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SOME FACTORS AFFECTING SHORT-RUN
GROWTH

RATES OF THE MONEY SUPPLY
Alfred

Broaddus

I.
introduction

Public interest in the monthly and weekly movements of the money supply’ has intensified since the
early 1970’s.
One manifestation
of this interest is
the extensive coverage of week-to-week
and monthto-month changes in the money supply in the financial press. A second indication is the intense scrutiny
of each new weekly or monthly money supply statistic
by financial market participants.
Indeed, one of the
major current rituals in the markets is played out
late every Thursday afternoon as investors across the
nation hover around news wire machines awaiting
the release of the latest weekly money supply figures.
The increased attentidn to short-run money supply
movements
dates back to 1970 when the Federal
Open Market Committee (FOMC),
the Federal Reserve’s principal monetary policymaking
body, began
to place greater weight on achieving specific longerrun growth rates for particular monetary aggregates.”
Under the current strategy of monetary policy,3 the
FOMC
periodically
specifies
desired
longer-run
growth rates (extending
roughly a year ahead) for
These growth objeccertain monetary
aggregates.
tives are publicly announced
in quarterly
testimony
before one of the Congressional
banking committees.
At its monthly meetings the FOMC then reviews the
state of the economy and compares the actual growth
of the aggregates with their desired long-run
paths.
‘There
are several
concepts
of the money
supply.
and
statistical
series
corresponding
to each
of these
“monetary
aggregates”
are
published
regularly
in the Federcrl
Reserve
Bulletin.
This
article
deals exclusively
with
the short-run
behavior
of MI, the most
narrowly
inclusive
aggregate,
which
is comprised
of
(1)
currency
outside
the Treasury,
Federal
Reserve
Banks,
and
vaults
of commercial
banks;
(2)
demand
deposits
at commercial
banks
other
than
domestic
interbank
and U. S. Government
deposits.
less cash
items
in process of collection
and Federal
Reserve
float;
and
(3)
MI is the
foreign
demand
balances
at Federal
Reserve
Banks.
aggregate
most
closely
watched
by financial
market
participants
and the general
public.
Also,
much
of the short-run
variability
of
the more
broadly
defined
aggregates
(all of which
include
i%)
is
due to the variability
of ML
*This
change
in emphasis
is evident
in the evolving
language
of
the FOMC’s
directives
to the Trading
Desk at the Federal
Reserve
Bank of New York.
Prior
to 1970, the directives
generally
instructed
the Desk
to seek
a desired
condition
in the money
markets
as
indexed
by interest
rates or free reserves.
Since
1970, in contrast,
most
directives
have
instructed
the Desk
to foster
monw
market
and reserve
supply
conditions
consistent
with
more
rapid,
slower,
or unchanged
growth
of the monetary
aggregates.
*See
Lomhra
and
Torte
C41 for a
current
strategy
of monetary
policy.

2

detailed

description

ECONOMIC

of

the

and Timothy

Q. Cook

Based, on this review the FOMC specifies short-run
“tolerance ranges” for the growth rates of the aggregates over the two-month
period covering the current and following months.
The aim in setting these
tolerance ranges is to define the near-term
growth
rates most likely to be consistent with achieving the
existing long-run growth objectives.
Consistency
in
this context, however, does not necessarily
imply
The short-run
ranges can and often do
equality.
deviate
numerically
from the long-run
objective
either because the FOhilC is attempting
to offset
some unintended
deviation in earlier months or because some temporary
but foreseeable factor is espetted to affect short-run
growth.
In any event, once the short-run
tolerance ranges
are set, the FOhlC
specifies a Federal funds rate
range (normally
from 50 to 100 basis points in
width)
believed to be consistent
with short-run
monetary growth within the bounds of the tolerance
In this tactical framework,
an emerging
ranges.
deviation of the actual two-month growth rates from
the specified tolerance ranges might lead the Federal
Reserve to alter the Federal funds rate (by increasing or decreasing the supply of nonborrowed
reserves
to member banks) in order to hold the growth rates
Finally-a
point of
within the tolerance
ranges.
considerable
importance-both
the long-run
monetary growth objectives and the two-month
tolerance
ranges are expressed in terms of seasonally adjusted
annual rates of growth.
It should be evident from this description
of the
Federal Reserve’s operating strategy that despite the
longer-run
time. horizon in which basic monetary
growth goals are cast, the procedure
by its nature
tends to focus day-to-day
attention
on short-run
monetary movements.
First, from the standpoint
of
the Federal Reserve, the key tactical operating specification is the two-month tolerance range. Setting an
appropriate
range requires
close attention
to the
numerous
factors
affecting
current
weekly
and
monthly growth rates.
Further,
incoming
weekly
and monthly data must be continuously
tracked and
evaluated against the criteria established by the toIerante ranges.
Second, the procedure naturally stimu-

REVIEW, NOVEMBER/DECEMBER

1977

lntes financial market interest in the short-run
behavior of the aggregates.
Given this procedure, these
nlovements
strongly
influence
market expectations
regarding
the likelihood
that the Federal Reserve
\vill seek a change in the Feder;~l funds rate that will
in turn influence tlie lx-ices and yields of other financial instruments.
;is a I-esult. considerable resources
\vitliin the markets are no\v devoted to “watching”
hot11
the Federal Resell-e 2nd the money supply.
Tlie major difficult). that arises in this institutional
fr:liiie\vork
is that short-run
monetary
data, even
after seasonal adjustment.
xe highly volatile.
It is
therefore difficult to project short-run
movements,
even for the immediate future, and equally difficult
to evaluate incoming data.
Cliart 1 illustrates
this
volatility.
It conilx~res tlie originally
published or
“l)reliminar~“~
seasonally
adjusted
one- and twomonth ;\I1 grokvth rates (at annual
rates) in 1975
and 1976 \vith the full year g-ro\vth rates during the
surrounding
12-month period.
Table I provides a
‘As
evidence
of this expectational
impact.
the corwlation
coefficient between
the chanse
in MI announced
Thursday
and the char.re
in the three-month
Treasury
bill rate
the followins
day
was
26
over the 52 weeks
of 19i6,
which
is statistically
significant
at the
5 percent
level.
z Throughout
this article,
first
published
covering
the most recently
revised
be on the preliminary
data
both the Federal
Keserve

“preliminary”
refers
to the MI statistic
a particular
period.
“Final”
refers
to
statistic
for a period.
The emphasis
will
since it is the preliminary
data to which
and the financial
markets
react.

1

PRELIMINARY
.’
18 t

The purpose of this article is to provide some insights into the difficulties inherent in interpreting
the
short-run
behavior of the seasonally adjusted monetary aggregates
and to provide a framework
for
The
analyzing
certain kinds of short-run
swings.
article lvill focus on variations
caused by factors
other than changes in basic underlying
conditions in

Chartl~“,

I

Ml

GROWTH
*

Percqt
1

SHORT-RUN

further illustration.
It shows the standard deviations
of the annualized
preliminary
one- and two-month
l\iI, growth rates in each of the last ten years.
The
average standard deviation is 5.5 percentage
points
for the one-month
growth rate and 3.8 percentage
points for the two-month
growth rate.
Strikingly,
the standard deviation of the one-month growth rates
actually exceeds the average monthly growth rate in a
number of years. This volatility of short-run growth
rates relative to trend would not constitute a serious
problem if it were possible to distinguish,
on a current basis, between
transitory
changes in money
growth and more permanent changes related to basic
economic developments.
Unfortunately,
making such
distinctions
is an extremely
difficult task.
Consequently, the possibility always exists that the shortrun behavior of the monetary aggregates might mislead either the Federal Reserve or market participants observing
and trying to anticipate
Federal
Reserve actions.

_

I,

d_

RATES COMPARED
(SAAR)

*

TO LONGER-RUN

GROWTH

RATES

I: A
c i

1’6.

-----

P-Month

.---a

FEDERAL RESERVE BANK OF RICHMOND

1 -Month

-

l-Year

Table

STANDARD

DEVIATIONS

PRELIMINARY

I

SHORT-RUN

AND

MEANS

Ml GROWTH

OF
RATES

(SAAR)
One-Month
Standard
Deviation
~

Growth

Rates

-Mean

Two-Month

Growth

Rates

standard
Deviation

Mean

1967

6.7

6.6

4.0

6.6

1968
1969

4.9
3.6

6.5
1.9

3.7
2.1

6.1
2.1

1970

6.0

4.5

3.5

4.2

1971

6.5

6.1

5.5

6.3

1972

4.9

8.0

3.2

7.5

1973

5.1

5.6

4.1

5.4

1974

4.5

4.9

3.0

5.1

1975

7.7

4.7

5.4

4.7

1976

5.2

5.6

3.3

5.2

Average

5.5

Source:

Federal

Reserve

3.8

Bulletin.

the economy. As indicated in the sections that follow,
these noneconomic
factors are responsible for a sub
stantial portion of the observed illouth-to-moIltl~
and
week-to-week
variations
in monetary
growth rates.
The next section of the article describes in general
terms the various kinds of noneconomic
factors that
produce short-run movements in the preliminary
XI,
data. Special attention is devoted to movements that
result from the nature of the procedures
currently
used to seasonally adjust the data. The third section
illustrates
some of the points made in the second
section with specific examples of factors affecting
The
monthly
M1 growth rates in recent years.
fourth section provides
further
illustrations
with
The final
reference to the weekly M1 statistics.
section contains a brief summary of the article and
presents a few conclusions.

periods of several weeks. Moreover, seasonal adjustment techniques,
despite notable improvemer, ts in
recent ).ears. are far from perfect. Over long periods,
variations
in the M1 data related to both special
adjustment
problems
should
events and seasonal
wash out. But factors such as these produce sharp
fluctuations
in short-run growth rates.
It will be useful in organizing
the discussion
to
distinguish two classes of variations : ( 1) movements
that result from shortcomings
in the method currently used to seasonally adjust the data and (2)
irregular
variations
due to special nonrecurring
events.
Each of these two categories of factors will
be addressed
in turn.
The focus throughout
this
section is primarily on the monthly data.
Variations
Due to Deficiencies
in the Seasonal
Adjustment
Procedures
Chart 2 shows the annualized monthly growth rates of ~of seasonally adjusted M1 in 1973, 1975, and 1976. It is evident
from the chart that these growth rates are extremely
variable, ranging from over 3070 to under -3070,
and that they are dominated
by recurring
seasonal
Inovenients.
A glance at the chart suggests two of
the major forces underlyin, 0 this seasonal movement :
tax dates--April,
in particular, \vheii individuals
accumulate balances to pay income tnses-and
the iticreased business activity during the Christnlas season.
As described in Box I on 11. 5, the M1 data are
seasondly
adjusted
with seasonal factors computed
I)): the I<ureau of the Census’ S-1 1 Variant of the
Census Metllotl I1 Seasonal Adjustment
Program
(referi-etl to below as X-1 1)
Judgmental
modifications are then made by the Federal Reserve staff in
\
,*

i-

:

