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Improving the
Monetary Aggregates

Staff Papers

Board of Governors of the Federal Reserve System


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Published in November 1978

Library of Congress Catalog Card Number 76--14548

Copies of this report may be obtained from Publications Services, Division of Administrative Services,
Board of Governors of the Federal Reserve System,
Washington, D.C. 20551. The price is $4.00 per copy;
in quantities of 10 or more sent to one address $3.75
each. Remittances should be made payable to the
Board of Governors of the Federal Reserve System in a
form collectible at par in U.S. currency. (Stamps and
coupons are not accepted.)


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Improving the
Monetary Aggregates

Staff Papers

Washington, D. C.


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Federal Reserve Bank of St. Louis


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Preface

In early 1974 the Board of Governors of the
Federal Reserve System appointed the Advisory Committee on Monetary Statistics to
provide a technical evaluation of, and a report on, the quality of the monetary aggregates used by the Federal Reserve in the
formulat10n and implementation of monetary
policy Improving the Monetary Aggregates
Report of the Advisory Committee on Monetary Statistics was published by the Board in
June 1976
The Advisory Committee on Monetary Statistics was chaired by Professor G L Bach
(Stanford University), Professor Phillip D
Cagan (Columbia University) served as Executive Secretary Other members of the Committee were Professor Milton Friedman (University of Chicago), Professor Clifford G
Hildreth (University of Minnesota), Professor
Franco Modigham (Massachusetts Institute of
Technology), and Dr Arthur M Okun (the
Brookings Institution) Professor Paul W McCracken (University of Michigan) was a member of the Committee originally, but withdrew
because of the pressures of other duties
At its final meeting, the Advisory Committee requested the publication of certain of
the research papers that had been prepared
by the Board staff for the Committee's use
The Committee concurred with a recommendation of the Board staff that rev1S1ons of the
studies be prepared for pubhcat10n, provided
that the final versions would contain essentially the same information that had been

made available to the Committee during the
course of its dehberat10ns The Committee
also requested further investigation of its tentative proposal for an alternative method of
calculating M 1 , and a paper presenting this
further work is included in this volume
For three other papers, addit10nal staff research is also presented, this work serves to
support the analysis onginally presented to
the Committee "Transitory Variations in the
Monetary Aggregates" expands upon the
sources, estimat10n, and interpretat10n of
transitory vanat10ns in the aggregates "Demand Deposit Ownership Survey" contains
new staff research on the demand for demand
deposits by var10us sectors Finally, m "Foreign Demand Deposits at Commercial Banks
m the Umted States," addit10nal results are
presented from attempts to model the demands for foreign deposits mcluded in M 1
Support of the work of the Advisory Committee on Monetary Statistics by the staff of
the Board of Govei nors was supei vised
throughout most of the penod by James L
Pierce, who at the time was Associate Director
of the Div1S1on of Research and Stausucs and
1s now Professor of Economics at the Umversity of Cahforma at Berkeley, subsequent staff
work was overseen by Edwaid C Ettm, Associate Director of the D1v1Sion of Research and
Statistics Board staff economists working
closely with the Committee, aside from the
authors of the papers m this volume, were
Arthur B Hersey and Thomas Thomson

J Charles Partee,Member of the Board
Chairman, Board Committee
on Research and Statistics


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Contents

Preface

Transitory Variations in the Monetary Aggregates

I

Richard D Porter, Agustin Maravall, Darrel W Parke, and David A Pierce

Foreign Demand Deposits at Commercial Banks in the United States

35

Helen T Farr, Lance Girton, Henry S Terrell, and Thomas H Turner

Nonmember Banks and Estimation of the Monetary Aggregates

55

Darrel W. Parke

Seasonal Adjustment of the Monetary Aggregates

71

David A Pierce, Neva Van Peskz, and Edward R Fry

Demand Deposit Ownership Survey

Helen T Farr, Richard D Porter, and Eleanor M Pruitt


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91

Contents-continued

Sources of Data and Methods of Construction of the Monetary Aggregates

117

Darwin L Beck

An Alternative Method for Calculating M1

135

Anton S Nissen and Darwin L Beck

Developing Money Substitutes· Current Trends and Their Implications
for Redefining the Monetary Aggregates

Steven M Roberts


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147

I

Transitory Variations in the Monetary Aggregates
Richard D Porter, Agustin Maravall, Darrel W Parke, and David A Pierce

Most of this work was completed in early
1977 Smee then updated estimates of transitory variations in the aggregates have been
computed for the 1968-76 period These estimates are similar to the estimates reported
here, though there appears to have been a
small increase in the transitory variations in
1975 and 1976 Also, alternative methods of
interpolating components that are not observed daily have been tried, and it seems that
the choice of interpolation procedure has
very little effect on the resulting estimates of
transitory variation
The views presented here are those of the
authors and do not necessarily represent the
views of the Board of Governors of the Federal Reserve System This paper contains materials presented to the Advisory Committee
on Monetary Statistics as well as additional
materials developed later We believe that the
principal findings of this study are consistent
with evidence that the Committee reviewed
in making its recommendations It is hoped
that additional results reported here improve
the estimation of transitory variations tn the
aggregates We wish to thank Greg Connor
for very able assistance m all phases of this
work We also wish to thank Darwin Beck,
Edward Ettm, Donald Hester, John Kalchbrenner, David Lindsey, Juan Perea, and
Steven Zeller for helpful comments
Day-to-day movements m the not seasonally
adjusted monetary aggregates display several
systematic patterns Overall, there 1s a gradual upward trend m the senes with some
cyclical vanat10ns Strong and fairly systematic shorter cycles for monthly, weekly, and
NOTE -The authors are on the staff of the Divmon
of Research and Statistics


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even mtraweekly time spans are also evident
For example, the demand deposit component
of M 1 tends to fall on Fnday, while the currency component tends to nse Nevertheless,
after accountmg for these systematic effects,
unsystematic, or transitory, day-to-day variat10ns remam In this paper, the magmtudes
of these unobserved transitory vanat10ns are
mvest1gated m order to appraise the sigmficance of observed variat10ns m the monetary
aggregates
Day-to-day variat10ns m monetary aggregates sprmg from short-run payments flows
between the nonbank pubhc and commercial
banks, the Treasury, or the Federal Reserve
Potential sources of day-to-day variation m
private deposit balances mclude (I) compositional shifts m the allocation of private balances-dec1S1ons by the pubhc to shift from
currency to demand deposits, from time deposits to demand deposits, and so forth, (2)
shifts m balances held by the U S Government and commercial banks m relat10n to the
public's holdmg of balances, (3) variations m
the rate at which private deposits are created
m the bankmg system, (4) fluctuations caused
by Items delayed m transit or by reportmg
errors
To date, only hm1ted theoretical and empineal work has been done on deposit vanabihty at commercial banks 1 The report of
1 See, for example, Lyle E Gramley, "Deposit In
stab1hty at Individual Banks," m Essays on Commercial
Banking (Federal Reserve Bank of Kansas City, 1962),
pp 41-53, C RangaraJan, "Deposit Vanabihty m Individual Banks," National Banking Review, vol 4
(September 1966), pp 61-71, and Fredenck M Struble
and Carroll H Wilkerson, "Bank S1Ze and Deposit
Vanab1hty," Monthly Review, Federal Reserve Bank
of Kansas Ctty (November-December 1967), pp 3-9,
and "Deposit Vanab1hty at Commercial Banks,"
Monthly Review, Federal Reserve Bank of Kansas Ctty
(July-August 1967), pp 27-34

2

Improvmg the Monetary Aggregates Staff Papers

the Advisory Committee on Monetary Stat1st1cs was, m fact, the first study of day-to-day
transitory vanat1ons m monetary aggregates 2
Like the report of the Advisory Committee,
this paper approaches the problem of measurement of transitory variauons empirically
It neither attempts to explam m economic
terms which part of observed vanauons is
transitory and which is not, nor relates the
systematic component to othei relevant senes
m calculatmg the transitory component
Rather, four different statisucal models are
considered Each model contams a different
spec1ficat10n and, therefore, a different measurement of transitory and systemauc vanat10ns
Each of the models allows for two types of
systematlc effects zntraweekly effects that account for systematlc differences between Mondays and Tuesdays, Mondays and Wednesdays,
and so forth, and longer-run trends that mclude seasonal movement (other than mtraweekly effects) as well as trend and cychcal
mov,ements m the usual sense Because there
1s no need to obtam separate esumates of
seasonal and trend-cycle parts, both will be
grouped mto one term, the "trend "
In each model, the observauons are the
logarithms of the measured aggregates, and
trend 1s determmed locally m each model by
smoothmg or averagmg the observed senes
around each dally observat10n The four
models differ essenually m the precise weights
used m computmg the local trend The estimated transitory component (the part of the
senes due to transitory variations) m each
model 1s obtamed by subtractmg the estimated
systematic part from the series
Daily trend estimates for three of the four
stat1st1cal models are based on an average of
five weekday observauons 3 In the analys1sof-vanance (ANOVA) model, the esumated
trend for each weekday m a given statement

Summary of empirical results

lmprovmg the Monetary Aggregates Report (Board
of Governors of the Federal Reserve System, 1976)
a The day-to-day vanauon m the aggregates 1s cons1derably less on weekends than on weekdays Thm,
the analysis was limited to weekday observations, see
the section "lntraweekly heteroskedastmty," p 19, for a
further d1scuss1on of this pomt

On balance, emp1ncal estimates for the
1968-74 sample penod md1cate that 95 per
cent of the observed, annuahzecl, monthly
growth rates of M 1 and M 2 he wlthm 4 and 2
per cent, respectively, of the unobserved systemJ.tlc growth rates Correspondmg values for

2


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week (Thursday to Wednesday) 1s the arithmetic mean of the five weekday observat10ns
m that statement week In contrast, daily
trend estimates m the symmetrical equal
weights (SEW) model are based on an anthmeuc movmg average of five observat10ns centered on the current day Thus, esumated
daily trend m the SEW model changes from
one day to the next w1thm a statement week
Fmally, m the symmetric quadratic weights
(SQW) model, the estimated daily trend 1s a
weighted movmg average (centered on the
current day) with the largest weight attached
to the current day
In the fourth model, the trend for a given
clay 1s also a symmetric weighted average of
the observat10ns cente1ed around the current
day However, the weights are not fixed a
priori as m the three prev10us models but are
estimated directly from the aggregate series
Under certam assumpuons, aggregate data
may be used directly to obtam the optimal
statistical decompos1t10n (OSD) of the aggregate series mto Its transitory and trend components, each 1s a symmetric weighted average of
the observations on the aggregate Because the
ume-senes charactensucs of different senes are
not 1clent1cal, the weights used m the OSD
trend estimate will be specific to each senes
The paper proceeds m the followmg way
First, there 1s a sh01 t summary of the emp1ncal results A descnpuon of the four staUstlcal
models 1s presented m the followmg sect10n
Next aie sections clealmg with the est1mat1on
of the models and related statistical tests, empn 1cal comparisons of the sources of transitory
variat10ns, and exammat10n of confidencemterval estimates of the systematic component
The conclus10ns are followed by two techmcal
appendixes

Transitory Variations

the Monetary Aggregates

in

TABLE 1 95 Per Cent Confidence Intervals for
Monthly Annuahzed Growth Rates,
Alternative Methods
Percentage pomts
Monetary aggregate
Method

Currency I Demand
deposits

I

M1
I

ANOVA
SEW
SQW
OSD

42
2 4
I 6
na

5
4
3
4

7
4
3
3

Other time
and savmgs
deposits

4 5
3 3
2 5
na

I 0
9
7
na

I

M,

2 3
I 6
I 2
na

n a Not available

the four different statistical models are presented m Table I For example, the ANOVA
estimate for M 1 of 4 5 per cent md1cates that
about 95 per cent of all measured monthly
growth rates of M 1 will he w1thm 4½ percentage pomts of the (unobserved) systematic
growth rate of Mv and about 5 per cent of
all measured monthly growth rates will depart from the systematic growth 1ate of M 1
by larger amounts These estimates apply only
to not seasonally ad1usted data For data that
are seasonally ad1usted usmg the Census X-11
program the values would be smaller, about
nme-tenths of those m Table I

Methodology
Because monetary agg1egates tend to grow
as the economy expands, transitory errors,
measured m dollars, can be expected to have
a long-run pos1t1ve trend m absolute terms
Thus, lt 1s convement to put the stat1st1cal
problem m 1elat1ve terms and work with the
natural logarithm of the daily aggregate Tlus
logarithmic transformat10n will tend to stabilize the transitory variance The equation
of inte1 est is, therefore,
(1)

Yt

=

'Y/t

+

f3t

+

Et

where

3

The mdex t runs over successive 5-day penods
excludmg weekends 4 The sum 7/t + f3t represents the systematic part of the model The
parameter f3t allows for systematic differences
between days w1thm a week The trend term
7/t represents long-run trends, mcludmg seasonal movement (other than the mtraweekly
seasonal /3 1) as well as trend and cychc movemen ts m the usual sense If the systematic mtraweekly effects are constant across weeks, as we
shall assume, then

for all t The funct10n f3t 1s thus a periodic
funct10n of time with period equal to 5 The
day-of-week terms will be normalued to sum to
zero ove1 a week, 3 that 15, for any t,

We assume that the trend changes gradually
and, therefore, 1t 1s esumated by averagmg
observat10ns near t Given a particular spec1ficat1on of the trend, It may then be estimated
along with the day-of-week effect
The term E 1 m Equat10n 1 reflects the t1ans1tory vanat10ns m the observed series, y 1
It 1s generally assumed that Et has expected
value zero [E( Et) = OJ and constant variance
[EM) = o- 2], and 1s serially mdependent In
other words, the effect of transitory components on Yt 1s, on average, zero with variance
umform (homoskedasuc) across days, weeks,
and months, and the current transitory error
1s mdependent of past or future transitory
errors The assumpt10n of homoskedastiCity
w1tlun a week will be relaxed m part of the
analysis, and separate (heteroskedasuc) estimates of the transitory variance for each weekday will be computed

y = the natural logarithm of the aggregate
ri = the systematic trend (for y)
/3 = the systematic day-of-week term
E = the
nonsystematic or transitory
term
t = a time subscript mdex (m days)


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4 We have excluded weekend observations because
they rcqmre a substanually different ueatment from
weekday observat10ns, see the section "Transitory vanatlons m averages of daily data," pp 18-21
5 Although this simple spcc1ficat1on of the day of
week terms will be adequate for most weeks, weeks
contammg bank holidays may reqmre some special mod1ficat1ons, see the section "Emp1ncal results," pp 8-15

4

Improvmg the Monetary Aggregates Staff Papers

The ANOVA, SEW, and SQW models
for transitory variations
The four models differ m their spec1ficat10n
of trend The report of the Advisory Committee on Monetary Stat1st1cs .tssumes cl constant trend for all days withm a week but
allows the trend to va1 y over d1ffe1 ent weeks 6
That model 1s a standard two-way analysis
of vanance (ANOVA) model with five d.ty-ofweek column effects and as mclny row effects
as there are weeks m the sample·
To assume, alte1 ncltively, thclt the trend fo1
each day 1s app1 oprutely e5timated by ,t symmetn'c 5-day weighted clverclge of y 1 cente1ed
cltound that day affords a mo1e symmetnc
tieatment of days w1tlun weeks than 1s furmshed by the ANOVA model That 1s, each
dcly 1s viewed as lymg m the center of 1ts own
week (rather than cl fixed calendar or st.ttement
week), and the trend fm th.tt day 1~ estimated
hy
2

~, = ~

(2)

c,Yt+• = c_2Yt-2

B=-2

+ Cl)'1+1

where for symmetry c,

=

oper,ttm defined by Biy

1

+ c_1Yt-1 + coy1
+ C2Y1+2 = c(B)y,

c_,, B 1s the backsh1ft

=y

2

_
1

,
1

c(B)

= ~c B

8
,

8

,~2

.tncl
2

~ c. = 1

(3)

•=-2

or c(I) = 1 8
The estimate m Equation 2 1s cl (symmetnc)
,~e1ghted ave1 .tge of y1-the 1esult ot .tpplymg
a linear filter to y 1 If the weights {e's} are
equal,
1
(4)
c, = 5' s = - 2, -1, 0, 1, 2
G

[mprovmg the Monetary Agg1egatcs

Report, pp

26-28
, It 1s pnmanly the contmual shift of the ttend
between weeks that d1stmgmshc.s the trans1to1 y com
ponent m Equation I from the "irregular" component
of seasonal adJustmrnt model~ In the latter models
the defimuon of the trend 1s generally mo1e restnc
uve (see, for example, David A Pierce, Neva Van Pesk1,
and Edward R Fry, "Seasonal Adjustment of the
Moneta1y Aggregates," this volume), thm the. 11rcgula1
,anance 1s higher than the transitory vanance m this
paper
s For a d1scuss10n of such approachc.s, ~cc Thcodo1e
W Anderson, The Stat1st1cal Analysis of T1111e Series
(Wiley, 1971)


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such a trend filter will be called the symmetnc
equal weights (SEW) filter
The SEW model 1s qmte s1m1lar to the
ANOVA model Assummg the sample consists
of .tn mtegral number of weeks, the day-ofweek effects m both models can be estimated
by takmg the differences between the averclge
of all Mondays and the over-all average, the
.tverage of all Tuesdays and the ove1 -all aver,1ge, .tnd so fo1 th In cldd1tion, for the m1ddleot-the-week or third observat10n, the estimated
residual and trend will be the same m both
the SEW and ANOV A models As stated
ear her, the ANOVA model specifies trend a5
the arithmetic mean of the obse1 vauons m a
fixed week Hut 101 the third or middle observ.ttion of a fixed week, the SEW estim.tte will
,tverage the s.tme 5 d.tys .ts the ANOV A, and
hence both models '\\'Ill 1et111n the same 1emlu.tls and uend e5t1mate5 for th15 day Thus,
if we define a week as the statement-week
mterval from Thm sday to Wednesdcly, both
models will show the same llend estimates
,md res1duah on l\Iondcly-m1dway th1ough
the 5tatement week The SEW model 15 les5
,trb1t1.try th.tn the ANOVA model, then, smce
the 5EW t1eclt5 each clay as the center of a
movmg 5-dcly week, wherea5 the ANOVA
treats clclys as membe1 s of fixed, .i.rb1tranly
defined weeks 9
Of course, the essential d1ffe1ence between
the two models 1s the degree of smoothness m
the t1 encl e5t1mate Trends ,tcross weeks change
more smoothly m the SEW model than m the
ANOV A model 10
Further general11at10ns of the ANOV A
model are possible W1tlun the framework of
Fquattons 2 and 3 the weights do not need
"On the other hand, rcsene requnement~ for mcm
hc1 hank~ arc ha~cd on avu age dcpo~1t~ O\el ,1
Thmsday th1ough \Vc.dnc~da} 11c.ck To the c.xtcnt that
1c~erve 1cqunc.mc.11ts affect depo\1t~, choosrng 'I hun
day th1ough Wednesda} to compute. the t1c.nd 1s not
entirely arbitrary
10 A related pomt 1~ that under ~mtablc assump
t1orn, the estimated scne~ on •t 1s ~tauona1 y for the
~EW c~t1111atc. of the t1cnd but not fo1 the ANOVA
c~t1m.itc I or Lxamplc, mmg the ~t.1tc.ment 11 c.c.k, the
I.1st day (Wcclncscl,1}) estimate 1s complete!} clctcrmmed
by the p1cv10m da} \ c~t1m,1tc.~, .1 property one 110111d
not orchnanly want to asc11bc to the transitory com
ponent of a senes

5

Transitory Variations in the Monetary Aggregates

to be equal Suppose that the weekly trend
were a polynomial of degree 2,
(5)

71t+J

=

Wot

+ Wu) + W2tJ2
J

= -2, -1, 0, 1, 2

where w01 , wit, and w2 t are parameters Then
the appropriate symmetric filter m Equation
2 has weights given by11
(6)

Co

d1t10ns, the nature of such a process is determmed by its autocovariances,

= 17/35,

'-1

=

C1

C-2

= 12/35,
= C2 = -3/35

Because the weights displayed m Equation 6
are designed to ehmmate quadratic trends,
we will refer to Equations 2 and 6 as the symmetric quadratic weights (SQW) model Given
a 5-day smoothmg mterval, the SQW model
is the highest-order detrendmg filter available,
withm the class of lmear symmetric filters,
for ehmmatmg polynomial time trends

'Ylk)

= E(rJ17/t-k)

which for lags k = l, 2,
specify the way m
which '1/t is related to its own past By the
statlonarity assumption, the autocovariances
do not change with the time t-that is,
E(7Jt'1/t-k) = E(7Jt-s'1/t-s-k) for all s and k The
lag 0 autocovariance, E( 711) = 11~, is the variance of 7/t, and y 71 (k) = y 71 (-k) As before, Et
is assumed to be serially mdependent-that is,
a white-noise process, y.(k) = 0, k ~ 0-and
mdependent of 7/t Consequently,
(8)

}, the optimal
Given {xt t = 0, ±1, ±2,
(mm1mum mean square error) estimate of '1/e
1s of the form
(9)

Stochastic process rationalization of the
transitory models: the OSD model
The trend weights that have been considered so far are given a priori and, moreover, are chosen according to a "deterministlc"
assumption about trend-that is, that locally
it is well approximated by a polynomial m
time Yet, the trend estimates (and hence the
estimates of the transitory component), which
are symmetric movmg averages or filters of
the observed series, are appropriate for a
model m which the data contam a "stochastic"
component as well 1 2
Consider Equauon 1, rewritten as
(7)

Xi

= y, - /31
= 7j1 + E1

- (over-all mean)

but where the redefined trend '1/t is assumed
to follow a stationary, nondetermmistic, zeromean stochastic process 13 Under smtable con11 For the derivation of these weights and further
d1scuss1on of this approach, see Anderson, Statistical
Analysts, pp 46--56
12 The remamder of this seclion 1s more techmcal
than much of this paper and may be neglected with
out losmg the essenlial ideas of the study
1a See, for example, George E P Box and Gw1Iyn
M Jenkms, Time Series Analysis Forecasting and
-control (Holden-Day, 1970), Wayne A Fuller, Intro
duction to Statwnary Time Series (Wiley, 1976), and


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where c(B) 1s a symmetric filter as m Equauon 2 but 1s now given by

where

1s the autocovariance-generatmg funct10n of
the series {7/t} 14
For example, suppose '1/t tollows a firstorder autoregressive process
(11)

7/t

= 'P'llt-i

+ Ef, I'Pl < 1

where {ED is a white-noise process with mean
zero that 1s mdependent of Et Then the autocovariance-generatmg function of 7/t 1s

Peter Whittle, Predictwn and Regulation by Linear
Least Square Methods (Enghsh Umvers1ues Press, 1963)
In the subsequent apphcal!ons to the aggregates, x 1
will not be stat1ona1y and fmther transformations will
be required, see the d1scuss1on concernmg Equation 20
below
14 See Whittle, Prediction and Regulation, p 57

Improvmg the Monetary Aggregates Staff Papers

6

and c(B) is of the form

~ B•Rl•I
(B) -- X.r,o(l (3- (32).~
,.,

(13)

C

s=-co

where15

f3 = 1
~

+

x.(1 ztr,o,,02) - ~, \f3\

<1

= v'l + 2X.(1 + r,o2) + x_2(1 _ r,o2)2

Thus, the span of the weights is infimte, but
the weights approach zero since l,81 < I
The vanances of both 1/t and Et can be
estimated directly from observations on xt
alone, provided the process generating x 1
obeys certain restnct10ns To illustrate this
1 esult, rewnte Equations 7 and 11 as
(14)

Xt

=

,,OXt-1

+

E~

+

Et -

,,OEt-1

Then, mult1plymg successively by Xt-t and
Xt_ 2 and takmg expectations,

(15)

-y.,(1)

=

r,o[-y.,(O) - u;]

-y,,(2) = r,o-y,,(1)

(16)

ured with error at umform discrete time intervals accordmg to the equation Xt = '17t + Et,
where Et 1s a wh1te-n01se random error that 1s
independent of 1/t Then the stationary and
mvertible autoregressive-moving average
(ARMA) processes that approximate the contmuous process m discrete ume are identified
(almost everywhere) from observations on x 1
Without gomg through the proof, the content of the result can be set out 17 Note first
the assumption that the aggiegate exists in
continuous time At every mstant there 1s a
well-specified aggregate, but 1t 1s measured
or sampled at d1sciete time pomts, say, at the
close of each busmess day At each mstant, the
aggiegate (actually the log of the aggregate)
1s equal to the sum of a systematic part, 1/t,
and a transitory part, c;t,
Xt

(18)

r,o
u~

=

'Y z(Z)
-yz(l)

= 'Yz(O) - -yz(l)
r,o

Thus, 1f 1/t follows a first-ordei autoregiess1ve
process, all the parameters m Equation 11
may be estimated directly from observations
on the Xt process alone, that is, the model
(for 1/t) 1s 1dent1fied 16 Moreover, this example
is not an isolated special case but exemplifies
a general result
Theorem Let {'17e} be a stationary stochastic
process m continuous time Let 1/t be measIbid, pp 35, 58-59
While Equations 17 and 18 mdicate that rp and
u~ are identified, they do not necessarily provide the
most efficient means for esumatmg these parameters
15
16


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Federal Reserve Bank of St. Louis

'Y/t

+

Et

where '17s and Et are mutually mdependent fo1
all s and t The process on Et 1s assumed to
be independent between days but may be
autocorrelated within a specified day Fm ther,
'17t 1s assumed to follow a continuous-time
stationary process, wluch can be wntten as

Smee xt 1s observed, its variance y.,,(O) and
lagged covanances y.,,(l) and y,,(2) may be
estimated Then, from Equations 15 and 16,
(17)

=

=[

'Y/t

c(t - u)df(u)
00

where {,J,(t)} 1s a continuous process with
independent stationary mcrements and with
differential d,J,(u). Given these assumpuons,
the resultmg process for the trend, '17t, at the
discrete sampled points (t = 0, ± I, ±2, ±
)
1s an autoregress1ve-movmg average model of
ordei (n, n - l) 18
n

(19)

1/t -

~
i=l

n-1

,,0,'Y/t-•

=

E~ -

~ 8,E~-,
i=l

11 The proof 1s developed m Agustm Maravall, "Estl
matlon of the Permanent and Transitory Component
of an Economic Variable with an Application to M1,"
Special Studies Paper 85 (Board of Governors of the
Federal Reserve System, 1976)
1s The approx1mat10n mentioned m the theorem 1s
based on the followmg result Every lmearly regular,
stationary, stochastic process m contmuous time 1s the
hm1t m a Hilbert space of d1screte-t1me auto
regressive-movmg average processes of order (n, n - l),
as n approaches mfimty

7

Transitory Variations in the Monetary Aggregates

where { Et } 1s a wh1te-n01se process that 1s
mdependent of {Ee} 19 Fmally, whenever the
autoregressive part of the model has a greater
order than the movmg average part, all of the
underlymg parameters are 1dent1fied m the
econometric sense 2° Further, the 2n + I parameters, ip 1 , <p2,
, 'Pn, 011 02,
, 0,._1 , u;,
u?,, can be estimated solely on the basis of
observations on Xt
Under the same cond1t10ns, the argument
can be applied to d1screte-t1me stochastic
processes m which the natural time umt of
the process 1s small relative to the mterval m
which observations are available Fmally, the
systematic part, T/t, can have a nonzero and
even nonconstant mean (for example, a determm1st1c day-of-week effect) and be generated
by a homogeneously nonstationary process
Homogeneously nonstat10nary processes mclude processes that may be transformed mto
stationary processes by apphcat1on of one or
more d1fferencmg operations Thus, the transformation from the homogeneously nonstat10nary process, T/t, to the stationary process, 81,
1s achieved by
h

(20)

51

= II

(1 - B••)d•T/t

=

D(B)rii

i=l

wheres, and h are pos1t1ve mtegers and the d,
are nonnegative mtegers Lettmg
Zt

= D(B)yi

and
Ct= D(B)Et

m terms of the transformed senes we have
(21)
10 The ,p's must satisfy appropriate statlonanty restrictions that imply that the roots of the polynom1al
equation, q,(B) = 0, he outside of the umt cucle, where

,p(B)

=1 -

<p1B -

<p2B 2 -

-

'PnBn

Smee 8t 1s stat10nary, 1t can be approximated
to any desired degree of accuracy by an ARMA
model of order (p, q) for some p and q

The cond1t10n on p and q m Equat10n 22
that 1s necessary for 1dent1ficat10n of the paiameters on the nght-hand side of Equat10n
211s that p + d > q, where 21

d=

h

~
i=l

d,s,

In the stat10nary case without d1fferencmg
(Equat10n 19) p = n and q = n - l, so the parameters of the discrete-signal process are identified 22 But for situations m winch p + d .e::::. q,
the parameters are not identified For example, consider a weekly stationary ume senes
m which the weekly observation is an average
of seven daily observations, endmg on Wednesday Thus, the weekly observat10n can be seen
as systematic samplmg (every Wednesday) of
an aggregate of daily observations Assume
that the underlymg stochastic process for the
daily time senes 1s contmuous and repre-,
sentable by a differential equation Wlule the
discrete-time ARMA eqmvalent would be of
order (p, p - l ), the pnor operat10n of aggregat10n over a week would transform the model
mto an ARMA (p,p) Fmally, systematic samplmg would produce an ARMA of order
(p,p) 23 Hence, the correct weekly model 1s not
identified However, It still may be possible
to determme an upper bound for a; from the
data (see the section on empirical results)
Express10ns for the signal m terms of the
parameters are also readily available Correspondmg to Equations 9 and IO we have

81 =

d(B)zr

where

To 1dent1fy the movmg average palt of the model, 1t
1s also assumed that the roots of 9(B) 0 he on or
outside the umt cucle, where

d(B) = - - - - - - ' - - - - ' ' - - -1 - G.(B) + D(B)D(B- )u;

See Marcello Pagano, "Estimation of Models of
Autoregressive Signal Plus White Noise," Annals of
Stat1st1cs, vol 2 Ganuary 1974), pp 99-108, and Agustm
Maravall, Ident1ficat1on m the Shock Error Model
(Sprmger-Verlag, forthcommg)

For a proof, see Maravall, 'Estimation "
See Pagano, "Estimation of Models "
23 See Kenneth R W Brewer, "Some Consequences
of Temporal Aggregation and Systematic Samplmg for
ARMA and ARMAX Models," Journal of Econometrics,
vol l (June 1973), pp 133-54

G.(B)

=

21

20


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22

Improvmg the Monetary Aggregates Staff Papers

8

and

G6(B) = ~ 'Y6(k)Bk
k=-oo

Last, given d(B), the lmear filter for the signal

= c(B)zi

~t

can be constructed

24

Empirical results
Standard error estimates for the
ANOVA, SEW, and SQW models
Estimated transitory standard errors are displayed m Table 2 for five aggregates and for
three detrendIDg techmques, the ANOVA,
SEW, and SQW Because the tl ansitory errors
ID dollars turn out to be small relauve to the
levels of the aggregates, the transitory standard errors of the logarithm of an aggregate
can be IDterpreted (approximately) as a percentage of the aggregate's level (Appendix 1

shows that the error ID this approximauon 1s
very small) These standard errors are estimated by usIDg 1,815 daily residuals for an
IDtegral number of weeks from 1968 through
1974 The residuals from each model are
grouped by day of week, by year, and collecuvely For each entry, the sum of squared residuals is divided by an appropriate constant to
obtaID an estimate of the standard deviauon 25
The aggregate displayIDg the most transitory
variation (expressed as a per cent of the level)
is demand deposits, followed ID order by Mi,
by currency, by M 2 , and by other time and
25 Let N, be the number of residuals associated with
column I of Table 2 The d1v1sor, D,, 1s

D,

= N,

N,
See, for ex.imple, Whittle, Prediction and Regu
lation, chap 8
21

- N. - ND

where N, 1s a number associated with the detrendmg
procedure (reflecting the fact that the residuals are
estnnates of [l - c(B)]Et rather than •t themselves),
and N n 1s the "prorated" share of the degrees of free
dom lost by esumatmg the day of-week parameters
For the ANOVA model, N, = the numbe1 of weeks
m N, For the SEW or SQW

= coN,

\\here co= 1/3 for the SEW and 17 /33 for the SQW,
~ce Anderson, Statistical Analysis, p 53, Equation 28

TABLE 2 Estunates of the Standard Deviation of the Transitory Component, Alternative Methods
Per cent
Days

Years

Aggregate and method

Mon
Currency

ANOVA

SEW

SQW

I

Tues

I

Wed

I

Thu

Fn
I

1968

I

1969

I

1970

I

1971

I

1972

I

1973

I

1974 1196874

(I)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

4167
4165
2468

4121
2522
1816

5963
2664
1542

7331
3298
1776

3922
2275
2005

4988
2849
1642

5065
3243
2044

4847
2993
1776

5156
3019
2015

5475
3187
2112

5662
3143
2023

5666

2974
1964

5273
3062
1947

7164
7162
5278

5912

8436
4850
3311

8116

4404

5329
3571

5460
4307
3973

6517
4598
3285

7824
5540
4074

7428
5773
4356

6603
5636
3935

6516
5104
3506

7251
5360
4437

7601
6301
5272

7116
5485
4166

5159
5157
3804

4724
4207
3255

6750
3762
2560

6609
4017
2782

4405
3313
2967

5168
3534
2534

6206
4309
3099

5815
4454
3344

5219
4236
2945

5090
3764
2497

5749
3960
3261

5999
4649
3844

5614
4137
3104

1469
1468
1152

0919
0852
0639

1161
0743
0489

1193
0902
0612

1383
1361
1105

0972
0878
0601

1180
1060
0740

1044
0921
0821

1209
0920
0693

1010
0950
0679

1491
1405
1073

1658
1459
1164

1240
1104
0846

2491
2490
1779

2380
2110
1521

3366
1816
1278

3406
2009
1428

2279
1687
1510

2771
1850
1346

3312
2310
1603

3192
2399
1844

2648
2075
1467

2449
1805
1209

2724
1802
1385

2650
2011
1650

2828
2041
1512

Demand deposits

ANOVA

SEW

SQW

5355

M1

ANOVA

SEW

SQW

Other time and savings
d~os1ts

AN VA

SEW

SQW
M,

ANOVA

SEW

SQW

NOTE -The estimates are expressed as a percentage of the level

Thus, the entry m column I for the ANOV A model of the logarithm
of currency md1cates that the estimated standard dev1at1on on Mon
days was 4167 per cent of the level of currency The ANOV A estimates differ slightly from the estimates reported m /mprovmg the
Monetary Aggregates Report of the Advisory Committee on Monetary
Statistics (Board of Governors of the Federal Reserve System 1976),


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table 5, p 27 The yearly estimates here are based on day of week
effects estimated for the entire sample period, m table 5 of lmprov111g
the Monetary Aggregates Report, the annual estimates are based on
separate ANOV A's for each calendar year The t.~blc 1bove also
corrects a mmor data error m the ANOV A calculauons m /mprovmg
the Mo11etary Aggregates Report for both the other time and sav,ngs
component of M, and M, Itself

Transitory Variations

in

the Monetary Aggregates

savmgs deposits The estimates provided by
the ANOVA method are umformly higher
than those from the other two methods Evidently, the more restrictive trend specification results m greater vanah1lity m the residual Except for other time and savmgs deposits, the ANOVA estimates are about 2 to
2 5 times as large as the SQW estimates and
about 1 3 to 1 7 times as large as the SEW
estimates For other time and savmgs deposits,
the ANOVA estimates are about 1 5 times as
large as the SQW estimates and about 10 per
cent larger than the SEW estimates

Assessment of intraweekly
heteroskedasticity
The over-all vahd1ty of the vanous models
depends on, among other thmgs, the vahd1ty
of the assumptions concernmg the residuals,
namely, homoskedastic1ty and lack of senal
correlation Senal correlat10n 1s treated later
m the d1scuss1on of autocorrelation tests Concermng heteroskedast1c1ty, 1£ the transitory
variance itself exh1b1ted a systematic patternfor example, an mtraweekly pattern-the foregomg efforts could not he aimed at a smgle
measure of transitory vanab1lity hut only at
a composite or average of such measures It
1s, therefore, important to ascertam 1f heteroskedast1c patterns exist
The degree of heteroskedast1c1ty across
weekdays 1s reported m columns 1 through 5
of Table 2 for different aggregates and methods For each of the methods, there are s1gmficant differences m the estimated mtraweekly standard deviations Observe that the
ANOVA and SEW models are virtually equal
on Mondays As noted earlier, this equality
holds because a Thursday-to-Wednesday statement week was used to define a week m the
ANOVA method It ts mterestmg, therefore,
to compare Monday standard deviations with
the other mtraweekly standard deviations for
the three methods Table 3 presents the ratio
of the standard deviation of each day of the
week relative to the standard deviation for
Monday, for each method On the basis of
the SEW and SQW estimates, 1t appears that


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9

TABLE 3, Relative lntraweekly Standard Deviations
for M1 andM2
Method

Tuesday

Wednesday

Thursday

Fnday

92
82
86

1 31
73
67

1 28
78
73

85
64
78

96
85
85

1 35
73
72

1 37
81
80

91
68
85

M,

ANOVA
SEW
SQW
M2

ANOVA
SEW
SQW
NOTE -Computed

from columns 1 through 5 m Table 2

Monday has the highest transitory standard
deviation With the ANOVA estimates, on the
other hand, It appears that Wednesday and
Thursday are the most n01sy days w1thm the
week For the ANOVA method 1t appears,
moreover, that the relative rankmg of the
4 days depends on how far the day of the
week 1s from the center of the statement week
(Monday) Assummg that the underlymg trend
1s centered on each day, the ANOVA method
distorts what 1s occurrmg by est1matmg the
trend usmg three-fifths of the appropnate
days for Wednesday and Thursday and fourfifths for Tuesday and Fnday Thus, 1f 1t 1s
true that Mondays have the highest transitory
variance, the resultmg mtraweekly pattern m
the ANOVA estimates 1s fully explicable
Tuesday and Fnday trend estimates contam
only one spurious day, so their standard dev1at1ons are smaller than the Wednesday and
Thursday estimates, which contam two spurious days each The ANOVA heteroskedast1C1ty
may, therefore, be regarded as evidence of the
mappropnateness of the detrendmg procedure
for this method
In the other procedures (SEW and SQW),
the observed differences between the estimated
daily transitory variances appear to be smaller
Nonetheless, there 1s evidence that Monday's
transitory vanat1on 1s largest This add1t1onal
random movement on Mondays may reflect
desired adjustments of balances by the pubhc
and banks that emerge after the close of business on Fnday but are not implemented until
Monday transactions take place In what follows, It 1s important to recogmze also that
Fnday tends to have less transitory variation
than the over-all esttmate

Improving the Monetary Aggregates· Staff Papers

10

Autocorrelation tests
Recall that one of our assumptions 1s that
the transitory component, Et, 1s senally uncorrelated Indeed, 1f 1t were autocorrelated
(at least at lags other than a day or two), such
a feature could scarcely be considered "transitory " 26 On the other hand, 1t 1s important
to note that each of the detrendmg methods
mduces mtraweekly senal correlation m the
residuals In the ANOVA procedure, the residuals are con5tramed to sum to zero over a
statement week, m the two movmg-average
procedures, the residuals are estimates not of
E1 but of [I - c(B)] Et The mduced autocorrelations, say, p11 p 2 , p 3 , and p4 can be calculated
on the assumption that Et 1s itself senally
uncorrelated (Table 4) Also affected are the
standard errors of the sample autocorrelations
of the residuals, as they depend on the population autocorrelations {p,J, 27 they are also
shown m Table 4
Based on these results, statistics bearmg on
the adequacy of the senal-mdependence assumption for the transitory component, Et,
are displayed m Table 5 The actual sample
autocorrelations of the residuals, rk, mmus
the theoretical autocorrelations Pk, are presented for lags I to 4 Also, bened.th each autocorrelation 1s the statistic, zk = (rk -pk)/
vvar(r,3 A value of zk larger than 2 m absolute value 1s evidence of senal correlation Inspection reveals substantial low-order autocorrelation for all aggregates and methods The z
statistics m column I for the lag I autocorrelation are all highly s1gmficant Columns 5, 6,
and 7 present the autocorrelations for monthly,
quarterly (r6 ;), and annual (r260 ) lags 28 For the
AN OVA and SEW, the correlation at these lags
26 For example, 1f •t ,\ere seasonal, part of the com
ponent could be predicted on the basis of \\hat occurred a month ago, a year ago, and so forth
27

var(rk)

1

"'

= N ,.f"' (p, +

=

2

P•-kP•+k
-

4P,PkP,-k

+ 2p~pi]

where N
the sample sIZe, see Maunce S Bartlett, An
Introduction to Stochastic Processes, 2nd ed (Cam
bndge, England Cambndge Umvers1ty Press, 1966)
2s The monthly effect has a lag of about 20 or 21 days,
the maximum of the two rm's 1s reported


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Federal Reserve Bank of St. Louis

TABLE 4. Expected Residual Autocorrelations and Their
Standard Errors Under Alternative
Detrendmg Methods
Lag

Method

I

1
ANOVA

SEW
SQW

-

160
( 021)
- 300
( 016)
- 800
( 0091)

I

2
-

120
( 023)
- 350
( 014)
400
( 030)

I

3

-

(
(

-

(

080
024)
100
027)
114
036)

4
-

I

040
( 025)
050
( 028)
014
( 038)

>S

.

( 024)

*

( 028)
( *038)

* Neghg1ble
NoTE -The autocorrelations are denved under the null hypothesis
that ., 1s not senally correlated Standard errors are shown m parentheses For a white noise process, the standard error 1s 1/(1815)'"
= 0235

1s unquestionably s1gmficant and often important For example, consider the annual autocorrelation m the AN OVA model for currency,
r 260 = 0 65 The autocorrelations at the next
two multiples of 260 are r 520 = 0 34 and
r 180 = 0 11 Ignormg all the other autocorrelations m the currency residuals, this would suggest that the residuals follow a process of the
form 29
Et

=

65Et-260

+ Ut

where u 1 1s the true transitory (white noise)
process with vanance
u!

=

(1 -

65 2 )u~

=

5775u~

That 1s, the 1mphed daily transitory standard
deviation for currency would be about
0 76u, = 0 4007 per cent, and not 0 5273 per
cent Only the residuals from the SQW model
display some signs of senal mdependence at
the monthly and quarterly lags Also, It 1s
worth notmg that except for other time and
savmgs deposits, the magmtude of the autocorrelation at the annual lag for the SQW
model 1s markedly lower than that for the other
two models However, the ANOVA and SEW
methods have substantial monthly and quarterly effects that have not been ehmmated The
monthly effect 1s qmte noticeable m the md1v1dual autocorrelations for M 1 that ate listed
m Table 6 for the three methods Observe that
for the ANOVA and SEW models, there are
persistent autocorrelations at a monthly frequency (20 or 21 days and multiples thereof)
,o See Box and Jenkms, Tune Se11es Analysis

Transitory Variations

in

the Monetary Aggregates

11

TABLES Residual Autocorrelations and Related Statistics, Selected Lags
Method and aggregate

r1 -

Pl

(I)

ANOVA
Currency

Demand deposits
M1

Other time and saV!ngs
deposits
M,

SEW
Currency
Demand deposits
M1

Other time and sa V!ngs
deposits
M,

SQW
Currency
Demand deposits
M1

Other time and sa V1ngs
deposits
M,

I
I

r2 -

p2

(2)

I
I

ra -

I
I

r, -

P'

(4)

I

I

Tm

(5)

I

I

"'

(6)

I

I

r2ao
(7)

51
(24 3)
33
(15 9)
34
(16 2)

- 02
(- 9)
- 08
(-3 6)
- 09
(-3 9)

- 20
(-8 3)
- 14
(-5 7)
- 16
(-6 9)

- 25
(-9 9)
- 16
(-6 4)
- 16
(-6 2)

40
(16 7)
16
(6 7)
22
(9 2)

51
(21 3)
36
(15 0)
42
(17 5)

65
(27 1)
47
(19 6)
48
(20 0)

19
(8 9)
35
(16 8)

- 21
(-9 0)
- 09
(-4 0)

- 22
-(9 0)
- 17
(-7 1)

- 06
(-2 5)
- 16
(-6 5)

24
(10 0)
22
(9 2)

19
(7 9)
45
(18 8)

24
(10 0)
48
(20 0)

49
(30 3)
26
(16 5)
28
(17 3)

03
(2 I)
- 06
(-4 3)
05
(3 8)

- 31
(-11 6)
-0 1
(-3 7)
- 10
(-3 8)

- 11
(-4 0)
- 03
(-1 0)
- 04
(-1 4)

18
(6 4)
10
(3 6)
10
(3 6)

21
(7 5)
11
(3 9)
14
(5 0)

48
(17 I)
24
(8 5)
22
(7 9)

25
(15 6)
30
(18 7)

- 13
(-9 6)
- 04
(-2 9)

- 29
(-10 8)
- 13
(-4 7)

- 02
(- 9)
- 06
(-2 I)

21
(7 5)
II
(3 9)

21
(7 5)
16
(5 7)

17
(6 I)
21
(7 5)

06
(7 0)
07
(7 5)
07
(7 8)

- 11
(-3 6)
- 15
(-5 1)
- 16
(-5 4)

05
(I 4)
12
(3 3)
13
(3 6)

- 02
(- 7)
- 03
(- 8)
- 02
(-1 I)

02
( 5)
- 02
(- 5)
- 01
(- 3)

03
( 8)
- 01
(- 3)
- 01
(- 3)

30
(7 9)
16
(4 2)
13
(3 4)

06
(7 0)
07
(7 6)

- 15
(-5 I)
- 15
(-5 2)

19
(5 5)
12
(3 5)

- 25
(-6 8)
- 03
(-1 0)

20
(5 3)
- 02
(- 5)

13
(3 4)
01
( 3)

16
(4 2)
08
(2 I)

NOTE -Figures m parentheses are

Zk

values

and that these autocorrelat10ns show no tendency to die out as the lag increases This
pattern suggests that the underlying process
for Et has a seasonal (monthly) nonstatlonanty

Holiday effects
Bank holidays likely represent an add1t1onal
source of vanat10n m the time senes models
under cons1derat1on Several attempts were
made to mcorporate dummy variables for maJOr bank holidays mto the spec1ficat1ons of
the ANOVA, SEW, and SQW models While
these results most often yielded stat1st1cally
s1gmficant regression coefficients for maJor
bank holidays, on balance 1t appears that most
of the effect 1s confined to Monday hank
holidays
The problem can readily he illustrated by
cons1dermg the outliers for demand deposits
from the ANOVA method In the sample,


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Federal Reserve Bank of St. Louis

pa

(3)

there were 29 Monday holidays on wluch all
or a substantial port10n of commercial banks
were closed, all of the residuals from these
Monday holidays for the ANOVA model for
demand deposits were negative, and all but
one were greater m absolute value than one
standard error The root mean square residual for the Monday holidays 1s I 35 per
cent of the level of demand deposits, which
is nearly twice as large as the over-all standard
error for Mondays The source of the problem
1s an mteractton between the day-of-week
effects and Monday holidays A holiday on
which all or substanttally all of the banks are
closed should properly receive the day-of-week
effect on the nearest preceding day that banks
were open Thus, Monday holidays should
1ece1ve the Fnday day-of-week effect rather
than the Monday day-of-week effect
The average residual on the Monday holidays was -1 30 per cent of the level of demand deposits This value 1s highly s1gmfi-

12

lmprovmg the Monetary Aggregates Staff Papers

TABLE 6. Autocorrelations for

M1

Lags

Lags
2

3

5

4

7

8

05
05
16
03
04
19
09
03

07
07
- 01
04
- 10
03
03
02

- 06
22
13
11
- 03
15
- 09
01

03
10
11
08
05
01
01
02
03

02
- 13
- 13
- 01
13
12
13
- 01
11

07
11
12
08
05
10
30
- 01
- 10

04
02
07
11
18
08
00
10

-

9

10

11

12

-

04
09
14
21
- 02
14
- 11
- 02

- 03
03
01
07
- 09
04
- 09
- 07

00
- 00
- 16
- 02
04
02
- 04
- 15

04
- 04
- 10
- 10
- 12
04
04
01

01
- 03
- 05
- 09
06
- 01
- 10
- 04
- 05

- 06
10
14
- 02
00
- 15
- 06
- 04
- 02

-

-

- 08
- 05
- 08
06
09
01
04
- 13

- 06
- 09
- 12
00
43
09
04
- 07

- 02
- 06
- 03
02
05
18
- 01
- 00

02
04
04
21
04
04
- 00
- 04

-

01
08
04
01
05
03
11
02
- OS

02
03
03
03
- 08
- 02
14
06

6

ANOVA residuals
113253749617385-

12
24
36
48
60
72
84
96

97-108
109-120
121-132
133-144
145-156
157-168
169-180
181-192
193-204
205-216
217-228
229-240
241-252
253-264
265-276
277-288
289-300

18
07
- 01
- 02
- 12
- 13
- 03
19
-

15
16
06
13
11
02
02
03
08

-

21
02
- 00
05
- 13
- 14
- 03
10

-

10
28
01
11
09
01
07
05
12

- 09
03
02
09
04
01
- 05
- 06

- 00
03
- 17
- 06
02
05
- 02
- 13

-

-

-

- 24
- 13
02
04
- 05
- 07
- 06
04

20
10
01
00
13
14
- 01
- 03

-

-

-

-

-

01
08
08
08
09
07
10
00
38

-

-

16
04
04
02
02
17
07
03
17

06
08
06
08
02
42
05
- 03

-

05
04
08
09
04
06
03
- 01

11
07
02
- 10
- 13
- 06
05
11

40
01
05
05
00
05
01
09

- 00
- 03
- 03
- 03
- 01
- 00
03
13

01
06
01
02
01
05
06
04

- 09
- 02
03
- 10
01
14
03
- 02

03
05
- 01
- 01
- 01
- 01
- 03
- 03
01

02
04
02
- 10
- 07
00
- 04
- 02
15

-

00
02
01
07
04
03
01
03
16

- 02
- 06
- 10
04
- 02
- 02
08
07
03

03
02
03
01
03
02
00
- 07

- 02
- 04
01
- 07
- 06
- 03
- 05
01

-

-

-

-

-

11
00
02
04
- 11
- 08
03
- 00

10
03
39
07
04
06
10
08
04

05
02
18
11
05
- 01
- 11
- 14
03

02
07
03
02
02
- 06
- 07
- 13
05

- 02
- 15
- 06
- 01
20
08
09
01

02
02
00
- 03
- 05
00
01
10

08
15
16
02
'6
11
02
02

-

01
11
29
01
14
07
03
11

08
02
05
14
- 00
- 09
00
- 07

-

11
16
02
- 04
00
- 03
- 05
01

07
06
02
00
02
04
02
02

01
- 05
- 03
- 07
- 08
01
- 05
- 04

- 02
- 01
- 02
- 04
03
05
09
00
- 04

- 05
- 02
- 07
03
20
02
01
- 03
- OS

-

05
01
05
01
10
- 04
- 01
02
- OS

-

06
02
18
04
OS
01
06
03
01

- 01
05
12
04
- 03
03
- 10
- 12
- 02

12
08
00
03
03
06
00
04
02

-

-

04
01

04
04
08
06
03
05
02
04

-

09

-

-

-

03
02
02
00
03
08
02
- 03

-

-

-

-

-

-

SEW residuals
113253749617385-

12
24
36
48
60
72
84
96

02
04
02
02
08
07
02
01

-

-

97-108
109-120
121-132
133-144
145-156
157-168
169-180
181-192
193-204

06
17
- 04
- 02
- 01
- OS
- 06
01
- 03

205-216
217-228
229-240
241-252
253-264
265-276
277-288
289-300

01
14
04
03
05
07
04
01

-

73
OS
04
03
04
05
06
03

24
04
- 01
- 02
05
- 04
03
- 03

-

02
00
01
02
04
03
01
03

- 03
- OS
- 00
06
02
- 02
01
- 01

09
01
09
03
01
- 00
01
- 02
- 02

- 06
00
08
06
02
- 00
01
- 01
- 03

02
- 03
- 07
- 04
- 04
02
- 00
02
03

01
03
07
01
02
02
02
04
01

-

-

02
- 03
- 02
02
- 02
- 05
- 07
02

01
02
04
01
- 02
- 07
- 03
02

-

-

06
12
03
04
04
04
06
01

-

-

01
04
04
06
09
02
02
08

-

-

-

03
02
01
03
06
04
12
- 00

-

04
22
09
02
- 05

-

-

01
10
08
03
00
09
07
02

OS
05
05
04
22
01
03
01

-

-

-

-

04
05
19
04
05
01
OS
09

-

02
07
09

04
- 06
- 00
- 08
- 09

SQW residuals
113253749617385-

12
24
36
48
60
72
84
96

97-108
109-120
121-132
133-144
145-156
157-168
169-180
181-192
193-204
205-216
217-228
229-240
241-252
253-264
265-276
277-288
289-300


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

-

-

03
05
04
01
03
- 03
04
01

-

- 01
02
01
03
05
03
07
- 04

-

-

-

00
08
02
06
00
01
00
02

03
01
07
04
- 00
00
03
OS
01

-

02
02
02
04
- 04
- OS
- 03
01
-

- 02
- 08
- 01
01
- 01
03
00
02

06
03
- 01
02
02
- 02
- 02
- 00

-

06
01
01
00
- 03
02
05
- 02

01
- 01
01
- 02
03
- 04
- 05
02

-

-

03
OS
02
01
02
01
03
06
02

01
08
03
- 04
- 06
- 01
04
07
02

-

01
09
06
06
07
02
03
06
00

02
08
04
- OS
- 02
- 02
00
03
- 02

-

04
- 00
- 02
08
11
02
05
- 02

- 04
- 01
06
03
- 16
- 01
- 03
02

03
01
- 06
00
- 13
04
01
- 02

- 02
01
04
01
04
- 02
- 01
- 01

01
- 04
- 04
01
02
- 01
01
04

-

-

-

-

01
06
01
02
04
00
04
03
03

04
01
02
02
04
- 09
02
05

05
05
03
00
05
08
- 04
- 08

-

00
07
00
03
01
03
06
08
02

01
00
01
02
04
03
- 07
- 07
- 02

-

01
05
05
04
- 02
02
01
- 02

- 04
- 05
- 03
05
01
- 02
- 03
- 04

Transitory Variations

in

the Monetary Aggregates

TABLE 7 Differences JD Day-of-Week Effects JD the
ANOVA Model for Demand Deposits
Days

Difference
95
-1 31
04
34
- 02

Thursday, Fnday
Fnday, Monday
Monday, Tuesday
Tuesday, Wednesday
Wednesday, Thursday

cant 30 But 1f our assessment 1s correct, on
average the Monday holiday residuals should
be approximately equal to the difference between the Friday day-of-week effect and the
Monday day-of-week effect, which 1s -1 31
per cent (Table 7) The data are thus remarkably consistent with our hypothesis 31 Table
7 also md1cates why the holiday problem 1s
essentially a problem only for Monday hobdays Most of the other differences are small,
and the only possible competitor, Friday, 1s a
day with a relatively small number of holidays m most years This mterpretat10n 1s also
supported by an outlier analysis of those holidays that were switched to Mondays by an
act of the Congress George Washmgton's
Birthday, for example, did not contam persistent residual outliers until 1971, when It
became tied to Monday
Fortunately, this m1sspec1ficat1on m the dayof-week effect 1s rather small For example, 1f
the Monday-holiday residuals were dropped
from the sample, the over-all AN OVA standard
error would fall only from O7116 to O6966

Estimates based on the OSD model
The model for optimal statistical decompos1t10n (OSD) discussed earher is apphed m
this paper only to weekly (7-day average) data
on the demand deposit component of M 1 over
a 215-week sample period from November 24,
1971, to December 31, 1975 32 The logarithm
30

13

of the series, say z1, appears to be nonstat10nary and a stationary series has the form
Zt = (1 - B52) (1 - B13)y,

(23)

= Yi

S,(B)

=

1

-1 30 =

u,!v'n

-1 30
= -9 84
111G/y29

31 S1m1lar results were obtamed for the SEW and
SQW models
32 In subsequent work we shall apply this technique
to all aggregates at a daily level For a fuller descn ptlon than that presented here, see Maravall "Estima-

tion"


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

Y1-1a -

Y1-02

+ Y1-6s

+ B + B2 +
+Erl= 1 - Bi
1 - B

then
z1

=

(1 - B) 2Sia(B)Ssz(B)y,

=

D(B)y1

and 1t follows that z1 may be thought of as
bemg generated m the followmg way First,
pass the logarithm of the aggregate through
two successive annual and qu<1rterly smoothmg filters, Sni(B) and S13 (B), and then take
second differences of the smoothed series Consequently, the stat10nary quantity, z1, represents the acceleration (difference m the rate
of growth) of a highly smoothed aggregate In
Appendix 2, 1t 1s explamed how Equation 7,
together with
(24)

01

(25)

Ot

(26)

Zt

=
=
=

D(B)r, 1
(/101-i

Ot

+ E~

+ Ct

(where e 1 = D(B)e1), 1s a reasonable first approximation to the data Equation 25 md1cates that the systematic trend component 1s,
after d1fferencmg and smoothmg, a first-order
autoregressive process
Usmg a quas1-max1mum-hkehhood techmque an iterative algorithm was devised to
estimate Equations 24 to 26 33 The estimates
obtamed by this procedure are
fp

=

The appropriate test statistic 1s

t =

-

that 1s, both quarterly and annual d1fferencmg of the data are req mred to achieve
stationarity
Lettmg

89,

u?, = 226 X 10-4
u? = 561 X 10- 5

If the daily transitory errors are serially mdependent, the daily standard error associated
with this weekly value of u; 1s

v' 561
33

X 10-5 X

v'7 =

Ibid, pp 12-16, for further details

006267

Improving the Monetary Aggregates Staff Papers

14

This calculat10n assumes the errors have the
same variance m each day Alternatively, one
may wish to assume that the error on Saturday and Sunday 1s essentially that of Fnday,
which implies that the dally standard deviation of demand deposits 1s

V 561

X 10- 5 X

y'49/13 = 004598

or 1t can be assumed that the error on Sundays
is equal to that of Saturdays, which implies
that the daily standard error 1s34

V 561

X 10- 5 X

y49/9 = 005527

Thus, the implied standard deviation for daily
demand deposits runs from about O 46 per
cent to O 63 per cent dependmg on the treatment of weekend observat10ns This range of
values 1s below the ANOVA estimate of 071
per cent but mcludes the SEW estimate of
0 55 per cent
Stnctly speakmg, the use of weekly-average
data to implement the OSD model is not appropnate That model applies only to data sampled once m some mterval, not to the average
of successive sampled values, and 1t applies
stnctly only to stattona1y senes It follows that
we cannot mvoke the aggregat10n-contmmty
mterpretation of that section to Justify the
empmcal specification of Equation 7 and Equat10ns 24 to 26 However, there 1s an alternative
way of completmg the model that has a legit!
mate basis
To brmg out the essential ideas m this
alternative approach, let us temporanly s1m
phfy the problem and suppose that et m
Equation 26 1s a wh1te-no1se process To recap the model, then, we observe z 1
(27)
and have decided on the basis of empmcal
evidence that z 1 1s generated by an ARMA
model of order (1,1)
(28)

Zt

=

<,?Zt-1

+

a1 -

Oa1-1

where at 1s a wlute-no1se process There are
two possible models for the signal Bt that
34 The relationship between weekly and daily stand
ard errors will be discussed m more detail later


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

are consistent with the over-all model for Zt
m Equation 28 Either Bt 1s a pure autoregress1 ve process,
(29a)
or Bt 1s also an ARMA model of order (1,1), 35
(29b)
If daily data were bemg used, we could adopt
Equation 29a on the basis of the results above
With weekly-average data, however, there 1s no
reason to re1ect the less restnct1ve spec1ficat10n
Equation 29b, which 1s still consistent with the
over-all observed model for Zt But there 1s a
catch m this alternative spec1ficat1on The
model cons1stmg of Equations 27 and 29b 1s
not identified m the econometnc sense To
identify the model, add1t10nal restnct10ns on
the parameters must be imposed One useful
restncuon 1s to set 0 = -1 m Equat10n 29b
Tlus choice 1s optimal 1f one does not wish to
understate the impact of the transitory vanatlons, or, eqmvalently, 1f one wants to mm1m1ze the contnbuuon of the systematic vanat10n to the over-all observed vanat10n 36
35 Stnct notJ.tlon l\ould 1equne that \\e d1~tmgmsh
bet\\een the white noise errors m Equations 29a and
29b Also, Equation 29a 1s a special c.a,e of Equation
29b ,\hen 8 0 Neverthdess, 1t 1s meful to cons1de1
these as d1~tmct model~ became they d1fft.r m the
number of parameters
36 To ~ee this exphc1tly, observe that

=

(A)
(B)

u;

2
= -y,(O) = ( 1 +1 0_

-

2,pO) u~, -I u;

<p 2

- (1 - ,pO)(,p - 0)
')', (1) 1 - <p2

2

"•'

(See Box and Jenkms, Time ~eries Analysts, Equation
3 4 7) Thus, max1m1zmg u; given y,(O) and 'Y,(l) and <p
(which 1s identified) 1s eqmvalent to mm1mmng
(C)

1 + 02 - 2,pO ]
[ (1 - ,pO) ( 'P - 0) -y,(l)

\\Ith respect to 8 D1fferent1atmg Equation C with
respect to 8 and setting the derivative equal to zero,
1t can be shown that 8 -1 gives the mm1mum
value for ui, or maximum value for a;, given 'Y,(l)
and q:,
The idea of closmg the model m this \\ay was taken
from t\\O papers, David A Pierce, "Seasonal Adjust
mcnt When Both Determ1mst1c and Stocha~tlc Sea
,onahty Are Present," and George E P Box, Stephen
Hilmer, and George C T1ao, "Analy~1s and Modehng
of Seasonal Time Senes," prcscntul at the Nat10nal

=

Transitory Variations in the Monetary Aggregates

Returmng to the more general specificatton
m which e 1 = D(B)Et, a similar analysis shows
that the maximum value for the transitory
variance, ut consistent with the observattons
on z1 is also achieved where 0 = - I m Equation 29b And 1t can also be shown that the
maximum transitory variance, say, u; (max)
and u; m the (1,0) ARMA specification (29:-),
are related by the equation

2(

(30)

) _

2+

u. max - u,

(l

25u;,

+

q, 2)

15

TABLE 8 Standard errors for OSD and Alternative
Methods
Per cent of the level of demand deposits
Transitory
standard

Conversion factor

error

-v'7

u;

(max)

= 561 X 10- 5

6267

4598

5527

5485
SEW

4166
SQW

5485
SEW

7095

5206

6257

7116
ANOVA

5485
SEW

5485
SEW

OSD estimate
Nearest altemat1vc
estimate

Estimate
Method

u, (max)
OSD estimate
Nearest alternative

Estimate
Method

7192 X 10- 5 X y7 = 007095

transitory variances m currency and demand
deposits, and the covariance between the
transitory components of demand deposlts and
currency
The separate sources of tl J.nsitory VJ.nations
m an aggregate are assigned m the followmg
way Let Y 1 be an aggregate that is equal to
the sum of m component aggregates Y ,t,

7192 X 10-5 X ~

(31)

+

25 X 226 X 10- 4
(1 89) 2

=

7192 X 10_ 5

= (2 682 X 10-3) 2
The alternative daily standard deviations are
then

y
y
y

V49/9

I

u,

estunate

Substitutmg mto Equat10n 30 the estimated
values for rp, u;,, and u;, we find that

y49/13

I

7192 X 10- X
5

v49/9

=

005206

= 006257

Thus, dependmg on the assumptions made
concernmg transitory errors on the weekends,
values of the daily transitory standard error
can be found that are very close to one of the
three predetermmed trend weights Table 8
provides a summary of correspondmg values

Sources of transitory variations
in the aggregates
Transitory variations for any aggregate that
1s the sum of various components may be expressed as a weighted average of the var1at10ns
m the component parts and the covariance
terms between the transitory parts of each of
the components Thus, the transitory variance
m M 1 1s equal to a weighted average of the
Bureau of Economic Research-Census Conference on
Seasonal Analysis of Economic Time Series, Washmgton, DC, September 9-10, 1976, m these papers s1m1lar restrictions were imposed on seasonal adjustment
filters


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

Yi= ~Y,1
i=I

Recalling that
Yi

= In

(Yi)

=

'111

+

f31

+

Et

=

/1

+

Et

it follows that
Yi

= exp (/1) exp (Ei)

Because Et 1s generally very small (for example, the standard error of Et for demand
deposits is about 005), the first-order approximation
(32)

exp (1:1)

= 1

+

Ei

is an identity for all practical purposes 37
Thus, from Equation 32
(33)

Yi

::l::

exp (Ji)(1

+

Ei)

= Fi +

Ei

= exp (Ji), Ei = Yi - Fi ::l:: E,Fi
Equation 34, 1f Et = 005, the error m

(34)

Fi

In
the
approximation amounts to about 3¾ millions
37 This approximation 1s almost as accurate as that
hsted m Table A-1 m Appendix I

Improvmg the Monetary Aggregates Staff Papers

16

for an aggregate totalmg 300 billion Note
also that

(35)
where the second approx1mat10n 1s also highly
accurate (see Appendix I)
Returnmg to Equation 31, 1t 1s desired to
assess the contribution of the transitory variation m each component aggregate, Y,t, to that
of Yt itself Note that the 1elat10ns analogous to Equations 32 to 35 hold for eacl1 component aggregate, for example,
Y,1
E,t

=

= Y,t

F,t
-

+
f,t

E,1

=

Ey,t
,t

Thus, we have

(36)

=

In

(1 + !:)

(37 ) = Et = Et = ~ E,t = ~ Y,t
Fe
Ye
,=I Ye
,=I Ye

E,t

Y,e

where the approximations m Equation 37
follow from Equations 32 and 35 Lettmg
(38)

W,t

Y,t
= Yi

Equation 37 becomes

(39)
Assummg that the deposit shares are fixed, the
relative transitory variance of Yt 1s approximated by
m

(40)

m

m

o-; = ~
w!ut + ~ ~ w,w, cov(e,t, e,e)
i=-1
1=1
1c::1l

,;,,,

where cov(e,t, e1 t) denotes the covariance between the component transitory errors 38 This
38 The approximation error 1s potentially much
larger over longer time mtervals, but the emp1ncal
decompos1t1ons given later md1cate that 1t 1s generally
qmte small


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

expression md1cates that the over-all transitory
variance of an aggregate may be expressed
approximately as a weighted average of the
component variances and the covariance terms
Table 9 lists three decomposit10ns-f01
gross deposits less cash Items at member banks,
for Mi, and for Mi In each decompos1t1on,
the terms on the right-hand side of Equat10n
40 are listed separately as a percentage of the
over-all transitory variance All numbers are
based on the ANOV A estimates, though we
believe that the other methods would produce
very similar results 39 The discrepancy term
1s mtroduced to account for the error m Equation 40 that arises because the deposit shares
do not stay constant over the sample periods
and because Equation 40 1s an approximate
relation
For M 1 and M~ Table 9 shows that almost
all of the variat10n m both of these aggregates
1s due to the volatility m demand deposits
The contribut10ns of the variat1ons m currency and other time and savmgs deposits are
very small m relation to demand deposits, as
are the contribut1ons of the covariance terms
The other variance decomposition given 1s
that of gross deposits less cash Items at membe1 banks This aggregate was chosen because
a very high proportion of transactions mvolves
offsettmg changes m gross deposits and cash
Items For gross deposits less cash items, the
relative contribut1ons are somewhat more
equal, with demand deposits ad1usted and mterbank bank deposits accountmg for much
of the variation The direct effect of government deposits declined s1gmficantly by the
end of the sample period Though the share
of government deposits 1s qmte small-averagmg around 3 3 per cent of the level of gross
deposits less cash 1tems-1ts daily transitory
standard deviat10n was far larger than any
other aggregate, averagmg about 14 7 per cent
39 This belief follows from the empmcal result that
alternative methods give approximately the same relative rankmg of transitory standard deviations for different aggregates For example, the ratio of the transitory standard deviation of M 1 to that of M 2 was
about 2 for each method

Transitory Variations

in

the Monetary Aggregates

17

TABLE 9 Relative Contnbution to the Over-All Transitory Vanance of Selected Aggregates, 1968-74
In per cent
.Aggregate and source of vanauon
Gross deposits less cash items at member
banks
Demand deposits ad1usted (DDA)
Government (GOVn
Interbank (IB)
Covanance (DDA, GOVn
Covanance (DDA, IB)
Covanance (GOVT, IB)
Discrepancy
M1
Currency
Demand deposits
Covanance
Discrepancy

1968

1969

1970

1971

1972

66
99
23
-60
-9
3
-21

5
3
5
9
7
2
8

4
98
-3
-

47
6
01
07

3 2
98 0
-1 I
- 01

3 3
99 3
-2 S

4 8
96 6
-1 4

*

*

4
99
2
-3
-2
*

S
0
S
0
7
3

3
98
I
-1
-2
*

3
92
2
-2
3

74
72
34
-46
-16
-3
-14

0
9
0
6
0
8
6

76
56
58
-35
-43
2
-15

7
5
8
6
7
2
0

101
33
118
-II
-140
II
-II

8
9
0
8

73
37
86
-23
-58
-5
-9

4
0
0
2
I
7
4

S 8
99 4
-SI

.

1974

1968-74

-2 0

36 7
12 4
52 2
-69
-7 9
12 I
I 4

58
32
47
-17
-21
4
-4

3
0
8
3
0
3
1

S I
95 I
I
- 2

4 8
94 7
7
- 3

4
97
-1
-

3
4
6
2

5 4
101 8
7 1
1
-16 7
2 5
- 2

107 1
9 5
8
-25 8
3 0
- I

ss

4
98
4
-1
-7

3
I
7
6
0
7
8

1973

40
24
48
-13
2

*

7
3
I
I
0

M,

Currency (CUR)
Demand deposits (DD)
Other time and savmgs (OTS)
Covanance (DD, CUR)
Covanance (DD, OTS)
Covariance (CUR, OTS)
Discrepancy

2
7
S
1
9
5

1
5
3
3
S
8
2

4
95
4
-1
-4

7
6
6
4
7
7

s

6
103
4
-5
-9

0
9
S
4
7
5
1

*Negbg1ble
Norn -For each aggregate decompos1t1on, the weighted vanance
terms, w:u;,, are hsted as a per cent of the over.all transitory vanance

for that aggregate, that 1s, as 100 w1u;.fu; Beneath the variance
components are the relative covariance terms, 200 w,w; Cov(u,e,)/ul
The discrepancy 1s also expressed as a per cent of u;

of the level of government deposits over the
1968-74 sample period 40
From the M 1 and M 2 decompos1t1ons, it
appears that demand deposits are the maJor
source of transitory variation m these aggregates However, recent developments may alter
this pattern In particular, passbook savmgs accounts at commercial banks probably now
behave more hke demand deposit accounts m
the short-run payments mechamsm 41 These
developments appear to stem from several recent changes m bank regulations mcludmg
passbook savmgs accounts for corporat10ns and
State and local governments, telephomc transfers between passbook savmgs accounts and demand deposit accounts, and negotiable orders
of withdrawal (NOW) accounts As a result of
these changes, fluctuatmg payments between
the pubhc and commercial banks or between
the pubhc and the Treasury are more hkely to
mclude some very short-run variatton m aggregate passbook savmgs deposits at commercial

banks To mvestigate this possibility, we constructed ANOVA models of transitory variation for aggregate passbook savmgs accounts
at member banks over two periods, before the
mtroductlon of corporate passbook accounts
and after the mtroductlon of such accounts 42
The estimated standard error before the
change was O II I per cent of the level, tt
Jumped to O 160 per cent afte1 the change
m regulations regardmg corporate passbook
accounts The appropriate F-stat1st1c to test
the equality of the transitory variances m the
two periods is F(l27,1423) = 2 03 Thus, the
data mdicate a highly s1gmficant mcrease m
the transitory variance of passbook savmgs
accounts at member banks smce corporations
have become ehg1ble to hold passbook savmgs
accounts 43

40 Government deposits 1s the only aggregate we have
considered for which the approximation represented
by Equation 32 1s not highly accurate
41 See John D
Paulus and Stephen H Axilrod,
"Regulatory Changes and Fmanc1al Innovations Affect
mg the Growth of the Monetary Aggregates," staff
memorandum (Board of Governors of the Federal Reserve System, November 1976)


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42 Corporations became eligible to hold such ac
counts on November 10, 1975, about a year later than
State and local governments The two penods used m
this paper were from 1969 through the statement week
endmg on November 5, 1975, and from the statement
week begmnmg on November 13, 1975, to June 30,
1976
43 The data also md1cate that the change did not
occur much earlier If the m1t1al ANOVA estimates
are derived from the begmmng of 1974 to November
5, 1975, the resultmg standard error 1s only slightly
larger, 112 mstead of 111 The associated F-statlstlcF(l27,379) 1 94-is also highly s1gmficant

=

18

Improving the Monetary Aggregates Staff Papers

Transitory variations in averages
of daily data
To examme transitory vanauons m mtervals longer than a day, one must mvest1gate
transitory variances of sums or an thmeuc
means of aggregates Let Y: be the anthmeuc
mean of n successive daily observations for
which u, 1s the daily transitory standard deviation of the natural log of Y t measured
daily (The subscripts mdexes the n-day period
contrasted with t, which denotes the daily mdex)
As before, 1t 1s assumed that the trans1 tory
errors m the daily aggregates are stat1st1cally
mdependent of the systematic movements
This mdependence 1mphes that the Federal
Reserve does not mtervene and does not alter
the systematic trend m the aggregates to offset
5ome or all of the accumulated transitory vanattons that occur Estimates of the impact of
transitory variations on monthly and quarterly
growth rates, which will be considered below,
are sufficiently small so that this mdependence
assumption 15 unlikely to be violated m most
penods
If the errors, Et, are serially mdependent, it
1s natural to assume that the relative transitory standard deviation for Y: 1s44
(41)

.✓,i

In fact, a more appropnate formula 1s
(42)
where Vn is the coefficient of vanauon fo1 the
systematic part of Y: over the period s 45
If, mstead of the anthmeuc mean, the geometnc mean were used, then the simpler Expression 41 for the transitory standard devia44 Throughout this section, the standard deviation
of a daily aggregate will be expressed relative to the
level of that aggregate (expressed either as a pe1cent
age or 1/100 of a per cent)
<5 The matter 1s complicated owmg to the nonstatlonanty of the systematic part of Yi, generally,
the current "level" of the series 1s substituted for the
nonexistent population mean m V n


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uon would be appropriate Because Expression 41 1s always smaller than Expression 42,
the geometric mean will have a uniformly
lower transitory standard deviation than the
anthmetic mean It follows that the rate of
growth of an aggregate formed by takmg the
geometric mean of daily observations will
have a lower observed transitory variance than
will a daily-average aggregate Empmcal calculations confirm this result However, the differences between the estimated vanances are
extraordmanly small and have no practical
s1gmficance (They are nearly equal because
rates of change m the aggregates-at least for
daily, weekly, monthly, or quarterly dataare gene1ally so small that anthmetic and
geometnc means will be very close to each
other as will their trans1 tory variances ) A related empirical calculation mdicates that the
term Vn m Expression 42 is very small so that
Expressions 41 and 42 are practically equal
Accordmgly, we will adopt the simpler expression, u,/Vn, to represent the relative standard
deviation of a daily average of n observations

Serial correlation in the residuals
If the transitory errors are sen ally conelated, then the autocorrelations must be taken
mto account when computmg the standard
deviation of the daily averages Because the
large autocorrelations m the estimated models
tend to be positive, the imphed reduction m
the standard deviation-from u, daily to
u,/Vn for Y,:'-is probably too large 46 On
the other hand, 1f one were to model the
residuals from the ANOVA, SEW, or SQW
model as a stationary stochastic process, the
resultmg estimates of the transitory standard
deviation would be lower This is true because
there would be useful mformation m the
model residuals about future "transitory" residuals and the fundamental uncertamty
about the true transitory component would
1G

The actual standard deviation 1s a, V k/n, where
n-1

k

= 1 +2 I: (1 -1/n)p,
,-1

and p1 1s the autocorrelation of lag J

Transitory Variations

in

the Monetary Aggregates

actually be less Models with a large degree of
senal correlation m the transitory component
(estimated residuals) seem to behe the notion
of "transitormess" and redomg these models by
mcorporatmg a time senes model to explam
the senally correlated residuals would lower
the standard error 47 Thus, it seems reasonable
to regard the estimate u,/yn as an upper
bound for the underlymg transitory standard
deviation of Y: and to expect the bound to be
closer to the correct standard deviation for
models and aggregates havmg a smaller
amount of autocorrelation m the residuals

From daily to weekly estimates
By excludmg weekends it is a straightforward matter to go from estimates of daily
standard errors to monthly or quarterly estimates However, because alternative values
for the weekend effects will be considered, it
is convement to work with an aggregate Y:
m mtervals of n/7 weeks
Let u. be the daily standard deviation and
assume that the transitory components are mdependent from day to day If the weekly
average is an average of seven mdependent
daily figures, the implied standard deviation
m the weekly figures is, m accordance with
Expression 41,
(43)

u,/v?

