Q, which was
an additional factor influencing the money supply process
in the latter period.
17Charts plotting monthly values of controlled money are
given in Working Paper No. 14.
Page 11

FED ERAL R ESE R V E BANK OF ST. LOUIS

tained with controlled money. The following proce­
dure was used:
(1) A model linking changes in the money stock to
changes in nominal GNP was chosen. The
model used was the Andersen-Jordan (A-J)
spending equation which relates changes in
GNP to current and lagged changes in the
money stock and high employment government
expenditures.18
18Leonall C. Andersen and Jerry L. Jordan, “Monetary and
Fiscal Actions: A Test or Their Relative Importance in
Economic Stabilization,” this Review (November 1968),
pp. 11-24.

Page 12


O CTOBER 1971

(2) Actual high-employment government expendi­
tures were used in both simulations. This pro­
cedure assumes that forecast high-employment
government expenditures are always equal to
the actual.
(3) The A-J equation was used to project quarterly
GNP with a constant 4 per cent growth of
money. This projected GNP path is the policy
objective. Then, the A-J equation was used to
project GNP for the same period, with the
growth pattern of money as generated by our
control procedure when aiming at a constant 4
per cent money stock growth. This is the GNP

FED ERA L R ESER V E BANK OF ST. LOUIS

Table III

OCTOBER 1971

Controlled C o m p are d to Desired Q uarterly
A v e ra g e s of the M o n e y Stock1
(Billions of Dollars)

1 9 6 2 -1 9 6 5

Controlled
Level

Desired
Level

Difference Between
Controlled and Desired
Levels

1962 1
II
III
IV

$146.1 1
147.12
148.22
150.94

$ 1 4 6 .5 7
148.03
149.48
150.94

$ - .46
— .91
-1 .2 6
0

196 3 1
II
III
IV

151.65
153.99
155.63
155.90

152.40
153.85
155.31
156.76

1964 1
II
III
IV

157.50
159.02
161.54
162.06

158.22
159.68
161.13
162.59

—
—

1965 1
II
III
IV

163.68
165 .37
167.24
168.61

164.04
165.50
166.95
168.41

-

Quarter

M e an value of deviations: Absolute
W ith Sign
Variance of deviations:

Absolute
W ith Sign

M ean squared deviations:

—

—

—

Per Cent Error
Between
Controlled and Desired
Levels
—
—

.3 %
.6

— .8
0

.75
.14
.32
.86

—

—

.72
.66
.41
.53

—
—

.36
.13
.29
.20

—
—

—

.50
-.3 3

Difference in
Annual
Q uarter-to-Quarter
Growth Rates
(Controlled M inus Desired)
— 1 .3 %
— 1.2
-0 .9
3.4

.5
.1
.2
.5

— 2.0
2.4
0.5
-3 .0

.5
.4
.3
.3

0.4
0.2
2.7
— 2.3

.2
.1
.2
.1

0.4
0.5
1.0
-0 .2

M ean of Per Cent Error
(Absolute)
.32

.1 1
.25

M ean of Difference
in Growth Rates
.04

Per Cent Error
Between
Controlled and Desired
Levels

Difference in
A nnual
Quarter-to-Quarter
Growth Rates
(Controlled M inus Desired)

.36

1 9 6 6 -1 9 6 9

Controlled
Level

Desired
Level

1966 1
II
III
IV

$168.71
170.28
173 .06
174.22

$168.21
169.89
171.56
173.23

1967 1
II
III
IV
1968 1
II
III
IV

174.82
177.13
177.73
178 .96

Difference Between
Controlled and Desired
Levels

174.90
176 .57
178 .24
179.91
181.58
183.25
184.92
18 6 .6 0

Quarter

1969 1
II
III
IV

181 .56
185.14
185.13
187.26
188.54
189 .24
192.08
193 .37

$

188 .27
189.94
191.61
193.28

M e an value of deviations: Absolute
W ith Sign

—

.08
.56
— .51
— .95
— .02
1.89
.21
.66
—

.61
.33

Variance of deviations:

.50
.39
1.50
.99

.25
.51

Absolute
W ith Sign

.27
.70
.47
.09

.3 %
.2
.9
.6

1 .2 %
-0 .3
2.6
— 1.2

.0
.3
— .3
— .5
.0
1.0
.1
.4

— 2.5
1.5
-2 .4
— 0.9
2.1
4.2
-3 .6
1.0

.1
.4
.2
.0

-0 .9
— 2.0
2.5
— 0.8

—

M ean of Per Cent Error
(Absolute)
.33

M ean of Difference
in Growth Rates
.03

M ean squared deviations:
.62
Q u a r te r ly av erag e s o f controlled m oney w ere com puted by a v e ra g in g m o n th ly values achieved by the m oney stock control procedure. M onthly,
controlled m oney stock d a ta is given in W o rk in g P a p e r No. 14.

that would have actually resulted from policy
actions.11
1

Several important points about this procedure
should be emphasized. It is assumed that the GNP
19The desired quarterly growth rate of money was computed
from the desired quarterly average money stock levels re­
ported in Table III.



that would have resulted from a constant 4 per cent
growth rate of money and from controlled money
would have been the GNP projected by the equation
relating changes in money to changes in GNP. There­
fore, the only source of error between the policy ob­
jective GNP and the GNP resulting from money stock
control is the error in money stock control.
Page 13