Money

Growth

Short-Run

Movements

Rates: A General

in

Description

This section will discuss in general terms some of
the noneconomic
factors that produce variations
in
seasonally adjusted short-run
Ml growth rates. Observed growth rates are no doubt related in some
way to changes in economic conditions.
But factors
totally unrelated
to current business conditions
can
cause significant
variations
in these growth rates.
Special nonrecurring
events can have an important
effect on demand deposit balances in some cases over
4

ECONOMIC

;&g12”

h~~“jl
3,;
“-

e
pi

NOT SEASbNALLY “ADJUSTED
MONTHLY M, GROWTH RATES ~

II.
Some Factors Affecting

”

REVIEW, NOVEMBER/DECEMBER

1977

s”

,‘

Box I
SEASONAL

ADJUSTMENT

OF THE MONEY

As indicated
in the text, money
supply
data are
seasonally
adjusted
I)y the Federal
Reserve
staff
using
the Census
Bureau’s
S-11
Variant
of the
Census
Method
I I seasonal
adjustment
model,
referred
to belo\v simply
as X-11.
ITsing unadjusted
data for a period
of years,
this ~notlcl generates
a
seasonal
adjustment
factor
for each entry
in the
series:
for example,
for each individual
month
in a
In determonthly
series
of money
stock
data.
mining
the final seasonal
adjustment
factors
actually cmploycd
in developing
the published
seasonally adjusted
money
supply
series,
the staff may
alter the adjustment
factors
derived
from the model
where
the
staff’s
knoxvledge
of special
circumstances
affecting
the X-11 factors
suggests
such
What
follows
is a brief
alterations
are in order.
description
of some
of the problems
encountered
(For
a
in applying
X-11 to money
supply
data.
detailed
description
and analysis
of Federal
Reserve
procedures
used in seasonally
adjusting
the money
supply,
see the accompanying
article
I)y Lawler.)
Like most conventional
seasonal
adjustment
procedures,
X-11 assumes
tllat the lcvcl of an unadjusted
data
series
(call it Munad
in the case of
monthly
money
supply
data)
at any point in time
reflects
the combined
influence
of four underlying
determinants:
long-term
trend
movements
(T),
recurring
seacyclical
movements
(C), regularly
sonal
movements
(S),
and
irregular
movements
(I).
The version
of X-11 used
the Federal
serve assumes
four determinants
related
to
another
in
multiplicative,
i.e.,
fashion:
hl

=

T

c X

2; I.

this general
one can
two alternative
under
xvhich
the
unadjusted
influences
might
supply
data:
a condition
the pattern
constant
from
to year
seasonal
influences
(2) a
where the
changes
from
year to
next.
111
iirbt case,
multiljlicativc
proportionate
inlpact
seasonal
influon tlie
data is
hame for
particular
calendar
(say, January)
all of
years covered
the series.
these condiany
computed
of seasonal
factors,
S,
January,
February,
respectively,
should
constant
over
full span
years
covered
the series.
the second
the proimpact
of
influences
during
given calendar
changes
over
To rethese changes
seasonal
adjustment
for each
month
should,
general,
change
out year
the next.
has alternative
modes designed
deal with
of these
sets of
As applied
any set
monthly
data,
X-11
model
essentially
a
average
seameans
that
adjustment
procedure.
seasonal
adjustment
are derived
developing
of (1)
unadjusted
data
individual
months
example,
June
in the
to

SUPPLY: THE PROBLEM OF MOVING

SEASONALS

(2)
average
of
months
data
on
that
Such a
is calculated
each
individual
in the
The seasonal
justment
factor
each individual
is then
by averaging
ratio
for
month
with
ratios
for
corresponding
calendar
in other
The two
modes
mentioned
enter
the
as follows.
the pattern
seasonal
influences
the data
believed
to
stable
over
a single
adjustment
factor
derived
for
of the
calendar
months
an average
all of the
ratios
for that calendar
month
over the full series.
If the pattern
is believed
to be changing
over time,
a moving
average
of such ratios,
covering
a more
abbreviated
time span, is used to compute
a distinct
adjustment
factor
for each individual
month
in the
series.
For the reasons
given in the text, it is clear that
the seasonal
pattern
of the unadjusted
monthly
money
supply
series
is not constant
but changes
over time.
Therefore
the version
of X-11 used to
adjust
the money
supply
data derives
seasonal
adjustment
factors
for each individual
month
in the
series from a weighted
7-term
moving
average
of
the ratios in the corresponding
calendar
months
of
surrounding
years.
Where
a month
is in one of the
terminal
years of the series, the span of the moving
average
is reduced
since data for a full centered
7-term
moving
average
are not available.
For
example,
the presently
published
adjustment
factor
for January
1973 (an example
of what
is called
“final” data in the text) is derived
from a weighted
average
of the January
ratios
for the years
19701976, inclusive.
The presently
published
factor
for
January
1976 is derived
from the four year period
1973-1976,
inclusive.
It is important
to note that under this procedure,
the factors
used to seasonally
adjust
incoming
data
during
the current
year-the
all important
“preliminary”
data to which both the Federal
Reserve
and
the markets
react-are
derived
from ratios
of preceding years and do not directly
reflect any changes
in seasonal
patterns
in the current
year.*
For example, the seasonal
factor
used to adjust
the January 1973 figure
when
the figure
was initially
released in early February
1973 was derived
from the
January
ratios
for the years
1969-1972,
inclusive.
Therefore,
if the seasonal
pattern
is in fact changing in the current
year, it is particularly
likely that
the procedure
will
distort
the preliminary,
i.e.,
current,
data.
Ironically,
this is precisely
the data
of greatest
importance
to Fed policymakers
and the
markets.
The discussion
in the text describes
some
of the distortions
that arise and shows
that these
distortions
are a source
of seasonal
movement
in
the seasonally
adjusted
money
supply
data.

* Strictly
speaking
the
preceding
year ratios
procedure
to anticipate
small extent.

FEDERAL RESERVE BANK OF RICHMOND

weights
attached
to these
might
implicitly
cause
the
current
year changes
to a

5

an effort to compensate for some of X-11’s deficiencies.”
As indicated in the ljox, the purpose of se;lsonally adjusting
lhf , is to eliminate the impact of
seasonal forces, leaving only trend, cycle and irregular movements.
In practice, however, the influence
of seasonal forces is often not eliminated
from tile
preliminary
seasonally adjusted M, data.
A majoi
reason for this residual seasonality is that X-l 1 necessarily relies solely on past data in calculating
preliminary
seasonal adjustment
factors and therefore
cannot take full account of changes in seasonal l)ehavior currently
in progress, despite the program’s
allowance for “moving”
seasonnls described in tile
Box.
A variety

of developments

impact of seasonal
particular
month.
tiutling of seasonal

Consider
hs,

commodating,
underlying

the relative

should

capture

there are changes in the
For example, in 1955 the

the program

of nonwithheld

example,

shifting

calendar

position

averfinal

the

seasonal

First,
events.

fact,

patterns
average

changes

sonal event affecting

changes

the

centered,

that occur abruptly.
change

M1 occurred

even the final adjusted

might

not adequately

in

On the other hand,
well suited to dealing

that a lasting

Here,

of the Easter

since

is not particularly

assume

gmdrta!

by its very construction

changes.

such

with permanent

individual

in the

nioving

after
nioving

on the money

Federal income taxes was permanently
shifted from
March 15 to April 15. A contrasting
example is the

weighted

seasonally adjusted
data for that year.’
For this
reason, the program is especially well suited to ac-

seven-year

in a

As indicated

on a given year in deriving

age of data centered

supply

can change

first the final data.

S-l 1 uses a seven-year

events

final day for the payment

continuously

ally over :I period of years or abruptly.
Moreover,
tile inil)act of tliese changes on the preliminary
(i.e..
first l)ul)lislietl) adjusted data for a particular month
is likely to differ from tlleir impact on the final
revised tlata for the month.
The folloning
paragr~plis will el:J)ornte these points.

abruptly

monthly

capture

As an

in some senin 1973.

data for 1973

the change

since

the

holiday. Second, the relative magnitude of sctrsonnl
force can change. The aggregate amom7t of individ-

final data, derived
from the seven-year
centered
moving average, would be based partly on experience

ual or corporate taxes paid in a given month relative
to the level of the money supply, for instance, might

preceding

deviate

from the usual

norm.

This

deviation

during

balances

during

periods

wanage

characterized

their UIOIIE~

by recurring

seasonal events can change.
For example, improved
corporate cash management
practices have probabl)
compressed the necessary lead-time for the accumLilation

of cash balances

prior

to scheduled

tax pay-

ments.
Finally,
neza, seasonal events appear from
time to time. In late 1972, for instance, the Federal
government
ments

initiated

at the beginning

sizable

revenue-sharing

pay-

of each quarter.

1972-all

years

the more
of whether

significant
preliminary
a permanent
change in

underlying
seasonal
forces occurs
gradually
or
abruptly, the preliminary
adjusted growth rates are
likely to be distorted
in the seiise that they will

payments
over the various
periodic tax payment
dates within the year. Third, the VUWULCY which
in
and bzrsincss firms

1970, 1971, and

the change.

Consider
next
data. Kegardless

might

be due either to a change in the total tax liability
relative to M1 or to a change in the distribution
of

households

the years

probably

differ systematically

from revised

data pub

lished later. The reason for these distortions is that
S-l 1 derives preliminary
adjustment
factors from
actual data for years preceding the year in question.
(See Box.)
Consequently,
the preliminary
factors
fail to capture
lying seasonal
viously

the full effects of changes in underbehavior.
Such
distortions
are ob-

significant

since it is the preliminary

Ml data that condition current monetary
the behavior of the financial markets.

adjusted
policy and

The impact of these several changing
seasonal
forces on short-run
seasonally adjusted
Ml growth

A couple of hypothetical
examples
clarify the nature of these distortions.

rates is likely to vary, depending

begimiing in 19S0, the unadjusted
growth rates of
hII in the month of October began to display a

particularly

on (1)

might help to
Suppose that

whether the change is permanent
or temporary
and
(2) if permanent,
whether the change occurs gradu-

g~~drtnl

0 See the accompanying
article
by Lawler
for a description
of these
judgmental
modifications.
In making
these modifications
the staff
faces
many
of the same difficulties
anticipating
changes
in seasonal
patterns
encountered
by the X-11 proaram
itself.
For this reason
it is not
clear
that
the
modifications
significantly
improve
the
preliminary
data.
In any case,
this
article
does
not
attempt
to
evaluate
these modifications.