=

378u,

This estimate treats the transitory component
on weekends as bemg fully eqmvalent to the
component on weekdays But banks are closed
on Sundays, makmg the Saturday observation
1dent1cal with Sunday's Thus, whatever transitory part exists m the Saturday observation
1s also present m the Sunday observation
When 1t 1s assumed that the Saturday transitory
component counts twice, the weekly transitory
standard deviation becomes
(44)

✓ (1 + 1 + 1
=

~2

1

+ 1 I+ 22)

~=

(Ti

3/7u. = 429u.

That 1s, the residuals from the times senes model
would have a lower standard deviation
47


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Federal Reserve Bank of St. Louis

19

If the Fnday transitory component remams
m both weekend observations and 1£ 1t 1s
assumed that there 1s no mdependent source
of transitory vanation on Saturday itself, then
the Fnday transitory component counts three
times m computmg the transitory standard
deviation for the weekly observation 48 Under
this assumption the 1mphed weekly trc1ns1tory
standard deviation 1s
(45)

✓ (1

+ 1 + 1 + 1 + 3 )u;
2

72

/13 2
- '\J49 u,

515u,

The correct weekly deflatmg factor 1s probably much closer to Equation 45 than to
Equation 44 A convement compromise figure
1s to assume that
(46)

<Tw

=

u,/2

1s the weekly standard deviation for c1 dally
aggregate

I ntraweekly heteroskedasticity
All of the foregomg blow-up factors fall to
account for the mtraweekly vanation (heteroskedast1oty) m the estimated standard deviations As noted above, Fnday estimates are
weighted more heavily than those of other
weekdays m denvmg weekly standard deviations Because of the apparent difference between the standard deviation for Fndays and
the over-all standard deviation, it 1s useful to
consider the modifications that occur by takmg
these differences mto account Instead of
Equation 45, the appropnate substitute for
the weekly standard deviation 1s
(47)

(ti <Ti, + 9<Ti5)

112

where J = 1 denotes Monday, J
and so forth

/

=

7
2, Tuesday,

From weekly to longer intervals
To go from weekly standard deviations to
monthly, quarterly, or other standard dt:v148 The Advisory Committee on Monetary Statistics
adopted this assumption m Its report, Improving the
Monetary Aggregates Report, p 28

20

Improvmg the Monetary Aggregates Staff Papers

auons, one must, essentially, count the number of weeks m the ume mterval 49 Consider
an "average" month m a 365-day year, which is
viewed as havmg 28 cl.i.ys with prob.i.bihty
l/12, 30 clays with probability 4/12, and 31
clays with probability 7/12 For tlus aver.i.ge
month the transitory variance, CT~" is
2

(48)

CT;,

;; [7/28

+

+

4(7/30)

(54)

where CT~ 1s the weekly transitory standard
deviation In view of Equ.i.uon 46, the monthly
transitory standard deviauon is
Um

=

(½)

35987'
156240 u, = 240 u,

Similar expressions exist for 2-month averages
(2m), qu.i.iterly averages (q), semiannual .i.ver,tges (sa), and annual averages (a)

(SO)

U2m

uU(7/59)

=

+

2(7/62)
12

=

+

9(7/61)1

1694CT, =

= 1385u, =
(52)

Usa

=

uM(7 /181)

+ (7 /183) + (7 /184) +

Um

V2

Um

0

(7 /182)]

4

0979CT, =
(53)

Ua

=

~=

0692u. ==

n·

7(7/31)]

- 35987 2
- 156240 u,,,

(49)

an n-day average Notice that In (1 + g;')
= In (Y!') - In (Y;'_ 1) = g~' Hence g!,' has
approximately the same transitory variance as
In (Y:') - In (Yf-i) But the relative transitory
variance of
is identical to that of In (n')
Accordmgly, the variance of g!,' is

CTm
v6

02

assummg that the averages Y:,i and Y!,'_i are
uncorrelated Given the special treatment of
weekend observations this result can be expressed for the growth rates of designated
averages

v"M

(55)

Ug(m)

(56)

u g(q)

(57)

Ug(2ni)

= ~ = 2396CT,

(58)

Ug(sa)

= ~ = 1385u,

(59)

Ug(a)

=

=

= 3394CT,

~ = 1959u,

vrz;I

= 0979u,

where g( ) denotes the gi owth i .i.te ot the
,tver.i.ge withm the p.i.rentheses
By convenuon monthly growth rates foi the
monet.i.1y aggregates ,Lt the Federal Reserve
Board are put .i.t .i.nnual percent.i.ge rates of
change by multiplymg the simple monthly
growth g(m) by 1,200, for quaiterly giowth
rates the corresponding factor is 400, and so
forth for other statistics Because the standard
devi.i.uons for the transitory components are
expressed as a pe1 cent of the level to obtam
the standard deviation for the transitory component of an "annualized" growth rate, each
of the expressions 55 through 59 should be
multiplied by an annuahzmg factor 12 for
monthly averages, 4 for quarterly averages, and
so forth

Growth rates
Let g!' = (Y!' - Y!'-i)/Y!'-i be the growth
rate at time s for an aggregate Y measured as

Interval estimators for the systematic
component of an aggregate

4 9 It also matters how many Fridays arc m, say, a
month and the configuration of weekends wllhm the
month However, these aspects will be ignored m the
d1scuss1on that follows as they tend to average out
over time

Let Za; 2 be the pomt on a standardized
(mean= 0, variance= 1) normal distribution
such that the probability that a standardized
normal random variable exceeds Za; 2 is a/2


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Federal Reserve Bank of St. Louis

Transitory Variations in the Monetary Aggregates

Then with confidence coefficient I - a, the
interval

12g(m) ± 12Za/20"g(m)
is a 100(1 - a) per cent confidence interval
for the systematic part of an annualized
monthly growth rate 50 If a = 0 05, z1112 = 1 96,
the 95 per cent confidence interval is

±
12g(m) ±
12g(m)

(60)

12(1 96u 0 cmJ) or
7 983u.

in view of Expression 55
To illustrate these calculations let us take
the SEW estimate of the daily transitory
standard deviation for M 1 of 0 4137 per cent
for the 1968-74 period (Table 2) The imphed
confidence interval is

12g(m)

±

(7 983)( 4137)

= 12g(m) ±

3 3 per cent

Table IO presents the relevant information
for constructmg confidence-mterval estimates
for two aggregates (M 1 and M 2 ), three methods (ANOVA, SEW, and SQW), and five confidence coefficients (50, 80, 90, 95, and 99 per
cent) These estimates are based on the overall standard errors for each model for the
1968-74 sample period The table shows that
if, for example, the measured monthly average
growth rate were 8 per cent, the 95 per cent
mterval estimate for the systematic growth
rate m M 1 would range from 4 7 per cent to
11 3 per cent based on the SEW method
The label "2-month-A" refers to growth
rates computed by using Equatron 50 while the
label "2-month-B" refers to the 2-month
growth rates considered m certam short-run
pohcy specifications of the aggregates 51 The
growth rates for 2-month-B are computed by
takmg 6(Ym - Y8 _ 1 )/Y8 _ 1 , wheres denotes the
current month when the specrfications are
chosen, for example, m September the growth
5o On average, 100(1 - a) per cent of the mtervals
computed m this fashion will contam the underlymg
systematic growth rate
51 See "Numerical Spec1ficat1ons of Fmanc1al Van
ables and Their Role m Monetary Policy," Federal
Reserve Bulletin, vol 60 (May 1974), pp 333-37


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Federal Reserve Bank of St. Louis

21

rate for the September-October period is
chosen based on the October average relative
to the August average Panel B displays comparable mformation usmg the alternative
heteroskedastic formula, Equatron 47 The
entries m Panel B are generally slightly smaller
than those m Panel A

User-specified time intervals
Consider Y: for various n The larger n
rs, the smaller will be the transitory standard
deviation of Y: How large must n be so that
the (1 - a)IO0 per cent confidence mterval for
an n-day growth rate will have a predetermmed length r~ For example, suppose we wish
to determme for the ANOVA estimate of M 1
the appropriate n, such that 95 per cent of obse1 ved growth rates will be withm 1 per cent of
the systematic growth rates In general, we have
(61)

4 112
) (~) Za/ 2

(3~ )(1n
5

= ;

and wish to determine n, given rr., a, and r
For the present example, r = 2, z111 ~ = I 96,
rr. = 5614, so from Equation 61

ny'n = 365

V14 ( 5~14)

1 96

which yields
n

= 82 64

For this example, then, g10wth rates based on
83-day averages will have the desired property
of bemg w1thm I per cent of the systematic
growth rate m 19 out of 20 "tnals"

Effects of seasonal ad1ustment
on estimates of transitory variations
A rather thorny problem m the assessment
of transitory vanat10ns, which rs not considered either m the report of the Advisory
Committee on Monetary Statistics or thus far
m this paper, is the effect on transitory variations of seasonal adjustment of the data The
seasonal adJustment process itself may change
the extent of transitory vanations (and may
change rt differently m prehmmary and m final

Improvmg the Monetary Aggregates· Staff Papers

22

TABLE 10• lmphed Variation m Monetary Growth Rates Due to Transitory Fluctuations
In percentage potnts
Growth-rate
Interval
and method

M1

Monthly
ANOVA
SEW
SQW
Quarterly
ANOVA
SEW
SQW
2month-A
ANOVA
SEW
SQW
2month-B
ANOVA
SEW
SQW
Semiannual
ANOVA
SEW
SQW
Annual
ANOVA
SEW
SQW

Confidence coefficient, per cent

One standard
devtatlon
I

M,

so
M1

I

M,

I
I

80
M,

I

90

I

M,

I

M,

I

I

l

95

I

M,

M,

I

M,

I

99
M,

I

M,

A Estimates based on alternative over-all standard deviations
2 29
I 69
I 27

I 15
83
62

44
32
24

22
16
12

30
22
16

81
60
45

41
29
22

I 14
84

I 5
I I
8

8
6
4
15

3 0
2 2
I 6

3 8
2 8
2 I

I 9
I 4
I 0

4 S
3 3
2 5

2 3
I 6
I 2

5 9
4 4
3 3

3 0
2 I
I 6

28
21
15

7
5
4

4
3
2

9
6

s

4
3
2

I I
8
6

6
4
3

s

7

I 6
I 2
9

8
6
4

2 I
I 5
I 2

I 0
8
6

2 2

I I
8
6

3 0
2 2
I 6

I 5
Io
8

I S
I I
8

08

II

6
4
3

4
3

27
20
IS

I 0
8
6

4
3

I 3
I 0
7

4

58
42
31

8
6
4

38
28
21

I S
I I
8

8
6
4

I 9
I 4
I 0

I o
7
6

II

10
08
06

05
04
03

20
15

09

08
06
04

II

10
07
05

26
19
14

II

08

30
22
17

II

08

40
30
22

20
15
II

055
040
030

028
020
01S

04
03
02

02
013
010

07
05
04

04
026
019

09
07
05

046
033
024

II
08
06

054
039
029

14
10
08

07
052
038

64

16

s

s

13

I 6

I 2

15

B Est,mates based on heteroskedast,c model of mtraweeklv standard dev,atlons
Monthly
ANOVA
SEW
SQW
Quarterly
ANOVA
SEW
SQW
2-month-A
ANOVA
SEW
SQW
2-month-B
ANOVA
SEW
SQW
Semiannual
ANOVA
SEW
SQW
Annual
ANOVA
SEW
SQW

2 I
I 5
I 3

I 0
8
6

I 4
I 0
8

7

s

4

2 6
2 0
I 6

I 3
I 0
8

3 4
2 S
2 I

I 7
I 3
I 0

40
29
24

20
15
12

27
20
16

14
10
08

SI
38
31

26
19
16

6S
48
40

33
24
20

73
54
45

37
27
22

49
36
30

2S
18
IS

93
69
57

47
35
29

I 2
89
74

61
45
37

5

70
50
40

35
25
20

6S
50
40

I 7
I 2
I 0

85
6S
50

I 0
75
6S

4
3

I 3
I 0
8

4 0
3 0
2 5

2 0
I 5
I 2

5 3
4 0
3 3

2 7
2 0
I 6

40
29
24

I 0
76
63

52
38
31

I 4
I I
9

73
53
44

I 9
I 4
I 2

96
70
58

2 0
I 5
I 2

I 0
15
60

2 6
2 0
I 6

78
58
48

I 4
I 0
8

14
10
08

07
05
04

09

07
06

05
04
03

18
13
11

09
07
06

23
17
14

12
08
07

27
20
17

14
10
08

36
27
22

18
13
II

07
05
03

036
026
022

05
035
020

024
018
014

09
07
04

046
033
028

12
08
OS

06
04
04

14
10
06

07
OS
04

18
13
08

09
07
06

Non - Entries define the range, plus or mmus, around the systematic growth rate withm which the specified percentage (SO, 80, 90, 95, or 99)
of observed growth rates will (on average) fall

data) Seasonal adjustment rs basically an ave1agmg or smoothmg process, and smce necessarily both the transitory and the systematic
components of the senes are smoothed, It rs
generally true that seasonally adjusted data on
the monetary aggregates exhibit fewer transitory vanations than do not seasonally adJusted
data
The magmtude of tlus effect depends heavily
on the seasonal adjustment procedure employed In general, seasonal factors that are


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relatively "fixed" are determmed from a relatively large amount of data, and the cur1ent observation carnes relatively less weight,
thus, the variance (whether trans1to1 y, nontransrtory, or total) is reduced correspondmgly less by the adjustment process By contrast, seasonal adjustment procedures such as
X-11 allow for a rapidly changmg seasonal
that must be estimated from a smaller amount
of data Thus, greater weight is given to the
clllrent observat10n and mo1e of the variance

Transitory Vanations in the Monetary Aggregates

(mcludmg transitory variance) 1s removed
from this observ<1t10n as a result of seasonal
adjustment 52
To illustrate, cons1de1 a "fixed" seasondl
est1m<1ted h om a movmg m-ye<1r regression
on sedsonal dumnues If y 11 1s the observat10n
from month J and yea1 t (assumed for s1mphc1ty to have a tero mean), the estimated
seasonal component for month J is
Y1

=

1
m

-

,n

~Yt1

t=I

and the seasonally adjusted v<1lue 1s
m - 1

= -m--Y11

1
m

~ y,.
,,.,1

with t1<1ns1tory vauance (dssummg 5tausucal
mdependence)

(m - 1)

2

+m-

m2

1

o-;=

( 1-1)
m

o-;

where a~ zs the transitory variance of not seasonally ,tdJusted y Thus, 1f m = (<1llowmg
tor a more rapidly chdngmg sedsondl), tr<1ns1to1 y Vdri<1ncc 1s 1educed through se<1son<1l <1d1ustment by 33 per cent, 11 m = !J, season,11
ad1ustment lowers the variance by 11 per cent
The effect of the X-11 procedure on t1,ms1tory variance would be expected to fall between these two, as 1t 1s based on a 7-year
dverage (though a weighted average, weightmg most heavily the current observauon), thus
the ti ans1tory standard deviation 1s reduced
by probably somethmg hke IO per cent 53
The fmegomg d1scuss10n concerm the effects
of final seasonal factors applied to final datd
52 An opposite effect should also be nottd The pie,
cnce of transitory error can increase the error 111 the
t.sUmated sedsonal factors, tending to produce a
'no1s1er' scdsonally adjusted senes When the sea~onal
pattern 1s relauvely fixed, this effect can offset much
of the smoothing effect discussed here
5 J The daily procedure developed by Pierce and
others m "Seasonal Adjustment of the Monetary Ag
gregates," this volume, and recommended by the Adv1s
ory Committee m Improving the Monetary Aggregates
Report, however, would have very little effect on transitory variance because a given daily observat10n contributes almost nothmg to its own seasonal component


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23

A separate effect stems from the 1ev1s10n of
prehmmary seasonal factors ,ts ,tclcht10n<1l datd
become available The first-published sedsonally adjusted 5eries 1s subject to two somces
of 1ev1s10n e1101-th,1t discussed ed1he1 £01
not season,1lly adjusted datd <1ncl, ,1dd1t1on<1lly,
th.tt due to 1ev1s10ns m 5e,1son,tl f.tcto1s Howe\-e1, even the fit st pubhshe<l 5e,tson.1lly <1dJ Usted d.tta will gene1,1lly h,t\-e sm.1llc1 t1<1ns1t01 y variance (,ts d15tmct horn the v.1u<1nce of
these 1ev1s10n e1101s) than the fost published
not 5eason<1lly ,tdJmted datd, ,15 the ,t\-eiagmg
cffec.t chscussed ,tbove for fin,tl d,tt.t 1s p1esent
wheneve1 ~e<1so1ul ,1d1ustment 15 unclertaken
It will be a1gued m the followmg 5ect10n
that the data rev1s1om that occm m not season,1lly ,tdJnsted d,1t,1 c,m 1e,150n,1bly be assumed to be st.1t1st1c<1lly mdependent of the
tr<1ns1tory v,mauons Th15 mdependence assumption 1s equdlly vahd for the seasonal
factm rev1s10ns 1f the 1ev1s10n method (conllasted with the adjusted data p1ocluced by
the method) 1s determmed mdependently of
the data bemg 1ev1sed-lor ex.tmple, a fixed
f.tcto1 01 1egiess10n method or X-11 with
unch,mgmg movmg ,1ve1 .tge weights Tlus assmnpuon could break down m situations
whe1e, fo1 ex.tmple, d sequence of J,11ge t1dns1tory 01 not seasonally ,telJusted 1ev1s10n errm s
produced seasonal-1rregul<1r 1.1t1os that would
c<1use a chfferent ll end-cycle cm ve to be selected, or altern,1t1vely, whe1e Judgmental review 1s a part of the 1-e.1sonal adjustment procedure 54

Summary and conclus1ons
We have ex<1mmecl four st<1t1st1cal models to
isolate the part of the Vdriauons m M 1 and M 2
and their components that anse from very
short-run transitory fluctuations On the basis
of these results, lt appea1s that the standard
deviation of the transitory component of daily
not seasonally adJmted M 1 1s m the neighbor54 "Seasonal irregular rauos" are defined as the rauo
of the not seasonally ad1usted series to the trend cycle
component, which for the multrpltcatrve seasonal ad1ustment procedures, 1s equal to the product of the seasonal
and trregular components

Improvmg the Monetary Aggregates Staff Papers

24

hood of ½ of I per cent, for M 2 1t 1s about ¼
of a per cent The SEW and SQW models produced somewhat lower estimates, while the
ANOVA estimates weie slightly higher 55 For
annualized monthly rates of growth, the ½ of
a per cent figure for M 1 1mphes that the 95 per
cent confidence-mtei val estimate of the growth
rate of the systematic component of M 1 1s equal
to the measured growth rate plus or mmus 4
percentage pomts, wlule for Mi 1t 1s equal to
the measured growth rate plus or mmus 2 peicentage pomts 56 Thus, on the average, about
95 per cent of all measured monthly growth
iates of M 1 will he withm 4 percentdge pomts
of the systematic component of M 1 , and about
5 per cent of all obse1 ved monthly growth rdtes
of M 1 will deviate by more than 4 percentdge
pomts from the systematic component of Mi,
due to day-to-ddy transitory fluctuat10ns F01
quarterly 1ates of growth, the 95 per cent confidence mterval mcludes the measured growth
rate plus or mmus ¾ of a percentdge pomt for
M 1 and plus or mums 1/s of a percentage pomt
for Mi Confidence-mterval estimates for other
agg1egates or estimates can readily be determmed from Equat10ns 43 through 59
As md1cated m the precedmg section, the
magmtude of the t1ans1tory vanat1ons m seasonally adjusted data depends on the method
of seasonal ddjustment The daily procedure of
5easonal adjustment recommended by the Advisory Committee would leave essentially the
same transitory effects m seasonally adjusted
senes that existed m the not sedsondlly adjusted
senes However, the effect of the X-11 seasonal
adjustment proceclme would be to reduce the
standard deviation of the transitory component
by about IO per cent for seasonally adjusted
data
In all hkehhood, there are several sources
of these transitory vanatlons, but we have
not tned to explam the transitory vanat1ons
55 These estimates are based on the 1968-74 sample
period and are hsted m Table I
56 For example, for M 1 the 4 per cent figure 1s ob
tamed by substituting ½ for u, mto Equation 55 and
then multlplymg by a factor of 12 to annualize and a
factor of I 96 to make a 95 per cent confidence interval
3394 X ½ X 12 X I 96 3 99


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=

m terms of an exphc1t economic model We
did, however, work out an emp1ncal decompos1uon of the variation m Mv M 2 , and gross
deposits less cash items For M 1 and M 2, the
hon's share of the observed transitory vandt10n stems from transitory vanat1ons m the
demand deposit component of M 1 There dre
also some signs that vanat10ns m passbook
savmgs accounts will account for more of the
transitory vanat10ns m M 2 as these deposits
become close1 substitutes for demand deposits

Joint effects of data revisions and
transitory variations in not
seasonally ad1usted data
This paper llds dealt ldl gel y with trans1 t01 y
vanauons m the not sedsonally adjusted monetary aggiegates that are m final (revised) f01m
For purposes of current andlys1s, there are add1t10nal sources of vanat10n owmg to rev1s10ns m
the data fiom the time they dre first published
to their appearance m final f01m We exdmme
here the rev1S1on m ~easondlly unadjusted cldta,
havmg cons1de1ed the effects of sedsonal ddjustment, mcludmg rev1s1ons m seasonal factors, m
the precedmg section
The "first-pubhshed" estimdte of the aggregates for each month 1s released about IO
cidys after the end of the month More complete mcommg weekly data from member
banks will often modify this first-published
number durmg the next month Add1t1onal
1ev1s10ns are made periodically when call report data for nonmember banks become available Irregular rev1S1ons aie made either when
1eportmg errors are uncovered or when a review of the construction of the money stock
leads to specific repairs m the senes-for example, the 1976 rev1s1on m the adjustment for
cash-items bias 57 Given the nature of these
rev1s10ns, It 1s plausible that the difference between the first-published not seasonally adjusted series and the final revised not seasonally
adjusted senes 1s stat1st1cally mdependent of
57 See Edward R Fry, Darwm L Beck, and Mary F
Weaver, "Rev1s10n of Money Stock Measures," Federal
Reserve Bulletin, vol 62 (February 1976), pp 82-87

Transitory Variations

in

the Monetary Aggregates

TABLE 11 Re,.Sion Errors m Monetary Aggregates,
Jfot Seasonally AdJusted
In annual percentage rates of growth
Monthly