FED ERA L R ESER V E BANK OF ST. LOUIS

Controlled and Desired M oney Stock a

O CTOBER 1971

employment and prices and then convert these into a
desired growth rate of nominal GNP. An analysis of
what a given growth of GNP implies for prices and
employment could be carried out by using a larger
model.
Em pirical results —The results of the GNP simula­
tions are presented in Table IV and the following
chart. The monetary policymakers are assumed to
have chosen objectives for GNP, and then, based on
the information they have about the relationship be­
tween money and GNP, they have decided that a 4
per cent monetary growth rate will best achieve
these GNP objectives. The second column of Table IV
contains the growth path of GNP the policymakers
desire to achieve ( quarterly averages of nominal GNP
projected by the A-J equation when a constant 4 per
cent growth rate of money is assumed). The first
column of this table shows the quarterly averages of
nominal GNP projected by the A-J equation when
the money stock resulting from our operating proce­
dure for those years is read into the A-J equation.

□ .T h e d e s ir e d g r o w t h p a t h fo r m o n e y is a s s u m e d to b e a c o n st a n t 4 p e r cent
s e a s o n a l ly a d ju s t e d g r o w t h rate. Q u a r t e r l y d a t a fo r c o n t ro lle d m o n e y a r e
c o m p u t e d b y a v e r a g i n g m o n t h ly v a lu e s of m o n e y re su lt in g fro m the m o n e y
st o c k co n tro l p r o c e d u r e .

Second, instead of the A-J equation, any other econ­
ometric model that relates changes in money to
changes in nominal GNP could have been used. Other
economists might work out the implications of this and
other money control procedures for the ability of pol­
icymakers to hit a desired value of GNP, using al­
ternative forecasting and structural models of the econ­
omy. Such results would provide valuable supple­
mental evidence on the adequacy of proposed money
stock control procedures.
A third point is that only the influence of money
stock control on nominal GNP was considered. The
ultimate objectives of monetary policy are variables
such as employment and prices. However, this article
is not concerned with the influence of different GNP
growth rates on employment and prices. It is as­
sumed that the policymakers pick desired values for

Page 14


At an operational level, the Trading Desk is di­
rected to follow an open market policy to achieve the
4 per cent growth rate of money. To carry out its
“directive,” the Trading Desk forecasts the money
multiplier by our procedure, and then supplies the
amount of net source base each month that is required
to achieve the level of the money stock consistent
with the 4 per cent growth of money. Since there are
deviations between the quarter-to-quarter growth rate
of money achieved by the control procedure and the
desired 4 per cent rate, there are deviations of
achieved GNP from the policy objective.
Under the simulation exercise, the success of the
policymakers in achieving their desired GNP objec­
tives on average is approximately the same in both
sample periods. The largest percentage error in the
levels is seven-tenths of one per cent, and in both
periods 10 of the 16 quarterly misses are three-tenths
of one per cent or less. The mean difference between
money stock control and policy objective (desired)
quarter-to-quarter growth rates of GNP is .01 per cent
in the 1962-65 period and .02 per cent in the 1966-69
period.
The simulations indicate that the Federal Reserve
would have been about equally successful in achiev­
ing its GNP objectives in both periods. This result
follows from two conditions. First, although there are
more frequent large deviations in the achieved money
stock in the 1966-69 period, they are not maintained
for a long period. On average the degree of control is
about the same in both sample periods; deviations

FEDERAL RESERV E BANK OF ST. LOUIS

OCTOBER 1971

GN P Projections: Policy Objective GNP Compared With M oney Stock Control G N P 1
C o m p a riso n of N o m in al G N P Levels
B il l i o n s o f D o l l a r s

B il l i o n s o f D o l l a r s

B illions o f D o l l a r s

B illions of D o ll a rs

680

660

640

620

600

580

560

C o m p a riso n of Q uarter to Q uarter A n n u a l Rates of C h a n ge of GNP
Per C en t

Per C e n t

Per C e n t

Per C e n t

12

12

10

10

L]_The A n d e r s e n - J o r d a n (A-J) s p e n d i n g e q u a t io n w a s u s e d to p ro je c t q u a r t e r ly G N P w ith a c o n st a n t 4 p e r c e n t g r o w t h o f m o n e y . T h is p ro je c t e d G N P p a th is the p o lic y
o b je ctiv e . Th e n , the A -J e q u a t io n w a s u s e d to pro je ct G N P , w ith the g ro w t h p attern o f m o n e y g e n e r a t e d b y the m o n e y sto c k c o n tro l p r o c e d u r e w h e n a im in g a t a
c o n st a n t 4 p e r cent m o n e y st o c k g ro w th . A c t u a l h i g h - e m p lo y m e n t g o v e r n m e n t e x p e n d it u r e s w e re u s e d in b o th s im u la tio n s , a s s u m i n g th a t p roje cted
h ig h - e m p lo y m e n t e x p e n d it u r e s a r e a l w a y s e q u a l to the ac tu al.
F o r a d is c u s s io n o f the A -J e q u a tio n , se e L e o n a ll C . A n d e r s e n a n d J e rry L. J o r d a n , " M o n e t a r y a n d F isc a l A c tio n s : A Test of T h e ir R e la t iv e Im p o rt a n c e in E c o n o m ic
S t a b iliz a t io n , " F e d e r a l R e s e r v e B a n k o f St. L o u is R e v ie w { N o v e m b e r 1968), p p. 11-24.

above the desired growth path are followed by devia­
tions below the growth path. Second, in the GNP
equation, the influence of changes in the growth rate
of money are distributed over time. The whole impact
of a change in money on GNP does not occur in the
same quarter. The influence of money on income in­
cludes the growth of money over the preceding four
quarters.