7 The term “final”
may be slightly
misleading
in that money
susplr
data is always
subject
to further
revision.
The term
is used hers,
to refer
to revised
adjusted
data available
beginnina
in the fourth
year following
the year to which
it applies.
Such data is seasonally
adjusted
using adjustment
factors
that are derived
from
actual
data
for the full seven-year
period
covered
by the seven-term
movins
average
in the X-11 program.

6

ECONOMIC

REVIEW,

but

NOVEMBER/DECEMBER

persistent

1977

decline

due,

perhaps,

to a

decline in the relative volume of business sales in
that month.
Suppose further that this trend persisted through the year 1990. Under these circumstances, the X-11 seasonal adjustment
factor used to
compute the prelinlinary
seasonally adjusted growth
rate in, say, October 19S5 would reflect the movement in M, in the years 19Sl-19%.
Consequently,
this preliminary
factor would be biased upward and
the preliminary
seasonally
adjusted
growth
rate
In subsequent
years the
\voultl
l)e understated.X
October 19% gro\vth rate \vould
be revised upward.
The preliminary
gro\vth rates for Octoijer in ensuing
J’ears, ho\vever. would continue to differ systematically from revised gro\vth rates as long as the trend
continued.
Consider next an ab,-lip1 future change in a seasonal event such as, for instance.
a hypothetical
change in the deadline for iiidi~idual Federal income
t;ls l~:tyinents from April 15 to May 15. Suppose
that such :I cllange Ivent into effect in 19S6. In that
case, beg-inning in 19SG the unadjusted
growth of MI
in April would be low \\hile not seasonally adjusted
gro\vth in Slay would
be high relative to the pattern
in earlier years.
Here, the preliminary
seasonal adjListment factors for April and Llay 19SG would be
I)asetl on i\l, I)ehavior over tlie 19S2-19S5 period.
Consequently,
the preliniinnry
adjusted growth rate
for April 19SG would proba1~1y I)e unusually
low,
\\-bile the R’lny 1924 growth rate \vould be significantly inflated.
In the absence of further changes.
however, the problem would tend to disappear by
1990 since by that year all of the data used in deriving the preliminary
April and May adjustment
factors would reflect the 19SG tax date change.
Beyond the more durable seasonal developments
discussed to this point, temporary changes can also
affect short-run seasonally adjusted monetary growth
rates. As ;L final ex;unple, suppose that Federal tax
payments by individuals were unusually large relative
to the level of Ml in April 19S3, but that in 19S3
and subsequent years, the payments fell back to more
normal levels. In this case the preliminary
seasonal
adjustment
factor for April 19S3, which would be
based on 1979-1932 experience, would be low relative
Hence, in the
to the level of the tax payments.
absence of some other ulwsual
event tending to depress growth, the preliminary
seasonally adjusted RiIl
growth rate for April 19S3 would be relatively high.
Further, the final revised data for this month would

also show a relatively
circumstances.

RESERVE

rate under

these

It should be clear from this discussion
that the
procedure presently used to seasonally adjust monetary data is itself an important
potential source of
short-run
variations
in adjusted
monetary
growth
rates.
Irregular

Variations

In addition

of changing

seasonal

the seasonal

adjustment

growth

patterns

nonrecurring

sonal movements

to the

working

procedures,

rates are also strongly

irregular,

no effort

short-run

influenced

events.

effects
through
M,

at times by

In contrast

to sea-

is made to remove

such

irregular
movements
from the adjusted
Ml data.
While the events underlying
these movements
are
not always
explanation
examples

fully understood,
in many instances the
is straightforward.
One of the best
of a large

irregular

movement

in recent

years was the bulge in Ml in May and June 1975
following the $9 billion disbursement
of tax rebates
and supplemental
social
Treasury to the public.!’

security

payments

by the

It should be noted parenthetically
that the distinction between ( 1) irregular movements
and (2)
the movements discussed above reflecting temporary
changes in seasonal forces is not always clear.
In
the preceding section the example used to illustrate
temporary seasonal forces was unusually large individual tax payments
in one year.
Some analysts
might prefer to regard such an occurrence
as an
irregular event. The criterion adopted in this article
is that events that recur with some definite periodicity are seasonal in nature, while other events are
irregular.
Whatever the distinction
in principle, in
practice both categories of events are likely to produce short-run movements in the seasonally adjusted
M1 data, As indicated above, the X-11 program is
unlikely to remove the effects of temporary changes
in seasonal patterns
from the seasonally
adjusted
data, and irregular movements are left in the adjusted
series by design.‘”
The following section illustrates the foregoing discussion with specific empirical examples from recent
experience.
!‘See
Breimyer
impact
of the
rates
in 1975.

and Wenninaer
[z]
rebntes
on seasonally

for empirical
evidence
adjusted
monthly
Ml

on the
growth

‘OIt might
be added that both irregular
movements
and movements
due to temporary
changes
in seasonal
forces
can present
additional
problems
if they
are mistakenly
treated
as permanent
changes
in
In addition.
computed
seasonal
patterns
by the X-11
pro!zram.
seasonal
adjustment
factors
might
be distorted
by cyclical
developSee Lawler
13, p. 241 and Poole
and Lieberman
[6, pp.
ments.
325-3341.

‘The
X-11 prozram
does contain
an adjustment
designed
to correct
See r7, p, 161.
partially
for trend
changes
in seasonal
behavior.
As long as the chanaes
continue
nt roughly
the same pace.
however.
the correction
will be only partial,
and the bias discussed
in the text
will persist.

FEDERAL

high growth

BANK

OF RICHMOND

7

III.
Factors Affecting

Short-Run Money

Some Empirical

Gradual

Changes

Christmas
adjusted

growth

months

prior

following
flects

with

during

increased

pattern
for

rises

un-

in the

presumably

transactions

business

and the reduced

the holiday.

The

2, the

and falls in the months

This

demand

Rates:

Patterns:

in Chart

of M1 typically

to Christmas

Christmas.

the holiday

Seasonal

As shown
rate

the rising

associated
after

in

Cycle

Growth

Examples

activity

re-

balances
prior

to

need for such balances

The behavior

this period forms a regular

of unadjusted
“Christmas

M1
cycle”

that appears to begin as early as late August, peaks
in the first week of January, and reaches a trough in

Chart 3

THE CHRISTMAS CYCLE
Percentage increase in Not Seasonally
Adjusted M1 From late August Trough
Percent

The net increase from the late
late February.”
August trough to the late February trough generalI>
is roughly equal to the trend rate of iLlI1 growtll.
Hence, the cycle is complete in the sense that the preChristmas seasonal rise has nashed out by the end
of February.
As suggested by Chart 3, the shape of the Christmas cycle has undergone
:I sulMaiitia1 and fairI>
continuous
change since the mid- 1960’s. despite the
fact that the typical percentage rise from the August
trough to the January peak has been fairly stable. In
particular,
the c).cle has become narrower
to\vartls
the base, so that ;I greater part of the pre-Christmas
rise now occurs in the November-December
period,
and a greater part of the post-Christmas
runoff occurs in January.
This information
is convey-ed in a
different way in Table II, which shows that the increase in the percentage of the post-Christmas
runoff
occurring in January has been remarkably persistent
over the longer run. Similarly, except for 197G, the
percentage
of the pre-Christmas
rise occurring
in
November and December has risen quite steadily.
1’ Of course,
other seasonal
forces
affect
the movement
Christmas,
however,
appears
to
MI in this period.
pattern
of the unadjusted
data over these months.

Table
-

II

1963-65

THE CHANGING

- ...-..... ,96*.,0
---

of unadjusted
dominate
the

SHAPE OF THE CHRISTMAS

% of Decline
in NSA Ml
Occurring in
Jan.

% of Rise
in NSA ,441
Occurring in
Nov.-Dec.

1973-75

1961

50.5

51.7

1962

51.3

47.9

1963

47.5

40.8

1964

40.5

61.9

63.4

1967

62.9

62.7

1968

67.5

67.3

1969

73.1

60.7

1970

71.6

81.4

1971

70.5

81.9

1972

71.7

77.7

1973

75.2

90.2

1974

77.6

87.0

1975

90.8

86.5

1976

ECONOMIC

41.0

50.1

1966

8

48.8

1965

SOUVX

62.7

82.6

Federal

REVIEW, NOVEMBER/DECEMBER

Reserve

1977

Board

Release,

CYCLE

H.6.

Table

III

SUCCESSIVE REVISIONS
Ml GROWTH

OF JANUARY
RATES

(SAAR)
Published
1971
1970
--I_-----

1972

Growth

1973

Rates for

1974

1975

1976

1977

As of:
1970

9.0

1971

9.4

1.1

1972

9.2

2.8

3.7

1973

10.3

2.7

1 .o

1974

10.4

3.3

1.5

4.7

-3.1

1975

10.9

4.3

3.1

5.2

-2.7

1976

9.2

5.5

8.2

9.4

3.5

-5.1

1.2

1977

9.2

5.5

9.2

10.3

4.4

-4.2

2.0

+5.1

+ .a

0.0

-9.3

5.4

Cumulative
Revision
+.2

Note:
Source:

+4.4

Diagonal
Federal

+5.5

shows
Reserve

+10.3

preliminary

+7.5

growth

rates

for each

yeor.

Bulletin.