Quarterly

Aggregate Standard
Mean
/
error RMSE error

5':~~'J

3 07

3 10

53

71

71

deposits
Mi

2 98
2 26
85

3 03
2 33
86

63
60
21

1 19
91
42

l 66
1 25
51

M,

/
/
/

~~~

rd
S~~r: RMSE

-

16
1 18
87
40

NoTE -Error equals difference between annual percentage rate of
growth of first-published estimate and final revised estimate (as of
December 1977) for 1968-74 penod RMSE denotes root mean
square error

the transitory vanat10ns If this 1s so, we can
combme the two parts-the vanations caused
by data rev1S1ons (other than seasonal-factor re'vlSlons) and the transitory vanat1ons m the
revised senes-to obtam an over-all estimate of
the noise m the current (first-pubhshed not seasonally adjusted) senes
The mean error, standard deviation, and
root mean square error of the rev1s10n errms
for M 1 , M 2, and their components are shown m
Table 11 58 Table 12 combmes the vanat1ons resultmg from the rev1S1on errors 1eported m
Table 11 with the vanations resultmg from
movements m the transitory component to
give an estimate of the over-all nmse m the
first-pubhshed senes For example, for monthly
rates of growth of M 1 the over-all standard
deviation of about 3 pe1 cent 1s determmed
from the equation 3 04 = y2 26 2 + 2 03 2 ,
based on a rev1s10n standard error of 2 26 per
cent and a transitory standard error of 2 03 per
cent 59 The 1mphed 95 per cent confidence58 These eslimates are comparable to those m Im
proving the Monetary Agg1egates Report, table 4, for
seasonally adJusted data
59203 = 12 X ½ X 3344

TABLE 12. Over-All Estimate of Error m Rate of
Growth Due to Both Rev1s1on and
Transitory Errors
Standard deY1at1ons of annual percentage rates of
growth, m percentage pomts
Aggregate
Currency
Demand deposits
Mt
M,


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Federal Reserve Bank of St. Louis

Monthly
growth rate
3
3
3
1

36
60
04
33

Quarterly
growth rate
1 06
1 25
99
46

25

mterval estimate of the systematic component
for first-pubhshed monthly growth rates of M 1
would, thus, be dehmited by ±5 96 percentage
pomts, the correspondmg figure for monthly
rates of growth of M 2 1s 2 60 percentage pomts
The comparable figures for the quarterly rates
of growth are considerably reduced, the 95 per
cent quarterly confidence mterval covers ± I 94
percentage pomts for M 1 and ±0 90 percentage pomt for M 2

Concluding observations
Undoubtedly, users of monetary statistics
should be aware of the transitory vanations
m the senes, and the estimates thdt we have
presented h1ghhght the range of magmtudes
mvolved However, these estimates represent
first eff01 ts, and there are several possible refinements
I Day-of-week effects There 1s some evidence that the day-of-week effects are not mvanant over time In particular, the Fnday
day-of-week effect for demand deposits generally fell over the sample penod And, when
the Fnclay residuals from the ANOVA method
were regressed on a short-term mterest rate
(the Federal funds rate or commerodl paper
rate), the regress10n coefficient was negative
and s1gmficant A similar regression for the
residuals from other clays md1cated no relat1onsh1p with mterest rates It 1s possible that
when mterest rates are nsmg, the use of bankmanaged demand accounts mcreases, and the
process has its largest daily impact on Fndays
because Fnday deposit figures essentially count
for 3 days m computmg reqmred reserves 60
The results were less clear-cut for the residuals
horn other methods, but it would be useful
to examme this phenomenon m more depth
2 Periodically correlated processes It has
been observed that the transitory vanab1hty
1s not constant across days of the week Yet,
for the most part, the detrended data have
60 See Stephen M Goldfeld, "The Case of the M1ssmg
Money," Brookings Papers on Economic Activity, 3 1976,
pp 683-730, and Raymond E Lomb1a and Herbe1t M
Kaufman, "Commercial Banks and the Federal Funds
Market Recent Development and Imphcatiom,' Eco
nomic Inquiry, vol 16 (October 1978), pp 549-62

26

been modeled as stationary series A mo1e appropriate techmque may be to assume that the
data are periodically correlated rather than
stationary 61
3 Width of the detrending interval For
the ANOVA, SEW, and SQW models 1t 1s
apparent that we have not selected the appropriate smoothmg mterval to determme the
trend The residuals from each of these models
were correlated at several lags, mcludmg fairly
long ones If the true trend at time t 1s a
function not only of the observations m the
"week" mcludmg t but also of more distant
observations, such as those a year apart from t,
1t 1s not surprismg that a m1sspec1ficat1on 1s mtroduced m the ANOVA, SEW, and SQW
models that produces the large autocorrelat10ns at annual lags, among others The results
from the exphnt ume-series modelmg exercises md1cate that the appropriate smoothmg
span to determme the trend 1s much longermore on the order of five quarters rather than
a week Thus, fixed-weight detrendmg methods with a much wider smoothmg mtervaland with weights that largely follow an mverted V pattern-could be exammed
4 Correlated transitory components The
transitory variations have been defined to be
mdependent from day to day However, It
r,1 See, for example, Wilham P Cleveland, "Analysis
and Forecasting of Seasonal Time Senes" (PhD chsser
tatlon, University of Wisconsin, 1972), Harry L Hurd,
"Survey on Periodically Correlated Proces5es" (paper
presented at the Multiple Time Senes and System Identification Confe1ence, Umve1s1ty of North Carolina at
Chapel Hill, January 2-6, 1973), Richard D Porter
and Paul N Rappaport, "Forecastmg Net Ba5in Sup
plies on the G1eat Lakes" (paper presented at the
TIMS Conferrnce, Houston, Texas, Apnl 1972), and
Howard E Thomp5on and George C Tiao, "Analym
of Telephone Data A Case Study of Forecasting Sea
sonal Time Senes," Bell Journal of Economics and
Management Science, vol 2 (Autumn 1971), pp 515-41


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Federal Reserve Bank of St. Louis

Improving the Monetary Aggregates Staff Papers

\

may not be desirable to 1mpose0trict serial
mdependence for the first two or three lags
A "bhp" m the daily data, which tak}l_a few
days to d1ss1pate, might with JUst1ficat1on~t1II
be regarded as "transitory " Hence, an exphc1t
times series model, m which there 1s a low-order\
movmg average process for the transitory com- ,
ponent combmed with a mixed (ARMA) model \
\
for the trend component, may be a useful
model to consider 62
5 Estimated data sources The daily series
on the monetary aggregates are based m part
on daily data reported by various financial
mst1tut1ons and m part on estnnates of components that are not reported dally 63 For
example, m December 1974 the estimated port10n of the daily series was nearly a third of
the total for the demand deposit component
ot M 1 Acrnrdmgly, changes m the reportmg
frequency of data that are not available daily
may hctve an impact on est1mcttes of transitory
va11at10ns m the aggregates The sIZe of the
impact would depend on the transitory variat10m of those data aml their wrrelat1on with
data that are now available daily 64 Also, there
<1.1e <1.lternat1ve ways of estlmatmg or mte1polatmg data that are 5ampled only l day
per week or more mfrequently, and m further
work It would be useful to examme the effects
that alternative mterpolat10n procedures have
on estimates of transitory variations

62 In general, the 1denuficauon of such models 1s
more difficult than that of models in nh1ch the tlan
s1tory component is independent See the references in
footnote 20
1,1 for ,1 breakdown of M I data 5ources and then
1epo1 tmg frequencies, sec Improvmg the Mone/my
Aggregates Report, table 3
G4 The new sample of nonmember bank data that
11as started in July 1977 may have a 51gmficant impact
on c5Umatc.s of transitory vanatlom in the aggregate5

\

27

Appendix 1: The Relationship between Et
and the Relative Transitory Error

Let

so that

(A-1)

/1

= /31 +

(A-6)

7/1

be the systematic part m logarithms) of Equat10n I
(page 3) and
(A-2)

F1

= exp (/1)

be the systematic part of the model m levels The
1mphed transitory error m dollars 1s

E, = Ye - Fe

(A-3)
where
(A-4)

E

Y,

= Et

upon droppmg second- and higher order terms m
the Taylor-senes expansion of exp(-Ei) Table A-1
shows that the accuracy of the approximation m
Equauon A 6 for values of Et less than or equal to
0 01 1s very good For example, for a 1 per cent
value of Et, Et= 01, the approx1mauon mtroduces
a discrepancy of only $15 mdhon when 1t 1s app1ed to a monetary aggregate of $300 bdhon
TABLE A-1 Discrepancy between •1 and Ei/Y,

Y1

= exp (y,) = exp (/, +

Ee)

.

(1)

1s the level of the aggregate (m dollars) Also, m
view of Equations A-4 and A-2
Y,

(A-5)

= F, exp (E1)

The relative transitory error, E 1/Yt, 1s
Ee= F1 exp (E1) - F1
Yt
F, exp (E1)


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Federal Reserve Bank of St. Louis

= 1 _ exp (-E,)

001
002
003
004
005
006
007
008
009
010

Et/Yt

D1screpancyt

(2)
000999
001998
002995
003992
004987
005982
006976
007968
008960
009950

(3)
I 45 X 10•
5 0 X 105
I 35 X 10•
240X10•
3 74 X 10•
539XIO•
7 33 X 106
9 37 X 10•
I 21 X 107
1 50 X 10'

t Column 1 mmus column 2 muluphed by $300 b1lhon

28

Appendix 2: Empirical Specification and Diagnosis of OSD Model

-y.,(12)

Model specification1
Consider first the plot of the autocorrelation
function (ACF) for Zt, given m Chart I The first
IO autocorrelations (AC) decrease exponentially followmg the pattern of an AR(l) model with ap
proximately Ip = 0 85 (the m1t1al estimate of rp)
Let p1 and r1 be the population and sample 7thlag autocorrelation Assummg that Zt follows an
AR(l) process, the variance of r1 is approximated by
2
2
(A-6) v(r,) = __!_ [(l + 'P ) (l - 'P ') - 2J'P2,J
N
1 - cp 2

=

For J 13, the confidence reg10n for the sample esumate is given by (0 85) 13 ± 2[v(ri 3 )]1l 2
0 1209 ± 0 39 The sample estimate r 13 -0 35
falls outside this region, and the same is true for
r 12 and r 14 Furthermore, the ACF displays high
peaks at lags 39, 52, and 65 In particular, the
large lag approximation

=

=

with all other autocovariances equal to zero
For J > 66, the variance of the estimated r1 1s
approximately given by the express10n
(A-8)

p14

Pas

1mphes that, after lag 67, all r1 can be assumed
to be approximately zero
Now, consider the model consistmg of Equations 24 to 26 In terms of the observable variable,
z1, It can be rewritten as

=

E~

+

p39

P4o
Po1
Po2
Poa
Pe4
PB&
Pse

(1 - cpB) (1 - B 13) (1 - B•2)E 1

wluch mdicates that the variable

x1 = (1 - cpB)z1
follows a movmg-average process Chart 2 repro
duces the time series [x 1] for rp
85 The theo
retlcal ACF for x 1 is given by

=

-y.,(0)
-y.,(1)
-y.,(13)

= 4(1 + cp 2)u; + u:,
= -4cpu;,
= -y.,(52) = -2(1 + cp 2)u; =

-2-y.,(39)

= -2-y.,(65)
1 We shall use the followmg notat10n m this appendix
for a variable x, {x,} will denote a stochastic process, [x,]
will denote a time series reahzauon of the process, and x1
will denote the value of the variable at time t, AR(J) Will
denote an autoregressive model of order /, MA(J) will de
note a movmg average model of order 1


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Federal Reserve Bank of St. Louis

- 18
085
- 18
085
- 042
085
- 042
085
- 18
085
- 042
085
- 042

Pl
P12
Pia

2

(1 - cpB)z 1

v(r,) = ~{1

+ 2~

p:}

Chart 3 contams a plot of the ACF of Xt The
dotted Imes represent the value ±2[v(r1)]1l 2 for
J > 66 It is seen that all PJ for J > 66 can be assumed to be O Furthermore, comparing the theoretical (nonzero) autocorrelauons, co11espondmg to
the mit1al values of the estimates with the sample
autocorrelations, we have 2

cp )
hm v(r,) = - 1 (1-+
-J--+ 00
N 1 - cp 2

(A-7)

= -y.,(14) = -y.,(51) = -y.,(53) = 2cpu:
= -2-y.,(38) = -2-y.,(40) = -2-y.,(64)
= -2-y.,(66)

r1

r12
r1a
r14
ras
T39

r40
ro1
r52
roa
T04

rs.
ree

=
=
=
=
=
=
=
=
=
=
=
=
=

- 19
03
- 28
08
- 06
08
- 04
- 06
- 21
04
- 04
09
- 01

The two sequences present a fairly similar pattern We conclude that, as a first approximation,
-c 1 can be assumed to follow the MA process
Xt

=

E~

+

(1 - cpB) (1 - B13) (1 - B62)E1

with rp, u!, and u, bemg approximately given by
the mmal estimates Recalling that x 1 (I - rpB)zt,
Equations 24 to 26 are JUStlfied as a first approximation to the process generatmg [z1]

=

2 The m1t1al values-~= 85, a:, = ( 4)10-•, a; = ( 3)10_,,_
are derived m Agustm Maravall, "Est1mat10n of the Permanent
and Transitory Component of an Economic Variable with an
Apphcat1on to M1 " Special Studies Paper 85, Board of Gov
ernors of the Federal Reserve System, 1976

Transitory Variations in the Monetary Aggregates

Model diagnosis

Chart 6 displays a plot of the partial ACF for
Only the values correspondmg to lags 2 and 14
fall outside the approximate 95 per cent confidence
region, given by ±2yN
Thus, the estimated senes [tt] seems to be reasonably close to the theoretical model given by
Equauon A-4
Fmally, Equation A-5 imphes that the theoretical
ACF for et is given by
A

Once the model has been specified and the final
esumauon has been perfon:ned, diagnosuc checks
should be applied to the fitted model The Box
Pierce test cannot be applied to our calculated
residuals [et], and the fact that the esumator 81
does not converge m probability to the true /l 1
makes 1t difficult to denve appropriate tests Yet,
a diagnosuc check can be earned out m the followmg way
If our model is correct, the process {ll 1} is an
AR(l) process, given by
(A-9)

lli

Pia
p39

Ct

=

Et -

Et-13 -

Et-62

+ Et-66

We shall use the esumated senes [8 1] and [et]
to check whether both assumptions seem reason
able
Chart 4 plots the ,tutocorrelauons of 81 Under
the assumption that 81 follows the AR(!) process
gnen m Equation A 4, express10ns A-1 and A-2
yie~d the variances of the sample autocorrelat10ns
of 81 Base~ on these variances, the implied correlogram of [llt] seems to be m agreement with our
model Chart 'i compares the autocorrelauons of
the two senes [z 1] and [8 1] Although the two plots
follow the same general pattern, the autocorrela
t10ns for [z1] have bigger oscillations The pattern
of the autocorrelations for (8 1] seems to follow an
i\R(l) model more closely than those for [z,] The
lugher order effects present m the ACF of (8 1] may
,tnse because we are dealmg with sample auto
correlat10ns of an estimated time senes 1

-5
25

Pa2
P66

= - 5
= 25

and all other lagged correlauons equal zero Usmg
the estimated senes [et], we obtam the values

and the process [et] is an MA process given by
(A-10)

29

713

- 55

752

739

27

766

= - 38
= 21

which are m close agreement with the theoretical
dUtocorrelations Also, by usmg Equauon A-8, all
correlauon for lags greater than 66 can be assumed
to be zero Chart 7 presents a plot of the auto
correlations for the senes [et] Agam, the estimated
5enes are m reasonable accordance with the theo
retical model given by Equat10n A-8, and we con
elude that our fitted model offer5 an acceptable
,tpprox1mat1on to the stochasuc process that gen
crates the time senes [z,]
1 Recall that the covariance between t"o sample correla
lions given approximately by

1

cov(rk,rk+,)

= N .~.,P•P•+•

can distort the plot of the ACF, \\h1ch may fat! to damp
out 1ccordmg to expeclatlons
see George E P Box and
Gw1lyn l\l Jenkms 7 1111e ~enes A11al) us Forecasting n11(/
Control (Holden Day, 1970), p 35

CHART I Sample Autocorrelation Function for [ztl

8

4

0

-4

20


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Federal Reserve Bank of St. Louis

40

60

80

100

120

140

Improvmg the Monetary Aggregates Staff Papers

30

CHART 2 Time Series Plot of [xtl

20

0

-20

20

40

60

80

100

120

140

CHART 3 Sample Autocorrelation Function of Xt

8

4

0

-4

100

140

CHART 4 Autocorrelation Function for [ot]


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Federal Reserve Bank of St. Louis

8

4

0

-4

Transitory Variations

tn

the Monetary Aggregates

31

CHART 5 Autocorrelation Function for [zt] and ['ot]

8

4

0

ACF for

[ot]
-4

20

40

60

80

100

120

140

CHART 6 Partial Autocorrelation Function for [ot]

8

4

0

-4

20

40

60

80

100

120

140

CHART 7 Autocorrelation Function for [e 1]

8

4

0

-4

20


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Federal Reserve Bank of St. Louis

40

60

80

100

120

140

32

Improvmg the Monetary Aggregates Staff Papers

Bibliography

Anderson, Theodore W The Statistical Analym of Time Series New York
Wiley, 1971
Bartlett, Maunce S An Introduction to Stochastic Processes 2nd ed Cam•
bndge, England Cambndge Umvermy Press, 1966
Board of Governors of the Federal Reserve System Improving the Mon
etary Aggregates Report of the Advisory Committee on Monetary Sta•
tistics Waslungton Board of Governors, 1976
Box, George E P , Stephen Hilmer, and George C Tiao "Analysis and
Modelmg of Seasonal Time Senes" Paper presented at the National
Bureau of Economic Research-Census Conference on Seasonal Analysis
of Economic Time Senes, Washmgton DC, September 9-10, 1976
- - - , and Gw1lyn M Jenkms Time Series Analysis Forecasting and Con
trol San Francisco Holden-Day, 1970
Brewer, Kenneth R W "Some Consequences of Temporal Aggregation
and Systematic Sampling for ARMA and ARMAX Models" Journal of
Econometrics, vol 1 (June 1973), pp 133-54
C..leveland, Wilham P "Analysis and Forecastmg of Seasonal Time Senes"
PhD dissertation, Umvers1ty of W1sconsm, 1972
Fry, Edward R, Darwm L Beck, and Mary F Weaver "Revmon of
Money Stock Measures" Federal Reserve Bulletin, vol 62 (February
1976), pp 82-87
Fuller, Wayne A Introduction to Stationary T11ne Series New York
Wiley, 1976
Goldfeld, Stephen M "The Case of the M1ssmg Money " Brookingl
Papers on Economic Activity, 3 1976, pp 683-730
Gramley, Lyle E "Deposit Instab1hty at Ind1v1dual Banks," m Essays on
Commercial Banking Federal Reserve Bank of Kansas City, 1962
Hurd, Harry L "Survey on Penod1cally Correlated Processes " Paper pre
sented at the Muluple Time Senes and System Idenuficauon Conference, Umvers1ty of North Carolma at Chapel Hill, January 2-6, 1973
Jones, Richard H, and Wilham M Brelsford "Time Senes with Penod1c
Structure" Biometrika, vol 54 (December 1967), pp 403-08
Lombra, Raymond E , and Herbert M Kaufman "Commercial Banks ,tn
the Federal Funds Market Recent Development and Imphcauons
Economic Inquiry, vol 16 (October 1978), pp 549-62
Maravall, Agustm "Esumauon ot the Permanent and Transitory Com•
ponent of an Economic Vanable with an Apphcauon to M 1 " Special
Studies Paper 85 Washmgton Board of Governo1s of the Federal Reserve System, 1976
- - - Identification in the Shock-Error Model New York Sprmger•
Verlag, forthcommg
"Numencal Specifications of Fmancial Vanables and Their Role m Mon•
etary Policy" Federal Reserve Bulletin, vol 60 (May 1974), pp 333-37


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Federal Reserve Bank of St. Louis

Transitory Variations in the Monetary Aggregates

Pagano, Marcello "Estimation of Models of Autoregressive Signal Plus
White Noise" Annals of Statistics, vol 2 (January 1974), pp 99-108
Paulus, John D, and Stephen H Axllrod "Regulatory Changes and Fmancial Innovations Affectmg the Growth of the Monetary Aggregates "
Staff memorandum Washmgton Board of Governors of the Federal
Reserve System, November 1976
Pierce, David A "Seasonal Adjustment When Both Determmisuc and
Stochastic Seasonality Are Present" Paper present,ed at the National
Bureau of Economic Research-Census Conference on Seasonal Analysis
of Economic Time Senes, Washmgton, D C, September 9-10, 1976
Subsequently published as Speoal Studies Paper 107 Washmgton Board
of Governors of the Federal Reserve System, 1977
Porter, Richard D , and Paul N Rappaport "Forecastmg Net Basm Supplies on the Great Lakes " Paper presented at the TIMS Conference,
Houston, Texas, Apnl 1972
Rangarapn, C "Deposit Variability m Individual Banks" National Banking Review, vol 4 (September 1966), pp 61-71
Struble, Frederick M , and Carroll H WIikerson "Bank Sile and Deposit
Variability" Monthly Review Federal Reserve Bank of Kansas City,
November-December 1967, pp 3-9
- - - "Deposit Vanabihty at Commercial Banks" Monthly Review
Federal Reserve Bank of Kansas City, July-August 1967, pp 27-34
Thompson, Howard E , and George C Tiao "Analysis of Telephone
Data A Case Study of Forecastmg Seasonal Time Senes" Bell Journal
of Economics and Management Science, vol 2 (Autumn 1971), pp
515-41
Whittle, Peter Prediction and Regulation by Linear Least Square Methods London English Umversities Press Ltd, 1963


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Federal Reserve Bank of St. Louis

33


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35

Foreign Demand Deposits at Commercial Banks in the United States
Helen T Farr, Lance Girton, Henry S Terrell, and Thomas H Turner

This paper was completed

in

early 1976

Foreign depositors held about $13 brlhon m
demand deposits at commercial b,mks m the
Umted States at the end of 1975 Demand deposits that are held by foreign banks, nonbanks (m<lividuals, partnerslups, ,md corpm auons-IPC's), and official mstituuons are currently mcluded m tabulat10ns of the narrowly
defined money supply (M 1 ) of the Umted
States As of December 1975, foreign-owned
demand deposits accounted for about 4 per
cent of M 1
In this papei we discuss the genera] characteristics of these deposits dnd attempt to
1dent1fy empirically the factors th.1t <letermme
the <lemdnd for them We also attempt to determme whether these deposits are closely
related to U S macroeconomic variables and
whether the relationship, if 1t exists, 1s suffinently similar to that of the other components
of U S monetary aggregates so that foreign
deposits should contmue to be mcluded m
these aggregates The evidence p1esented, although not conclusive, md1cates that foreign
demand deposlts at U S banks m general, and
demand deposlts of foreign commercial banks
dnd official mstitut10ns m particular, are not
1 elated to US activity variables m the same
manner dS are other components of the nar1 owly defined money supply

Charactenst1cs of foreign demand
deposits at U S commercial banks
The followmg sect10ns discuss m detail the
charactensucs of the various kmds of foreign
NoTE -Helen T Farr 1s on the ~t,1ff of the D1vmon
of Research and Stat1st1cs, Lance Girton and Henry S
Terrell are on the staff of the D1v1s10n of Internat10nal
l mance, and Thomas H Turner was formerly on that
staff


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demand deposits held at US commercial
banks those of foreign commercial banks, of
foreign md1v1duals, p.1rtnersh1ps, and corporat10ns, and of foreign official msututrons

Deposits of foreign commercial banks
at U.S. banks
Demand baldnces of lorergn commercial
banks at U S banks are the largest and most
volatile of foreign deposits, havmg grown from
$3 4 brlhon m December 1971 to $7 5 b1lhon
m Decembet 1975 1 At times, fluctuations m
foreign bank demand deposits at U S commercial banks have had an apprenable impact
on the growth of the narrowly defined money
supply 2
The largest US banks currently mdmtam
between 1,500 and 6,000 demand accounts for
foreign commernal banks Of tlus total, 100
to 200 are usually characterued as active accounts belongmg to the largest foreign banks
thdt are heavily mvolvecl m mternauonal finance The remammg, ~mailer, accounts tend
to be relatively mactrve Most maJor foreign
banks mamtam demand balances at several
US money center banks
The accounts of ma1or foreign banks dre extremely active Daily turnover m an account
can be several hundred times the average endof-day balance A smgle transact10n through
one of these accounts rs often several times as
large as the average end-of-day balance, tins
rs particularly true of Euro-dollar transact10ns,
1 Information m this section has been enhanced b}
chscuss10ns with representative~ of US ,111d foreign
tommercial banks
2 These deposits do not mcludc balances o\\ed hy
US banks to the11 foreign branches or thosl. oned by
U S agencies and branches of foreign banks to their
head offices

36

lmprovmg the Monetary Aggregates Staff Papers

m which often neither the dehvermg nor the
receivmg bank is a US bank 3 Foreign banks
use their accounts with domestic offices of U S
banks to deliver and accept payment on their
Euro-dollar transactions because US banks
reqmre that the large credit Judgments associated with these transactions be made at their
head offices • A related reason for clearmg
dollar transactions m the Umted States is the
prox1nnty of the Federal funds market, m
which market participants can acqmre and
place large sums of dollars on short notice
The second-largest type of transaction m
these accounts results from the settlement of
foreign exchange contracts, an unknown portion of which is directly related to the financmg of exports or imports of the Umted States
Some foreign exchange transactions reflect
third-country trade and the special role of the
dollar as a settlement currency m mternational
t1 ade Also, a proportion of the transactions
1eflects the attempts of foreign banks to
achieve a desired position m foreign exchange
markets, either for their own account or for
their customers
Aside from the general purpose of clearmg
Euro-dollar and foreign exchange transactions,
Japanese banks, which are usually large net
borrowers of funds from banks m the Umted
States, utilize their demand balances at U S

pattern of behavior appears to be limited to
Japanese banks 5 As a general rule, a U S
bank would not extend credit to a foreign
bank that did not mamtam a demand balance
at the U S bank
An understandmg ot the mstitutional background is important m developmg a model to
explam the behavior of foreign demand deposits over time and to compare this behavior
with that of other components of the money
supply From discussions with market participants, it appears that demand for such deposits by foreign banks is positively related to
their needs for transactions balances m the
Umted States and negatively 1elated to then
costs of obtammg such funds m the market
F01 US banks, the costs of supplymg these
funds mclude the cost of servicmg transactions
through the accounts Servicmg costs mclude
the cost of U S banks' servmg as standby lenders m case a foreign bank's demand balance is
m deficit durmg the day or after the close of
busmess An important way that the U S banks
are compensated is through the value of the
mterest-free funds mamtamed on deposit by
the foreign banks The value of these deposits
to the US banks is determmed by an mternal
mterest rate that reflects the cost savmgs from
obtammg mterest-free demand balances compared with the costs of obtammg funds m the

banks for an add1t10nal purpose To obtam

market

funds, Japanese banks have established numerous unsecured Imes of credit with U S banks
and often agree to mamtam compensatmg demand balances of about 10 per cent of the Imes
of credit The compensatmg balances play the
role of commitment fees When the Imes of
credit are drawn down, the Japanese banks
often are reqmred to mamtam compensatmg
balances of the same magnitude as those reqmred of domestic nonbank borrowers This
a An account with an average end of-day balance
of $1 mdhon may have transactions totahng several
hundred million dollars on any busmess day
• For example, durmg the course of a busmess day
the payment orders from an account may exceed the
funds received m that account and the U S banks
must decide whether or not to honor the orders, thus
extendmg credit (sometimes m large amounts) to the
foreign commercial bank These mtrabusmess-day extensions of credit are often termed "daylight" overdrafts


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6

Deposits of foreign individuals,
partnerships, and corporations
The second-largest category of foreigners
holdmg demand balances at U S banks are
5 Canadian banks, which have important US operations, do not mamtam large demand balances at U S
banks However, they do not borrow large amounts
from U S banks because most of their Euro dollar and
foreign exchange transactions are cleared through their
New York agencies
s US banks often mamtam complex relallonships
with foreign commercial banks of which the demand
deposit relationship is only one part Vanous mteracuons mclude, among other thmgs, parllcipation m
iomt ventures, correspondent relationships, mtroductions to clients, and the provision of various mforma
tion and trammg services In some cases, a U S bank
might reduce its demand balance reqmrements to a
foreign bank as a "loss leader" to develop a more
profitable relationship m other busmess areas

Foreign Demand Deposits at Commercial Banks in the United States

foreign !PC's At the end of 1975, foreign
!PC's held about $3 2 billion m demand balances m the Umted States, or about 1 pe1 cent
of total M 1 Deposits of foreign !PC's do not
show the same short-run volatility as deposits
of foi eign commercial banks The nature of
the transactions through the IPC accounts is
harder to describe than are transactions mvolvmg deposits of foreign commercial bank&
because of the larger number of depositors and
the greater diversity among depositors 7
The factors determmmg the demand for
IPC deposits are vaned, and it is difficult to
assign a pnon weights to particular reasons
for holdmg these deposits First, some deposits
are held to finance exports from and imports
to the Umted States, while others may be held
to finance tlurd-country trade 8 Second, some
deposits might be held to avoid confiscation
of eai mngs of convertible currency by the governments of some developmg countries, although m this case lt 1s difficult to estabhsh
a preference for a demand balance rather than
an mterest-bearmg account Third, some deposits serve to mamtam Imes of credit at US
banks for foreign commercial boirowers

Deposits of foreign official institutions
The term "foreign official mstitutions" covers a variety of mstitutions, mcludmg central
banks, monetary authonues, governmentowned development banks, government-owned
mstitutions that conduct commercial bankmg
operations in their home country, some mternational orgamzauons, U S purchasmg missions, and embassies and consular offices At
the end of 1975, foreign official mstitutions
mamtamed about $2 6 billion m demand balances m the Umted States, mcludmg about
$350 million of demand balances m Federal
Reserve Banks 9 These deposits constitute
1 As noted earlier, most of the transactions in the
demand deposit accounts of foreign commeraal banks
are conducted by a small number of banks active m the
Euro dollar market
s For example, a Brazilian company may pay for its
imports from Japan by drawing on its demand balance
at a bankmg office m the Umted States
9 Foreign official demand deposits at Federal Reserve Banks are now included in the U S money supply


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Federal Reserve Bank of St. Louis

37

only a small fraction of the hqmd assets held
m the Umted States by foreign official mstitutions As of December 31, 1975, foreign official
msututions had $60 billion m U S Treasury
securities and $17 billion m earmarked gold
m custody at Federal Reserve Banks 10
As m the case of foreign nonbank depositors, the diversity of mstitutions and of nationalities m this category makes it qmte difficult to identify any general motives for mamtammg demand balances at bankmg mstitutions m the Umted States

Empirical analysis
In tlus section, we examme the issue of mclusion of foreign-owned demand deposits m
the narrowly defined money supply 11 First,
the degree of correlation between mcome and
money, mclusive and exclusive of foreignowned demand deposits, is reviewed by regressmg changes m mcome on changes m
alteinative measures of the money supply
Second, demand functions for alternative defimuons of money are estimated, and the foreign deposit components are regressed separately on the same demand variables The
estimated coefficients are then compared to
see whether the factors that explam the demand for money also explam the demand for
the foreign deposits Regressions are run from
the middle of 1963, the first penod for wluch
data on foreign demand deposits are available,
through the end of 1974 Both monthly- and
quarterly-average data are used, and all data
are seasonally adJusted 12
10 Secuulles mclude marketable US Treasur} bills,
certificates of indebtedness, notes, bonds, and nonmarketable Treasury securities payable m dollars and
m foreign currencies The earmarked gold 1s valued
at $42 22 per ounce, which understates its market
value In add1t1on, it should be noted that foreign
official mst1tut1ons hold about $20 b1lhon in dollardenommated assets at foreign branches of U S banks,
an unknown portion of which 1s payable on short
notice
11 The empirical analysis of the next two sections
refers solely to the question of inclusion or exclusion
of various foreign owned demand deposits m the narrowly defined money supply (M1)
12 The data on foreign commercial bank deposits
are derived primarily from averages of smgle day
(Wednesday) observations for any month, whereas the

38

lmprovmg the Monetary Aggregates Staff Papers

TABLE 1 Quarterly Changes m GNP as a Function of Changes m Alternative Definitions of Money 1
Regression
stat1sucs

Independent variables
Defimt1on of money
Constant

M
MN
MN+ FJPC
MN

+ FfPC + FCB

MN

+ FIPC + FOFF

FIPC
FCB
FOFF

1 445
( 5)
999
( 3)
897
( 3)
1 089
( 4)
I 074
( 4)
18 351 2
(7 4)
15 952 2
(6 9)
19 358 2
(9 4)

I AM, I
2
1
(3
1
(2
1
(2
I
(2
I
(3
46
(I

19
(I

12
(I

941
3)
731 3
6)
7732
7)
8262
9)
9202
1)
037
7)
023
7)
606
7)

AM1-1
1
(6
1
(5
I
(6
I
(6
1
(6
19
(I

9
(2
7
(I

644•
8)
719'
9)
723 2
I)
659 2
5)
7252
5)
743
6)
613 3
6)
507
6)

I

I

AM1-2
1
(4
1
(4
I
(5
I
(5
I
(5
1

301'
9)
540 2
9)
520•
0)
3932
0)
4352
0)
992

3
(
3
(

005
6)
742
7)

AM1-a
(2
I
(3
I
(3
1
(3
1
(3
-7
((1
(

( I)

913 2
8)
194•
2)
1662
2)
027•
0)
052 2
1)
215
4)
800
1)
221
2)

I

I

AM,_,
(2
(2
(2
(2
(2
-7
(-1
((-

479,
O)
681•
4)
659 3
4)
563•
2)
573 3
2)
879
5)
801
4)
265
7)

I

Standard

Sum

R•

279 2
5)
864 2
2)
842 2
4)
6 468 2
(10 4)
6 704 2
(10 8)
52 678
(I 9)
29 0403
(2 6)
25 079 2
(3 4)

488

6 747

449

6 997

458

6 942

477

6 819

475

6 705

198

8 442

226

8 294

188

8 493

6
(IO
6
(10
6
(10

error

1 1-stat1st1cs appear m parentheses
2 S1gmficant at 99 per cent confidence level
• S1gmficant at 95 per cent confidence level

Income as a function of money
Table l presents the results of regressions
run with quartelly data In each equation, the
change m gross national product (GNP) 1s the
dependent variable Each of the defimt10ns of
money used as the mdependent variable 1s
one or a combmation of the followmg M =
M 1 as currently defined, MN= M 1 mmus all
foreign deposits, FfPC= foreign IPC deposits,
FCB = foreign commercial bank deposits, and
FOFF foreign official deposits A seconddegree polynomial d1stnbuted lag 1s estimated
on the first differences of alternative defimt10ns of money and ts constramed to zero at
t - 5 All equations have a first-order correction for serial correlation of the residuals
Table 2 presents the results for the regressions run with monthly data In each equat10n,
the change m personal mcome 1s the dependent variable and the defimuons of money

=

data for foreign official and foreign IPC deposits are
denved from smgle day end of month observations
In contrast, the data for demand deposits m M 1 are
denved pnmanly from monthly averages of daily deposits Therefore, the three senes on foreign demand
deposits may show greater month to month variation
than the deposit senes m total M 1 For this reason,
demand functions for the foreign components may
have higher standard errors than those for monetary
aggregates that mclude domestic deposits (Sec the appendix for a more complete treatment of the data
sources used for foreign deposits)


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are the same as those used m the quarterly
regressions A second-degree polynomial distributed lag ts estimated on the change m the
alternative defimuons of money and 1s constramed to zero at t - 16 For compactness,
only the sum of the distributed-lag coefficients
1s presented, all distributed-lag coefficients are
pos1t1ve
The quarterly and monthly regressions yield
consistent results Includmg each of the foreign deposit components m the defimtion of
TABLE 2 Monthly Changes m Personal Income as a
Function of Changes m Alternative
Defimhons of Money 1
Independent variables Regression stat1st1cs
Defimuon of money

Sum of
Constant coefficients
on Amoney

I

759
( 8)
929
( 9)
851

M

MN
MN+ FIPC

( 8)

MN

+ F/PC + FCB

MN+ FIPD
F/PC
FCB
FOFF

+ FOFF

696
( I)

(
4
(11
4
(8
5
(13

857
9)
9542
1)
028'
4)
465•
2)

5 1362
(22 6)
5 273 2
(21 4)
5 3162
(21 9)
5 2482
(22 6)
5 260•
(22 1)
95 873 2
(13 9)
39 3262
(13 8)
29 0232
(14 5)

• 1-stat1sucs appear m parentheses
' S1gmficant at 99 per cent confidence level

R•

Standard

I

error

180

4 093

148

4 171

154

4 158

174

4 107

162

4 137

068

4 363

148

4 171

027

4 458

Foreign Demand Deposits at Commercial Banks in the United States

39

TABLE 3 95 Per Cent Confidence Intervals for Regression Variances

M
MN
MN+ FIPC
MN + FIPC
MN + FIPC

I

Quarterly regressions

Definition of money

Variance
45
48
48
46
46

+ FCB
+ FOFF

I

521
965
193
494
692

Confidence mterval
30
32
32
30
31

25~76
545-81
032-,80
902-77
034-78

money results m a shght mcrease (decrease)
m R. 2 (standard error of estimate) relative to
the regressions on money excludmg that component The improvements are small, however,
and the question of their s1gmficance remams
The 95 per cent confidence mtervals for the
variances of each regress10n are compared
with the pomt estimates of these variances m
Table 3 13 (The degrees of freedom used m
computmg the confidence mtervals are 37 and
I 18, respectively) It 1s apparent that the confidence mterval for each equat10n's variance,
monthly or quarterly, encompasses the variance of each of the other monthly or quarterly
equations Although this 1s not a rigorous statistical test, the fact that the confidence mtervals overlap to such a large degree suggests
that the variances may not differ s1gmficantly 14

191
955
663
819
151

I

Monthly regressions
Variance
16 751

17
17
16
17

396
289
868
116

I

Confidence mterval
13
13
13
13
13

181-22
690-22
650-22
274-22
468-22

004
853
712
159
484

where Rep 1s the 30- to 59-day commercial
paper rate, and Y 1s GNP m the quarterly regress10ns and personal mcome m the monthly
regress10ns The second set of equations m
the panels drop the lagged dependent variable

and estimate distributed lags on Rep and Y
The coefficients presented for Rep and GNP
(Pl) are the sum of current and lagged coefficients on the respective variables The polynomials are second degree constramed to zero
at t - 4 for the quarterly equations and at
t - 10 for monthly equat10ns
The results here are mixed In three of the
four regress10ns for FfPC, the mterest rate
enters negatively, though not sigmficantly In
the fourth regress10n (monthly, distributed
lag), the mterest rate enters positively and s1gmficantly In all FfPC regress10ns, mcome enters pos1t1vely but only m the quarterly distributed lag regress10n 1s it s1gmficant at the
95 per cent confidence level (At an 80 per cent
confidence level, 1t is also sigmficant m the
monthly d1stnbuted lag regress10n ) For FCB,
the mterest rate enters negatively and not s1gmficantly m the demand equat10ns with a
l.tgged dependent variable and positively and
s1gmficantly m the distributed-lag regress10ns 15
In all but the monthly regress10n with a lagged
dependent variable, FCB 1s pos1t1vely and
s1gmficantly related to mcome at the 90 per
cent confidence level or better Fmally, m all
regressions, FOFF 1s pos1t1vely related to the
mterest rate (sigmficantly m the distributedlag regressions) In no regress10n is FOFF
s1gmficantly related to mcome, though the
estimated relationship is positive
Turnmg to the demand functions for the
alternative defimt1ons of money, the mcome

13 See, for example, Henn Theil, Principles of Econo
metrics (Wiley, 1971), pp 13~31
14 Rigorous statistical tests are not possible, given
the way the alternative definitions of money are con
structed If, mstead, the change m mcome 1s regressed
on the changes m MN, FCB, FOFF, and FIPC as sepa
rate mdependent variables, the standard types of tests
on the coeffic1ents can be performed Smee the foreign
components do not enter the regressmns separately but
are summed with MN, such tests are not possible here

1 • An early memorandum presented to the Commit
tee on Monetary Statistics did show FCB deposits
negatively related to mterest rates, see Stephen Thur
man, "Prehmmary Results of Tests on Inclus1on of
Foreign Deposits m the Money Supply" (Board of Governors of the Federal Reserve System, October 1974)
The coeffic1ents were significant at the 90 per cent
confidence level The data ust.d m these earlier regressions have been substantially revised, which may explain the difference m results

Demand functions
Table 4 presents estimated demand functions for money and for the different foreign
deposit components on a quarterly and on a
monthly basis The first set of equations m
panels A and B are all of the form
ln M = ao


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Federal Reserve Bank of St. Louis

+

a1 ln Rep

+

a2

ln Y

+

aa ln M_1

Improving the Monetary Aggregates Staff Papers

40

TABLE 4 Demand Funct10ns for Foreign Deposits and Alternative Defimbons of Money 1
Independent
vanables
and re11ress10n
statlStlCS

Dependent vanables
lnFIPC

I

lnFCB

I

In FOFF

I

lnM

I

In MN

I

ln(MN +
FIPC)

+
I ln(MN
FIPC +
FCB)

I

ln(MN +
FIPC+
FOFF)

A Quarterly demand functtons
Equations with lagged dependent vanables
Constant
In RcP
In GNP
In M-1

.R•

Standard error

(-2
(-

848
5)
010
5)
018
( 5)
1 0852
(12 9)
9695
0242

-2 331
(-1 8)
- 003
(- I)

226

(I 7)

1 455
( 8)
100
( 9)
081

- 0132
(-3 2)
175 2
(2 9)
7762
(9 3)
9995
0040

( 7)

906 2

631 2
(4 7)
8068
0910

-26 7532
(-7 3)
051
(I 9)
2 5022
(5 2)
9972
0241

4 289
( 7)
4402
(4 2)
158

(12 I)
9977
0226

373
(I 7)

379

397

325

(I 8)

(I 8)

(I 7)

- 0142
(-3 6)
163 2
(2 8)
788 2
(9 6)
9994
0042

- 0142
(-3 5)
1672
(2 9)
783 2
(9 6)
9994
0042

- 0132
(-3 4)
1662
(2 9)
7902
(10 0)
9995
0042

2
(6
(-9

I
(5
(-9

450
(1 9)
- 0132
(-3 3)
1762
(2 9)
7682
(9 O)
9995
0040

Equations with d1stnbuted lags
Constant
In Rep
In GNP

-17
(-1
(1
(3

.R2

Standard error

272
9)
002
7)
7262
3)
9623
0265

I
(8
(-8

7632
5)
0432
6)
768•
(8 4)
9993
0044

( I)

8038
0921

2 0032
(6 7)
- 0502
(-9 9)
750 2
(8 2)
9993
0044

7102
4)
0462

2
(6
(-9

0044

7722
(8 4)
9993
0045

0692
9)
0462
2)
7462
(8 3)
9993
0044

240 2
(2 9)
- 007 2
(-5 3)
0662
(3 9)
9092
(35 8)
9997
0029

2003
(2 6)
- 007 2
(-5 0)
0632
(3 7)
915•
(37 I)
9997
0029

212•
(2 5)
- 007 2
(-5 I)
0592
(3 4)
919 2
(35 8)
9998
0027

012•
7)
0492
7)
750'
(8 2)
9993

1)

B Monthly demand Cuncttons
Equations with lagged dependent vanables
Constant
In Rap
lnP/
lnM-1
.R2

Standard error

(-1
(-

206
7)
000
0)
010
( 8)
1 0102
(34 7)
9631
0268

((-

250
9)
005
8)
020

( 6)

1 000 2
(52 4)
9978
0221

201
( 5)
017
( 6)
016
( 6)
9412
(25 6)
8535
0812

1723
(2 2)
- 006•
(-4 8)
0562
(3 3)
926 2
(37 2)
9998
0028

240 2
(2 9)
- 008 2
(-5 3)
067•
(3 9)
9082
(35 6)
9997
0029

Equations with d1stnbuted lags
Constant
In Rep
In PI

.R•

Standard error

- 485
(- 2)
067•
(2 9)

581
(I 3)
9511
0304

-21 369 2
(-7 2)
007
( 4)
2 161 2
(6 5)
9976
0226

3 257
( 8)

2412
(3 8)
289
( 2)
8391
0850

2
(10
(-24

5812
9)
052 2
8)

7222
(17 9)
9998
0027

2
(16
(-25

831 2
I)

0552
8)

2
(16
(-25

702 2
(16 9)
9997
0028

851 2
I)
054 2
I)

7012

(16 7)
9997
0028

2
(12
(-23

588•
8)
052 2
9)
721 2
(17 0)
9997
0029

2
(14
(-25

8712
I)
053•
8)

700•
(17 6)
9997
0027

1 1-stattstlcs are m parentheses
2 S1gruficant at 99 per cent confidence level
3 S1gmficant at 95 per cent confidence level

and mterest rate coefficients are all significant
and have the expected signs the R. 2 's and
standard errors are approximately the same
across regressions In three cases the standard
error of the equation for MN is slightly higher
than that for the equation for M, suggestmg
that we may not wish to exclude all foreign
components from the defimt10n of money In
three of four cases m which FOFF is mcluded
m the definition of money, the standard error
is slightly lower than that for an equation excludmg this foreign component In two regressions mcludmg FCB m the defimuon of money,


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Federal Reserve Bank of St. Louis

the standard error is slightly higher than when
The remammg standard
errors are md1stmgmshable
In summary, the differences among the
standard errors for the demand functions for
the alternative definitions of money are so
small that little can be said, based on these
regressions, about which foreign components
should or should not be mcluded m the
defimt10n of money More mformauon 1s
gamed from the demand functions for the foreign components In no case does Rap enter
significantly mto a demand function for a

FCB 1s excluded

Foreign Demand Deposits at Commercial Banks in the United States

foreign component, except when the sign of
the coefficient is positive 16 This result suggests
that 1f the demand for any given foreign component 1s affected by movements m the commercial paper rate, 1t 1s affected m a manner
that 1s very different from the way these movements affect the demand for the other components of the money supply There 1s some
evidence of a relat10nship between FCB and
mcome and less evidence of a relat1onslu p between FIPC and mcome Of course, the mcome
variables may act as proxies for another transactions variable that 1s actually the determmant
of the demand for these balances This conJecture will be mvestlgated further m the next
section Fmally, while all the .R's are qmte lugh,
the standard errors for the foreign components
are very high relative to those for M, suggestmg
that although domestic income and mterest
rates do a good Job of explammg the demand
for M, other variables may be relevant m determmmg the demands for the foreign deposits

An alternative approach
In this section we attempt to develop a more
c.omplete model to explam the demand for
demand deposits of foreign commercial banks
(FCB) at U S banks For the demand deposits
due to foreign official mst1tut1ons and to foreign md1v1duals, partnerships, and corporat10ns, further efforts are made to establish the
existence of meanmgful correlations between
the deposits and domestic macroeconomic
variables Seasonally unad1usted quarterly and
monthly data are used m these analyses, with
quarterly and monthly dummy variables employed to remove the effects of any determm1st1c seasonal The hm1tat1ons imposed by the
available data are discussed more fully m the
appendix

Demand deposits due to foreign
commercial banks
Foreign commercial banks hold demand deposit balances at US banks as part of broad
10 In the alternative model specified m the next section, the estimated coefficient on Rap 1s negative and


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Federal Reserve Bank of St. Louis

41

commercial relationships These balances facilitate the clearmg of their dollar transactions
and serve to mamtam Imes of credit at U S
banks U S bankers, as reported earlier, emphasized th<1t the returns and costs associated
with these demand deposits are momtored
closely both by the U S banks that accept the
deposits and by the foreign banks that make
the deposits
In this sect10n a simple transact10ns model
1s set out to explam the level of foreign commercial bank deposits held m US banks
Monthly d<1ta fiom 1971 through 1975 are used
to test f01 the s1gmficance of the explanatory
variables suggested by the transact10ns model
A simple model of foreign commercial bank
deposits Foreign banks are <1ssumed to attempt to mmtmlle costs associated with clearmg dollar tr<1nsact1ons m the Umted States
For a typical foreign bank the total cost of
clearmg transactions, per time period (TC),
1s given by17
(1)

TC= A(T,D)

+ roD +

S

where
A(T,D)

=

T

=

D
ro

=

S

=

=

the mternal accountmg and admm1strat1ve costs mcurred by the foreign
bank m executmg its dollar transact10ns
the dollar value of transact10ns
through the account
the level of demand deposits held
the opportumty cost per dollar to the
foreign bank of deposits held, m
terms of mterest forgone
the explicit service charges levied by
the U S bank for clearmg transac-

s1gmficant when another short term rate 1s entered m
the regressions
11 In prmc1ple, Equation l and subsequent equations
should be expressed m pnce deflated magmtudes This
has not been done because of problems m choosmg
the appropriate deflators for the different nommal
magmtudes Also, costs should probably be related
separately to the number of transactions and the average value of a transacuon Data hm1tat1ons prevent this
refinement In the emp1ncal work we use a time trend
m some of the regress10ns as a proxy for, among other
thmgs, secular changes m the average value of a transaction

42

Improving the Monetary Aggregates· Staff Papers

t10ns mmus charges for any nonclearmg services provided by the
U S bank and not charged for
explicitly
Because data on the level of service charges
(S) are not available, we need to denve an
expression for S m terms of observable variables To do this, we look at the cost of servicmg the foreign demand deposits at the U S
bank Service charges, m terms of dollars per
time period, are equal to the difference between the costs of serv1cmg the foreign account, mcludmg profits, and the return the
U S bank can earn on funds made available
from the deposit 18
(2)

S

=

C(T,D)

+ F(L) + 1r(D)

- rLL

=

L

=

F(L)

=

1r(D)

=
=

rL

the cost borne by the US bank m
clearmg transactions through the
foreign deposit account
the volume of loans (or other asset
purchases) that can be made with
the funds held on deposit by the
foreign bank
the cost of serv1cmg the loans made
with the deposit funds
profits
the loan rate at the U S bank

We assume that the level of transactions
costs-both for the foreign bank and the U S
bank-mcreases with the volume of transact10ns, and that mcreases m deposit balances
reduce clearmg costs mcurred by both the foreign bank and the U S bank Also, we assume
that the costs of serv1cmg loans mcreases with
volume That 1s,
AT,CT

(3)

>

0,

AD,CD

<

0,

and

FL

>

0

where subscripts denote partial derivauves of
the functions

L

=

(1 - p)D

where pis the reserve ratio Usmg Equation 3
to ehmmate L from Equation 2 and subsututmg the resultmg express10n for S m Equation I, then
(4)

TC= C(T,D) + A(T,D)
+ 1r(D) + [r0

+ F[(1
-

- p)D]
(1 - p)rL]D

The foreign bank is assumed to hold the
level of deposits that mmim1zes the costs of
clearing its dollar transactions The costmm1mizmg condition obtamed by takmg the
partial derivative of the cost function, Equation 4, with respect to D 1s 19
(5)

where
C(T,D)

The US bank can use the deposited funds
(D) to make loans of

- (CD

+ AD)
=

To -

(1 - p)(TL - FL)

+

7rD

The cost-mmimizmg level of deposits 1s given
when the margmal cost savmgs per dollar of
deposits [-(Cn + An)] is equal to the difference between r 0 , the opportumty cost of funds
to the foreign bank, and rn, the margmal value
of funds to the US bank, adjusted for the
profits, where rn = (1 - p)(rL - FL) + 1rn
Solvmg Equat10n 5 for D yields the mmimum-cost level of deposits
r
(6)
D = H(T, To, TD)
The demand for deposit balances (D) 1s a
funct10n of the volume of transact10ns (T),
the opportumty cost of holdmg the deposits
(r0), and the rate of return on the deposits (rn)
From the assumpt10ns made above, the partial
derivatives of H with respect to the mterest
rates have signs as follows Hr 0 < 0, Hrn > 0
Followmg standard transactions models, we
would expect that for a given level of deposits,
the value of margmal deposits m reducmg
10 We assume that T, p, To, and TL do not depend
on D The second order cond1t1on 1s that

18 The level of service charges (S) may be positive
or negative If the level of deposits 1s such as to pro
vide abnormal profits with zero exphc1t charges, the
U S bank 1s assumed to provide other bankmg services
at less than full costs S 1s variable smce we assume
that the US bank pays a competitive rate on the de
posit even m the face of the prohibition on exphc1t
mterest payments


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Federal Reserve Bank of St. Louis

Cnn

+ Ann + (1

- p) 2FLL

+ 1rnn > 0

where double subscripts denote second order partial
denvauves
If the US bank max1m1zes profits, then 'll'n
0
The rest of this section 1s consistent with profit maxi•
m1zauon by the U S bank, but only the slightly
weaker assumption that 'll'n 1s constant 1s needed

=

Foreign Demand Deposits at Commercial Banks in the United States

transact10n costs mcreases with the level of
transactions, that 1s, (CDT+ AvT) > 0 This
assumption 1mphes that HT> 0
Empirical est1mat1on The exact form of the
deposit demand function, H( ), will depend
on the precise spec1ficat10n of the cost funct10n Here, we do not set out a fully developed model of transactions costs, but rather
assume for estimation purposes that the H
funct10n 1s log-hnear 20 All vanables--except
the time trend-are m natural logarithms of
levels
Because data on md1v1dual deposit dccounts
are not available, data on total demand deposits of foreign commeroal banks and total foreign dollar transact10ns cleared through U S
banks are used to estimate the relat10nsh1p
We contmue to assume that T, r 0 , and rv do
not depend on the level of foreign deposits
In the regress10ns reported below, the level
of deposits (D) 1s pnmanly based on a monthly
average of Wednesday figures The transact10ns vanable 1s represented by the monthly
,1verage of daily dollar figures for the Cleanng
House Interbank Payments System (CHIPS) 21
Several mterest rates are used to represent
r O the 90-day Euro-dollar rate (RE 90 ), the 30to 59-day commeroal paper rate (Rep), and the
p11mary rate on 90-day U S certificates of
deposit (Rev) 22
A maJor problem 1s the determmauon of a
senes to represent the 1mphc1t rate of return
on deposits (rn) As defined earher,
rv

= (1 -

p)(rL -

FL)

+ 1rv

Fm the banks acceptmg these foreign deposits,
margmal reserve reqmrements (p) were essentially unchanged over the sample penod Also,
20 The model md1cates that the algebraic difference
m the interest rates should enter the H function We
estimated the function m vanous form~ but the supenonty of any one form could not be established The
1egress1ons that are reported use the logarithm of
the interest rates entered separately
21 CHIPS 1s an electronic system e~tabh~hed m 1971
by the large New York banks to clear their mternauonal dollar transactions
22 The market yield on 180-day Euro dollars and the
90 day US Treasury bill rate were also used The
findings were entirely consistent with those to be re
ported later


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Federal Reserve Bank of St. Louis

43

1f FL and 1rn are constant, then rv 1s a lmear
funct10n of the loan rate (rL) 23
Several different rates could be used to represent rL For three reasons, m the regress10ns to be reported the pnme rate (RP) 1s
the loan rate used First, the pnme lendmg
market 1s a fairly competitive market with
small <tdm1mstrat1ve costs, this rate then
should move closely with the true cost of funds
to the U S banks 21 Second, 1t was reported
and venfied that overdrafts on the accounts of
foreign commeroal banks are frequently
charged at the pnme rate Assummg that U S
banks perform then calculat10ns carefully, the
rate such banks charge on overdrafts m these
accounts should reflect the margmal mternal
value of these deposits Third, although the
Federal funds rate and the rate on repurchase
agreements are also plausible candidates fo1
the loan rate, the performance of these rates
was dommated m our empmcal work by the
pnme rate
Because deposits and transact10ns grew at a
very rapid rate over most of the penod, the
equations were estimated with and without a
time trend The time trend was used as a
rough proxy for omitted vanables to help explam tlus rapid growth
23 Several US
banks md1cated that they use an
average of several rate, to calculate a "treasurer's rate"
for internal use m determmmg the profitab1hty of
customer relat1onsh1ps See Beniamm Klem, "Com
pet!Uve Interest Payments on Bank Depo~lts and the
Long Run Demand fo1 Money," American Economic
Review, vol 74 (December 1974), pp g3J-49, and
Robert J Barro and Anthony M 5antom<-ro, Home
hold Money Holchng~ and the Demand Dc.pcmt Rate,"
fournal of Money, Credit and Banking, vol 4 (May
1972), pp 397-413, for work that tnes to mea\ure rn
c.hrectly
21 Borro,\lng at the pnme rate normally carnes a
compensatmg balance reqmrement To the extent that
the compensating balance reqmrement 1~ d result of
the 1mpl1C1t payment of interest on deposits by lend
mg at a favorable rate, the pnme rate will be less than
the pure lcndmg rate and may be less thdn or greater
than the 1mphc1t deposit iate A\summg 1ero mtc.rmc.chauon co~t~, the relationship bctwc1.n the pnme
1ate and the 1mphc1t deposit rate depends on the re
\erve ratio and the compensating balance ratio For
exdmple, 1f the margmal resc.rve 1c.qmrement 1s 17
pu cent with a 20 per c1.nt compensatmg balance
1eqmrement, the 1mphc1t deposit 1ate 1s 996 of the
pnme lendmg rate

44

Improvmg the Monetary Aggregates· Staff Papers

TABLE 5 Estimates of the Demand Function for Demand Deposits Due to Foreign Commercial Banks 1
In FCB, = a In RP,

0

+ /3 In r, +

~ 'Y, In CHIPS,_,

,-o

+ at + t + (seasonal dummies)

Independent vanables

r,
/3

a
I

'Y•

'Y1

I

'Y2
I

I

-r,

'Ya
I

I

'Y•
I

I

'Yo

I

0

t

I

A Regress10ns mcludmg a trend term
RE,,
Rep
Ren

559•
(5 74)
571•
(5 16)
574•
(4 99)

(-2
(-2
(-2

209•
43)
237 6
19)
222•
14)

013
( 25)
031
( 55)
031
( 55)

(((-

043
76)
026
45)
034
59)

- 580•
(-5 12)
- 689•
(-8 90)
- 647•
(-9 07)

081
( 96)
113
(I 58)
109
(1 55)

(((-

053
62)
003
03)
025
34)

(((-

040
70)
037
63)
036
61)

079
(1 37)
063
(I 05)
080
(I 36)

((-

004
07)
003
06)
002
( 04)

068

(I 25)

060

(I 06)

052
( 94)

007•
(7 54)
007•
(5 00)
007•
(4 84)

- 009
(- 18)
019
( 34)
007
( 14)

5
(42
5
(23
5
(23

640•
41)
604•
95)
450•
70)

3
(24
4
(34
4
(35

933•
28)
227•
65)
243•
36)

B Regressmns without a trend term
RE,,
(6
Rep
Ron

(10
1
(10

928•
42)
998•
40)
010•
63)

(-1
(-1
(-1

104
22)
089
19)
083
12)

021
( 24)
- 006
(- 08)
047
( 61)

(((-

012
15)
016
23)
001
01)

137

(I 70)

093

(I 28)

069
( 97)

107

(I 45)

163
(2 65)
128•
(2 09)
5

1 t-stat1sucs appear m parentheses All data are monthly, not
seasonally adJusted, for the penod August 1971-November 1975
'F-stattsttc for test of ('Yo=
= 'Yo= 0) F(7,30) for regressions
mcludmg a trend term, F(7,31) for regresston without a trend term

3 F-stat1sttc for all variables except seasonals, trend, and constant
F(9,30) for regressions with a trend term, F(9,31) for regresstons
without a trend term
• S1gmficant at 99 per cent confidence level
5 S1gmficant at 95 per cent confidence level

In add1t1on, one set of regress10ns w<1s run
with only a smgle mterest rate To the extent
that funds are arbitraged between the U S
bank loan market and the market that the foreign banks use for funds, rL and To are directly
related If arb1 tr age were perfect, the two rates
would be equal, and only a smgle rate would
appear m the demand deposit equation The
smgle mterest rate would enter with a negative
sign m the deposit demand function with pos1uve reserve reqmrements If, however, the regress10n with a smgle rate were actually a m1sspec1ficat1on m the form of an omitted vanable-that 1s, the other rate-then the estimated coefficient on the entered rate would be
biased 25
Estimated relat10nsh1ps, usmg Rp plus a
second rate for TO and an unconstramed lag
d1stnbut1on on current and six past values of
CHIPS data, are summarized m Table 5 (with
a time trend m panel A and without one m
panel B) In all cases Rp has the expected
positive sign and 1s s1gn1ficantly different from
zero at least at the 99 per cent confidence
level The F-stat1st1c for JOmt s1gn1ficance of
all coefficients except those on the constant,
trend, and seasonal dummies 1s s1gn1ficant at

well <1bove the 99 per cent confidence level m
all cases
Takmg the regressions as a whole, there are
several mterestmg results First, when RP 1s
used m conJuncuon with a second rate, each
of the rates used for To enters with the expected negative sign and each 1s s1gmficant at
least at the 95 per cent level 26 Second, m all
cases the F-test for JOmt s1gmficance of the
coefficients on the lag d1stnbut1on for CHIPS
1nd1cates that these coefficients taken as a
group are s1gmficantly different from zero at
least at the 95 per cent confidence level Furthermore, m all cases the coefficient on current
CHIPS has the expected pos1t1ve sign, although none of these 1s s1gn1ficantly different
from zero Few of the md1v1dual coefficients
m the lag d1stnbut1on are equal to or greater
than their respective standard errors However,
smce 1t 1s not difficult to conceive of models
m which the transactions variable would enter
with a d1stnbuted lag and smce collectively
our estimated coefficients are s1gmficantly different from zero, reJecuon of the hypothesis
that current and lagged values of the level of
foreign transact10ns (as reflected by CHIPS)

25

See, for example, Theil, Principles, pp 548-56


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2s This result 1s also obtamed by usmg the rates
mentioned m note 22

Foreign Demand Deposits at Commercial Banks in the United States

TABLE 5-Contmued

Regression staUstlcs

F stattsucs

R•

(')

(')

Standard DW
error

p

2:'Y,

2 653•

23 644•

979

034

2 10

188

0064

2 812•

24 534•

980

035

I 94

143

1062

2 634•

23 419•

979

015

I 99

168

1028

6 956•

58 497•

911

055

1 58

356

1778

29 568•

130 144•

959

047

I 88

202

2544

28 571•

133 655•

960

046

I 89

204

2426

are a s1gmficant determmant of FCB 1s not
possible 27
The exclusion of a time trend from the estimated relation alters the s1gmficance level, and
on occasion the sign, of some of the estimated
coefficients In all cases the coefficient on the
rate used for r0 remams negative, but It becomes s1gmficant at well above the 99 per cent
level when the trend 15 omitted Additionally,
the test for JOmt s1gmficance of the coefficients
on current and lagged CHIPS md1cates s1gmficance at well above the 99 per cent confidence level 28 The standard errors of the
21 It should be noted that our theory does not pro
v1de a solid a pnor1 foundation for the expected form
of the lag d1stnbution The regres~mns ID Table 5
also have been earned out by employ1Dg a quadratic
lag chstnbuuon over six periods, the sixth be1Dg con
stra1Ded to equal zero In each case the coefficients on
the two mterest rates have the expected s1gns, and
each of the rates used as r0 1s s1gmficant at approx1
mately the 90 per cent level The exact shape of the
lag d1stnbut1on differs, of course, from the esllmated
unconstralDed lag d1stnbulion (mdeed, the constramed
form always yields a coefficient on current CHIPS with
a negallve sign, although 1t 1s never s1gmficantly different from zero) But ID each case the sum of the coefficients 1s s1gmficant at least at the 95 per cent confidence level Thus, while the exact form of the lag
d1stnbution may not be clear from the results, the
CHIPS data do appear to be s1gmficant m expla1Dmg
the level of these deposits
2s Alternative forms of the estimates ID Table 5 also


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45

md1v1dual coefficients m the lag d1stribut1on
are large, but m two cases coefficients on
CHIPS 1_6 are s1gmficant at the 95 per cent
level However, these 1esults could be spurious
The sens1tiv1ty of macroeconometric results
to the mclus1on or cxclus10n of a time trend
1s a well-known phenomenon, and 1t underscores some of the uncertamties and madequac1es mherent m cm rent econometric work
A final note concei ns the signs and s1gmficance of the coefficients on the two mterest
i <1tes The results m panel B of Table 5 could
reflect a trend m the spread between the rates
However, the ume series on Rl' and on the
other rates md1cate that the spread between
the iates narrows m the eatly part of the
period considered <1nd widens agam over the
final 15 to 16 months 29 Furthermore, ,1s Panel
A shows, the mclusion of a trend does not alter
the roles of the two iates m the equation
Table 6 presents the results of regressions
that parallel those reported m Table 5 but
have only a smgle mterest rate The pos1uve sign on the rate-a negative sign 1s predicted by the model-and the rate's s1gmfiCdnce only m the presence of a trend constitute
the most notable results of the regressions Use
of a smgle mterest rate appears to be madequate and to result m specification error
Given this hkely spec1ficat10n error, lt 1s not
wrprismg that the coeffioents on the CHIPS
lag distribution are s1gmficant only m the
absence of a trend 30
have been obta1Ded by us1Dg shorter lag d1stnbut10ns
on CHIPS data In all cases the results are highly
sensitive to 1Dcius1on or exclusion of the trend ID terms
of the s1gmficance of the coefficients on both CHIPS
and 1Dterest rates
20 The 90 day and 180 day Euro dollar rates do not
follow this pattern with respect to Rp, although the
regression results with these rates are very similar to
those reported with domesllc rates However, the prob
!ems of senal correlation are more severe m tests with
these rates
30 Regressions correspond1Dg to the results reported
ID Table 6 for Rap and RE 90 also have been run by
us1Dg a quadrallc lag d1stnbullon on the CHIPS data
The coefficients on the rates are s1gmficant at the 95
per cent confidence level and pos1llve, but when the
trend-s1gmficant at the 99 per cent level-1s mcluded, the sum of CHIPS coefficients 1s not s1gmficant

46

Improving the Monetary Aggregates Staff Papers

TABLE 6 Estimates of the Demand Function for Demand Deposits Due to Foreign Commercial Banks 1
In FCB,

=

a In re

+

6

~ {J, In CHIPS,_,

·-•

+ -rt + Ii + (seasonals)
Independent vanables

r,

a

{J,

{Ji

{Jo

I

I

I

I

fJa

fJ,

I

fJ•

I

I

fJ•

Ii

'Y
I

I

A Regressmns mcludmg a trend term
REoo
RoP
Rev

189<
(2 88)
247<
(3 41)
232•
(3 44)

019
( 30)
003
( 05)
007
( 11)

114
(1 35)
127
(I 24)
123
(1 26)

055
( 79)
053
( 74)
055
( 77)

(((-

008
14)
084
63)
023
41)

(((-

027
47)
030
54)
031
55)

021
( 32)
005
( 02)
012
( 19)

(((-

016
25)
024
37)
023
36)

065
(I 13)

070
(1 26)
052
( 94)

004
( 07)
- 001
(- 02)
- 007
(- 13)

030
( 55)
040
( 77)
045
( 87)

009
( 17)
- 019
(- 36)
- 009
(- 16)

0044
(5 67)
004<
(6 20)
005•
(6 34)

2
(16
2
(17
2
(17

310'
74)
472,
05)
555,
62)

B Regressmns without a trend term
RE,o
RoP
ROD

075

(I 27)

071

(I 20)

062

(I 05)

026
( 44)
023
( 38)
019
( 32)

062

(I 05)

075

(I 31)

077

(I 34)

050
( 87)
047
( 79)
057
( 98)

836•
(7 31)
917 4
(7 75)
909•
(7 77)

i I-statistics appear m parentheses All data are monthly, not
seasonally adiusted, for the period August 1971-November 1975
'F statistic for test of (/30 =
= fJ• = 0) F(7,31) for regressions
mcludmg a trend term, F(7,32) for regresstons without a trend term

' F-statlsllc for test of (a = {Jo =
= {Jo = 0) F(8,31) for regressions mcludmg a trend term, F(8,32) for regressions wllhout , trend
term
• S1gmficant at 99 per cent confidence level
' S1gmficant at 95 per cent confidence level

In order to obtain consistent estimates, as
well as to provide a basis for mterpretmg the
estimated relations as representative of behavioral relat10ns, T, r 0 , and rn must be
statistically exogenous with respect to D 31
Utilizmg C W J Gr,mger's defimtton of
causality and the eqmvalence of that defimtton
with the econometrician's defimt10n of statistical exogeneity established by Christopher A
Sims, one attempt is made-the direct empirical 1mplementat10n of Granger's defimt10nto determme if these conditions are met for
the estimated relat10ns reported here 32 The
iesults of these tests, which are summarized m
Table 7, suggest that while we are not Justified m reJectmg the hypotheses that each of
our right-hand variables is exogenous with
respect to these deposits, neither are we JUStlfied m reJectmg the hypothesis of exogeneity

of deposits with respect to each of the nghthand vanables considered 33 Thus, while
CHIPS and each of the rates pass this test for
exogeneity with respect to FCB, the results
suggest that we should mterpret neither a regression of FCB on those vanables nor regress10ns m the reverse direct10n as representative
of behav10ral relauonslups It should be noted
that these tests are all bivariate tests To mamtam consistency with the model, the data penod should be extended and the tests reformulated m a four-variate representat10n reflectmg
the relauonslups m Table 6 Because of the
limited stze of the available d&ta set, further
tests have not been earned out Thus, these
results imply that caut10n must be exercised
m mterpretmg these regress10ns as iepresentauve of actual demand or behav10ral relat10nships
Some final caveats regardmg our results are
m order The p mdicated m Table 6 represents <1n estimated first-order autoregressive
parameter for the disturbance m the equation
No attempt is made to correct for higher than
first-order senal correlat10n m the residuals

31 In est1matmg the demand function for depostts,
1t 1s assumed that the value of transactions (T) 1s
determmed by factors other than the rates mcluded m
the demand 1elat10n To the extent that T 1s corre
lated w!lh these rates, the estimators are meffic1ent
a2 See Granger, "Invest1gatmg Causal Relat10ns by
Econometnc Models and Cross Spectral Methods," Econ
ometrzca, vol 37 (July 1969), pp 424-38, and Sims,
"Money, Income, and Causality," American Economic
Review, vol 62 (September 1972), pp 540-52


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33 The 180-day Euro-dollar rate 1s the one except10n to this, the 1ate appeanng to be exogenous with
respect to FCB but not the reverse

Foreign Demand Deposits at Commercial Banks in the United States

TABLE 6-Contmued

Regression stat1sucs
F-stattsttcs
(')

(')

R•

Standard
error

ow

p

2;(3,

940

3 604•

838

0402

2 27

665

0922

466

4 221•

849

0386

2 36

667

0282

358

4 380•

858

0388

2 31

654

0343

3 319•

3 807•

350

0451

2 14

850

2726

2 588'

4

ISO•

371

0456

2 03

842

2503

2 568 5

4 179•

371

0456

2 04

842

2541

In adcht10n, any seasonal biases that remam
after the determmistic sedsonal effects repre5ented by the dummy Vdnables dre accounted
for are not cons1deied H Many of these results
are reported as F-tests on the JOmt s1gmficance
of groups of coefficients Given the small number of observdt10ns, the relatively few degrees
TABLE 7 Tests Employing Granger's Definition of
Causahty 1
Y,

= ,-1~'

y

In FCB
In CHIPS
In Rp
In REoo
In Rep
In Ren

a, y,_,

+

X

In CHIPS
In R"
In Rcr
In RE,o
In Ren
In FCB

.

~ fJ,X,-,
,-1

+ -rt + Ii + (seasonals)

F(6,22) 2
I 380
I 300
I 098
I 962
I 469
828
819
I 305
764
982

F(9,22) 3
13 739•
4 930•
5 541•
10 299 6
5 312•
22 756•
30 126•
19 844•
22 638•
25 0664

1All data are monthly, not seasonally ad1usted, f01 the pc11od
October 1971-November 1975
' F-sta t1sttc for test of ((31 =
= fJ• = 0)
3 F-stausuc for test of (ai =
= a, = 0)
4 Stgmficant at 99 per cent confidence level
• S1gmfican t at 95 per cent confidence level
34 For a ch~cuss1on of these t}pes of problem~. ~ec
Christopher A Sims, "Seasonality m Regressmn," Journal of the American Statistical Association, vol 69 (Sep
tembcr 1974), pp 618-26, and Kenneth F Wallis,
"Seasonal Adjustment and Relations between Vanables,"
Journal of the American Statistical Association, vol 69
(March 1974), pp 18-31


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47

of freedom m many of our estimated relat10ns,
and the mconclusiveness of the results, the
F-tests could be considered weak tests of the
ielevant hypotheses
In summary, given the hm1tat10ns imposed
by the data, mconclusiveness m certam results,
and some mcompleteness m the theory, the
evidence supports the content10n that demand
deposits due to foreign commercial banks are
determmed m large part by the level of foreign
transact10ns cleared through CHIPS These
transact10ns are generated primarily by financtdl transfers m the Euro-dollar market and
foreign exchange markets Smee only a small
proport10n of these foreign transactions are
related to sales of goods and services produced
m the Umted States, our results suggest that
proximate determmants of these deposits may
he better represented by foreign transactions
than by U S macroeconomic variables

Demand deposits due to foreign
offecial institutions
An eff01 t 1s made to supplement the 1esult5
tlldt employ sedsonally adjusted data to exdmme demand deposits due to foreign official
mst1tut10ns (FOFF) Smee no monthly figures
comparable to GNP (but not seasonally adJUSted) are avd1lable, the monthly mdex of
mclustnal p1oduction (IPI), not seasonally adjusted, 1s used as a measure of U S economic
dct1v1ty to capture dny relat10nsh1p that may
exist between these deposits and their use for
purchase of U S goods and services These
deposits a1e pos1uvely correlated wtth some
sh01 t-term mterest rates (Table 8), but they
do not exl11b1t any s1gmficant correlat10ns with
US economic act1v1ty as measured by the
IP[ Removal of the trend does not s1gmficantly altei the results, m most cases, the correlat10ns are reduced to even lower levels
Table 9 shows the results of regress10ns of
quarterly GNP on current and lagged Vdlues
ot various components of M wtth seasonally
und<lJusted data The coefficients on FOFF,
whethei taken dS a group or smgly, are not
s1gmficantly chfferent from zero regardless of

48

Improvmg the Monetary Aggregates Staff Papers

TABLE 8 Correlations of Demand Deposits Due to Foreign Official Institutions with Short-term Rates and Index
of Industrial Produchon 1
In FOFF, = a In r,

+

6

I:

,-o

/3, In /Pli-,

+ "It + li + (seasonals)
Independent variables

"

a

/3o
I

522•
(2 17)
526•
(3 23)
575•
(2 73)
282
(I 73)
582 6
(2 98)

RP

RFF
RcP
REoo
RcD

/3,

/31

I

-I
(-1
(-1
(-1
(-1
(-

513
( 25)
- 413
(- 22)
- 028
(- 01)
148
( 07)
- 343
(- 18)

609
54)
668
57)
841
65)
316
45)
515
54)

{J,

{Ja

I

I

1
(
1
(
I
(
1
(

770
58)
012
34)
709
59)
583
52)
954
( 33)

-1 088
(- 36)
348
( 12)
-1 059
(- 37)
- 740
(- 25)
- 406
(- 14)

1 t-stat1st1cs appear 1n parentheses All data are monthly, not
seasonally adJusted, for the period August 1971-November 1975
'F stattStlc for test of ({Jo=
= {J, = 0)

{J,

{Jo
I

I

2
(
2
(
2
(
2
(
3

711
88)
151
72)
806
95)
538
83)
124
(I 07)

I

-3
(-1
-4
(-1
-3
(-1
-3
(-1
-4
(-1

662
21)
220
42)
862
34)
425
15)
529
58)

li

"I
I

1
(
1
(
(
1
(
1
(

107
50)
220
59)
977
47)
570
72)
232
61)

I

007 6
(4 72)
009'
(7 91)
007°
(6 50)
008 6
(6 48)
008 6
(6 74)

4 423

(I 88)

8
(3
7
(2
2

844 6
01)
103•
52)
726
(I 37)
7 7266
(2 75)

'F-stat1st1c for test of (a = {Jo =
= {J, = 0)
• S1gmficant at 95 per cent confidence level
• S1gmficant at 99 per cent confidence level

foreign items due to mdividuals, partnerships,
and corporations (MN + FIPC), the mtroducuon of current and lagged values of FOFF
results m coefficients on FOFF that, taken as
a group, are not sigmficantly different from
zero m explammg GNP

the presence or absence of a trend (However,
considerable first-order autocorrelat10n obviously remams m the estimated relations )
Table IO further mdicates that whether GNP
is regressed on current and lagged M net of
all foreign-owned items (MN) or MN plus

TABLE 9 Regressions (Quarterly) of GNP on Vanous Money Measures 1
6

~ a, In M,_,

In GNP, =

,-o

+ {Jt + "I + (seasonals)
Independent variables

M

a,

ao
I

a,
I

ao

a,

aa
I

I

I

a,
I

{J
I

"I
I

A Regressions mcludmg a trend term

M
MN
FCB
FOFF
FIPC

1 0498
(2 79)
973 3
(2 70)
2048
(2 17)
021
( 94)
152
(I 79)

((-

8943
74)
8243
67)
214
94)
017
52)
385
94)

((-

169
34)
121
28)
023
( 20)
026
(I 04)
088
( 95)

(
(
(((

243
42)
290
60)
062
54)
010
38)
053
58)

729

(I 30)

(I

(
(
(

720
53)
050
42)
004
15)
004
04)

201
39)
146
32)
012
( 11)
009
( 36)
037
( 35)

((-

381
( 87)
381
( 95)
- 056
(- 46)
- 033
(-1 27)
- 096
(- 90)

(((((-1

225
66)
214
64)
014
12)
021
87)
168
60)

((-

002
84)
002
83)
005•
(3 90)
007•
(34 96)
007•
(13 16)

- 790
(-1 24)
- 794
(-1 18)
2 168•
(176 04)
I 918 4
(198 35)
1 925•
(59 30)

B Regress10ns wtlhout a trend term
M
MN
FCB
FOFF
FIPC

(2
(2
(I

(
(I

152
31)
138
32)
036
( 27)
023
( 68)
386
(I 87)

(
(
(
((2

115
21)
173
37)
028
22)
009
27)
417
05)

727

(I 31)

677

(I 47)

123
( 93)
002
( 05)
465•
(2 14)

1 l•sta t1st1cs appear m parentheses All data are quarterly, not
seasonally adJusted, for the period 1965 Q2-1973 Q4
2 F-stallsllc for test of (ao =
= a, = 0) F(7,23) for regressions
mcludmg a trend term, F(7,24) for regressions without a trend term


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Federal Reserve Bank of St. Louis

(((-

332
67)
268
63)
009
07)
005
( 13)
338
(I 42)

394
( 91)
372
( 94)
002
( 01)
- 037
(-1 06)
245
(I 02)

(-1
(-1

346
13)
327
08)
171
(I 49)
- 018
(- 53)
274
(I 15)

S1gmficant at 95 per cent confidence level
• S1gmficant at 99 per cent confidence level

3

(-4
(-3
1
(204

243•
17)
215•
65)
656•
64)
359•
(52 78)
1 111 •
(28 73)

Foreign Demand Deposits at Commercial Banks in the United States

49

s1gmficantly different from zero m explammg

TABLE 8-Conhnued

FOFF
Regression stausucs
F(7,31) 2 F(8,31)'
528

R'

Standard
error

DW

:E/3,

p

2 502•

734

099

1 90

412

-

2583

890

3 688'

790

094

1 93

355

-1 5696

779

2 954,

746

095

1 98

428

-1 2980

458

2 079

695

099

1 93

460

3583

896

3 240•

760

093

1 94

417

-1 4831

It might also be hypothesized that deposits
hke FOFF could be held for purchases such
as m1htary items As the last hne of Table 10
shows, neither the coefficients on current and
lagged GNP nor those on current and lagged
US m1htary export sales are, taken as a group,

TABLE 9-Contmued

Regression statistics

R•

Standard

2 687 3

982

009

2 17

793

1 8077

2 234

979

009

1 96

808

1 8843

F-stausuc•

error

DW

Xa,

p

2 065

987

011

I 76

582

994

983

012

I 47

636

I 507

984

Oil

I 84

632

0069

97 231•

981

009

2 03

801

1 3003

73 381•

979

009

1 85

822

1 3122

120 112•

975

013

1 42

677

5653

376

910

017

86

948

14 560•

864

026

54

749


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Federal Reserve Bank of St. Louis

1579
-

-

The evidence, m shoi t, does httle to suggest that demand deposits due to foie1gn offiCial mst1tut10ns ale ielated m any sigmficant
way to US output or mcome

0003

0019
2 5120

Demand deposits due to foreign
individuals, partnerships, and
corporations
Results of the efforts to supplement the
earher analysis of demand deposits due to foreign mdividuals, partnerships, and corporat10ns (FIPC) are presented m Table 11 Coefficients on current and lagged IP/ are, as a
group, sigmficantly different from zero at the
95 per cent level or above only when Rp or
RE. 111 1s mcluded m the estimated relat10n
Furthermoie, when the trend 1s removed, even
these results d1sappea1 As Table 9 shows,
however, when the trend 1s removed from the
quarterly regress10ns, the coefficients on FIPC
are s1gmficant at well above the 99 per cent
confidence level Unfortunately, the poss1b1hty
of senous first-order autoconelauon m this
estimated relat10n also exists Table 12 md1cates that coefficients on FIPC a1e not, as a
group, s1gmficant m explammg GNP when mcluded ma regress10n of GNP on M net of all
foreign Items (MN) The same type of relat10nslup, estimated monthly by usmg IP/ for
output, shows these coefficients to be s1gmficant at the 99 per cent level both when a trend
is mcluded and when It 1s excluded Agam,
however, m these cases there 1s strong evidence
of senal correlation m the estimated relation
(Indeed, tests usmg an estimated first-order
autoregressive parameter resulted m no improvement, as mdicated by the Durbm-Watson
statistic)
In summary, these results do little to resolve
the question of meanmgful relationships between demand deposits due to foreign IPC's
and U S macroeconomic variables

50

Improvmg the Monetary Aggregates Staff Papers

TABLE 10 Further Evidence on the Correlation of FOFF with GNP 1
Independent vanables
a,

ao

a,

(Jo

(J,

/j1

-y

(Ja

3

!: a, In MN,_, + I:' /Ji In FOFF,_, + -rt + ll + (seasonals)

A In GNP,=
883'
(2 07)

068
(- 11)

070
( 12)
3

3

,-o

595

~

0002
( 001)

(I 12)

3

a

,-o

,-o

005
( 24)

- 909
(-1 21)

0009
(- 41)

+ -YI + ll + (seasonals)

fJ, In FOFF,-i

010
( 45)

021

(I 47)

745
(- 36)

3 061

(I 45)

010
( 46)

!: a, In (MN + FIPC),_, +

0002

005
( 22)

( 01)

0009
(- 40)

- 919
(-1 23)

- 031
(-1 56)

-7 320
(-1 37)

!: a, In GNP,_, + !: /J, In MIL,_, + -rt + ll + (seasonals)

C lnFOFF,=
766
( 38)

022
(I 15)

,-o

088
( 15)

083

(- 14)

,-o

607
(I 51)

B In GNP,=
895•
(2 10)

,-o

1 126
( 54)

022
( 20)

108

097
( 96)

(I 03)

1 1-stattst1cs appear m parentheses MIL = VS military export
sales All data are quarterly, not seasonally adJusted, for the per10d
1965Q2-1973Q4
2 F-stat1st1c for test of (ao =
= (Jo
= 0)

016
(- 14)

' F-stat1sttc for test of (ao =
= aa = 0)
• F stat1st1c for test of (/Jo =
= (Ja = 0)
• S1gmficant at 95 per cent confidence !eve I

TABLE 11 Correlations of Demand Deposits Due to Foreign lndmduals, Partnerships, and Corporations with
Short-term Rates and Index of Industrial Produchon 1
In FIPC,

= a In r, + ,-o
!:' /J, In JpJ,_, + -YI + ll + (seasonals)
Independent variables

"

a

(Jo

167•
(2 09)
043
( 61)
039
( 45)
035
( 58)
058
( 73)

RP
Rrr
Rep

R&o
RcD

(J,

(J1

I

I

-1
(-1
-1
(-1
-1
(-1
-1
(-1
-1
(-1

538
75)
752
94)
680
86)
715
89)
736
93)

1
(
1
(
I
(
1
(
I
(

(J,

(Ja
I

I

-

296
92)
360
96)
325
95)
399
99)
361
97)

- 661
(- 47)
- 392
(- 27)
- 498
(- 35)
- 478
(- 33)
- 452
(- 32)

616
(- 43)
- 531
(- 37)
- 483
(- 34)
- 521
(- 36)
- 571
(- 40)

1 t-stat1st1cs appear m parentheses
All data are monthly, not
seasonally adiusted for the period August 1971-November 1975
' F-stat1st1c for test of ((Jo =
= fJ• = 0)

I

I

2 736

(I 90)

2 503
(I 72)

2 548

(I 77)

2 563

(I 75)

2 607

(I 79)

I

-2 784
(-1 94)
-2 859
(-1 98)
-2811
(-1 98)
-2811
(-1 93)
-2 897
(-2 02)

ll

-y

(J,

(Jo

I

I

009 5

639
( 66)
I 049
(I 07)
I 043
(I 06)
I 049
(I 06)
I 023
(I 05)

(14 96)
009•
(15 75)
008•
(15 17)
009•
(15 88)
009 5
(15 61)

9
(8
7
(5
6
(4
7
(7
7
(5

087•
69)
262 5
13)
785•
97)
021 5
35)
342 5
34)

-

155'

F-stat1st1c for test of (a = (Jo =
= fJ• = 0)
S1gmficant at 95 per cent confidence level
• S1gmficant at 99 per cent confidence level
3

4

TABLE 12, Further Evidence of Correlations between FIPC and US Economic Actmty 1
Independent vanables
a,

ao

aa

...

A Quarterly estimate In GNP,
1 026'
(2 53)

363
(- 71)

194
( 40)

=

3

3

,-o

1-0

I 338

391
( 37)

(I 05)

310
( 24)

055
( 72)

370
(- 37)

I 056
( 62)

525
( 28)

318
( 15)

576
( 43)

=

6

6

,-o

,-o

031
( 36)

385
( 30)

I 441
( 72)

1 l-stat1st1cs appear m parentheses Quarterly data are for the period
1965 Q2-1973 Q4 monthly data are for the penod August 1971December 1975 All data are not seasonally adiusted
2 F stat1st1c for test of all a, = all (J, = 0


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Federal Reserve Bank of St. Louis

009
( 09)

117

(I 23)

!: a, In MN,_, + !: /J, In FIPC,_, + -YI + ll + (seasonals)
232
( 31)

129 6
(2 10)

073

(I 16)

C Monthly estimate, without trend Same as B, ncept -Y
- 110
(- 05)

(Ja

!: a, In MN,_, + !: /Ji In FIPC,_, + -YI + ll + (seasonals)

579

(I 96)

(J,

(Jo

a,

(I 71)

B Monthly estimate, with trend In /Pl,
1 262

a,

-1 105
(- 98)

112
(I 14)

s

056
( 56)

044
( 67)

049
(- 73)

(-2 43)

- 006
(- 06)

- 029
(- 27)

- 230'
(-2 32)

0

' F stat1sttc for test of all a, = 0
' F-stat1st1c for test of all (J, = 0
• S1gmficant at 95 per cent confidence level
• F(8,22)

Foreign Demand Deposits at Commercial Banks in the United States

51

TABLE 10-Contmued