Assessing the Effect of Money Stock
Control on Policy Objectives
In the previous section, the growth path of GNP
projected assuming no errors in money stock control
was compared to GNP projected with money stock
control using our control procedure. The comparisons
were made for two sample periods. However, even
Page 15

FED ER AL R ESE R V E BANK OF ST. LOUIS

O CTOBER 1971

Table IV

N om inal G N P Levels and C o m po un ded Annual Rates o f C h a n g e
G enerated by the Andersen-Jordan Equation
(Billions of Dollars)

1 96 2 -1 96 5

Difference Between
Controlled and Desired
Levels

Per Cent Error
Between
Controlled and Desired
Levels

Difference in
A nnual
Quarter-to-Quarter
Growth Rates
(Controlled M inu s Desired)^

Quarter

Controlled
Level

Desired
Level1

1962 1
II
III
IV

$ 5 4 4 .5 4
5 5 3 .5 4
5 6 0 .8 9
5 6 8 .7 4

$ 5 4 5 .2 0
5 5 5 .6 0
56 4 .7 8
57 2 .3 3

$ — .66

1963 1
II
III
IV

5 7 5 .8 6
5 8 5 .9 2
5 9 6 .7 4
60 4 .8 5

5 7 9 .3 7
588.21
5 9 7 .4 2
6 0 5 .95

— 3.51
— 2.29
— .68

— 1.10

—

.2

—

.3

1964 1
II
III
IV

615.61
6 2 8 .44
6 3 8 .3 7
64 6 .2 3

6 1 7 .7 9
63 1 .38
6 4 0 .35
647 .98

-2 .1 8
-2 .9 4
— 1.98
— 1.75

—
—
—

.4
.5
.3
.3

—

.7
.5
.7
.2

1965 1
II
III
IV

6 5 3 .9 7
6 6 5 .0 6
6 8 0 .3 0
6 9 5 .9 9

6 5 5 .5 7
66 6 .44
6 8 0 .85
6 9 5 .8 7

— 1.60
— 1.38
— .55

—
—

.2
.2

M ean value of deviations: Absolute
W ith Sign
Variance of deviations:

Absolute
W ith Sign

M e a n squared deviations:

-2 .0 6
— 3.89
— 3.59

—
—
—
—

. 1%
.4
.7
.6

—
—

.6
.4

.1

— .1

1.2

.5 %

— 1.1
— 1.4
.3
.9

.1
.2
.5
.4

— .1

.12

1.89
— 1.88

-

.0
M e an of Per Cent Error
(Absolute)
.32

1.24
1.29

M e an of Difference
in Growth Rates
.01

Per Cent Error
Between
Controlled and Desired
Levels

Difference in
Annual
Quarter-to-Quarter
Growth Rates
(Controlled M inus D e sire d )-

4.82

1 9 6 6 -1 96 9

Difference Between
Controlled and Desired
Levels

Controlled
Level

Desired
Level1

1 96 6 1
II
III
IV

$ 7 2 8 .1 3
7 4 4 .0 3
7 6 0 .7 9
7 7 7 .4 3

$ 7 2 7 .4 7
742 .58
7 5 7 .2 4
7 7 2 .19

1 96 7 1
II

79 1 .13
80 2 .19
80 8 .86
8 1 6 .4 7

7 8 6 .43
7 9 8 .4 7
8 0 7 .44
8 1 7 .6 7

4.70
3.72
1.42
— 1.20

II
III
IV

827 .63
8 4 6 .6 7
8 6 2 .9 7
8 7 5 .86

829 .78
8 4 6 .2 0
860.21
8 7 1 .6 6

— 2.15
.47
2.76
4.20

1 96 9 1
II
III
IV

883 .42
888 .92
8 9 9 .46
9 1 3 .0 4

879.71
8 8 7 .7 2
899 .03
9 1 2 .83

3.71
1.20
.43
.21

Quarter

11
1
IV
1968

1

M ean value of deviations: Absolute
W ith Sign

2.32
1.90

Variance of deviations:

2.60
4 .3 7

M e an squared deviations:

Absolute
W ith Sign

7.97

1A ssu m in g a sim ple 4 p e r c e n t g ro w th ra te fo r m oney.
2C om pounded a n n u a l ra te s.


Page 16


$

. 1%
.2
.5
.7

.66
1.45
3.55
5.24

.6
.5
.2

.4 %
.5
1.2
.9

— .1

— .3
— .6
— 1.2
— 1.3

—

—

.3

.1
.3
.5
.4

.1
.0
.0
M e an of Per Cent Error
(Absolute)
.29

.5
1.4
1.1
.7

— .3
— 1.2
— .4
— .1
M ean of Difference
in Growth Rates
.02

FED ER AL R ESER V E BANK OF ST. LOUIS

O CTOBER 1971

though the control procedure worked reasonably well
during the sample periods, it will not necessarily do
as well in some time interval outside the sample
periods.-"
In an actual policy application, the procedure
would be used outside the sample period. Therefore,
policymakers must have some means of assessing
what a suggested control procedure implies for their
ability to achieve policy objectives in a forecasting
situation. This criterion can be a comparison of the
ability to attain policy objectives when there are no
errors in the control procedure, with the case where
there are errors in the control procedure. In this ar­
ticle GNP was chosen as the policy objective, and
policy was implemented using a money stock control
procedure. Therefore, the basis for judging the control
procedure is the amount by which the errors in money
stock control a d d to errors in forecasting the GNP
that would result from a desired growth rate of money.
In this section, representative GNP prediction con­
fidence intervals are presented. In arriving at these
confidence intervals, allowance is made for the relia­
bility of the sample estimates of the model’s para­
meters and the multiplier forecasts. A modified stand­
ard error of forecast statistic is used to specify con­
fidence intervals for GNP projections when money is
controlled. These confidence intervals are then com­
pared with confidence intervals for GNP projections
when there are no errors in money stock control.21