The gradual change in the shape of the Christmas
cycle since the mid-1960’s has probably been due at
least in part to the steady rise in interest rates during
this period.
As Table 11 indicates, the cycle began
to change in 1966, the year interest rates began their
strong upward trend.
The underlying
logic here is
straightforward.
Higher interest rates have made it
progressively
more costly for business
firms and
households to hold Mt balances rather than alrertiative, interest-bearing
assets.
Hence, the buildup in
Mt balances prior to Christmas
has been progressively delayed.
Further, after Christmas the public
has attempted to convert the Mt balances acquired
during the holiday period into interest-earning
assets
with greater speed.
These efforts to economize on
M1 balances have probably been aided by the proliferation of credit cards and a variety of other financial instruments
permitting
improved cash balance
management.
Whatever the cause, the gradually changing shape
of the Christmas cycle has had a large impact on the
seasonal adjustment
factors for some of the Christmas cycle months.
First, the final revised factors for
these months have changed continuously
from one
year to the next since the mid-1960’s.
For example,
the January factor has declined steadily since 1965.
More importantly,
the preliminary
factors and the
preliminary
adjusted growth rates for these months
in recent years have been substantially
revised with
the passage of time.
Consequently,
the preliminary

reported growth rates for these months have been
nofably unreliable during the last several years. This
is illustrated
in Table III which compares the preliminary January
seasonally
adjusted
growth rates
with successive revisions.
The cumulative
revisions
have been very large, frequently increasing the January growth rates by more than 5 percentage points
and in one case by more than 10 percentage points.
While a small part of these revisions might be unrelated to seasonal adjustment,
it is clear that the
preponderant
share are due to revisions in the seasonal adjustment
factors. The direction of the January revisions is consistent with the changing shape of
the Christtnas cycle. As data for succeeding years
becomes available, the progressively
more rapid decline in M1 following the early January
peak produces a lower January adjustment
factor and a higher
adjusted January growth rate.l’
Abrupt
Changes
in Seasonal
Patterns:
The Rise
in Federal
Income
Tax Refunds
Due to heavy
overwithholding
of Federal income taxes, the Treasury typically pays out sizable tax refunds to individuals during the first half of the year, primarily in
the period from March through May. Since a large
portion of these funds are initially deposited in demand deposits, they affect the level and growth rate
of not seasonally adjusted Ml.
For several years
prior to 1973, the time profile of these disbursements
was relatively stable, as was the total amount relative
to the outstanding
money supply. Consequently,
the
seasonal impact of the refunds on Mt was probably
adequately captured by the X-l 1 seasonal adjustment
factors.
“Another

example

of

a

long-run

trend

in

a

seasonal

force

that

had a large impact on a monthly seasonal factor was the rapid
growth
in nonwithheld
individual
income taxes paid in April.
relative to the money supply,
between the mid-1950’s and the mid1960’s.
This
growth
in tax payments
caused
a steady
seasonallr
adjusted
April
M1,
resulting
in gradual
increases in the April adjustment
factor.
See Lawler

rise

in

not

progressive
13.

p.

261.

Table IV

INDIVIDUAL

INCOME
As Q Percent

1968

1973

4.9
4.9

8.5

1975
1976

9.0
9.0

5.9

1972

1974

6.2
6.4

1969
1970
1971

Note:

TAX REFUNDS
of Ml

8.4

1977

9.0

Ratios we total tax refunds for the year divided by not
seasonally
adjusted level of Ml in December of the preceding
year.
The figure for 1977 is an estimate.

Source:

Federal

FEDERAL RESERVE BANK OF RICHMOND

Reserve

Bulletin.

9

the 1970-1972
1972 period
growth

on the one hand and the postSpecifically,

of not seasonally

June period

adjusted

has probably

been stronger

in the latter
of the X-11

in the preceding

section

might expect this shift to distort
sonally adjusted

M, growth

of this article,

one

the preliminary

sea-

rate over the March-June

period in 1973, since this growth
using

the seasonal

Ml in the March-

On the basis of the discussion

years.13
model

period

on the other.

seasonal

through

adjustment

1972 only.

downward

based

More specifically,

pect X-11 to produce
nary growth

rate was calculated

factors

an upward

on

data

one would ex-

bias in the prelimi-

rate over this period in 1973, leading
revisions

as additional

high refund

to

years

were use to calculate the 1973 seasonal adjustment
factors.14 (As suggested in Section II, however, even
the final adjusted
surge in refunds

1973 data might

reflect the abrupt

to some extent since the final adjust-

ment factors are based partly on pre-1973, low-refund
year experience.)
The same general process should
.-.-.-

1970- 72

affect the 1974 and 1975 data.
In fact,
March-June

the preliminary
growth rates over the
period in the years 1973, 1974, and 1975

have been significantly
reduced by subsequent
re-.
visions.
Annualized,
seasonally adjusted M, growth
from a base comprising
and February

the average

of the Januar)

to a terminal value comprising
the average of the four months March through
June
has been revised downward on average by 2.49 percentage points for these years, a fairly dramatic indication

figures

of the magnitude

of &I1 revisions

that

ca!n

occur. It shows that the average revision of the Ml
growth rate over this period was in the neighborhood
of the typical 2 to 2yz percentage
tween the upper and lower limits
longer-run
In 1972, however, increased withholding
for numerous individual taxpayers went into effect, causing
a sharp increase in refunds from $14 billion in 1972
to $22 billion in 1973. As indicated in Table IV, the
result was an abrupt jump in total refunds from about
6 percent of M, to roughly 8% percent of M,. Chart
4 shows the monthly profile of the tax refunds relative to MI in the years following 1972 compared to
The monthly
the pattern
in the 1970-72 period.
profile of the disbursements
was very similar (1) in
the years 1973, 1974, and 1975 and (2) in 1976 and
1977.
Consequently,
these two sets of years are
grouped together in Chart 4.
Presumably,
the abrupt increase in the level of
refunds in 1973 altered seasonal patterns as between
10

ECONOMIC

Ml growth

point

range

be-

of the FOMC’s

targets.

The precise implications
of these downward
revisions, however, is clouded by the fact that they
might

have been influenced

and by ad lzoc judgmental

by benchmark
adjustments

revisions

made by the

1J June
is included,
even
thouph
the bulk of the refunds
are paid
before
June, for two reasons.
First,
there is normally a lag between
the receipt
of refunds
and their expenditure
or conversion to Other
Consequently,
the daily
average
level of MI balfinancial
assets.
ances
in June
is likely
to be affected
by refund
disbursements
in
May.
Second, refund
checks
mailed
in May
(the
refund
data
are
reported
on a mailing
date basis)
may not actually
be cashed
until
JUWZ.
14 Note that the increase
in the level of refunds
tends to increase
the
daily average
level of not seasonally
adjusted
Ml in each of the fsxxr
Therefore,
the impact
of the
months
of the March-June
period.
refunds
on any
individual
month’s
growth
rate
depends
on the
profile
of the refund
flow.
The
discussion
in the text
refers
to
growth
over the entire
March-June
period:
i.e., the increase
in the
daily
average
level
of Mt for
the four-month
March-June
pwiod
over the average
daily level for some base period.

REVIEW, NOVEMBER/DECEMBER

1977

staff of the Board of Governors as well as by changes
in the underlying
zX-l 1 seasonal adjustment
factors.
In order to abstract from these other factors, comparable growth rates were calculated using the factors
generated by the X-l 1 model without any modification.
First, unmodified
X-l 1 seasonal adjustment
factors were calculated
these factors
nary”

using

data through

1973 base).
for 1974 and

growth

rates

in a similar

manner.

magnitude

changes

of seasonal

Patterns

changes

in the timing
forces

can

In

in seasonal
and relaalso

affect

factors

using

1975 were
preliminary

to “final”

derived

computed
revisions

Preliminary

These

rates were then compared

rates for the same periods
X-11

temporary

tive

Seasonal

1973 period

(over a January-February

The implied

patterns,

in

durable

a “prelimi-

rate for the March-June

March-June
derived

Changes
to relatively

1972, and

were then used to develop

growth

growth

Temporary
addition

growth

from unmodified

data

are -1.70

through

percentage

1976.
points

in 1973, -1.56 percentage points in 1974, and -1.06
percentage
points in 1975-an
average revision of
-1.44 percentage points. This analysis suggests that
successive
contributed

changes
heavily

in the underlying
X-11 factors
to the revision in the published

M1 data summarized
To this point
impact

in the preceding

the discussion

of the increased

paragraph.‘”

has centered

tax refunds

on the

on the prelimi-

nary seasonally adjusted
M, data over the MarchJune period. More broadly, there is evidence that the
increased
generally

refunds in conjunction
biased the preliminary

with the X-l 1 model
seasonally adjusted

growth rates upward in the second quarter and downward in the third quarter in 1973 and subsequent
years.
Chart 5 shows the week-to-week
movements
of a ratio of three-month

Ml growth

trend growth
justed

and

to longer-run

on both a (preliminary)

basis

an unadjusted

seasonally

basis.

The

panel of the chart shows the movements
prior to the abrupt
panel

shows

increase

increase

the movements

in the refunds.

ad-

upper

in 1972, just

in the refunds.

The lower

in 1973, just after

If the increased

the

refunds

to-

gether with the X-l 1 model have in fact produced

the

biases mentioned above, one would expect a greater
degree of (in this particular case positive) correlation
between the unadjusted
and adjusted movements
of
the ratio in 1973 than in 1972. The chart indicates
rather clearly that the correlation
is indeed considerably greater in 1973 than in 1972. Specifically, the
correlation
-.22

coefficient

is .70 in 1973 compared

to

in 1972.
to

‘6It
is possible
that these results
are influenced
the June
1975 tax
rebate
payments.
Excluding
analysis.
however,
does not greatly
alter the results.

some
June

FEDERAL

extent
from

by
the

RESERVE

BANK

OF RICHMOND

11

Although
seasonally adjusted
M1 growth rates.‘”
X-11 attempts to take account of lasting changes in
the profile of seasonal forces influencing
M, through
the construction
of moving adjustment
factors, the
model is simply not designed to deal effectively with
temporary
changes in these forces.
Basically, the
model treats such changes as though they were irregular movements
in the not seasonally
adjusted
data. Consequently,
most of their impact is probably
passed on to the seasonally
adjusted
data.
For
example, since there is a positive relationship
between the relative magnitude of April tax payments
and the unadjusted
lMl growth rate in April, unusually large April tax payments in a given year probably tend to inflate the seasonally adjusted April M1
growth rate in that year.
A somewhat more esoteric example involves the
timing of April tax collections
by the Treasury.
Individuals
generally pay nonwithheld
income taxes
by check. Many of these checks are mailed close to
the April 15 deadline.
Individuals
typically accumulate the balances needed to cover these checks at the
time they are mailed, but the Treasury
often takes
two or three weeks to process the checks. Because of
the huge sums involved, even a small variation
in
processing time can significantly
affect average daily
M1 balances in April and seasonally adjusted April
M, growth rates.‘?
A final example is a recent change in the procedures surrounding
monthly social security retirement
and survivors benefit (SSA)
disbursements.
Prior
to mid-1976 all of these disbursements
were made bj
check. The checks were usually posted so that they
would reach .their recipients
on the third of the
month. When the third fell on a Saturday, payment
was made on that day even though some financial
institutions
are closed on Saturdays.
If the third fell
on a Sunday, payment was made on the preceding
Saturday.
In mid-1976 this schedule was changed
in conjunction
with the introduction
of facilities permitting the direct deposit of some of these clisbursements through electronic media.
Specifically,
payments are now made on the preceding Friday when
the third falls on either a Saturday or a Sunday.‘8
Since a sizable portion of the disbursements
are converted into -R/I1 balances, these changes in payment
In As indicated
in Section
II of this article.
the distinction
between
(1)
temporary
changes
in seasonal
patterns
and
(2)
irregular
movements
in not
seasonally
adjusted
data
is not
always
clear.
Consequently.
the choice
of examples
in this and the following
subsections
is somewhat
arbitrary.
17 See

Auerbach

[ 11.

lRThese
changes
apply
ments
by check,
which
total
payment
volume.