Regression stat1st1cs
F(8,22) 2

F(4,22)'

F(4,22)'

2 643 5

4 139 5

0 741

2 652 5

4 156•

0 687

0 895

0 850

0 551

Standard

-

error

DW

988

00983

1 82

988

00982

l 83

608

092

11019

I 39

638

p

TABLE 11-Contmued

Regress10n sta Ust1cs
F(7,31) 2

F(8,31) 3

R•

Standard
error

DW

3 720 5

3 256•

930

042

2 02

208

9291

2 150

2 094

905

044

2 01

292

6211

p

J;{J,

2 044

I 956

897

044

2 03

319

5558

2 368•

2 135

907

044

2 00

281

5144

2 175

2 107

904

044

2 02

297

66S0

TABLE 12-Contmued
Regresston sta usucs
{J,

{J,

I

- 151'
(-2 45)

-1 55•
(-2 56)

- 258 6
(-2 72)

- 273•
(-2 96)

I

'Y

I

(')

I

(')

I

I

(•)

I

R•

I

Standard
error

- 0009
(- 45)

- 606
(- 85)

2 473 5 ,,

3 220•, 7

638 7

985

00939

- 016'
(-6 51)

-48 676'
(-8 60)

69 539,,,

17 855•,10

6 664', 10

961

0131

-12 2458
(-9 04)

29 611•, 11

25 794,,12

45 856',12

901

0208

'F(4,22)
8 S1gmficant at 99 per cent confidence level
• F(l4,26)


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Federal Reserve Bank of St. Louis

a

F-stat1sucs

10
11
12

F(7,26)
F(l4,27)
F(7 27)

jow

I

2 00

69

49

p

707

'

52

Appendix: Discussion of Data Used

In order to perform the emp1ncal work requested
by the Committee on Monetary Statistics, as well
as to construct the body of supportmg evidence
presented m this study, It 1s important that each
of the series used be constructed m a consistent
manner over the entire period used m the study
Unfortunately, this consistency 1s not easily obtamed for the series on foreign demand deposits m
the money stock, and some compromises have been
necessary The particulars regardmg the series on
foreign-owned demand deposits m U S commercial
banks are discussed here

Demand deposits due to foreign
commercial banks
The prmc1pal sources of data on these deposits
are the Treasury-Foreign Exchange Reports B-1
(TFEX) data and the deposits reported by weekly
reportmg banks that are members of the Federal
Reserve System The TFEX data do not yield a
consistent series because, prior to December 1971,
hab1hties of U S banks to their foreign branches
were included as demand deposits due to foreign
banks Smee no separate senes exists for these
latter deposits pnor to that date, It 1s 1mposs1ble to
remove them from the compiled senes
The figures compiled from the reports of weekly
reportmg member banks do not yield a complete
measure of the desired senes In particular, data
are not mcluded for demand deposits due to foreign banks at (I) US agencies and branches of
foreign banks, (2) Edge Act corporations, (3) member banks not reportmg weekly to the Federal Reserve, and (4) nonmember banks Accordmgly, an
estimated senes has been constructed m an effort
to overcome these om1ss1ons wlule mamtammg as
much consistency as possible m the resultant senes
Estimates for nonweekly reportmg member banks
and nonmember banks have been obtamed by mterpolat1on from call report data 1 Added to these

figures are last Wednesday-of-the-month figures for
(I) agencies of foreign banks m the Umted States
and mvestment compames m the Umted States
that are ma1onty owned by one or more foreign
banks, and (2) Edge Act corporations, complied
from Federal Reserve Reports 886a and 886b, respectively (For the penod pnor to November 1972
these figures are estimates based on a monthly compounded growth rate for the penod over which
data are available, November 1972 through November 1975) Finally, data have been obtamed for
branches of foreign banks m the Umted States
from Federal Reserve Report 886a (For the penod
pnor to January 1973 these figures are mcluded m
the estimates for nonweekly-reportmg member
banks and nonmember banks ) These senes are
added then to the averages of Wednesday figures
for weekly reportmg member banks, and this resultant senes 1s used m the empmcal work Although
this senes does not measure the desired senes exactly, It 1s as consistent as available data will permit and mvolves mm1mal extrapolations when data
are not available

Demand deposits due to foreign official
institutions and to foreign individuals,
partnerships, and corporations
Smgle observation, end-of-month data for these
senes are taken from the Federal Reserve Bulletin,
"Short-Term Liab1hties to Foreigners Reported by
Banks m the Umted States, by Type " These data
were chosen m order to provide the longest consistent senes possible and, m the case of foreign
official mstltutions, to avoid the om1ss1ons mherent
m the average data available for weekly reportmg
member banks The data used are revised as of
January 1976

Other data series employed

1

Estimates were provided by the Board of Governors of
the Federal Reserve System, D1v1s1on of Research and Stat1st1cs


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Federal Reserve Bank of St. Louis

The CHIPS data used are monthly averages of
daily close of-busmess figures for the Clearmg

Foreign Demand Deposits at Commercial Banks in the United States

House Interbank Payment System These averages
are based upon the number of busmess days m a
month, the daily figures bemg provided by the
Federal Reserve Bank of New York The penod
for the monthly regressions employmg the CHIPS
data 1s determmed by the penod of available
CHIPS data, that 1s, the daily data are not available pnor to January 1971
AU other monthly and quarterly data, with the
exception of GNP and personal mcome figures,
seasonally adjusted and not seasonally adjusted,
are taken from vanous issues of the Federal Reserve Bulletin or provided by the D1v1S1on of Research and Statistics, Board of Governors of the
Federal Reserve System The seasonally adJUSted
data were prepared by usmg the version of the
X-ll seasonal adjustment program available at the
Board of Governors The quarterly unadjusted
GNP figures are taken from pubhcat1ons of the


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Federal Reserve Bank of St. Louis

53

Department of Commerce 2 (At the ume tlus study
was bemg conducted, these figures were bemg substantially revised, and consequently, data were available only through the fourth quarter of 1973) In
addition, not seasonally adjusted GNP 1s not recorded m exactly the same way as are other not
seasonally ad1usted data, and the results obtamed
with those data should be mterpreted with this m
mmd The supplemental work was done m response
to a subsequent request by the Committee The miual penod for the quarterly regressions with unadJUSted data 1s determmed by the earliest penod for
wluch the FOFF and FIPC senes were available,
that 1s, begmnmg m July 1963
2 National Income and Product Accounts of the United
States, 1929-1965, Statistical Tables, Supplement to the Sur
vey of Current Business (August 1966), US National Income
and Product Accounts, 1961-69 (July 1973), and Survey of
Current Business, vol 54 (July 1974)

54

Bibliography

Barro, Robert J , and Anthony M Santomero "Household Money Holdmgs and the Demand Deposit Rate" Journal of Money, Credit and
Banking, vol 4 (May 1972), pp 397-413
Granger, C W J "Invesugatmg Causal Relations by Econometric Models
and Cross-Spectral Methods" Econometrica, vol 37 (July 1969), pp
424-38
Klem, Benpmm "Compeuuve Interest Payments on Bank Deposits and
the Long-Run Demand for Money" American Economic Review, vol
74 (December 1974), pp 931-49
Sims, Christopher A "Money, Income, and Causality" American Economic
Review, vol 62 (September 1972), pp 540-52
- - - "Seasonality m Regress10n" Journal of the Ame11wn Statisttwl
Association, vol 69 (September 1974), pp 618-26
Theil, Henn Principles of Econometrics New York Wiley, 1971
Thurman, Stephen "Prelimmary Results of Tests on Inclusion of Foreign
Deposits m the Money Supply" Memorandum Washmgton Board of
Governors of the Federal Reserve System, October 1974
US Department of Commerce The National Income and Product Accounts of the United States, 1929-1965, Statistical Tables Supplement
to the Survey of Current Business, August 1966
US National Income and Product Accounts, 1964-69, July 1973
- - - Survey of Current Business, vol 54 (July 1974)
Wallis, Kenneth F "Seasonal Adjustment and Relations Between Vanables" Journal of the American Statistical Association, vol 69 (March
1974), pp 18-31


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Federal Reserve Bank of St. Louis

55

Nonmember Banks and Estimation of the Monetary Aggregates
Darrel W Parke

This paper, written in early 1976, presents a
case for expanded collection of deposit data
from banks that are not members of the Federal Reserve System In June 1977 the Federal
Deposit Insurance Corporation began collecting daily deposit data from a sample of about
600 nonmember banks This survey will continue for the next 2 years, after which the
mues discussed in this paper will be reassessed
In June 1976 the Federal Reserve estimated the narrowly defined money stock (M 1)
f01 January 1976 to be $301 3 b1lhon Of this
dmotmt, $161 9 billion was m demand deposits
,tt commernal banks that are members of the
Federal Reserve System-demand deposits adJUsted (DDA) at member banks, $73 7 billion
was m cun ency, and $62 5 bilhon was m
DDA at nonmember banks 1 The Federal Reserve constructs M 1 by adclmg these estimates
to estimates of other components 2 Thus, to
obtam accurate current estimates of total M 1 ,
1t 1s imperative to have accurate current estimates of nonmember bank DDA because 1t
constitutes more than 20 per cent of M 1
Unf01 tunately, estimates of nonmember
bank DDA have often been maccurate Deposit d.tta are available from nonmember

banks for only 4 days each year-the call report dates The estlmatmg procedure, which
will be descnbed m detail m the next sect10n,
1s based on an extrapolation of the nonmember DDA se11es from prev10us call report dates
to obtam a current or "m1t1al" estimate This
estimate 1s successively revised as add1t10nal
call reports are processed until the call reports for elates surrounclmg the penod m
quest10n are dvailable, at which time a "final"
estimate 1s made A list of m1t1al and final
estimates for the weeks of the call dates smce
1970 1s given m Table I
Exammat1on of Table I reveals that the
rev1S1ons have been a5 large a5 $2 billion, or
.tbout 4 per cent of aggregate nonmember
bank DDA The average of the absolute values
of the rev1S1ons 1s $9~2 million, and the root
mean 5quare of the rev1s10ns 1s $1,116 million
To gam some perspective on these numbers,
consider the computation of a quarter-toquarter growth rate m M 1 Suppose the value
of M 1 for the base quarter 1s known, but the
TABLE 1 Weekly-Average Estimates of Nonmember
Bank DDA for Selected Weeks around
Call Dates
In milhons of dollars

NoTF-The author 1s on the staff of the Div1S1on
of Research and Statistics He wishes to thank Stephen
Taubman and Lucy McCurdy for their programmmg
assistance, staff members of the Federal Deposit In
~urancc Corporation for helpful comments on earlier
d1afts, Gerald Nickelsburg for assistance m the early
5tagcs of this study, and Richard Porter for many
valuable d1scuss10ns
1 Federal Reserve Bulletin, vol 62 (May 1976), p Al2
All figures used m this report arc not seasonally ad
Justed
2 See Darwm L Beck, "Sources of Data and Methods
of Construction of the Monetary Aggregates," this
volume


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Total

Imual
estimate

Fmal
estimate

1970-June
Dec
1971-June
Dec
1972-June
Dec
1973-Mar
June
Oct
Dec

36,388
40,406
39,251
44,133
43,874
51,761
47,496
50,228
52,011
57,100

35,475
40,476
39,368
45,104
45,490
52,489
48,831
52,220
53,821
57,475

-913
70
117
971
1,616
728
I, 335
1,992
I 810
375

1974-Apr
June
Oct
Dec
1975-Apr
June
Sept
Dec

56,491
56,996
57,460
59,554
59,970
59,109
58,560
63,111

55,349
55,755
57,236
58,830
58,136
58,638
58,272
62,729

-1,142
-1,241
-224
-724
-1,834
-471
-288
-382

Call date

rev1s1on

56

estimate for the current quarter is understated by $2 billion At the current level of
M 1 -about $300 billion-the annualized rate
of growth would be understated by 2 7 percentage pomts
To aid the Federal Reserve m developmg
improved estimates of nonmember bank deposits, the Federal Deposit Insurance Corporation (FDIC) conducted an experimental survey m late 1974 and early 1975 The FDIC
asked all of the I 78 nonmember banks with
more than $100 milhon m deposits and a
sample of 395 smaller nonmember banks
stratified by size to report their deposit balances on a weekly (daily-average) basis The
FDIC then supplied the Federal Reserve with
deposit data aggregated m various ways, although it retamed the mdividual bank data
m order to mamtam confidentiality
This study aims to determme (1) whether
mformation extracted from the FDIC survey
can be used to modify and improve the present estimation procedure, and (2) whether
estimates based on the sample data from the
survey are substantially more accurate than
the present estimates
This paper presents a descnpt10n of the
present method of estlmatmg nonmember
bank DDA by the Federal Reserve and some
of the hmitatlons of this method, a comparison of the present method with estimates
based on the sample data, an assessment of
the accuracy of the sample estimates, a discuss10n of alternative estimation procedures,
and some concludmg remarks

Present-method estimates
All member banks report their deposit balances for each day of the year Most of these
banks report withm a week after the close
of the statement week, and the remamder report withm 2 or 3 weeks All msured banks
report deposit data as of the last day of each
quarter on the call reports 3 These data gena Durmg the period under study, the sprmg and fall
call dates vaned from year to year
Data for nonmsured banks are available only for
the June and December call dates No s1gmficant problems appear to have been encountered m esumatmg
the deposits of these banks


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Federal Reserve Bank of St. Louis

Improvmg the Monetary Aggregates· Staff Papers

TABLE 2 Ratios of Nonmember DDA to Country
Bank Data
Call date
1967-June
Dec
1968-June
Dec
1969-June
Dec.
1970-June
Dec
1971-June
Dec
1972-June
Dec

Rt
5471
5562
5614
5730
5969
6136
6178
6307
6365
6585
6808
6953

Call date
1973-Mar
June
Oct
Dec
1974-Apr
June
Oct
Dec
1975-Apr
June
Sept
Dec

R,
7230
7357
7361
7553
7587
7709
7796
7889
7849
8029
8057
8174

erally become available 4 or 5 months after
the call date
To estimate nonmember DDA for a given
statement week by the present method, the
Federal Reserve staff first tletermmes the ratios
of nonmember DDA to the DDA of a subset
of member banks, the "country banks," 4 on
the call dates that precede and follow the
statement week A series of these ratios 1s displayed m Table 2 A lmear mterpolation of
the call-date ratios with smtable adjustment
for changes m bank structure yields the estimated ratio for the statement week The estimate of nonmember DDA 1s obtamed by
muluplymg the estimated ratio by the reported country bank DDA for that week
Before the rat10s of nonmember DDA to
country bank DDA become available for the
call dates, they are estimated by extrapolatmg
the senes of ratios obtamed from the call reports that are available Suppose, for example,
that the statement week is the first week m
January The "1mual estimate" of nonmember DDA is made durmg the fourth week m
January even though the series of known
ratios from the call reports extends only to
June of the precedmg year 5 Extrapolations are
4 "Country banks" 1s the class1ficat10n of a group of
member banks pnor to November 9, 1972 Although
the term 1s no longer officially used to descnbe these
banks, the group still exists and will be referred to as
country banks m this report
s In this report, we will be d1scussmg revmons and
errors m the esl!mates of nonmember DDA Smee the
d1scuss1on begms with the estimate made 3 weeks after
the statement week, rev1s10ns and errors will be due
solely to uncertamty about nonmember DDA and not
to uncertamty about country bank DDA, which 1s
known by this lime Our "m1tial esl!mate" corresponds to the first rev1S1on discussed m Improving the
Monetary Aggregates Report of the Advisory Com
mzttee on Monetary Statistics (Board of Governors of
the Federal Reserve System, 1976), p 25

57

Nonmember Banks and Estimation of the Monetary Aggregates

made f10m this known senes to obtam 1at10s
for December and March, which are mterpolated to obtam the estimated rat10 for the
January statement week Mult1plymg tlus
estimated rat10 by reported country bank DDA
for the statement week yields the m1tial estimate In February, the September rat10 1s
calculated by usmg the September call report
data, which have JUst become available New
extrapolations are made to rat10s for December and March, the mterpolation procedure
1s repeated, and a revised estimate 1s obtamed
for the January statement week In May, when
the Decembc1 call report data are available,
a new extrc1polat1on 1s made to March, and
the known December and extrapolated March
1at10s are mterpolated as before to obtam a
third estimate for the January st,ttement week
The March call report data then become
available m July Interpolatmg the known
December and March rat10s yields the fourth
and final estimate of nonmember DDA for
the statement week
Each of the estimates was made by usmg
the same value for country bank DDA, only
the estimate of the ratio of nonmember bank
ODA to country bank ODA 1s revised In the
hypothetical example, four estimates were
made, and the final one was made 6 months
,tfter the statement week In practice, three or
four estimates (or, rarely, two) are made with
the final estimate made 3 to 8 months after
the statement week The number of estimates
and the lag depend on the position of the
statement week with respect to the call dates,
the time between the call dates, and the time
1 eqmred to process the call report data
Throughout the procedure, the estimates
,md proJecuons are modified to account for
structural changes (banks droppmg their
membership, nonmember banks mergmg with
member banks, and so on) For example, 1£
a country bank resigns from the System, the
estimated rat10 for that week 1s revised upward, and rat10s for succeedmg weeks are
obtamed by mterpolatmg between the revised
rat10 and a revised extrapolated rat10 for the
next call date
The process of extrapolatmg the series of
ratios was exclusively a Judgmental one prior


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Federal Reserve Bank of St. Louis

to 1974 In early 1974 a regress10n model was
developed that appeared to explam, m large
part, the variation m the series 6 Tlus model
1s now used to provide pred1ct10ns, which a1e
Judgmentally mochfied, of the nonmembe1
DOA and count1 y bank DOA ratios The regress10n model 1s of the fo1m
(1)

Rt =

bo

+

bit

+

b2ti

+

b3 RTBi

whe1e R 1 1s the estimated rat10 of nonmember bank DDA to country bank DDA at time
t and RTB 1 1s the average 91-day T1easury
hill rate fo1 the half year precedmg t The
Treasm y bill rate 1s a proxy for the constellation ot sh01t-tc1m money market mte1est rates
beheved to mfiuence the demand f01 demand
deposits It enters the equation with a s1gmficantly positive coefficient presumably beCc1use the elasticity of the demand funct10n
for demand deposits at nonmember banks 1s
Iowe1 than that at counu y banks The present
procedme 1s to refit Equation I to the ratios
each time a new ratio becomes available and
then to extrapolate the resultmg equat10n
The extrapolations then undergo some Judgmental adjustments, and the estimat10n proceeds as described earher
Equat10n 2 1s an example of how the regress10n model provides a good fit This equation was estimated on May 13, 1974, when
the December 1973 call report data first became available The estimated equation and
standard errors of the coefficients (m parentheses) are
(2)

R., = 52496 + 00559t
( 00817) ( 00163)

+

00064t 2
( 00010)

+

00359RTB 1
( 00121)

whe1e t = I for June 1967 and mcreases one
umt each 6 months The equation explams
99 4 pet cent of the vanat10n m Rt The
standard enor of the estimate 1s O0034 Country bank DDA was about $78 3 b1lhon at the
time, so the O 0034 standard error for the
a See Darwm L Beck and Joseph Sedransk, "Rev1S1ons
of the Money Stock Measures and Member Bank Reserves and Deposits," Federal Reserve Bulletin, vol 60
(February 1974), pp 81-95

58

Improvmg the Monetary Aggregates Staff Papers

rat10s translates mto a standard error of about
$266 million for nonmember bank DDA estimates
Unfortunately, Equat10n 1 does not fit as
well outside the sample penod as it does mside
the period For example, when Equation I
was extrapolated after receipt of the December
1974 call report data, the estimated ratios for
Apnl and June 1975 were 0 7697 and 0 7845,
respectively As can be seen from Table 2,
these estimates are m error by O 0110 and
0 0136 or, m dollar terms, about $860 million
and $1,060 milhon-far m excess of the standard error withm the sample penod Why
the equat10n breaks down outside the sample
penod is not known
The present-method estimates over the
penod studied, from the week endmg August
28, 1974, to Apnl 16, 1975, are shown m Table
3 The first entry m each line of the table is

the mitial estimate for that statement week
(made about 3 weeks later), followed by succeedmg estimates as additional call reports
aie processed The last entry m each lme is
the final estimate, and the differences between
the final estimates and the early estimates are
given m the columns labeled "Revision"
For example, the June 1974 call report was
not available until October 30 The imtial
estimate for September 18 of $57,251 million
was based on an extrapolation from the Apnl
1974 call report The senes was revised on
October 30, takmg mto account the June call
1eport data This revis10n yielded an mtenm
estimate fo1 September 18 of $56,774 milhon
This estimate was further revised on January
31, 1975, when the October 1974 call report
data were processed By this time, direct observat10ns of the ratio of nonmember to country
bank DDA were available for dates before and

TABLE 3 Estunates of Nonmember DDA Usmg the Present Method, 1974-75
In m11hons of dollars

Last call report avadable at time of estimate
End of week

Apr 1974
Estimate

1974-Aug 28
Sept 4
11
18
25
Oct

2
9
16
23
30

I

Rev1s1on

I
I

June 1974
Estima\e

I

Revtston

I
I

Oct 1974
Estimate

I

I

Revts1on

I

I Apr 1975
I RevtSton I Estimate

Dec 1974
Estimate

55,204
56,006
57,390
57,251
55,620

-534
-571
-614
-641
-652

54,785
55,566
56,926
56,774
55,142

-115
-131
-150
-164
-174

54,670
55,435
56,776
56,610
54,968

55,064

-679

55,113
56,228
57,460
56,852
55,983

-188
-205
-224
-257
-290

54,925
56,023
57,236
56,616
55,749

-21
-56

56,595
55,693

Nov

6
13
20
27

56,859
57,846
57,514
56,620

-334
-406
-412
-442

56,634
57,627
57,292
56,392

-109
-187
-190
-214

56,525
57,440
57,102
56,178

Dec

4
11
18
25

57,711
58,354
58,685
58,451

-560
-602
-640
-674

57,487
58,134
58,465
58,229

-336
-382
-420
-452

57,151
57,752
58,045
57,777

1975-Jan

1
8
15
22
29

59,554
60,389

-724
-775

59,338
60,221
59,464
58,057
56,054

-508
-607
-682
-732
-772

58,830
59,676
58,912
57,510
55,525

-62
-130
-185
-243

59,614
58,782
57,325
55,282

Feb

5
12
19
26

56,322
56,586
56,412
55,620

-857
-940
-1,020
-1,074

55,767
56,006
55,816
55,020

-302
-360
-424
-474

55,465
55,646
55,392
54,546

Mar

5
12
19
26

56,539
57,437
56,959
56,239

-1,185
-1,290
-1,351
-1,410

SS,900
56,759
56,271
55,547

-546
-612
-663
-718

55,354
56,147
55,608
54,829

Apr

2
9
16

57,077
58,979
59,970

-1,500
-1,687
-1,834

56,364
58,169
59,087

-787
-877
-951

55,577
57,292
58,136


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Federal Reserve Bank of St. Louis

Nonmember Banks and Estimation of the Monetary Aggregates

after September 18, and an mterpolation
yielded the final estimate of $56,610 million 7
Thus, the Federal Reserve's estimate of nonmember DDA for the week of September 18,
1974, was $57,251 million until October 30,
from October 30 to January 31, 1t was $56,774
million, and after January 31, It was $56,610
million The total rev1s10n was $641 million,
and the rev1s1on of the mte11m estimate was
$164 million
During the study pe11od, each successive
estimate was closer to the final estimate than
was Its predecessor Typically, one would expect the revised estimate to be better than
the m1trnl one, but there 1s no guarantee of
this A rev1s10n of an m1trnl estimate 1s simply
a new estimate that uses the add1t10nal mformatlon provided by new call report data
There 1s no guarantee of the accuracy of the
final series, which 1s JUSt a set of estimates
made after all data believed to be relevant
are available Only nonmember deposits as
of the smgle day call report dates are known
with certamty
Insofar as rev1s10ns are concerned, the study
pe110d 1s typical of the general experience
5mce 1970 The root mean square of the total
rev1s10ns for the weeks of the three call dates
(October 15, December 31, and April 16) covered by the study period 1s $1,146 million The
1oot mean square of all such revISlons from
1970 to September 30, 1975, 1s $1,116 million
A few of the weekly-average estimates could
be improved 1f the call report data had been
processed more qmckly If, for example, the
June 1974 call report data had been processed
w1thm ~ rather than 4 months-that Is, by
September 30-the 1mt1al estimate of $57,251
million for the week of September 18 would
not have been made Instead, the m1t1al estl7 A m1S1nterpretat1on of the October 1974 call report resulted m an overstatement of nonmember DDA
fo1 October 16 of $574 mllhon The error wa~ dis
covered and corrected m May 1975 dunng the Decem
ber benchmarkmg In an effort to ehmmate the effects
of the mmnterpretauon, which 1s totally unrelated to
the matters at hand, $574 m1lhon was subtracted from
all estimates based on the October call data Thus, for
example, the total rev1S1on for Apnl 16, 1975, was
actually $2,408 m1lhon but 1s given m Tables I and 3
as $1,834 m1lhon


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59

mate would have been the one m the June
column of Table 3-$56,774 million-and the
total benchmark revIS1on for that week would
have been $164 milhon, not $641 mzlhon On
the othe1 hand, the 1mtial estimate for the
week of September 4 would still have been
based on call data only through April, so the
total rev1s10n of $571 m1ll10n for that week
would be unaffected by the I-month reduction
m processmg time In general, 1f processmg
time were reduced to 3 months, 11 of the 34
total revIS1ons considered here would have
been reduced

FDIC-sample estimates
The FDIC experimental sample was d1v1<led
accordmg to the banks' total deposits mto
5even strata, 1angmg from less than $5 million
to more than $100 million Average nonmember bank DDA for week t, for example, was
estimated by usmg the separate ratio estimator
(3)

Y(t)

where y11 (t) 1s the average aggregate DDA of
the stratum h sample banks durmg week t,
y11 (c) 1s the aggregate DDA m the sample banks
as reported on the most recent available call
report, and Y11 (c) 1s the aggregate DDA m all
stratum h nonmembe1 banks as repo1 ted on the
most recent call report The first formula-the
one most often found m textbooks-expresses
the notion that the aggregate of all stratum h
banks 1s estimated to have grown at the same
rate as the aggregate of sample stratum h
banks
The second formulation of the estimator m
Equat10n 3 1s p1esented m order to emphasize
the similarity between the sample estimator
and the present-method estimator In the present method, a projection of the ratio of nonmember bank DDA to country bank DDA 1s
made and, m turn, 1s mult1phed by the known
weekly-average country bank DDA The sam-

Improvmg the Monetary Aggregates Staff Papers

60

DDA are presented m Table 4 The difference
m total rev1S1ons between the sample and the
present-method estimates 1s stnkmg While
total rev1S1ons of the present-method estimates
ranged from $205 million to 11,1,834 million
over the study penod, those of the sample
estimates were much smaller, rangmg from
$20 million to $410 million 8 Of the 65 m1t1al
and mtenm sample estimates m Table 4, only
2 reqmred larger rev1S1ons than did the correspondmg present-method estimates

ple estimate for stratum h banks 1s constructed
by estimatmg the ratio of nonmember bank
DDA to sample bank DDA and then mult1plymg by the known weekly-average sample
bank DDA Summmg all strata gives the estimated aggregate The accuracy of either
method depends on the accuracy of the estimates of the respective rat10s
The mtenm and final sample estimates are
also analogous to those of the present method
When a new call report becomes available,
an updated ratio of nonmember bank DDA
to sample bank DDA 1s obtamed and applied
to the known sample bank DDA for week t
When call reports for dates before and after
week t are available, a lmear mterpolation
of the two ratios 1s applied to the sample
bank DDA fo1 week t m order to obtam the
final estimates
.,,
The sample estimates of nonmember bank

s The revmons m Table 3 for the present-method
c~Umates are "smooth" funct10ns of time This 1s due
solely to the mterpolat10n procedure In prmc1ple, the
revmons of the sample estimates should also be smooth
They were not because (1) structural changes occurred
mvolvmg the sample banks, (2) data from as many as
15 banks per week were screened out as "outliers," and
(3) ddfermg numbers of banks reported each week Of
the 573 banks asked to report, the number actually
reportmg ranged from 439 to 550

TABLE 4 Sample Estimates of Nonmember DDA, 1974-75
In m11lmns of dollars
Last call report available at time of estimate
End of week

1974-Aug 28
Sept 4
11
18
25
Oct

2
9
16
23
30

Apr 1974

I

June 1974

I

Oct 1974

I Revts1on

53,618
54,881
56,064
56,094
54,078

410
389
287
204
363

53,778
55,109
56,408
56,374
54,392

290
161
-57
-76
-49

54,028
55,270
56,351
56,298
54,441

54,250

408

54,676
55 958
56,959
56,324
54,924

-20
28
47
191

-18

54,658
55,938
56,987
56,364
55,124

7
-9

56,371
55,115

Estunate

I

Revision

I

Esttmate

I

I Apr 1975
I Rev1s1on T Esttmate

Dec 1974

Estimate

I

I Revts1on

I

Estimate

Nov

6
13
20
27

56,603
57,445
56,992
55,842

284
129
34
23

56,867
57,513
57,041
55,941

20
61
-15
-76

56,887
57,574
57,026
55,865

Dec

4
11
18
25

56,817
57,331
57,862
57,106

162
51
71
261

57,049
57,422
57,870
57,418

-70
-40
63
-51

56,979
57,382
57,933
57,367

1975-Jan

1
8
15
22
29

58,081
59,820

133
296

58,430
59,963
58,429
58,046
54,858

-216
153
259
-59
145

58,214
60,135
58,666
57,953
54,906

-19
22
34
97

60,116
58,688
57,987
55,003

Feb

5
12
19
26

na
55,995
55,935
54,709

-67
-69
53

na
55,905
55,898
54,693

23
-32
69

na
55,928
55,866
54,762

Mar

5
12
19
26

56,396
57,001
56,765
54,793

-290
-235
-91
30

56,147
56,801
56,498
54,582

-41
-35
176
241

56,106
56,766
56,674
54,823

2

55,643
57,911
58,564

-133
-213
-179

55,619
57,888
58,531

-109
-190
-146

55,510
57,698
58,385

Apr

9

16
n a Not available


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61

Nonmember Banks and Estimation of the Monetary Aggregates

In add1t10n to requmng smaller benchmark rev1s10ns, the sample provides a somewhat different vers10n of the h1stoncal senes
from that of the p1esent method These estimates-the last columns of Tables 3 and 4aie repeated in Table 5 The sample estimates tended to be lower than the presentmethod estimates in 1974 and higher in 1975
In part, these differences may be clue to the
single-day call reports The accuracy of either
method depends upon its ratio (nonmember
to country bank or nonmember to sample
bank) as determined from the call report data
and how rep1esentat1ve 1t 1s of the days and
weeks surrounding the call report date To the
extent that the rat10s of weekly (or monthly)
averages are subject to less random vanat10n
than smgle-day rat10s, the accuracy of the
e~t1mates would be improved 1f all nonmem-

ber banks reported deposit data for a week
(month) along with their call rep01 ts 9
On the other hand, there 1s cons1de1 able
week-to-week vanab1hty in the differences between the two senes For example, the sample
estimate was $1 bilhon lugher than the cor1esponding present-method estunate for March
19, but a week later 1t was $6 million lower
Tlus vanat10n in the differences would still
1emain 1f add1uonal data were available on
the call 1ep01 ts That 1s, even 1f, for example,
deposit data for a week had been provided
on the call 1eports, there would still have
been large d1ffe1ences between the sample
and the present-method estimates because of
the chffe1ent week-to-week movements in the
deposits of the sample banks and the deposits
of the country membe1 banks

Accuracy of the sample estimates
TABLES Fmal Nonmember DDA Series Generated by
Two Methods, 1974-75
In mdbons of dollars
End of week
1974--Aug 28
Sept 4
11
18
25

Present
method

Sample

54,670
55,435
56,776
56,610
54,967

54,028
55,270
56,351
56,298
54,441

642
165
425
312
527

Difference

Oct

2
9
16
23
30

54,925
56,023
57,236
56,595
55,693

54,658
55,938
56,987
56,371
55,115

267
85
249
224
578

Nov

6
13
20
27

56,525
57,440
57,102
56,178

56,887
57,574
57,026
55,865

-362
-134
76
311

4
11
18
25

57,151
57,752
58,045
57,777

56,979
57,382
57,933
57,367

172
370
112
410

1975-Jan

1
8
15
22
29

58,830
59,614
58,782
57,325
55,282

58,214
60,116
58,688
57,987
55,003

616
-502
94
-662
279

Feb

5
12
19
26

55,465
55,646
55,392
54,546

na
55,928
55,866
54,762

-282
-474
-216

Mar

5
12
19
26

55,454
56,147
55,608
54,829

56,106
56,766
56,674
54,823

-752
-619
-1,066
6

Apr

2
9
16

55,577
57,292
58,136

55,510
57,698
58,385

67
-406
-249

Dec

na Not available


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Federal Reserve Bank of St. Louis

The usual formula for estimating the samphng vanance of the separate ratio estimator
(the estimator used to construct the sample
estimates) 1s10
(4)

s2

=

L

~ Nh(Nh -

nh)sh2/nh

h=l

whe1e N,. 1s the numbe1 of banks in stratum
h, n,. 1s the number of sample banks in stratum
h, L 1s the number of strata, and sh 2 1s the
sample vanance around the stratum h regress10n line
nh

(5)

Sh2 = ~ [yh,(t) - ThYh,(c)]2/(nh - 1)
,~1

where Yh,(t) 1s the DDA of the tth bank in
stratum h at time t, y11 ,(c) 1s the corresponding
value on a call report, and

9 Smee March 1976 the FDIC has been collecting 7
days of deposit data from nonmember banks along with
each call report
10 See, for example, Wilham G Cochian, Sampling
Techniques (Wiley, 1963), p 158 The sampling variance refers to the variation among estimates based on
the potential samples that could be selected, not to
the vanat1on of weekly estimates based on a given
sample

62

Improvmg the Monetary Aggregates Staff Papers

is the estimated ratio of stratum h DDA for
the statement week to its DDA given on the
call report Equation 4 is appropnate when
the samplmg withm a stratum is done on a
purely random basis In the application discussed here, the samplmg was not done on a
purely random basis, rather, the sample was
constramed so that its distribution (geographic, urban-rural, and so on) would reasonably reflect that of the populat10n of nonmember banks Thus, Equat10n 4 would not
seem to be an appropriate estimator of the
variance of the sample estimates
However, 1t can be plausibly argued that
Equation 4 should give an upper bound (possibly a crude one) for the variance of the sample estimates Let u::ii represent the variance of
estimates based on any conceivable sample,
mcludmg the ones that would have been reJected as unrepresentative Roughly half of
the samples will yield s 2 's smaller than u~ii
and half will yield s2's larger than u;11 Among
the samples yieldmg smaller s2 's will be the
geographically homogeneous ones, precisely
the ones that would have been reJected as
unrepresentative The samples yieldmg the
larger s2 's are the ones that mcorporate the
geographic variat10n-the "representative"
samples Thus, smce representativeness is reqmred, the value of s2 yielded by the sample
1s likely to overestimate uJii
Furthermore, u~ 11 Itself is likely to overstate
the actual samplmg variance smce 1t is the
variance of a set of estimates that should have
a larger dispersion than has the set of estimates based on representative samples
Equat10n 4 was applied to the sample data
for the week of October 16, 1974, and the June
1974 call report data to obtam an estimated
upper bound for the sampling standard error
of the mitial estimate of about $300 million
Calculat10ns for other weeks gave similar results Usmg the normal approximation, we
may say that we are at least 68 per cent confident that a sample imtial estimate is withm
$300 million of actual nonmember bank DDA,
or at least 95 per cent confident that a sample
1mtial estimate is w1tlun $588 million of
actual nonmember bank DDA The sample


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final estimates, bemg eqmvalent to weighted
averages of imtial estimates, will have somewhat smaller sampling standard errors 11
From Table 5, we note that the presentmethod final estimates differ from the correspondmg sample final estimates by as much
as 3 5s ($1,066 million for the week of March
19, 1975) We mfer that the present-method
final estimates depart substantially from
"truth" as well as that movements of nonmember DDA between call dates differ from
those of country banks
A more direct way of mvestigatmg the accuracy of these particular sample (and presentmethod) estimates is to consider estimates
made for the call dates Aside from reportmg
errors-and the deposits of nomnsured banks
on the sprmg and autumn call dates-we
know aggregate nonmember bank DDA on
these dates We can construct estimates for
these dates m exactly the same way as we constructed weekly-average estimates JUSt substitute the call date DDA for the weeklyaverage DDA for the sample banks or for
the country banks m the present-method
estimates Then by comparmg the mitial estimate with the aggregate determmed from the
call report, we obtam the erro1 resultmg from
the method for that smgle day In the case
of the sample estimates, these smgle-day errors
are likely to be larger than those for weeklyaverage estimates because of the additional
day-to-day vanat10n 12
The results of these calculations are given
m Table 6 The Imes labeled "Estimate" give
the actual estimates that were made, while
the Imes labeled "Estimate with
call data"
gwe the estimates that would have been made
had the sample banks (or the country member
banks for the present method) reported the
same deposits m the survey as they did m the
call report The differences between these two
Imes mdicate the effects of reportmg errors
11 As shown m Appendix 1, the samplmg standard
error of a final esumate for a week about halfway
betneen two call dates 1s at most about i240 m1lhon
12 This pomt 1s elaborated m Appendix 2, where 1t
1s also shown that errors committed by the sample
estimates of weekly averages are hkely to be smaller
than the rev1s1ons of those estimates

Nonmember Banks and Estimation of the Monetary Aggregates

63

TABLE 6 Estimates of Nonmember DDA on Call Dates, Selected Methods, 1974-75
In mtlhons of dollars
Last call report avatlable at time of estimate
Method and data used

I
I

June 1974
Estimate

I

Error

Oct 1974
Estimate

I

Error

I
I

Dec 1974
Estimate

I

Error

Estimate for October 15, 1974 (actual = 58 228)
Present method
Estimate
Estimate with Oct call data
Sample method
Estimate
Estimate with Oct call data

58,452
58,583

224
355

58,124
58,192

-104
-36
Estunate for December 31, 1974 (actual = 60,333)

Present method
Estimate
Estimate with Dec call data
Sample method
Estimate
Estimate with Dec call data

60,858
61,041

525
708

60,659
60,474

326
141

59,917
60,198

-416
-135

60,290
60,579

-43
246

Estimate for Apnl 16, 1975 (actual = 58,658)
Present method
Estimate with Apr call data
Sample method
Estimate
Estimate with Apr call data

The actual present-method mitictl estimates
chffered from the three call report aggregates
by $224 million, $525 million, ctnd $1,755
milhon The sctmple mitial estimates differed
from the call report aggregates by $104 million, $416 million, and $141 milhon-a 74
per cent improvement on average If the sample banks and the country membe1 bctnks had
reported in the1r respective surveys the data
they lctte1 reported in the call reports, the
peicentage improvement would have been
even greater
The root mean square error of the five sample smgle-day miual and mtenm estimates
was $210 million As shown m Appendix 3,
tlus amount translates mto a root mean square
error for the final sample weekly-average estii ates of, at most, $130 million to $167 million,
with the size of the bound dependmg on the
closeness of the statement week to the call
date Thus, the final sample senes appears to
be considerably more accurate than the present
h1stoncal senes

60,413
60,499

1,755
1,925

59,558
59,642

900
984

58,799
58,809

141
151

58,776
58,787

ll8
129

raises two questions Would estimates of nonmember bank DDA based on data from a
group of member banks similar to the FDIC
sample banks perform equally well? Can satisfactory estlmcttes be obtamed by using data
from a subset of the sctmple-for example, the
178 large nonmembe1 bctnks? The following
d1scuss10n addresses these issues

The matched-banks method
For each of the 573 sample nonmember
banks, the staff of the FDIC found ct membei
bank that was similar with respect to size and
location Dally deposit data are available for
these matched banks as they are for all member banks Estimates of nonmember bank
DDA were then constructed by using the
matched banks as 1f they constituted the sample of nonmember banks, that 1s, Equation 2
was applied with the matched-banks DDA
substituted for the sample-banks DDA
The results can be summauzed in two ways
First, the rev1s10ns of the matched-banks estimates are presented in Table 7 13 The re-

Alternative est1mat10n procedures
The increased accuracy of the FDIC sample
esumates over the present-method estimates


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Federal Reserve Bank of St. Louis

13 At the time this portion of the expenment wa~
conducted, sufficient data for makmg estimates were
available only through January I, 1975

64

Improvmg the Monetary Aggregates Staff Papers

TABLE 7. Estimates of Nonmember DDA Usmg Matched Member Banks, 1974-7S
In mtlhons of dollars
Last call report available at time of estimate
End of week

Apr 1974
Estimate

1974-Aug 28
Sept 4
11
18
25
Oct

2
9
16
23
30

I

June 1974

I

Revmon

I

Estimate

I

I

l

Oct 1974

I

Rev1s1on

Estimate

I

Revmon

I

Dec 1974
Estimate

53,248
53,969
55,171
55,037
53,452

1,309
1,342
1,527
1,534
1,503

54,488
55,237
56,470
56,332
54,705

69
74
228
239
250

54,557
55,311
56,698
56,571
54,955

53,514

1,567

54,770
56,164
57,263
56,864
55,982

311
291
338
348
372

55,081
56,455
57,601
57,201
56,338

11
16

57,212
56,354

Nov

6
13
20
27

56,814
57,611
57,064
56,158

483
505
515
523

57,252
58,056
57,504
56,595

45
60
75
86

57,297
58,116
57,579
56,681

Dec

4
11
18
25

57,257
57,993
58,203
57,656

491
500
335
310

57,714
58,456
58,666
58,117

34
37
-128
-151

57,748
58,493
58,538
57,966

1975-Jan

I

58,912

290

59,377

-175

59,202

v1s1ons, rangmg up to $1 5 b1lhon, are considerably larger than the rev1S1ons of the sample estimates (Table 4) and are of the same
order of magmtude as those of the present
method (Table 3)
Second, a comparison of final estimates for
the matched-bank and sample methods 1s
given m Table 8 Smee these estimates differ
by as much as $1 2 billion, It appears that the
matched banks do not track nonmember deposits very well between call dates

TABLE 8 Nonmember DDA Senes Generated by Two
Methods, 1974-75
In mtlhons of dollars
End of
week
1974-Aug 28
Sept 4
11
18
25

Sample
method

Matched-banks
method

54,028
55,270
56,351
56,298
54,441

54,557
55,311
56,698
56,571
54,955

-529
-41
-347
-273
-514

Difference

Oct

2
9
16
23
30

54,658
55,938
56,987
56,371
55,115

55,081
56,455
57,601
57,212
56,354

-423
-517
-614
-841
-1,239

Nov

6
13
20
27

56,887
57,574
57,026
55,865

57,297
58,116
57,579
56,681

-410
-542
-553
-816

Dec

4
11
18
25

56,979
57,382
57,933
57,367

57,748
58,493
58,538
57,966

-769
-1,111
-605
-599

58,214

59,202

-988

1975-Jan


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Large-banks method
To evaluate the usefulness ol depos1 t data obtamed only from the 178 large nonmember
banks, an estimator was constructed that 1s
essentially a mix of the present-method and
sample estimators The data for the 178 large
nonmember banks were used to estimate the
DDA of those nonmember banks reportmg
more than $100 million (the lughest stratum)
m total deposits m the call report, JUSt as they
were m the sample method The DDA of the
smaller nonmember banks was estimated by
formmg the rat10 (small nonmember bank
DDA)/(country member bank DDA), for each
call date smce 1967, fittmg a regressionquadratic m time and lmear m mterest rates-to these ratios, and proceedmg exactly as m
the present method We call this the largebanks method The estimates and their rev1s1ons are given m Table 9 These estimates
reqmred larger rev1S1ons than did those of the
sample but represented a considerable improvement over the present method Experience with the present method md1cates that
care should be taken m extendmg the results
of the large-banks method beyond the mitlal
study period The regressions for estimatmg
small nonmember bank DDA may easily deteriorate as did the present-method regress10ns The final estimates for large banks dif-

Nonmember Banks and Estimation of the Monetary Aggregates

65

TABLE 9, Estunates of Nonmember DDA Usmg the Large-Banks Method, 1974-75
In m1lhons of dollars

Last call report available at time of estimate
Apr 1974

End of week

Estimate
1974-Aug 28
Sept 4
11
18
25
Oct

2
9
16
23
30

I Rev1S1on

June 1974

I
I

Estimate

I

Rev1S1on

Oct 1974

I
I

Esllmate

I

Rev1S1on

I
I

Dec 1974
Esllmate

54,912
55,994
57,107
57,185
55,119

-475
-489
-373
-372
-483

54,589
55,682
56,952
57,060
54,896

-152
-177
-218
-247
-260

54,437
55,505
56,734
56,813
54,636

55,163

-326

55,112
56,144
57,275
56,669
55,667

-275
-301
-328
-347
-368

54,837
55,843
56,947
56,359
55,313

-37
-14

56,322
55,299

I

Revmon

l
I

Apr 1975
Esllmate

Nov

6
13
20
27

57,033
57,814
57,610
56,506

-336
-380
-368
-311

56,734
57,488
57,302
56,269

-37
-54
-60
-74

56,697
57,434
57,242
56,195

Dec

4
11
18
25

57,295
57,785
58,183
57,833

-339
-533
-503
-423

57,083
57,509
57,936
57,703

-127
-257
-256
-293

56,956
57,252
57,680
57,410

1975-Jan

I
8
15
22
29

59,151
59,927

-412
-307

59,059
59,609
58,479
57,117
55, IOI

-320
11
-222
-344
-333

58,739
59,681
58,348
56,888
54,919

-61
-91
-115
-151

59,620
58,257
56,773
54,768

Feb

5
12
19
26

na
55,574
55,538
54,562

-416
-433
-382

na
55,349
55,338
54,467

-191
-233
-287

na
55,158
55,105
54,180

Mar

5
12
19
26

55,827
56,551
56,270
55,432

-525
-528
-603
-592

55,559
56,320
55,927
55,133

-257
-297
-260
-293

55,302
56,023
55,667
54,840

Apr

2
9
16

56,244
57,961
58,820

-534
-539
-589

56,117
57,857
58,701

-407
-435
-470

55,710
57,422
58,231

n a Not available

fered from the correspondmg sample final
estimates by dS much as 1H billion, mdicatmg
that the movements of nonmember deposits
between call dates have still not been captured
TABLE 10 Series for the Estunahon of Small
Nonmember Bank DDA 1
Call report
date
1967
Dec 1967
June 1968
Dec 1968
June 1969
Dec 1969
June 1970
Dec 1970
June 1971
Dec 1971
June 1972
Dec 1972
Spnng 1973
June 1973
1973
Fall
Dec 1973
Spnng 1974
June 1974
Fall
1974
June

SNM/LNM

3
3
3
3
3
3
3
3
3
3
2
2
3
2
3
2
3
3
3

5612
4898
4701
4701
2417
1893
1286
1529
0354
0886
9816
9519
0428
9462
0733
9805
0861
0253
1380

SNM/CB

4403
4499
4465
4570
4620
4715
4709
4811
4818
4973
5041
5123
5284
5354
5413
5521
5575
5582
5687

Treasury bill
rate

4 085
4 185
5 275
5 39
6 14
7 18
6 89
5 84
4 04
4 615
3 595
4 535
5 28
6 15
7 46
7 91
7 56
7 885
8 17

1 SNM = small nonmember banks, LNM = large nonmember
banks, CB = commercial banks


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Anothet suggested approach is to use the
large nonmember banks to estimate the DDA
of the small banks duectly We have been
unable to find any relationship between the
large and small banks that works as well as
the method Just outlmed Call report data
used to pursue this alterndtive are presented
m Table 10

Conclusions
This study was mitiated m response to mcreasmg concern about the large revisions of
the money stock brought about by the extensive revis10ns of the estimates of nonmember
bank DDA These revis10ns, m turn, are
caused by a lack of understandmg of the forces
that cause movements of nonmember bank
deposits to differ from those of member bank
deposits One approach to reducmg the s12e
of the revisions is to gam a better under-

66

Improvmg the Monetary Aggregates Staff Papers

standmg of the forces governmg nonmember
bank deposits, but given the paucity of data
on nonmember deposits-which are available
for only 4 days per year-the p1ospects for
this approach appear hm1ted
A second app1oach 1s to estimate nonmember DDA directly by collectmg daily deposit
data from a subset of nonmember banks s1m1lar to the sample selected by the FDIC The
estimates based on the sample reqmred much
smaller rev1S1ons than did the present-method
estimates-the accuracy, as measured by the
errors made on call dates, was improved by
nearly 75 per cent While the study period
was admittedly short, covermg only three call
dates, 1t 1s difficult to conceive of any results
that could have been obtamed from the FDIC
experiment that would have more strongly
Justified the use of a sample 14
14 The FDIC plans to remstitute the sample program
begmnmg m late 1976 or early 1977


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Another problem 1dent1fied m this study 1s
that even after all rev1s10ns have been made,
the historical estimates of nonmember DDA
may be wide of the mark except on call dates
The sources of these errors are the different
movements of member and nonmember deposits between call dates-for example, different seasonal patterns and the poss1b1ht) that
the ratio of nonmember DDA to country bank
DDA on the call date may not be representative even of the penod immediately surroundmg the call date Reasonable measures
of the relative contributions of these sources
of error are not available because of the shortness of the study period Nevertheless, 1t 1s
clear that some improvement m the presentmethod final estimates could be obtamed 1f
deposit data for more than 1 day were supplied by all nonmember banks m conJuncuon
with the call reports Sample estimates would
also benefit from the avallab1hty of such
data

67

Appendix 1: Sampling Standard Error of a Final Estimate

The final esumate 1s a weighted average of two
rauo esumates, one based on the call report 1ust
precedmg, and the other based on the ca11 report
JUSt followmg the statement week The weights
reflect the relative lengths of the time mtervals between the statement week and the two caB dates
For convemence, assume that the statement week
1s halfway between the two ca]] dates, and suppose that the vanances of the two estimates are
equal (to a- 2) Then the samplmg vanance of the
final estimate 1s

V(f) = u 2 (1

=

$232 million

We may tlunk of aggregate nonmember DDA,
say Y(t), as havmg a trend component, TR(t), and
an error component, e 1, which 1s senally mdependent

Y(t) = TR(t)

+ ee

Inchv1du,tl nonmember banks behave s1mdarly
J (t)

= tr(t) + Ut

To show that p can be equal to -1, we assume
that et= Uc= 0, for all t Thus, when we draw a
sample of banks to follow over time, we are really
drawmg ,t sample of trend5 Further assume that
the trends are sud1 that for any s

R.(t) = Y(t)/y.(t) = a,

+ b.t

where y.(t) 1s the aggregate DDA of the banks


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and

The final esumate 1s
Y(t)

=

+ p)/2

where p 1s the correlauon coefficient between the
two estimates A bound on u ($300 million) was ob
tamed m the text We now show that, under
reasonable assumpt10ns, p 1s no more than 0 2 ,md
may be near -1, winch implies that the standard
error of the final estimate hes between zero and
(300) (1 2/2) 1 12

m sample s at time t Let t1 and t2 be two consecutive call dates, t 1 < t < t 2 The estimates of
Y(t) based on the call reports are

[(t2 - t)R.(t1)y.(t)
+ (t - t1)R.(t2)y.(t)]/(t2 - t1)

[(12 - t)R. (ti)
+ (t - t1)R.(t2)]y.(t)/(t2 - t1)

=

R,(t)y.(t)

= Y(t)

l hus, the final estimate 1s Y(t) regardless of which
~ample 1s drawn, the vanance of the final estimate
1s Lero, and the correlauon coefficient p
I
As the error v<1.nances become large relative to
tl1e trend m R,(t), the correlation moves away
from -I Io obum an upper bound for p, we
take the extreme case that R.(t) 1s a constant-that
1s, all banks follow the same trend and the only
source of vanauon m the estimates 1s the random
component
Specifically, we assume that the variance of an
aggregate 1s proportional to Its s12e, that Y(t 1) and
Y(t 2) are known, and that the mean of a sample of
banks vanes mdependently over time A straightforward extension of the proof of Theorem 2 5 m
Cochran's Sampling Techniques shows that the
correlat10n between Y 1 (t) and Y2 (t) 1s approximately the same as the correlation between

=-

and

y, (t) - G2y, (t2)

=

=

where G1 Y(t)/Y(t 1), G 2 Y(t)/Y(t 2), and y,(t)
represents tl1e mean of the sampled banks at ume

Improving the Monetary Aggregates Staff Papers

68

t G1 and G 2 are the unknown trends that all nonmember banks are assumed to follow
Now the covariance matrix of y,(t 1 ), y,(t 2 ), and
y,(t) IS
0
1/G2
0
(The G's reflect proporuonabty to size and the
13/49 1s the variance of a 7-day average) Hence
the covariance matnx between y,(t) - G1 y,(t 1) and


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y,(t) - G2 y,(t2) IS
v

2 (13/49 + G1
<r
13/49

13/49 )
13/49 + G2

So the upper bound on the correlation between
Y 1 (t) and Y 2 (t) 1s approximately
p

=

!! [G! + G1)G! + G2) Jl/2

= 02
when the trend 1s fairly umform over (t 1, t 2) and
G1 and G 2 are close to 1

69

Appendix 2: On the Relationship between Errors and Revisions

Consider the sample estimates of nonmember
DDA for some week t fallmg between the October
and December 1974 call dates For convemence,
we neglect &trauficauon, nonreporters, structural
changes, and so on The esumates are

Initial (Xi/x1)Y1 = r1Yt
Interim (X./x.)y, = r.y,
Final a,(X./x.)y, + (1 - a1)(Xd/xd)y1
= [a,ro + (1 - a1)rd]Y1
where X 1, X,,, Xd are the population aggregates
and x1' x 0 , xd are the sample aggregates on the
June, October, and December call reports, Yt 1s
the average aggregate of the sample banks for week
t, and a 1 1s the proporuon of days between the
October and December call dates that remam after
ume t
The 1ev1swn of the m1trnl estimate (Table 4)
can be written

(A-1)

r1y1 - [a1ro

+

(1 - a1)rd]Y1

= y,{ri - [a1ro

+ (1

- a,)rdl)

,md the rev1S1011 of the mterim esumate can be
written
(A-2)

roJt - [a1ro

+

(1 - a1)rd]Y1
= y 1(1 - a,)(r. - Td)

From Equation A-1, we see that the revmon of the
mmal estimate will be small 1f and only 1f the
difference between the rauo r1, determmed from
the June call report, and the weighted average 0£
r 0 and rd, determmed from the October and De
cember call reports, 1s small From Equation A-2 we
see that the revmon of the mterim esumate will
be small 1f and only 1f the difference between r0
and ra 1s small or at 1s large (at 1s large when week
t 1s close to the October call date)
The error made by the m1t1al estimate 1s

(Xi/x 1)y, - Y,

= y,(Xi/x1

-

Y,/y,) = y,(r1

-

r,)

where Yt 1s the actual population aggregate for
week t Similarly, the error made by the mterim
esumate 1s
v,(r. - r,)


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and the error made by the final estimate 1s

y,[a,r.

+

(1 - a,)rd - r,]

I hese errors will be small 1f rt 1s close to r1, 1 0 ,
and ra
Is Tt close to r1, 1 0 , and 1,1? We cannot directly
compare rt wuh the other r factors because us
numerator, Y 1, 1s unknown But cons1dcr the sequence r 1 , 1 2 ,
of daily rauos of the population
aggregate to the sample aggregate We have observed a sample of five of these ratios m tlus study
r1, r"' rd, and the April 1974 and April 1975 call
report rauos 'I he unobserved rauo 1 1 for week t
can be regarded as an average of five of these daily
rauos 1 Now the r's are sub1ect to two sources of
variauon a trend, and random day-to day fluctuation If the trend effect 1s large, then the revmons
will be large and perhaps only the final esumate
will be reasonably accurate (smcc only the final
estimate exphc1tly mcorporates a trend effect) If
the random fluctuations are large, the rev1s1ons
will be large and none of the estimates 1s hkely to
be very accurate (although the final estimate 1s
hkely to be more accurate than the others) But we
have evidence that neither the trend effect nor the
random fluctuations are large That evidence 1s
the sample of five ratios we obtamed from the
call reports That there was not much variab1hty
m these ratios 1s evidenced by the smallness of the
benchmark revmons We therefore mfer that smce
the sample of 1 's showed little variability, the population of r's also would show little variability
Thus we can say that rt 1s likely to be close to
r1, r0 , and rd, and that the errors mcurred by usmg
r1, r0 , or r,1 m the estimate are small
We have shown that small rev!Slons of the simple
rauo estimate are associated with small errors of
the estimate To see that the same conclusion applies to the separate ratio estimate, the argument
1s applied to the md1v1dual strata
1 Actually, r 1s a ratio of weekly averages, not an average
1
of daily rat10s This d1stmct10n 1s not crucial to the argu
ment, however

70

Appendix 3: Root Mean Square Error of the Final Estimates

It was shown m the text that the root mean
square error (RMSE) of the five sample m1t1al and
mtenm estimates of nonmember DDA on call dates
was $210 million Here we formulate a simple
model m order to translate that RMSE mto a
bound on the RMSE of final weekly-average estimates As before, we neglect stratification, nonreporters, structural changes, and so forth
Let t 1 and t 2 be two call dates The ratio estimate of nonmember DDA for day t 2 based on the
t 1 call report data 1s

that an estimated upper bound for 2u 2y2 can be
obtamed by settmg f3 = 0 But then,

Ee;2 = 2u2), 2
1s not a function of ume and can be estimated by
the mean square error of the five call date estimates ($210 million) 2
Let w be the average value of t for the state
ment week and rw be the average of the rt's for
that week We regard rw as approximately equal
to the ratio of the weekly averages of Yt and y 1
The final estimate for the statement week 1s
[(1 - a)r11

where rt= Yt/Yt, Yt 1s nonmember DDA, and Yt
1s the sample-banks DDA on day t The estimate
1s m error by

where t 1 and t 2 are the call dates preceding and
following the statement week The error committed
by the final estimate 1s
ew

The use of the ratio estimate amounts to guessmg
that rt 2 = r 11 and the error, of course, 1s a function
of the difference between the r's Suppose that,
m fact, rt 1s given by

rt = a + {3t + Et
where et 1s serially mdependent with mean zero
and variance o- 2 Approx1matmg Yt by a constant
y (m fact, Yt vanes over short mtervals of time
by only a few percentage pomts), the expected
squared error may be calculated


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Federal Reserve Bank of St. Louis

+ ar12]y,., - r,.y,.
a)r11 + ar,2 - rw]

= [(1 -

a)r11

= y[(1 -

where agam we have approximated Yw by y After
some algebraic mampulauon, we have
e,.

= y[(1

-

a)E11

+ aE12 -

e,.]

where Ew 1s the average of the E t's for the state
ment week and thus has variance 13 o- 2 /49 The
mean square error of the final estimates 1s

Ee!

= y 2u 2[(1

- a) 2

+ a + 13/49]
2

Settmg 2u 2y2 to our empmcal bound ($210 million) 2 , we obtam the estimated bound on the mean
square eror of the final estimate -call It M 2 (a)

M 2 (a)
By msertmg the appropriate values for ti and t 2
m Equation A-3, we can calculate the expected
squared error for any call date estimate
For our ultimate purpose of obtammg an upper
bound for the root mean square error of a final
weekly-average estimate, we will see that we need
an upper bound for 2u 2y2 Now, given an empirical estimate of Ee~2 , 1t 1s clear from Equation A-3

+ ar12]Yw

=

210 2[(1 - a) 2

+ a 2 + 13/491/2

M(a) reaches its maxunum value when a= 0 or I,
when the statement week 1s the week of a call date

M(O)

= M(1) = $167 million

M(a) reaches its mm1mum value when a= 1/2,
halfway between two call dates

M(l/2)

= $130 million

71

Seasonal Adjustment of the Monetary Aggregates
David A. Pierce, Neva Van Peski, and Edward R. Fry

Research for this paper was completed in
1975 and early 1976 Consequently, the applzcatwns of seasonal ad7ustment procedures and
statistical tests discussed in the paper do not
take account of data after 1974 or 1975
Seasonal ad7ustments f 01 the published
monetary aggregates series were 1evzsed in
February 1977 and March 1978 in accordance
with procedures described in the discusszon of
"Seasonal ad7ustment of published M 1 series"
There was some evidence in monthly data fo1
1976 and 1977 that a new qua1 terly 5easonal
pattern wa5 developing in the demand deposit
component of M, Based on Census X-11 seasonal ad7ustments, the quarterly pattern of fiuctuation wa5 partially eliminated in the 1978
1evt5ton
The Boa1 d's staff has continued to develop
and experiment with the daily seasonal facto1
method, as described later The baste program
ha1 been improved by including an optwnal
log t1ansformatzon and by improving the
rnPthod of selectmg harmonic terms to include
m the regression In addztzon, work is in progress to take account of changes m the seasonal
pattern, by using a iatzo-to-momng-average
technique to 1emove seasonality remaining in
the irregular component from the series ad7usted by the method desc1 ibed here Thzs is
analogous to X-11 except that the weights of
the moving aveiage a1e designed to match the
1tatzstzcal characteristics of the particular
1eries

Seasonah ty 1s a widespread phenomenon m
economic time se11es, and much has been and
contmues to be written regardmg Its nature
NoTL -The

.iuthon .ire on the
of Research and Statistics


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\t.iff

of the D1v1s1011

and its treatment The monetary aggregates
<1re no exception Particularly with the mcreasmg attention duected toward the monetary aggregates as an mdicator and a target
of monetary pohcy, it 1s important to have
,1vailable reluble means for se<1sonally adJustmg the monetary aggregates m order to disentangle purely penodic, calendar-lmked
movements m the narrow measure of the
money supply (M 1) and related sene5 from
others, perhaps economically more meanmgful Procedures for <1ccomph~hmg d reh,1ble
5eason,1l adjustment, mcludmg particularly
the development and apphcat10n of a new
method, <1re reviewed and compared m this
p<1per
The adjustment of a senes for "se<1sonal
v,m<1t10n" presupposes a not10n or concept of
what the term means For the monetary aggreg,1te~ there are at lea 5t three meanmgs The
5ea5onal (facto1 01 component) m the money
,;tock that actually occurs m the data is referred to as the dcsn iptive seasonal In general, It 1s the combmed result of two conceptually distmct clements, referred to as the
natural seasonal and the policy seasonal The
former anses not only from natur,11 phenomena such as the weather but also from
mcial phenomena such as holidays or taxpayment dates The latter 1s the iesult exphotly or implicitly of pohcy decJS1ons of the
Federal Reserve-for example, whether to accommodate an mcrease m the natural seasonal
m money at Chnstmas 01 to allow mterest
rates to nse
These chstmct10ns <1re descnbed m more
detail m another Board pubhcation, 1 they are
1 Improving the Monetary Aggregates Report of the
Advisory Committee on Monetary Statistics (Board of
Governors of the Fuleral Reserve System, 1976)

72

Improvmg the Monetary Aggregates Staff Papers

made here pnmarily to focus this paper Except for the section on the published seasonally
adJusted series, which discusses how the policy
seasonal is now estimated, this paper is concerned largely with the descriptive seasonal and
with alternative ways to estimate it
The first sect10n discusses briefly the nature
of seasonality and seasonal adJustment procedures, mcludmg regression and movmgaverage approaches This is followed by a descript10n of the Board's current seasonal adJustment procedure
Another section presents an alternative procedure to the Census Bureau X-11 method,
suggested by Friedman and developed by one
of the authors (Van Peski), for adJustmg any
monetary aggregate or other time series for
which dally data are available This procedure
has the feature that, once daily seasonally
adJusted data are determmed, then weekly,
monthly, or quarterly seasonal adJustments
can immediately be calculated and will be
consistent with each other Included also m
this section are several tests for stable versus
movmg seasonality, concentratmg on the
period from 1968-74 (prior to which seasonal
shifts such as tax-date changes were known to
have occurred)
The last section compares three seasonal adJUStment procedures, the ordmary and "fixedfactor" X-11 procedures and the daily procedure developed earlier It is found that, for
demand deposits and currency durmg the
time period studied, the daily seasonal method
gives results qmte close to both the ordmary
and the fixed-factor X-11 seasonal adJustment
(which are fairly close to each other)
This paper is confined largely to an analysis
of currency and demand deposits-the two
components of M 1-although the procedures
developed or described are equally applicable
to M 2 as well as to reserve aggregates, mcludmg, with mmor modifications, those series for
which weekly but not daily data are available 2
2 See David A Pierce, "Relationships-and the Lack
Thereof-Between Economic Time Senes, with Special
Reference to Money and Interest Rates," Journal of
the American Statistical Association, vol 72 (March
1972), pp 11-26


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Nature of seasonality and
seasonal adjustment
The primary problem m seasonally adJUStmg a monetary aggregate or other time series
is the determmation of the part of the series
that is purely "seasonal" This determmation
is often facilitated by simultaneously determmmg a "trend cycle" as well, with the remamder of the series then referred to as "iri egular " There are two basic schemes for
representmg this decompos1t1on The multiplicative seasonal model for a time series {Yt}
IS

(1)

where Pt, St, and E 1 aie, respectively, the trendcycle, seasonal, and irregular factors of Y 1,
all at time t Ordmanly the trend factor is
the dommant part of the series and retams the
umts (dollars, m the case of monetary aggregates) associated with the senes The seasonal
and irregular factors, expressed as ratios to
trend cycle, are umty when there are no seasonal or irregular effects, and are above or
below l, respectively, when the effect of seasonal or irregular mfluences is to mcrease or
decrease the level of the series
Many economic series exlubit exponential
growth and for these the muluphcatlve model
is most appropriate For other series, however,
an additive model may be more smtable In
fact, the additive model may be derived from
the multiplicative model by takmg logarithms
I£ Yt = log Yt, Pt= log Pt, and so forth, then
Equation l becomes
(2)

Yt

= Pt +

St

+ et

which is the additive seasonal model The term
St is the seasonal component of Yt Of course,
m many cases {yt} will be actual series rather
than the logarithm of a multiplicatively generated series
The seasonally ad7usted series Yf and yf
are then
(3)

Seasonal Ad1ustment of the Monetary Aggregates

and
(4)

yf = Yt - St

where the circumflex denotes that the "true"
seasonal 1s never known but mstead must be
estimated ma smtable manner The problem
of (descriptive) seasonal ad1ustment 1s thus the
problem of obtammg estimates of the seasonal
components or factors To accomplish this,
some restrictive assumpt10ns regardmg the nature of the senes must be made, particularly
concernmg the nature of the seasonal component St (or factor S1) The remamder of this
section bncfly descnbes the assumptions underlymg the X-11 and regress10n procedures for
seasonal adJustment
Methods now m use for seasonal adjustment
generally fall mto one of two broad categories,
dependmg on whether the senes' seasonality
1s assumed to be "determm1st1c" (capable of
representation by such determm1stic funct10ns
of time as smes and cosmes, dummy variables,
and mteraction of these with powers of
time), or "stochastic" (representable by a seasonal autoregressive movmg-average-ARMA
-model, or as a component of such a model)
A determ1mst1c seasonal has the feature that it
can be predicted without error from seasonals
of previous years For example, 1f m Equation 2
the data are monthly and the seasonal component 1s
(5)

where d 11 ,
, d 121 are seasonal dummy vanables and }:8 J = 0, then year after year the
January seasonal 1s 81 , February's 1s 82 , and so
forth In general, regression methods for seasonal adJustment are appropriate for determm1st1c seasonality, and the simplest of these
would be a regression on the seasonal dummies
m Equation 5 A flexible regression method,
which allows for changmg trend and seasonality, 1s that of Stephenson and Farr 3
a "Seasonal Adjustment of Economic Data by Apphcatton of the General Linear Stat1st1cal Model," Journal of the American Statistical Association, vol 67
(March 1972), pp 37-45


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73

For stochastic seasonality 1t 1s known that
the optimal (mm1mum mean square error)
procedure consists of the application of a symmetric movmg average to estimate the seasonal, 4 that 1s,
(6)

where 8_, = 8, Insofar as Yt is stochastic and
only partially predictable from its past, St will
also exh1b1t these features Moreover, s 1 and
s t+ 12 (for monthly senes) will r,u ely be identical, a pomt to wluch we return shortly The
Census X-11 program 1s essentially of this
form,5 and m fact Cleveland and Tiao have
found a particular ARMA model for which
X-11 is nearly optimal 6
The d1stmct1on between determm1stic and
stochastic seasonality 1s conceptually a fundamental one, however, m practice it is not always obv10us whether the seasonality ma senes
is determm1st1c, stochastic, or both The money
supply 1s a pnme example lt i& generally adJUSted by usmg the X-l l program, yet ma subsequent subsect10n 1t will be seen that its
seasonality can sometimes be adequately captured with monthly dummy variables And the
daily method to be presented uses features of
both the regression and the movmg-average
approaches
A related distmct10n m seasonal adJustment
concerns the issue of fixed versus movmg seasonality A senes displays fixed or stable

4 Wilham P
Cleveland and George C T1ao, "A
Model for the Census X II Seasonal Adjustment Pro
gram," Techmcal Report 312 (Umvers1ty of W1sconsm,
1974), and Peter Whittle, P1ed1ction and Regulation by
Linear Least Square Methods (English Umvers1lles
Press, 1963)
s See "The X-11 Variant of the Census Method II
Seasonal Adjustment Program," Bureau of the Census
Techmcal Paper 15, revised (Government Prmtmg
Office, 1967) Add1t1onal features of X II that are outside the symmetric filter framework mclude provmons
for outliers and tradmg day variation See Kenneth F
Wallis, "Seasonal Ad1ustment and Relat10ns Between
Variables," Journal of the American Statistical Assoc1at1on, vol 69 (March 1974), pp 18-31, as well as
"X-II Variant"
s See Cleveland and T1ao, "Model for the Census
X-II"

74

seasonality 1f its seasonal factor for each month
remams unchanged from year to year, otherwise, 1t possesses movmg seasonality A fixed
seasonal 1s necessarily a determ1mst1c seasonal,
as, given knowledge of the true model, 1t can
be predicted from year to year without error
However, methods such as X-11 can produce
estimates of a fixed seasonal 1f constramed to
do so, and regressron methods can mcorporate
a movmg determrmstic seasonal
In mvestrgatmg alternative ways to seasonally adJust the monetary aggregates, It rs important to ascertam whether the evidence 1s
m favor of a fixed or a movmg seasonal pattern This quest10n rs addressed m several ways
m the third section, as the method presented
there assumes a constant monthly seasonal
pattern (apart from tradmg-day effects)

Improvmg the Monetary Aggregates Staff Papers

CHART I M 1 Total and MaJor Components
Billions of dollars
300

260

-+Not seasonally adjusted

220

Seasonal adjustment of published
M1 series
On a contmumg basis the Federal Reserve
publishes a seasonally adJusted monthly money
supply (M1), and revises the monthly seasonal
factors periodically (m general every year) 7
The procedure employed consists essentially
of (1) applymg the X-11 program and then
(2) Judgmentally mod1fymg the X-11 seasonal
factors to take account of elements of both
natural and policy seasonals felt to be madequately captured by X-l l (a descnptive
method) In this section both aspects of this
procedure are discussed
The pubhshed seasonally adJusted M 1 series
rs derived by summmg separately adJusted
currency and demand deposit components
This procedure has been followed over the
years smce m1t1al publication of the money
supply data because of analytical mterest m
the two component series 8 Chart 1 shows total
1 The data and seasonal factors are published m the
Federal Reserve Bulletin For example, the rev1S1on
published m Apnl 1978 reflected both revmons m
seasonal factors and other techmcal adjustments See
"Money Stock Revmons," Federal Reserve Bulletin,
vol 64 (Apnl 1978), pp 338-39
a Compansons of direct adjustment of total M 1 with
sums of separately adjusted components md1cate that
the resultmg differences m movement are relatively
minor


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Federal Reserve Bank of St. Louis

180

80

60

1971

1973

1975

M 1 and the cm rency and demand deposit
components, both seasonally adjusted and unadJusted, as pubhshed m January 1976 It rs
evident from the chart that most of the fluctuation m total M 1 , not seasonally adJusted, reflects seasonal changes m deposit balances The
seasonal pattern of currency rs well defined but
relatively small m dollar terms Currency
growth makes a substantial contributron to the
longer-run trend of M 1 , while demand deposits
not only contribute to growth but also account

75

Seasonal Ad1ustment of the Monetary Aggregates

for most of the irregular fluctuat10ns and
longer-run slufts m growth rates

The X-11 computation
As ment10ned earlier the X-11 program is
a ratio-to-movmg-average procedure that m
some respects provides considerable flexibility
for identifymg seasonal characteristics and for
tailoring seasonal adjustment to mdividual
series u The X-11 opt10ns employed m adjustmg M 1 mclude computat10n of multiplicative seasonal factors and use of moderately
flexible movmg averages to take account of
movmg seasonality
For M 1 , a mult1plicat1ve relationship of the
seasonal component to trend appears to be
appropriate for most months smce, under the
assumpt10n of an additive relationslup, the
seasonal and trend-cycle components appear
often to be strongly related, by contrast, the
facto1s or components m Equations 1 or 2 are
generally assumed to be mdependent This
i elat10nship of seasonal to trend-cycle components is seen m Ch,trt 2 (pages 76-77), which
chsplays relat10nships of seasonal-irregular
differences to trend cycle as computed by
an X-11 adcht1ve adjustment for the period
1965-75 As may be noted, the correlauon coefficients mserted on the scatter diagrams are
relatively high for 9 of the 12 months Similar
correlat10ns for the currency and demand deposit components (not shown m the chart)
also are relatively high for 8 of the 12 months,
suggestmg that strong relat10nships exist between the dollar amounts of the seasonal component and the level of M 1 Proport10nal
changes m the dollar amount of the seasonal
and the trend cycle represent multiphcat1ve
relat10nships While a multiplicative relationship 1s not perfect, it appears more representative of the seasonal characteristics of M 1 than
is the addiuve seasonal alternative, and multiplicative adjustments are used for the published M 1 senes 10
See "X-11 Vanant"
Correlat10ns for January, Apnl, and August are
relat1vely weak for total M 1 , reflectmg either greater
relative fluctuations m the irregular component or
9

10


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Another X-11 opt10n employed m M 1 seasonal adjustments is the use of moderately flexible movmg averages to allow for movmg seasonality The X-11 program provides tests for
movmg seasonality for mdividual months,offermg the possibility of controllmg the flexibility
of the process by which average seasonal factors
are derived for each month from the seasonalirregular (SI) rauos 11 These tests suggest that
movmg seasonality was a sigmficant characteristic of both the currency and the demand deposit components durmg the 1965-75 period 12
Fmal X-11 seasonal factors were derived by
smoothmg the SI rat10s by a 3-term average of
a 5-term average of the rat10s

Judgmental modifications
Fm several reasons the seasonal factors produced by X-11 may not adequately mcorporate
httle relat10nsh1p ben1een the size of the seasonal
component and the level of M 1 m the5e 3 months It
1s likely that the M 1 5ea5onal 1eflects a wmbmatlon
of muluphcame and acl<htnt. 1clat10mh1p5 fhe mulu
phcat1ve opt10n 1, used becamt. 1t appear5 to be most
wns1stent nllh the obsuved 1dauonsh1p of !vf1 sea
5onaJ5 to trend qcle It m,ty he noted th,ll an adchuve
adJmtment of a sencs that d1spl,1y5 muluphcauve
relauomh1ps ,1 ill also give reason,1hle rc5ults 1f the
add1t1vc dolla1 seasonal factor5 shift horn }l.Jr to yea1
by amounts com1stent with the muluphcauve 5ea5011al
1at105 for 5cncs m which the ,ea5onal component 1s
changmg m p10poruon to an expandmg trend cycle,
this relat10mh1p can be expres5ed c1thc1 as a stable
1at10 (muluphcat1ve) 01 as a ch.ingmg dolla1 ,,mount
(adtht1ve) It 5cems prefeiable to apply ,L muluphca
t1vc procedme 111 this case, especially 1f Judgmental
mod1ficat10ns are to be made h15toncally and 111 pro
iectccl factors for a year ,thead To the c.xtent that
mult1phcat1ve relat10ml11ps can be 1ep1e5entcd m stable
1at10 factors, 1t may be ca51er to 1clent1fy ch.tngmg
5c.asonahty resultmg from other mfluence5
11 SI ratios represc.nt the 5<-a5onal 11 regular com
ponent of the senes-that 1,, th<- rat10 of the not sea
sonally adiusted data to the trend cycle component as
computed by X 11
12 Movmg 5ca~onahty rat10s (MSR'5) computed by
X 11 1clate average year to year changes of the megu
Jar and sea~onal components, 111d1catmg the 1mpo1
tance of average year to year changes 111 the seasonal
for a given month relative to changes 111 the nregula1
I his rat10 can be used as a gmdc fo1 controllrng the
flex1b1hty allowed m X I I computauom of 5easonal
factor5 for any month MSR's computed for M 1 5ugge,t
that moderately flex1blc movmg average5 are appropnate for I l of the 12 calendar months 111 the case of
currency and for IO months 111 the case of demand
deposits

76

Improvmg the Monetary Aggregates Staff Papers

the seasonality present m the money supply
First, while the smoothed movmg averages are
moderately flexible m allowmg for movmg
seasonality, Judgmental modificat10n of the X11 results has been desirable to stabilize the
computed seasonal factors m some penods and
to make them somewhat more flexible m
others Such modifications are based on analysis of the computed SI ratios for each month
at vanous stages of the X-11 computat10nal
process Factors causmg a change m seasonal
patterns are taken mto account when known,
and impacts of nonseasonal mfluences on the SI
ratios also are weighed m modifymg the computed factors If an abrupt shift occurs m SI
ratios for a given month, the X-11 averagmg
process would take account of this shift only
gradually m the seasonal factors for surroundmg years, but the timmg of the change can
be sharpened by Judgmental modification
when appropriate, as for example m the case
of a modification m tax remittance schedules

that results m a change m seasonal needs for
money
In addition, the computed seasonal factors
are sometimes changed Judginentally to reduce
the weight of SI rat10s that are thought to
reflect nonseasonal mfluences m particular
years Seasonal factors computed for the latest
years get special scrutmy, because X-11 movmg
seasonals sometimes are more responsive to
fluctuations m SI ratios m termmal years of a
senes than seems Justified by contemporary
mformat10n on seasonal mfluences In such
cases, Judgmental modificat10ns often are made
to stabilize the seasonal factors for the last
few years of the senes, unless a trend m SI
rat10s has been well established or unless there
is a known mfluence causmg a shift m the
seasonal pattern Judgmental modificat10ns of
the computed seasonal factors are constramed
by the reqmrement that monthly factors must
average approximately 100 per cent over the
year (or total 1,200) while hmitmg tendencies

CHART2 Relat1onsh1p Between Seasonal Component and Trend-Cycle Component, 1965-75
Seasonal
January

r= 395
66

•
•

••

•
••

•

••

• •

•
•

50

••

• •

August

•

-14

••
•
•
••
••

r= 192

280

* Scales dtffer for February and December

200
240
Trend-cycle

•
280

•

r=- 777

September

-18

•

-3 0

•

-0 4

• • •• • • •

-2 2

-3 8

-1 0

•


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Federal Reserve Bank of St. Louis

-2 2

•

r=- 822

•

04

-12

240

March

•
••

200

•
• • •

•
er= 945

•
·-

•

r=- 937
-0 6

58

July

•

February*

•

-0 4

•

• •••

-1 2

••

•

-2 6

• •
200

240

280

-2 0

Seasonal Adjustment of the Monetary Aggregates

toward repetitive movements m the seasonally
adjusted data m successive years On balance,
these modified X-11 (3 X 5) seasonal adjustments have produced movements m M 1 that
tend to be between X-11 (3 X 5) and X-11
(3 x 9) adjustments, movements that have
tended more toward a stable seasonal than the
X-11 (3 x 5) seasonal adjustments
In recent years, a major concern m reviewmg the X-11 M 1 seasonal adjustments has been
the tendency toward rapid expansion of this
senes m the first half of the year, followed
by slower growth m the second half This pattern 1s evident m the half-year growth rates
for the most recent years, as shown m Table I
In fact, the ummg of all six of the major shifts
m expans10n rates m the 11 years was such
that first-half growth rates exceeded secondhalf rates substanually However, m each instance these major shifts m growth rates appeared to be trend-cycle m nature rather than
seasonal From a techmcal v1ewpomt, some of

r= 207

Apnl

77

TABLE 1 Half-Year Changes m M 1
Seasonally adiusted annual rates m per cent

•

•

•

4
0
5
7
5

5
0
6
7
I

8
1
5
9
9

1970
1971
1972
1973
1974
1975

4
9
8
6
5
5

6
3
1
9
3
6

5
3
9
4
3
2

6
5
9
8
9
7

NOTE -Data are derived from seasonally ad1usted levels for June
and December Growth rates based on half-year or quarterly averages
show similar patterns, except m 1975, m which second-half expansion
exceeded that m the first half by these alternattve computations

the shifts did not occur m successive years and
the t1mmg of turnmg pomts m monthly
growth rates vaned from February to August
l\Ioreover, the durat10n of fast and slow
growth differed somewhat m these periods
Most important, the second-half slowmg and
the rapid expans10ns that followed m each of

r=- 866

••
• •
•••
••
r= 523 •

November

•

-0 4

•• •

-0 4

•
240

•

•

•

December*

r= 920

24

•
08

•
280

•

•
• ••
•
•• •
200

NOTE -Amounts are m b1lhons of dollars Variables denved from X-11 additive seasonal adJustment of Mt


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•

• •

200
240
Trend-cycle

-0 2

-1 0

•• • • •

16

-1 2

•