GNP being within ±$8.64 billion of the projected
level. On average, over the four quarters in 1970,
money stock control would have reduced the proba­
bility of the actual value of GNP falling within the
given confidence interval from 95 per cent to 93.3
per cent. These results indicate that, for 95 per cent
confidence intervals, the errors in money stock con­
trol implied by our control procedure would have
had only a very small effect on the policymaker’s
ability to forecast GNP.

Conclusions
The implementation procedure for monetary policy
developed in this article provides the basis for a welldefined operational procedure for controlling money.
The money stock control procedure does not require
the use of any information which the Federal Reserve
does not already have available. In fact, it greatly
simplifies the operating instructions which would be
issued to the Trading Desk. The FOMC would issue
a directive to the Trading Desk stated in terms of a
growth rate for money. The Desk would convert this
growth rate of money into a monthly daily-average
net source base figure by using the procedure de­
veloped in this article to forecast the monthly money
multiplier. During each month, the Desk would use
open market operations to set the net source base at
the level consistent with the growth rate of money
stated in the directive. The Desk would not have to
interpret the “consensus of the members of the
FOMC.” Each month the Desk would have a precise
monthly daily-average net source base figure to attain.

Table V presents 95 per cent confidence intervals
for GNP projections, assuming no errors in money
stock control for the four quarters of 1970. The final
column in Table V presents the probability of the
Using a simulation technique, this article presented
actual value of GNP falling within these same con­
evidence on the effect this money stock control profidence intervals, given that our control procedure
is used to control money. For example,
there would have been a 95 per cent
Table V
probability of actual GNP being within
Quarter to Q uarter G N P Projections for 19 7 0 1
±$8.64 billion of the projected level in
Probability of Actual Value
11/1970, assuming there was no possi­
Falling W ithin Confidence Interval
bility of errors in money stock control.
Confidence Interval
Error in
about the
N o Error in
If money had been controlled by our
M o n e y Stock Control2
Projected Level
M o n e y Stock Control
procedure, there would have been a
(Billions of Dollars)
93-94 per cent probability of actual
1/1970

20This result can occur because the point
estimates of the parameters of the model
differ from their unobservable population
values.
21The deviation of the SE F statistic and the
technical aspects of specifying these confi­
dence intervals are discussed in the Ap­
pendix at the end of this article, and in
the technical appendices available in Work­
ing Paper No. 14.



±

$ 8 ,1 2 0

95%

(8 9 .5 -9 4 .3 )%

11/1970

±

$8,641

95

(9 3 .3 -9 4 .4 )

111/1970

± $8,2 2 8

95

(9 3 .3 -9 4 .3 )

IV / 1 9 7 0

± $ 8 ,3 4 7

95

(9 3 .3 -9 4 .4 )

1A n d e rse n -Jo rd a n equation
(a ) sam p le p erio d 1/1953 to IV /1969.
(b) A lm on specification: both la g d istrib u tio n s em ploy 4th degree polynom ial w ith lags
t - f l an d t —5 co n strain ed to equal zero.
2T he first n u m b e r in each p a ir is associated w ith a q u a rte rly m u ltip lier e quation and
th e second w ith a m on th ly m u ltip lie r e quation. F o r a fu r th e r discussion see p ag e 21.

Page 17

FED ERAL R ESER V E BANK OF ST. LOUIS

cedure would have had on the ability of policymakers
to achieve GNP objectives. In both of the four-year
sample periods the largest percentage error in GNP
levels was less than one per cent, and in each period
10 of the 16 quarterly GNP errors were three-tenths
of one per cent or less. To assess the effect of money
stock control, moving outside the sample periods, the
standard error of forecast statistic was developed to
permit the construction of appropriate confidence in­
tervals for GNP projections. For the four quarters of
1970, the money stock control procedure only reduced
the probability associated with the 95 per cent con­
fidence interval to 93.3 per cent.
The final judgement on airy monetary policy pro­
cedure ultimately rests with the members of the Fed­
eral Open Market Committee. As an ideal situation
the FOMC would want no errors in achieving their
policy objectives. However, this ideal cannot be real­
ized. Therefore, the policymakers must have some
means of comparing the effects of different control
procedures on their ability to achieve their policy ob­
jectives. This article presented some information on
these matters for a money stock control procedure.
The Federal Reserve in operating such a money
stock control procedure would have additional infor­
mation that could be used to more closely monitor its
control process. The multiplier-base framework used
in this article is taken from a fully developed specifi­
cation of the money supply process, within which the
influence of changing economic conditions on the
money supply process may be analyzed. Also, a per­
centage change in the money stock may be decom­
posed into the percentage changes due to the net
source base and the multiplier. The percentage
change in the multiplier may then be broken down
into the percentage change due to each of its com­
ponents. For example, at times when large inflows
and outflows of time deposits are induced by changes
in market rates relative to Regulation Q ceilings, this
factor may exert an important influence on the
money multiplier. Using this additional information,
the Federal Reserve should be able to improve its
control of the money stock.22
When a money stock control procedure is suggested,
a question that is frequently raised is “What does such
22Also, this procedure does not imply that the value of the
multiplier forecast for the coming month at the end of this
month should be the one used throughout the month. Each
week of the month, as new data on the money stock in the
preceding period becomes available, a new forecast of the
monthly multiplier could be prepared. Based on this addi­
tional information, the net source base target for the month
might be altered.