12

not only
continue

to direct
deposits
to account
for

but also
well
over

ECONOMIC

to payhalf
of

REVIEW,

schedules have altered the seasonal behavior of not
seasonally
adjusted
M, in these months for two
reasons.
First, the timing of the payments
with
respect to calendar dates has changed compared to
earlier years.
Second, since the payments are no\\
made prior to rather than after a holiday or a weekend, the funds are likely to be held in the form of Ai,
balances for a longer period (specifically the one or
two days of the holiday or weekend)
before being
spent or converted into other financial assets, thereby
raising average daily balances
and growth
rates.
Again, to the extent that these changes are ignored
by seasonal adjustment
procedures,
they are likely
to affect seasonally adjusted M, growth rates.‘”
It is interesting
to note that all of the conditions
described in these examples were present in April
1977 when RI1 grew at a record annual rate of 19.7
percent.
First, individual nonwithheld
ta% payments
were larger relative to the level of M, than in any
other year since the Treasury began publishing these
data in 1954. Second, Treasury processing of these
payments appears to have been considerably
slower
than in the three preceding years perhaps due to the
magnitude of the pnyn~ents.2n Third, April 3 fell on
a Sunday so that social security payments were made
on Friday, April 1. Finally, April tas refunds were
unusually high, as shown earlier in Chart 4. These
observations
are not intended
to imply that these
factors explain all or even most of the unusually
large prelitninary
April 1977 M1 growth rate. They
do illustrate,
however, how temporary
changes in
seasonal forces can cloud the meaning of a specific
preliminary
monthly M, growth rate.
The factors
conIrregular
Movements
in M,
tributing
to short-run
variations
in seasonally
adjusted Mt growth rates discussed thus far have all
been related to changes in the underlying
determinants of the seasonal behavior
of M1.
Irregular
movements
in seasonally adjusted growth rates, in
contrast, result from special or unusual events. Some-times these events can be identified and anticipated.
More often, unfortunately,
they are neither identifi-

“~The
third
has fallen
on a nonbusiness
day three
times
since
the
schedule
chance
went
into
effect:
October
1976.
April
1977. and
The preliminary
seasonally
adjusted
Mi growth
rates
July
19’77.
(at annual
rates)
for these months
were 13.7 percent.
19.7 percent.
and 18.3 percent,
respectively.
These
growth
rates
exceeded
both
trend
growth
and
other
monthly
rrowth
rates
during
the
postchance
period
by wide margins.
It is likely
that the change
contributed
to these
hiah
prowth
rates.
although
the extent
of the
effect
cannot
be specified
precisely.
~1 This
statement
is based
on a comparison
of tax
collections
in
April
and in early
May,
respectively,
using
data
published
in the
Trcasur?/
Zlullet,n.
(The
collection
date
is the date
on which
the
Treasury
actually
clears a check.)
This comparison
indicated
that a
significantly
higher
proportion
of total collections
in 1977 occurred
in May
as opposed
to April
than
in the three
preceding
years,
strongly
suggesting
slower
processing
in 1977.

NOVEMBER/DECEMBER

1977

al)le nor foreseeable.

Consequently,

movements

in

proper monetary
policy response
when the event is anticipated.

seasonally adjusted M 1 growth rates due to irregular
events resemble variations resulting- from changes
in
seasonal

forces in that they complicate

monetary
fundamental

policy

IJ~

changes

making

it difficult

in the trend

rate of Ml from some transitory

the conduct

of

The Weekly

Data

growth
Up to this point this article has focused on shortrun movements in the ~zonthly M, growth rates. The
Federal Reserve also publishes seasonally adjusted
weekly Ml data. These data take the form of daily
average balances over Federal Reserve “statement”
weeks, which run from Thursday
through Wednesday, inclusive.
This section will extend the preceding
discussion
by describing
some of the factors that
influence the weekly behavior of M1.

change.

As suggested
above, the most obvious
recent
change in M1 growth caused by an irregular
event
was the sharp acceleration
in May and June 1975
due to the $9 billion of tax reljates and supplemental
social security benefits paid during those months.
In
hindsight, it seems clear that while the FOMC expected these payments to enlarge growth rates over
this period, the full magnitude of the impact was not
anticipated.
As a result, the FOMC appears to have
concluded that the acceleration was attributable
to a
considerable
extent to the expansion of business activity just beginning to gather steam at that time and
put upward pressure on the Federal funds rate in
order to restrain it. The R/I1 growth rate dropped
abruptly in July, however, and remained minimal for
several months, prompting
the Committee to reduce
the funds rate to its pre-rebate level in October and
November.”

The first point that needs to be made about the
weekly M, data is that they are exceedingly volatile:
the change in Ml this week-whether
measured in
dollars or as a percentage growth rate-is
likely to
be very different from the change next week. Chart
6 provides a visual demonstration
of this point using
preiiminary
1976 data.
Each point on the graph
shows the ratio of the dollar change in seasonally adjusted M, during a given week to a moving 53-week
average of weekly changes centered on that week. As
the chart indicates, there are both wide variations in
weekly growth over the year as a whole and, in
many instances,
sharp fluctuations
from one week
to the next.

A number of other recent swings in short-run seasonally adjusted M, growth rates can be linked to
specific nonrecurring
events. For example, the -3.2
percent rate of decline in December 1975 almost certainly resulted partly from the change in Federal Reserve Regulations
Q and D permitting business firms
to hold savings deposits. But while it is often possible
to evaluate irregular
variations
in Ml growth in
terms of specific events sucli as these after the fact,
it is extremely difficult in most cases to specify the
probable impacts on short-run
growth rates in advance with any degree of quantitative
precision.
Obviously the absence of suc11 information
makes the

Chart 6 suggests that there is little if any
atic relationship
between weekly changes in
of Ml-viewed
either individually
or over
of several weeks-and
longer-run
trends in
of M1 growth.

“As events
actually
unfolded
in May and June of 1975, the rise
that took place in the money
supply was much
larger
than the
Federal
Reserve
staff
had estimated
would
occur
as a result
of
the
rebate
program.
The
inference
we drew
was
that
the
demand
for money
was expanding
rapidly
quite apart
from
the
rebate
program.
We therefore
took
mildly
restrictive
action
toward
the end of June to reassure
the Nation
that the Federal
Reserve
would
not countenance
monetary
expansion
on a sca:e
that
might
release
a new
wave
of inflation.
Differences
of
judgment
existed
then-and
still do-as
to the appropriateness
Let me say only
that
if we
of that
mild tightening
action.
erred.
the mistake
was
technical
in origin-that
is, it grew
out of the difficulty
in making
good estimates
of the tax-rebate
In any
event,
monetary
growth
impact
on deposit
growth.
rates soon moderated,
and we lost very little time in returning
to an easier
monetary
stance.”

RESERVE

Nonetheless,

as pointed

systemthe level
a period
the rate

out in the

introduction
to this article, the FOMC’s
current
procedures
for implementing
monetary
policy tend
to focus the attention of both policymakers and financial market participants
on the weekly data. Apart
from these procedures,
though, the simple fact that
the most recent weekly M1 figure is usually the latest
information
available regarding
monetary
developments quite naturally
stimulates
interest.
The remainder
of this section attempts
to provide some
perspective for evaluating
the informational
content
of the weekly statistics.
In general, the same kinds
of factors that produce variations
in the seasonally
adjusted monthly R/I1 data also produce variations in
the seasonally adjusted weekly MI data. Abstracting
again from fundamental
changes in underlying
economic conditions,
these factors are : (1) irregular
events and (2) changes in the timing and magnitude
of seasonal movements not captured by the seasonal
adjustment
factors used to adjust the data.

:‘I The policy
record
for the FOMC
meeting
held May 20. 1975. refers
explicitly
to the Committee’s
recoanition
that short-run
MI tolerance
ranges
in the May-June
period
should
be relatively
liberal
to allow
for the rebate effect.
The ran&~ was set at 1 to 9% percent.
The
actual
(preliminary)
growth
rate for the two-month
period
was 14.4
percent.
See Board
of Governors
of the Federal
Reserve
System,
This
episode
was later
reviewed
by
Annual
Report.
1975.
P. 197.
Chairman
Arthur
Burns
of the Federal
Reserve
in testimony
before
the Senate
lludget
Committee
March,
1977:

FEDERAL

even

IV.

to distinguish

or cyclical

problematic

BANK

OF RICHMOND

13

Jirly

*_

Aug.”

Oct. -~

Nov.

Dec.” 4

Box II
SEASONAL

ADJUSTMENT

The
technique
used
to seasonally
adjust
the
weekly
Ml data is essentially
an extension
of the
procedure
used to develop
monthly
seasonal
adjustment factors.
Indeed,
the weekly
adjustment
factors arc derived
directly
from
the seasonally
adjusted
monthly
data as follows.
First,
the adjusted
monthly
data
are centered
at mid-month,
and a
provisional
seasonally
adjusted
level for each stateis derived
by interpolation
of the
ment
week*
monthly
series.
Second,
so-called
“original”
ratios
of the unadjusted
weekly
data to the provisional
adjusted
weekly
data are derived
for each statement
week,
and,
through
interpolation
of these
statement
week ratios,
“offset”
ratios
are derived
for weeks ending
on days other than a Wednesday.
Following
these calculations,
a ratio exists for each
individual
day in the entire data series, covering
the
calendar
week
ending
on that
day.
Third,
a
weighted
moving
five-year
average
of these ratios
is calculated
for each statement
week in the series.
This
calculation
uses the ratio
for the statement
week
in question
along
with
the “original”
or,
* Statement
weeks
are Federal
weeks
running
from Thursday
lowing
Wednesday.