280

•• •

••

06

•
-44

•

r=-944

October

200

••

-3 6

•

•

•

•

-2 8

08

•
•• •

Seasonal
r= 853

June

• •

• •

•

Hi!

3
5
6
7
4

May

16

I

HI

1965
1966
1967
1968
1969

24

•

Change

Year

240

9I

• 75
59

280

Improvmg the Monetary Aggregates Staff Papers

78

the six periods were associated with monetary
or other national economic policy act10ns that
are considered nonseasonal mfluences
As a further check on the nature of these
movements, several alternative seasonal adjustment procedures were compared m conjunct10n with the M 1 rev1S1on published m
January 1976 13 In general, the alternative
procedures also reflected these shifts m M 1
growth as trend cycle, rather than seasonal, m
nature

Behavior of M 1 adjusted series
and seasonal factors
The extent of change m the published M 1
seasonal factors over the past two decades 1s
shown m Table 2 The largest net changes m
M 1 seasonal factors over the past 20 years have
been m February, Apnl, and July, with shifts
m demand deposit seasonals most important
Smee 1965 the largest changes m M 1 seasonal
factors have mcluded reduct10ns of nearly I
percentage pomt m the January and February
factors and mcreases exceedmg I percentage
pomt m the June and July factors S1gmficant
port10ns of the latter shifts were recogmzed
m the rev1S1on published m January 1976,
13 See Edward R Fry, "Seasonal Adjustment of M 1 Currently Published and Alternattve Methods," Staff
Economic Studies 87 (Board of Governors of the Federal
Reserve System, 1976)

based on trends m SI rat10s that appeared to be
developmg m the last several years However,
add1t10nal data will be needed to determme
whether or not these slufts are still m process
As has been noted, the seasonal adjustments
computed for M 1 components are based on
monthly levels However, observers of current
monetary cond1t1ons tend to focus on monthly
changes m the seasonally adjusted levels expressed at annual rates Chart 3 shows monthly
changes m dollars m the upper panels and
percentage changes at the bottom It may be
seen that much of the monthly fluctuat10n m
the not seasonally adjusted M 1 levels (top
curve) 1s removed as seasonal change (second
curve), leavmg relatively small and usually
positive residual changes m the seasonally adjusted senes (third curve) The tendency for
monthly seasonally adjusted changes to be
pos1t1ve, of course, reflects underlymg growth
m the money stock However, monthly fluctuat10ns 1n the Irregular component, pos1t1ve
and negative, are large enough relative to
short-run growth to obscure shifts m underlymg rates of growth This is especially evident m the bottom panel of Chart 3, which
shows the seasonally adJusted monthly changes
m per cent and also m per cent at annual
rates While It 1s common to express monthly
seasonally ad1usted money stock changes at
annual rates, this practice unavoidably gives
equal weight to the irregular and trend-cycle

TABLE 2 Changes m Seasonal Factors for Money Stock, 1955-75
In percentage pomts
Total Mi 1
Month

Level
of seasonal
factor
1975

Demand deposits
Level
of seasonal
factor

Change
1965-75

Jan
Feb
Mar
Apr
May
June

102
98
99
100
98
99

04
78
05
55
35
76

- 91
- 92
- 05
02
40
I 14

July
Aug
Sept
Oct
Nov
Dec

100
98
99
99
100
102

07
92
36
65
62
86

-

1 08
53
08
61
32
17

I 1955-65
35
- 78
- 58
I 35
- 70
-

-

72

08
33
03
32
26
55

1975
102
98
99
100
97
99

9
8
0
9
9
6

99
98
99
99
100
102

2
6
6
3

Currency
Level
of seasonal
factor

Change
1965-75
- 9
-11
- I
3
1 3

1

1955-65
s
9
- 7
I 7
9
-1 0

1 25

9

5

-

-

55
1

7
3
I

-

5

1

5

3
7

1975

Change
196s-1s

l

1955-65

99
98
99
99
99
100

35
70
20
45
75
25

- 42
- 23
08
31
48
45

- IS
- 29
- 12
04
03
30

100
100
99
99
100
JOI

75
35
85
80
70
85

32
12
- 13
- 33
- 39
- 18

30
29
- 22
- 36
09
03

1 Total Mi IS derived by summmg separately adJusted demand deposits and currency Implied seasonal factors shown were derived by
d1v1dmg the not seasonally adJusted total Mi by the seasonally adJusted total


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Seasonal Ad1ustment of the Monetary Aggregates

CHART 3 1M1 ,Total, Month-to-Month Change
Btlhons of dollars

IO

+
0

I . ! . . - - - ' - - - - ' - - - - ' - - - - ' - - - ~ - ~ 10

79

data are available, was suggested to the Federal
Reserve staff by Professor Milton Fnedman
As thus far developed, It computes stable daily
seasonal factors, makmg no allowance for
movmg seasonality However, monthly factors
calculated from the daily factors vary from
year to year because the daily factors mclude
.in ad1ustment for mtraweekly movements and
the weekdays mcluded m a given month vary
from year to year In add1t10n, the mtroduct10n of dummy vanables to adjust for hobdays and other special events also provides
flex1b1hty

Description of the method
Seasonally adjusted, per cent
Annual rate

L---L----l-----'---......__ _........-:--=-__,10
1973
1975
1971

components However, irregular fluctuations
seldom cumulate m one direction over a span
.is long as a year, m contrast to the trend-cycle
component Consequently, m assessmg the underlymg growth rate, 1t 1s necessary to view
average fluctuations m the money stock over
a long enough span to reduce the importance

In the daily seasonal method, the first step
1s to compute day of-the-week factors and use
them to remove mttaweekly movements, then
ttend 1s removed from this adjusted senes to
arnve at seasonal-irregular ratios A Founer
transfo1m of the5e rat10s 1s made and the sme
and cosme terms havmg the largest amplitudes
are selected to form an estimate of the seasonal In order to mcorporate dummy vanables, the coeffioents of the terms selected are
determmed not from the Founer transform,
hut fl om .i 1egress10n usmg the seasonalirreguidI ratios as the dependent vanable and
both the sme and cosme terms and the dummy
vanables as mclependent vanable5 Daily sea5onal facton computed from the regression
coefficients are combmed with mtl aweekly factors to seasonally adjust daily observat10ns

of irregular changes or to consider the season-

A detailed cle5ci 1pt10n of the method fol-

ally adjusted level of the money stock m relation to a longer-run trend level 14

lows
I Removal of mtraweekly movements
a The rat10 of each clay's observat10ns
to a 7-day centered movmg average 1s computed
b The rat10s for each day are ave1 aged
by quarters, and analyses of vanance tests are
made for changes m the rat10s between years
and between the quartet 5 w1thm a year
c If the tests m (b) show no s1gmficant
change, seven day-of-the-week factors are computed by .iveragmg rat10s for all Mondays, all
Tuesdays, and so forth If there 1s s1gmficant
between- or w1thm-year change, day-of-the-

A daily seasonal adjustment procedure
A seasonal adjustment method for senes
such as the money supply, fo1 which daily

14 Alternative methods for measuring the contnbu
uon of the irregular component, or at least that part
of the 1rregular component that arises f1om ve1y
short run day to day variations m M 1 , are proposed m
Richard D Porter, Agustm Maravall, Darrel Parke, and
David A Pierce, "Transitory Variat10ns m the Mon
etary Aggregates," this volume


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Federal Reserve Bank of St. Louis

lmprovmg the Monetary Aggregates Staff Papers

80

week factors must be computed that allow for
the change (So far, this has not been done )
d Observations m the origmal series are
divided by appropriate day-of-the-week factors
to get an adjusted series used m subsequent
calculations
2 Calculation of seasonal factors
a A trend-cycle component is estimated
by calculatmg for each observat10n a 365-day
centered movmg average of the adjusted series
b The trend-cycle curve is d1v1ded mto
the series derived m l(d) to obtam seasonalirregular rat10s In leap years, the February 28
rat10 1s calculated by averagmg the February 28
and 29 rat10s, and February 29 1s omitted
c A Fourier transform is made of the
seasonal-irregular ratios, calculatmg the A and
B coefficients m the equation
(7) Yt

=

½Ao+

~ AK cos(~!~)
1s2
+ fj

Bk sm

(2k1rt)
365

d A regress10n 1s run with the seasonalirregular rat10s as the dependent variable and
the N largest sme or cosme terms, plus dummy
variables for holidays, tax dates, and other such
effects as mdependent variables 15 Dummy
variables are used for holidays or other events
that fall on a different date each year or that
cause the series to "spike" too sharply to be
represented adequately by sme and cosme
terms The coefficients estimated by the regress10n are used to construct a final dally seasonal
factor series
3 Fmal adjustment and calculat10n of
weekly and monthly averages
a An adjustment factor for each day 1s
constructed as the product of the daily seasonal
factor and the appropriate day-of-the-week factor (For February 29, the February 28 dally
seasonal factor 1s used) Future daily adjustment factors may be projected usmg the regression coefficients and day-of-the-week factors
The origmal series 1s d1v1ded by the dally
15 Thus far, no smgle cntenon has been selected for
determmmg N For the money supply components, 30
terms were used, see note 16


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adjustment factor to get a final seasonally adjusted series
b Weekly and monthly seasonally adjusted series are calculated as the appropriate
averages of the dally seasonally adjusted data
c Implied monthly (and weekly) seasonal
factors may be calculated for periods for which
origmal data are available by d1vidmg the
monthly average of the origmal data by the
monthly average of the seasonally adjusted
data For projectmg future monthly seasonal
factors, the projected dally adjustment factors
may be averaged, these factors (for most series)
will differ only slightly from the imphed
monthly factors, which can be calculated only
after origmal data become available

Application of the daily seasonal
method to M 1
This sect10n presents the results of applymg
the daily seasonal adjustment to the demand
deposit and currency components of M 1 for
the years 1969-74, and compares them with
an X-11 adjustment
The computation of day-of-the-week factors
(see item l above) yielded the factors shown
m Table 3
The origmal series was adjusted for the mtraweekly pattern, the estimated trend was
divided mto this adjusted senes to yield seasonal irregular rat10s, and a Fourier transform
of this ratio series was made The 30 sme or
cosme terms havmg the largest amplitude
were selected as mdependent variables m the
regress10n used to compute the seasonal factors 16 The mdependent variables m the regres16 The number of terms used was determmed experimentally by computmg three seasonal factor senes havmg, respectively, 18, 30, and 50 sme-cosme terms and

TABLE 3 Day-of-the-week Factors for Money
Supply Components
Day
Monday
Tuesday
Wednesday
Thursday
Fnday
Saturday
Sunday

Demand deposits
1
i
1
1

00614
00578
00227
00322
99326
99472
99458

Currency
99625
98959
98936
99405
I 00995
I 01050
1 01031

Seasonal Ad1ustment of the Monetary Aggregates

TABLE 4 Summary Measures, Demand Deposit
and Currency Regressions, 1969-74
Measure

R'

Standard error of estimate
Fstat1st1c

Demand deposits

Currency

886
0068
420 8

421

887
0039

81

made by d1v1dmg the ongmal daily observat10ns by a factor cons1stmg of the product of
the day-of-the-week factor and the daily seasonal factor

5

Tests for changing seasonal pattern
s1on mcluded, m adcht10n to the sme and
cosme terms, 11 dummy variables These
dummy variables were for Washmgton's Birthday, the April 15 tax date, Easter Monday,
Memorial Day, July 4, Labor Day, Columbus
Day, Veterans Day, and the days before
Thanksg1vmg, Christmas, and New Year's
The treatment vaned when hohdays fell on
Saturday and Sunday, some hohdays are commonly observed by makmg an ad301mng weekday a nonworkmg day when the hohday falls
on a weekend In such cases the postt1on of
the dummy variable was slufted accordmgly,
otherwise, the dummy was omitted for the
year m which the holiday fell on a weekend
Some results of the two regress10ns are given
m Table 4
The coeffioents of the 41 variables were used
to compute 365 daily seasonal factors 11 Seasonal ad3ustment of the daily series was then

,

companng the vanance of the differences between the
actual seasonal uregular rat10s and the computed sea~onal factors For the demand deposit component, the
vanance was s1gmficantly smaller when 30 rather than 18
,.inables were used, but usmg 50 rather than 30 van.ibles did not make a further ~1gmficant reducuon For
currency, there was a statistically s1gmficant ~mailer
~tandard deviation when 50 variables were used, how
ever, as the dollar magnitude of the cu11ency senes
(and thu~ of the reduction m standard dev1at10n) is
much smaller than that of the demand deposit senes,
1t was clec1ded to use 30 terms here also
11 Actually 40 vanables plus the constant term The
latter is eqmvalent to the expression (½)Ao m Equat10n 7

Several tests were performed m an attempt
to determme whether, at least over the 196974 period, the evidence 1s m favor of fixed or
changmg seasonal factors We present here the
results of tests for stab1hty m the day-of-theweek effect and several tests for stab1hty of
the monthly factors The tests do not always
yield 1denttcal conclus10ns, however, they are
all consistent wtth the assertton that any
changes occurrmg m the descripttve seasonal
ovet this period have been mild
We consider fitst a test of stab1hty m the
mtraweekly patterns, that 1s, m the day-of-theweek factors Analysis of variance was used m
order to test for slufts both between years and
between quarters w1thm a year The data used
were the rat10 of each daily observation to a
centered 7-day average of daily observations
Seven tests were made, one for each day of the
week In e,tch test, all the data for 1 day
(say, Monday) were d1v1ded mto 24 cells-6
years and 4 quarters-and the variances of the
quarterly means and the yearly means were
compared wtth the wlthm-cell variance Table
5 shows, m the columns headed "Quarters,"
the rat10 of the variance of quarterly means
to the w1thm-cell variance, and m the columns
headed "Years," the ratio of the variance of
yearly means to w1thm-cell variance Under
the hypothesis of unchangmg mtraweekly factors these rattos possess F-d1stnbut10ns with
degrees of freedom as md1cated m Table 5

TABLE S F-tests for Change m lntraweekly Factors
Demand deposits
Day
Monday
Tuesday
Wednesday
Thursday
Fnday
Saturday
Sunday
t

Significant at 5 per cent level


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Quarters

F(3,289)
I 0993
5304
2 76291
2158
I 8424
6069
3 06611

I

Years

F(5,289)
1 0585
3080
1 0163
I 8763
3893
5 02061
3 47131

Currency
Quarters

F(3,289)
4244
I 6845
I 6868
1281
I 9050
I 4876
6442

I

Years

F(5,289)
I 8134
2 74091
3181
2 1411
3704
6185
5025

82

Improving the Monetary Aggregates Staff Papers

Those ratios that md1cate stat1st1cally s1gmficant between-quarter or between-year differences are md1cated m a footnote Wlule there
are s1gmficant differences for some days, either
m years or m quarters, most days show no
s1gmficant differences, and hence stable rather
than movmg mtraweekly factors were used m
the daily seasonal adjustment of the M 1 components
Three tests were conducted to examme the
poss1b1hty of a change m the monthly seasonal
factors The first test 1s based on the monthly
averages of the residuals from the regression
Each monthly average 1s assumed to be an
estimate of the residual mean, and a test 1s
made (assummg a normal d1stribut10n for the
residuals) of whether this estimate of the mean
differs s1gmficantly from the "true" mean 18 In
fact, the test was made by usmg two different
estimates of the "true" mean residual In one
test the true mean residual was assumed to be
the average residual for that month, m the
other, the true mean residual was assumed to
be zero The variance of the mean was estimated for each month separately, usmg data
for that month for all 6 years m the series If
average residuals are s1gmficant m a given
month, a shift m seasonal patterns could be
md1cated
Table A-1 m the appendix shows the results of this test It contams two groups of five
columns, one group for demand deposits and
the other for currency The first two columns
18 The variance of the mean was computed as

k) ]

Sm2 =s2
- [n-1
:E ( 1 - -n k
p
nk=O
where

Pk =

N

:E (xD2

1-1
S2

= variance of observat10ns for the given month
over the whole series

S! = variance of mean for the given month
n = sample size (number of days m the given
month)
pk

= correlat10n coefficient for observations k days
apart calculated from the set of N = 2190

m each group show the deviat10n of the mean
residuals from the true mean, adjusted for the
estimated variance of the mean, m the first
column, the "true" mean 1s assumed zero,
while m the second column, the true mean was
estimated for each month as the average of the
residuals m that month over the entire series
On the assumption that these stat1st1cs are
normally distributed, those that exceed 90 per
cent confidence hm1ts (5 per cent m each tail)
are marked with an asterisk, those that exceed
95 per cent limits, with a dagger The table
shows a susp1c1ously large number of months
with high residuals However, the fact that
they generally cluster together suggests a defect
m the esumation of trend rather than a s1gmficant change m seasonal
The second test for movmg seasonahty 1s
based on the idea that 1f seasonality remams
m the residuals from the regression (thus md1catmg movmg seasonality), 1t will be reflected m the autocorrelat10ns of the residuals
at the "seasonal" lags-that is, m the correlations of observat10ns in successive years or
quarters Thus, with daily data, large residual
autocorrelat10n at or neat lag 365 would md1cate an annual seasonal pattern unaccounted
for by the daily seasonal adjustment method,
and sigmficant autocorrelat10n at or near lags
91, 182, or 273 would pomt to a remammg
quarterly pattern
However, when the autoc01relat10ns of the
daily residuals are exammed, any possible
existence of seasonality 1s masked by the dominant first-order autocorrelation Tables A-2 and
A-3 show these autocorrelat10ns, from the demand and currency regress10ns, respectively,
for the first 370 lags These autocorrelation
coefficients are m both cases largest at the
lowest lags In fact, this low-order autocorrelation remforces the conclus10n that it 1s trend
more than seasonality that is madequately
treated
A common approach m the presence of such
serial correlat10n patterns is to compute first
differences (daily changes) of the series 19 In

regression residuals

x'

N

= deV1at1on of observations (that 1s, the residuals)
=

from their mean
number of observations 1n entire series


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19 See George E
P Box and Gw1lyn M Jenkms,
T11ne Series Analysis Forecasting and Control (HoldenDay, 1970)

Seasonal Ad1ustment of the Monetary Aggregates

TABLE6 Quarterly and Annual Autocorrelatmn m
F1rst-D1fferenced Residual Senes
Interval

Lag m days

3 months

91
92
182
183
273
274
364
365
366
28
35
63

6 months
9 months
I year
4 weeks
5 weeks
9 weeks

Value for
demand
deposits
153
039
149
025
133
038
155
125
- 064

*

*
*

Value for
currency

-

-

208
003
195
044
148
023
269
154
129
157
122
139

* Neghgtble

the present context we would expect at least
that the presence or absence of seasonality
would be more clearly revealed after detrendmg the residuals m this way This was found
to be true, and m fact the lughest autocorrelation coefficients m the senes of daily residual
changes occur at the quarterly and annual
lags Table 6 shows these coefficients While
they are never h1ghei than O 27 and are usually
below O 20, they are m several mstances very
lughly s1gmficant statistically owmg to the
large sample site, the standard error of a sample autocorrelation coefficient 1s about O03
To examme the possible impact of this, consider a simple case m wluch the annual autocoirelation coefficient has a value of O 155 (the
sample value for demand deposits) and other
coefficients are essentially zero This would
imply that the residuals (first-differenced), say
c 1, had an annual autoregressive model of the
form
(8)

Ct

= 155

Ct-365

+

Ut

For the demand deposit component the standard deviation of Ct was O0052, thus the
standard deviation of (0 l55ct_ 365), whICh 1s
the change m the ratio at time t resultmg from
takmg this autocorrelation mto account, is
0 0008 This could affect the seasonally adJUSted (dally) demand component figures (if
their level 1s $200 billion) by ±$160 million
Wah currency the comparable effect would be
about ±'$50 milhon While occasionally a
cumulative effect of several such occurrences


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Federal Reserve Bank of St. Louis

83

could be substantial, this effect on the whole
would appear to be rather mild
The third test of stable seasonality 1s similar
to the one Just described except that It is based
entirely on monthly data As md1cated earlier,
the log of the seasonal factor 1s the seasonal
component of the log of the senes We therefore estimated the regression equation
12

(9)

A log Mu = ~ a 3d 3 t
J=I

+

Ct

First differences of the loganthms are used m
order to obtam senally uncorrelated regression residuals, however, 1t can be shown that
seasonal components for levels are all unchangmg 1f and only 1f this 1s true for the
differences As m Equation 5, dit,
, d 12 t are
seasonal dummy vanables 20
Smee the seasonal dummies m Equat10n 9
capture all the fixed seasonality, any seasonality m the regress10n residuals ci mdicates
movmg seasonality m A log Mu (hence m M 1 i)
To test for seasonality m Ct the autocorrelations of tlus senes were computed, they are
chsplayed m Table 7, for lags 1-30 (an autocorrelation of lag k 1s the sample correlation
coeffioent between residuals k months apart)
Sea5onahty m tlus senes would ordmanly mcluce 5enal correlation at the annual lags of
12, 24,
, ,md perhaps also at the quarterly
lags 3, 6,
The standard errors of these autocorrelation coefficients, under the null hypothesis that there 1s httle actual senal correlation m the residual senes, are about O 12, so
that sample values above O 24 could be regarded as statistically s1gmficant (at the 5 per
cent level) In Table 7 1t 1s seen that no autocorrelation coefficients are 51gmficantly nonzero, m particular, those at the seasonal lags
give no evidence whatever of any seasonality
remammg m tlus senes We conclude from
this test that the fixed seasonal model (Equa20 The term ~a,d,t m Equat10n 9 also mcorporates a
constant term (which 1s the average rate of growth of
M 1 over this period), so that ~a, ~ 0, contrasted with
the case m Equation 5 If a = ~a,/12 denotes this
constant, then the a's m Equation 9 and the o's m Equat10n 5 are related by a, = a + o, The seasonal component for the Jth month 1s o, = a, - a

ImprovIDg the Monetary Aggregates Staff Papers

84

TABLE 7. Autocorrelations of Residuals from Fixed Seasonal M1 Regress10n
Lags
1-10
11-20
21-30

-

13
03
04

2

3

4

- 08
- 07
- 03

- 14
- 20
03

05
01
- 06

t10n 9) adequately captures seasonality ID the
money supply over this period (1969-74)
However, the fact that a fixed-seasonal
model appears adequately to capture seasonality m a series does not necessarily imply
that the series does not contam movmg seasonality There 1s rather limited mformauon
m only a few years' data-six ID this mvest1gat1on of M 1-concernmg various seasonal
patterns possible, and so the tests employed
are likely to have low power Indeed, the
prev10us two tests do find evidence for changes
ID the seasonal factors over this penod, with
no more-though also no less--ev1dence than
m Table 7 that any seasonality remams after
applymg these procedures
Even the regress10n on seasonal dummies,
however, revealed movmg seasonality m prior
sample penods A very different seasonal structure was found for M 1 for the penods 1959-68
and 1965-75 21 Also for the former sample
penod, application of the Stephenson and Farr
method found s1gmficant seasonal-trend mteract1ons, a clear md1cat1on of movmg seasonality 22 On the other hand, for the 1969-74
penod, the techmque descnbed and applied
to M 1 above has also failed to find movmg
seasonality for M 2 as well as for the currency,
demand, and time deposit components of these
aggregates separately One possible conclus1on
is that over shorter penods seasonality 1s generally best described by fixed-factor procedures

An alternative detrending method
Both the tests on monthly residual means
and the daily autocorrelation analysis JUSt described have IDd1cated an madequate trend
21 David A Pierce and Richard D Porter, "Lmear
Models and Lmear Filters m the Analysis of Seasonal
Time Senes," American Statistical Association, 197J
Proceedings of the Business and Economic Statistics
Section, pp 537---42
22 "Seasonal AdJustment of Economic Data"


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6
16
- 04
- 03

09
08
- 05

7
-

02
01
06

8
- 07
- 01
11

9

-

00
06
08

10

08
- 02
- 05

removal m the daily procedure In order to
get a more flexible trend lme than 1s provided
by a 365-day movmg average, the basic daily
seasonal adjustment method was altered by
makmg a prelimmary seasonal adjustment of
the origmal senes by usmg daily seasonal factors constructed from the 30 sme and cosme
terms havmg the largest coefficients as well as
the day-of-the-week factors A quadratic was
then fitted to N days centered on each date m
this seasonally adjusted series (Values of N
of 181 and 365 were tned) For each day the
rat10 of the origmal data (adjusted for day of
the week) to the middle term of the quadratic
centered on that day was computed, and these
ratios were then used m exactly the same way
as the rat10s of daily data to 365-day averages
were used m the baste adjustment methoda Founer transform was made and the 30 sme
and cosme terms havmg the largest amplitudes
were used with 11 holiday dummies m a regress10n
There are a variety of comparisons that can
be made between the baste method and the
quadratic-trend vanant Comparmg the residuals from the regression shows that a quadratic fitted to 365 terms reduces the mean
square deviat10n s1gmficantly, and that usmg
a 181-term quadratic reduces 1t even further
It 1s necessary to be cautious m mterpretmg
this result, however A quadratic does not
eliminate seasonal movements, hence, a seasonal remammg m the seasonally adjusted
series from which the trend was computed
with the quadratic could be mcorporated mto
the trend component In addition, a sufficiently
flexible trend could mcorporate some of the
irregular movement m the senes For both of
these reasons the over-all variance of the
seasonal-irregular ratios would be reduced,
and the smaller sIZe of the deviations from the
regress10n would not necessarily mdicate a
superior trend computation

Seasonal Adjustment of the Monetary Aggregates

Runmng the residual-means test for a changing seasonal for the two van an ts also shows
mterestmg comparisons Estimatmg trend with
a 365-term quadratic yielded results qmte similar to the basic method m that there were
nearly as many "s1gmficant" deviations of
monthly-average residuals from the "actual"
mean deviat10n However, usmg a 181-term
quadratic reduced the number of months m
which a changmg seasonal was triggered for
demand deposits to ll, it was 19 under the
basic method In addit10n, the pattern of
seasonal-change signals with the 181-term quadratic trend 1s quite different from that with
the basic method With the basic method,
spurious signals come m clusters, all bearing
the same sign and thus seemmg to come from
defects m the estimate of trend, but with the
181-term quadratic, signals, when they occur
close together, have opposite signs
These results mchcate that further work 1s
needed to improve the detrendmg procedure
m the daily seasonal method

Comparison of daily and X-ll seasonal
adjustment procedures
Table A-4 m the appendix shows the money
supply, Mv adjusted by three different methods
-a stable-seasonal variant of X-1 I, the standard (movmg-seasonal) X-11 adjustment, and
the daily seasonal adjustment 23 In all cases
the demand deposit and currency components
were adjusted separately, and the results
summed Table A-4 also shows the differences
between the daily seasonal method and these
two vers10ns of the X-11 method Table 8
5hows summary measures of the differences
The results of the X-11 movmg adjustment
5hown here are not those that would be obtamed were the same method used on a longer
time span A 6-year penod may contam too
few observations to identify meanmgful
23 The senes shown here does not mcludc the latest
revmons and hence differs from current published
figures In addition, m a few months there are small
d1ffcrences between these figures (which come from the
daily file) and published figures (which come from the
monthly file) that result from differences m the averaging methods used for Edge Act deposits


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Federal Reserve Bank of St. Louis

85

TABLE 8 Alternative AdJustments of M,, 1969-74 Data
In mdhons of dollars

---------...- - -.......- - - - Absolute
Comparison

Dally seasonal versus X-11
movmg seasonal
Dally seasonal versus X-11
stable seasonal

average
difference

Range of
difference

218

- I, 151 to 414

153

-652 to 256

moving-seasonal factors, given the problem of
separatmg seasonal from irregular and the fact
that a large proport10n of the factors m a 6year senes are estimated by special procedures
for termmal years at both ends of the senes
Given a longer time span, the X-11 movingseasonal method could give results either closer
to or further from those shown m Table 8
One would expect that the daily seasonal
method, which computes stable seasonal factors, would give results closer to the X-11
stable-seasonal adjustment than to the X-1 I
moving-seasonal adjustment, and Table 8
shows this to be true However, when the seasonally adjusted components of the money supply are exammed separately, 1t 1s seen that the
daily seasonal adjustment of the demand deposit component 1s closer to an X-11 stableseasonal adjustment, wlule the daily seasonal
adjustment of the currency component 1s
(shghtly) closer to an X-11 movmg-seasonal adjustment (see Table 9) Evidently, the mtraweekly pattern m the currency component (the
"tradmg-day" vanat10n) 1s strong enough to
account for a substantial part of the year-toyear movement 1n the seasonal factors generated by the X-11 movmg-seasonal program
The stable-seasonal X-11 1s constramed to compute a constant seasonal factor for each month
and thus cannot allow for the effect of mtraweekly movements
To summarize, a daily seasonal adjustment
method has been presented that, at least for
the money supply components, produces seasonally adjusted senes not greatly different
from those produced by X-11 over the past
several years The method produces stable
daily seasonal factors and thus monthly factors
that are stable except for "tradmg-day" vanat1on

86

Improving the Monetary Aggregates. Staff Papers

TABLE 9 Alternative AdJustments of M1 Components, 1959-74 Data
In millions of dollars
Demand deposits
Companson

Daily seasonal versus X 11
movmg seasonal
Dally seasonal versus X-11
stable seasonal

Average
absolute
difference

Range of
difference

Average
absolute
difference

206

-1, 111 to 400

52

-93 to 155

128

-645 to 196

53

-132 to 162

I

Several refinements and further work with
this method are still needed The effects of
usmg logarithms have not yet been mvest1gated, no method has yet been developed for
dealmg with a changmg mtraweekly pattern,
and further work 1s needed concernmg the
number of sme-cosme terms to mclude as
mdependent variables m the regress10n But
perhaps the most basic issue 1s the question of
whether to adJust the money supply with
stable or movmg seasonals If It 1s decided to
use stable seasonals, the daily method has the
advantage of allowmg for the mtroduct10n of
dummy variables to adJust for holidays and
other special events It also gives consistent
weekly and monthly seasonal adJustments,
which present a problem when X-l l 1s used
On the other hand, apphcat10n of the dally
method to M 1 adJustment would reqmre determmat10n of which segments of the series can


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

Currency
I

Range of
difference

be appropriately adjusted by a constant seasonal procedure and how such segments can
be lmked together durmg periods when seasonal factors are known to be changmg
If 1t is decided to use a movmg-seasonal
method, X-1 l 1s an obv10us choice, though
there 1s still the question, m estimatmg the
descriptive seasonal, of whether to use the results "raw" or to adJust for known special
events and pohcy changes Judgmental review
ts used, at present, to ehmmate effects on the
X-l l factors considered to be mduced by nonseasonal movements Wlule this adJustment is
based largely on Judgment, such effects can be
quantified by usmg artificial series constructed
with a known seasonal pattern 24
21 Results of a pn.hm1na1y study of this nature a1guc
agamst mmg an X 11 adiustmcnt without iudgmcntal
review

87

Appendix Tables
TABLE A-1 Test for Change m Seasonal
Monthly averages of residuals from the regressmn, baste daily seasonal ad1ustment
Demand deposits

Month
X/SD

1969-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
1970-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
1971-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
1972-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
1973-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
1974-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

2
2
I
1

450527t
34961lt
961078t
148012
531941
- 206847
- 948509
-I 849700*
- 974997
0
- 387205
-1 580070
I 420191
- l 846124*
- 690009
0
- 780180
-2 068474t
-3 035229t
- 756696
1 665619*
I 289507
172091
-I 061610
- I 448038
- I 208371
435795
- 337651
I 914988*
1 802527*
I 517614
I 975815t
934372
564159
-2 022070t
-1 802268*
-2 366986t
-1 077699
544744
303886
-1 205733
-1 950275*
-1 169827
- 882811
243749
886536
0
2 049155t
I 531579
939845
-1 380017
-2 464849t
0
I 713878*
I 612464
798734
-2 153116t
-2 619309t
- 043023
I 061610
- 863254
167829
907907
337651
0
I 241083
1 391147
966889
0
523862
I 548820
962856

-

Jex M)/SD J
144221t
517440t
961078t
418132
461016
- 088649
- 569106
- I 723583*
- 934372
0
043023
-1 333185
I 113875
- I 678293*
- 690009
270121
- 851106
-1 950275*
-2 655825t
- 630579
1 706243*
1 289507
602319
- 814725
-I 754354*
-1 040542
- 435795
- 067530
I 844062*
1 920726*
1 897017*
2 101932t
974997
564159
-1 591843
-l 555383
-2 673302t
- 909308
544744
574006
-1 276658
-1 832076*
- 790424
- 756696
284374
886536
430228
2 29604lt
I 225264
1 107674
-I 380017
-2 194730t
- 070925
I 832076*
1 991869t
924850
-2 I 12493t
-2 619309t
387205
1 308496
-1 169569
335659
907907
607771
- 070925
1 359282
1 770550*
1 093004
040625
523862
1 979048t
I 209742

X

2
2
1
1

--

---

-

-

-

-

-

-

-

0088
0070
0054
0034
0015
0007
0030
0044
0024
0
0009
0064
0051
0055
0019
0
0022
0070
0096
0018
0041
0032
0006
0043
0052
0036
0012
OOIO
0054
0061
0048
0047
0023
0014
0047
0073
0085
0032
0015
0009
0034
0066
0037
0021
0006
0022
0
0083
0055
0028
0038
0073
0
0058
0051
0019
0053
0065
0001
0043
0031
0005
0025
0010
0
0042
0044
0023
0
0013
0036
0039

I

M

0011
- 0005
0
0008
0002
0004
0012
- 0003
0001
0
- 0010
- 0010
0011
- 0005
0
- 0008
0002
- 0004
- 0012
0003
0001
0
- 0010
- 0010
0011
- 0005
0
- 0008
0002
0004
- 0012
0003
- 0001
0
0010
- 0010
0011
- 0005
0
- 0008
0002
- 0004
- 0012
- 0003
- 0001
0
- 0010
- 0010
0011
- 0005
0
- 0008
0002
0004
0012
- 0003
- 0001
0
- 0010
- 0010
0011
- 0005
0
- 0008
0002
- 0004
0012
- 0003
- 0001
0
- 0010
- 0010

--

--

-

--

-

Nom -The symbols have the followmg defimllons
X
M

= average of residuals for that month

= average of residuals for the given month over the enttre
series, that 1s, all January's have the same value
SD = estimated standard dev1at1on of the mean for the given
month, estimated over the entire series, that 1s, all
January's have the same value


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

I

SD

0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041
0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041
0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041
0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041
0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041
0036
0030
0028
0030
0028
0034
0032
0024
0025
0025
0023
0041

I
I

Currency
X/SD

2
1
1
-1
-2
-1
-

391307t
993044t
026415
769279*
583534t
364684
228294
843187
769371
2 174907t
I 570616
050072
- 341615
- I 845411 *
-I 710692*
-1 873355*
1 022649
1 213053
1 712202*
I 037767
839314
- 679659
-I 094671
- 951367
-I 229815
- 442899
-I 026415
- 312226
- 538236
227447
3 19611lt
2 91872lt
3 077483t
I 631180
- 380755
-1 552230
-I 844723*
- 222082
1 283019
- 468339
- 322942
- I 516315
-I 198542
-2 010675t
-1 538741
543727
285566
650935
068323
811981
- 342138
I 873355*
I 560885
2 426105t
570734
- 518884
-I 049142
-2 310839t
-2 094154t
- I 852662*
- I 708076*
- 147633
1 881763*
2 603882t
1 991474t
227447
-1 598056
- I 491791
- I 328913
0
1 285048
1 151654

-

I (X M)/SD I
527953+
214493
111950
300941
422062t
516315
027322
389163
349714
2 174907t
1 903775*
751079
- 204969
-1 623961
- I 625158
-l 405016
1 184119
l 061420
913175
582745
419657
- 679659
- 761511
- 250360
-1 093168
- 221449
- 940881
156113
- 376765
075816
2 397082t
2 464699t
2 657826t
1 631180
- 047594
- 851223
-1 708076*
0
I 368554
0
- 161471
-1 667948*
-1 997570t
-2 464699t
-1 958398*
- 543727
618727
1 351942
204969
- 590532
- 256604
2 341693t
1 722356*
2 274474t
- 228294
- 972908
-1 468779
-2 310839t
-1 760993*
-I 151654
-1 571430
073816
1 967297f
3 070221
2 152944t
075816
-2 397082t
-I 945815*
-1 748569*
0
1 618210
I 852662*
2
2
1
- I
-2
-1
-1

X

-

-

-

-

-

-

--

-

-

-

0035
0027
0012
0034
0048
0018
0004
0013
0011
0032
0033
0001
0005
0025
0020
0036
0019
0016
0030
0016
0012
0010
0023
0019
0018
0006
0012
0006
0010
0003
0056
0045
0044
0024
0008
0031
0027
0002
0015
0009
0006
0020
0021
0031
0022
0008
0006
0013
0001
0011
0004
0036
0029
0032
0010
0008
0015
0034
0044
0037
0025
0002
0022
0050
0037
0003
0028
0023
0019
0
0027
0023

I

M

-

-

-

-

-

-

-

-

--

-

--

-

-

-

-

0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014
0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014
0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014
0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014
0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014
0002
0003
0001
0009
0003
0002
0014
0007
0006
0
0007
0014

I

SD

0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020
0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020
0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020
0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020
0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020
0015
0014
0012
0019
0019
0013
0018
0015
0014
0015
0021
0020

XI SD= monthly average of daily residuals, ad1usted for
standard dev1at1on of the mean
(X - M) / SD monthly average of difference between daily
residuals and monthly average of residuals
for that month, ad1usted for standard dev1atton of the mean
• S1gmficant at 90 per cent confidence level
t S1gmficant at 95 per cent confidence level

=

88

lmprovmg the Monetary Aggregates Staff Papers

TABLE A-2 Autocorrelations of Residuals from Demand Deposit Regression
Lags
1- 10
11- 20
21- 30
31- 40
41- 50
51- 60
61- 70
71- 80
81- 90
91-100
101-110
111-120
121-130
131-140
141-150
151-160
161-170
171-180
181-190
191-200
201-210
211-220
221-230
231-240
241-250
251-260
261-270
271-280
281-290
291-300
301-310
311-320
321-330
331-340
341-350
351-360
361-370

-

704
347
289
226
217
145
084
031
034
061
076
109
093
056
039
057
017
033
032
016
036
033
005
071
081
086
040
080
081
087
076
015
063
080
097
072
136

-

2

3

4

534
343
291
217
190
162
081
030
050
024
072
086
123
069
021
033
035
032
078
011
025
038
020
055
096
075
053
040
069
081
061
022
060
084
105
076
117

457
366
300
216
173
165
058
037
068
037
083
087
123
067
012
000
029
022
037
007
016
072
042
056
089
076
048
012
063
073
064
007
086
089
118
092
065

436
394
298
215
138
150
026
015
094
071
081
069
112
066
002
009
027
000
021
001
015
073
058
047
061
091
057
014
056
067
094
012
049
075
112
111
028

-

-

-

410
372
311
226
II I
129
024
002
096
076
070
060
104
067
007
014
011
026
052
002
006
065
065
041
035
092
067
063
076
052
097
030
034
035
123
119
029

-

6

7

8

9

0

381
327
278
226
Ill
109
036
008
074
092
086
062
092
078
038
037
003
032
047
007
002
059
061
065
056
072
086
092
059
032
075
037
029
031
122
127
044

375
299
274
243
116
078
034
014
064
110
093
082
083
069
050
020
031
023
042
008
024
055
071
083
068
052
108
083
043
026
057
039
034
073
106
132
079

367
293
295
260
117
062
032
000
074
116
108
090
068
062
053
018
045
033
049
022
046
053
075
095
047
042
101
081
036
038
051
055
062
098
096
149
101

362
276
297
262
126
047
011
010
049
096
125
062
044
044
051
020
033
026
061
036
052
028
080
097
045
016
097
095
060
075
031
064
074
082
066
146
109

347
286
263
241
125
056
009
021
007
082
123
057
042
039
057
030
029
015
047
043
037
001
071
088
058
029
092
087
077
091
000
064
083
084
055
136
132

-

-

-

-

TABLE A-3 Autocorrelations of Residuals from Currency Regression
Lags
1- 10
11- 20
21- 30
31- 40
41- 50
51- 60
61- 70
71- 80
81- 90
91-100
101-110
111-120
121-130
131-140
141-150
151-160
161-170
171-180
181-190
191-200
201-210
211-220
221-230
231-240
241-250
251-260
261-270
271-280
281-290
291-300
301-310
311-320
321-330
331-340
341-350
351-360
361-370


https://fraser.stlouisfed.org
Federal Reserve Bank of St. Louis

2

-

683
317
283
272
207
155
108
097
Oil
085
055
097
084
191
175
158
201
182
091
129
130
023
067
090
022
000
067
025
032
020
026
014
016
023
016
015
018

-

534
311
285
283
210
152
134
102
014
022
076
098
114
203
161
147
196
164
019
098
134
057
060
093
027
020
037
015
010
038
022
003
005
011
014
028
003

-

3

4

5

6

7

8

9

0

464
305
299
287
216
151
147
089
034
037
Ill
IOI
129
204
154
098
183
153
068
113
147
075
068
083
009
017
017
077
003
041
035
004
014
007
034
026
094

414
329
300
284
190
143
072
056
042
038
131
099
132
198
160
059
182
174
144
141
128
083
074
063
034
009
017
046
007
025
035
019
010
004
025
021
239

375
327
294
294
184
135
044
030
005
033
123
102
134
194
171
116
184
148
164
160
IOI
072
090
062
045
016
020
002
038
021
018
020
009
049
008
020
215

327
313
268
225
180
147
080
Oil
013
030
121
102
158
186
168
162
203
150
157
159
097
061
090
070
015
024
013
000
056
018
005
006
012
068
010
044
092

293
307
290
206
180
155
IOI
001
006
043
117
118
197
197
160
138
199
141
136
149
080
067
084
076
045
055
011
018
058
007
016
004
023
002
017
066
048

277
309
359
222
176
146
112
022
015
055
109
111
204
203
131
150
193
147
142
148
070
094
075
066
023
059
006
030
046
010
010
008
025
036
024
058
019

308
306
332
226
164
123
103
033
028
068
108
066
187
197
136
149
204
155
138
136
063
102
076
038
011
055
004
019
016
042
014
014
014
019
014
031
008

318
290
287
223
155
105
093
023
019
065
099
058
179
191
156
173
198
155
137
129
008
079
081
022
013
073
004
007
001
055
025
024
016
008
002
025
027

-

-

-

-

-

-

-

-

-

-

-

-

-

89

Seasonal Adjustment of the Monetary Aggregates

TABLE A-4 Alternative Seasonal AdJustments of M1
In m1lbons of dollars
Month

Stable
X-11

I

Col 3
Moving I Dally
I less
X 11
seasonal
col 1

I

Col 3
less
col 2

Month

Stable
X-11

I

Col 3
Moving I Daily \ Col 3 I less
X 11
seasonal
c~"\
col 2

(5)
-652
-314
-3
11
208
2
-42
112
241
348
-44
-658

1972-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

236850
238678
240724
241663
242333
243034
245383
247564
249722
25151 l
252776
256366

(2)
237131
238654
240769
241763
242334
242957
245410
247504
249605
251426
252670
255905

(3)
236336
238482
240701
241765
242334
243229
245639
247602
249756
251578
252758
256078

(4)
-514
-196
-23
102
l
195
256
38
34
67
-18
-288

(5)
-795
-172
-68
2
0
272
229
98
151
152
88
173

1969-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

204138
204603
204930
205125
205527
205861
206129
206616
207616
208667
209132
209183

(2)
204340
204657
204893
205158
205384
205988
206362
206602
207325
208363
209256
209531

1970-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

211835
210472
211902
212915
213851
213992
214522
217001
219280
220148
220880
221822

211952
210415
211819
212899
213695
214067
214725
216992
219027
219912
221000
222059

211375
210285
211803
213018
213877
214098
214761
217050
219257
220202
220916
221516

-460
-187
-99
103
26
106
239
49
-23
54
36
-306

-577
-130
-16
119
182
31
36
58
230
290
-84
-543

1973-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

257897
258465
258268
259058
261877
264295
265303
265869
265669
266741
269388
271977

258351
258527
258384
259236
262013
264157
265235
265817
265692
266808
269239
271251

257245
258228
258264
259128
261892
264515
265523
265946
265701
266813
269400
271604

-652
-237
-4
70
15
220
220
77
32
72
12
-373

-1106
-299
-120
-108
-121
358
288
129
9
5
161
353

1971-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

223279
224732
226258
227384
229854
231115
232237
233566
234313
235082
235084
235766

223419
224652
226197
227375
229749
231138
232375
233531
234105
234912
235096
235680

222838
224538
226187
227471
229887
231254
232491
233571
234299
235237
235028
235488

-441
-194
-71
87
33
139
254
5
-14
155
-56
-278

-581
-114
-10
96
138
116
116
40
194
325
-68
-192

1974-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

272019
273681
275189
276279
277151
278904
279724
280287
280724
281863
283410
284935

272525
273734
275304
276486
277372
278712
279608
280297
280905
282116
283349
284181

271374
273443
275200
276300
277216
279126
279951
280379
280702
281957
283436
284496

-645
-238
11
21

-1151
-291
-104
-186
-156
414
343
82
-203
-159
87
315

(!)


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Federal Reserve Bank of St. Louis

(3)
203688
204343
204890
205169
205592
205990
206320
206714
207566
208711
209212
208873

(4)
-450
-260
-40
44
65
129
191
98
-50
44
80
-310

(I)

65

222
227
92
-22
94
26

-439

90

Bibliography

Board of Governors of the Federal Reserve System Improving the Monetary
Aggregates Report of the Advisory Committee on Monetary Statistics
Washmgton Board of Governors, 1976
Box, George E P, and Gw1lyn M Jenkms Time Se1tes Analysts Forecasting and Control San Francisco Holden-Day, 1970
Cleveland, Wilham P, and George C Tiao "A Model for the Census
X-11 Seasonal Adjustment Program" Techmcal Report 312 Madison
Umvers1ty of W1sconsm, 1974
Fry, Edward R "Seasonal Adjustment of M 1-Currently Published and
Alternauve Methods" Staff Economic Studies 87 Washmgton Board
of Governors of the Federal Reserve System, 1976
"Money Stock Rev1S1ons" Federal Reserve Bulletin, vol 64 (Apnl 1978),
pp 338-39
Pierce, David A "Relauonsh1ps-and the Lack Thereof-Between Economic Time Senes, with SpeCial Reference to Money and Interest Rates "
journal of the American Statistical Association, vol 72 (March 1972),
pp 11-26
- - - , and Richard D Porter "Lmear Models and Lmear Filters m the
Analysis of Seasonal Time Senes," m American Statistical Association,
1973 Proceedings of the Business and Economic Statistics Section (Washmgton), pp 537-42
Stephenson, James A, and Helen T Farr "Seasonal Adjustment of Eco
nom1c Data by Apphcauon of the General Lmear Stausucal Model"
Journal of the American Statistical Association, vol 67 (March 1972),
pp 37-45
US Department of Commerce "The X-11 Variant of the Census Method
II Seasonal Adjustment Program" Bureau of the Census Techmcal
Paper 15, revised Washmgton Government Prmtmg Office, 1967
Walhs, Kenneth F "Seasonal Adjustment and Relations Between Vanables" Journal of the American Statistical Association, vol 69 (March
1974), pp 18-31
Whittle, Peter Prediction and Regulation by Linear Least-Square Methods
London English Umvers1ues Press, 1963


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91

Demand Deposit Ownership Survey
Helen T Farr, Richard D Porter, and Eleanor M Pruitt

This paper was initially completed in the
summer of 1976 It has been updated (Jee particularly pages 103-()6) to make 1 eference to
additional wo1 k that has made uJe of the
Demand Deposit Ownership Swvey
Theoretically, the determm,mts ol: the dem,md fo1 money differ among VJ.nous classes
of holders ol: demJ.nd deposits Howeve1, until
1970, when the Federal Reserve began to collect sample data on demand deposit holdmgs
by ownership category, there were no 1egularly
available monthly data that could be used to
test hypotheses about sectoral money demands
About 5½ years of dat,t now exist thJ.t appear
to be reliable m the sense that they accurately
1eport ownenh1p ol deposits by md1viduals,
pa1tne1 sl11 ps, J.nd cm pm a t10ns (IPC' s)
Even with severe data hmitations, reasonable sectm J.! demand functions have been successfully estimated The results suggest quite
1>t1ongly that estimates of aggiegate money
demand cJ.n be imp1oved by usmg the mformat10n m chsagg1egated, sectoral demand funcuons 'I he sectoral demand funct10ns can be
used du ectly, and the mf01 mat10n on elasticities and speeds of adjustment that are dellved from the estimated sectoral demand
equat10ns can also be used m constrammg
estimated coefficients m aggregate demand
funct10ns
The first two 5ect10ns desc11be the natme of
the demand depo5lt ownership survey (DDOS)
and the test5 of the 1ehab1hty of the reported

NOTE -Helen T Farr and Richard D Porter an.
members of the staff of the D1v1s10n of Research ,md
Statistics Eleanor M Prmtt, ,~ho has since died, was
liso a member of that staff


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data 1 1 he next sect10ns detail the results oi
esumatmg secto1al demand funct10m and examme seve1 J.l othe1 cuuent uses of the DDOS
data evaluat1on1, ol 5hort-run movements m
the agg1egates, J.nalysis of the short-run impact
oi tc1x rebates ,mcl refunds on deposit holdmgs, e,umat10n of the Boa1d's monthly money
mai ket model, 1,tud1e, of 5ectorc1l veloot1es c1nd
deposit turnover rates, and the usefulness
of the DDOS data as a data somce for other
,e11e, A b11cl 5111 vey of potentIJ.l longer-term
5tud1e1, 15 followed by two c1ppemhxe5

H1sto1 y and outlme of the survey
~mce June 1970 c1 Fede1 ,tl Reset ve ~ystcm
survey h,ts p1ov1dcd dc1tJ. on the ownership
ol dem,md depo1,1t bc1Lmcc, of !PC's 2 1 he
DDOS c!J.ss1fie1> totJ.l IPC halc1nce1> mto fi'vL
mutuc1lly exclu~1vc cate,~011e5 financial bu1,1
ne,s, nonhnc1noc1l bmme'>'>, homehold, foreign,
c1nd J. 1c,1duJ.! (<1tcgory tc>uned ,ti! othe1 IPC
deposits, wluch mdude5 depo51t'> ol nonp1 oht
msu tu uons c1ml ti us t depc11 tmen t 5 of I epo1 t1 ng
banks Monthly s,1mple dat,1 J.l e med to p1 epc11 e esumates on c1 d,uly-ave1 c1ge bas1, £01 e<1ch
cc1tegory at weekly 1epo1 tmg bc1nk 5, c1ml ,m
expc1nded s<1mple pi ov1des e1>t1mc1te~ 1:oi ,ti!
commeic1,1! bank5 l:or the Lt,t month ol: ec1cl1
quc1rte1
In the ongmal survey, 413 banks weie
<hosen to supply repo1 ts for the end-monthof-qu,n te1 e5t1mate, am! 225 of these were J.lso
10 ,upply monthly 1cpo1 t5 Became of me1gen
1 These ~ccliom .i.nd Appemhx I J.tc based 011 ca1 hu
unpublished I cdcral Re~e1ve staff \\ork ot James L
Pierce and Martha S 'ic.i.nlon
2 For a more deta1led descnpt1on of the survey, see
Sm vey of Dc.mand Deposit 0\\ nushtp," Federnl Re
,ewe nullctw, 10! r,7 (June. l!J71), pp 4'16-67

92

lmprovmg the Monetary Aggregates Staff Papers

and other problems, the numbe1 of reportmg
banks has declmed and it actually fluctuates
somewhat from month to month At present,
about 380 banks report m the quarterly sample and about 215 report monthly
The sample 1s divided mto strata based on
s1Ze classification All banks with IPC deposits
of more than $1 b1ll1on were mcluded m the
first stratum, and a stratified random-samplmg
techmque was used to select banks m the other
five size classes Durmg the m1t1al 6 months
of operat10n of the survey-m the latter half
of 1970-there were a number of problems
associated with procedures for reportmg and
ed1tmg the data Staff at the reportmg
banks, the Reserve Banks, and the Board
attempted to solve these d1fficult1es, and except
for occas10nal problems, they have made substantial progress m estabhshmg procedures
that produce timely and accurate reportmg of
data Results are tabulated w1thm 5 to 6 weeks
of the close of the survey month and are
published m the Federal Reserve Bulletin
with a 2-month lag

Reliability of the DDOS data
No benchmark data on ownership of demand deposits by category are available to
edit sample data or to test the validity of the
published estimates directly An mdirect test
of data quality, which mvolves comparmg the
DDOS total for IPC demand deposits with a
measure of gross IPC demand deposits denved
from money stock data, suggests that the total
IPC estimates from the DDOS are reliable
Table 1 shows the dollar amount of the difference between the quarterly estimates from the
DDOS and from the money supply senes
Appendix 1 provides an explanation of the
relationship between the two
The DDOS figures have differed from the
denved money stock balances by amounts
rangmg from less than $50 million to as much
as $3 5 billion, with the average absolute difference over the survey penod amountmg to
approximately $600 million, about O4 per
cent of gross demand deposits In most penods
the absolute difference was less than 1 per


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TABLE 1 Comparison of the Estimate of Gross IPC
Demand Deposits Derived from M1 with
the Estwate from DDOS
In billions of dollars, not seasonally ad1usted

Quarter
1970-Q3
Q4
1971-Ql
Q2
Q3
Q4
1972-Ql
Q2
Q3
Q4
1973-Ql
Q2
Q3
Q4
1974-Ql
Q2
Q3
Q4
1975-Ql
Q2
Q3
Q4
1976-Ql

Mi

estimate

167
174
169
175
178
186
182
188
195
207
200
206
209
220
211
218
218
226
215
223
227
236
228

2
6
8
8
1
0
6
0
6
9
4
7
2
l
4
5
6
7
4
8
5
9
4

DDOS
estimate
167
175
170
175
177
187
181
188
195
208
200
206
210
220
211
215
216
225
216
222
227
236
227

9
1
9
8
9
5
2
4
4
0
0
3
3
1
2
0
8
4
3
2
0
9
9

Difference
1n estimates

Difference as
percentage
of M1
estimate

4
3
6

- 7
- 5
-1 I
2
-1 6
I 4
- 4
2
- 1
4
4
-I I

-

1
8
8
2
1
0
2
2
5

2
3 5
1 8
1 3
9
I 6
5

0
I 6
8
6
4
7
2

5

2

cent of gross IPC demand deposits In 1974
the DDOS estimates of gross IPC deposits
began to diverge s1gmficantly from the prelimmary estimate denved from M 1 However,
subsequent rev1S1ons m the M 1 data brought
the money stock-denved estimates back m lme
with the DDOS figures, suggestmg that the
survey does provide a reasonably reliable mdependent estimate of gross IPC deposits
The DDOS was cles1gned pnmanly not to
estimate total IPC demand deposits but rather
to estimate the distribution of deposits among
the var10us ownerslup categories The appropriate test of the quality of the data would
be a companson between movements m the
DDOS estimates of the various ownership
categones and the true values Unfortunately,
no such benchmark data exist
DDOS estimates are sub1ect to both reportmg and samplmg errors Some concern has
been expressed from time to time about the
quality of the reported data However, a recent analysis of the variance of percentage
shares reported quarterly by each of the md1vidual banks on the panel md1cated that senously maccurate data appeared to be a problem at only about 2 per cent of the banks As
for sampling error, the standard errors of

Demand Deposit Ownership Survey

93

TABLE 2 IPC Demand Deposit Ownership, by Type of Holder, All Commercial Banks1
In bllbons of dollars, not seasonally ad1usted
Type of holder
Month

Financial

Foreign

I 3
( 2)

5
2)
4
3)

1
(
1
(

4
1)
5
2)

11 0
(I 7)
12 3
(1 5)

188
(1
208
(2

4
6)
0
2)

67
(3
70
(2

2
0)
2
8)

2
(
2
(

0
2)
4
2)

11 7
(I 6)
11 7
( 8)

206
(2
219
(I

1
3)
8
4)

9
0)
2
0)

71
(2
73
(2

2
2)
I
0)

2
(
2
(

I
2)
3
2)

11 1
(I 2)
11 7
(I 1)

214 6
(2 0)
224 1
(I 4)

1
2)
I
0)

74 8
(I 2)
78 0
(2 4)

2
(
2
(

3
2)
4
2)

10 6
( 8)
11 3

222 2
(2 4)
236 9
(I 6)

60
(2
65
(2

l06
(3
116
(3

6
5)
4
2)

18 2
( 8)
18 9
(I O)

111
(3
118
(4

19
(
20
(1

115
(3
125
(3

1973-June
December

17
(1
17
(

1
1)
3
9)

85
(1
92
(I

18
(
18
(

1
9)
5
8)

89 6
(2 0)
98 4
(I 2)

17
(
18
(

9
9)
9
7)

97
(2
l09
(3

18 5
( 7)
19 0
( 7)

1974-June
December

4
8)
1
0)

Total

175 8
(I 2)
187 5
(2 0)

6
4)
9
5)

December

I

10
(1
IO
(1

1 3

1972-June

All other

162 5
(I 9)
175 1
(I 3)

2
7)
6
3)

December

I

9 6
(I 3)
10 3
(I 0)

56
(1
58
(2

1971-June

1

I

1
(
I
(

December

December

I

Household
49 0
(I 7)
53 6
(1 9)

1970-June

1975-June

I

Nonfinanc1al
3
4)
7
8)

6
1)
3
1)

( I)

5
4)
7
2)

( 6)

Figures m parentheses are two standard errors of the est1111ate Figures may not sum to total because of rounding

estimate have been small relative to the estimated deposit levels for all ownerslup categories throughout the survey penod, especially
for the largest ownership categones-nonfinancial businesses and households (See
Table 2)

Money demand studies

Motivation for disaggregated studies
Several considerations suggest that disaggregating the demand for demand deposit balances by sector will improve our knowledge of
the aggregate demand for such deposits
First, each of the elasticities in the aggregate
demand function 1s a weighted average of the
corresponding disaggregated sectoral elasticities with the weights equal to the share of deposits held by each sector 3 For example, the
a To demonstrate this pomt, first let the deposit
demand function for the 1th sector be written as

D, = D,(x)
where x 1s a vector of explanatory variables If elements of x do not belong m a particular sector, the
associated coefficients m the function D,(x) will be zero
Hence, It can be assumed that x 1s common to all


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Federal Reserve Bank of St. Louis

aggregate interest rate elast1c1ty is a weighted
average of the rate elasticities for households,
nonfinancial businesses, financial businesses,
and so forth This averaging implies that were
the shares held by each sector to change, the
aggregate rate elasticity would change even 1f
the chsaggregated elastic1t1es were unchanged
Though the sectoral shares appear to have
been relatively constant to date, they are hkely
to change in response to particular changes
in the payments mechamsm that are currently
developing But more important, given disaggregated estimates, It 1s possible to test
&ectors Aggregate deposits, D, are the sum of deposits
m the md1v1dual sectors

D = ,-1
fn,
where p 1s the number of sectors It follows that the
aggregate elast1c1ty of D with respect to the rth component of x, x,. ts

aD)(x')
( ax,
/) _=

f

,-1

f

,-1

(aD
aD, )(aD,)(x')
ax, D

(aD•)(::.1:)(D•)
ax, D D, =

f

,-1

(aD,)(:."....)
ax, D, (/,)

where f, ts the share of aggregate deposits held by 1th
sector

94

Improving the Monetary Aggregates Staff Papers

whether the elast1c1ties that are estimated by
usmg aggregate data alone are "correct" or are
statistical artifacts In addition, the disaggregated coefficients suggest plausible values for
the aggregate coefficients that can, 1£ It 1s warranted, be imposed (with any level of prec1S1on
desired) on the aggregate estimates themselves
usmg Bayesian or mixed estimation techmques
For example, lt 1s worthwhile to consider a
s1gmficant puzzle m the standard aggregate
equation for demand for demand deposits Estimates of the long-run elastiot1es for the shortterm rate, the commercial paper rate or the
Treasury bill rate, generally range from about
-0 04 to -0 25, while the elast1C1ty for the
savmgs deposlt rate-however measured-is
generally two to three times larger m absolute
value Smee over sample periods before November 1974 only consumers would be affected
by the savmgs deposit rate and smce consumers hold only about a third of deposits, lt
1s unclear why the savmgs deposit elasticity
should be so large relative to that of the commercial paper rate (or the Treasury bill rate)
The disaggregated equations shed some hght
on this puzzle
Next, the basic dete1mmants of money demand presumably differ somewhat across sectors Until recently, corporat10ns could not
hold savmgs accounts at commercial banks,
and so the savings rate was an alternative
yield for consumers but not for firms S1m1laily, smce consumers hold less than 1 per cent
of commercial paper outstandmg, the commercial paper rate 1s presumably not a particularly
relevant alternative rate for most consumers
Also, the relevant scale (transact10ns) variable
will also differ across sectors For example,
consumei dem,md for money probably depends on a consumer transact10ns measure
(personal mcome or consumption), and nonfinanoal busmess demand may depend on
busmess sales 4 At the aggregate level, such
4 Intmt1vely, busmess sales appear to be a reasonable
measure of tran~att1ons volume for nonfinancial firms
Goldfeld used this variable m his work, see Stephen
M Goldfeld, "The Demand for Money Revmted,"
Brookings Pape1s on Economic Activity, 3 1973, pp
577-643 Miller and Orr have developed a model of


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transact10ns variables are qmte collmear, and
it is difficult to obtam reliable estimates of
their separate impacts Fmally, sectors are also
d1stmgmshed by how qmckly the money holders m each ad1ust to changes m transactions
measures and mterest rates-the relative speeds
of adjustment Fmancial firms appear to adJUSt very qmckly, much more qmckly than
nonfinancial firms, which, m turn, appear to
ad1ust more qmckly than households
Because none of the md1vidual sectors represents more than about half of the total demand
for demand deposits, the demand equations for
mdividual sectors may each exlubit less simultaneous-equations bias than the equation for
aggregate demand for demand deposits
Besides the primary cletermmants of the
demand for demand depo~its (mterest rates
,md transact10ns), there a1e secondary vanables that affect only particular sectors Undoubteclly, one of the most important of these
1s the compensatmg-balance reqmrement that
banks impose on commercial and mdustnal
loans Deposit holdmgs of nonfinancial businesses may well depend on the level of commeroal and mclustrial loans m add1t1on to
the transact10ns and mte1est rate variables'
th<. demand for money m which the "~cale" variable 1~
th<. "arian(e of the change m th<. daily deposits of a
fnm havmg stochastic mflows and outflows Although
the1e u, a positive relat10mh1p bet\\ccn this variance
and sales, Miller and Orr md1cate that the relation
ship 1s loose, see Merton H M1llcr and Dame! Orr,
'A Model of the Demand for Money by Firms,"
Quarte1 ly Journal of Econo1111cs, vol 80 (August 1966),
e:.pec1ally pp 425-26 See also Dame! Orr, Cash Man
agement and the Demand for Money (Praeger, 1971)
,, To be sure, the relat1onsh1p bet\\een the demand
fo1 demand deposits and compensatmg balances 1s
complex The rationale for a loan variable (or compcnsatmg balances) m the demand funct10n 1s not
well established Desired transactions balances for some
firms may match, on average, their compensatmg
balance~, and, accordmgly, the loan coefficient for those
hrms 1s zero See Jared Enzler, Lewis Johnson, and
John Paulus, "Some Problems of Money Demand,"
B1ookzngs Papers on Economic Actnnt)', I 1976, p 274,
and Orr, Cash Management, pp 98-100, for further
d1scuss1ons of this pomt Moreover, there are other
1casons for holdmg compensatmg balances, such as
payment for Imes of credit and payment fo1 other
~erv1ces that cannot be econom1cally pnced directly,
~<.c, for mstance, Richard Homonoff and David Wiley
Mullms, Jr, Cash Management (Lexington Books,
1975)

Demand Deposit Ownership Survey

In an aggregate demand deposit regression, the
effect of compensatmg balances as represented
by commercial and mdustrial loans can be lost
m the welter of other variables and mfluences,
but lt shows up sigmficantly m the disaggregated regression explammg deposits of nonfinancial busmesses
Another secondary variable is the change m
government deposits Tlus variable probably
has a transitory impact on all of the sectors,
but the impact disappears m a matter of days
or weeks for most The only sector m which
the impact of the monthly change m government deposits could be measured is the household sector Fmally, speculative motives for
holdmg deposits appear largely m the financial
sector, accordmgly, "speculative" variables,
such as the expected change m short-term
mterest I ates, appear to have a decisive mfluence there but not elsewhere In summary, one
advantage of d1saggregatmg deposit demand
1s that tlus procedure permits us to obtam
reliable estimates of the elasticities of some
~econdary variables that are qmte difficult, 1£
not 1mposs1ble, to estimate directly at the
,iggiegate level

95

the penod of fit permitted us to simulate over
this period and test the gam from usmg disaggregated demand functions
All equations were estimated m natural
logarithms, only the equat10n for financial
busmesses 1s not m real terms The variables
(h5ted below) are not seasonally adjusted except personal mcome, which 1s available only
on an adjusted basis Data are monthly and
thus deposit data are for the weekly reportmg
banks only All equations were estnnated by
usmg a two-stage least-squares techmque 7 with
a "rho" term Polynomial distributed lags were
second degree constramed to zero at the nghthand tail
The follow mg hst pi ovides the symbols and
abbrev1at10m used m the equations and tables
below
HO USR

GOVR

PIR
RPQ
R90

Sectoral money demands
In Appendix 2, we analyze a standard
money demand funct10n and show that sigmfican t differences exist among sectors m their
responses to changes m mterest rates and mcome Given this evidence that the ma1or holders of deposits react differently to some "standard" set of determmants of deposit holdmgs,
demand equat10ns were estimated for each
sector with explanatory variables that differed ao oss sectors The series contammg
"reliable" DDOS data begm m December
1970, thus, the periods of fit of most of the
equations begm m January 1971 The second
half of I 97 4 and all of I 97 5 were excluded
from the penod of fit because a number of
5tud1es have md1cated that standard aggregate
money demand functions do very poorly m
explammg tlus penod 6 Such exclus10n from
6 Sec, for example, Enzler and others, "Some P1ob
!ems," pp 261-80, and Charles Lieberman, "The


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Federal Reserve Bank of St. Louis

= balances of households deflated by

U1-1

R. 2

SE
DW
DF

=

P

the consumer pnce mdex (CPI),
not seasonally adjusted
government deposits deflated by
the CPI, not seasonally adjusted
personal mcome, deflated by the
CPI
Regulation Q ce1lmg on savmgs
90-day Treasury 6111 rate
lagged error term
squared coefficient of correlation,
adjusted for degrees of freedom
standard error of estimate, adJusted for degrees of freedom
Durbm-Watson statistic
degrees of freedom
superscript denotmg that a polynomial d1stnbuted lag was estimated

T1 ansact10ns Demand fo1 Money and Technological
Change, ' Review of Economics and Statistics, vol 59
(August 1977), pp 301-17
7 The reduced fo1m was
Ci In R,

=

ao

+ a1Ci. In Pl{' + a2 Ci In Mf,_
+

1

In RFFf'--i
here R 1s the commercial pape1 rate (RCP) or the
'JO da} I 1easmy bill rate (R90), Pl 1~ penonal rncome,
and RFF t~ the I ulcul funds tale Ih1, 1uluced fo1m
1s consistent with the money ckm1.nd funct10ns m the
monthly money market model and an ,1ssumed "1eact1on funct10n" that relate\ change~ m the Federal
funds r,lte to deviations of the la~ged rate of g1011 th
of money f1om mme de,11ul 1,1te
11

a 3 Ci

96

Improving the Monetary Aggregates Staff Papers

s,
NFBR

= seasonal dummy variables
= balances of nonfinancial

CILR

BSR

=

RCP
FIN

=

DEBF

=

NYSE
TOTR
SUM

businesses deflated by wholesale pnce
mdex net of farm products
(WPIN), not seasonally adjusted
commercial and mdustnal loans
deflated by WPIN, not seasonally
adjusted
manufacturmg and trade sales deflated by WP[ N, not seasonally
adjusted
rate on 30- to 59-day pnme commercial paper
balances of financial busmesses,
not seasonally adjusted
debits at seven financial centers,
not seasonally adjusted
New York Stock Exchange mdex
sum of HOUSR and NFBR
projection of TOT R from disaggregated equat10ns

Demand of households. The explanatory
variables chosen for the household equation are
the change m government deposits, the level
of personal mcome, the Regulation Q ceilmg
on the savmgs rate, 8 and the 90-day Treasury
bill rate The pnce mdex used to deflate household demand deposits, personal mcome, and
government deposits was the consumer price
mdex, not seasonally adJusted Among households, nonfinancial busmesses, and financial
busmesses, the change m government deposits
-at least over a period as long as a monthseems to be related only to household holdmgs
of money, when tned in the other two equations, it did not enter sigmficantly Personal
mcome is obviously a transact10ns proxy that
is relevant only to households Until recently,
savings accounts were an alternative asset
holdmg only for mdividuals, and thus the
savmgs deposit rate belongs m the household
equation but not m the equat10ns for nonfinancial and financial busmesses 9 Finally, the
90-day Treasury bill rate was also mcluded
s Savings rates offered were essentially at the ce1lmg
rate m the penod under study
9 State and local governments and corporations became eligible to hold such accounts m the fall of 1974
and 1975, respecuvely, after our esumauon penod
ended

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Federal Reserve Bank of St. Louis

Goldfeld used the commercial paper rate m
his household demand equation, he also used
flow of funds data on holdings of M 1 10 However, mdividuals have greater access to the
bill market than to the commercial paper
market, and so we prefer the specification that
uses the bill rate
The results of estimatmg the equation and
mformation on the lag characteristics are given
in Table 3 11 Note first that all variables have
the correct sign and only the savmgs rate is
not statistically sigmficant at the 90 per cent
confidence level The lack of significance for
the savmgs rate is not surpnsmg given the
very short sample period and the smgle change
m the rate durmg the relevant time span
Also, the elastIC1ty for the savmgs rate (-0 152)
1s only slightly larger than that for the Treasury bill rate ( -0 110) This result suggests that
estimates of the elasticity for the savmgs deposit
rate two to three times larger than that for the
Treasury bill rate (or the commercial paper
rate) m aggregate equations are statistical artifacts and do not possess an empirical basis m
the microeconomic relations that underpin the
aggregate equation
Demand of nonfinancial businesses Commercial and mdustnal loans, busmess sales,
and the commercial paper rate appear as explanatory variables m this equation, shown
in Table 4 The loan variable, as expected,
appears to affect only the demand of nonfinancial busmesses, 12 when tried m the other
Goldfeld, "Demand for Money "
In all tables presentmg estimated equations, the
numbers m parentheses are t-staUst1cs The long run
coefficients of the d1stnbuted-lag variables are presented m the exposition of the equation, and md1v1dual monthly coefficients are presented below Mean
lag 1s the average length of lag (m months), length
of lag 1s the total number of lagged months m the d1stnbut10n
12 The magmtude of the loan coefficient may provide
a rough estimate of the fract10n of firms that, on average, hold more m compensatmg balances than 1s required to carry out transactions Alternatively, a pure
transactions model may be appropnate, but our scale
vanable (busmess sales) 1s the wrong measure If both
the level of loans and the level of sales are functionally related to the true scale vanable, say, the aggre
gate vanance of daily cash flows, the sum of the
coefficients on loans and sales may represent a mixture
of the underlymg Miller and Orr transaction elast1c1ty
and the coefficients relatmg loans and sales to the
true scale vanable
10

11

Demand Deposit Ownership' Survey

97

TABLE 3 Balances of Households, Equation with R90
In HOUSR, = - 021 A In GOVRf + 602 In Pl Rf - 152 In RPQf - 110 In R90f
(-1 75)
(4 62)
(-0 91)
(-4 30)
Per10d of fit July 1971-June 1974
R2 = 9671,SE = 0060,DW =217,DF = 16
Item

A In GOVR,

lnPIR,

I

I

+

12

~

/3,S,,

·-•

lnRPQ,

+

589 U,_,
(4 38)

I

In R901

Polynom1al d1str1buted lag weights
Lag
t

-

I
t - 2
I - 3
1-4
t - 5
t-

010
012

239
168
109
061
025

550

I 117
4

-

033
037
036
029
017

I - 6
t - 1
t - 8

DMtnbuted lag character,stlcs
Mean lag
Length of lag

I

two equations, it was not s1gmficant and often
entered the equation with the wrong sign 11
The deflator used 1s the wholesale pnce mdex
net of farm products A certificate of deposit
rate was mcluded along with the commercial
pape1 rate, but these rates did not enter simultaneously and RCP performed better
Our results for nonfinanoal busmesses are
m sharp contrJ.st to those of Goldfeld 14 His
transact10ns variable did not enter s1gmficantly,
his long-run mterest rate elasticity was only
-0 018, and his speed of adjustment only 0 I
per quarter, wlule our longest lag 1s only 6

I 741
4

p 274
14 Goldfeld, m "Demand for Money," p 629, con
\1dered the results for this sector to be unsatisfactory

TABLE 4 Balances of Nonfinanc1al Busmesses
12

=

583 In CILR, + 731 In BSRf - 241 In RCPf + ~ (3,S,, + 915 U1-1
(2 98)
(2 17)
(-6 98)
·-•
(14 74)
Period of fit January 1971-June 1974
R2 = 9796, S E = 0086, D W = I 94, D F = 26
Item

In BSR,

I

lnRCP,

Polynomial d1str1buted l~g weights
Lag
I

1-1
I- 2
I - 3
I- 4
I - 5
I - 6

Dlslr,buled lag charac1er1s11cs
Mean lag
Length of lag


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Federal Reserve Bank of St. Louis

074
110
131
136
125
099
057
2 895
6

004
010
014
016
017
017
015
Oil
006

4 171
8

months Given these 1esults, the DDOS data
appear to yield more reasonable results than
the flow of funds data
Demand of financial busmesses. Fmanc1al
busmesses represent a hodgepodge of deposits
held by (I) trust departments of other banks,
(2) sales, commercial, and pe1sonal finance compames, (3) security brokers, dealers, and exchanges, (4) commodity contracts brokers,
dealers, and exchanges, (5) other nonbank
finanoal 111st1tut10ns (mcludmg holdmg and
other mvestment compames, clearing house associations, 1nsm ance earners, mortgage compames, savmgs and loan assocrnt10ns, agricultural credit assoc1at10ns, and so forth), and
(6) mutual savmgs banks Goldfeld treated
this sector as 1f it represented exclusively
money holdmgs by savmgs and loan assoc1a-

11 Unconstramed estimation l\1th aggregate data has
failed to produce a s1gmficant positive loan vauable,
~cc, for mstance, Enzler and others, "Some P10blems,"

In NFBR,

-

-

064
056
046
036
025
013

I 756
5

Improvmg the Monetary Aggregates Staff Papers

98

t10ns and mutual savmgs banks 15 Though
money holdmgs of these thrift mstitutions are
sizable, they represent slightly less than a
quarter of money held by financial businesses 16 Thus, it is not too surprismg that the
scale variable of total deposits at savmgs and
loans and mutual savmgs banks did not perform satisfactorily the sum of deposits at
these mstitutions had a negative coefficient
When these variables were entered separately,
deposits at savmgs and loans had a negative
sign, while deposits at mutual savmgs banks
had the antiCipated sign and were sigmficant
It appears that the motives of other financial busmess deposit holders are not well
represented by these transactions proxies Instead of trymg to develop separate proxies for
each holder, one composite variable was constructed-a proxy for financial debits, defined
as total demand deposit debits at New York
City and six other large financial centers 17 This
transaction measure enters sigmficantly m
the estimated equation for balances of financial busmesses
In FINi = 086 In DEBFi + 075 A In RCPi
(5 86)
(3 12)

+

142 Aln NYSEi
(2 64)

+

12

~ (3,S, 1
i=l

+

436
(3 14)

Ui-1

Period of fit January 1971-June 1974

R. 2

= 8731,SE = 0109,DW =150,DF =27

The equation also contams the change m
the commercial paper rate-a speculative
money demand variable mdicatmg extrapolative expectat10ns-and the change m the New
York Stock Exchange mdex (NYSE) NYSE
may be viewed as a close proxy for changes m
wealth Alternatively, because changes m stock
market mdexes and stock market volume are
posltlvely correlated, the stock market variable
15 Recall that Goldfeld, m "Demand for Money,"
used flow of funds data for M1
16 See Flow of Funds, Assets and L1ab1lities Out
standing, 1974 (Board of Governors of the Federal Reserve System, 1975), pp I, 2
11 The six other centers are Boston, Ph1iadelphia,
Chicago, Detroit, San Franc1sco-Oakland, and Los
Angeles-Long Beach


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Federal Reserve Bank of St. Louis

may be viewed as an additional transactions
proxy Other than the speculative mterest rate
variable, no mterest rate was sigmficant 18
Furthermore, as expected, all explanatory vanables entered without lags, reflectmg the very
high speed of adjustment m this sector
A pnon, one might expect that demand by
financial busmesses for money balances would
be m real terms, as are the demands of households and nonfinancial busmesses Efforts to
estimate a real demand equat10n for financial
busmesses were not too successful The best
equation was
In FINR 1 = 063 In DEBFR 1 + 065 A In RCPi
(1 58)
(1 96)

+

171 A In NYSERi

~1~

+

12

~ (3,S, 1

-

1

+ 84 Ui-1
000~

Period of fit Januaiy 1971-June 1974

R.

2

= 8573, SE = 0189, D W = 90, D F = 33

where R appended to the mnemomc mdicates
that real values were used In terms of R 2 and
standard error, this equat10n is similar to the
one 1n nommal terms However, when the
equation 1s simulated over the last half of
1974 and all of 1975, 1t exh1b1ts severe detenorat1on In dynamic simulation, the root mean
square error 1s nearly 12½ times the standard
error On the other hand, when the equation
for financial busmesses in nommal terms 1s
simulated, the root mean square error m dynamic s1mulat10n over the same penod 1s only
a little more than twice the standard error
(See the next subsection for further details )
Implicit m estimatmg a money demand
equat10n m real terms 1s the assumpt10n that
the coefficient on pnces 1s I We tested this
homogeneity restnct10n m the case of the
equation for financial busmesses by regressmg
nommal deposits on pnces, on the other real
variables, and on mterest rate terms (all m
natural logarithms) In fact, the estimated coefficient on prices 1s s1gmficantly different from
1 ~ This mcludes Goldfeld 's proxy vanable for the
outflow of deposits at thrift mst1tut10ns (the Treasury
bill rate divided by the savmg deposit rate) See Goldfeld, "Demand for Money "

99

Demand Deposit Ownership Survey

TABLE 5 Total Balances of Households and Nonfinancml Busmesses
In TOTR,

=

516 In CILR, - 012
(3 15)
(-2 38)

ll.

In GOVR,

R2 =
Item

+

369 In P/Rf - 179 In RCPf - 303 In RPQf
(-7 39)
(-2 68)
Period of fit January 1971-June 1974
9838, SE = 0062 D W = 1 49, D F = 22
(I 62)

In PIR,

I

12

+

~

{J,S,,

,-1

lnRCP,

+ 880
(12 01)

u,_,

In RPQ,

I

Polynomral d1stnbuted lag weights
Lag
I
,_
1

t - 2
I - 3
t-4
I -

159
210

- 042
- 040
- 035
- 029
- 022
- 012

569

1 918
5

5

Distributed lag characteristics
Mean lag
Length of Jag

I

I, suggestmg that a real demand equation may
not be <tppropnate for financial busmesses 19
Nevertheless, much more work on the specification of this sector is undoubtedly necessary
before one can accept the test result at face
value and drop the reqmrement of homogeneity with respect to pnces
A comparison with an "aggregate" equation
for households and nonfinancial busmesses
To illustrate what 1s lost or ludden by aggregat10n, ,i simple ,iggregate equation for the
total of deposits of households and nonfinanci,il businesses, TOTR, was also considered A limitation m the distributed lag
estimation program prevented mclusion of all
of the v,iriables appearmg m the sectoral
equat10ns, therefore, the Treasury bill rate
was dropped smce 1t 1s, m general, highly
correlated with the commercial paper rate
However, even without this rate, the aggregate
equation was not sensible In particular, sigmcant coefficient estimates for both transactions variables, real personal mcome and
real busmess sales, could not be obtamed Smee
mcome worked better m terms of the R. 2 and
standard error of the equation, It was used
alone with the results reported m Table 5
Except for mcome, all the variables are sigmficant at least at the 98 per cent sigmficance
level The equation displays the curiosity,
noted earlier, that the long-run savmgs deposit elasticity 1s more than l ½ times the comGoldfeld, m "Demand for Money," also estimated
his financial busmess equation m nominal terms
19


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Federal Reserve Bank of St. Louis

- 213
- 081
- 010

2

329

merc1al paper rate elasuc1ty This result contradicts our disaggregated estimates
Table 6 compares the direct ,iggieg,ite estimates with two sets of aggregate estimates
made by usmg the disaggregated coefficients
and weightmg them by the average share of
deposits held by consumers (0 308) and nonfinancial busmesses (0 692) The first estimate
1s based on the assumption that the Treasury
bill rate elasticity is the same as the commercial paper rate elast1c1ty for households, while
the second estimate uses an alternative equation for households, which contams the commercul paper rate explicitly (see Table 7)
The two sets of derived estimates are very
similar but differ s1gmficantly from the direct
aggregate estimates Thus, the disaggregated
equations do not support the aggregate findmg Because consumers hold an average of
only 30 8 per cent of the total deposits held
by nonfinannal busmesses and households, a
<.hsaggiegated elast1C1ty for household demand
with respect to the savmgs deposit rate of
-0 984 would be reqmred to yield this aggregate elasticity This implausibly large value
(m absolute terms) is nearly 6½ times the
disaggregated elasticity e~t1mated directly,
TABLE 6 Alternative Elasticity Estimates
Type of estimate
Direct aggregate estimate
Denved aggregate estimates
D1saggrega ted model I
Disaggregated model 2

Savings
depos1 t rate

Commercial
paper rate

-

303

-

179

-

047
053

-

201
200

100

Improvmg the Monetary Aggregates Staff Papers

TABLE 7 Balances of Households, Equation with RCP
In HOUSR, = - 019 A In GOVRf + 680 In PIRf - 112 In RPQf - 107 In RCPf
(-1 76)
(4 80)
(-0 99)
(-4 35)
Period of fit July 1971-June 1974
R• = 9693, SE = 0058, D W = 2 34, D F = 16
Item

In GOVR,

I

In PIR,

I

12

+ l:

{J,S,.

,-1

In RPQ,

+

634
(4 92)

I

u,_,

lnRCP,

Polynom1al d1stnbuted lag weights

Lag
I

t-1
1-2
I- 3
I - 4
I -

I I I -

- 008
- 011

5
6
7
8

Distributed lag characteristics
Mean lag
Length of lag

I

561

-0 152 It appears, then, that the disaggregated
equations provide more reasonable estimates
of the aggregate elasticities This result exemplifies the sigmficant payoff to disaggregatmg
the money demand function or, at least, mcorporatmg mformation derived from the disaggregated esumates mto aggregate estimates 20
Simulations It 1s mstructive to examme the
post-sample predictions from each of the
equations These simulat10ns are reported m
Table 8, for the period from July 1974 through
December 1975, for consumers (HOUSR),
nonfinancial busmesses with the loan variable
(NFBR) and without the loan variable (NFBR
-no CILR), 21 financial busmess (FIN), and
the sum of HOUSR and NFBR (TOTR) with
and without loans and government deposits 22
It was pomted out earlier that ma true aggregate equation the impact of loans or govern20 The aggregate equation presented here probably
understates the gams from disaggregation because only
household and nonfinancial busmess deposits are aggregated When a s1m1lar equation is estimated with the
demand deposit component of the money supply as