Page 18


OCTOBER 1971

a procedure imply for the stability of the money
market?” The Federal funds rate is commonly used
as a summary measure of short-run (daily or weekly)
conditions in the money market. If, as implied in our
simulations, the Desk had exactly achieved its tar­
geted net source base level each month, would there
have been significantly greater fluctuations in the
Federal funds rate? The answer to this question re­
quired the use of a tested, very short-term, money
market model that relates daily or weekly fluctua­
tions in the Federal funds rate to changes in the net
source base. Unfortunately, such a model is not avail­
able. Using quarterly models, some evidence can be
gained on the quarterly average results of money
stock control on interest rates. However, these results
are not satisfactory to individuals interested in daily
or weekly fluctuations.
The money stock control procedure in this article
does not necessarily require that the Desk hit the
targeted level for the net source base each day or
week of the month. The Desk is to attain a dailyaverage monthly net source base target. Therefore, as
a practical operating strategy, the Desk would have
some latitude to offset short-term shocks to the money
market within each month. However, the Desk would
have to give primary consideration to achieving the
net source base target. The Desk would have to guard
against allowing one short-term special situation to be
followed by another, resulting in a deviation of the
target base level from the one necessary to achieve
the desired monetary growth path.
One tentative piece of evidence related to the
problem of aggregate control versus money market
stability has been presented by Richard Davis.23
Davis analyzed the effect that control of nonborrowed
reserves would have had on short-term money market
rates for a sample period in 1967. He concluded that
Having said that certain features of the experiment
tend to overstate the degree of potential money m ar­
ket instability, however, the writer is inclined to the
view that the degree of instability indicated is never­
theless rather surprisingly mild. T h e computed aver­
age absolute weekly change in the Federal funds
rate tends to be only around 5 0 basis points, cer­
tainly substantially larger than the average changes
23Davis’ method consisted of computing the weekly levels
of free reserves that would have resulted during an historical
time period if the System had provided a constant weekby-week growth in nonborrowed reserves during that pe­
riod, given the historical pattern of actual changes in re­
quired reserves. An equation relating the Federal funds
rate to free reserves and the discount rate is then used to
estimate what the funds rate would have been had the
System followed the quantity target. The computed funds
rate was then compared to the actual rate for the period.

FED ER AL R ESER V E BANK OF ST. LOUIS

OCTOBER 1971

that actually occurred (around 17 basis points), but
not more than the market would seem able to
handle without undue stress.24
It is important to the well-being of the whole econ­
omy that monetary policy be implemented using
the procedure that offers the highest probability of
policymakers achieving their policy objectives. Other
economists have proposed alternative strategies for
implementing policy. However, a useful comparison
of our procedure with these alternative procedures
24Davis, p. 61.

can only take place when these alternatives are ex­
plicitly formulated and the effects on GNP of using
these procedures is illustrated. Criticism of this
money stock control procedure is welcomed. Propo­
nents of other policy procedures are challenged to
explicitly formulate their proposals so the effects of
these procedures on attaining policy objectives can
be analyzed. In this manner monetary policy can be
implemented and improved on the basis of empirical
evidence, rather than implemented on the basis of
conjecture, personal belief, and tradition.

APPENDIX
In this appendix the technical aspects of the forecast­
ing equation for the money multiplier, the error response
mechanism, and the development of the standard error
of forecast statistic are presented.

Forecasting Equation for the
Money Multiplier

as a seasonal dummy variable. The influence of the d, is
to shift the intercept from period to period.
(3) The reserve adjustment magnitude is introduced
to capture the effects of reserve requirement changes.
Reserve adjustments are expressed in dollar amounts
which are positive when average reserve requirements
fall and are negative when reserve requirements rise.27

Xi

= three month moving average of past
value of the multiplier,

(4) The regression equation’s Durbin-Watson (D-W)
statistic indicates the existence of significant autocorrela­
tion in the equation’s errors. With this condition it is
possible to get improved estimates of the money multi­
plier over time by including an additional variable in the
prediction equation. This variable which “allows” for the
autocorrelation is the lagged value of the error (Ht-i)
in the estimate of the money multiplier times the correla­
tion coefficient Rho (p) for consecutive-error terms in the
equation during the sample period.28

Xa

= reserve adjustment magnitude in the
forecast month,

One means of judging the forecasting ability of the
multiplier equation is to compare the root mean square

di

= dummy variables to account for seasonal
factors,20

Each month’s multiplier is forecast using the following
equation:25
nit =

bo +

b iX it +

b ^ X 2t +

2

bj_j_2di +

PHt—i

i= l

where: ( 1 )