Reserve
through

reporting
the fol-

OF THE WEEKLY Ml

DATA

where
necessary,
the “offset,”
ratios
for corresponding
calendar
weeks
in the four surrounding
years, with truncation
of the average
for terminal
years
in tile series.
For example,
the weighted
average
used in calculating
the currently
published
factor
for the statement
week
ending
March
7,
1973, is based on the ratios
for the calendar
weeks
ending
h,Iarch
7 in the years
1971.1975,
inclusive.
The average
used in calculating
the currently
published
factor
for
the
statement
week
ending
March
3, 1976, is Ijased
on the ratios
for corresponding
\veeks
in the years
19741976.
inclusive.)
This
third
step
is designed
to take
account
of
moving
weekly
seasonality
and resembles
the procedure
used to take account
of moving
seasonalit)
in the derivation
of the monthly
factors.
(See
Box I on p. 5.) Fourth,
the average
of the weekly
ratios
for a given
calendar
month
is adjusted
to
approximate
closely
the
corresponding
monthly
seasonal
adjustment
factor.
Fifth,
these ratios
are
judgmentally
adjusted
by the Federal
Reserve
staff.
It should
be clear
even from
this brief summary
that
the weekly
seasonal
adjustment
factors
are
subject
to the same
kinds
of limitations
as the
monthly
adjustment
factors
and for roughly
the
same reasons.
J

14

ECONOMIC

REVIEW, NOVEMBER/DECEMBER

1977

Irregular
Events
As we have seen, irregular
events can have a sizable effect on monthly
M1
growth rates. They can also have a marked impact
on the weekly data, particularly
if the event is of
relatively
short duration.
Two illustrations
from
recent experience are relevant.
In late January 1977,
the eastern and midwestern
portions of the United
States experienced the most severe winter weather in
several decades, disrupting
production
and sales activity in these areas.
Seasonally adjusted M, fell a
total of $3.0 billion over the two statement
weeks
ending January
26, compared
to declines of only
$100 million and $700 million in the corresponding
periods in 1976 and 1975, respectively.
It is likely
that the unusual
weather
was partly responsible.
R4ore recently, there was a precipitous
$5.0 billion
increase during the statement week ending July 20,
1977. The magnitude of the rise contrasted
sharply
with the moderate growth typical of mid-July. While
the full explanation
for this increase is unclear, the
July 13 power failure in New York City, which disrupted interbank settlements there, may have been a
contributing
factor.
While it is sometimes possible
to anticipate irregular events such as these, they are
more often not anticipated, leading in some instances
to substantial
market reactions.
Changes
in the Magnitude
and Timing
of Seasonal Gains
As in the case of the monthly
data,
short-run swings in the adjusted kveekly data are also
caused by changes in the magnitude
and timing of
seasonal movements
not captured
by the seasonal
“Distortions”
adjustment
factors.
of the adjusted
weekly data of this sort result from inherent
deficiencies in the procedures
used to derive weekly
seasonal adjustment
factors similar to those discussed
in Section II of this article with respect to the derivation of the monthly adjustment
factors.
(The procedure for seasonally adjusting
the weekly h4, data
is outlined briefly in Box II on 11. 14.)
There is
evidence that the distortion
of the preliminary
adjusted weekly data clue to these deficiencies is sizable.
The results of one recent study suggest that
the mean absolute revision of the preliminary
adjusted data, espressed il! terms of annualized growth
rates, is on the order of 13 percentage points.‘“” Two
specific cases are discussed below.
Enstcv Week Since the week containing the Easter
holiday varies from year to year over an al,prosimately four calendar week span, the timing of this
seasonal influence on the unadjusted
weekly M, data

L” See

Wood

[7],

especially

Table

II.

Table V

RATIO OF WEEKLY Ml

LEVEL TO CENTERED

FIVE-WEEK AVERAGE

IN WEEKS

SURROUNDING
(Seasonally

Week
1
----__-

EASTER

Adjusted

Dote)

Week
2

Week
3*

Week
4

Week
5

Date of
Easter
Sunday

1968

0.999

0.998

1.009

0.997

0.995

April 14

1969

0.997

0.998

1.011

1.005

0,996

April

1970

0.992

0.990

1.018

1.005

0.999

6

March 29

1971

1.001

1.008

1.006

0.997

0.990

April 11

1972

1.000

0.997

1.003

1.001

0.998

April

1973

1 .ooo

1.003

0.994

1.001

1.000

April 22

2

1974

1.001

1 .ooo

1.003

1.000

0.998

April 14

1975

0.999

0.999

1.000

1.001

1.000

March 30

1976

0.998

1.005

1.004

0.996

0.998

April 18

1977

0.991

1.005

1.004

0.999

1.004

April 10

preliminary

data.

* Includes
Note:
.SOWC.%

Easter Sunday.

Ratios

are calculated

Federal

Reserve

using

Bulletin.

The weekly seasonal adjustment
proalso shifts.
cedure described in the Box makes no allowance for
these shifts.“3 Consequently,
one would expect that
the seasonal adjustment
factor for the week containing Easter would typically be too small, and,
correspondingly,
the reported seasonally adjusted M,
level in that week would be too large.
The data in
Table V tend to support this assertion.
Each entry
in the table is the ratio of the seasonally adjusted M1
level for the indicated week to a five-week average
of weekly levels centered on that week. Ratios are
reported for the Easter week and the two surrounding weeks in each of the last ten years. In five of the
years, the Easter week ratio is the largest of the five
ratios.
It is the second largest in four of the remaining five years, strongly suggesting a systematic
upward bias affecting that week.
Cllangcs in the Intra~uonthly Seasonal The second
example involves the effect of a somewhat more
general phenomenon
on the behavior of the seasonally adjusted weekly data: namely gradual changes
in the seasonal behavior of the unadjusted
data z&l&z
a calendar month.
To the extent such change does
in fact occur, it would tend to introduce an intra-

“Since
the week
containing
Easter
is known
well in advance.
its
seasonal
effect
on the weekly
Ml data
could
presumably
be anticipated
throulrh
judgmental
adjustments
to the preliminary
seasonal
adjustment
factors.
The evidence
supxnarized
in Table
V, however.
indicates
that if judgmental
adjustments
have been made. they have
not been adequate.

FEDERAL RESERVE BANK OF RICHMOND

15

------ ,960
-‘-.--,9&j

---

1968

---

1968

. . . . . . ..-...

,972

-

1976

-

1976

monthly seasonal movement into the preliminary
adjusted weekly data in a manner analogous
to the
impact of the Christmas
cycle on the adjusted
monthly data.24
There is ample evidence that intramonthly
seasonal patterns change.
The two panels of Chart 7
depict the intramonthly
pattern of the not seasonally
adjusted
MI data during four separate years spanning a 16-year period for the months of July and
August.
These months were selected since they are
less influenced than other months by tax dates and
other events that might obscure the evolution.
While
this evolution has by no means proceeded at a steady
pace, a careful examination
of both panels of this
chart suggests that there is now relatively
greater
strength in the data during the first half of the month
and a sharper decline during the second half. Comw Bee

16

Section

III,

pp.

8-9.

ECONOMIC

parable data for other months suggest that a similar
change may be occurring in these moriths.“5
While
this evolution
is not as neat and persistent
as the
similar gradual change in the Christmas cycle affecting the monthly data, it does appear to be influencing
the behavior of the adjusted weekly data.
Chart 8
provides evidence supporting
this contention.
The
chart shows the average change in preliminary
seasonally adjusted Ml for statement weeks ending on a
given calendar day of the month over the 12 months
of 1976, smoothed by a moving average.
The chart
clearly indicates an upward bias in the seasonall)
adjusted
movement
of Ml in the first half of the
month and a downward bias in the second half of the
month, a pattern consistent with the evolution of the

SThe
cause
changes
in
and receipts,
ing factor.

of this
evolution
the
intramonthly
however,
are in

REVIEW, NOVEMBER/DECEMBER

1977

Systematic
is not
entirely
clear.
pattern
of
Treasury
disbursements
all likelihood
an important
eo‘otribut-

procedures to capture fully the impact of changes in
the seasonal behavior of Ml, especially when such
changes are actually in progress.
Specifically, the
discussion has indicated that the observed variation
in short-run
growth rates has been produced
by
forces as broad and persistent as the apparent longerrun change in the seasonal demand for M1 balances
during the Christmas season and the abrupt change
in the level of Federal income tax refunds in 1973
to such seemingly
innocuous
developments
as the
recent change in the timing of monthly social security
disbursements
and year-to-year
variations in the time
required to process tax payments.

71

Moving Average

-2

‘_ -3

-

IIIIIIIIIIIIIIIILLL
2 4 6

8

10 12 14

16 18 20 22 24 26 28 3

Day of the Month

.
*
(.
_. : F

The dotted line is the average change in the
Note:
seasonally adjusted money supply for all statement weeks in 1976 that ended an the day
The solid line is a centered $-day
plotted.
moving average of the points on the dotted
I Jinr,
So&w:

Federal Reserve Board Release, H.6:

intramonthly
pattern of the not seasonally
data illustrated in Chart 7.

adjusted

Monetary economists, both inside and outside the
Federal Reserve, frequently point out that too much
attention is paid to monthly and weekly M, growth
Short-run
growth rates are important,
howrates.
ever, because the Federal Reserve’s current procedure
for implementing
monetary
policy on a day-to-day
basis makes them important.
As pointed out in the
introduction
to this article, preliminary
estimates of
current two-month
Ml growth rates are one of the
major factors determining
policy actions under existing operating procedures.
Federal Reserve policymakers
are well aware of
the existence of short-run
disturbances
of the kind
discussed
in this article.
The problem faced by
policymakers-and
by financial market participants
attempting
to anticipate
Federal Reserve policy-is
that the immediate causes of short-run
M1 growth
rate variations are not usually apparent on a current
basis.
But the appropriate
policy response to sucli
movements depends critically on the conditions causing them.

Suppose,

for esample,

that

M1 growth

over a two-month period exceeded the desired longerIf it were clear that this divergence rerun rate.
flected an increase in the demand for transactions
1)alnnces due to excessive final demand for goods

V.
Conclusion

and services

FEDERAL

RESERVE

in the economy

at large,

policymakers

know that the acceleration should be resisted.
Conversely, if the increase were obviously the result
of some temporary disturl~nnce likely to wash out in

This article has attempted to identify and esplnin
some of the factors that produce the high degree of
observed variability
in short-run
seasonally adjusted
Ml growth rates.
Sonic of this varial)ility undouhtedly results from fundamental
changes in economic
conditions
that produce changes in the underlying
demand for and supply of n1, balances.
A large part
of the olzerved variation,
however, appears to have
little ‘ro do with economic conditions, and it is with
these noneconomic
determinants
that this article has
lIeen concerned.
In particular. the article has argued
that many short-run
swings in M, growth
rates
result frolli ( 1 ) special events that occur irregularly
or (2) the inability of existing seasonal adjustment

woultl

the near future, policymakers would presumably pursue ;I steady policy course. The principal implication
of the analysis in this article is that making such
determinations
on a current basis with any degree of
certainty is always difficult and often impossible.
As
the preceding sections have attempted to demonstrate,
a wide variety of factors unrelated to basic economic
trends can and do affect short-run
Ml growth rates,
particularly
the preliminary
growth rates that actually determine policy actions.
BANK

OF RICHMOND

17

Unfortunately,

no

simple,

this problem-either
servers-is

likely

circumstances,
individual
pears

the

not

times

incoming

Beyond
however,

promising

presented

seasonally

changes

and

short-run

the

more

Under
analysis

of
rates
In

in this article

with

M1

patterns

tactical

ol)-

policy.