the dependent vanable, the results pomt up even more
strongly the mformat10n lost m aggregation In the
demand deposit equat10n, neither loans nor government
deposits enter s1gmficantly Thus, the disaggregated
equations yield mformat1on about the impact of these
vanables that we would not have otherwise An even
more stnkmg result 1s that the estimated savmgs rate
elast1c1ty m this aggregate equation 1s eight times the
estimated commernal paper rate elastmty
21 See Table 9 for the specification of this equation
22 See Table 10 for the spenficauon of this last
equation


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Federal Reserve Bank of St. Louis

123
161
166
142
086

- 048
- 044
- 037
- 028
- 015

I 862

I 534
4

4

-

014
015
015
015
014
012
010
007
004
3 311
8

ment deposits could not be identified Smee
TOTR mcludes the deposits of only the ownership classes that these variables affect, the
equation ism some sense biased toward bemg
able to identify these impacts Thus, the
TOTR equation mcludmg these variables provides more mformation than an equation for
a broader aggregate probably would Therefore, a more accurate illustration of what can
be lost m aggregation may be provided by
simulatmg an aggregate equation without
these variables Fmally, an alternative estimate
of TOTR, denoted SUM, was also constructed
by addmg predictions of the separate equations for consumers and nonfinancial businesses
Overall, most of the equations tended to
overpredict money demand startmg m the
second half of 1974 This period comcides
with a similar breakdown m the aggregate
equation for demand deposits of both of the
Board's econometric models-the monthly
money market model and the quarterly Massachusetts Institute of Technology-Umversity of
Pennsylvama-Social Science Research Council (MPS) model Only the financial busmess
equation does not eventually overpredict by
a sizable percentage Though the percentage
errors and the root mean square errors are
large for consumers and nonfinancial businesses, the disaggregated equations, when
summed (SUM), do better m simulation than
either equation for the aggregate (TOTR)

Demand Deposit Ownership Survey

101

TABLE 8 Post-Sample Sunulahons, July 1974--December 197S
Not seasonally adiusted

Standard error
ofesttmated
equation
(per cent)

Root mean square error

Correlatton
squared of actual
and predicted

Bdhons of dollars

HOUSR
NFBR
NFBR (no CILR)
FIN
TOTR
TOTR (no CILR, GOVR)
SUM

0072
4977
2994
4698
0035
0004
1863

1 452
3 452
4 447
346
6 797
8 228
4 870

HOUSR
NFBR
NFBR (no CILR)
FIN
TOTR
TOTR (no CILR, GOVR)
SUM

5302
8304
6893
5056
8088
7619
8155

672
802
125
341
409
855
315

Equation

I

Per cent

Mean absolute
error

(b1lhons of
dollars)

Mean error

(b1lhons of
dollars)

Dynamic s1mulat1on
7
8
10
2
11
13
8

65
17
97
35
35
53
24

60
86
98
I 09
62
76
na

I 304
3 257
4 123
289
6 390
7 659
4 561

-I
-3
-4
-6
-7
-4

304
257
123
043
390
659
561

598
655
928
277
1 203
1 717
1 159

-1
-1
-1

598
544
840
018
203
717
143

Nondynam1c s1mulauon

I
1
l

1

3
2
2
2
2
3
2

63
06
88
33
44
22
29

60
86
98
1 09
62
76
na

n a Not available

rhe aggregate equation mcludmg the loan
,md government deposit variables has approximately a 40 per cent higher root mean square
error and mean absolute error m dynamic
s1mulat1on than does the total based on the d1s,1ggregated equat10ns (SUM) When loans and
government deposits are excluded from the
equation, these errors are almost 70 per cent
higher than the errors for SUM S1m1larly,
error statistics mcrease when compensatmg
balances are excluded from the equation for
nonfinancial busmesses (NFBR-no CILR) as
wmpared with the equation mcludmg these
balances (NFBR) Smee It 1s difficult to measure the effects of compensatmg-balance reqmrements at the aggregate level, the ab1hty

to do so by usmg d1sagg1egated data
,1gmficant

Conclusions regarding money demand
functions
The DDOS d<1ta <1ppear to yield reasonable
d1saggreg<1ted equations for the demand for
money The results of the estimated demand
equat10ns suggest that different factors mfluence the demands of different sectors Although many mterest rates-and transactions
vanables-are collmear and could probably
be substituted for one another m regression
analysis, theoretically the rates and transactions vanables mcluded m the demand equa-

TABLE 9 Balances of Nonfinanc1al Busmesses, Equation Excludmg CILR
12

871 In BSRf - 204 In RCPf + ~ {J,S,, + 873
(2 90)
(-6 35)
•·1
(11 58)
Period of fit January 1971-June 1974
R•= 9732,SE = 0098,DW = 223 DF = 26

In NFBR,

=

Item

lnBSR,

I

u,_,

lnRCP,

Distributed lag weights
l.Ag
I

1- 1
1-2
t-3
I - 4
I - 5
I - 6
Distributed lag characteristics
Mean lag
Length of lag


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Federal Reserve Bank of St. Louis

185
173
155
134
107
076
040
2 225
6

1s

-

050
046
040
032
023
013

1 860
5

Improving the Monetary Aggregates Staff Papers

102

tions for each sector are the most appropriate
for that sector Further, such variables as the
change m government deposits (m the household equation) and the level of commercial
and mdustrial loans (m the equat10n for nonfinancial busmesses), when tested m other demand equations, proved to be ms1gmficant and
often of the wrong sign
----The large variety of determmants of money
demand disclosed by the sectoral demand equat10ns provides a great deal of mformat1on
about what may be happemng to the aggregate demand for deposits Much of this mformation could be lost when analysis 1s confined to an aggregate demand function First,
to the extent that common variables affect
different sectoral demands, an aggregate equation will estimate only an average impact, 1f
the sectoral impacts differ and the sectoral
shares change, mformation will be lost even
if the sectoral demand functions are lmear
Second, as seen from our "aggregate" equation,
which attempted to combme only two sectors,
all relevant variables cannot be mcluded m
the aggregated equauon Mult1colhneanty,
among other problems, produces msigmficant
coefficients and often wrong signs-the equat10n presented was the best m terms of tstatistics, expected signs, and standard error
If all mterest rates and all transactions vanables were perfectly correlated, the loss of
variables m the aggregate equat10n would be
ummportant, no mformation would have been
lost However, such perfect correlation 1s not
the case, and divergent movements could give"
us considerable mformation, assummg we were

dealmg with sectoral demand equations rather
than an aggregate one
The DDOS also permitted us to check
whether the elasticity of the aggregate demand
for demand deposits with respect to the rate
paid on short-term mterest-bearmg accounts
at commercial banks23 was too large The estimated aggregate elasticity does appear to be
larger than the disaggregated data would warrant This result casts some doubt on the large,
expans10nary GNP multiplier ,associated with
changes m Regulat10n Q ceilmgs that has been
adduced by some economists, who rely on more
traditional estimates of aggregate demand deposit elast1c1t1es 24
Our simulation results confirm the loss of
mformation m aggregation Summary statistics
are presented for TOTR (the aggregate equation for the sum of deposits of households
and nonfinancial busmesses) and for SUM, the
sum of the simulation solutions for the sectoral demand equations for households and
nonfinancial busmesses In dynamic s1mulat10n, all err01 statistics are higher when the
aggregate equat10n is simulated than when
the two sectoral equations are simulated and
the errors summed, the mcrease m the root
mean square error is better than 15 per cent
Furthermore, when loans and government deposits are excluded from the TOTR equation,
2a Spec1fically, the passbook rate ce1lmg, or an average of the passbook rate and the rate paid on conmmer type certificates of deposit, weighted by quan
t1ty
24 See Myron B Slovm and Mane E Sushka, Inter
est Rates on Savings Deposits (Lexmgton Books, 1975),
e~pecially chap 10

TABLE 10 Total Balances of Households and Nonfinanc1al Busmesses, Equation Excludmg CILR and GOVR
In TOTR,

Item

12

=

615 In P/Rf - 138 In RCPf - 324 In RPQf + I; {3,S,, + 837
(2 96)
(-5 47)
(-2 37)
••I
(9 90)
Period of fit January 1971-Junc 1974
R•= 9752, SE= 0076, DW = 185, DF = 24

lnPIR,

I

U1-1

In RCP,

I

lnRPQ,

D1strtbuted lag weights
Lag

t
t - I
t - 2
t - 3
t - 4
t - 5

439
177

024
028
028
026
020
012

- 080
- 135
- 108

2 197
5

I 087
2

-

Distributed lag characterrstrcs

Mean lag
Length of lag


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Federal Reserve Bank of St. Louis

I

287

103

Demand Deposit Ownership Survey

as would be likely m a more aggregated
equation, the mcrease m the root mean
square error 1s 40 per cent While even sectoral demand equations did poorly m terms
of the standard errors of the estimated equations, they still suggest that better results
would have been obtamed by usmg all the
mformatlon available from sectoral equations
than by usmg the more hm1ted mformauon
mcluded m an aggregate demand equation
Fmally, recent pred1ct10ns of the aggregate
demand for demand deposits relative to GNP
and short-term mterest rates have been cons1clerably off the mark, actual deposit growth
(at least through the first quarter of 1976) m
the current recovery has been unusually slow
compared with the predictions of many standard money demand equat10ns Apart from financial busmesses, the disaggregated equations
have also tended to overpred1ct deposit growth
The detenorat10n appears to be worse for nonfinancial busmesses (see Table 8) Smee dis-

aggregated ownership data help to identify the
sectors performmg least well, they may also be
useful m 1solatmg the factors causmg the detenorat10n-factors that 1t may not be possible to
isolate at the aggregate level

Preliminary results for an aggregate
demand equation using constraints
derived from the DDOS equations
After most of the work reported so far m
this paper was completed, a program became
<1.vailable that enabled us to estimate a dem<1.nd equat10n for the demand deposit component of M 1 <1.nd to make use of the mformauon gamed from our disaggregated
equat10ns to constram sums of current and
lagged coeffioents Table 11 prc5ents the
1 esults
We estimated chstubuted lags usmg the
Sluller techmque w1th soft (mexact) constramts
apphed JUSt to the sums of d1stnbuted lag

TABLE 11 Demand Deposit Component of Mi. Constramed Estimation 1
In DDR = 223 In P/Rf + 269 In BSRl - 012 a In GOVRf - 128 In
015 In DEBFR, + 014
(2 32)
(I 31)

+

R• =
Item

lnPIR,

I

In BSR,

RCPl -

055 In RPQl

a In NYSER, + 008 a In RCP, + 0 0 In WPINl + 998

(I 32)
Period of fit January 1968-June 1974
9676 S E = 0067, D W = 5225, D F
I

a In GOVR,

I

+ 310 In CILR,
(24 04)
U1-1

= 73

In RCP,

I

In RPQ,

I

In WPIN1

Shiller distributed lag weights
lag

I
r- I
I - 2
I - 3
I- 4

093
(4 43)
070
(7 61)
047
(5 06)
024
(2 09)
001
( 05)

t-5

I - 6

073
(6 26)
062
(10 05)
051
(12 60)
040
(7 79)
028
(4 76)
014
(2 85)
001
( 17)

- 004
(-1 16)
- 005
(-1 38)

((-

002
58)
000
05)

I - 7
I - 8

(-3
(-4
(-4
(-4
(-4
(-4
(-3
(-2
(-1

021
27)
018
68)
016
47)
015
13)
015
31)
015
37)
103
85)
010
99)
004
12)

-(I

(-1
(-1
((-

019
01)
015
70)
Oil
23)
007
71)
003
27)

Sum constramts2
1
2

-

Ill
034
142
212

238
191
105
- 021
- 186
- 177

I 012
4
22

I 291
6
26

3
-

846
01

3 230
8
- 15

DDR 1s demand deposits deflated by WPJN superscnpt S denotes a Shiller d1stnbuted lag
ln CILR = 030, In DEBFR = 001, .J. In NYSER = 002, a In RCP= 001


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Federal Reserve Bank of St. Louis

670

244

I - 9
I - 10
t - 11
Distributed lag
characterrst1cs
Mean lag
Length of lag

-

I 293
4
- 06

0 0

Improvmg the Monetary Aggregates Staff Papers

104

coefficients, 25 mdividual lag coefficients were
free to assume any value withm the constramts
on the degree of the estimated polynomial
The values of the sum constramts were derived by multiplymg sums estimated with the
disaggregated DDOS data by the average share
of the relevant component of total gross IPC
deposits, and addmg We did not estimate demand equations for the "foreign" and "other"
components m the DDOS, and variables affectmg the components for which we did estimate
equations could affect these other components
While the "foreign" and "other" shares of the
total DDOS deposits are small, which would
lead to a mimmal impact on coefficient sums,
tightness priors on sums were such that the
sums could deviate somewhat from those implied by the estimated component equations
Thus, the estimates may allow for the effects
of the other sectors as well as for the fact that
2s See Robert J Shiller, "A D1stnbuted Lag Estimator Derived from Smoothness Priors," Econometrica,
vol 41 (July 1973), pp 775-88

the demand deposits used here are "net" and
DDOS deposits are "gross" (see Appendix 1 for
the differences between the two concepts)
Program size constramts were such that we
could not mclude all relevant variables and
seasonal dummy variables as well, therefore,
the equat10n w<1s estimated m seasonally adJusted terms We also deviated somewhat from
the disaggregated DDOS equations by puttmg
financial busmess demands m real terms usmg
WPIN as the cleflator Fmally, an 11-period
distributed lag m WPIN with weights summmg to zeio was mcluded Without this distributed lag m prices, money holders are assumed to aclJust immediately to the current
price level Includmg the distributed lag m
prices permits lagged adJustment to price
changes, with the sum of the lag coefficients
constramecl to zero, however, long-run homogeneity with respect to prices 1s preserved
The distributed lag on prices affected the
estimated coefficients on the other mdependent
variables very httle, but 1t did result m a

TABLE 12 Demand Deposit Component of Mi, Unconstramed Estimation 1
In DDR

=

851 In PIRf -

093 In BSRf -

019 <I. In GOVRf -

057 In RCPf -

134 In RPQf

+

010 In DEBFR, + 006 <I. In N YSER, + 005 <I. In RCP, + 0 0 In WPINf
(070)
(0 52)
(0 49)
Penod of fit January 1968-June 1974
R• = 9876, SE = 0041, D W = 1 3031, D F = 64

Item

lnPIR,

I

lnBSR,

I

A

In GOVR,

I

lnRCP,

I

+

+

072 In CILR,
(0 66)
998 Ut-1

lnRPQ,

I

In WPIN,

Shiller distnbuted lag weights

Lag
I- 1
1-2
I - 3
I- 4

338
(5 51)
254
(5 57)
170
(5 50)
086
(5 09)
001
( 16)

I- 5

t-6

((((((-

28
54)
023
53)
018
51)
013
48)
008
44)
004
38)
000
( 12)

(-1
(-1
(-1
(-

005
42)
007
93)
004
24)
003
86)

t- 7
t - 8

- 004
(-' 77)
- 004
(-1 30)
- 005
(-1 69)
- 006
(-2 17)
- 008
(-3 01)
- 010
(-3 68)
- 009
(-3 62)
- 007
(-3 00)
- 003
(-1 14)

(-1
(-1
(-1
(-1
(-

046
68)
038
84)
029
85)
018
65)
004
56)

119

-

042
023
075

143
157
158
145
120
159

1 009
4

I 559

6

1 270
3

4 261
8

• DDR 1s demand deposits deflated by WPIN, superscnpt S denotes a Shiller d1stnbuted lag


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Federal Reserve Bank of St. Louis

-

115

I- 9
I - 10
I - 11

Distributed lag
characteristics
Mean lag
Length oflag

- 934

1 236
4

Demand Deposit Ownership Survey

105

somewhat more satisfactory lag pattern m the
estimated coefficients on the commercial paper
rate
Table 12 presents the results of est1matmg
the same equation without constramts except
that on the distributed lag m prices Only the
estimated elast1c1ty with respect to the change
m government deposits, debits, and the change
m the paper rate approximate those 1mphed
by the disaggregated equations Among other
thmgs, the estimated elast1c1ty with respect to
the commercial paper rate 1s less than half
what 1s 1mphed by the disaggregated equations, and we ag,un observe the phenomenon
of the estimated savmgs rate elasticity bemg
almost 2½ times the estimated paper rate
elasticity Further, without constramts, the
busmess sales variable has the wrong sign and
1s not s1gmficant Fmally, It 1s no longer possible to 1dent1fy the mfluence of such variables
as loans and debits smce their estimated coefficients are not significantly different from
zero
Table 13 p1csents the results of s1mulatmg
the constramed and unconstramed equations
Although the standard error of estimate of the
unconstramed equation 1s almost 40 per cent
less than the constramed equation, the results
of the dynamic simulations pomt up dramatically the gams from makmg use of the disaggregated elast1c1ty estimates to place con~tramts on the estimated aggregate elast1c1t1es
For example, the root mean square error of
the unconstramed equation 1s almost 2½
times as large as that of the constrained equation Further, m percentage terms, the constramed equation does better than our simple

aggregate equation (TOTR) m which we attempted to estimate determmants for only
two classes of money holders The potential
for makmg use of mformat10n derived from
disaggregated equat10ns 1s obviously sizable

Other current uses of the DDOS

Current analysis
The DDOS data are used m current analysis
to evaluate unusual movements m the aggregate demand deposit component of M 1 If, for
example, a strong surge m M 1 growth m a
a particular month or quarter 1s accompamed
by an unusual change m the deposit shares,
the source of the mcreased demand for balances can be more accurately pmpomted
The DDOS data have been particularly
helpful m evaluatmg the impact of tax rebates
and tax refunds on short-term movements m
demand deposits The results from this analysis
md1cate that, under current operatmg procedures of the Desk, about a quarter of rebates
distributed umformly over a given month
will be held m demand deposits m that month
,md about half of that (or about one-eighth of
the origmal dollar flow) will be present m the
followmg month Direct estimates of such impacts usmg only aggregate deposit data tend to
produce much more 1mplaus1ble short-term
impacts of rebates on aggregate demand deposits
As a source of data, the DDOS survey 1s
bemg used regularly by the Flow of Funds
Section of the Board's Division of Research
and Statistics to separate demand deposits
from cash holdmgs and to estimate deposit

TABLE 13 Summary Statistics of Post-Sample S1mulatlons,
July 1974-December 1975

Equation

Correlation
squared of
actual and
predicted

Root mean square errors
Billions of
dollars

I Per cent

Standard
error of
estimated
equation
(per cent)

Mean
absolute

Mean
error

error

(billions
of dollars)

(billions
of dollars)

6 056
14 94

-6 056
-14 94

1 332
1 451

- 370
-I 397

Dynamic s1mulauon
Constramed
Unconstramed

1540
0917

6 860
17 09

Constramed
Unconstramed

6503
9052

1 644
1 619

5 29
12 64

67
41

Nondynam1c s1mulat1on


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Federal Reserve Bank of St. Louis

1 30
1 28

67
41

Improvmg the Monetary Aggregates Staff Papers

106

holdmgs by sector, and also by the Department of Commerce for use m the national mcome and product accounts to estimate services
rendered without fee by financial mtermedianes other than hfe msurance earners Several
large commercial banks m New York City are
known to use DDOS data m analysis of money
stock movements, and it 1s believed that these
and other banks make use of the data m their
marketmg research

Monthly model
The elasticity estimates derived from the
DDOS demand equations have been used m
constrammg estimated coefficients m a simplified aggregate demand deposit equat10n (versus
the equation presented m the last part of the
previous section) In parucular, we constramed
the commercial paper rate elasucity to be m the
neighborhood of the disaggregated elasuciues
(weighted by deposit shares) In an unconstramed estimation, the elasticity of the rate
on other time and savmgs deposits ends up
bemg over five times that of the commercial
paper rate When the paper rate elasticity is
constramed, the rat10 is less than two to one
While our experience is limited, the constramed equat10n appears to produce more
reasonable responses of money growth to
changes m the paper rate It has also been
very helpful m evaluatmg the impacts of alternative monetary policies

Studies of velocity by ownership class
The DDOS-will also help m velocity studies
and, thus, m the pred1ct10n of mcome Table
14 presents the end-of-quarter-transaction velocities (computed with the quarterly DDOS
data) consistent with the different sectoral
money demand funcuons presented m the second section, VFIN is financial debits divided
by deposits of financial busmesses, VNF is business sales divided by deposits of nonfinancial
busmesses, and VCON is personal mcome (not
at an annual rate) divided by deposits of households Chart 1 plots these numbers
It can be seen that the sectoral velocities
move qmte differently from one another For
example, from the cyclical trough m the fourth
quarter of 1970 to the peak m the fourth quarter of 1973, the velocity associated with financial busmesses mcreased about 43 per cent, or
about 3½ per cent per quarter, while those
associated with nonfinancial busmesses and
households rose IO per cent and 3 per cent,
respectively, for average quarterly mcreases
of about O8 per cent and O 3 per cent For the
pe110d from the cyclical peak m the fourth
quarter of 1973 to the trough m the second
quarter of 1975, the average quarterly mcreases
m velocity were 2 7 per cent, 2 per cent, and
0 9 per cent, respectively Such d1ffermg behav10r 1s not likely to be captured m an aggregate relationship, thus, the use of disaggregated mformat1on may eventually lead to
better predictions of aggregate mcome

TABLE 14 Quarterly Transactions Veloc1ties
Quarter

VFIN

I

VNF

I

VCON

1970-Q4

40 931

1 1977

1 2761

1971-Ql
Q2
Q3
Q4

39
38
38
43

060
425
520
314

I
1
1
1

2953
3268
2678
2346

I
1
I
I

2878
2887
2588
2675

1972-Ql
Q2
Q3
Q4

38
44
41
47

446
117
272
190

1
1
1
1

3309
3223
2790
2378

1
1
1
1

4017
2713
2599
2640

1973-Ql
Q2

50 344
52 435

1 3942
1 3997

I 3088
I 2977

Quarter

VFIN

VNF

I

I

VCON

1973-Q3
Q4

49 314
58 429

1 3421
1 3197

1 3019
I 3161

1974-Ql
Q2
Q3
Q4

60
62
66
72

085
275
894
721

1
1
1
I

4917
5091
5000
3886

1
1
I
1

3240
3357
3675
3647

1975-Ql
Q2
Q3
Q4

68
67
67
75

763
964
653
239

1
I
1
1

4479
4858
4844
4485

I
1
1
1

3718
3873
3929
3891

1976-Ql

91 413

1 6206

1 4421

NorE -Veloc11les are not at an annual rate None of the data are seasonally adjusted except for personal mcome, which 1s available only m
seasonally adjusted form Sufficient quarterly DDOS data do not yet exist to seasonally adjust these senes


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Federal Reserve Bank of St. Louis

Demand Deposit Ownership Survey

107

CHART I Veloc1t1es

90

60

30

-

VNF

I 50

-

VCON
I 20

90
1971

1973

Owneiship data have also been used by
J &mes Pugash m esumatmg sectoral turnover
26
1 cttes
Pugash reported the followmg results
I Estimated demand deposit turnover rates
differed s1gmficantly across ownership categones
2 Estimated turnover rates by ownership
categones also differed across three bank sizes
3 The estimated sectoral turnover rates,
comparing the two cross-sectional estimates
made for June 1970 and June 1972, were sigmficantly different m most cases, suggesting
that, especially for consumers, the use of demand deposits changes over time
Most of Pugash's results are qmte plausible
26 S~e James Z Pugash, ' The Demand for Money m
Six Sectors," Unpublished m.inuscnpt (Board of Gov
ernors of the Federal Reserve System, January 1974)


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Federal Reserve Bank of St. Louis

1975

It is important, however, to try to go further
and explam the movements of turnover rates
ovei time as mclexecl by ownership category
and bank size Advances m cash management
techmques that lower the average level of
money balances 1elat1ve to some transact10ns
measure are difficult to measure at the aggregate level These disaggregated turnover measures should provide mdependent evidence of
such shifts For example, consider those banks
that offe1 large corporate custome1 s a bankmanaged account from which the banks automaucally mvest man ove1mght money market
mstrument all funds m excess of an agree<lupon balance If managed accounts become
s1gmficant, there should be a once-and-for-all
spurt m estimated corporate turnover at these
banks

108

Improvmg the Monetary Aggregates Staff Papers

Potential studies

Bank portfolio models

Innovations in the payments mechanism

The DDOS data may also be used to study
bank portfolio behavior It has been shown
that asset preferences of banks are related to
the compos1t10n of their liabilities This result
1eflects the different probabilities of withdrawal associated with each type of deposit
The probability of withdrawal will likely differ
not only between time and demand deposits
but also among different classes of demand deposit holders The differences m turnover rates
across sectors, noted earlier, are undoubtedly
related to these probabilities Thus, the disaggregated data from the DDOS can aid m
analysis of bank portfolio decmons

A variety of financial and techmcal mnovauons have mcreased the turnover rate of
demand deposits m the Umted States bankmanaged demand accounts, payable through
drafts, money market mutual funds with check
features, Imes of credit, telephomc transfers
between savmgs and demand accounts, and
other cash management techmques The
DDOS data may help to predict the aggregate impact of such mnovat10ns m the payments mechamsm If the mnovat10ns result
m shifts m deposit shares, we may, without
bemg able to predict the shifts, recogmze
earlier what 1s occurring
Several mnovat10ns that appear to have
qmte specific sectoral impacts are developing
The followmg illustrate these developments
l The spread of automatic clea1 mghouses
(ACH) The mcrease m ACH's will tend to
reduce bank float Smee ACH's facilitate almost
mstantaneous transfers of funds, corporations
may well reduce their balances to some mm1mum except for times when payments are to be
made Smee the funds for payments would be
deposited and almost immediately withdrawn,
lower average balances would be observed
2 Use of ACH's to facilitate the direct deposit of payrolls through preauthonzed payments, agam reducmg float
3 Pomt-of-sale termmals If these permit
retail customers to make direct transfers from
mterest-bearmg accounts, they may dramatically reduce the levels of demand deposits that
consumers will wish to hold for transaction
purposes
4 Contmuous real-time momtormg of mdividual bank accounts (mcludmg credits and
debits) Time-sharmg computer systems that
permit direct, contmuous readout of individual account mformat10n are likely to be
offered to and to be used by corporations Such
systems clearly offer timely mformat1on about
current cash flows, thus reducmg uncertainty
and therefore probably lowermg average cash
balances


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Expanding the linkages between real
and financial markets
Recent study has provided some empirical
evidence that the state of balance sheets 1s
important m determmmg expenditures 21 The
usefulness of this idea has been limited by
an mab1lity to explam the state of the balance
sheets However, 1t appears that we will now
be able to model the flow of funds accounts
because of a nearly completed project funded
by the N atlonal Science Foundation 28 The
project has already developed spec1ficat1ons
and estimates to explam the portfolio holdmgs of almost all of the maJor sectors m the
accounts The plan 1s to mcorporate this flow
of funds model mto the Board's quarterly
MPS model Several new lmkages between
financial markets and real activity (such as
21 See, for example, James R Kearl and Frederic S
M1shkm, "Ilhqmd1ty, the Demand for Res1dent1al
Housmg and Monetary Pohcy," forthcoming m Journal of Finance, Frederic S M1shkm, "Ill1qmd1ty, Con
sumer Durable Expenditure, and Monetary Pohcy,"
American Economic Review, vol 66 (September 1976),
pp 642-54, and Edward Yardem, "A Portfolio Balance
Approach to Corporate Fmance" (Ph D d1ssertauon,
Yale Umvers1ty, 1976)
2s The work has been earned out largely at Yale
Umvers1ty (by James Tobm, Wilham M Brainard,
Gary Smith, and Gary Fromm) and at the Umvers1ty
of Pennsylvama (by Lawrence R Klem and Albert
Ando)

Demand Deposit Ownership Survey

housmg, mventory mvestment, plant and
eqmpment expenditures, and consumpt10n)
can then be entertamed Thus, the DDOS will
be used mdirectly because 1t provides a basis for
constructmg more accurate estimates of the M 1
balances m the flow of funds accounts
In addition, some recent work by Tmsley 20
and by Kalchbrenner and Tmsley30 suggests
that quarterly real forecasts can be substantially
improved by takmg mto account the correlat10ns between the mnovat1ons m quarterly
1eal variables and those m monthly financial
variables The DDOS data can be of help m
mch filtermg exercises by expandmg the set
20 Peter A Tmsley, "On Proximate Explmtatlon of
Intermediate Information m Macroeconomic Forecast
mg," Special Studies Paper 59 (Board of Governors of
the Federal Reserve System, 1975)
ao John H Kalchbrenner and Peter A Tmsley, "On
the Use of Feedback Control m the Design of Aggregate
Monetary Polley," American Economic Review, vol 66
(May 1976), pp 349-55


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109

of monthly financial data mcluded m the
analysis

Summary
The precedmg d1scuss10ns of potential uses
of the DDOS data suggest the sizable .tmount
of research that this body of data may facilitate or enhance To date, many of these proJects have not been undertaken because of the
ielauvely small number of observations available m the DDOS data base, the number of
monthly observations may now be sufficient
for some 1elatively hm1ted studies, but the
quarterly base is still very small-about 22
observations The potential return from
monthly and quarterly ownership data appears
la1ge The ab1hty to be able to identify special
factors accountmg fo1 shifts m sectoral money
demands, and hence m aggregate money demand, alone has great potential for 1mprovmg
pred1ct10ns of money demand and mcome

llO

Appendix 1: Relationship of Gross IPC Demand Deposits
to the Money Supply

Gross !PC demand deposits differ from the demand deposit component of the money supply m
that the money supply deposit figure is net of
cash Items m process of collection (CIPC) and
Federal Reserve float and mcludes several types of
deposits besides !PC deposits (for example, de
posits of State and local governments, foreign
governments, foreign official mstitutions and foreign commercial banks,1 and certified and officers'
checks) These differences are expressed m Table
A-1 m terms of ad1ustments necessary to go from
the demand deposit component of the money
supply to gross IPC demand deposits by usmg
data for the fourth quarter of 1975
The figures for Federal Reserve float are, of
course, supplied by Federal Reserve Banks and
are the true daily-average values for this item for
each month All other data are partly estimated
Currency figures are as reported m money supply
data for these months They were denved by first
obtammg from the Federal Reserve Banks data
reflectmg the total volume of currency outstand1
lncludmg deposit balances mamtamed by foreign official
mst1tut10ns and mternat1onal ms11tut1ons at Federal Reserve
Banks

mg m each month The volume of currency held
by banks m their vaults was then deducted from
tlus total, data on the actual volume of currency
held by Federal Reserve member banks were combmed with an estimate of currency holdmgs at
nonmember banks The figures for CIPC are also
based on data reflectmg the actual volume of
these Items at Federal Reserve member banks and
estimates for tlus item at nonmember banks
The values for all of the vanous deposit categones were estimated by usmg data from weekly
reportmg banks and call reports Estimates of
daily-average balances m these deposit categones
mamtamed at weekly reportmg banks were obtamed by averagmg balances repo1 ted on each
Wednesday of the reference month, straight-lme
mterpolations were used m those mstances m
winch the week precedmg a Wednesday report date
spanned the end of a calendar month Estimates
for nonweekly reportmg banks were obtamed by
usmg a ratio esumatmg techmque Ratios reflectmg the relationship between the vanous deposit
categones at nonweekly reportmg banks and at
weekly reportmg banks outside New York on call
report dates were first calculated These ratios
were then used, together with data reflectmg esu-

TABLE A-1 Reconc1hation of the Money Stock with the DDOS,
Fourth Quarter, 1975
In mtlhons of dollars, not seasonally adiusted
Demand deposit component of Mi
Plus CIPC all commercial banks
Federal Reserve Hoat
Less Edge Act and Agency adJustment
CIPC plus Federal Reserve Hoa t, adJusted
Gross deposits m Mi
Less Mi-type balances at agencies and branches
Foreign official deposits with the Federal Reserve
Foreign commercial bank deposits, all commercial banks
Foreign government deposits, all commercial banks
Foreign adiustment-Total
All other deposits-Total
Less Cerufied and officers' checks, all commercial banks
Stale and local deposits, all commercial banks
Total cerufied and officers' checks plus State and local deposits
Derived estimate of IPC demand deposits
DDOS esllmate of !PC demand deposits
Difference


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Federal Reserve Bank of St. Louis

228,095

42,849
270,944

9,213
261,731
24,855
236,876
236,910
-34

Demand Deposit Ownership Survey

mates of daily-average balances m the vanous de
posit categories at weekly reportmg banks outside
of New York-calculated m the same way as were
the estimates for all weekly reportmg banks-to
obtam estimates for nonweekly reportmg banks
An estimate of gross IPC demand deposits based
on d,lta received on reports from DDOS sample
banks is presented m Table A-1 for comparison
with the gross IPC figures denved by makmg the
vanous adjustments to the money supply The
estimates are reasonably similar to each other


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Ill

It is not clear which of the two approaches yields
estimates that most closely approximate the true
daily-average values for gross IPC deposits Both
are subject to error-the DDOS estimate because
of samplmg vanation and the estimate denved
from the money supply because proxy estimates
were utihLed at vanous stages of the calculation
I he weakest estimates m the adjustment of the
money supply figure are the figures for "certified
and officers' checks" and for "State and local demand deposits "

112

Appendix 2: Tests of the Equality of Coefficients across Ownership
Classes Using "Standard" Money Demand Equations

One assumption underlymg the discussion of
potenual uses of the DDOS is that different ownership categories have different demand functions
for money, to assess the vahdity of this assumption, sets of tests were undertaken Both deal wtth
the three mam ownership categories m the DDOS
financial busmesses, nonfinancial busmesses, and
households These categories accounted for 92 8 per
cent of total IPC deposits as of December 1975
Demand functions were also estimated for total
DDOS deposits

Monthly, not seasonally adjusted data for the
sample subset of weekly reporting banks were
used m estimaung the equauons Data for the first
6 months of the survey were excluded because sur' ey start-up problems made those data less rehable
Data for the second half of 1974 and for all of
1975 were also excluded A number of staff studies
mdicate that standard money demand equations,
for some reason as yet not fully explamed, do very
poorly m explammg tlus penod Including these
data m the demand equauons discussed below
led to severe deteriorauon m the estimated relat10nships

NoTE -Helen T Farr and Arthur M Havenner prepared
this appendix

TABLE A-2 Demand Function Interest Rate Coefficients and Summary Statistics
Fmancial busmesses

Households
Interest rate
R30

Coefficient
(1-statisuc)
(-1
(-1
-

R90
RCP

(-2

CD,

(30-59 day)
CD,

(60-89 day)
CDa
(90-119 day)
RCDS

RFF

(-2
(-2
(-2
(-2
(
(-2

ROTS

0122
682)
0143
839)
0157
242)
0163
374)
0159
229)
0176
310)
0162
146)
0005
414)
1317
039)

I

R•

Coefficient
(l-stat1suc)

SB

I

0257

9833
0073
9836
0075
9844
0073
9847
0072
9844
0073
9846
0072
9842
0073
9817
0079
9841
0074

Nonfinanc1al busmesses

R•

Coefficient
(I stat1st1c)

SE
7965
0138
7934
0139
7960
0138
7975
0138
7980
0138
8011
0137
7976
0138
8067
0135
7831
0143

(I 473)

0254
(I 324)
0278
(I 451)
0286
(I 527)
0302
(1 550)
0346
(I 686)
0305
(1 530)
0049
(1 913)
0752
( 656)

(-2
(-2
-

(-3

(-3
(-2
(-2
(-2
(
(-1

I

R•

SB

Total
Coefficient
(-1
(-1
-

9874
0070
9876
0069
9892
0065
9891
0065
9889
0066
9887
0066
9885
0067
9860
0074
9870
0071

(-1

- 018
(-6 75)
001
( 85)
- 024
(-6 94)
- 021
(-8 53)

(-6
((-6
(-7

0193
192)
0220
384)
0262
188)
0258
070)
0258
983)
0268
913)
0255
791)
0015
658)
1463
658)

I

(1 Sla!ISIIC)

(-2

(-2
(-2
(-2
(-1
(2
-

0120
454)
0149
723)
0178
294)
0168
237)
0164
089)
0178
104)
0162
948)
0039
013)
1239
929)

R•

SE
9884
0061
9887
0061
9895
0058
9894
0059
9892
0059
9892
0059
9890
0060
9896
0058
9893
0059

TABLE A-3 Coefficients and t-Stat1stics for BIii Rate and Income
R90 coefficients

Deposit category
a

Sum of all DDOS deposits
2 Fmanctal bustness

(2
(

3 N onfinanc1al bustness
(I

4 Households


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Federal Reserve Bank of St. Louis

(3

012
24)
008
58)
012
61)
018
41)

I

a,

- 001
(- 30)
006
( 82)
- 004
(-1 24)
001
( 40)

I

a,

- 010
(-7 48)
003
( 98)
- 016
(-8 71)
- 011
(-8 62)

I

a,

- 016
(-7 75)
002
( 34)
- 022
(-8 24)
- 019
(-9 57)

I

a,

016
22)
000
02)
021
29)
019
97)

I

a,

(-5
(-

010
92)
000
07)
013
(-5 93)
- 012
(-7 00)

Demand Deposit Ownership Survey

113

First tests
In the first tests, all demand functions estimated
were of the form
In

D=

a.

+ a1 In R + a2 In Pl
11
+ aa In D_1 + ~
{3,S,
,~i

where D is the deposit category, R is an mterest
rate, PI is personal mcome, and S, are seasonal
dummies For each demand equation, nme different
mterest rates were tned separately the 30-day
Treasury bill rate, the 90 day Treasury bill rate,
the 30- to 59-day commercial paper rate, the 30- to
59-pnmary CD rate, the 60- to 89 day primary
CD rate, the 90- to 119-day primary CD rate, the
90-day secondary CD rate, the Federal funds rate,
and a composlle time and savmgs deposit rate
The mterest rate that gave the "best" equation
m terms of R. 2 and standard error vaned accordmg to ownerslup category For total DDOS depos!ls and for nonfinancial busmesses, it was the
commercial paper rate, for households, It was the
30- to 59 day primary CD rate 1 For financial businesses, nellher personal mcome nor any mterest
rate was s1gmficant Table A 2 gives the estimated
mterest rate coefficients and their t statistics (m
parentheses), the R. 2, and the standard error for the
estimated equations The results provide evidence
that different mterest rates are relevant for different holders of money

Second tests
In the second tests, demand functions were
estimated for the three mam ownership categories
1 As noted m the paper, most aggregate money demand
equatlons show a large and s1gmficant impact of the
time deposit rate Theory suggests that such an impact
would arise predommantly m the consumer sector (only smce
November 10, 1975, have corporations been permitted to
hold savmgs deposits) These results md1cate that the house
hold category 1s the only ownership category m which the
time deposit rate has a s1gmficant impact

and for aggregate deposits All equations were of
the form
6

In Di

=

~ a, In R901-,
1,-=-()

,~

11

+~
-y,S,1 + 'Y•
,=i
where D 1s the deposit category, R90 1s the 90 day
Treasury bill rate, Pl 1s personal mcome, and the
S, are seasonal dummies The coefficients and t statistics for the two mam mdependent variables of the
total and component equations are presented m
Table A-3 The equations were estimated by a
stacked regress10n techmque that took account of
the fact that the contemporaneous errors m -e,1ch
regress10n are probably correlated but that all errors
are uncorrelated over time The coefficients of the
polynomial d1stnbuted lags were assumed to he
along a second degree polynomial constramed to
zero at the tail, with a total length of 7 months
Tests were made of the s1gmficance of the differences between the a,'s, f1.'s, and y,'s of the compo
nent equations 'I he e, 1dence mchcates that the
coefficients of the component equations differ s1gmf1cantly from each other In evahutmg these results,
1t should be noted that only 37 observations were
used, that 1s, each equation had only 21 degrees of
freedom, which may be too few observat10ns to estimate adequately all of the differences among the var10us ownership categories However, even with the
limited degrees of freedom, the tests strongly md1cated differences If the ob1ect of the tests had
been simply to estimate the best equation for each
ownerslup category, different variables would have
been used for each category 2 By usmg separate
polynomial d1stnbuted lags on mcome and the
mterest rate, however, It was possible to allow
different time response patterns between the two
variables, unlike models that constram the re-

'See the section of this paper on

TABLE A-3-Contmued
Pl coeffic1ents

/Jo
364
(4 15)
578
(2 55)
120
(I 04)
264
(3 16)


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(6
(2
(2
(5

/31

/32

227
13)
263
75)
133
74)
185
25)

119
9)
257
26)
136
6)
120
6)

(26
(2
(23
(28

/3,
038
(I 43)
- 134
(-1 94)
129
(3 68)
068
(2 68)

/3•
((-2
(2
(

014
35)
217
14)
112
18)
031
82)

6

+ ~ (3, In P/1_,

/3,
((-2

037
96)
222
21)
085
(I 66)
007
( 18)

/3,
(-1
(-2

033
27)
150
25)
047

(I 40)
- 004
(- 14)

Money demand studies"

114

Improvmg the Monetary Aggregates Staff Papers

TABLE A-4 Test Results
Stat1st1c1

Type I error

Fa,"= 8766

24Xl0-"

2 Equabty of nonseasonal coefficients m all equations
a1, - a2, = 0 and a2, - aa,
0 and fJh - fJ2, = 0
and {J,, - /Ja, = 0, 1 = 0,6

Fa"= 17 869

7 I X 10-10

3 Equabty of seasonal coefficients m all equations
"Yb - 'Y2,
0 and 'Y2, - 'Ya.= 0, i = 0,11

F,.

=

1 3 X 10-"

4

F, '"

= 5 987

F,

=

18 045

2 6 X 10-11

=

34 538

1 4 X 10-"

Test
Equabty of coefficients m all equations
ab - a2,= 0 and a2, - aai,= 0 and /Jl, - /3h= 0 and
{J,, - {!,, = 0 and '>'1, - 'Yo,= 0 and 'Y2J - 'Ya,= 0,
I= 0,6,J=< 0,11

=

=

Equably of rate coefficients m all equations
a11 -

a2,=

76

13 381

0002

Oanda21- - aai= 0, i= 0,6

5 Equality of mcome coefficients m all equations
13,. - /3,, = 0 and /3,, - {J,, ""' 0, 1 = 0,6

10,

6 Equality of nonseasonal coefficients, financial and
nonfinanc1al equations
ai. - a,,= 0 and {J1, - {J,, = 0, I= 0,6

F. "'

7 Equably of nonseasonal coefficients, nonfinanc1al and
household equations
a2, - aa. = 0 and /32, - fJh = 0, 1 = 0,6

F,

,oa=

8 Equality of nonseasonal coefficients, financial and
household equations
ah - aa, = 0 and /j11 - {Ja, = 0, i = 0,6

F,

10,

1 At the 99 per cent confidence level, Fao so

= 2 03, Fa 100 ""'

2 69, Fu

sponse pattern by spec1fymg a lagged dependent
vanable
The statistic used to test equality of the coefficients 1s attnbutable to Zellner and 1s best
descnbed m his paper, "An Efficient Method of
Estlmatmg Seemmgly Unrelated Regress10ns and
Tests for Aggregation Bias " 3 Table A-4 presents
the values of the test statistics for the different
compansons made when, for example, the a 1 , are
the coefficients on the bill rate m the financial business equat10n, the {3 2 , are the coefficients on personal mcome m the nonfinancial busmess equation, and the y 3 , are the seasonal coefficients and
mtercept m the household equation
In order to argue that no additional mformat1on
1s gamed by d1saggregatmg mto ownership classes,
all respective coeffioents m all equations must
be equal (test 1) One can be 99 99999999999998
per cent certam that this 1s not the case (1 mmus
the type I error times 100) Test 2 md1cates that
3 Arnold Zellner, Journal of the American Statistical Association, vol 57 CT une 1962), especially pp 354-56


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Federal Reserve Bank of St. Louis

=

I 326

32 507

10

=

2 07, F.

265

I 4 X 10-10

100

=

3 51

this result 1s not due to the (nmsance) seasonal
coefficients, because the nonseasonal coefficients are
also s1gmficantly different The seasonal coeffi
oents are s1g111ficantly different also, however, as
test 3 demonstrates
Breakmg the coefficients mto subcategones, 1t
can be seen that wlule the responses to mterest
rate changes are s1gmficantly different (test 4),
the differences are not nearly so great as m the
case of mcome responses (test 5) D1saggregatmg
over ownership categories, tests 6 through 8 show
that whereas financial and nonfinancial holders
respond to mterest and mcome changes m a substantially different manner (test 6), households
are not s1gmficantly different from nonfinancial
mst1tut1ons (test 7) Smee households are not s1gmficantly different from nonfinancial busmesses,
1t 1s not surpnsmg that they are s1gmficantly different from financial busmesses (test 8) Tests run
with the 30- to 59 day commercial paper rate mstead of the 90 day bill rate gave essentially the
s<1me results

115

Bibliography

Board of Governors of the Federal Reserve System Flow of Funds, Assets
and Liabilities Outstanding, 1974 Washmgton Board of Governors,
1975
Emler, Jared, Lewis Johnson, and John Paulus "Some Problems of Money
Demand" Brookings Papers on Economic Activity, l 1976, pp 261-80
Goldfeld, Stephen M "The Demand for Money Rev1S1ted " Brookings
Papers on Economic Activity, 3 1973, pp 577-643
Homonoff, Richard, and David Wiley Mullms, Jr Cash Management
Lexmgton, Mass Lexmgton Books, 1975
Kalchbrenner, John H, and Peter A Tmsley "On the Use of Feedback
Control m the Design of Aggregate Monetary Policy" American Eco
nomic Review, vol 66 (May 1976), pp 349-55
Kearl, James R, and Frederic S J'vhshkm "Ilhqmd1ty, the Demand for
Res1dent1al Housmg and Monetary Pohcy" Journal of Finance, forthcommg
Lieberman, Charles "The Transactions Demand for Money and Technological Change" Review of Economics ancl ',tatisticv, vol 59 (August
1977), pp 307-17
Miller, Merton H, and Damel Orr "A Model ol the Demand for Money
by Firm~" Q11arte1 ly Journal of Economics, vol 80 (August 1966), pp
413-35
l\hshkm, Frederic S "Ilhqmd1ty, Consumer Durable Expenditure, and
Monetary Policy" Ame11cnn Economic Review, vol 66 (September 1976),
pp 642-54
Orr, Dame! Cash Managemrnt and the Demand for Money New York
Praeger, 1971
Porter, Richard D "Debits, Turnover, and Money Demand " Memo
randum Washmgton Board of Governors of the Federal Reserve System, January 1976
Pugash, James Z "The Demand for Money m Six Sectors" Unpublished
manuscript, Washmgton Board of Governors of the Federal Reserve System, January 1974
Sluller, Robert J "A Distributed Lag Estimator Derived from Smoothness
Priors" Econometrica, vol 41 (July 1973), p 775-88
Slovm, Myron B, and Mane E Sushka Interest Rates on Savings Deposits Lexmgton, Mass Lexmgton Books, 1975
"Survey of Demand Deposit Ownerslup " Federal Reserve Bulletin, vol 57
(June 1971), pp 456-67
Swamy, P A V B Statistical Inference in Random Coefficient Models
Berlm Sprmger-Verlag, 1971
Tmsley, Peter A "On Proximate Explo1tat10n of Intermediate Informat10n
m Macroeconomic Forecastmg" Special Studies Paper 59 Washmgton
Board of Governors of the Federal Reserve System, 1975


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116

Improving the Monetary Aggregates· Staff Papers

Yardem, Edward "A Portfolio Balance Approach to Corporate Fmance"
PhD d1ssertauon, Yale Umversity, December 1976
Zellner, Arnold "An Efficient Method of Est1matmg Seemmgly Unrelated
Regressions and Tests for Aggregauon Bias" Journal of the American
Statistical Assoc1at1on, vol 57 (June 1962), pp 348-68


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Federal Reserve Bank of St. Louis

117

Sources of Data and Methods of Construction
of the Monetary Aggregates
Darwin L Beck

This paper is a somewhat more detailed version of the study originally prepared for the
Advisory Committee on Monetmy Statistics zn
1976

The first senes on the money stock published by the Federal Reserve was based on
data for dem,mtl and time deposits of banks
and currency m circulation for June call dates
£01 the penod 1892 to 1922, and for June and
December call dates for 1923 to 1941 1 In
February 1944, the Board first began to publish smgle-day monthly data (for the last
Wednesday of the month) similar to that based
on call report data In October 1960 a revised
and improved measure became available for
the penod begmnmg with 1947, 2 it was a
daily-average, rather than a smgle-day, series
and was available twice each month
Wlule the money stock senes has been revised many times smce 1960, the narrow
measure, Mi, cmrently published by the Board
1s consistent with that first published, on a
semimonthly basis, m 1960 In August 1962, m
d. mmor rev1s10n, foreign demand balances
with Federal Reserve Banks and demand deposits of banks m US terntones and possess10ns held at U S commercial banks were
added to the demand deposit component of
the money supply At the same time weekly
estimates of the money stock back to 1959
were published for the first time 3
From 1963 to 1968 the money stock was
Norn -Danvm L Beck 1s a member of the staff of
the Board's D1vmon of Research and Statistics
1 Banking and Monetary Stat1st1cs (Board of Governors of the Federal Reserve System, 1943)
2 "A New Measure of the Money Supply," Federal
Reserve Bulletin, vol 46 (October 1960), pp 1102-23
a "Revmon of Money Supply Senes," Federal Reserve
Bulletin, vol 48 (August 1962), pp 941---51


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d.dJUSted five times to mc01 pm ate new benchmark dd.ta for nonmember b,mks and revised
seasonal factors based on add1t10nal data Furthermore, m 1969 and ag,1_m m 1970, the
money stock was adjusted to conect fo1 downward bias m the level and uend of the seues
that had developed m assoc1at10n with expans10n of check-clearmg ope1at1ons of f01e1gnielated mst1tut10ns m New York C1ty 4 In
early 1973, anothei statistical iev1sion a1ose
from changes m Federal Reserve iegulations
that c,tused a chscontmmty m the rep01 ted
data fiom winch money stock measures are
constructed"
In the early years, the narrow money stock
measure, Mi, was given the greatest emphasis
Time deposits adjusted were also published,
but no effort was made to construct broade1
monetary measures by addmg such deposits,
and deposits of nonbank mst1tut10ns, to M 1 6
However, m Apnl 1971, the Board also began
regularly to publish broader monetary aggregate measures, M 2 and M 3 More recently,
begmnmg m Apul 1975, the Board added
M 4 and M 5 to the published data
The tabulat10n below describes the public's
financial assets mcluded m each of the measures of monetary aggregates regularly published by the Board of Governors of the Federal Reserve System In general, the pubhc 1s
defined as all mdiv1duals and mst1tut1ons, do4 See "Revmon of Money Supply Senes," Federal Re
serve Bulletin, vol 55 (October 1969), pp 787-803, and
"Rev1S1on of the Money Stock," Federal Reserve Bulletin, vol 56 (December 1970), pp 887-909
s "Revmon of the Money Stock Measures and Member Bank Reserves and Deposits," Federal Reserve
Bulletin, vol 59 (February 1973), pp 61-79
a Time deposits adjusted are defined as total lime
and savmgs deposits at commercial banks less US
Government and mterbank time deposits

us

Improvmg the Monetary Aggregates. Staff Papers

mest1c and foreign, other than the U S Goverment and domestic commercial banks
Money
stock
measure

Assets
included

Currency m
crrculation

All currency and com outside the U S
Treasury and Federal Reserve Banks less
currency and com held m the vaults of
U S commercial banks or m transit to
or from Federal Reserve Banks
Currency m circulation plus demand
deposits ad3usted at all U S commercial
banks (gross demand deposits less de
mand deposits due to the US Government, demand deposits due to domestic
commercial banks, cash items m the
process of collection, and Federal Reserve
Reserve float), M 1 type deposits at Edge
Act corporations, branches and agencies
of foreign banks, and foreign investment
corporations, and foreign official deposits
at Federal Reserve Banks
M 1 plus total time and savings deposits
at all commercial banks less (a) negotiable time ceruficates of deposit issued
m denominations of $100,000 or more
by large weekly reporting banks, (b)
time deposlls due to domestic commer
c1al banks, and (c) time deposits due
to the U S Government
M 2 plus deposits at mutual savmgs
banks, savings and loan shares, and
credit umon shares
M 2 plus negotiable Ume certificates of
deposit issued m denommauons of
$100,000 or more by large weekly reportmg banks

Ms

Ma plus negotiable time certificates of
deposit issued m denommauons of
$100,000 or more by large weekly reportmg banks

Economists and financial analysts generally
agree that money stock series should be constructed by measurmg the various financial
assets that have been categorized as moneycurrency, demand deposits, savmgs deposits,
time deposits, and so on-from the records


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of the actual money holders This ts the
"holder record" concept of the money stock
However, umverse reportmg of actual money
stock on such a basts ts not possible, and a
sample survey also appears to be impractical
Even 1f an adequate sample could be drawn
or reportmg arranged for the umverse of
domestic holders of money stock assets, a
large segment-foreign holders-could not be
readily accounted for
A rough equivalent of the holder-record
measure of the money stock can be derived
from the records of the Treasury, Federal Reserve Banks, and other financial mstitut10ns
if proper adjustment 1s made for the recordmg of some items on the books of two banks
at the same time With that adjustment, such
a measure would differ from one based on
holder records only because of "mail float"checks issued and deducted from holders' records but not yet received and deposited m
payees' accounts
The mail-float discrepancy between holder
records and bank records may be offset, so far
as economic motivation 1s concerned, by the
expectation of an mflow of funds by the drawer
of the check before the check is presented for
payment To the extent that such an offset
exists, measures based on unduphcated bank
records and holder records are very similar
All of the measures of the money stock published by the Board are derived from the
records of the Treasury, Federal Reserve
Banks, domestic commercial banks, and other
financial mstitut10ns The basic adjustments
that must be made to these data mclude adJUstments for double countmg and est1mat1on
of weekly- and monthly-average levels of deposits at bankmg mstitut10ns that do not report on so frequent a basis In addition, deposits of some holders, such as foreign commercial banks, must be esumated usmg supplementary data because the basic data do not
provide a sufficient breakdown to permit direct
measurement
Inasmuch as currency m c1rculat10n 1s a
bmldmg block common to all of the broader
money stock measures, the description of the

Sources of Data and Methods of Construction of the Monetary Aggregates

construction of the monetary aggregates begms with it A discussion of the demand deposit component of the money stock is next,
followed by a descnpuon of the broader
money stock measures, M 2 through M 5

Currency in circulation
The currency component of the money
stock is defined as all U S currency and com
outside the Treasury, Federal Reserve Banks,
and commercial banks This component accounts for roughly 25 per cent of the narrow
money stock mec1sure, M 1 Daily data on currency m circulation outside the Treasury and
the Federal Reserve System are reported to
the Board on a regular basis
Table I shows for the last day of 1975 the
vc1nous items that make up the total of currency and com m circulation outside the U S
Treasury and Federal Reserve Banks The
bulk o[ currency c1nd com m circulation con5ists of Federal Reserve notes, followed by the
fractional com (quc1rters, dimes, mckels, and
so on) issued by the Trcc1sury Other relatively
large components are silver dollars currently
JSSued by the Treasury and U S notes issued
by the Treasury m earher years A mmor
TABLE 1 Currency m C1rculahon Outside the U S
Treasury and Federal Reserve Banks,
Year-End 1975 1
In mllbons of dollars

Type of currency
F R notes outstanding

Fractional c01n
Sliver dollars
Silver ceruficates
US notes
FR Bank notes
National Bank notes
Gold cerllfica !es
FR notes prior to 1923 series
Total currency and com
Less F R notes of other FR Banks and Treasury com
held by FR Banks
FR notes
Com
Held by the Treasury
FR notes
Com
Total

Amount
78 769

8,610
1,001
210
323
50

20

3

I
88,987

1,612
345
175
308
86,547

1 For a more detailed descr1pt1on of the components that make up
total currency m c1rculat1on, see Banking and Monetary Sta11s11cs,
1941-1970 (Board of Governors of the Federal Reserve System,
1976), pp 615-16


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Federal Reserve Bank of St. Louis

119

component, about $285 milhon, of assorted
currency still outstandmg but m the process
of retirement consists of silver certificates,
Federal Reserve Bank notes, National Bank
notes, Federal Reserve notes pnor to the 1923
senes, and gold certificates
The currency component of the money
stock measures excludes the vault cash (currency and com) held by commercial banks
Smee vault cash of member banks can be used
to meet reserve reqmrements, these holdmgs
aie mcluded on reports submitted to the Federal Reserve for the determmauon of reqmred
reserves, and are thus available on a dally
basis Vault cash at nonmember banks must
be estimated from quarterly or semiannual reports of condition of all commercial banks
Lmes 2 and 3 m Table 2 show the estimated
vault cash held at member and nonmember
banks on average m December 1975 7
Estimates of vault cash held at nonmember
banks a1e based on the ratio of vault cash of
nonmember banks to vault cash of membe1
banks on cc11l report dates Currently, these
benchmark relationslups c1Te avatlable for
weekly c1verc1ges surroundmg call dates £om
times each year Pnor to March 1976, they were
c1vallable for four smgle days each year, pnor
to March 1973 they were generally available
only for June 30 and December 31 8
Estimates of the ratio of vault cash for ec1ch
week between call report dates are based on c1
straight-hne mterpolation Weekly estimates
of nonmember vault cash are then denved by
muluplymg the est1mc1ted weekly ratio of vault
cash by the rep01 ted weekly-average vault cash
of member banks Monthly-ave1age vault cash
1s denved from a proration of the weekly estimates The ratio for the latest call report
1 Note that Table 1 shows currency and com com
ponents for the last day of December 1975, while
T dble 2 shows th<- monthly average for December 1975
of currency m c1rculat1on ancl vault cash at member
and nonmember banks
R Data for all commercial banks are ava1labk from
call rcpolts fo1 Jun<- 30 and December 31 The other
l\\O call~ provHk data for all mmred banks (Unmsured
banks a1e a rdal!vdy ~mall wmponent of the total
U S bankmg sy~tem )

120

Improvmg the Monetary Aggregates Staff Papers

TABLE 2, Construction of M,
Monthly averages

ID

mtlbons of dollars, not seasonally ad.Justed

Line, Item

Contr1button
December 1975

Source of data

85,847

Daily data reported by Federal Reserve Banks and Treasury
Department
Daily data reported by all member banks
Esttmated, based on data reported by member banks and call
report data

Currency ID c1rculat1on
2
3

Less

4
5
6
7

Equals Currency component of M1

8

9

10

Member bank vault cash
Nonmember bank vault cash

Demand deposits at member banks1
Less
F R float
Plus
Demand deposits at nonmember banks

8,097
2,649
75,101
155,722
3,096
62,082

Demand deposits due to foreign commercial banks

5,408

Demand deposits due to mutual savmgs banks

1,132

Daily data reported by all member banks
Daily data reported by Federal Reserve Banks
Estimated, based on daily data reported by small member
banks and call report data
Estimated based on SIDgle day (Wednesday) data for large
banks and call report data for other banks
Estimated, based on s1Dgle day (Wednesday) data for hrge
banks and call report data for other banks

Demand deposits due to banks tn terntones and
possessions
Cash items ID process of collection associated with
foreign agency and branch transfers•

3,319

Daily data reported by foreign-related 1Dst1tut1ons ID New
York City

12

Mi-type balances at foreign related mst1tut1ons ID
New York City

3,025

Esumated, based on daily reporting for large 1Dstltut10ns and
on reports for the last Wednesday of month for smaller

13

Deposits due to foreign oflictal 1Dst1tut1ons at
Federal Reserve Banks
Equals Demand deposits component of M,
Money stock (M1)-<:urrency plus demand deposits adJusted

391
228,093
303,194

II

110

Esumated, based on call report data

mstttuUons

14
15

1 Gross demand deposits less demand deposits due to U S Government and 1Dterbank deposits and cash items ID process of collection

period is held constant until another call report is available
Even though the currency component, defined as currency m circulation outside the
Treasury and the Federal Reserve Banks less
vault cash held at commercial banks, can be
measured quite accurately, the defimt10n deviates by some unknown amount from a
holder-record concept because it makes no
allowance for currency lost or destroyed In
addition, some of the currency may be held
m safe-deposit boxes or sent out of the country Thus the published measure overstates
the amount of currency m circulation m the
Umted States No effort has ever been made
to measure the currency "not in circulation,"
and any adjustment for it would be nothmg
more than a guess

Demand deposits component
of money stock
Data on the demand deposits component of
the money stock are not so readily available


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Federal Reserve Bank of St. Louis

2

Daily data reported by Federal Reserve Banks

Includes M, type deposits at Edge Act corporations

as are those for the cuirency component and
thus must be constructed from a number of
sources These mclude data available each
day and smgle-day data available weekly,
monthly, and from quarterly call reports
Nearly two-thirds of total demand deposits
are accounted for by member banks, and data
on these deposits are readily available on a
daily basis from the Report of Deposits submitted by member banks for determmation
of reserve requirements Because the purpose
of this report 1s to measure deposits subject
to reserve requirements, and not deposits to
be mcluded m the money stock, a number of
adjustments must be made m the basic data
reported by member banks The demand depos1 ts component of domestic nonmember
banks is derived from call report data and
estimates based on dally deposits data reported
by small member banks Deposits of other
financial mst1tut1ons, and other adjustments
to the deposits component of Mi, are derived
from a number of sources Each component is
discussed m detail below

Sources of Data and Methods of Construction of the Monetary Aggregates

Member bank demand deposits
From the Report of Deposits, filed weekly
by member banks, four items are used to construct the demand deposits component of the
narrow money stock, M 1 Three of these Items
aggregate to gross demand deposits U S Gove1nment deposits, demand deposits due to
other commercial banks, and "all other" demand deposits (that 1s, demand deposits due
to md1v1duals, partnerships, and corporations
-domestic and foreign, State and local governments, nonp1ofit orgJ.mzat10ns, and so on)
The fourth Item, cash items m the process of
col1ect1on (CIPC), 1s deducted from gross demand deposits m the construction of the
money stock
All U S Government demand depos1 ts are
excluded from the money stock and "all other"
demand deposits are mcluded A problem
anses m connect10n with demand deposits due
to banks At the present time, demand deposits
due to foreign commercial and mutual savmgs banks are mcluded m the money stock,
and demand deposits due to domestic commercial banks are excluded Because these Items
are not hsted separately on the Report of
Deposits but are mcluded m the "due to
hanks" component, alternative sources of data
must be used to estimate the demand deposits
due to foreign commercial banks and mutual
savmgs banks included m the money stock
The bulk of these deposits are held at large
banks that report on them each week (Wednesday) as part of a detailed balance sheet These
smgle-day weekly data, along with call report
data for all commercial banks, are used to
adjust the demand deposits data
The calculat1on of the demand deposits at
member banks included m the money stock
begms with gross demand deposits From this
figure total demand deposits of the US Government and those due to banks are deducted
In order to av01d double countmg of demand
deposits that are shown simultaneously on the
books of two banks, CIPC are also deducted
from gross demand deposits to denve the component of M 1 accounted for by the member
bank demand deposits (see lme 5 of Table 2)


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Federal Reserve Bank of St. Louis

121

Smee CIPC can be deducted m computmg
deposits subject to reserve 1eqmrements, It 1s
J.lso available on a daily basis from the Report
of Deposits CIPC shown on tlus report, however, is not b1oken down for items associated
with private demand deposits and those associated with all other operat10ns of the bank
It 1s known that gross CIPC overstJ.tes those
items that should be deducted from the money
stock deposits For example, cash Items assoClated with deposits due to banks, with US
Government deposits, with redeemed coupons
of US Government securities, and with bank
ued1t cards are mcluded m the gross cash
items data Past mvest1gat1ons and contacts
with bank accountants suggest that the distortions noted above J.re not large f01 domestic
transJ.ct10ns and that they 1emam fanly constant relative to total deposits A much more
senous p1oblem, discussed m some detail below, concerns the s1gmficant p10port10n of the
CIPC related to mterbank transfe1 s of funds,
associated largely with the clearmg of Eurodollar transactions m the New York City
money market between large member banks
and more specialized mst1tut1ons engaged m
mternJ.t10nal bankmg Such CIPC 1s added
hack vu data collected chrectly from mternatlonal bankmg mst1tut10ns

Federal Reserve fl,oat
Federal Reserve float, which is very similar
to CIPC, 1s also deducted fiom pnvate demand deposits m calculatmg M 1 (lme 6 of
Table 2) This float 1s deducted because on
some Items that are cleared through Federal
Reserve Banks crecht 1s passed to the sendmg
bank before the paymg bank has received the
item and reduced deposits When the sendmg
bank receives credit, the CIPC account 1s reduced on that bank's books even though deposit hab1ht1es on the books of the paymg
bank have not been reduced The amount of
double countmg m such mstances 1s reflected
m the float created by Federal Reserve Banks
rather than CIPC Deductions for both Federal Reserve and CIPC float serve to offset this
double-countmg effect

122

lmprovmg the Monetary Aggregates Staff Papers

Nonmember bank deposits
Domestic nonmember banks account for the
second largest deposit component of the money
stock (hne 7 of Table 2) Data for nonmember banks are available four times a year from
call reports In order to estimate their deposits
for other periods, the ratio of the demand
deposits of nonmember banks m M 1 to those
of the smaller member banks is computed for
each call report date A straight-lme mterpolation of this ratio ad1usted for changes m
bank structure is made between call report
dates 9 These estimated weekly rat10s are then
apphed to weekly data on average deposits
reported by smaller member banks m order to
obtam weekly and monthly estimates of the
demand deposits component of the money
stock at nonmember banks Monthly-average
estimates are derived from a weighted average
of the weekly estimates Beyond the current
call report date, rat10s are estimated based on
a regression equation and Judgment 10 As new
call report data become available, these estimates are revised and benchmarked to the
umverse data available from the call report
While demand deposits of member and nonmember banks account for the bulk of the
demand deposits component of Mi, a number
of additional adjustments must be made to
complete construct10n of M 1

Demand deposits due to foreign
commercial banks
As mdicated m the discussion of the demand
deposits of member banks, demand deposits
due to foreign commercial banks are mcluded
m mterbank deposits on the Report of Deposits Smee total demand deposits due to
banks were deducted from gross deposits, further ad1ustments must be made to mclude
deposits due to banks m foreign countries m
9 Changes m bank structure reflect shifts m bank
reportmg status due to changes m Federal Reserve
membership, mergers, and the like that affect the ratio
of nonmember banks to small member banks
1 For a descnpuon of this process, see "Rev1s10n of
the Money Stock Measures and Member Bank Deposits
and Reserves," Federal Reserve Bulletin, vol 60 (Febru
ary 1974), pp 81-95

°


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Federal Reserve Bank of St. Louis

the demand deposits component of M 1 Estimates of these foreign demand deposits are
based on weekly smgle-day (Wednesday) data
for large banks and on call report data As
part of a detailed balance sheet, on Wednesday of each week about 320 large commercial
banks report the breakdown of their deposits,
from which the demand deposits due to foreign commercial banks can be derived For
nonweekly reportmg banks, which account for
about 20 per cent of demand deposits due to
foreign banks, estimates are based on call
report data
Estimates of the demand deposits due to
foreign commercial banks mcluded m M 1 are
constructed as follows For each call report
the amount of demand deposits due to foreign
commercial banks at nonweekly reportmg
banks is calculated Between call report observat10ns, weekly estimates are derived from
a straight-lme mterpolat10n After the most
current call report date, the latest level of
deposits at nonweekly reportmg banks is earned forward as a constant The total of weekly
estimates for nonweekly reportmg banks and
Wednesday data reported by weekly reportmg
banks is then used as a proxy for the weeklyaverage level of deposits due to foreign commercial banks at all domestic commercial
banks Monthly averages are prorations of the
weekly data
Deposits due to foreign commercial banks
are a relatively small part of M 1 (lme 8 of
Table 2) However, because these deposits,
particularly as derived from Wednesday data
for weekly reportmg banks, can be qmte
volatile, they can have a sigmficant impact
on the changes m M 1 both from week to week
and from month to month Smee weekly reportmg banks account for roughly 80 per cent
of these deposits, measurement error should
be relatively small, except to the extent that
the smgle-day Wednesday data are a poor
estimator of the weekly-average level

Demand deposits due to mutual
savings banks
Demand deposits due to mutual savmgs
banks are also mcluded m the mterbank ac-

Sources of Data and Methods of Construction of the Monetary Aggregates

count on the Report of Deposits and thus
deducted from gross deposits Estimates of deposits due to mutual savmgs banks, to be
added back to the component of M 1 cons1stmg
of demand deposits adJusted, are denved from
the same sources as estimates of deposits due
to foreign banks-that 1s, weekly reportmg
banks and call reports Weekly estimates of
mutual savmgs bank deposits at nonweekly
reportmg banks are based on a stra1ght-lme
mterpolat10n between call report dates These
estimates plus Wednesday data for weekly reportmg banks ate used as a proxy for the
weekly-average level, and monthly data are
weighted averages of the weekly observat10ns
The component compnsmg deposits due to
mutual savmgs banks 1s small and relatively
stable (see lme 9 of Table 2) In addition,
weekly reportmg banks account for the bulk
of such deposits, about two-thirds m late
I q75 Thus any errors m est1mat10n of data
from nonweekly reportmg banks are small and
have httle impact on the total M 1 measure

Demand deposits due to banks
in territories and possessions
Demand deposits due to banks m terntones
and possess10ns are also denved from call reports However, these deposits must be estimated somewhat differently-from a special
tabulation of the call report showmg balance
sheet data fm banks located outside the Umted
States, sometimes referred to as banks m
"other areas " Included m tlus tabulation 1s
an asset item, demand deposits due from US
banks This Item 1s assumed to be eqmvalent
to demand deposits due to banks m terntones
and possess10ns mcluded m demand deposits
due to banks on the books of U S commercial
banks, and 1t 1s used as a proxy for such depos1 ts
Weekly estimates of demand deposits due
to banks m US terntones and possess10ns
(hne 10 of Table 2) are derived from a stra1ghtlme mterpolat10n between call report dates
Estimates between call report dates are earned
forward as constants, and monthy-average
estimates are derived from prorat10ns of the
weekly figures Smee these deposits generally

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Federal Reserve Bank of St. Louis

123

are less than $100 million on call report dates,
there 1s httle measurement error m this component

Adjustments for cash-items bias
CIPC, as reported by member banks on the
Report of Deposits, excludes some items that
should be deducted from demand deposits to
avoid double countmg of money stock deposits, and 1t mcludes some Items that should
not be deducted because they do not reflect
double countmg An example of the understatement of CIPC 1s the "due from banks"
bias Some banks, when forwardmg checks to
a correspondent bank for collect10n, 1mmed1ately mcrease their due-from-banks account
rather than their CIPC account Durmg part
of the collect10n ptocess, such accountmg entnes result m an overstatement of the money
stock because CIPC is understated and deduct10ns for double countmg are too small Duefrom-banks deposits are not deducted from
gross deposits m calculat10n of the money
stock Due-to-banks deposits, from the hab1hty
mle of the balance sheet, are deducted from
gross demand deposits If both due-to and
due-from deposits were deducted, the money
5tock measure would be grossly understated
No data exist to measure the amount of the
overstatement of the money stock related to
this bias, but 1t 1s generally thought to be
relatively small and to grow proport10nally
with the money stock Thus, while the level
of the senes 1s biased upward, month-to-month
and year-to-yea1 changes should not be senously affected
The overstatement of CIPC and the assonated understatement of the money stock have
been a much more senous matter, particularly
m the late l960's and early 1970's In the
sprmg of 1969, 1t was discovered that an mcreasmg volume of Euro-dollar transact10ns
of large banks with their foreign branches had
sharply expanded the dollar amount of items
m the process of collect10n While drafts issued
for the payment of such transfers ("London
drafts" and "bills-payable checks") mcreased
CIPC, they were not classified as deposits and
the associated expans10n m CIPC resulted m

124

Improvmg the Monetary Aggregates Staff Papers

unwarranted deductions from reported demand deposits m the estimates of the money
supply 11
The deduction of CIPC associated with
these Euro-dollar transfers also had the effect
of reducmg required reserves To prevent such
reductions, the Board changed Regulation D,
effective July 31, 1969, to require that member
banks mclude checks ongmatmg from transactions with foreign branches as deposits subject to reserve requirements To avoid a
sigmficant break m the money stock senes
associated with this change m Regulation D
and to correct for the understatement of the
money stock senes m previous periods, back
data were revised The revisions to correct
for Euro-dollar float were earned back to May
1967 Rev1S1ons for the first 7 months of 1969
weie based on weekly data obtamed from large
banks covering bills-payable checks and London drafts ongmatmg from transact10ns with
foreign branches Accordmg to these reports,
the total amount of such mstruments mcreased
from $1 8 billion m January 1969 to $3 3
billion m July, largely m the May-June
period, when Euro-dollar borrowmgs rose
sharply Revmons pnor to 1969 were mterpolated on the baSIS of the reported growth
rate of CIPC relative to gross demand deposits These data mdicated that growth m
cash items relative to demand deposits accelerated significantly about mid-1967 and agam
about mid-1968 12
In the sprmg of 1970, additional problems
with CIPC ansmg from mternat10nal transact10ns were uncovered Checks issued by Edge
Act corporations and agencies and branches
of foreign banks were recorded as CIPC on
the books of domestic banks However, these
checks were not picked up m the gross de-

posit figures used m the construction of the
money stock smce at that time liabilities of
these mstitutions were not mcluded m the
money stock The generation of CIPC without
recordmg a counterpart liability for money
stock deposits on the books of large New York
City banks resulted m a downward bias of
the level of the money stock This bias was
even larger than the one corrected m the
1969 rev1S1on And because the issuance of
such checks had grown rapidly durmg this
penod, the measured growth m the money
stock was also understated
In order to correct for this downward bias
m the money stock, data were collected from
Edge Act corporations and U S agencies and
branches of foreign banks, which served as a
proxy for the amount of CIPC improperly
deducted 13 On October I, 1970, mst1tut10ns
began to report daily data that reflect the
amount of mappropnate cash items mcluded
m the total figure deducted from demand
deposits (line 11 of Table 2) Smee that date,
money stock measures have been ad jUsted for
the CIPC bias by addmg back the amounts
reported by foreign-related mstitut10ns (Subsequently, m early 1973, the money stock was
also adjusted for CIPC bias generated by
foreign mvestment corporations located m
New York City)
With reported data available from October
1, 1970, m order to avoid a break m the
money stock senes, a method was needed to
estimate the s1Ze of the bias pnor to that date
To make correspondmg revisions m the back
data, lt was necessary to estimate the amount
of total cash-items bias mdirectly The sharp
fluctuat10ns m cash items and m mterbank
deposits that occurred on the books of the
major New York City banks around certam

"London drafts" and "bills-payable checks" were
checks drawn by or on behalf of a foreign branch of
a member bank on an account mamtamed by such a
branch with a domestic office of the parent bank Until
the change m Regulation D, effective July 31, 1969,
such checks were not mcluded m officers' checks by the
issumg bank
12 "Revmon of Money Supply Series,'' Federal Reserve Bulletin (October 1969), p 788

13 Smee Edge Act corporations are required to hold
reserves agamst deposits, these mstltutions submit a
weekly report similar to the report of deposits submitted by member banks The data from these reports
not only reflected the cash items bias generated by
Edge Act corporations but also a small amount of M 1 type deposits held at these mstltutlons Smee the cashitems bias and the M1 type deposits could not be separated, all of the Edge Act corporation ad1ustment was
mcluded m the adJustment for cash items bias

11


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Federal Reserve Bank of St. Louis

Sources of Data and Methods of Construction of the Monetary Aggregates

holidays-such as Easter and Christmas-when
European and U S bankmg practices with respect to workmg days diverge, provided a
basis for estimatmg the magmtude of the cashitems bias
In those hohday penods when New York
City banks were open and European banks
were closed, the declme m cash items typically exceeded the declme m money stock
deposits by several bilhon dollars The difference reflected a drop m mterbank deposits attnbutable to the collection of checks
issued the day before the European bank
hohday by agenoes, branches, and Edge Act
corporations Tlus difference 1s a 10ugh measure of the amount of bias assooated with
the mternational operations of such mstitutions The Euro-dollar market was closed on
the hohday abroad and the flow of overmght
transfers was mterrupted, but banks m New
York City remamed open and collected outstandmg checks When these checks were collected, cash items declmed sharply At the
same time, New York City banks debited "due
to banks"-that 1s, due to agenoes, branches,
and Edge Act corporations-for an equivalent
amount of check clearmgs agamst their balances The balances due to banks declmed
by an amount approximately equal to the residual declme m cash items Thus the hohday
declme m balances due to banks was about
equal to the volume of cash items generated
by these mstitutions m their normal daily
transactions Cash items and balances due to
banks returned to normal quickly followmg
the hohday Over the hohday, the ehmmation
of Euro-dollar cash items resulted m an "unbiased" measure of net deposits, as denved
from bank records
The declme m balances due to banks was
measured on each Good Fnday back to 1959,
and on Boxmg Day (observed as a holiday m
Britam on the day after Chnstmas) back to
1966, to provide benchmarks for ad1ustmg the
back data for cash-items bias Ratios of the
total bias to known Edge Act deposits were
mterpolated between the holiday benchmarks,
and the estimates of bias for mtervenmg weeks
and months were denved by multiplying these


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Federal Reserve Bank of St. Louis

125

estimated ratios by figures on Edge Act deposits
The adjustment for cash-items bias remams
a component of the construction of the money
stock However, the advent of new methods
of transferrmg funds m New Y01 k City-the
Clearmg House Inte1 bank Payments System
(CHIPS) m Apnl 1970 and the Paper Exchange Payment System (PEPS) m eaily 1972
-ehmmated much of the cash-item~ bias
Banks and other mstitutions usmg these fac1hties were required to record all of their
transactions 1n interbank accounts, either as
due to banks or due from banks, thus ehm1natmg any cash-items bias from transactions
related to CHIPS or PEPS
For a short time afte1 the 111tio<luction of
CHIPS, a few banks 111 New York City failed
to account properly for the transfers through
that system This problem was soon resolved,
however, and back data were collected to
correct for errors 1t had caused Currently, the
bulk of Emo-dollar transfers that ong111ally
generated cash-items bias are handled through
CHIPS Transfers outside CHIPS cont111ue to
create a bias, however Generally, tlus bias 1s
small and relatively stable While rare, the
cash-items bias can 111crease to a very s1gmficant factor when there 1s a failure of the
CHIPS faohty

Ad1ustment for Regulation

J

In late 1972, a change m the Board's regulations governmg check collection procedures
(Regulation J) required a one-time ad1ustment
to the data on the money stock to avoid a
break 111 the senes Pnor to that change, many
banks were on a "deferred payment" basis m
remutmg to the Federal Reserve for checks
presented to them for payment That 1s, when
the Federal Reserve presented checks to a
payee bank for payment, remittance m 1mmed1ately available funds was not due until
the followmg busmess day Payee banks, nonetheless, were able to reduce their customers'
demand deposit accounts on the day the check
was presented by the Federal Reserve For
one day the bank would carry the hab1hty m

Improvmg the Monetary Aggregates Staff Papers

126

a nondeposit account ("other habihties"), remittance due to the Federal Reserve Because