27Shifts of deposits between banks with different legal re­
serve requirements and between different deposit categories
( demand to tim e) also exert a slight influence on the
month-to-month changes in the reserve magnitude. The
variance of the monthly first differences of the reserve ad­
justment magnitude during 1963-69 was six times greater
(-it— = lagged value of the error in the estimate
i
of the money multiplier.
when all months were included, than when months in which
reserve requirement changes took place ( and adjacent
months) were excluded. For the 1962-69 period, except for
(2)
The coefficients bi are estimated by least squares
months where reserve requirements were changed, the Fed­
using the previous 36 months’ observations. Each month
eral Reserve could have assumed the forecast month’s re­
serve adjustment magnitude would be the same as the cur­
the coefficients are re-estimated by adding the most re­
rent month’s value without an appreciable error over the
cent month and dropping the first month of the previous
period.
p

= the correlation coefficient for consecutive
error terms in the equation during the
sample period,

36 observations. b0 is an intercept term which also acts

25Parameter estimates of the monthly forecasting equations
are included in the technical appendices in Working
Paper No. 14.
26Similar results were obtained by omitting the seasonal
dummy variables and instead adjusting not seasonally ad­
justed money by the seasonal factors used by the Federal
Reserve.



For an explanation of the method by which the reserve
adjustment magnitude is computed, see Leonall C. Ander­
sen and Jerry L. Jordan “The Monetary Base — Explana­
tion and Analytical Use,” this Review, August 1968, p. 8.
28This technique assumed first order autocorrelation. Rho is
estimated as

1-

DW
2
Page 19

OCTOBER 1971

F ED ERA L R ESE R V E BANK OF ST. LOUIS

error (R M S E ) of the forecasting procedure with the
R M S E of a no change extrapolation. T h e R M S E of
monthly predictions of the money multiplier in the 196265 period was .0151, which was 5 3 per cent as large as
the R M SE for a no change extrapolation. In the 1966-69
period the R M SE was .0200, which was 64 per cent as
large as the R M SE for a no change extrapolation.

then it is necessary to modify the standard error of fore­
cast statistic associated with the forecasting equation.
T he im portance of errors in money stock control can
then be assessed by comparing the S E F of the GNP
forecasting equation when there are no errors in money
stock control with the standard error of forecast statistic
( S E F ° ) of GN P estimates when there are errors in
money stock control.

Error-Response Mechanism

One statistic frequently used by economists to assess
the forecasting ability of an econom ic model is the stand­
ard error of estimate ( S E E ) . However, a more appro­
priate measure of the forecasting ability of a model is
the correctly specified standard error of forecast ( S E F )
statistic.29 T he value of the S E F statistic depends upon
the values assumed by the independent variables during
the forecast period, and upon the variances and covari­
ances of the parameters of the forecasting equation, as
well as upon the S E E statistic.

O nce there is a possibility of error in money stock
control, specification of an optimal operating strategy for
changing the net source base requires that the money
managers’ loss function b e specified. There are many
possible loss functions, each one representing somewhat
different preferences by the policymakers. In our pro­
cedure a quadratic loss function of the following form is
specified:
L = (M — Md)2

money manager’s
loss function

M = mtB, actual money
where: mt = money multiplier in period t
B = net source base
Md = desired money stock in period t.
In the above expression the product of the money
multiplier (m ) and the net source base ( B ) gives the
level of money achieved in period t by our operating
procedure. M d is the level of money consistent with a
given desired growth rate of money. This type of loss
function assigns proportionally more weight to large de­
viations of controlled money from desired than to smaller
deviations.
O nce the money manager’s loss function has been
specified, the optimal strategy w ith respect to the net
source base is the one that minimizes the expected
value of the loss function. T h e expected value (w here E
is used to denote an expected value) for this loss func­
tion may be written:
E (L ) = B2 var (mt ) + [Md - B E (m ,)]2
Minimizing with respect to B , gives the following ex­
pression for the optimal net source base ( B ° ):
Md
DO

E v ------ \

f --------- ----- j---- rl
I,

I

B = E<
mi) I 1 +

var

(m w l

[EOM p I

T o calculate the value for B ° in any period t, ( 1 ) we
used M d in period t, which is determined by the desired
growth rate; ( 2 ) we used E ( m t ) = predicted multiplier
in period t; and ( 3 ) var (m t ) was approximated by
taking the sum of squared residuals for the multiplier
equation and dividing by 3 6 - K - 1, where K equals 14,
the number of independent variables in the forecasting
equation for the multiplier.

Confidence Intervals for GNP
Projections with Money Stock Control
If a forecasting equation is used in which the money
stock is assumed to be controlled by some procedure,

Page 20


In this section, the S E F statistic which is appropriate
for our policy procedure is presented and a comparison
of it with the S E F which is associated w ith the A-J
equation when money is assumed to be perfectly con­
trolled is presented.30
T h e equation used in this article to project G N P spe­
cifies the quarterly change in GN P as dependent upon
current and lagged values of changes in money arid
government expenditures. T o simplify the exposition,
and to focus on the effect of errors in money stock con­
trol, the change in government expenditures is assumed
to b e predicted without error. Therefore, errors are
postulated to exist only in the GN P forecasting equation
and in the control of money. T h e predicted change in
money ( AM?-) n) in the forecast period and the actual
change in money (AM, n) are related in the following
manner:
A M t-fn =