Any

lqontl

data

each
appar-

suggests

seasonal

any

printe

these

or market

approach.

adjusted
(2)

to

solution

growth

(1 ) with

in these

the question
lies

eclectic

in short-run

familiarity

of the year

spective

forthcoming.

and

most

the analysis

policyrnakers

be

close

that a detailed

ating

to

fluctuation

to be the

ticular,

in

for

mechanical

patterns
at

certain

ongoing

or pro-

can assist

in evalu-

of evaluating
fundamental

incoming
issue

detailed

current

of

the

implementing

difficulties

short-run

doul)ts

sl)out

cedure.

of

this

R/l1 data,

however,

such as the esisting
short-run

short-run

growth

in n very

one,

rates

systenlatic

for improving

these

where.“G

would

appear

further

is well

de-

evaluating

is bound

to raise

operating

pro-

that focuses

largely

rates without

relating

to

desired

have

that

longer-run
Suggestions

fashion.

procedures

It

in

of any

growth

growth

monetary
issue

The preceding

inherent

the effectiveness

on nnnualized
these

for
analysis

the scope of this article.

scription

deserve

M1 data.

procedures

been

tllese

made

else-

suggestions

attention.

data,

of appro-

20 See, for example,

Poole [Sl.

References
1.

Surge in Ml Laid to
Auerbach,
Irving M. “Recent
IRS Delay in Processing
Taxes.”
The Money Manager, May 16, 1977, pp. 4-5.

5.

Poole, William.
“Interpreting
the Fed’s
Targets.”
Brookings
Papers on Economic
(1st quarter,
1976), pp. 247-259.

2.

Breimyer,
F. and Wenninger,
J.
“An Estimation
of the Effect
of Treasury
Tax Rebates and Social
Federal
Reserve
Security
Supplements
on M1.”
Bank of New York Research Paper No. 7611, March
1976.

6.

Poole, William and Lieberman,
Monetary
Control.”
Brookings
Activity,
(2nd quarter,
1972),

7.

3.

“Seasonal
Adjustment
of the
Lawler,
Thomas.
Money Stock:
Problems
and Policy
Implications.”
Economic
Review,
Federal
Reserve
Bank of Richmond, (November/December
1977)) pp. 19-27.

Bureau
of the
U. S. Department
of Commerce.
Census.
The X-11 Variapzt of the Census Method 1’1
Seasonal Adjustment
Progrum,
by J. Shiskin, A. II.
Young, and J. C. Musgrave.
Technical
Paper No.
15. Washington,
D. C.: 1967.

4.

Lombra, Raymond E. and Torto, Raymond
G. “The
Strategy
of Monetary
Policy.”
Economic
Review,
Federal
Reserve
Bank of Richmond,
(September/
October 1975), pp. 3-14.

8.

Wood, Cynthia W. “Money
non~ic Commentary,
Federal
land, May 16, 1977.

18

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

1977

Monetar:y
Aetivitbf,

Charles.
“Improving
Papevs ox Economic
pp. 293-335.

Stock Revisions.”
EeoReserve Bank of Cleve-

SEASONAL

ADJUSTMENT

OF THE MONEY

STOCK:

Problems and Policy Implications
Thomas A. Lawler

The short-run
behavior of the seasonally adjusted
money stock has received increased attention
from
l~olicyniakers.
economists,
and financial analysts in
recent years.
Quarterly,
monthly, and even weekly
changes in the adjusted money stock are scrutinized
carefully.
Recently, however, some economists have
questioned the adequacy of the method used to adjust
the money stock for seasonality,
and therefore the
quality of the seasonally adjusted data itself.’ Since
the Federal Reserve considers short-run
movements
in the seasonally
adjusted
money stock in formulating monetary policy, seasonal adjustment
problems
may adversely affect the Fed’s ability to achieve its
policy goals.
The purpose of this article is to discuss some of the
problems associated with adjusting
the money stock
for sensonality.
The article begins \vith a brief discussion of the general principles of seasonal adjustNest, it examines the method currently used
ment.
to adjust the monthly money stock (defined here as
or currency plus demand deposits) for seasonality. Finally, it discusses the policy implications
of
inadequate
seasonal adjustment.

hz,,

then it may not be offset within a year, and, in the
absence of any policy action, may affect long-run
money growth.
Seasonal Adjustment
Methods
There are various
seasonal adjustment
techniques
available.
Most of
these assume that an original time series (0) can be
broken down into separate components,
namely the
seasonal component, the trend-cycle component, and
the irregular
component.
The seasonal component
(S) embodies the intrayear pattern of variation that
recurs regularly from year to year. The trend-cycle
component
(C) is made up of long-term
trend and
cyclical movements.
The irregular
component
(I)
reflects the influence of short-run erratic fluctuations.
A seasonally adjusted series is composed of the trendcycle and irregular
components,
the seasonal component having been filtered out.
Experience
indicates that for most economic time series, including
the money stock [7, pp. 4-71, these components are
related
in a multiplicative
fashion
(i.e., 0 =
c x s x I).”
Ratio-to-Moving
Average
Method
The most
widely used multiplicative
method of seasonal adjustment is the ratio-to-moving
average niethod.3
For a
monthly series the basic steps of this method are:

Purpose of Seasonal Adjustment
The purpose of
seasonally adjusting a time series is to separate from
that series any short-run variations that tend to recur
at the same time each year. In this way longer-term
movements as well as unusual short-term fluctuations
can be distinguished
from these systematic intrayear
The distinction
between seasonal and
movements.
nonseasonal
movements
is important,
as the policy
implications
of the two types of movements
may
differ.
For example, the reaction of the Federal
Reserve to a change in short-run
money growth
\vill generally
depend on whether that change is
perceived as being consistent with some long-range
money growth target.
If 3 short-run
change in
money growth is due solely to seasonal forces, then
it will be offset later in the year, with no effect on
long-run
money growth.
Conversely,
if the change
in money growth is caused by nonseasonal influences,
‘E.g.,

see

IS],

Cl?].

1. A 12-month centered moving average
of the
original
series is constructed
so that short-run
intrayear
movements
are averaged
out and the
trend-cycle
component
can be estimated.4
The
average must be centered because a 12-month average falls between the sixth and seventh months,
and therefore
cannot
be associated
with either.
For example, the midpoint
of a 12-month average
from January to December, inclusive, falls between
June and July.
Similarly,
the midpoint
of a 12month average
from February
to January,
inclusive, falls between July and August.
However, the
average of these two 12-month averages is centered
on the month of July.
Therefore!
centering
a 12month moving average on a specific
month is accomplished
by taking
the average
of each two
consecutive
12-month averages.

‘This
c+s+1.
2 A good
numerical

is

in

contrast

discussion
example,

to

an

additive

relationship,

of the ratio-to-moving
is given
in [ZI.

4 A moving
average
is simply
an average
period
at a time.
dropping
one term
and

ClSl.

FEDERAL

RESERVE

BANK

OF RICHMOND

average

where
method,

that moves
forward
adding
another.

0
with

=
a
one

19

The X-11 Prqrnm
The basic steps of the X-l 1
program are described in the Box on page 23.” The:
X-l 1 program
is an iterative process that can br
broken down into three stages.
In the first stage 2.
preliminary
seasonally
adjusted
series is obtained
using a method similar to the ratio-to-moving
aveT-age procedure
described above, with an additional
step limiting the influence of extreme irregular movements on computed seasonal factors.
In the second
stage a weighted average of this preliminary
season-

2. This centered average is then divided into the
original series, and the resulting
ratios are known
as seasonal-irregular
(S-I)
ratios.
3. A moving average of these S-I ratios is computed separately
for each month (i.e., a separate
average
of the S-I ratios
for January,
the S-I
ratios for February,
etc.) so that irregular
movements are averaged
out.
This average
estimates
the seasonal
component,
or seasonal
factor,
for
each month.
The use of a moving average of the
S-I ratios
allows
for a seasonal
aattern
that
changes gradually
over time.
The t&e span over
which these S-I ratios are averaged
depends on
how fast the seasonal pattern is assumed to change
-the
more stable the assumed
seasonal
pattern,
the longer the span.
If the seasonal
pattern
is
believed to be constant over time, then the seasonal
factor
for each month is the average
of all S-I
ratios for that month.
4. These seasonal
factors
are divided
original
series
to obtain
a seasonally
series.

ally adjusted

of the trend-cycle

average

yields

does a simple

into the
adjusted

the original
better

Note that the seasonal factor in any time series
is simply the ratio of the unadjusted
value to the
adjusted value of the series.
Therefore,
a seasonal
factor (converted to an index number)
greater than
100 indicates that seasonal influences are tending to
push the series above the yearly average, while a
factor below 100 indicates that the series is depressed
by seasonal influences.
Seasonal

Adjustment

1 plots
monthly
ponents,

of the Money

Stock

Chart

the seasonally
unadjusted
and adjusted
money stock series (Ml) and its two comdemand deposits and currency,
from 1970

to 1976.
The chart indicates that the unadjusted
money stock series is subject to significant
seasonal
variation,
deposit

the greater
component.

seasonally

adjusted

part deriving
However,

from the demand

it is movement

series that commands

tion of most analysts

and policymakers.

describes
adjust

the monthly

The Fed separately
mand

deposit

in the

the atten-

used by the Federal

the method

This section
Reserve

to

M1 series for seasonality.
adjusts

components

of

the currency
hll

for

and de-

seasonal

vari-

ation.
Seasonal factors are first computed for each
Ml component using the Bureau of the Census’ X- 11
Variant of the Census Method II Seasonal Adjustment Program
(hereafter
simply X-11).
The X-l 1
is based on the ratio-to-moving
average method described above, although it is more complicated.
The
output of the X-11 is then reviewed by the Board
of Governors’ staff, and modifications
are made when
deemed appropriate.
The modified seasonally
adjusted currency and demand deposit series are added
together
to obtain the seasonally
adjusted
money
stock.
The two steps, the X-11 and judgmental
modification,
are discussed in more detail below.
20

ECONOMIC

REVIEW,

series is calculated

estimate

a smoother
12-month

series,

to obtain

component.
trend-cycle

centered

of the true

curve

moving

and is generally

representation

a revised

This weighted
than

average

thought

of

to be a

underlying

trend-

cycle component.
In the third stage this revised
estimate of the trend-cycle component is used to obtain revised calculations

for the irregular

the seasonal
series.

and the seasonally

component,

component,
adjusted

Jrrdglltcntal iZlodifiration
Once the X-l 1 program
has generated seasonal factors for each component of
the money stock series, the Board of Governors’ staff
reviews the X-11’s output, and any factor which in
its judgment
does not represent true seasonal influences is modified.”
These final modified season;>1
factors are divided into the original series to obtain
the final seasonally
adjusted series.
These judgmental
modifications
can either increase
or decrease the smoothness
of the X-11 adjusted
series, and, depending
on the circumstances,
either
type of modification
may be justified.
One justification for judgmental
modifications
that smooth the
series stems from the X-11’s use of 5- and 7-term
moving averages to separate the seasonal from the
irregular
component
[see Box, steps 3, 7, 11, and
131. The use of these moving averages assumes a
smooth, continuous
change in seasonal patterns.
If
something
occurs that would abruptly
change the
seasonal pattern of the series (such
as the shift in
the tax filing date from March 15 to i\pril
15 in
195.5), the X-l 1 would only reflect this change gradually. In such a case there seems to be good reason
to modify the X-11 generated seasonal factor to reflect this change.
This type of modification
tends to
smooth the series, since the change in the unadjusted
series caused by the shift in seasonal patterns
is
reflected in the seasonal factor. On the other hand, a
&For

a more

8 Ot course,
factors
over

detailed

description

these
modifications
any l&month
period

NOVEMBER/DECEMBER

1977

see

[ZOI.

especially

are constrained
must still sum

pp.

in that
to 12.000.