the demand deposit account at the payee bank
was reduced before the correspondmg cash
item or Federal Reserve float was reduced, the
level of the money stock was understated by
the amount of these remittance payments
The change m Regulation J, implemented
m November 1972, reqUired former deferredpayment banks to remit for checks presented
by the Federal Reserve for payment on the
day of presentauon The earlier remittance
by the affected banks resulted m the disappearance of this source of bias, and a one-tlme
mcrease m the money stock on the day the
change was implemented To avoid this break
m the series, the remittance-payments bias
was estimated usmg data collected from Federal Reserve Banks and regression analysis
For the pe11od I 966-72, the adJustment to
the money stock was based on the reported
credits to member and nonmember transit accounts at Federal Reserve Banks For the
period 1959-65, the adJustment was derived
from an estimated and simulated regression
equauon for transit-account ciedits based on
reported data for 1966-72 14 The effect of
these estimates was to raise the level of the
money stock about $300 million m January
1959 and about $4 5 billion m December 1972

Other

M1

components

The net of the components discussed above
--currency, demand deposits of member and
domestic nonmember banks, Federal Reserve
float, and the cash-items bias adJustmentaccount for 98 pe1 cent of the total money
stock, M 1 The remamder of the money stock
deposits are distributed among a number of
financial mstitut10ns, primanly foreign related, and nearly all of them are m New York
City (see Imes 12 and 13 of Table 2) While

14 For a complete descnpuon of the adjustment
process, see the appendix to "Rev1s10n of Money Stock
Measures," Federal Reserve Bulletin (February 1973),
pp 66-69


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Federal Reserve Bank of St. Louis

each mstitution accounts for a relatively small
port10n of the total money stock, their deposittype habihtles are mdistmgUishable from demand deposit habihues of commercial banks
and therefore rightly belong m an aggregate
U S money stock measure 15 The deposit-type
habihties of several of the remammg mstltuuons have been folded mto the money stock
measures smce 1970 As each mst1tut1on was
folded m, estlmates of money stock deposits
back to 1959 were denved

Deposits of U.S. branches
of foreign banks
Deposits of U S branches of foreign banks
have always been considered part of the U S
money stock Pnor to I 973 these deposits were
mcluded m the nonmember bank estlmates
derived from the call report Like domestic
commercial banks, U S branches of foreign
banks are reqUired to file call reports, but only
twice a year In late 1972, the Board began
to collect smgle-day data from branches each
month In most months, these observatlons
were as of the last Wednesday of the month
In June and December these reports were for
the last day of the month and comcided with
the call report date
Begmnmg m January 1973, smgle-day
monthly data were used to estimate deposits
at U S branches of foreign banks Weekly estimates were denved from straight-lme mterpolations between the smgle-day monthly data
In Apnl 1975, the Board began to collect
daily data on deposits from branches of foreign banks located m New York City Smee
then these daily data have been used to measure the contribution to M 1 of demand deposits at US branches of foreign banks
15 Demand deposits of mutual savmgs banks, which
are not mcluded m any of the measures of the money
stock, should also be mcluded m M1 when they are
clearly subject to withdrawal on demand In total, all
mutual savmgs banks reported demand deposit h.tb1h
ties of about $1 b1l110n at the end of 1975 The bulk
of the~e deposits was m escrow accounts, however, and
was not generally subject to withdrawal on demand

Sources of Data and Methods of Construction of the Monetary Aggregates

Mi-type balances of agencies of foreign
banks in New York City
By State law, agencies of foreign banks located m New York City are not permitted to
hold demand deposits However, these mstitutlons have credit habihues to customers'
accounts, which serve the same funct10n as
demand deposits The 1970 rev1S1on of the
money stock measures mcorporated credit habiht1es reported by these mst1tut1ons mto the
money stock
Agencies of foreign banks are reqmred to
file monthly reports with the New York State
Commissioner of Bankmg From early 1970 to
Apnl 1973 these monthly reports were used
to estimate the amount of habihues akm to
the money stock held at U S agencies of foreign banks Pnor to 1970, estimates of such
deposits were denved from end of-year summary tabulations published by the New York
State Commissioner of Bankmg Agam, weekly
observat10ns were denved from 5tra1ght-lme
mterpolations between end-of-year or monthly
smgle-day data Smee M,-type deposits at these
mstitut10ns were relatively small pnor to 1970,
esumatmg errors fo1 this component must
also be small, despite the limited mformauon
available for estimatmg back data
Smee Apnl 1975, agencies of foreign banks
m New York City, hke branches of foreign
banks, have reported data on M 1 -type deposits
on a daily basis These data are currently used
m the construct10n of the money stock measures

M 1-type balances of international
investment corporations
m New York City
Internat10nal mvestment corporat10ns chartered by the State of New York, and located
m New York City, also hold Mctype balances
to the account of customers that are mcluded
m the money stock measures Such balances
at these mstitutlons, only about $800 million
at the end of 1975, can be used m the same
manner as demand deposits at other mstitu-


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Federal Reserve Bank of St. Louis

127

t10ns and thus belong m an aggregate money
stock measure Balances at these mst1tut1ons
were first mcluded m the money stock m February 1973 Histoncal data were estimated
based on data denved from rep01ts of the New
York State Comm1ss10ner Qf Bankmg From
November 1972 to Apnl 1975, M 1 -type deposits of foreign mvestment corporations were
estimated based on monthly smgle-day data
similar to those i eported by agencies and
branches of foreign banks Smee Apnl 1975,
foreign mvestment corporations have reported
daily data to the New York Federal Reserve
Bank, which are currently used m the construction of the money stock senes

Deposits due to foreign offecial accounts
at Federal Reserve Banks
Smee 1962, deposits due to foreign official
accounts at Federal Reserve Banks (that is,
due to foreign governments, central banks,
,md mternattonal mstituuons) have been mcluded m M 1 The reason for the mclus10n
was that these deposits "may be used for mvestment or other expenditures m much the
same way as foreign demand balances with
commercial banks " Data for the5e accounts
are reported daily by Federal Reserve Banks
Their mclus10n has httle effect on the change
or the level of the money stock senes

Broader money stock measuresM2 through M.
In the October 1960 descnpuon of the construction of the money stock, the discuss10n
centered entirely on the narrow money stock,
M 1 There was an oblique reference to the fact
that "other financial mstruments perform m
varymg degrees some of the funct10ns of
money, particularly the store-of-value funct10n, but no other mstrument peiforms all of
[the funct10ns]" As our financial system
changes, new mstruments such as NOW (negotiable orders of withdrawal) accounts, telephomc transfer of funds, overdraft arrangements, and negotiable certificates of deposit

lmprovmg the Monetary Aggregates Staff Papers

128

TABLE 3 Construction of M2 through

M5

Monthly averages m mtlhons of dollars, not seasonally ad.Justed
Line, item

Money stock, Mi
Time and savmgs deposits at member banks
Time and savmgs deposits at nonmember banks

2
3

Plus

4

Less

5
6

7
8
9
10
11

Contnbutton,
December 1975

Time deposits due to banks
Time deposits due to US Government

Large denommatton ($100,000 or more) negotiable
CD's
Equals Money stock, M,
Plus
Thnft mstttutton deposits
Equals Money stock, Ma

Money stock, M,
Money stock, M,

(CD's) have blurred the distmctton between
demand deposits and other hqmd assets Consequently, the Board has periodically reviewed
and broadened the money stock concepts it
publishes on a regular basis The first such
broader concept was M 2-M1 plus time and
savmgs deposits at commercial banks other
than negotiable CD's m denommations of
$100,000 or more issued by large weekly reportmg banks Later, M 3 , M 4 , and M 5 were
added Table 3 shows the construction of
these broader money stock measures

Money stock,

M2

The construction of M 2 parallels very closely
the construction of M 1 so far as the member
and nonmember bank components are concerned (see Table 3) In addition to the currency and demand deposit components of M 11
M 2 mcludes time and savmgs deposits at all
commercial banks other than large negotiable
certificates of deposit and all deposits due to
the U S Government and domestic commercial banks The measure mcludes time deposit
habihties of branches of foreign banks but not
time deposits of Edge Act corporations and
other foreign-related mstituttons (There is no
theoretical reason for mcludmg the demand
deposits of these latt~r mstitutions m M 1 and
excludmg them from M 2 Importance and


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303,194
337,186
122,302
9,300
575
83,462
669,345
424,936
1,094,281
752,807
I, 177,743

Source of data
See Table 2
Daily data reported by all member banks
Estimated, based on dally data reported by small member
banks and call report data
Estimated, based on smgle day (Wednesday) data for large
banks and call report data for other banks
Estimated, based on smgle day (Wednesday) data for large
banks and call report data for other banks
Smgle day (Wednesday) data reported by large banks
Smgle day data for last day of month for mutual savmgs
banks, savmgs and loan assocIat1ons, and credit umons
M, plus large denommation negotiable CD's at large banks
M, plus large denommation negotiable CD's at large banks

data availability have been the criteria Historically, these latter mstitut10ns held a relatively small amount of time deposits)
Figures for total time and savmgs deposits
of member banks are available from the Report of Deposits submitted by these banks for
purposes of settmg reserve reqmrements, but
time and savmgs deposits of nonmember banks
must be estimated on the basis of call reports
The method used is similar to that for estimatmg demand deposits at nonmember banks,
that 1s, the rat10 of nonmember time and savmgs deposits to the ttme and savmgs deposits
of smaller member banks is derived from the
call report data, weekly ratios <1re estimated by
straight-lme mterpolation between call report
dates, ad1usted for changes m bank structure,
and these estimated rat10s are apphed to the
weekly time and savmgs deposits reported by
smaller member banks Adjustments to eliminate time and savmgs deposits due to the U S
Government and to domestic commercial
banks are derived from data for weekly reportmg banks and the call report
Negotiable CD's m denommations of
$100,000 or more issued by large weekly reporting banks are deducted from total time
and savmgs deposits m computmg M 2 16 For
16 Smee all large negottable CD's and all time de
posits due to the US Government and to domestic

Sources of Data and Methods of Construction of the Monetary Aggregates

this purpose monthly-average estimates a1e
based on a weighted average of the Wednesday
figures as reported by large weekly reportmg
banks A detailed descript10n of the construction of the historical CD series 1s presented
below

Money stock, Ms
The Ma money stock 1s defined as M 2 plus
deposits at mutual savmgs banks, savmgs and
loan shares, and credit umon shares Because
of the limited data available for these mst1tut10ns, the Ma series 1s published only
monthly
Time and savmgs deposits at mutual savmgs banks are reported as pa1 t of the balance
sheet data accompanymg the monthly "Research Analysis" of the Nat10nal Assoc1at1on of
Mutual Savmgs Banks (NAMSB) 17 These data
are based on a sample of 338 mst1tut10ns of a
total of 470 for the entire mdustry Accordmg
to the NAMSB, the mst1tut10ns m the sample
hold more than 90 per cent of all savmgs bank
deposits The sample estimates geneially are
available 6 to 7 weeks followmg the end of
the month Twice a year, m June and December, the NAMSB collects data from all savmgs
banks and revises the prelimmary numbers for
those months accordmgly Unless June and
December rev1s10ns are large, the first published numbers for other months are not
changed
Total savmgs capital at savmgs and loans
rs taken from a monthly release of the Federal
Home Loan Bank Board (FHLBB), "Selected
Balance Sheet Data, All Operatmg Savmgs and
Loan Associat10ns " These data are estimated
by the FHLBB staff on the basis of smgleday, end-of-month reports from all savmgs
and loan assoc1at1ons msured by the Federal
Savmgs and Loan Insurance Corporation
commercial banks are subtracted from time and savmgs
deposits, some time deposits-large negotiable CD's
issued to the U S Government or other banks-are
deducted twice No estimates of this double deduction
are available, but It 1s thought to be qmte small
11 This total excludes checkmg, club, and school ac
counts Mutual savmgs banks held a total of about
1:,600 mdhon m such accounts m late 1975


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129

Such assoc1at10ns hold about 97 per cent of
all mdustry deposits Usually, prelimmary data
are received with a 4-week lag, and final data
become available I month later
"Credit Umon Stat1st1cs," a monthly release by the Nat10nal Credit Umon Admm1st1at1on (NCUA), rs the source of data on credit
umon shares These data are estimated from
an end-of-month sample of about 6 per cent
of all credit umons, holdmg approximately
30 per cent of the deposits of these mst1tut10ns Figures are generally available with a
I-month lag and are 1ev1sed ammally to mcorporate benchmark data derived from endof-yea1 1eports filed by all operatmg Federal
cred1 t umons
Data on mutual &avmgs banks, Sa\mgs and
loan associat10ns, and credit umons are rep01 ted for a smglc day each month, usually
the last Smee the M 1 and M 2 numbers are
essentially monthly averages, two successive
month-end figures for thrift mst1tut1ons are
averaged m an effort to obtam consistent
series For example, the published figure for
the month of June for the thrift deposits component of M, would be the average of the
end-of-May and end-of-June data reported by
these 111st1tut1ons These "monthly average"
data are then added to M 2 to construct M 3
A techmcal problem arises as the money
stock measures are expanded to mclude the
hab1ht1es of mutual savmgs banks, savmgs
and loans, and credit umons Ideally, one
would hke to consolidate the hab1lit1es of
these 111st1tut10ns with those of commercial
banks For example, when the deposrt hab1ht1es of savmgs and loan assoc1at1ons are added
to M 2 , the deposit hab1ht1es of banks due to
savmgs and loans should be deducted to net
out mtermst1tut10n deposits The same rs true
for mutual savmgs banks and credit umons
Such consohdat1on already exists with the
nettmg of mte1 bank demand deposits m the
construction of M 1 Unfortunately, because of
the way the data on thrift mst1tut1on deposits
are collected and reported, such consohdat1on
rs, m most cases, qmte difficult and reqmres
add1t10nal data and a great deal of estimation

130

lmprovmg the Monetary Aggregates Staff Papers

Thus the Af 3 measure 1s essentially a combination of the liabilities of banks and thrift
mst1tut1ons rather than a consolidation

Negotiable certificates of deposit
Negotiable time certificates of deposit became important as a money market mstrument
m early 1961 At that time several large money
market banks m New York City began to offer
CD's m readily marketable form to their corporate depositors At about the same time, securities firms announced that they stood ready
to buy and sell CD's m open tradmg The
practice was soon taken up by other banks
and other dealers
In early 1964 the Federal Reserve System
began to gather weekly data on the volume of
negotiable CD's m denommat10ns of $100,000
or more outstandmg at large weekly reportmg
banks The panel of weekly reportmg banks
has been revised once, at the begmnmg of
July 1965
The resultmg break m the senes was relatively large The old panel of banks reported
outstandmg CD's of $15,203 million while the
new panel of banks reported outstandmg CD's
of $15,587 million, a difference of about 2½
per cent To avoid a break m series, and to
make the prev10us data comparable with the
new, the reported weekly data for the penod
January 1964 through June 1965 were mcreased by 2½ per cent
Data on negotiable CD's pnor to January
1964 were estimated based on a survey conducted m late I 962 and early 1963 The survey
showed that at the end of 1960 large-denom1nat10n CD's ($100,000 or more) issued by
banks totaled about $800 million By the end
of 1961 the total had nsen to $2 9 b1lhon, and
by late 1962 1t had reached $5 6 billion, a
sixfold mcrease m JUSt 2 years These totals
mcluded all large CD's, negotiable and nonnegotiable
Several assumpt10ns were made m the process of estlmatmg large negotiable CD's outstandmg for the penod 1961 to 1963 The
first was that no negotrable CD's were outstandmg at the end of 1960 Second, the $830


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million of large nonnegotiable CD's outstandmg at the end of 1960 were replaced by negotiable CD's durmg 1961 on a stra1ght-lme path
Third, the growth m total CD's, negotiable
and nonnegouable, from $800 milhon to $2 9
b1lhon m 1961 was estimated by straight-lme
mterpolauon of the log of the begmnmg and
endmg values Thus the week-to-week dollar
mcreases were greater at the end of the period
than at the begmnmg The difference between
the estimated total series and the estimated
nonnegotiable CD series was used as the estimate of large negotiable CD's for the year
1961 For 1962 and 1963, estimates were made
usmg stra1ght-lme mterpolatron between the
logs of the 1961, 1962, and 1963 year-end
values, $2 9 b1lhon, $5 6 b1lhon, and $9 8 billion, respectively Weekly observatrons were
derived, and monthly estimates were based on
the proratrons of the weekly data
Smee 1963, when Wednesday observations
became available, they have been averaged to
obtam a rough proxy for the weekly-average
level of CD's consistent with the weeklyaverage measurement of M 1 and M 2 Estimates
of the monthly-average level of large negotiable CD's are derived from prorat10n of estimated weekly-average levels 18

Money stock, M4 and Ms
The broader money stock measure, Jv1. 4, 1s
derived by addmg CD's, derived as described
above, to M 2 This measure corresponds
10ughly to all private deposits at commercial
banks plus currency m circulat10n It excludes
US Government deposits and net mterbank
deposits The M 4 measure 1s published on
both a monthly-average and weekly-average
basis
1s It should be noted that large denommat10n non
negotiable CD's serve the same purpose as negotlable
CD's In addilion, lt is not difficult for large banks to
convert a nonnegot1able CD to a negollable mstrument
Thus M 2 might logically be computed by deductmg
all large time deposits from total time and savmgs
deposits 1f h1stoncal data were available It is only
recently, however, that the Board has collected any
data on total large time deposits In December 1975
large lime deposits at commerc1al banks totaled about
$158 I billion and large negotiable CD's totaled about
~83 5 billion

Sources of Data and Methods of Construction of the Monetary Aggregates

The M 5 measure, the broadest one published by the Board, 1s derived by addmg
CD's to the Ms measure It mcludes not only
the private deposits of all commercial banks
but also the deposits of thrift mstitutions
(mutual savmgs banks, savmgs and loan assoc1at10ns, and credit umons) Like Ms, M 5 1s
published only as a monthly average

Seasonal adjustment of the monetary
aggregates
The measurement of the seasonal component 1n any economic time series 1s difficult,
and this 1s especially true of the money stock
The money stock 1s mfluenced not only by
normal seasonal swmgs but by other economic
factors The irregular component of the series
H large and highly volatile Moreover, changes
m the financial system, such as shifts m tax
collectron schedules, m disbursement dates
for large government transfer payments, and
m the form m which the public holds Its
hqmd assets ,tffect the seasonal pattern over
time Some of these changes are abrupt and
new seasonal patterns develop qmckly, but a
few years of data are reqmred to establish the
new seasonal pattern for most changes Some of
the changes evolve over a considerable period,
1 esultmg m contmuously sluftmg seasonal factors that also are measured only with a lag
In some mstances, several factors may be workmg simultaneously to change the seasonal
pattern, some havmg cumulative effects and
others offsettmg one another with unpredictable net impacts The existence of these
changmg mfluences makes measurement of
5easonal patterns m the money stock imprense and subJect to revisron, especially for the
most recent years
The various components of the money stock
-currency, dem,md deposits, time and savmgs
deposits other than large negotiable CD's,
large negotiable CD's, mutual savmgs bank
deposits, savmgs and loan shares, and credit
umon shares-are all seasonally ad3usted separately The published adjusted measures are
aggregates of these seasonally adjusted com


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131

ponents Most of the components are published along with the aggregate
All of the monthly seasonally adjusted series
are denved usmg the Census Bureau's X-11
seasonal ad3ustment method 19 A multiplicative movmg-seasonal variant of this program
1s used to update seasonal factors each year,
and the results are reviewed and m some mstances modified Judgmentally m an effort to
take account of known factors affectmg seasonals, random disturbances, or policy-mduced
changes m the series Usually the published
senes 1s close to the X-11 results
For all scnes the monthly seasonal pattern
1s denved fii st and the weekly seasonal factors
,ue forced to agree with the monthly seasonal
factors In other words, the weighted averages
of the weekly seasonal factors for any month
must equal the monthly seasonal factor, withm
a small range of tolerance Experience suggests
that the monthly seasonal patterns are more
5t<1ble than the weekly ones, because they are
mfluenced less by irregular movements m the
data and because factors causmg shifts m
mtramonthly patterns tend to average out over
the month While there 1s always considerable
uncertamty about the validity of current
weekly seasonal factors, they are anchored to
the more stable monthly seasonal factors, and
the seasonally ad1usted weekly and monthly
data will average about the same levels over
a penod of several weeks
The Board's weekly seasonal adJustment
program is es5entially a ratio method Seasonally ad1usted monthly data are centered
at midmonth, and estimates of seasonally adJusted weekly values are generated by a
5tra1ght-lme mtei polatron between these
values The unadJusted weekly data are divided by these estimated adJusted values to
obtam an estimate of the seasonal irregular
component of the senes The mtramonthly
pattern of these iatios is smoothed, first by a
3 x 3 movmg average of the seasonal-irregular
1 atros calculated for all the weekly obserrn For a desc11pllon of this program, see "The X-11
Vanant of the Census Method II Seasonal Adjustment
P10gram," Bureau of the Census Techmcal Paper 15
(Government Pnntmg Office, 1965)

132

Improving the Monetary Aggregates Staff Papers

vatlons over recent years, and then by a Judgmental modification to take account of any
apparent shifts m the mtramonthly pattern
Differences between the predetermmed
monthly factors and the average of weekly
factors are distributed to the weekly seasonal
factors so that the latter agree on average with
the former
After deriving unadJusted aggregates for the
currency and demand deposits component of
M 11 each component series is seasonally adJUsted separately Seasonal factors for currency
and demand deposits are computed and reviewed as described above The ad1usted series
are then aggregated to derive adJusted M 1 All
of the raw data, whether or not adJusted,
are estimated to millions of dollars, and the
aggregation of seasonally ad1usted data is also
done at this level However, these estimates
are not considered accurate to the nearest milhon so, for publication, all series are rounded
to the nearest tenth of a billion dollars Thus
rounding differences frequently appear between the published series on components
and on aggregates
Derivation of seasonally adJusted time and
savings deposits m M 2 is more complex Fust,
large negotiable CD's are subtracted from total
time and savings deposits at all member banks
and the residual senes on member bank time
and savmgs deposits is seasonally adjusted
Second, seasonal factors are derived for ad1usting total time and savings deposits at small
member banks A seasonally adjusted senes
on total time and savings deposits for nonmember banks is derived by applymg the expansion factors described above to total time
and savings deposits at small member banks,
seasonally ad1usted Next, the seasonally adJusted senes on total time and savings deposits
less negotiable CD's at member banks is aggregated with the seasonally adJusted total time
and savings deposits of nonmember banks
From this aggregate, time and savings deposits
due to the U S Government and domestic
commercial banks, not seasonally adjusted, are
subtracted (There is no measurable seasonal
m these deposits) The result is an adJusted
time and savings deposits component of M 2


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that parallels the adJusted demand deposits
component of M 1 in excluding deposits due to
the U S Government and other commercial
banks Seasonally adjusted M 2 is the aggregate
of seasonally ad1usted currency, demand deposits, and time and savings deposits other
than large negotiable CD's
Mutual savmgs bank deposits, savings and
loan association shares, and credit union
shares-components of Ma-are also seasonally
adjusted by the Board First, the reported
end-of-month data for each series are seasonally adJusted These numbers are then averaged, as explamed above, to approximate a
monthly-average series, which is added to seasonally adJusted M 2 to derive Ma Because
weekly data are not available for thnft deposits, only a monthly-average senes on Ma
can be constructed
Large negotiable CD's are also seasonally
ad1usted, both monthly and weekly Seasonal
factors are especially difficult to denve for
this senes, however, because of the large trend
and cyclical components Durmg the early
and mid-1960's, when CD's first became an
important financial asset, the senes was highly
dommated by trend In the late l 960's and
early 1970's, CD's-because of Regulation Q
ceilings on mterest rates-were heavily mfluenced by monetary policy and the level of
market mterest rates These two factors are
extremely difficult to untangle m derivmg
seasonal factors for the senes The seasonal
factors from the basic X-11 program are used
with only mmor Judgmental review Seasonally adjusted, monthly-average CD's are aggregated with ad1usted M 2 and M 3 to denve
ad1usted monthly-average M 4 and Ms, respectively Seasonally adJusted weekly-average CD's
are aggregated with adjusted M 2 to denve
adjusted weekly-average M 4 Weekly-average
Ms is not available

Conclusion
The measures of monetary aggregates currently constructed and published by the Board
are derived from a wide variety of data
sources The data have been revised and re-

Sources of Data and Methods of Construction of the Monetary Aggregates

fined several times over the yea1 s, as new data
sources developed or as measurement problems reqmred the collect10n of additional
data Nevertheless, all of the sen es on the
money stock are still only approximations of
the conceptual, holder-record measures mtended Problems of double countmg, inconsistency m accountmg entnes, dnd smgle-day


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Federal Reserve Bank of St. Louis

133

versus daily-average data all have an impact on
the accuracy of the senes The longer the time
span, the less senous are such data problems
However, those who use the money stock
measures for short-run analysis should be
,Lware of the extent of est1mat10n 1eqmred m
the construction of the senes and of the shortrun volatility mhe1ent m the clat.a


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135

An Alternative Method for Calculating M 1
Anton S Nissen and Darwin L Beck

This paper revises and updates the study
originally prepared for the Advisory Committee and contains information not available to
the Committee when it made its report
The Advisory Committee on Monetary Statistics mcluded as one of its recommendations
a new, simpler process of handlmg mterbank deposits and cash items m the process
of collection when consolidatmg data from
different financial mstitut10ns, m order to
ehmmate certam biases and to obtam a more
accurate measure of M 1 and other aggregates " 1
The Committee made this a tentative recommendation because of large statistical differences between a prehmmary construct of the
new series and the money stock then bemg
published by the Federal Reserve The Committee also recommended that the Board staff
mvestigate the new series further and resolve
the differences between the two measures The
Committee assumed that these differences
would be resolved and that the new method,
while still not perfect, would be a more accurate measure of the actual money stock
Smee the Committee report, the staff of the
Federal Reserve has made an mtensive effort
to reconcile the differences between the two
series This paper presents the mformation
available to the Committee at the time of its
report and mcorporates additional mformat10n collected by the staff smce the report was
published First, mmor biases m the published

money stock measure have been uncovered
These biases were corrected m 1976, and at
the same time, the staff improved the miual
estimates of the alternative money stock
measure 2
For contmmty, data on the current and
alternative money stock measures and mterbank deposits as they were origmally made
available to the Committee are presented m
Tables l and 2 These tables also show sources
of subsequent rev1S1ons to the series, the final
alternative series, and the money stock series
now bemg published The differences between
the two series are described m this paper
Information available at the time of the
Committee rtport md1cated that, despite the
large discrepancy between the two series, the
alternative method of constructmg the money
stock was an improvement over the current
method 3 Assumptions were that further re
search would explam the differences and that
the alternative measure would prove to be
superior Further research has not resolved
the differences, however, nor 1s 1t clear which
method of constructmg the money stock IS
superior, both measures can be affected by
changes m bankmg regulations, and both can
be affected by changes m accountmg procedures
The problem 1s one that 1s mherent m manv
economic time series Often, economic series
derived from different data sources provide
different measures of the same variable There

NoTE-Anton S Nissen 1s a member of the staff of
the Federal Reserve Bank of New York and Darwm L
Beck 1s on the staff of the Board's D1v1S1on of Research
and Statislics
1 Improving the Monetary Aggregates Report of the
Advisory Committee on Monetary Statistics (Board of
Governors of the Federal Reserve ~System, 1976), p 3

2 "Rev1S1on of Money Stock Measures," Federal Re
serve Bulletin, vol 62 (February 1976), pp 82-87 For
a detailed descnpl!on of these revmons, see the ap
pend1x
3 In December 1974 the level of the current money
stock measure was $8 0 b1lhon higher than the level
of the alternal!ve measure on a monthly average basis,
and about i5 5 b1lhon on an end of month basis


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Federal Reserve Bank of St. Louis

136

Improving the Monetary Aggregates Staff Papers

TABLE 1. Comparison of Alternative and Current M1 Measures
In millions of dollars, not seasonally ad.Justed
Ava!lable to the Advtsory Committee
on Monetary Statistics
Year-end

Alternative
M1

Current M,

Alternative
M1less
current M1

(I)

(2)
147,771
148,767
154,553
156,984
161,241
172,218
180,581
185,756
198,545
214,929
222,869
234,067
248,164
272,492
289,834
301,321

(3)
1,016
966
1,343
788
1,057
127
320
718
1,027
552
508
-4,579
-3,396
-5,892
-6,250
-6,504

1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
19752
19762

148,787
149,733
155,896
157,772
162,298
172,345
180,901
186,474
199,572
215,481
223,377
229,488
244,768
266,600
283,584
294,817

Adjustment
To alternative
M1for
mapprol?natc
Regulation J
adjustment

To current
M, for
reesumat1on
of cash
items bias

Adjusted
alternative
M,

(5)

(4)
-500

(6)

148,287
149,133
155,196
156,972
161,398
171,345
179,801
185,274
198,272
214,081
221,877
227,888
243,068
266,600
283,584
294,817
309,349
326,520

-600
-700

-800
-900
-1,000
-1,100
-1,200
-1,300
-1,400
-1,500
-1,600
-1,700

800
900
-2,600
-2,600
-1,600
-500
-1,000

Adjusted
current M11

Adjusted
alternative
M1 less
current M1

(7)
147,771
148,767
154,553
156,984
161,241
172,218
180,581
185,756
198,545
215,729
223,769
231,467
245,564
270,892
289,334
300,321
313,913
332,660

(8)
516
366
643
-12
157
-873
-780
-482
-273
-1,648
-1,892
-3,579
-2,496
-4,292
-5,750
-5,504
-4,564
-6,140

'See footnote 8 on p 138

•As revtsed and pubhshed m early 1976

a1 e, for example, statistical discrepancies between gross n<1t1onal product and national mcome accounts, between household and manhour employment surveys, and between different measures of the balance of payments
A similar unresolved stausucal discrepancy
appears to exist between the current and
alternative money stock senes
The currently pubhshed money stock senes

has been ad1usted £01 breaks associated with
regulatory changes and for ma1or biases assonated with convcnt10nal bank accountmg
The alternative money stock has also been
adJusted for I cgul<1tory changes, and 1t 1s not
distorted by accountmg procedures as 1s the
current money stock Further mvest1gat1on
suggests, however, that the alternative money
5tock measm e 1s affected by other data prob-

TABLE 2 Interbank Demand Deposits and Cash-Items Bias AdJustment
In milhons of dollars, not seasonally ad1usted
Available to the Advisory Committee
on Monetary Statistics
Deposits

Year end

I

I

Due to Due from Due to
banks
banks du!el:om
(1)

1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
19751
19761

13,445
14,882
15,900
14,058
13,460
15,718
16,016
17,195
19,029
21,566
23,651
26,713
28,357
30,616
32,630
41,089

(2)
12,429
13,916
14,473
13 230
12,403
15,153
15,519
16,416
18,002
20,208
21,675
24,932
26,048
33,424
35,932
43,915

1 See footnote 8 on p 138


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(3)
1,016
966
1,427
828
1,057
565
497
779
1,027
1,358
1,976
1,781
2,309
-2,808
-3,302
-2,826

To due
Adjust
from
ment Net mterbank less to remove
for
cash cash-items Regulation
items
bias
J d1scon
ttnmty
bias
(4)
84
40
438
177
61
806
1,468
6,360
5,705
3,084
2,948
3,678

(5)
1,016
966
1,343
788
1,057
127
320
718
1,027
552
508
-4,579
-3,396
-5,892
-6,250
-6,504

After adjustment for Regulation J and
reesttmatton or cash items bias

Adjustments

(6)

500
600
700
800
900
1,000
I, 100
1,200
1 300
1,400
1,500
1,600
1,700

To
cashitems
bias for
re esu
matton
(7)

800
900
-2,600
-2,600
-1,600
-500
-1,000

Deposits

I

Due to Due from
banks
banks
(8)
13,445
14,882
15,900
14,058
13,460
15,718
16,016
17,195
19,029
21,566
23,651
26,713
28,357
30,616
32,630
41 089
38,625
41,033

(9)
12 929
14,516
15,173
14,030
13,303
16,153
16,619
17,616
19,302
21,608
23,175
26,532
27,748
33,424
35,932
43,915
39,433
42,350

I

Due to
du!?:om
(10)
516
366
727
28
157
-435
-603
-421
-273
-42
476
181
609
-2,808
-3,302
-2,826
-808
-1,317

Adjustment Net mterbank less
for
cash- cash items
items
bias
bias
(II)

84
40
438
177
61
1,606
2,368
3,760
3,105
1,484
2,448
2,678
3,756
4,823

(12)
516
366
643
-12
157
-873
-780
-482
-273
-1,648
-1,892
-3,579
-2,496
-4,292
-5, 750
-5,504
-4,564
-6, 140

An Alternative Method for Calculating M 1

lems The lack of umformity among banks m
accountmg for mterbank deposits causes d1stort10ns m the accounts that reflect demand
deposits due to and due from banks, data senes
that are important m the construct10n of the
alternative money stock For example, changes
m accountmg practice associated with the 1mplementat10n of the Paper Exchange Payments
System (PEPS) m 1972 are believed to have
caused a serious d1stort1on m the alternative
money stock measure

Construction of the alternative series
The narrowly defined money stock, M 1 , has
two ma1or components-demand deposits adJUSted and currency m circulat10n outside the
Treasury, the Federal Reserve, and commercial banks 4 The first component 1s mtended
to measure pnmanly the net demand deposit
hab1ht1es of commercial banks m the Umted
States to both domestic private nonbank customers and to all foreign customers, bank and
nonbank At present, this component 1s calculated by subtractmg cash items m the process
of collect10n, as shown on the books of commercial banks, from so-called "other demand
deposits," which consist of demand deposit
hab1ht1es due to depositors other than the
U S Government and banks 5 However, a number of stat1st1cal problems m this basic procedure cause biases m the senes When possible, adJustments have been made to correct
for such bias, but for the purposes of this
paper, three data problems are important
First, cash items m the process of collect1on
mclude items drawn agamst accounts outside
of other demand deposits Second, some checks
drawn agamst accounts recorded m other
demand deposits and still m the process of
4 Smee the currency component 1s common to the
two money stock measures, 1t 1s not discussed m this
paper
5 In add1t10n to cash items m the process of collection, Federal Reserve float also 1s subtracted Cash
items m the process of collection represent pnmanly
checks m the process of collection for which the collectmg agent has not yet granted credit Federal Reserve
float also represents checks still m the process of collect10n, but for which the Federal Reserve has passed
credit even though 1t has not yet collected from the
banks on which the checks were drawn


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137

collection are not reported m cash items m
the process of collect10n And third, other
demand deposits, as used m the money stock
calculauons, do not mclude all deposits due
to money stock holders
The first problem-cash Items drawn agamst
deposits that are not mcluded m the money
stock-anses m connection with a large volume of checks drawn agamst due-to-banks accounts by agencies and branches of foreign
banks, foreign bank-owned mvestment compames engaged m bankmg, and Edge Act corporat10ns m New York City 6 Most checks are
drawn m the course of transferrmg funds related to mternauonal financial transact10ns
and typically are deposited m New York City
commercial banks on the day they are drawn
The New York City banks carry the checks deposited as cash Items m the process of collect1on, a procedure that results m an overstatement of cash Items for money stock purposes
and a consequent understatement of M 1 This
d1stort10n was first discovered early m 1970
Smee late that year, data have been collected
on the amounts of outstandmg checks drawn
by the agencies and branches of foreign banks,
foreign bank-owned mvestment compames engaged m bankmg, and Edge Act corporat10ns
m New York and have been used to correct for
this so-called "cash-Items bias " 7
The second problem 1s that many banks forward checks to correspondent banks for collect10n and immediately post them as demand
deposits due from banks rather than as cash
items Thus, other things being constant, the
amount of cash Items deducted m calculatmg
6 Other items mcluded m cdsh Items-such as checks
drawn on US Government accounts, food stamps,
redeemed savmgs bonds, credit card slips-also violate
the assm;npt1on Studies conducted by the Federal Reserve md1cate that the problem of checks drawn on U S
Government accounts 1s small, but no data are available
on the size of the other problems D1scuss1ons with
banks md1cate that 1t would be virtually 1mposs1ble to
have these items recorded m separate accounts
7 While discovered m 1970, the cash-items bias first
developed on a much smaller basis around the m1dl 960's Smee actual data on outstandmg checks were
not available until the late 1960's, adJustments to account for the earlier bias were estimated as descnbed
m the Federal Reseroe Bulletin, vol 56 (December
1970), pp 892-93

138

lmprovmg the Monetary Aggregates Staff Papers

demand deposits adjusted is smaller than it
should be (and the amount of demand deposits adjusted is larger) until the checks are
received and either charged directly agamst
a deposit dccount by the correspondent or
entered on its balance sheet as cash items and
forwarded for collection The resultmg overstatement of M 1 -referred to as the "duefrom-banks bias"-was recogmzed by the Federal Reserve System committee that had developed the money stock measure m the late
1950's However, smce the overstatement was
<tssumed to be relatively small on average
and to change relatively slowly over time, the
basic money stock calculation has not been
adjusted to correct for this bias
As mdicated, the tlurd problem is th<tt other
demand deposits do not mclude all relevant
money stock deposits In particular, this deposit category does not mclude demand deposits due to foreign commercial banks or
domestic mutual savmgs banks, so an adjustment has to be made to "other deposits" to
mclude the deposits due to these mstitutions
The only data av<til<tble upon which to base
such adjustments are smgle-day, Wednesdayas opposed to daily-average-data reported by
weekly reportmg banks and call report data
<tva1lable four times a year These estimated
data are mcorporated mto the money stock
calculations
The three problems were considered at an
early meetmg of the Advisory Committee on
Monetary Statistics, and an alternative method
for calculatmg the money stock was suggested
Briefly, the alternative was to mclude, along
with other demand deposits, all demand deposits due to banks (foreign and domestic)
,md to deduct, along with cash items m the
process of collection, demand deposits due
from domestic banks m computmg the demand deposits adjusted component of M 1
The alternative method was believed to have
three advantages First, it would ehmmate the
cash items bias and the consequent need for
correction of data to adjust for that bias In
this mstance, the deposits due to banks agamst
which the currently mappropriate cash items
are drawn would be mcluded m the deposits


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total from which the cash Items would be deducted Second, the alternative method would
ehmmate the due-from-banks bias because, by
deductmg both cash Items and demand deposits due from banks, the use of the due-from
<tccount by b<tnks forwardmg checks to correspondents for collection no longer would
result m the bias Fm<tlly, Wednesday and
call report data would no longer have to be
used to estimate demand deposits due to
mutual savmgs banks and foreign commercial
b<tnks, smce such deposits would be mcluded
on a daily-average basis as a part of demand
deposits due to banks A prion the level of
the money stock senes constructed by the alternative method w.15 expected to be slightly
lower than the present senes, reflectmg ehminat10n of the due-from-banks bias, but changes
m the two senes over any penod of timeexcept perhaps short ones-would be essentially the same
In 1esponse to the Committee's suggestion,
an alternative money stock senes was con5tructed on a monthly-average basis for the
1968-74 penod, and on a smgle-day basis,
December 31, for the 1959-74 penod (Table
I) 8 Comparison of the two revised senes for
December 31 (columns 6 and 7) mdicated that
a pnon expectat10ns were not borne out 9 As
can he seen m column 8 of Table l, the differences between the currently published and
the alternative money stock were contrary to
expectations m the early years and much
larger than expected m the later years Moreover, large discontmmties appear m 1968,
1970, and 1972
A further effort was made to explam these
differences Essentially, the procedure used to
calculate the alternative money stock series was
to add demand deposits due to domestic banks
to the current money stock series, and to subtract both demand deposits due from banks
and the adjustment for cash-items bias from It
s Call report data for December 31, 1975 and 1976,
available smce the Committee completed Its report, are
also shown
e The focus was on the December 31 senes smce the
monthly-average senes contam large estimated components for nonmember banks

An Alternative Method for Calculating M 1

This procedure 1s eqmvalent to addmg net
interbank deposits and subtracting the adJustment for cash-items bias In attempting to explain the unexpected differences between the
two senes, therefore, attention was concentrated on the behavior of net interbank deposits and the adJustment for cash-items bias Data
on net interbank deposits and the adJustment,
as ongmally presented to the Committee and
as later revised, are shown m Table 2

The 1959-67 period
The 1959-67 penod presents a mixed picture, but 1f allowance 1s made for the vagaries
of smgle-day data and the uncertainty of h1stoncal adJustment for the alternative measure, the currently published and the revised
alternative money stock senes track about as
expected (column 8, Table 1) Durmg this
penod, the levels of the two senes differ by
less than $1 0 billion and annual growth rates
differ, on average, by less than ¼ of a percentage pomt Nevertheless, there are some
unexpected differences between the two senes
Smee the adJustment for cash-items bias was
negligible durmg most of this penod, the mterbank deposits must be responsible for the
difference
The alternative money stock exceeded the
current money stock early m the 1959-67
penod (Table I), reflecting an excess of deposits due to banks over those due from banks
and contrad1ctmg the expectation of a bias m
the current money stock measure ansmg 1n
deposits due from banks
As noted earlier, the poss1b1lity of a duefrom-banks bias m the current money stock
senes had been suggested by a System committee m the late 1950's 10 The committee
The due-from banks bias, 1t will be recalled, was
hypothesized to anse because some banks forwarded
checks to correspondents for collection and wrote up
immediately the1r deposits due from banks Because
of unavoidable lags m transportmg such checks to
correspondents and m postmg by the correspondent
banks to cash items m the process of collection and
deposits due to banks, the cash items deduction from
money stock deposits was thought to be understated,
the money stock to be overstated, and deposits due
from banks to exceed deposits due to banks
10


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139

noted that, at least smce the m1d-1950's, deposits due to banks had exceeded deposits due
from banks by almost $1 billion The committee report hypothesized that some banks
did not post checks forwarded to correspondents for collection immediately to a due-frombanks account as had been assumed m adJUstmg for the due-from-banks bias Rather,
the committee suggested, the checks were
posted to the cash-items account and held
there until not1ficat10n was received from the
correspondent that they had been collected,
then the cash-items account was reduced and
the due-from-banks account was increased
Smee the checks bemg collected by correspondent banks appeared on the correspondent's books durmg the collect10n penod as
deposits due to banks, this phenomenon was
believed to explam the excess, on balance,
of due-to accounts over due-from accounts
Wlule this explanation appears plausible,
there 1s no practical way to check its h1stoncal validity
If this explanat10n 1s correct for the early
penod, the data md1cate that around 1964
either a shift m accounting practices or some
other structural change caused deposits due
from banks to grow more rapidly than deposits
due to banks From 1964 to 1968, deposits due
from banks consistently exceeded those due to
banks, but generally by ever-smaller amounts
(column 10, Table 2) Dunng this penod there
were no known changes m accountmg practices
or m structure that would explam the shift m
the relationship between deposits due to and
deposits clue from banks Thus the data do not
establish the supenonty of either senes over
tlus penod

The 1968-71 period
The 1968-71 penocl was a time of rapid
expans10n m transfers of funds through the
New York Clearing House by agencies and
branches of foreign banks, foreign bank-owned
investment compames engaged m banking,
and Edge Act corporat10ns located m New
York City These transfers of funds were related
pnmanly to expanding Euro-dollar transac-

140

t10ns As column 11 of Table 2 shows, the
adJustment for cash-items bias, a proxy measure for the volume of these transfers, 1s estimated to have mcreased rapidly dunng this
period In makmg transfers of funds through
the Clearing House, the vanous mst1tut1ons
mvolved typically would make deposits m
New York City correspondent banks, thus
leadmg to mcreases m cash items m the process of collection and demand deposits due to
banks on the books of those correspondents
Other tlungs constant, one would expect an
mcrease m the excess of deposits due from
banks over deposits due to banks that would
roughly equal the mcrease m the adJustment
for cash-items bias However, accordmg to the
data available, this did not happen
Over the 1968-71 penod, the adJustment for
cash-items bias mcreased nearly $3 2 billion,
while net mterbank deposits (deposits due to
banks less those due from banks) mcreased
less than $1 0 billion This discrepancy accounts for the sharp rise m the difference
between the current and the alternative series
From 1959 to 1967, deposits due to banks and
those due from banks mcreased, on average,
$700 million and $800 million, respectively,
per year From 1968 to 1971, these yearly mrreases rose to $2 4 b1ll10n and $2 1 billion,
1 espect1vely The mcreased growth m the deposits due to banks 1s explamed m part by
the mcreases m transfers of funds through the
Clearmg House by foreign-related mst1tut1ons
m New York City What 1s unexplamed, and
what ultimately causes the differences m the
money stock series, 1s the acceleration m the
growth of deposits due from banks Could
tlus growth reflect an mcrease m the so-called
due-from-banks bias? That 1s, were more banks
usmg a due-from-banks account rather than a
cash-items account when forwardmg checks for
collect10n? If so, the alternative senes might be
a better measure of the money stock Smee
hanks had no known reason to shift their
accountmg practices at this particular time,
1t 1s assumed that some other, unknown, factor
accounted for the change Whatever the cause,
there appears to be a break m the alternative
money stock measure, and given the sIZe of the


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Improvmg the Monetary Aggregates Staff Papers

change, 1t most probably reflects bias m the
series either before or after the change
During the 1968-71 period the alternative
money stock measure would not have been
so susceptible to the problem of cash-items bias
as was the current money stock The cashitems bias m the current money stock was,
however, 1dent1fied and corrected, albeit with
a lag It 1s not certam that the alternative
series was affected over this period by a bias
from deposits due from banks, but because of
the peculiar and unexplamed movement m the
deposits due from banks, that poss1b1hty cannot be d1sm1ssed At this pomt m time, 1£ there
1s a bias m the alternative measure, 1t can
be neither identified nor corrected Thus, for
the 1968-71 period, as for the 1959-67 period,
neither money stock measure 1s clearly superior to the other

The 1972-74 period
In 1972 the relat1onsh1p between demand
deposits due to banks and demand deposits
due from banks slufted sharply, by nearly $3 5
billion, and then remamed roughly constant
through the end of 1974 (Table 2, column
10) Whereas prior to 1972 demand deposlt5
due to banks had exceeded demand deposits
due from banks, at the end of 1972 deposits
due from banks exceeded those due to bank5
by about $2 8 billion Of that amount, about
'$1 7 billion (-$2 0 billion m due to, and
-$0 3 billion m due from) reflected the change
m the Federal Reserve's Regulat10n J m November 1972 11 When Regulation J was
changed, banks had to remit funds to the
Federal Reserve on the day checks presented
by the Federal Re5erve were received (Pnor
to the change, banks did not remit funds until
one busmess day after receipt of the checks
from the Federal Reserve ) Member banks actmg as correspondents for nonmember banks
that did not have a deposit account with the
Federal Reserve also were requued to remit
11 For a more detailed d1scuss1on of the impact of
the change m Regulation J on the current and alternative money stock, see the appendix

An Alternative Method for Calculating M 1

funds one day earlier for checks presented for
collection by the Federal Reserve to nonmember banks Because the nonmember banks for
the most part had already been accountmg
for deposits due from banks one day before
actual remittance to the Federal Reserve by
their correspondents, when payment was
speeded up a day the due-from accounts at these
banks were mostly unaffected, whereas the
due-to accounts at the correspondent banks
declmed
The source of the remammg part of the shift
m the differential between due-to and due-from
accounts m 1972 1s not certam However, It
seems to stem from the mtroduction by the
New York Clearmg House m February of that
year of the Paper Exchange Payments System
(PEPS) PEPS was an arrangement under which
a large number of agencies and branches of
foreign banks, foreign bank-owned mvestment
compames engaged m bankmg, and Edge Act
corporations located m New York C1ty met
at the New York Clearmg House each day to
exchange debit and credit advices arismg from
transfers of mternational-transaction funds
The purpose of PEPS was to obviate the need
to receive and deposit each day large volumes
of checks drawn on (or payable through) member correspondents of the New York Clearmg
House Although the accounts reflectmg deposits due from and due to banks at the Clearmg
House banks were affected by PEPS, any specific accountmg conventions that would have
led to the change m the due-to-due-from relationship have not been 1dent1fied Thus, the
1mt1ation of PEPS does not necessarily account
for the remamder of the 1972 shift The s1m1lar
timmg of these events, however, 1s difficult to
ignore and gives credence to the susp1c1on
that the explanation hes m PEPS
Both the current and alternative series were
adJusted to avmd a break m series when Regulation J was changed m late 1972 Thus, assummg that the ad1ustments were reasonably
accurate, there 1s no reason to expect thatWI th respect to the effects of the change m
Regulation J-one series 1s any better than
the other However, the current series has reqmred a larger adjustment than the alterna-


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141

t1ve because It was subject to bias from two
types of accountmg practices associated with
remittances to the Federal Reserve, whereas
the alternative series was sub1ect to a smaller
bias from only one of these practices
To the extent that the 1972 shift m the
due-to-due-from relationship was caused by
factors other than the change m Regulation
J, the Federal Reserve staff 1s unable to make
any Judgments as to the relative quality of the
current and alternative M 1 series over the
1972-74 period The staff has not been able
to 1dent1fy with any degree of certamty those
factors and how they affected the various accounts on banks' books that bear on the calculations of the two money stock measures
Even 1f the shift were related to the advent
of PEPS, there 1s still the question of what
were Its effects on deposits due to and due
from banks, and hence which of the two
money stock series was affected W1thout firm
evidence, however, more defimtive statements
cannot be made at this time

Summary
The difference between the current and alternative money stock measures contmued to
grow m the 1975-76 period (Table I, column
8) This growth, however, did not accelerate
sigmficantly, and the relationship between the
two measures did not shift noticeably after
the apparent break between 1971 and 1972
Thus, the later data provide no additional
mformat10n that might help to explam the
large differences between the two series
A review of the construction of the two
senes mdicates that both measures can be
distorted by regulatory changes and by changes
m accountmg practices The alternative measure appears to be particularly susceptible to
changes m accountmg procedures associated
with mterbank deposits
While attemptmg to reconcile the differences between the two series, the Board staff
became more acutely aware of mstances when
timmg or mterbank accountmg variations
could lead to discrepancies between deposits
due to and due from banks for the commercial

142

lmprovmg the Monetary Aggregates Staff Papers

bankmg system as a whole Of course, what 1s
important to an md1v1dual bank 1s not that the
book balances show its deposits due to and due
from other banks to be equal at dny pomt m
time, but rather that they can be reconciled
These mterbank accountmg vanat1ons can,
however, mJect senous bias mto the alternative money stock measure At this pomt 1t 1s
not known 1f the alternative money stock contams such biases or not The comc1dence of
some of the sharp changes m the differences
between the two senes and of known changes
m interbank accounting suggests that such
biases exist
On the other hand, except for the bias ansmg from deposits due from banks, which 1s still
believed to be small, the current money stock
measure has no known or suspected biases The
differences m levels created by tlus form of bias


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Federal Reserve Bank of St. Louis

1s not important for policy purposes, and the
1mt1al presumpt10n that this bias evolved
rather slowly on average with httle attendant
effect on monetary growth rates, wluch are
more important than levels for pohcy purposes,
appears to be vahd When biases have developed m the past, they have been found and
qmckly corrected
In conclus10n, neither method of constructmg the money stock discussed m tlus paper 1s
clearly superior As with other economic data
senes, analysts should be awdre that these statistical d1screpanc1es exist and that any con~truct10n of the money stock 1s only a near
dpprox1mat10n of the "true" money stock Data
on the money stock, regardless of the method of
construct10n, reqmre careful and constant
momtormg to avoid senous d1stort10ns m the
senes

143

Appendix: Adjustments to Money Stock Measures

In constructmg the alternative money stock measure and comparmg 1t with the current measure,
two data problems were uncovered The first related to a m1sesumation of the cash-Items bias
associated with the transfer of funds by foreignrelated mstitut1ons m New York (primarily Euro
dollar transfers), and the second related to an mappropriate adjustment to the alternative measure
associated with the change m Regulauon J m 1972
After discovery of the problem of cash-Items bias,
additional data were collected as necessary and new
estimates of the cash-Items bias associated with
foreign related funds transfers were derived The
revised estimates of cash-items bias were folded
mto the published money stock data m 1976 The
reasons for this revmon are described below
The impact on mterbank deposits and the current money stock of transfers of funds at the New
York Clearmg House for foreign-related msututions m New York C1ty was first discovered m the
sprmg of 1970, when there was a huge unexplamed
bulge m the money stock Investigation showed
that this bulge was caused by a large declme m
cash items m the process of collection at New York
City banks on Good Friday, which contmued unchanged over the weekend This declme m cash
items was matched not by a declme m other demand deposits, however, but by a declme m deposits due to banks Further mvestigation revealed
that London banks were closed on Good Friday,
while U S banks were open 1 With London banks
closed, there was thought to be little or no activity
m the Euro-dollar market-which gave rise to most
of the transfers discussed above-so that few, 1f
any, new borrowmgs were mltlated or outstandmg
ones repaid W1th New York C1ty banks open, however, all the transfers associated with Euro-dollar
borrowmgs and repayments that had been m1t1ated
on the precedmg day cleared out of the p1pelme
1 On December 26, Boxing Day, London banks are also
closed and U S banks are open, which leads to the same
phenomenon that occurs on Good Friday In those years when
December 26 falls on a weekend, there 1s, of course, no impact
on domestic money stock data


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As a result, deposits due to banks at New York
C1ty banks (specifically due to agencies, branches,
and Edge Act corporations makmg the transfers)
declmed sharply, along with cash Items m the
process of collecuon If usual accountmg pro
cedures had been followed by the agencies,
branches, and so forth, the problem with the money
stock could have been corrected by foldmg m
balance-sheet data reported by these msutuuons
However, convenuonal accountmg practices had
not been followed at most of these mstitutlons, so
their balance-sheet data were not adequate to correct the current money stock Instead, some proxy
measure was needed Thus, begmnmg m late 1970,
daily data on officers' checks outstandmg of these
mstitutions were collected for tlus purpose
For the period before actual data are ava1lable,
a method for esumatmg the impact of the transfers
of funds at the New York Clearmg House on the
current money stock had to be devised Given the
explanation for the declmes m deposits due to
banks and cash Items around Good Friday and
Boxmg Day, the size of these declmes was determmed to be a good measure of the cash-Items bias
Thus, estimates of the cash-Items bias for earlier
periods were based on mterpolat1ons between
"benchmark" data derived from earlier holiday declmes m deposits due to banks A s1m1lar mterpolat1on was made for the penod between Good
Fnday 1970 and early October 1970, when the
m1trnl "hard" numbers reported by agencies,
branches, and so forth became available
As suggested by the behavior of the cash-Items
adjustment, the total of the first actual numbers
received m October 1970 was much larger than the
estimate for Good Fnday, and 1t remamed much
larger, with some modest further growth mto 1971
The difference between the Good Fnday estimate
and the actual numbers was not suspect, however,
smce there were other md1cat1ons that activity m
the Euro dollar market was expandmg rapidly
Because of the mterpolauon between the estimate
for Good Friday and the first actual numbers m

144

Improving the Monetary Aggregates Staff Papers

October, however, the adjustment for cash Items
bias grew rapidly m 1970
In 1970 Boxmg Day was on a Saturday, so the
declme m the deposits due to banks could not be
checked agamst the adjustment for cash-Items bias
unul Good Fnday 1971 When the check was made,
the reported declme m the adjustment exceeded
the declme m deposits due to banks by perhaps
$3 b1lhon to $3 5 bilhon As will be discussed later,
about $2 billion to $2 5 bilhon of the difference
appeared to reflect an overstatement of the actual
adjustment, while $1 0 bilhon was the amount by
wluch the declme m deposits due to banks underestimated the cash-Items bias
One part of the overstatement m the reported
data on cash-Items bias denves from the fact that,
m some mstances, contrary to assumpt10ns, checks
received by agencies, branches, and so forth were
not bemg deposited m New York City banks on
the day of receipt In particular, the checks were
not bemg deposited until early the followmg day
Given these delayed deposits, the checks did not
appear as cash Items on the books of New York
C1ty banks on the day of receipt by the agencies
or branches Nonetheless, the checks were reported
by the agencies, branches, and so forth that had
wntten the checks as a part of the bias-adjustment
numbers, and so they were mcluded m the adjustment Data collected on the amounts of delayed
deposits suggest that the daily flow of "m1ssmg"
cash Items and the consequent overstatement of
the adjustment for cash-Items bias was about $2 0
bllhon m 1971
Another part of the overstatement of the adjust
ment for cash-items bias may be caused by the fact
that some checks drawn by agencies, branches, and
so forth were deposited m the same New York
City banks on which they were drawn In these
circumstances, the offset to the credit of the depositor's account was an immediate debit to the
account of the mst1tut1on that drew the check At
the same time, however, the amount was reported
by the agencies, branches, and so forth drawmg the
checks as part of the statistics for the adjustment
for cash-Items bias, and It was mcluded m the adjustment No data are available on the extent of
this particular problem, although the agencies,
branches, and so forth have suggested that the percentage of their total checks outstandmg that were
deposited m the banks on which they were drawn
was "small"-perhaps $500 million m 1970
The estimates of the cash items for Good Fnday
and Boxmg Day are understated because not all


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foreign bankmg offices active m the Euro-dollar
market are closed on those days Smee data on the
cash-items bias were first collected, a residual
amount of checks-about $1 0 b1lhon-never disappears m the reported adjustment for cash-items
bias, even when European banks are closed for
holidays Presumably these checks give nse to a
need for a contmued adjustment Smee the checks
are still m the p1pelme, however, there 1s no declme m deposits due to banks to match these
checks, and the estlmatmg procedure, usmg Good
Fnday and Boxmg Day declmes m deposits due to
banks, understates the true level of the necessary
adjustment
After cons1derat1on of all the foregomg details,
new estimates of the cash-items bias were denved
m 1976 and folded mto the h1stoncal money stock
senes For the penod 1968-74, the magmtude of
these rev1S1ons for the la5t day of each year ranged
from -S2 6 billion to 5900 million For earlier
penods the adjustment was neghg1ble
The second data problem was an mappropnate
adjustment to the origmal alternative senes asso
oated with a change m Regulation J m late 1972
Tlus mappropriate adjustment, wluch raised the
level of the senes for 1959-71, resulted from the
method used to construct the ongmal alternative
5eries The alternauve M 1 was calculated by usmg
current M 1 as a base That 1s, alternative M 1 wa5
constructed by addmg demand deposits due to
domestic banks to the current M 1 series and rnbtractmg demand deposits due from banks and also
the origmal adjustment for cash Items bias This
calculation 1s the same as addmg net mterbank de
posits and subtracting the cash-Items bias from
current M 1 In late 1972, current M 1 was adjusted
upward for the period extendmg back to 1959 2
That adjustment compensated for what was termed
the "remittance payment bias" that persisted untll
November 1972, when the Federal Reserve's Regulat10n J was changed For the current money stock,
the entire adjustment made at that time was
appropriate For the alternative M 1 , however, part
of that ad1ustment was not appropriate, but 1t was
inadvertently mcluded m the ongmal estimate because the estimate used the current money stock
measure as a base The reason for the different
treatment 1s described below
Pnor to November 9, 1972, payments for checks
presented by the Federal Reserve to banks outside
Federal Reserve ewes were not due to the Federal
2 Federal Reserve Bulletin, vol
61-77

59 (February 1973), pp

An Alternative Method for Calculating M 1

Reserve until the busmess day after presentation
Even so, banks reduced their customers' demand
deposit accounts on the day the checks were presented, and as an offsettmg entry banks mcreased
an other-habiht1es account, "remittance due to
Federal Reserve " In addition to followmg general
accountmg conventions, banks wanted to reduce
their deposit habihties as soon as possible m order
to mmimize reserve requirements other habiht1es
are not subject to such reqmrements Reductions
m demand deposit accounts generally occurred before the reducuon of the correspondmg cash Items
or Federal Reserve float Because the hab1hty for
remittance payment was not carried m a money
stock deposit account, the amount deducted for
these Hems was too large for money stock purposes
and the level of the series was understated
When Regulation J was changed, the total
amount of checks for which remittance was speeded
up by one busmess day was esumated at around
$4 0 billion The acceleration m remittance eliminated the write-up of other hab1ht1es Thus, the
contraseasonal declme m other hab1lit1es at member banks that immediately followed the change
provided a measure of the part of the $4 0 b1lhon
that was concentrated at member banks-roughly
$2 0 billion The remamder reflected faster remittance from nonmember banks through correspondents
Banks that do not have accounts at the Federal
Reserve remit through correspondent banks that
do have such accounts Prior to November 1972,
these banks could follow either of two accountmg
procedures First, they could, upon receipt of a
cash letter from the Federal Reserve, reduce their
customer accounts and the deposits due from domestic banks The next day, when the correspondent remitted to the Federal Reserve, 1t would
reduce an account reflectmg deposits due to banks
Given these transacuons and other thmgs bemg
unchanged, deposits due to banks would always
exceed deposits due from banks
In the alternative procedure, nonmember banks
could use essentially the same procedure as member banks, writmg down customer demand deposits and mcreasmg other habiht1es for I day
On the followmg day, when the correspondent
bank remitted to the Federal Reserve and reduced
deposits due to banks, the nonmember banks would
write down deposits due from banks and other
habdmes Under this accountmg procedure, deposits due to and due from banks remamed m bal
ance each day To the extent that the second ac-


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Federal Reserve Bank of St. Louis

145

countmg method was used, the contraseasonal
declme m other liabilities at nonmember banks
after the change m Regulauon J should provide a
measure of its magmtude Other hab1hues at nonmember banks showed a contraseasonal declme of
only about $300 m1lhon Subtractmg this $300 milhon from the $2 0 billion remittances through
correspondents by nonmember banks leaves $1 7
billion This 1s a rough estimate of the amount
by which deposits due from banks were reduced 1
day prior to the reducuon m deposits due to
banks 3
Smee neither other liabilities nor deposits due
from banks are used m calculatmg the current
money stock, adjustment for both transactions was
appropriate m order to avoid a break m series
after the change m Regulauon J For the alternative measure, however, m whose construction net
mterbank deposits were used, adjustment was
appropriate only for the other liab1hues related
to member banks' remittances for their own accounts and to nonmember remittances through correspondents when similar accountmg procedures
were followed No adjustment 1s necessary m the
alternative series for the remittances associated
with the early reduction of deposits due from
banks In fact, because the alternative money stock
measure used the current measure as a base, the
Regulation J adjustment was mcluded m both
series The result was that alternative M 1 as origmally calculated was overstated by the amount of
the mappropriate adjustment for remittance-payment bias
A new estimate of the overstatement of the alternative M 1 was derived by usmg the late-1972 estimate of $1 7 billion as a benchmark and reducmg
this level by $ I 00 m1lhon each year back to I 959
This 1s not a satisfactory procedure, but unfortunately, there 1s no better way to make this
adjustment Regardless of how the adjustment is
made, 1t is sufficiently small and would be spread
over a sufficiently long period of time that year-toyear distortion should be mmor
The adjustments for the current and alternative
money stock for the last day of each year from
1959 to 1974 are shown m Table I m the text As
md1cated, the adjustments for cash-items bias were
folded mto the published money stock series m
1976
3 The practice of wntmg down amounts due from banks
before remittance by correspondents might have been un
necessarily costly for nonmember banks because of lower
deposits that could be used to meet nonmember State reserve
reqmrements, and there is no economic explanation for its use


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Federal Reserve Bank of St. Louis

147

Developing Money Substitutes: Current Trends and Their
Implications for Redefining the Monetary Aggregates
Steven M Roberts

This paper was completed tn January 1977
It has not been revised to include any deposit
or other data available since late 1976 Nor
has any attempt been made to inc01porate any
regulatory or legal changes afjecting the monetary aggregates that have been made since
late 1976
In recent years the distmct10n between demand deposits and savmgs deposus at both
banks and nonbank depositary mst1tut10ns has
become mcreasmgly blurred The dnvmg
force behmd the regulatory and mstitut10nal
mnovat10ns leadmg to this development has
been greater compeuuon for funds among
financial mst1tut10ns, which m turn has resulted m expanded payments services and
lugher mterest returns to deposit owners For
example, depositary mnovauons that have
emerged withm the last few years mclude
negotiable orders of withdrawal (NOW) accounts m New England, telephomc and thirdparty transfers from savmgs accounts, credit
umon share drafts, and electromc transfers
of funds by means of customer bank commumcat10n termmals (CBCT's)
As a result of these and other mnovauonswhich suggest evolvmg savmgs-based transfer
systems-the tradit10nal meanmg of the narrow money stock (M 1), defined as private demand deposits at commercial banks plus cur-

NoTE-The author, formerly of the D1vmon of Research and Statistics, 1s currently Chief Economist, Com
m1ttee on Bankmg, Housmg and Urban Affairs of the
US Senate
He would like to thank Paul Boltz, Edward Ettm,
David Lmdsey, Raymond Lombra, Darrel Parke, John
Paulus, and John Williams for comments on early
drafts of this paper


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Federal Reserve Bank of St. Louis

rency m the hands of the public, as bemg
representative of the economy's media of exchange or cash balances, has been somewhat
eroded While the usage is thus far relatively
small, it can be expected that an mcreasmg
volume of fund transfers may be made from
mterest-bearmg accounts, and M 1 as currently
defined may account for a smaller proport10n
of total transact10ns m the years ahead Consequently, monetary pohcy formulat10n might
appropriately consider and evaluate movements m a broader array of monetary aggregates that exphcitly recogmze the development
of savmgs-based transfers and other recent developments
The Board of Governors of the Federal Reserve System and the Federal Open Market
Committee, through Chairman Burns' recent
series of congress10nal testimomes on monetary pohcy, are already on record as havmg
targets for the growth of several monetary
aggregates, mcludmg M 11 M 2 , and M 3 1 However, lt should be recogmzed that the ume
deposit components of M 2 and M 3 have specific maturities and stnct regulat10ns regardmg redempt10n pnor to maturity that make
them both relatively ilhqmd compared with
savmgs deposits and M 1 and not really representative of transact10ns balances, although
they may be considered near-money reposi1 These testimonies are published m the Federal Reserve Bulletin on a regular basis and also appear m
the Annual Report
M 2 1s defined as averages of daily figures for M1
plus time and savmgs deposits at all commercial banks
other than negotiable certificates of deposit (CD's) of
$100,000 or more at large weekly reportmg banks Ms
1s defined as M2 plus the average of the deposits at
the begmnmg and the end of the month at mutual
savmgs banks, savmgs and loan assocmlions, and credit
umons

148

tones for precautionary or speculative funds 2
Also, m recent years there has been a tendency
for small-denommation time deposit funds to
become mcreasmgly concentrated m the longer
maturities because mterest ceilmgs and rates
paid on such matunues make them relatively
more attractive, vis-a-vis market instruments,
than the shorter-maturity time deposits Thus,
the inclusion of longer-maturity time deposits
m M 2 and Ma has resulted m monetary aggregates that mclude, m addition to M 1 , both
hqmd (savmgs) and ilhqmd deposits
In add1t10n, the meanmg of M 2 and Ma as
currently defined may also be distorted by
the current treatment of large-denommatlon
(over $100,000) time deposits The current
definit10n of "other time and savmgs deposits"
-which are added to M 1 to obtam M 2-is
total time and savmgs deposits less negotiable
certificates of deposit (CD's) m denommat10ns
of $100,000 or more at weekly reporting banks 3
This definition of other time ,md savmgs deposits means that M 2 includes not only those
large-denommat10n ume deposits at weekly
reporting banks that are not m the form of negotiable CD's but also all large-denommation
time deposits, whether negotiable or not, at all
other banks Recently available data suggest
that movements of other time and savmgs deposits, as currently defined, may be significantly
mfluenced by large-denommatlon deposits that
tend to move hke negotiable CD's at weekly
reporting banks and do not parallel the behav10r of consumer-type (small-denommat10n)
deposits Thus, not only do M 2 and M 3 contam long-term maturity deposits, which are
unlikely to be used as part of the payments
mechanism, but M 2 also contains both small2 The penalty £01 early withdrawal of a time deposit
under Regulation Q (Section 217 4 as amended July r,,
1973, applicable to all time deposit contracts entered
mto after that date) 1s that mterest paid on the amount
withdrawn may not exceed the savmgs deposit ce1hng
1ate and that 3 months' mte1est 1s fo1fe1ted The Fed
eral Deposit Insurance Corporation (FDIC) and the
Federal Home Loan Bank Board (FHI BB) have s1m1
Jar regulations for the depositary msutuuom under
theu 1unsd1ct1on
a Weekly reportmg banks are the approximately 320
large commercial banks that report detailed balance
sheets to the Federal Reserve System each week


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Improvmg the Monetary Aggregates. Staff Papers

and large-denomination deposits, with the latter behaving differently from the former over
the business cycle
It should also be noted that nonbank thnft
institutions-that is, mutual savmgs banks
(MSB's), savmgs and loan associations (S&L's),
and credit unions-have been relatively more
active than commercial banks m developing
and marketing savmgs-based transfer services
for their customers 4 These services include
not only telephonic and third-party transfers
but also direct transfers between consumer and
business savmgs deposits as payment for goods
and services by means of remote terminals
Commercial banks have been able to offer similar services only smce 1975 The development
of savmgs-based transfers at nonbank thnft
institutions suggests that the Federal Reserve
will need more extensive and more timely
data on deposits at such mst1tut1ons m order
to monitor developments m the more broadly
defined stock of "money" used for payments 5
The remainder of this paper reviews these
developments m more detail and considers
their imphcauons for redefining the monetary
aggregates One sect10n focuses on the recent
1 egulatory changes and financial innovations
that have led to the development of money
substitutes Some of the new money substitutes
will be described and, whenever possible, data
on the dollar amounts outstanding and on
rate of growth will be presented The analysis
will indicate the causes for the recent changes
Another sect10n discusses two problems re4 The term nonbank thnft mst1tut1ons will be used
m the remamder of this paper to denote MSB's, S&L's,
and credit umons taken as a group
5 More timely and extensive data from the FDIC
pertammg to demand deposits at nonmember banks
have been recommended as necessary to the Federal Reserve's central monetary policy function m Improving
the Monetary Aggregates Report of the Advisory Committee on Monetary Statistics (Board of Governors, 1976)
Begmnmg with the March 1976 call report, the FDIC
agreed to collect 7 days of deposit data from non
member banks m order to provide weekly average
benchmark data rather than smgle-day data In add1
uon, the FDIC has agreed to remst1tute the callee
Uon of weekly data from a sample of about 575
nonmember banks Data from a s1m1lar sample of
nonmember banks was collected on an expenmental
basis from the summer of 1974 to the sprmg of 1975

Developing Money Substitutes

latmg to the current defimt10n of "other" time
deposits that are mcluded m M 2 The creat10n
of longer-maturity, small-denommat10n time
deposit categories under Regulation Q has
changed the maturity structure of these time
deposits sigmficantly This 1s true of time
deposits at S&L's and MSB's and thus affects
the current defimuon of M 3 also In addition,
this sect10n discusses the mclus10n of largedenommat10n time deposits m the defimuon
of M 2 and M 3 The final section draws on the
mitial port10ns of the paper and suggests several ways m which current defimt10ns of the
monetary aggregates nught be modified at
some future date

Recent regulatory changes and
financial innovations and
the development of M1 substitutes
Substitutes for transact10ns balances held
m the form of currency or demand deposits
have existed for a long time However, It 1s
only w1thm the past several years that regulatory changes and financial mnovauons have
resulted m new means of fac1htatmg payments for goods and services Today payments
may be made through deposits held at banks
and nonbank thnft mst1tut10ns without directly mvolvmg currency or demand deposits
F1om an mst1tut10nal pomt of view, the smgle
most important factor mfluencmg the development of savmgs-based transfers 6 1s the
proh1b1t10n of mterest payments on demand
deposits legislated m the m1d-1930's 7 In the
1950's and 1960's the pubhc-part1cularly the
busmess sector-sought to reduce non-mterestheanng claims m favor of highly hqmd earnmg assets that could be easily transferred mto
,t payments medmm, these claims-money
market assets 5uch as Treasury bills, commernal paper, and negotiable CD's-were generally available only m large denommat10ns A
6 Savmgs-based transfers 1s a term that will be used
m this paper to denote payments mvolvmg an m1t1al
or duect transfer from mterest-beanng deposits, ~hares,
and so forth
7 Section 19 of the Federal Reserve Act a~ amended
by the Bankmg Act of 1933