A M t+ n

+

6 t+ n

where 0t+n is an error term.
W ith errors in the money stock control procedure, an
S E F which assumes perfect money stock control is no
longer appropriate. This S E F statistic could be too large
or too small.31 In other words, policymakers should not
use this statistic to construct the confidence interval for
their GN P forecasts. T h e probability of over-or underes­
tim ating GN P could be greater or smaller than that in­
dicated by this S E F statistic.
29For a discussion of this subject, see Carl Christ, E cono­
metric M ethods and Models, John Wiley Co., 1968, pp.
549-564.
30The derivation of the SE F statistic is presented in the
technical appendices available as Working Paper No. 14.
31For example, if the forecasting equation for the money
multiplier results in an overestimate of the money multi­
plier (which results in the actual money stock being less
than the desired), and if, in addition, the A-J equation
overestimates the effect of a change in the money stock on
GNP, then the influences of the two errors (negative cor­
relation) tend to offset one another. However, when the
errors in predicting the money stock and forecasting GNP
are in the same direction (positive correlation), then the
errors reinforce one another, and the error in GNP forecasts
is increased.

OCTOBER 1971

FED ER A L R ESER V E BANK OF ST. LOUIS

The standard error of forecast statistic ( S E F ° ) for the
A-J equation, assuming errors in money stock control, is
given by:

Table VI

S ta n d a rd Errors o f Forecast
For the G N P Equation for 1 9 7 0 1

SE F ° = [( S E F )2 + PI var ( 0 t + n ) +
2 |3l COV ( 0 t + n ,

E t + n ) ] 1/2

where: S E F denotes the standard error of forecast sta­
tistic when there are no errors in money stock control,
and [3, is the coefficient for contemporaneous changes in
the money stock in the GNP equation.
Exam ining the expression for S E F ° , it can be seen
that the existence of errors in money stock control in­
troduces two extra terms in the standard error of fore­
cast statistic, involving the error in the money stock con­
trol procedure (0tH n) and the error in the G N P equa­
tion ( e t + n ) . Term s with the variance ( 0 i : n ) and the
covariance ( 0 t + n , £ t + n ) are introduced. Since in general
these terms are not equal to zero, S E F ° is unequal to
S E F . As remarked earlier, the cov ( 0 t + n , £ t + n ) may be
either positive or negative. If it is positive, then this
factor would increase the S E F 0; if negative, it might be
large enough to make S E F “ less than S E F .32
Standard error of forecast statistics are dependent
upon the particular values of the independent variables
which apply to the prediction period. In particular, an
S E F statistic assumes its absolute minimum value when
the respective independent variables which enter into it
take on values that equal their sample means. All other
sets of values of the independent variables will generate
larger values of the S E F statistic. T he reason for this
result resides in the statistical uncertainty surrounding
the regression estimates of the coefficients in the fore­
casting equation.
For the period 1/1953 -11/ 1969, the minimum S E F of
the GN P equation is $3.87 billion. As an illustration of
how the S E F statistic actually differs in practice from its
minimum value, let us consider the hypothetical problem
of predicting GNP for each of the four quarters of 1970.
Under conditions of perfect money stock control, the
S E F statistic would assume the values given in row A
of T ab le V I which are from approximately 7 to 14 per
cent larger (row B ) than the minimum value of the
S E F statistic.
For the money stock control procedure, the S E F " sta­
tistics are given in rows C and F of Table V I. T he S E F °
statistics in row C correspond to the quarterly average
performance of the monthly money stock control proce­
dure in the simulations with the GNP equation. The
SEF® statistics in row F correspond to a quarterly money
stock control procedure, and are rigorous “outer bounds”
to the S E F ° statistics given in row C .33
32For any given quarter, it is possible for the S E F 8 statistic
to be smaller than the traditional S E F statistic if certain
conditions are met. Let p be the correlation between the
error in money stock control (0 t) and the error in predict­
ing GNP (£t). The following can be shown to hold.
If

<

Pi [var 9t ]i/2 holds,
var £t

then S E F * < SEF.
33The simulation value of v a r(0 t), or simulation var(0t), is



(Dollar Am ounts in Billions)
1/1970
SEF with no error in
money stock control

11/1970 111/1970 IV / 1 9 7 0

4.259

A

$ 4 ,143

4.409

4.198

B

7 .1 %

13 . 9 9 %

8.5 %

C

$ 4 ,2 6 7

4.5 2 6

4.3 2 0

4.379

Percentage increase
of C over A

D

3.0 %

2.7 %

2 .9 %

2 .8 %

Ratio of B to D

E

2.4

5.2

2.9

3.6

F

$ 4 ,9 8 6

4.7 1 4

4.503

4 .5 5 0

Percentage increase
of F over A

G

20 .3 %

6.9 %

7.3 %

6 .8 %

Ratio of B to G

H

.35

2.02

1.2

1.5

Percent increase of A
over minimum SEF of
$3,868.

1 0 .1 %

SEF* with error in money
stock control:
simu. var. ( 0 t ) and
simu. cov. (0t,£t)

SEF* with error in money
stock control:
equa. var. (0t) and
simu. cov. (0t,£t)

where:
1)

variance (E t ) —

2)

simulation variance (0 t) — 0.6 7 4

14.7 4 9 (corresponds to SEE of 3 .840)

3)

simulation covariance (0 t,E t) = 0 . 0 1 1

4)

equation variance (0i t)>
1/1970;

(quarterly multiplier
equation R2 = 0.2 7 )

11/1970;

1.835,

(quarterly multiplier
equation R2 — 0.5 0 )

111/1970;

1.751,

(quarterly multiplier
equation R2 = 0.5 9 )

IV/1 970 ;
5)

5.1 19,

1.696,

(quarterly multiplier
equation R2 = 0.7 7 )

G N P equation is the A-J
1/1953 to IV/1 9 6 9 ).

equation

(sam ple period

irThe S E F sta tistic s in each q u a rte r a re com puted u sin g actual changes
in m oney and g o v e rn m e n t e x p en d itu re s, except th a t th e contem po­
raneous change in m oney is given as th e sim ple 4 p e rc e n t increase
over th e lagged level o f th e m oney stock.

T h e S E F ° statistics associated with our monthly money
stock control procedure are only 3 per cent larger than
the S E F statistics assuming no errors in money stock
control (see row D ). T o further understand the implicaprobably the most reasonable estimate for the variance in
money stock control, given that a monthly money stock
control model is used in conjunction with a quarterly fore­
casting model of GNP. Unfortunately, the statistic simula­
tion var(0t) makes no allowance for the imprecision in the
coefficients of the multiplier forecasting equation. However,
as is shown in the technical appendices, this shortcoming
can be overcome if the quarterly money stock control pro­
cedure is used. In that case, the equation var (0 t) equals
B r-i X ( S E F )2 (quarterly multiplier equation) which is
the most appropriate estimate of var (0 t). This variance is
just the square of the lagged level of the base times the
squared standard error of forecast of the multiplier forecast­
ing equation.
Page 21

FED ER AL R ESE R V E BANK OF ST. LOUIS

tions of the standard errors of forecast in Table V I, it is
helpful to refer back to Table V on page 17. The data in
Table V show that the errors in money stock control have
a negligible effect on the policymaker’s ability to forecast
GNP, if 95 per cent confidence intervals are used as
standards of comparison.-14
:!4An illustration of how the confidence intervals in Table V
were computed is given below. Consider the perfect money
stock control case given in the first quarter of 1970 entry in
row A of Table VI, SEF = $4,143 billion. Because the
errors in predicting changes in GNP can be shown to be
normally distributed for large samples ( see the technical
appendices in Working Paper No. 14), it is appropriate to
set up confidence intervals, using a table of the standard




OCTOBER 1971

normal distribution. A range of ± 1 .9 6 standard deviations
gives a 95 per cent confidence interval for the standard
normal distribution, whose standard deviation is unity by
definition.
Consequently, the distribution of normally distributed
errors with an SE F value of $4,143 has a proportionately
larger 95 per cent confidence interval of ± (1.96) X
(4.143) equals ± $8,120. When errors in money stock con­
trol raise the value of the SE F statistic to $4,267 (row C ),
the probability of achieving the same confidence interval of
± $8,120 billion is reduced to 94.26 per cent, since now
only ± 1.90 standard deviations of the standard normal
distribution will give that same confidence interval,
[i.e., ± (1.90) X (4.267) equals ± 8.120]
For a comparison of 90 and 80 per cent confidence intervals
see the technical appendices available in Working Paper
No. 14.

This article is available as Reprint No. 72.

FED ERA L R ESER V E BANK OF ST. LOUIS

OCTOBER 1971

WORKING PAPERS
S IN G L E COPIES of the following working papers are available to persons
with a special interest in these research areas, and any discussion or comment
would be welcomed by each author. For copies write: Research Department,
Federal Reserve Bank of St. Louis, P. O. Box 442, St. Louis, Missouri 63166.
Title of Working Paper

Release Date

The Three Approaches to Money Stock Analysis
(Now available in our Reprint Series as No. 24)

July 1967

Chapter on Agribusiness Prepared for American
Institute of Banking Textbook Agricultural Credit
(50 pages)

Aug. 1967

Monetary Policy and the Business Cycle in Post­
war Japan (108 pages) Revised

April 1968

The Influence of Fiscal and Monetary Actions on
Aggregate Demand: A Quantitative Appraisal
(53 pages) Revised

March 1969

The Development of Explanatory Economic Hyphotheses for Monetary Management (48 pages)

Nov. 1968

A Model of the Markets for Consumer Instalment
Credit and New Automobiles (60 pages)

Jan. 1969

A Summary of the Brunner-Meltzer Non-Linear
Money Supply Hypothesis (65 pages) Revised

May 1969

The Market For Deposit-Type Financial Assets
(205 pages)

March 1969

Impact of Changing Conditions on Life Insurance
Companies (23 pages)

March 1969

Adjustments of Selected Markets in Tight Money
Periods (206 pages)

June 1969

11

A Study of Money Stock Control (41 pages)

July 1969

12

Empirical Test on the Effect of Changes in Money
Supply in Developing Economies

May 1970

13

Historical Analysis of the “Crowding Out” of Pri­
vate Expenditures by Fiscal Policy Actions

January 1971

14

Money Stock Control and Its Implications for
Monetary Policy: Technical Appendices

October 1971

Number

1
2

3
4

5
6
7
8
9
10




Page 23

S u b s c r i p t i o n s to this bank’s

R

e v ie w

are available to the public without

charge, including bulk mailings to banks, business organizations, educational
institutions, and others. For information write: Research Departinent, Federal
Reserve Bank of St. Louis, P. O. Box 442, St. Louis, Missouri 63166.