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Federal Reserve Bank of St. Louis

149

second important mst1tut10nal factor leadmg
to savmgs-based transfers has been the statutory monopoly of demand deposit powers by
commercial banks Tlus monopoly has led to
vigorous efforts by nonbank thnft mst1tut10ns
to develop payments alternatives that they
can offer to their customers as substitutes for
demand deposlls It 1s clear that the nonbank
thnft mstitut10ns as an mdustry have been
more mnovauve m the payments area because
they have been forced to compete with banks
tor payment-type deposits 8
Although nonhank thrift mstltutions m general may not issue payment-type deposits,
commercial banks may not pay mterest on
the1r demand deposits 9 Thus, as the thrift
mstitut1ons have mtroduced money substitutes, commercial banks-seemg the1r compeuuve advantage erodmg-have sought
changes m reguL1t10ns m order to make bank
savmgs deposlt5 ea5ier to transfer In the past
5 years there have been sigmficant changes
1elatmg to ownership and transfer of savmgs
deposits at banks
Innovc1t1om and regulatory changes made
m the penod smce 1970 that affect components
of M 1, M 2 , and MJ are shown m Table I
If these types of mnovat1ve changes contmue-as seems hkely, given both their rapid
recent mcrease and the changes that will be
mduced by activity under electromc fumh
transfer systems (EFTS)-the ba5ic monetary
aggregates may have to be redefined to mclude
m M 1 or some new aggregate all, or part, of the
new demand deposit 5uhst1tutes The remainder of tins sect10n provides speofic mformat10n
relatmg to several of the recently developed
money substitutes

NOW accounts
A NOW account 1s a savmgs deposit that
pe1m1ts the owner of the deposit to withdraw
s 5&.L's and MSB s have, of course, been given ~ome
compct1t1ve advantage over banks 1n the time and
savmgs deposit markets because of the ¼ percentage
pomt mterest ceilmg advantage they enJoy
9 Appenchx l provides a State by State rundown of
t1ansfcr powers of State chartered thnft mstltutions

Improving the Monetary Aggregates Staff Papers

150

TABLE 1: Innovations and Regulatory Changes Since 1970
Change

Date of change
Sept 1970
June 1972
Sept 1972
July 1, 1973
July 5, 1973
Nov 1, 1973
Jan 1, 1974
Jan 1974

Early 1974
Aug 1974
Nov 27, 1974
Dec 23, 1974
Apr 7, 1975
Apr 16, 1975
Sept 2, 1975
Nov 10, 1975
Jan 16, 1976

Feb 27, 1976
Mar 15, 1976

May 26, 1976

S&L's were permitted to make preauthonzed nonnegotiable transfers from savmgs accounts for
household-related expenditures 1
State-chartered MSB's m Massachusetts began offermg NOW accounts
State-chartered MSB's m New Hampshire began offenng NOW accounts
Federal regulatory authont1es mtroduced a 4-year time deposit (ce1lmg free) with a mm1mum denom1nat10n of $1,000
Federal Reserve amended Regulation Q to modify penalties for early withdrawal of time deposits
Interest rate cedmgs were imposed on 4-year $1,000 mm1mum time deposits (7¼ per cent for banks
and 7½ per cent for S&L's and MSB's)
All depositary mst1tut1ons m Massachusetts and New Hampshire (except credit umons) were authonzed by the Congress to offer NOW accounts 2 Accounts s1m1lar to NOW's, but non-mterest
beanng, offered by State-chartered thnfts m additional States through the year 3
First Federal Savmgs and Loan, Lmcoln, Nebraska, mstalled customer bank commumcat1on termmals
(CBCT's) m two Hmky Dmky supermarkets, allowmg its customers to make deposits to or withdrawals from savmgs accounts Such withdrawals can be used to pay for merchandise purchased
from the stores The First Federal system, known as Transmat1c Money System (TMS), 1s now bemg
franchised to other S&L's
Money market mutual funds (MMMF's) came mto existence on a large-scale basis These funds,
which mvest m money market instruments, allow their shareholders to redeem shares by checks
drawn on accounts estabhshed at designated banks, by wife transfer, or by mad
Federal credit umons were permitted to issue credit umon share drafts, which are check-hke mstruments payable through a commerc1al bank 4
Commercial banks were permitted by Federal regulatory authonUes to offer savmgs accounts to
domestic State and local government umts
Federal regulatory authont1es mtroduced a 6-year time deposit, mm1mum denommat1on $1,000,
with a 7½ per cent ce1hng for banks and 7¾ per cent ce1lmg for S&L's and MSB's
Member banks were authonzed by Federal Reserve to make transfers from a customer's savmgs
account to his checkmg account upon telephomc order from the customer
The FHLBB broadened its 1970 action to allow S&L's to make preauthonzed th1rd-party nonnegotiable transfers for any purpose
Commercial banks were authorized by Federal regulatory authontles to make preauthor1zed thirdparty nonnegotiable transfers from a customer's savmgs account for any purpose
Commercial banks were authonzed by Federal regulatory authont1es to offer savmgs accounts to
partnerships and corporations operated for profit, hm1ted to $150,000 per customer per bank
The Federal Reserve adopted an mtenm pohcy for access to System-operated automated cleanng
houses (ACH's) that md1cated that ACH transfers could "ongmate from any account havmg thirdparty powers, for example, savmgs, NOW, and share draft accounts," as well as from demand deposit
accounts
Federal leg1slat1on authonzmg NOW accounts m Connecticut, Mame, Rhode Island, and Vermont
became effective
The Federal Reserve and the FDIC proposed for comment an amendment to Regulation Q to permit
banks upon request of a customer to cover overdraft of a demand deposit account by automatic
transfer of funds from the customer's savmgs account At this wntmg the rule change has not been
made
All State-chartered S&L's and MSB's m New York were granted consumer demand deposit powers
pursuant to Chapter 225 of the laws of 1976

i Authonty contamed m the Housmg Act of 1970
2 Pubbc Law 93-100, signed August 16, 1973
• According to Manlyn G MathIS, "Thnfts contmue to gatn tn
third-party payment plans," Banking, vol 66 (December 1974), pp
32-38, non-mterest-beanng NOW's were offered by at least some
thnfts m Connecttcut, Delaware, Indiana, Maryland, New Jersey,
New York, North Carolma, Oregon, Pennsylvama, Rhode Island,
and Utah In 1975 several other States enacted legislatton pernuttmg


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State chartered mstitutions to offer sinular accounts These States
mclude Illmois, Mame, Nebraska, and Vermont See Appendix 1 for
a list of transfer powers authonzed for State chartered mstitutions
• Secllon 721 3, Rules and Regulallons of the Nallonal Credit
Union Adnumstrallon (NCUA), estabbshed rules for expenmental
pilot programs for electromc funds transfers (EFT) that mclude
share draft plans

Developing Money Substitutes

funds by wutmg a negotiable order of withdrawal-hence the acronym NOW 10 The withdrawal document is a negotiable draft that
can be used to make payments to tlurd parties,
essentially like a check drawn on a bank demand deposit This f01m of savmgs account
came mto bemg followmg a rulmg by the
Massachusetts Supreme Judicial Court on
June 12, 1972, that found no restriction m
the State charter of MSB's prohibitmg withdrawals from savmgs accounts through the use
of NOW drafts
State chartered MSB's m Massachusetts soon
entered the NOW market, and m September
a savmgs bank m New Hampshire began to
offe1 NOW's after havmg dete1mmed that,
as m Massachusetts, there we1e no statutory
1cstnct10ns on the manner of withdrawal from
savmgs accounts Immediately, State-regulated
savmgs banks m the two States held a competitive advantage over Federally charte1ed or
msmed mstitutions, which could not offer
NOW accounts These mstitut10ns sought relief from Federal agencies, which led to congressional legislation (Pubhc Law 93-100),
signed mto law August 16, 1973, authonzmg
all depositary financial mstitut10ns (except
crecht unions) m Massachusetts and New
Hampshire to offer mterest-beanng deposits
on which negotiable mstruments of withdrawal
could be drawn As a result of this legislation,
1egulations by the Federal Reserve, the
FHLBB, and the FDIC authorized NOW's for
Federally chartered depositary msututions m
Massachusetts and New Hampshire as of Janu,n y I, 1974, limited exclusively to mdividuals
and nonprofit orgamzat10ns 11 The three agencies agreed to impose a umform interest rate
ceilmg of 5 per cent on NOW's and to restnct
the advertisement of such accounts to Massarhusetts and New Hampshire
Outstandmg NOW balances at vanous types
10 Much of the material m this subsecl!on 1s based
on the work of my colleague John W1lhams
11 From November 1974 until authonzatton was with
drawn m Apnl 1975, State and local governmental
umts were permitted to hold NOW accounts at commercial banks


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151

of depositary mstitut10ns m Massachusetts
and New Hampshire from September 1972 to
December 1975 are shown ml able 2 Growth
m NOW accounts has been 1apid throughout
the penod Table 2 ,tlso shows market shares,
which h.tve changed conmlerably over time
and have not as yet stabilized fully Ongmally,
MSB's-wh1ch p10nee1ecl NOW accountsdommatecl the market, but more recently commc1 cial banks h,tve entered the NOW ma1ket
aggressively, and then share of that market
has grown veiy iap1dly A few commercIJ.l
hanks have converted all eligible savmgs acwunts to NOW's, and some have notified
customers that their demand deposits are
ehg1ble foi conveis10n to a NOW account
Table 3 compa1es some of the characteristics
of NOW accounts at competmg mstltutions as
of Decembe1 31, ICJ75 Most mstltutions were
paymg 5 pe1 cent mte1 est on a day-of-depositto-day-of-withdrawal basis A maJonty of these
mst1tut10ns also compounded mterest dally or
contmuously and offe1ed free NOW drafts
The lugher proport10n of free drafts at nonbank mstitut10ns suggest5 that they see NOW
accounts as a means of clrawmg funds from
commercial bank demand depo~1 ts-that is, via
the ,tbsorption of clearmg costs as a nonprice
means of competitive advantage Table 4
shows how charges pei draft and activity per
month have changed smce January 1974 Accounts with free draft privileges are typically
the most active Furthermore, NOW account
activity has mcrea5ed consideiably as more
mst1tut1ons offer free drafts 12
On February 27, 1976, congressional legislation authorinng NOW accounts m Connecticut, Mame, Rhode Island, and Veimont became
effective Although little mformat10n is yet
available regardmg the newly authorized NOW
markets, it appears that commercial banks entered this market more rapidly than did thrift
mstituuons durmg the first month of expanded
12 For add1ttonal mformauon on NOW account act1v1ty m 1974 and 1975, see John D Paulus, "Effects of
NOW Accounts on Costs and Earnmgs of Commercial
Banks m 1974-75," Staff Economic Studies 88 (Board of
Governors of the Federal Reserve System, 1976)

Improvmg the Monetary Aggregates Staff Papers

152

TABLE 2 Outstanding Balances and Shares-NOW Accounts
Dollar amounts ID thousands

Date

Commercial banks

All
offermg
1nst1-

T ota I

tullons

Massa-

I chusetts

I

Share
of
HNew
amp- total
shire NOW's

Share Savtngs and loan assoc1at1ons Share
of
of
New
total
MassaNew
Hamp- total
chusetts
Hamp- NOW's
shire NOW's Total
shire

Mutual savmgs banks

I

Total

M assachusetts

I

I

I

1972-Sept
Oct
Nov
Dec

11,094
22,386
34,823
45,272

11,004
22,386
34,823
45,272

11, 0'.14
22,386
34,363
44,522

-460
750

1973-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

60,726
73,451
86,118
94,606
102,045
108,381
113,418
117,005
120,223
130,361
136,872
143,254

60,726
73,451
86,118
94,606
102,045
108,381
113,418
117,005
120,223
130,361
132,872
143,254

59,661
71,975
84,162
92,341
99,633
105,688
110,486
113,852
116,259
125,873
131,795
138,028

1,065
1,476
1,956
2,265
2,412
2,693
2,932
3,153
3,964
4,488
5,077
5,226

1974-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

143,190
150,447
165,157
174,682
180,637
191,229
204,646
232,386
249,033
270,813
293,305
312,576

2,556
4,338
6,588
9,689
11,052
13,771
17,919
32,955
39,253
46,776
55,994
65,249

2,274
3,857
5,916
8,458
9,296
11,156
14,175
28,450
33,597
40,245
48,563
56,989

282
481
672
1,231
1,756
2,615
3,744
4,505
5,656
6,531
7,431
8,260

02
03
04
06
06
07
09
14
16
17
19
21

139,779
143,764
154,007
157,412
159,591
164,733
171,503
180,335
187,721
197,758
206,764
213,661

134,832
138,453
147,845
150,309
151,510
155,946
161,544
169,119
175,340
184,830
192,577
200,083

4,947
5,311
6,162
7,103
8,081
8,787
9,959
11,216
12,381
12,928
14,187
13,578

98
98
93
90
90
86
84
78
75
73
71
68

855
2,345
4,562
7,581
9,994
12,725
15,224
19,096
22,059
26,279
30,547
33,666

855
2,345
4,325
6,913
8,351
11,089
13,223
16,781
19,314
23,316
26,689
29,747

237
668
I, 143
1,636
2,001
2,315
2,745
2,968
3,858
3,919

01
02
03
04
05
07
07
08
09
10
10
II

1975-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct

339,982
395,190
449,638
472,864
514,018
580,331
630,402
670,790
713,419
761,967
796,533
839,339

82,861
107,481
137,519
150,999
172,653
210,838
233,513
256,992
289,308
305,214
325,519
359,023

73,517
96,647
124,706
136,165
155,318
185,923
201,607
217,936
235,029
254,821
271,691
302,112

9,344
10,481
12,813
14,834
17,335
24,195
31,096
39,056
45,279
50,393
53,828
56,911

24
28
31
32
34
36
37
38
39
40
41
43

220,725
236,580
262,797
268,571
283,322
304,633
327,417
337,684
351,612
368,271
378,792
386,560

206,797
221,506
246,259
250,780
263,978
283,134
303,805
213,117
324,005
338,580
347,145
356,319

13,928
15,074
16,538
17,791
19,344
21,499
23,612
25,567
27,607
29,691
31,647
30,241

65
61
58
57
55
53
52
50
49
48
48
46

36,396
41,482
49,322
53,294
58,043
64,860
69,472
76,114
81,499
88,482
92,222
93,756

32,369
37,215
43,980
47,185
51,388
57,315
61,554
67,519
72,407
78,785
81,863
84,168

4,027
4,267
5,342
6,109
6,655
7,545
7,918
8,595
9,092
9,697
10,359
9,598

II
II
II
II
II
II
II
II
II
12
12
II

Nov

Dec

Norn -Monthly data are released by the Federal Reserve Bank of Boston
SouRCE -John D Paulus, "Effects of NOW Accounts on Costs and Earmngs of Commercial Banks m 1974-75," Staff Economic Studies 88
(Board of Governors of the Federal Reserve System, 1976}

authorization This development 1s s1gmficantly different from the experience m Massachusetts and New Hampshire Almost all of the
mst1tut1ons that offered the new accounts were
paymg the ce1lmg rate of 5 per cent, although
relatively few were offermg free drafts The
TABLE 3 Characteristics of NOW Accounts, by Type
of Institution, December 31, 1975
In per cent
Interest
Institution

Commercial banks
Mutual sa vtngs banks
Sa vtngs and loan
assocta t1ons
All mst1tut1ons


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Federal Reserve Bank of St. Louis

Contmuom From day
dally of deposit
5 per cent orcomto day of
poundmg withdrawal

Free
drafts

96
97

45
86

73
98

30
77

99
97

69
69

92
89

82
63

total of the newly authorized NOW balances
m the four States as of March 31, 1976,
amounted to only $43 mtlhon

Commercial bank savings deposits
From November 1974 to March 1976 the
Federal bankmg authorities made four regulatory changes, and proposed a fifth, which
have greatly expanded the poss1b1ht1es for
substitut10n of savmgs deposit balances for
balances now mcluded m M 1 , particularly demand deposits These changes have been of
two types (I) to allow for expanded ownerslup of savmgs deposits, and (2) to permit
banks to offer their customers new services
that would fac1htate the use of savmgs deposits for transact10ns purposes

Developing Money Substitutes

153

TABLE 4 NOW Account Actmty and Charges
Charges per draft
(per cent of 1ssumg msutuuons)

Month
Free
1974-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

32
31
35
34
34
33
34
42
53
56
60
61

5
2
1
0
8
5
5
5
7
0
4
7

1975-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

62
64
66
66
66
64
65
67
65
65
65
63

1976-Jan
Feb
Mar

I

10¢
17
18
16
16
16
18
18
15
14
12
JO
10

I

15¢

I

Other•

Drafts per
account dunng
average month•

5
4
4
5
2
5
5
8
4
3
9
8

50
45
42
42
40
40
39
31
21
19
16
12

0
4
7
0
7
5
9
2
8
9
I
5

5
5
7
8
7
7
10
10
11
12
14

0
8
4
3
5
1
5
1
9
6
9

7
7
7
8
8
8
8
8
8
8
8
9

3
0
8
5
5
I
5
0
2
8
9
5

3
0
0
6
2
4
7
2
6
8
3
5

8 9
8 2
7 7
6 2
5 6
5 1
4 7
3 9
3 7
3 6
40
4 0

10
10
8
9
8
7
6
5
5
5
5
6

8
4
6
6
8
9
7
6
9
8
7
0

18
17
17
17
19
22
22
23
24
24
24
26

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

9
8
10
10
10
10
10
9
10
10
10
11

3
8
0
5
4
4
3
8
3
7
2
0

63 4
61 6
54 9

3 4
3 7
3 4

5 1
5 3
5 S

28 0
29 5
36 2

10 7
10 3
II 6•

1 Includes a combmat1on of free drafts plus a charge for each draft over a specified number, and
free drafts m exchange for a specified mm1mum balance
' Excludes accounts with no act1V1ty durmg the month
3 Includes NOW accounts m Connecticut, Mame, Massachusetts, New Hampshire, Rhode Island
and Vermont

Domestic governmental umts were first permitted to hold savmgs deposits at commercial
banks m November 1974 Effective November
10, 1975, commerCial banks were permitted
to offer savmgs accounts to partnerships and
corporat10ns, hm1ted to J150,000 per customer
per bank These accounts have grown more
qmckly than ongmally ant1npated and by
the end of March 1976 amounted to about
$2 r:i bilhon at the weekly reportmg banks and
$5 4 billion at all msured commercial banks
Authonzat10n to make telephomc transfers
from savmgs to demand deposits and pre,mthonzed third-party nonnegotiable transfers
directly from savmgs deposits provides banks
the opportumty to offer their customers more
convement methods for usmg savmgs deposits
to make payments Because these savmgs-based
~erv1ces are new, 1t 1s difficult to gauge with
any degree of certamty their quantitative impact on M 1 The direction of impact, however,
1s clear these services, 1f widely offered and
utilized, would tend to reduce further the
d1stmct10n between demand and savmgs deposits, and thus would erode the s1gmficance


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of M 1 and would alter its relauonslup to the
gross national product
Compeuuon from thnft mst1tut1ons and
the proh1b1uon of mterest payments on demand deposits suggest that commercial banks
will offer these new services based on customer
demand It 1s difficult to quantify the extent
to which these new savmgs transfer services
a1e bemg used, however, through mformal
surveys and momtormg of developments by
the Federal Reserve Banks and the FHLBB,
1t appears that telephomc transfer services are
hemg offered on a fairly wide geographic basis
by both large and small banks and also by
S&L's Preauthonzed third-party nonnegotiable
transfer services do not appear to be widely
offered
On March 15, 1976, the FDIC and the
Federal Reserve issued a proposal to allow
banks to offer automatic overdraft protection
from savmgs accounts by means of preauthor11ed transfers from savmgs to cover overdrafts
If adopted, tlus new service would be complementary to those savmgs-based transfer
services already perm1ss1ble Such a service,

Improving the Monetary Aggregates Staff Papers

154

pnced to compete with consumer overdrafts
by takedowns of Imes of credit, could be widely
marketed by banks, has the potential for consumer acceptance, and could mduce expanded
use of complementary services If these developments were to take place, the average
size of demand deposit accounts would tend
to declme It should be emphasized that overdraft services would be an add1t10nal factormdeed, an extremely important one-tendmg
to mcrease the relative importance of savmgs
deposits m the payments process, while reducmg the s1gmficance of M 1 as tt 1s currently
defined

Money market mutual funds
Money market mutual funds (MMMF's) are
a fairly new form of mvestment company, the
first was orgamzed m 1971, and others began
operat10n m 1974 It was not until after the
period of nsmg mterest rates m early 1974
that the MMMF's began to grow rapidly m
number and dollar s12e As Table 5 shows,
between January and December 1974 the number of money market funds mcreased from
4 to 30 and net assets of the mdustry grew
from less than $200 million to about $2 5 b1lhon The number of funds mcreased through

I 975, although the dollar amount of assets
stabilized at about $3 6 billion as market mterest rates declmed
Designed basically as cash management vehicles, these funds provide shareholders with
an mterest return that vanes with rates m
the money market They typically mvest m
mstruments that are issued m large denommat10ns such as Treasury bills, large-denommat10n CD's, bankers acceptances, and commercial paper, while reqmrmg shareholders to
mvest relatively small m1tial amounts such as
$500 to $1,000 Shares m these funds can be
purchased and redeemed easily, often without
transaction charges Management fees of the
funds are also relatively low Because of the
high hqmd1ty of shares, near-market rate of
return, zero or near-zero transact10n costs, and
low management fees, shares m money market
funds provide an attractive substitute for both
demand and savmgs deposits offered by depositary mstitutions
Most of the funds calculate and pay dividends on a daily basis, shares can be redeemed
by check or wire transfer at little or no cost,
.i.nd most funds have no sales charges The
check redemption feature 1s especially mterestmg The shareholder may receive a book of
ordmary checks from a bank (designated by

TABLES Growth m Money Market Mutual Funds January 1974--March 1976
Change over
month (mtlltons
of dollars)

Assets
(mtlltons of
dollars)

1974-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

4
6
6
7
8
10
13
17
18
22
26
30

174
208
244
303
412
542
792
1,106
1,393
1,860
2,208
2,439

34
36
59
109
130
250
314
287
467
348
231

19
17
24
36
31
46
39
25
33
18
10

5
3
2
0
6
1
6
9
5
7
5

1975-Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

32
35
36
37
38
39
40
40
42
42
46
47

3,042
3,501
3,786
3,862
3,911
3,795
3,694
3,787
3,750
3,723
3,645
3,645

604
458
285
76
49
-116
-101
93
-37
-27
-19
-59

24
15
8
2
1
-3
-2
2
-1
-1

8
1
1
0
3
0
7
S
0
7
5
6

9 0
7 3
6 S
S8
6 4
5 1
5 7
6 0
62
6 1
S 6
S 6

1976-Jan
Feb
Mar

48
48
48

3,701
3,736
3,719

56
35
-17

-

1 5
9
5

5 3
5 0
5 1


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Federal Reserve Bank of St. Louis

Growth rate
(per cent
per month)

Average yield
(per cent
per month)

Number of
funds

Month

8
8
7
8
10
10
11
11
11
10
9
9

6
1
8
7
0
2
2
3
3
5
4
0

155

Developing Money Substitutes

the particular fund) and can use these checks
to make payments However, arrangements
often specify mm1mums such as $500 per
check When the check 1s presented to the
payee bank, the bank, actmg as the shareholder's agent, mstructs the mutual fund's
transfer agent to redeem a sufficient number
ot shares m the shareholder's account to cover
the amount ot the check This procedure allows the shareholder to earn mterest on his
mvestment until payment 1s made to the bank
In a similar manner, shareholders with a large
amount of funds mvested can arrange for
wire transfer of funds both out of and mto
their share accounts at their commercial banks
The ease with which shares may be purchased and redeemed with mm1mal transactions costs suggests that the MMMF's make
extremely good mvestments for cash management purposes In fact, a large proportion
(about 40 per cent) of all accounts are owned
by mst1tutional mvestors that use them to mcrease cash management efficiency But both
consumers and households may find MMMF's
to be useful substitutes for demand, savmgs,
and time deposit balances, and consequently
they are another factor altenng the relat1onsh1p between market rates and the monetary
.tggregates, and between the aggregates and
gross national product

Credit union share drafts 13
I

Credit umon share drafts are a new type
of payment mstrument and thus are neither
widely known nor widely used However, there
are approximately 23,000 credit umons m the
Umted States, with total assets of about $35
billion, and 1f the current rapid growth of
credit umon shares contmues, the potential
impact on M 1 and M 2 of widespread use of
share drafts will be large
A share draft 1s a negotiable payments mstrument drawn on the 1ssmng credit umon
but payable through a commercial bank It 1s
1a Add1t10nal mformation may be obtamed from
Savings and Loan News, vol 97 (April 1976), and "Share
Drafts The Fust Six Months" (report of the Credit
Umon National Association, 1975)


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one form of the legal payments mstrument
known as "payable-through drafts " U nhke a
check that 1s drawn directly on the deposit
hab1hty of a commercial bank, a credit umon
share draft 1s drawn on the credit umon that
has established a cleanng arrangement with
the "payable-through bank " In the clearmg
process, these drafts are treated the same as
checks until they are received by the payablethrough bank, which notifies the credit umon
as to the drawer, the amount, and the debit to
the credit umon's account at the bank for
payment of the drafts The credit umon will
then debit the shareholder's account The important pomt 1s that mterest will be paid on
the shareholder's funds until the draft 1s
cleared and the .tccount 1s debited
In many respects share draft accounts are
hke NOW accounts and have the same advantages over non-mterest-paymg checkmg accounts As Table 6 md1cates, the number of
ned1t umons now offermg such accounts 1s
only about 1 per cent of the total, but the
recent growth rate has been 1mpress1ve as early
problems have been resolved As md1cated
above, share draft plans have been authonzed
for Federal credit umons by the National
Crecht Umon Admm1strat10n (NCUA) only
smce August 1974 In order to make the share
draft attractive to their shareholders, many
credit umons are not, at least at this time,
chargmg for drafts With mterest on share
accounts m many cases above the maximum
that commercial banks, S&L's, and MSB's can
pay on savmgs deposits, share draft accounts
are an attractive payments alternative Shareholder knowledge of, and demand for, share
draft pnv1leges are the key unknown elements
at this time

Changes affecting
the time deposit components
of M2 and Ma
The prev10us section focused on recent regulatory changes and financial mnovatlons that
have mduced the creat10n of new substitutes
for M 1 Savmgs deposits, which are mcluded
m the "other time and savmgs" component

Improvmg the Monetary Aggregates· Staff Papers

156

TABLE 6• Share Drafts at Credit Uruons

Month

Credit umons offenng drafts

Federal

I

State•

I

Credit umons
approved to
offer drafts•

Drafts drawn per month•
(thousands)

Federal

' Total

I

Total

Federal credit umons
offenng share drafts

I

Amount drawn Shares subJect to
h
withdrawal by
draft per month
per mont
Thousands of dollars

1975-May
June
July
Aug
Sept
Oct
Nov
Dec

5
6
11
16
27
53
65
81

7
8
15
17
19
19
29
37

12
14
26
33
46
72
94
118

12
29
54
81
96
120
143
170

15
20
26
32
51
184
106
179

23
33
44
59
91
144
171
278

1,100
1,200
1,800
2,100
3,100
4,500
5,600
9,300

2,208
3,471
3,972
5,028
6,759
9,453
12,111
14,395

1976-Jan
Feb
Mar

108
118
131

55
63
59

163
181
190

189
203
223

189
247
375

304
399
575

12,300
13,939
20,846

23,092
29,718
37,879

1

Data for State-chartered credit unions mclude an mcomplete mdustry sample
• Federally chartered, mcludes those now offenng drafts
'Partially esllmated by the Nauonal Credit Umon Adm1mstra11on
SOURCE -NCUA

of M 2, have been sigmficantly affected by recent regulatory changes This section analyzes
two changes m the time deposit component
of "other time" deposits First, the effect of
penalties for early withdrawal and the estabhshment of higher mterest rates for the newly
created, longer-maturity time deposits with
small mmimum denommations are discussed
Second, the mclusion of some large-denommation time deposits withm the current definition of other time deposits will be exammed

Longer-maturity,
consumer-type time deposits
Two recent changes m the Federal regulations governmg mterest payment on deposits
by depositary 'mstitutions have affected the
composition and meaning of the time deposit
components of M 2 and M 3-penalties for early
withdrawal of time deposits and the establishment of higher mterest rate ceilmgs on newly
created, longer-maturity time deposits 14 The
former decreases the liqmdity of time deposits
because the dollar value of the penalty mcreases as the maturity date approaches The
latter has lengthened the maturity composition of other time deposits because of the
relatively attractive rates paid on longermaturity deposits It also has decreased the
14 Much of the mformauon m this sect10n 1s based
on work done by Gerald N1ckelsburg, while a member
of the research staff of the Board of Governors


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ove1-all hqmdity of other time deposits and
reduced the substitutability between smalldenommat10n time deposits and demand deposits Time deposits have become more like
securities and less hke deposits
In July 1973 the Federal Reserve amended
Regulation Q to modify the structure of mterest penalties for withdrawal of time deposits
prior to maturity, the FDIC made a correspondmg change m its regulations One reason
for this change was to make the penalties for
early withdrawal of time deposits the same
for banks and for thrift mstitutions The penalty for early withdrawal was established as
(1) the forfeiture of 3 months' mterest and
(2) for the remamder of the period durmg
which the withdrawn amount was held, the
1eduction of the rate paid to the regular passbook rate 15
In addition to the establishment of the
modified penalty, banks were also reqmred
under Regulation Q to describe fully and
clearly by written statement how the penalty
provisions apphed to time deposits Table 7
provides an example to illustrate the penalty
for early withdrawal of a 4-year $1,000 time
certificate of deposit It displays the mcreasmg
dollar cost of withdrawal of the deposit prior
15 The rule for early withdrawal m effect before July
1973 permitted a bank to pay a time deposit before
maturity only m an emergency, when the withdrawal
was necessary to prevent great hardship to the depositor In such cases, the depositor forfeited accrued
and unpaid interest for a penod of up to 3 months

Developing Money Substitutes

157

TABLE 7 Penalty for Early Withdrawal of a $1,000, 7 ¼ Per Cent, 4-Year Certificate
Dollars, except as noted
Year and
quarter

Imputed value 1f
held to matunty

Value 1f withdrawn
pr10r to matunty 1

Penalty for early
withdrawal

Effecllve rate of
return 1f withdrawn
at given date'
(per cent)

1-1
2
3
4

1,018
1,036
1,055
1,074

12
58
37
49

1,000
1,012
1,025
1,037

00
50
16
97

18
24
30
36

12
08
21
52

2 49
3 33
3 74

2-1
2
3
4

1,093
1,113
I, 113
I, 154

97
80
99
53

1,050
1,064
1,077
1,090

95
08
38
85

43
49
56
63

02
72
61
68

4
4
4
4

00
16
28
37

3-1
2
3
4

1,175
1,196
1,218
1,240

46
77
46
54

1,104
1,118
1,132
1,146

48
29
27
42

70
78
86
94

98
48
19
12

4
4
4
4

44
50
54
58

4-1
2
3
4

1,263
1,285
1,309
1,332

03
92
23
96

I, 160
1,175
1,189
1,204

75
26
95
82

102
110
119
128

28
66
28
14

4
4
4
4

61
64
66
69

'$1,000, plus mterest actually earned, calculated as follows loss of 90 dws' (I quarter's) mterest,
with mterest paid for remamde1 of the penod actually held at the passbook rate of 5 per cent, com
pounded quarterly
2 Annual percentage rate assummg quarterly compoundmg

to matuuty as the maturity date approaches
The calculations assume an interest rate of
7¼ per cent compounded quarterly if the deposit is held for the full 4-year contract life
The p,mbook rate is assumed to be 5 per
cent, also compounded quarterly The penalty
represents the "cost of hqmd1ty" imposed by
the current regulations The effective rate of
1 eturn if an early withdrawal is made is shown
m the last column
Also m July 1973, the Federal Reserve, the
FDIC, <1.nd the FHLBB created a new time
deposit category with a 4-year maturity and
J. lugher ceilmg rate than had previously been
<1.vailable These 4-year certificates were at that
time, and are still, quite popular since they
bear a 7¼ per cent rate ceilmg for banks and
a 7½ pet cent ceiling for MSB's and S&L's 16
As a result, substantial shiftmg of funds from
~horter to longer maturities began in July
1973 The shifting was reinforced in Decemhct 1974 by the introduction of a 6-year ume
rn Ongmally, the 4 year deposits with mm1mum de
11ommat1ons of $1,000 had no mterest ce1lmgs and were
known as "wild card" or "topless" certificate~ However,
followmg complamts from many depo~1tary mstilut10ns
that note competition was adversely affectmg their
lendmg rates, the Congress made clear Its desue that
ce1lmg rates be established for the 4 year certificates
I:ffect1ve November I, 1973, the Federal agencies imposed mterest rate ce1lmgs on these deposits of 7¼
per cent for banks and 7½ per cent for S&L'~ and
MSB's


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Federal Reserve Bank of St. Louis

deposit maturity category with ceiling rates
of 7½ per cent for b<1.nks and 7¾ per cent
for S&L's and MSB's
As shown m T <1.ble 8, which presents data
on time <1.ml savings deposits by maturity for
rommerCIJ.l b,mks, the trend toward a lengthened matunty d1stribut10n of time deposits
ts fairly easy to identify Similar mformauon
is given for MSB's m Table 9 and for S&L's
in Table 10
At each type of inst1tut10n, the longerm<1.turity, small-denommauon time deposits
have grown at a considerably more rapid pace
than have the shorter-maturity certificates In
fact, outstanding small time deposits with matunues of less than 2½ years declined or remamed constant m absolute sIZe and declined
1 elative to total 5mall-denommat10n ume deposits except for the latest observat10n-Janu<11 y 1976-when market mtere5t rates were low
t elative to time deposits The most rapid
growth occurred m small-denommauon time
deposits with maturities of 4 years or more 11
17 Tht:, S&L data a1e reported as remammg maturity,
and thus the 4 year accounts represent only recent
~ales of certificates for each survey By the time of
the next survey, those 4 year certificates previously
mued ,\Ill have lc~s than 4 years remammg to ma
tuuty and thus will be counted m the 2 to 4 year
matunty category This explams a large part of the
growth m accounts with 2- to 4-year rcmammg maturity

Improvmg the Monetary Aggregates Staff Papers

158

TABLE 8 Time and Savmgs Deposits at All Commercial Banks, 1973-76
Savings
Date

Total

I

Small ume

I

f~~rs
over

Total
savings
and
small
time

48,510 9,956 3,181
45,554 13,262 12,954
41,422 15,663 21,027
37,741 17,365 28,786
36,372 19,500 35,956
36,506 20,453 42,070

238,532
245,987
255,267
264,149
291,514
317,417

118,487
132,309
158,185
169,267
153,816
144,223

104,173
119,298
148,580
157,557
135,975
124,300

14,314
13,011
9,605
11,710
17,841
19,923

67
65
62
61
65
69

33
35
38
39
35
31

29
32
36
36
31
27

4
3
2
3
4
4

to 11 to 2'/212 to 41
I Up
1 year
years
years
1
/2

Total NOW Other

Total

130,584 na 130,584
130,923
3 130,920
137,307 17 137,290
141,122 83 141,039
158,515 234 158,281
171,321 394 170,927

107,948
115,064
117,960
123,027
132,999
146,096

46,301
43,294
39,848
39,135
41,171
47,067

37
35
33
33
36
37

30
30
29
28
30
32

13
11
10
10
9
10

4

Large ume
Total

1 year
to I and
I Up
1 year
over

Millions of dollars
7-31-73
1-31-74
7-31-74
1-31-75
7-31-75
1-31-76

357,019
378,296
413,452
433,416
445,330
461,640

7-31-73
1-31-74
7-31-74
1-31-75
7-31-75
1-31-76

100
100
100
100
100
100

Per cent of total
37 na
35
*
33
*
33
*
36 *
37 *

3
4
4
4
4
4

14
12
10
9
8
8

I
3
5
7
8

8

n a Not available
* Less than O 5 per cent of total
NoTE -Data from FR Quarterly Survey of Time and Savtngs
Deposits, Weekly Cond1t1on Report of Large Commercial Banks
and Domestic Subs1d1anes, Reports of Deposits of Member Banks,
Report of Condition of All Commercial Banks (call report)-Large
Denommatlon Time Deposit Supplement
The denommational breakdown of time deposits-under and over
$100,000--1s available twice each year on the June and December
call reports begmrung December 31, 1973 The matunty breakdown
oflarge time deposits 1s taken from the monthly Survey of Negotiable

CD Maturity Structure at Weekly Reportmg Banks, and 1t ts assumed
that all other large time deposits have the same maturity structure
A special survey m February 1975 provided evidence for this assumption The weekly reportmg bank data provide mforma t1on on large
negotiable CD's, and smce 1975 on all large time deposits The maturity d1str1but1on for most small time deposits 1s , eported four times
per year m the Survey of Time and Savmgs Deposits These data
are for md1v1duals, partnerships, and corporations only
Details may not add to totals due to rounding All data are m
ongmal maturity

Savmgs deposits at S&L's and MSB's declmed
m relative, though not nommal, amounts durmg this period Savmgs deposits at commercial
banks, however, experienced a large percentage mcrease This mcrease may be due to the
convemence factor of havmg savmgs and demand accounts at the same mstltuttons, while
longer-maturity time deposits are more hkely

to be placed at the mstitution offermg the
lughest yield
The relative mcreases m the longer-maturity
categories, coupled with their relatively ilhqmd nature due to the penalty cost for withdrawal prior to maturity, suggest that not only
are those deposits quahtat1vely different from
savmgs deposits but also they are qmte un-

TABLE 9, Time and Savmgs Deposits at FDIC-Insured Mutual Savmgs Banks, 1973-76
Savmgs
Date

Total

I

Small time

I

Total NOW Other

Total

f~rs
over

Total
savmgs
and
small
tune

5,954 2,046
5,183 7,596
5,328 11,525
5,360 14,372
5,431 17,962
5,639 19,985

82,122
83,511
84,064
85,248
91,949
97,061

694
711

99
99
99
99
99
99

1
1
1
1
1
1

to 11 to 2½ 12½ to 41
I Up
I year years
years

4

Large time
Total

I

Upto
1 year

year
I 1over
and

Mtlhons of dollars
7-31-73
1-31-74
7-31-74
1-31-75
7-31-75
1-31-76

82,496
83,977
84,607
86,070
92,643
97,772

59,300
56,694
56,305
56,341
60,267
62,207

7-31-73
1-31-74
7-31-74
1-31-75
7-31-75
1-31-76

100
100
100
100
100
100

72

113
140
172
221
327
401

59,187
56,554
56,133
56,120
59,940
61,806

22,822
26,816
27,759
28,907
31,682
34,854

72

28
32
33
34
34
36

1,439 13,383
1,433 12,605
I, 191 9,715
1,304 7,871
1,394 6,895
1,728 7,502

374
466
543
822

143
213
334
638
482
485

231
253
209
184
212
226

Per cent of total
68

67
65
65
64

*
*
*
*
*
*

68

67
65
65
63

* Less than O 5 per cent of total
NOTE -Aggregate MSB deposit data are avat!able as I-day figures
for the last day of each month The matunty dtstnbut1on of these
deposits 1s reported four times a year, on the same day as the commercial bank STSD, m the FDIC Quarterly Survey of Most Common


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Federal Reserve Bank of St. Louis

2
2
1
2
2
2

16
15
11
9
7
8

7
6
6
6
6

6

2
9
14
17
19
20

*
*
*

1

1

*

*
*
*
**
*

Rates of IPC Time and Savtngs Deposits m FDIC-Insured Mutual
Savmgs Banks
Details may not add to totals due to roundtng All data are m
ongmal matunty

Developing Money Substitutes

159

TABLE 10 Savmgs Deposits at FSLIC-Insured Savmgs and Loan Assoc1at1ons, 1973-76
Passbook savmgs
Date

Total

Term savmgs
Matunty

Total

NOW

Other

Total

Total
passbook
and
small term
savings

Size

Uptol 1110212103½
year
years
years 1

I years
3½

1

Small

I

Large

M1lhons of dollars
9-30--73
3-31-74
9-30--74
3-31-75
9-30--75
3-31-76

207,997
228,842
231,721
249,491
270,133
294,912

99,667
104,504
102,763
109,399
116,819
124,557

9-30--73
3-31-74
9-30--74
3-31-75
9-30--75
3-31-76

100
100
100
100
100
100

48
46
44
44
43
42

0
4
19
44
72
98

99,667
104,500
102,744
119,356
116,747
124,459

108,330
124,339
128,957
140,092
153,315
164,091

48
46
44
44
43
42

52
54
56
56
57
56

58,856
66,672
59,999
53,867
56,800
54,276

34 254
22,072
18,408
17,443
20,613
38,388

6,088
13,405
30,954
17 110
55,577
46,146

9,132
22,100
19,596
21,672
20,325
25,281

105,671
120,904
125,218
134,752
148,024
158,502

2,659
3,435
3,740
5,340
5,290
5,589

205,338
225,408
227,980
244,151
264,844
283,059

3
6
13
19
21
16

4
10
9
9
8
9

51
53
54
54
55
54

I
2
2
2
2
2

99
99
98
98
98
96

Per cent of total

••
•
••

28
29
26
21
21
18

16
10
8
7
8
13

1 These maturity breaks are those used by the FHLBB
* Less than O 5 per cent of total
NOTE -Aggregate days are reported as I-day figures for the last
day of each month The maturity breakdown of savmgs capital 1s
reported m the FHLBB Serm-Annual"'survey of Selected Interest/

D1v1dend Rates and Account Structure, for March and September
of each year These data are reported as remammg maturity and no
attempt was made to convert to ongmal maturity
Details may not add to totals due to roundmg All data are m
remammg matunty

hkely to be used for transactions purposes
Portfolio theory suggests that the hqmd1ty of
these longer-maturity deposits makes them
more hke secunues, and thus complementary
to, rather than substitutes for, hqmd assets
In order to evaluate movements m the monetary aggregates relative to economic act1v1ty,
some consideration might be given to segregatmg longer-maturity deposits from those deposits that might be more readily usable for
transact10ns purposes by the depositor

small-denommatlon time deposits, wluch are
subject to mterest ce1lmgs, and, therefore, rates
on large-denommat10n time deposits tend to
be sticky, so that such deposits are sens1t1ve
to market rates of mterest 18
To the extent that the time component of
M 2 mcludes la1ge-denommat1011 time deposits,
M 2 and MJ a1e more heterogeneous measures
As currently defined, the time deposit component M 2 consists of total time and savmgs
deposits at all commercial banks less large
negotiable CD's at weekly reportmg banks
Tlus defimt1011 was ongmally adopted 111 large
part because no data on large-denommatlon
time deposits other than CD's were readily
available In add1t1on 1t was felt that negotiable CD's at large banks accounted for a
s1gmficant share of the volume of, and the
volat1hty m, total large time deposits However, the d1stmct1on between negotiable and
nonnegotiable deposits may be largely techmeal smce 1t 1s reported that many banks permit convers10n from one form to the other
Moreover, the exclus10n of such deposits from

Large-denomination time deposits
In addition to the mclus1on of both shortand relatively long-maturity time deposits m
the other time components of M 2 and M 3 ,
these aggregates mclude varymg amounts of
time deposits m denommat10ns of $100,000 or
more that further distort their conceptual
meamng Changes m large-denommat10n time
deposits often reflect changmg bank aggressiveness m seekmg funds Smee they are exempt
from the Regulation Q ce1lmg, these deposits
have offermg rates that vary with market rates
Also, a bank's aggressiveness m seekmg funds
through large-denommat10n time deposits will
depend on its deposit flows, loan demand, relative rate on other sources of funds, and so forth
These deposits often behave differently from


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18 Thrift institutions tend to have relatively ins1gmficant levels of large denomination time deposits Thus
the large time deposits in M 2 and Ma come mainly from
large negotiable and nonnegotiable time deposits issued
by nonweekly reporting banks and nonnegotiable deposits issued by weekly reporting banks

160

lmprovmg the Monetary Aggregates Staff Papers

M 2 and M 3 merely because they are habihties
of large rather than small banks is somewhat
arbitrary
The growth of large-denommat10n time deposits at all banks-regardless of whether they
are m negotiable or nonnegotiable form-is
different from that of small-denommation time
deposits For example, m some periods movements m the other time component of M 2 were
not consistent with observed patterns of thnft
deposit flows This suggests that either the demand for small-denommation accounts at
thnft msututions is different from that for
similar accounts at banks, or that changes m
the nonexcluded large-denommauon time deposits have been obscurmg the movements m
small-denommat10n time deposits As noted below, the evidence supports the second hypothesis
While the mclus10n of large-denommation
time deposits m the other time and savmgs
deposit data has been of concern for some
time, evaluation of the quantitative sigmficance of such deposits has been hampered by
the sparseness of the data Although the data
now available are still extremely limited and
can be analyzed only under very gross assumptions, they do shed some hght on the
magmtude of the problem Begmnmg m June
1973, when margmal reserve reqmrements were
imposed on all large time deposits above a
$10 million base, the approximately 900 member banks affected by these reqmrements began to report the total amount of their time
deposits m denommations of $100,000 or more
on a daily-average basis 19 The volume of these
deposits reported was surpnsmgly large At
large weekly reportmg banks the volume of negotiable CD's ranged between $58 billion and
$67 billion m the latter half of 1973 Dunng
that same penod other large time deposits at
all member banks ranged from $30 billion to
$40 billion
Recogmtion of the existence of a sigmficant
10 Data were also gathered on large denommatlon
time deposits at all member banks as part of the special
monthly survey conducted from October 1973 to June
1974 to momtor the growth m 4-year certificates at
commercial banks


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amount of large-denommat10n time deposits
that were not counted as CD's led the Federal
Reserve to collect data on total large-denomination time deposits from its large weekly
reportmg bank sample begmnmg m January
1975 These data permit comparison with data
on large-denommat10n time deposits dVailable from special supplements to the June and
December call reports smce December 1973 20
With these data as a base, Table 11 shows
some very rough estimates of both other time
and savmgs deposits and M 2, with estimates of
total large-denommation time deposits-not
JUSt negotiable CD's at weekly reportmg banks
-removed for each month of 1975 Also shown
are other time deposits and M 2 as currently
defined A comparison of the adjusted seneskeepmg m mmd that the data are only rough
estimates-with the senes as currently defined
suggests that movements m large-denommation
time deposits sigmficantly mfluence M 2 21 As
20 The December 31, 1975, call report was taken on
a Wednesday, allowmg for a direct comparison with
\\eekly reportmg bank data, which are always for
Wednesdays, the last day of the bank statement week
A comparison of large time deposits reported on the
<-all and on the weekly report turned up many reportmg errors on both reports This suggests that
problems still exist with the data on large time deposits
and that any estimates based on either the weekly
1eportmg bank sample or the call report should be
recogmzed as crude Unfortunately, smce the supple
ment to the call report on large denommallon time
deposits was mtroduced m December 1973, no June or
December call date other than December 1975 was on
a Wednesday This makes 1t more difficult to detect
1eporting errors
21 The ad Justed senes m Tables 11 and 12 were con
structed by subtractmg total large denommatlon time
deposits from total time deposits, both not seasonally
ad1usted, and then applying the seasonal factors for
other time and savmgs deposits at all commercial
banks The series on large time deposits 1s based on
data from the call report, the survey of time and
savmgs deposits, the report of deposits when margmal
reserve reqmrements were imposed, and the weekly re
porting data senes It should be recogmzed that the
crude method of seasonal adjustment used m con
structing the adjusted other time and savings deposits
and the ad1usted M2 senes bestows on them certam
characteristics, which are difficult to quantify How
ever, m the absence of suffiaent data to derive
seasonal factors for these adJusted senes, a Judgment was
made that 1t was better to use these data, constructed by
the best method ava1lable, than to use data not seasonally adjusted The point I wish to illustrate is that
movements of M2 as currently defined and of M 2 less all

Developing Money Substitutes

161

TABLE 11 Other Time and Savmgs Deposits, M2, and Large-Denommatmn Time Deposits at Weekly
Reportmg Banks, 1975
Othert1me
and savmgsl
Month

Other lime
and savtngs,
adjusted'

Large denommauon time
M2•

M2, • adjusted

Total

Seasonally adJusted annual growth rates, monthly averages
(per cent)
(I)

Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec

12
13
9
JO
15
18
14
6
6
10
11
7

0
0
6
3
I
4
0
4
0
4
9
9

(2)
14
26
13
21
21
29
24
8
2
11
18
13

0
7
3
I
7
I
I
9
9
I
7
7

(3)
4
7
9
6
13
16
9
5
4
5
10
3

I
2
3
I
4
5
5
7
2
I
8
I

Negotiable

Other

I

I

Ra 110 of other
to total

Levels, last Wednesday of the month, not seasonally adjusted
(b1Ihons of dollars)

(4)
3
12
13
II
16
21
3
7
2
5
13
5

I

(5)

8
8
I
7
4
5
5
I
3
2
8
5

128
125
124
120
119
116
114
114
117
116
116
116

(7)

(6)

6
0
8
3
6
3
8
6
4
7
I
5

91
87
89
84
83
82
81
81
84
83
83
82

3
9
0
2
5
0
2
2
7
3
3
8

37
37
35
36
36
34
33
33
33
33
32
33

(8)

4
I
8
I
1
3
6
3
2
4
8
7

29
30
29
30
30
29
29
29
28
29
28
29

1 Total time and savmgs deposits less large denommat1on negotiable time deposits at weekly reportmg banks
2 Total lime and saVIngs deposits less all large denommatwn time deposits
3 M1 plus other lime and savmgs deposits
• M1 plus adjusted other lime and savmgs deposits

can be seen in column 8, the behav10r of
l.11ge-denominat1on time deposits other than
negotiable CD's at weekly reporting banks
appears to be similar to that of CD's the rat10
of nonnegotiable to total large-denomination
time deposits is fairly constant-that is, the
two senes move together
In order to examine further the relat10nshi p between the components of total large
time deposits and total time deposits at the
weekly reporting banks, weekly data available
since January 1975 were examined The simple
correlat10n coefficient between negotiable CD's
and all other large-denominat10n time deposits
was calculated to be O 84 in levels (0 24 in
first differences) More important, the correlat10n between other large-denominat10n time
deposits and small-denommatlon time and
~avings deposits was found to be negauve,
-0 90 m levels and -0 68 in first differences
These conelat10ns suggest that at the weekly
reporting banks the behav10r of negotiable
CD's and that of all other large-denommat10n
time deposits are similar, and that largeclenominat10n time deposits other than nelarge denomination time deposits are different To the
extent that the seasonal factors for other time and sav
mgs deposits as currently defined were used to adJust
"ad1usted" other time and savmgs deposits, any bias 1m
parted to the data because of the seasonal ad1ustment
should be toward greater, rather than le~~. s1milanty m
behav10r between the senes


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TABLE 12 Growth Rates of Other Time and Savmgs
Deposits and M 2 before and after
AdJustment to Exclude LargeDenommatlon Time Deposits
Quarterly averages, seasonally ad1usted annual rates

Quarter
1973-Q4
1974-Ql
Q2
Q3
Q4
1975-QI
Q2
Q3
Q4

Other
time and
savmgs 1
12
13
9
8
8
9
12
12
9

5
0
I
3
4
9
5
6
I

Other tune
and savmgs,
ad1usted 2
2
IO
3
I
5
13
22
19
II

9
3
I
7
6
0
3
4
I

MEMO

M,'

8
9
7
6
6
5
10
10
6

9
6
5
4
4
6
2
I
I

Ma•
~d1usted

4
8
4
3
4
6
14
13
6

I
0
4
I
7
5
4
0
8

Nonbank
time and
savmgs 6
7
7
5
4
6
10
16
18
14

6
7
I
3
7
6
6
3
2

1 Total time deposits less large denommatlon negotiable CD's at
weekly reportmg banks
2 Total time deposits less estimated total large denommat1on time
deposits
3 M, plus other time and savmgs deposits as defined m note I
• M1 plus adjusted other time and savmgs as defined m note I
r. Deposits '\t S&L's MSB's and CU's

got1able CD'~ behave inversely to smalldenominat10n time deposits Tlus supports the
hypothesis that banks manage all large-denominat10n time deposits, not JUSt negotiable CD's
Fm.illy, Table 12 compares M 2 and other
time deposits with correspondmg adjusted
~e11es that exclude all large-denominat10n time
deposits on a quarterly-average basis from
1973 Q4 to 1975 Q1 22 Fm comparison pm22 Sec note 21, which dl\Lllbcs the data and thl.
mcthocl med to estimate large ttmc dcpo~Its The dat,t
~hould be viewed as rough estimates 1athcr than actual
mlasuted stocks

162

poses, the nonbank thrift deposit component
of Ma is also shown Even on a quarterlyaverage basis, removal of large-denommation
time deposits from M 2 results m an adjusted
~eries that is qmte different from M 2 as currently defined For example, during each of
the last three quarters of 1974, the adjusted
M 2 series grew much more slowly than M 2 as
currently defined and then grew more qmckly
through all of 1975 This difference is understandable, of course, smce the series on other
time and savmgs deposits as currently defined
is qmte different from the series on other time
and savmgs with total large time deposits removed The correlat10n between M 2 and "adJUSted M/' is only O55 m levels, about the same
as the correlat10n (0 49) between other time
and savmgs as now defined and nonbank time
and savmgs More important, the correlation
between the adjusted series on other ume and
savmgs deposits and the series on nonbank
time and savmgs deposits is O92 Inasmuch as
the components of these deposit series are characteristically similar, it is not surprismg that
their movements are highly correlated

Possible recomposition
of the monetary aggregates
The regulatory changes and financial mnovat10ns discussed 1n the precedmg sect10ns
suggest that the characteristics of the components of the monetary aggregates, as currently defined, have been altered greatly m the
past few years to become more heterogeneous
The pace of change has been rapid, and the
distmction between time deposits and savmgs
deposits is more clearly defined now than prior
to 1973, conceptually, demand and savmgs
deposits are more similar The components of
time deposits have become more distmct m
themselves as longer-maturity, small-denommat10n deposits with higher mterest rate ceilmgs
have been created and as banks have mcreased
their use of all large-denommatlon time deposits-not JUSt negotiable CD's-as a flexible
source of funds
Because recent changes either have already
affected the behavior of the monetary aggre-


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Federal Reserve Bank of St. Louis

Improvmg the Monetary Aggregates Staff Papers

gates or are expected to do so, 1t is appropriate to consider how current defimtions
might be altered to reflect evolvmg developments Two defimtional changes are suggested
by the prev10us discuss10n First, the development of savmgs-based transfer systems and the
hqmdity of savmgs deposits relative to time
deposits other than negotiable CD's suggest
that some combmation of M 1 and savmgs deposits at banks and thrift mstitutions might
be considered to represent transactional balances Second, the changmg maturity structure
of small-denommauon time deposits and the
behavior of large-denommat10n time deposits
suggest that the defimtion of other time deposits, excludmg savmgs, ought to be reconsidered Such a defimtional change would
affect M 2 and Ma and the higher-numbered
M's but would have no effect on M 1 The possible permutat10ns and combmations stemmmg from these two types of defimtional
changes are fairly large Therefore, the remamder of this paper focuses not on every
possible type of monetary aggregate that might
be considered but more broadly on the two
ma1or categories of change
At present the extent to which regulatory
changes and mnovations relatmg to savmgs
deposits have affected, or will affect, the monetary aggr_egates is unclear Money transfers
will m the future mvolve both demand and
savmgs deposits, and so long as the prohibition
of mterest payments on demand deposits remams, easily faohtated transfers from savmgs
will make those deposits a highly attractive
transactions asset Currently, savmgs deposits
have a small but growmg role m the payments
mechamsm, with a large potential for further
growth
Historically, the motives for holdmg M 1
balances and savmgs deposits have been different, and therefore movements m these two
variables have been different Although both
are directly related to mcome and mversely
related to market mterest rates, flows of funds
mto and out of savmgs deposits have been
determmed primarily by the relationship between the ceilmg on the savmgs deposit mterest
rate-the "own" rate-and short-term market

Developing Money Substitutes

rates-competmg rates In addit10n, until recently the transact10ns costs for transferrmg
funds between savmgs deposits and M 1 -type
balances have been s1gmficant, often mvolvmg
such mconvemences as personal presentation
of a passbook at the depositary mstltution
This fact suggests that, although statistical
,malysis of historical movements m an aggregate that combmes M 1 and savmgs deposits
may provide some msight as to the appropriateness of such a defimtion at this time, the
dec1S1on to mclude savmgs should probably
rest on evidence that mdicates the ongomg
substitution of savmgs for demand deposits
m the payments mechamsm 23
Recent changes suggest that substitution is
takmg place m the payments mechamsm and
that the conceptual differences between savmgs deposits and M 1 balances have m fact
already been reduced NOW accounts, which
are available m New England, are essentially
savmgs deposits that can be transferred to a
third party by written draft Share draft accounts at credit umons are similar to NOW's,
although there are legal differences between
them Both types of drafts are legal payment
mstruments, as are commercial bank checks
However, such accounts allow the depositor to
earn mterest on the funds subject to draft
until payment 1s made, whereas demand depos1 ts earn no mterest As mentioned earlier,
several types of savmgs-transfer systems, md udmg telephomc transfers from savmgs to
demand deposits, third-party nonnegotiable
transfers directly from savmgs, and pomt-ofsale transfers from savmgs, have been developed The first type appears to have gamed
widespread acceptance among banks, S&L's,
and MSB's, although the actual volume of use
of the transfer arrangements 1s difficult to
measure
At some pomt, consideration must be given
to creatmg a new monetary aggregate by
mergmg mto M 1 those deposits that are close
substitutes for M 1 balances Current mformation suggests that NOW accounts, share draft
23 Appendix 2 presents the results of some recent
staff analysis of M1 plus savmgs usmg h1stoncal data


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163

accounts at credit umons, and checkmg accounts available at State-chartered thrift mstitutions would be the first categories of M 1
substitutes that might be considered exphc1tly
as transactions balances Such balances can
be qmte easily identified and measured, so
foldmg them mto current M 1 should present
only mmor problems The next category of
deposits thc1t can be considered as a substitute
for M 1 is savmgs deposits at banks and thrift
mst1tutions from which transfers can be 1mt1ated As savmgs-based transfer systems contmue
to develop and spread, the subst1tut10n of savmgs deposits for demand deposits can be expected to take place and thm what may evolve
1s one or more monetary aggregates composed
of currency, demand deposits, saHng~ deposits
c1gamst which some form of negotuble draft
can be drawn, and all other savmgs that can
directly or md1rectly be utilized f01 makmg
payments
Just when such defimt1onal changes ought
to be made 1s unclear The proportion of savmgs deposits used for transactional purposes
at this time 1s small but growmg, and 1t 1s
hkely that some s~vmgs will always be used
for the trad1t10nal reasons-that is, as a
temporary abode of purchasmg power Unless
some method can be devised to distmgmsh
clearly the t1ansact10nal from the nontransact10nal components of ~avmgs deposits, 1t
would be better to mclude all savmgs m a new
Mi-type aggregate, rather than ignore the mcreasmg use of such deposits Savmgs deposits
that can be readily used to make paymentsthat 1s, for transactions purposes-should be
mcluded m the defimuon of M 1 But not all
savmgs deposits are transact10nal m nature
The suggested mclusion of all savmgs deposits raises the question of whether the traditional d1stmction between deposits at commercial banks and at thrift mstitut1ons should be
mamtamed or dropped The necessity for such
a d1stmct1on seems to be fadmg as the thrift
institutions contmue to assert their presence
m the payments mechamsm Their expanded
role has been recogmzed by the Federal Reserve's mterim access pohcy to System ACH's
(adopted m January 1976), which mdicated

lmprovmg the Monetary Aggregates· Staff Papers

164

raises certam problems that have been noted
earlier For example, what is the appropriate
maturity break for separatmg security-type,
small-denommation deposits from other small
time deposits? From a conceptual standpomt,
2½ years is not much shorter than 4 years,
however, it is sigmficantly less than 6 years
The ch01ce of the breakmg pomt could be dictated by data availability Prior to July 1973
all small-denommatlon time deposits with miual maturities of 2 years or more were subject
to the same mterest rate ceilmg It is unlikely
that a large share of deposits subject to that
ceilmg had maturities of 4 years or more Moreover, data collected after the mtroduct10n of
4-year certificates m July 1973 are reliable and
so, on the basis of data considerations, the most
reasonable maturity break would be deposits
with an miual maturity of less than 4 years
compared with those with an miual maturity
of 4 years or more With large-denommauon
deposits, most of the problems are related to
data availability and comparability through
time Data available before 1973 are scanty and
may not permit accurate estimat10n of total
large time deposits Thereafter, data are better
but still allow only crude estimates of total
large time deposits
In order to see how much the exclus10n of
longer-maturity small time deposits and all
large time deposits affects the profile of the
growth of M,, available data were used to create new aggregates, as shown m Table 13 The

that ACH transfers could "origmate from any
account havmg third-party payment powers"
without distmgmshmg between commercial
banks and thrift mst1tut10ns
The discussion m the section on recent
regulatory changes suggested that the "other
time" deposit component of M 2 suffers from
at least two conceptual problems The first
problem is that longer-maturity small-denomination time deposits are relatively less hqmd
compared with those with the shorter maturities, yet it is the longer-maturity deposits
that have paid the highest mterest rates and,
therefore, have attracted relatively more funds
than the shorter deposits The 4- and 6-year
deposits are more hke securit1es than deposits
and, therefore, can be expected to behave differently from the other maturities The second
problem stems from the fact that other time
deposits contam large time deposits other than
negotiable CD's at weekly reportmg banks,
and accordmg to recently obtamed evidence,
these deposits behave hke negotiable CD'sthat is, banks manage such deposit habihties
by seekmg to mcrease them when funds are
needed and allowmg them to run off when
funds are not needed In both cases, it is not
unreasonable to categorize both types of time
deposits conceptually as bemg different from
5mall-denommat1on time deposits with short
matuntles that are, in many portfolios, "temporary abodes for purchasmg power "
Redefinmg Mi along these conceptual Imes

TABLE 13. Companson of M2, M~, and M?, Not Seasonally AdJusted, 1973-76

I

Levels (b!lhons of dollars)
Date
7 /31/73
1/31/74
7 /31/74
1/31/75
7 /31/75
1/31/76

M,

551
581
597
619
647
674

I

1
1
8
5
8
1

Mi

496
502
606
511
537
550

I

7
2
9
1
8
3

M''

486
489
491
492
518
529

8
0
2
7
3
8

I

Annuahzed percentage changes
M,

IO
5
7
9
8

9
7
3
1
I

I

Mi

2
I
I
10
4

2
9
3
9
6

I

M~'

9
9
6
10 4
4 4

NoTE -When possible, data are for the date shown If they are unava!lable, data for the closest day
were used
The following defimt1ons are used
M, = Mi plus total time and savings deposits less negotiable large denomination CD's at weekly
reporting banks (current M,)
M; = M2 less all large denommat1on time deposits at all commerctal banks and small time
deposits with maturities of 4 years or more
M;' = M, less all large-denommatlon time deposits at all commercial banks and small time
deposits with matunties of 2 ½ years or more


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Federal Reserve Bank of St. Louis

Developing Money Substitutes

data are not seasonally adJusted and are smgleday estimates correspondmg to dates of the
Survey of Time and Savmgs Deposits (STSD) 24
For most of the time penod shown m Table
13, the growth rates of the newly defined M 2type aggregates were s1gmficantly different
from those for Mi a~ It 1s currently defined
Moreover, Mi defined to exclude large time
d.nd longer-matunty small time deposits exlub1ted substant1d.lly lower growth rates m each
penod except for July 1975, when mflows to
l4 Some <latJ. are for the Wednesday closest to thL <late
of the STSD


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Federal Reserve Bank of St. Louis

165

other time and savmgs deposits were pnmanly
m the form of savmgs deposits
The apparent differences m growth among
M 2 , M;, and Mr are stnkmg, and the causes
for the differences can easily be traced Table
13 suggests that growth m M 2 as currently
defined may give m1sleadmg 1mpress1ons of
changes m the mix of the public's holdmgs
of deposits that serve as a temporary abode
of purchasmg power More important, 1t 1s
clear from the table that the behavior of
the time deposit components excluded from
the M; and Mr vanables IS s1gmficantly different from that of the remammg components

166

Appendix 1: Third-Party Payment Powers
of State-Chartered Thrift Institutions

The regulatory changes that have expanded the
third-party payment powers of Federally chartered
thrift msutut10ns do not, m general, automaucally
apply to similar msutuuons that have been chartered under the laws of the States m which they
are located A number of States have bankmg laws
that provide for parity m payments powers, and
consequently, m those States all thrift msutuuons
generally can now offer authorized telephonic transfer and preauthorized third-party nonnegouable
transfer services to their customers When parity
does not exist, some mstituuons have broader payment powers than Federally chartered thrift mst1tuuons Bankmg laws m many States are not specific about payment powers, and thus the msutuuons depend on case-by-case rulmgs by the State
bankmg authority
In order to ascertam the status of State-chartered
thrift mst1tut1ons m the payments mechanism, a
special survey of State bankmg authorities was
conducted on a State-by-State baS1S m June 1976
The results of that survey are summarized m
Table A-1, which reports data on five types of payment powers checking accounts, NOW accounts,
credit union share drafts, telephonic transfers, and
preauthorized nonnegotiable transfer services The
checkmg accounts are non-mterest bearmg and are
md1stmgmshable from checkmg accounts at nonmember banks m terms of the payments mechanism
clearmg process In some States these have existed
for a long ume and remam today because of grandfather clauses m ex1stmg laws In other States the
checkmg powers are fairly new, resultmg from
efforts by State legislators to provide thrift mst1tut1ons m their States with powers similar to those


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Federal Reserve Bank of St. Louis

of commercial banks Interest-bearing accounts
agamst wluch written drafts may be drawn are
primarily m two forms-NOW accounts and credit
umon share draft accounts ~ he former are available primarily m New England, although some thrift
mstttuuons m Delaware apparently can offer accounts very much hke NOW's Many States permit
their credit umons to offer share draft accounts
A ma1onty of States have laws that permit thrift
msutuuons to offer transfer services to owners of
savmgs accounts Table A-1 shows two types of
savmgs-based transfer services telephonic transfers
from a ~avmgs account at a thnft mstituuon to a
checkmg account at a commercial bank, and preauthorized nonnegouable transfers (b1ll-paymg
services) In those States whose bankmg laws are
silent about the power of thnft msutuuons to offer
such services State bankmg authoriues have usually
allowed such services upon request by thnft msutuuons w1thm their 1urisd1cuon
The State bankmg authorities were also asked m
the survey whether they expected State laws to be
mtroduced or amended m the near future to allow
State-chartered thrift msutuuons to offer add1t1onal
third-party payment powers The predommant response was that State leg1slat1on would follow smt
should Federal laws be modified to allow expanded
payment powers for thrift msutuuons In States
m which compeuuon among financial msutuuons
for deposits appears to be strong, however, the State
legislatures are hkely to consider the quest10ri of
expanded payment powers m the near future
Those States mclude New Jersey, Pennsylvania,
M1ch1gan, W1sconsm, Mmnesota, Montana, and
Nebraska

Developing Money Substitutes

167

TABLE A-1. Third-Party Payment Powers of State-Chartered Thrift Institutions, June 1976
State
Alabama
Alaska
Arizona
Arkansas
Cahfomta
Colorado
Connecticut
Delaware
Flonda
Georgia
Hawaii
Idaho
Ilhnots
Indiana
Iowa
Kansas
Kentucky
Louisiana
Mame
Maryland
Massachusetts
Mtchtgan
Mmnesota
M1ss1ss1pp1
Mtssoun
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carohna
North Dakota
Ohto
Oklahoma
Oregon
Pennsylvanta
Rhode Island
South Carohna
South Dakota
Tennessee
Texas
Utah
Vermont
Vtrgmta
Washtngton
West Vtrgmta

Checking accounts

MSB
MSB, S&L
MSB, S&L

MSB, S&L
MSB

MSB, S&L
MSB

CU share drafts

cu
cu
cu
cu

cu

S&L
MSB

silent
silent
(,U

MSB, S&L

CU, MSB, S&L

cu
cu
cu
stlent
cu

Telephonic transfers

Preauthortzed
nonnegotiable transfers

parity

parity

parity

panty
S&L
silent

silent
MSB
parity
panty
S&L
S&L
S&L
parity

parity
anty
~ &L
S&L
CU silent

stlent
stlent
silent

MSB, 1-&L
silent
MSB, S&L
CU, S&L
CU, S&L
stlent
S&L

MSB
stlent

parity

silent
MSB, S&L
MSB
MSB, S&L

S&L
MSB

stlent

MSB, S&L

stlent

MSB, S&L
stlent
silent

MSB, S&L

MSB, S&L

W1scons1n

Wyommg

CU = credtt untons
MSB = mutual savmgs banks
S&L = savtngs and loan assoc1at1ons


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NOW accounts

cu
cu
cu
cu
cu
cu
cu
cu
silent

cu
cu
stlent
cu
cu

parity
stlent
MSB
partly
MSB, S&L
S&L
CU, S&L
parity

partly
MSB, S&L
MSB
parity
MSB, S&L
S&L
CU, S&L
S&L

cu

stlent
stlent
silent

panty
CU, MSB
CU, MSB, S&L
silent
silent

partly
silent

partly
MSB, S&L

panty
silent
MSB, S&L
parity

partly
silent
MSB, S&L
parity

Panty = State-chartered mst1tut1ons have the same powers as
Federally chartered mst1tut1ons
Stlent = law does not say, pennttted tf approved by bankmg
authonty

168

Appendix 2: Savings Deposits at Banks and Thrift Institutions
as Transactions Balances

For a number of reasons, savmgs deposits at
commercial banks and thnft msutuuons-or more
precisely, a growmg proportion of such depositshave come to be used as transactions balances
rather than simply as repositories of mterest bearmg
hqmd assets The secular uptrend of mterest rates
has raised the opportunity cost of idle, non-mterestbearmg deposits, mducmg holders of such bal
ances to seek out convement alternatives In add1uon, regulatory changes perm1ttmg telephonic
transfers between savmgs deposits wherever held
and demand deposits at commercial banks, and
nonnegotiable transfers to third parties at both
banks and thnft msututions, have facilitated the
uuhzauon of savmgs deposits for such purposes
The authonzation of savmgs deposits for profitmakmg enterprises has widened the scope of users
of such accounts to mclude relatively more soph1st1cated depositors
These developments suggest the possible need
for the formulation of a broader transactions vanable than M 1 While M 2 , M 1 , and still more comprehensive aggregates can be studied for their 1mphcauons for the general hqmd1ty of the economy,
they do not purport to be transactions balances
An aggregate broader than M 1 but not so broad
as M 2 (which mcludes time deposits) might be appropriate to reflect the changmg habits of the
pubhc regardmg transactions balances Four such
aggregates are exammed here demand deposits
plus savmgs deposits at all commercial banks
(DD+ SB), 1 M 1 plus savmgs deposits at all commercial banks (M1 + SB), demand deposits at all
commercial banks plus savmgs deposits at banks
and thnft msutuuons (DD + SB + ST),2 and M 1
NoTE -Paul Boltz prepared this appendix The comments
of Raymond Lombra, John Paulus, and Steven Roberts were
very helpful m the wr1tmg process
1 Though technically not broader than M , DD+ SB 1s
1
evaluated as a separate aggregate smce the developments m
the payments mechanism toward mterest bearmg transactions
balances may have had only a mmor mfluence on the demand
for currency Excludmg currency serves to focus the results
on the subst1tutab1hty between demand and savmgs deposits
2 Thrift mst1tut1ons mclude S8cL's, MSB's, and CU's


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plus savmgs at banks and thnft msutuuons (M1 +
SB+ ST) The prmc1pal ob1ecuve of the analysis
1s to compare the broader monetary aggregates with
M 1 m tradmonal money demand equations to
determme whether the addition of savmgs deposits
to the money stock strengthens or weakens the mfluence of GNP (as a proxy for transactions) In add1uon, savmgs deposits themselves are regressed as
the dependent variable m money demand equations m order to 1denufy what, 1f any, relauonsh1p
exists among these variables
This analysis 1s part of a complex issue that
extends well beyond the demand for money A
change m the defimt10n of M 1 to account for all
deposits that can be used for transact10ns balances
necessarily has 1mplicat10ns for the defimuons of
Mi and of the broader aggregates as well In
add1t10n, any redefimuons of the monetary aggre
gates along structural Imes may complicate the
conduct of monetary policy 1f the new aggregates
are less subject to the control of the monetary
authority than their predecessors The lmkages be
tween real economic activity and the newly defined
aggregates may still be evolvmg and may be difficult to specify, further comphcatmg the determmauon of monetary pohcy
The basic structural form of the estimated money
demand equations hypothesizes the monetary aggregate to be a function of mterest rates, GNP, and
the aggregate itself lagged one penod 3 The ordinary least squares regressions were run m log form
and m real terms, the deflator bemg the consumer
pnce mdex The Cochrane-Orcutt techmque was
used to ad1ust for senal correlation The results
of the regress10ns are summarized m Tables A-2
and A-3
Savmgs deposits at banks (SB) can be shown to
bear a s1gmficant relation to GNP durmg the 9year penod from 1966 Q3 to 1975 Q2 (Equation
I m Table A-2) The penod of observation was
~hortened to the most recent 5 years to evaluate
1
The source of !he data was the data files of the FRBMIT-Penn quarterly econometric model

Developing Money Substitutes

169

TABLE A-2 Coefficients of Variables m Demand-for-Money-Type Equations
for Savmgs Deposlts 1
Independent vanables
Equation

I
2
3

Intercept
- 119
(- 52)
376
( 42)
046
( 05)

I

Lagged
dependent
vanable

863
(20 06)
971
(4 68)
795
(5 27)

I Treasury
bill
rate

- 075
(-8 44)

(-3
(-3

074
80)
059
87)

Regression sta t1st1cs

Rate on

savings
I deposits I

035
(1 84)
05J_
(I 19)

GNP

119
(2 79)
- 027
(- 112)
146
( 75)

Standard
error

I

R.2

0086

972

0089

960

0090

959

1 The dependent vanable 1s savmgs The period 1s 1966 Q3 to
1975 Q2 for Equation 1, and 1970 Q3 to 1975 Q2 for Equations 2
and 3 The numbers m parentheses are I stausucs For a one tailed

test at the 95 per cent confidence level, the critical value of the I-statistic
1s I 76 for the shorter per10d (1970 Q3 to 1975 Q2) and I 70 for the
longer period (1966 Q3 to 1975 Q2)

whether the relationship between savmgs deposits
and GNP has strengthened m recent years and to
evaluate the changmg effects of mterest rates, which
reached unprecedented levels m recent years It was
found that the relat1onsh1p between savmgs deposits
at commercial banks and GNP4 deteriorated mto
ms1gmficance m the most recent period (Equat1ons
2 and 3 of Table A-2) It appears from these equations that the trend rate of growth of such deposits
and market mterest rates were the prmc1pal determmants of savmgs deposit movements m recent
periods The "own" rate on savmgs deposits 1s itself
an ms1gmficant explanator of movements of savmgs
accounts m Equation 2, but this may be rat1onahzed
by the lack of variation (because of mterest rate
ceilmgs) m the savmgs deposit rate after 1970 Removal of the savmgs deposit rate m Equation 3
only slightly improves the performance of GNP m
the equation, which m any event remams ms1gmficant
Equat10ns m Table A-3 show M 1 , DD+ SB,
DD+ SB+ ST, M 1 + SB, and M 1 +SB+ ST run
m similar money demand equations for the period
1966 Q3 to 1975 Q2 and 1970 Q3 to 1975 Q2 M 2
and Mg are also shown for reference to still broader
aggregates The equations estimated over the
shorter period are labeled "a" and those for the
longer period are denoted "b "
The results m Table A-3 md1cate that the rate
on savmgs deposits 1s an ms1gmficant determinant of the broader aggregates DD + SB and
M 1 + SB, though a s1gmficant explanator of DD
and M 1 The hkely reason 1s that the rate on savmgs
deposits 1s an "own" rate for SB but a competmg

rate for M 1 and DD These opposite mfluences cancel each other when the savmgs deposit rate 1s used
to explam DD + SB or M 1 + SB The equations
also show that although SB Itself 1s not s1gmficantly
explamed by GNP over five recent years, the relationship of DD and M 1 to GNP 1s not s1gmficantly
weakened by the add1t1on of SA The coefficients of
GNP are s1gmficant m a one tailed test at d 95 per
cent level of confidence m all the equations with
DD, DD + SB, M 1 , and M 1 + SB m Table A-3 In
deed, the relationship of GNP 1s more s1gmficant,
though only margmally, to DD + SB than to DD
alone m both periods shown (Equations 4a, 4b, 5a,
and 5b)
The add1t1on of all savmgs deposits at banks
and thrift mst1tut1ons to DD and M 1 creates
broader aggregates that bear a stat1st1cal relationship to the mdependent variables used m the regressions, a relat1onsl11p that 1s s1m1lar to M 1 or
DD alone The bank rate paid on savmgs accounts 5
remams s1gmficant for both periods shown for
DD+ SB+ ST and M 1 + SB + ST Also, GNP
1s a highly s1gmficant explanator of the broader
aggregates Indeed, the s1gmficance of GNP as an
mdependent variable 1s strengthened by the addition of savmgs deposits to DD, and the relationship
between GNP and M 1 1s about the same Comparmg these aggregates to M 2 and Mg shows that
DD plus savmgs deposits and M 1 plus savmgs
deposits have a more consistent relationship to
GNP than M 2 or M 3

• The ch01ce of GNP as the appropriate scale variable IS
open to questlon, and personal mcome or some other com
prehens1ve flow variable of the economy could arguably be
substituted for 1t m these equations However, smce m
fluencmg GNP 1s an objective of monetary policy, It was
used as the scale variable throughout


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If at present there exists a transactional component m savmgs deposits, Its behavior 1s apparently swamped by the movements of the level of
savmgs deposit~ mduced by changes m mterest
• A series on the average rate paid by thrift mstltutlons
for savmgs deposits (excludmg time deposits) was not avail
able for testmg

lmprovmg the Monetary Aggregates· Staff Papers

170

TABLE A-3. Coefficients of Variables m Demand-for-Money Equations for Six Concepts of Money 1
Independent vanab\es
Equation'

Defimt1on of
money

4a

DD

4b

DD

Sa

DD+ SB

Sb

DD+ SB

6a

M,

6b

M,

7a

M,+SB

7b

M,+sB

Sa

M,

Sb

M,

9a

M,

9b

M,

-

Intercept

I

Money
vanablc
lagged

I

Treasury
bill
rate

I

Regression sta t1st1cs
Rate on
savm11s
deposits

I

GNP

Standard erro1

I

R•

- 223
(- 47)
378
(I 66)

830
(6 90)
790
(8 46)

(-1
(-2

031
83)
022
53)

(-1
(-2

059
62)
072
90)

179

0078

960

125
(2 07)

0071

956

- 325
(- 08)
269
(I 38)

647
(3 84)
835
(13 80)

(-2
(-6

040
62)
041
84)

(-1
(-1

060
53)
026
58)

314
(2 lO)l
112
(2 67)

0070

964

0063

969

- 062
(- 13)
505
(2 23)

747
(5 12)
681
(6 JS)

(-1
(-2

028
81)
019
63)

(-1
(-3

055
74)
068
35)

226
(2 30)
198
(2 86)

101
( 25)
310
(1 57)

622
(3 25)
810
(11 65)

(-2
(-6

037
58)
039
67)

(-1
(-1

051
42)
025
60)

322
(2 04)
130
(2 75)

722
( 76)
I 170
(2 25)

844
(6 13)
751
(8 31)

(-3
( -6

037
69)
044
81)

- 003
(- 49)
009
( 65)

- 045
(- 07)
211
( 59)

I 029
(8 54)
910
(11 17)

(-3
(-6

038
17)
046
40)

- 017
(- 87)
002
( 11)

(I 98)

0064

960

0057

971

0064

965

0056

974

197

0047

990

305
(2 74)

0050

996

(I 40)

- 034
(- 21)

0056

992

156

0054

997

(I 32)

• The numbers m parentheses are I stattst1cs
The esttmatton pe11od 1s 1970 Q3 to 1975 Q2 for cquJt1ons 11belcd "•" and 1966 Q3 to 1974 Q2 fm cqu1t1ons labeled "b"

2

rates Thus, aggregate savmgs deposits alone ,ire
not as yet transaction.ti m character to a discernible
degree, nontransacttonal savmgs deposits apparently still dommate movements m the senes Moreover, It 1s not possible to estimate with prec1s10n
the mm1mum proportion of savmgs that must become transactional m character before bemg recogmzed m trad1t1onal money demand analysis If
savmgs deposit growth 1s whipsawed m commg
penods by d1smtermedtat1on followed by large mflows, then the transactional component of savmgs
will be largely obscured On the other hand, 1f
nontransactlonal savmgs accounts follow a steady
path of growth, a relatively small transactional
component-say, IO to 20 per cent of savmgs-may
be adequate to be perceived m many demand
equations
The analysts also suggests that a broader aggregate than M 1 constructed only from deposits at
commercial banks may not adequately summarize
the available transactional hqmdtty m the economy DD plus bank savmgs deposits and M 1 plus
bank savmgs deposits did not have a s1gmficantly
weaker relattonshtp to GNP than did DD or M 1
alone, but the mterest rate payable on savmgs
deposits was predictably found to be pos1uvely
related to SB but negatively to M 1 and DD The
contrary mfluences render this rate an ms1gmficant
explanator of DD+ SB or M 1 + SB as 1t affects

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the parts of the aggreg,tte differently Thus, an
important rate m an M 1 equ,ttlon ceases to be
~1gmficant m an equ.tuon relatmg DD+ SB or
M 1 + SB to other mterest rates and GNP The
elasticity of demand with respect to this savmgs
deposit rate could be very !ugh when market rates
are near ce1hng rates
The hqmdity of thnft savmgs deposits 1s unquestionably comparable to that of bank savmgs,
and the 1usuficatton for hm1tmg an M 1 -type trans
actions aggregate to bank deposits 1s conceptually
weak when bank savmgs deposits are mtroduced
Moreover, the mclus10n of all savmgs deposits,
rather than bank savmgs deposits alone, results m
an aggregate with s1gmficant and more consistent
relauonslups to the bank rate on savmgs deposits
and GNP The hkely explanation for the rate's
remammg s1gmficance ts that It affects the M 1 and
'>T components the same way-negattvely-overcommg the opposite mfluence on SB The strength
and consistency of the relat10n of GNP to the movements of these aggregates are comparable to those
of M 1 , and m recent pertods better than those of
M 2 , though neither DD plus all savmgs nor M 1
plus all savmgs clearly dommates DD or M 1 alone
The results are, however, suggestive of the need
for a contmumg exammatton of the conceptual
and empmcal Justtficauons for the present defimuons of the monetary aggregates


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