8-11.
seasonal

Chart 1

Ml

TOTAL AND COMPONENTS
1970-76

$ Billions
320

NOT SEASONALLY ADJUSTED (N.S.A.)
300
300

-

280

-

260

-

240

-

-----

SEASONALLY ADJUSTED (S.A.)

I

220

200

DEMAND DEPOSITS

180

60
CURRENCY

possible justificnfion
for jiidgmentnl
modifications
that decrease the smoothness
of the seasonally adjusted series is that the 5- and 7-term moving averages of the S-I ratios conqxttetl I)y X-1 1 may not be
long enough to ayerage out sufficiently the influence
of relatively large nonseasonal movements
(i.e.. those
nonseasonal nlovements that are large but not thrown
out as estreme).
If it npl)ears that a large nouseasonal movement in the money stock series for ;I given
month (such as the June 19i.5 jump in MI caused 11)
the tax r&ate) has untlul~~ influenced the S-1 1 generated seasonal factor for that month, then it seems
jnstifinl)le to alter that seasonal factor. This type of
modification
makes the series less smooth, as the
nonseasonal
movement
in the series is no Iongel
compensated for by the seasonal factor.

Ml seasonally adjusted by S-11 alone, from 1970 to
1976.’ Also plotted is the difference between the two
gro\vth rates.
The chart shows that while the two
growth rates generally
move together,
judgmental
changes have often significantly affected the published
A4I growth rates. The correlation coefficient of these
t\vo growth rates is only S67, which suggests that
judgmental
decisions play a significant role in determining the final published rates of growth.
To determine
the net effect of these judgmental
modifications
on the smoothness
of the M, series,
the standard deviation of each of the two growth rate
series was calculated.
For the period 1970 to 1976,
the two standard
deviations
are almost identical,
suggesting
that over the whole period judgmental
changes did not alter the smoothness
of the series
(though as Chart 2 indicates, judgmental
changes

Impact
of Judgmental
Modifications
Chart 2
plots the monthly annualized
rates of growth of MI
seasonally adjusted by the I3oard of Governors
and
FEDERAL

RESERVE

i The X-11’s
default
options
demand
deposit
series
using

BANK

OF RICHMOND

were
data

used
from

to adjust
1965 to

the currency
1976.

and

21

-

SEASONALLY ADJUSTED BY X-11 ALONE

---4

SEASONALLY ADJUSTED BY BOARD OF GOVERNORS

1970

I

I

I

I

-1OI

1971

1972

I

I

I
1973

1974

1975

*CONTINUOUSLY COMPOUNDED ANNUAL RATES.
L

Sburce:

Federal

Reserve Bulletin.

have at certain times smoothed the series and at other
times made the series less smooth) .R
Iio~\.If just the 197576 suhperiod is considered,
ever, the standard
deviation
of the pul~lishetl 14 1
growth rates (5.5) is sul~stantially greater than that
of the X-l 1 generated growth rates (3.5)) meaning
that judgmental
changes decreased the smoothness
of the M, series in that suhperiod.
Chart 2 also shows
that judgmental
modifications
have been larger in
these two years.
One ‘possible reason for modifying
the X-11’s seasonal factors for 1975 and 1976 in this
fashion involves the X-11’s use of data before antl.
when available, after a given year in determining
seasonal factors.
Since 1975 and 1976 are the two
end years for the series used in this article, sufficient
year-ahead data are not available to compute 5 and
/‘-term moving averages of S-I ratios centered
in
these years. As noted in the description of the X-l 1
[see Box], relatively higher weights are assigned to
end year data to compensate for this lack of future
This procedure
increases the chance of the
data.
8 The standard
deviation
of the MI growth
rate for the period
1970
to 1976 seasonally
adjusted
by the Board
of Governors
is 4.27, while
seasonally
adjusted
by X-11 it is 4.31.
The standard
deviation
is a
valid measure
of the relative
smoothness
of the two series
because
by definition
their trends
are the same.

22

ECONOMIC

S-l 1 incorporating
nonseasonal
movements into the
seasonal factors for the end years.
Apparently
the
staff at the I!oartl of Governors thought that the large
nonseasonal
movements in the M1 series in 1975 and
1976 (especially
in January
1975 and April 1976)
\vere at least partly incorporated
into the X-l 1 seasonal factors, and they modified the seasonal factors
to take account of this possil)ility.
Unfortinlately,
these judgmental
decisions do not
alw:~ys ljerfcctly compens:~te for deficiencies
in the
X-l 1, It is extrenlely difficult to (letermine preciz;ely
the effect :I gixven occurrence
will have on seasonal
factors, or what portion of the X-l 1 seasonal factors
rq)resents the “true” seasonal pattern and what l)ortion reflects nonseasonal
influences.
Shortcomings
of the Present
Method
There are
a nunll)er of shortcomings
of the present seasonal
xljustment
method. These shortcomings are inherent
in almost all seasonal adjustment
techniques.
Therefore, in discussing the prol,lems associated with the
currently
used seasonal
adjustment
process,
this
article does not mean to imply that the present process is a “bad” one, or that there exist other methods
that are unambiguously
better.

REVIEW, NOVEMBER/DECEMBER

1977

Box
BASIC STEPS OF THE X-l 1 SEASONAL

ADJUSTMENT

PROGRAM

-tllis
time \vith extreme
values
replaced
as tlescribed
in step 6-to
obtain
modified
first-round
seasonal
factors.
Again,
these seasonal
factors
are
;ctljustctl to sum to 12.000 over any IL-montll
period.
8. Tl~ese nlodificd
first-round
seasonal
are divided
into the original
scrics
to get
liminary
seasonally
adjusted
series.

3. .\ \vciglltctl
.i-!crnl
111ovilq avcrs,qe
of tllese
for
S-l rati<,h (\vitll \veights
1.7.3.7.1 ) is computed
cacl~ of tile 11 calc~ltlar
liloirtl\5 ~cl)aratel?;
to aver;16c out tllc illilucllcc
of irrc~ular
lllovements
and to
ol)taill iir.<t-round
cstinlatcs
of the ieaional
factors.
‘l‘lie ,151: of a nloving
average
yield5 a tli5tillct
bca‘l‘hus,
soll:ll factor
for cacll lilnnth
of cacl1 year.
the iir>t-round
SK,WII~I
iwor
fur. SLY. January
1973 is tlerivetl
frown 111~ five January
S-I Iratio\ for
tile years
1971 to 1075. inclu5ivc.

9. A special
weighted
moving
average
(the socalled
Hentlcrson
average)
is applied
to this prcliminar)
seasonally
adjusted
series
to ol,taiu
;I
revised
cstimatc
of the trelltl-cycle
componcnt.~’
The span of this moving
average
depends
on the
variability
of the irregular
component
relative
to
that of tile trcntl-cycle
component.
with the more
A preirregular
the series,
the longer
the span.
liminary
estimate
of the variability
of the irregular
relative
to the trend-cycle
is obtained
using a 13month
Henderson
average
[ZO, p. 341.

I-niortunatcly.
sufficient
year-alleatl
tlat;c arc not
at the end of a titllc series
available
for tllc 2-years
ITor ex:1n1ple. a
to calcu!nte
tllis J-term
avcragc.
.i-tern1 average
cclltcretl
in 1976 rcrluire>
S-l ratios
for 197-1 through
lY78. inclusive,
wllilc
ior this
article
1976 is tllc last year for \vhich data arc available.
To conlpcllsate
for tllc lack of future
data,
the S-l I wcigllts
the availal)lc
S-I ratios
(which
for 1076 factors
are the S-l ratios
for 1974. lY75,
and 1976) more
hea:~ily than
if future
data xverc
For csample.
in calculating
the firstavailable.
round
seasonal
factor
for January
1976 (\vith data
through
1976). ti~c January
1976 S-I ratio is given a
\veight
of .107. wllilc in computing
the first-round
scaso~lal
factor
for January
1973. the January
1973
S-l ratio is given a weight
of only .333 [?O, p, 611.

10. This revised
trend-cycle
into the original
series to obtain

seasonal
to get an

factors
estimate

12. These
revised
seasonal
factors
are divided
into the S-I ratios
to get new estimates
of the
irregular
component,
and the S-I ratios
are modified for extremes
by the same method
as described
in step 6.

(a) greater
than 2.5,
it is considered
an extreme
value.
and the corresponding
S-I ratio is
removed
and replaced
hy an average
of the two
nearest
preceding
and t\vo nearest
follo\ving
full
\veight
(i.e..
unmodified)
S-I
ratios
for
that
month:
then the corresponding
is given full weight;

13. A weighted
7-term
moving
average
of these
modified
S-I ratios is computed
separately
for each
month
to obtain
the X-11’s final seasonal
factors.
(Of course,
these
factors
are adjusted
to sum to
12.000 over any 12.month
period.)

S-I

14. These
final seasonal
the original
series to obtain
ally adjusted
series.

2.50 and I..;, a linearly
graduated
Cc) bet\vccn
\velght
I)et\vccn
0.0 and 1.0 is assigned
to the
irregular,
and the corresponding
S-I ratio is replaced
with
an average
of the ratio
times
its
assigned
weight
and the two nearest
preceding
and t\vo nearest
following
full lveight
S-I ratios
for that month.

ing

:\ xveighted
j-term
is again calculated

S n+1=

FEDERAL

RESERVE

S,

=

the

‘* A Henderson
squares
of the
discussion
of
age see [12],

moving
average
of the S-l
separately
for each month

BANK

factors
are divided
into
the X-11’s final season-

15. Preliminary
seasonal
year are estimated
from

where

This graduated
treatment
of extremes
is designed
to limit the influence
of unusually
large irregular
movements
on seasonal
factors.
7.
ratios

is divided
S-I ratios.

Sufficient
year-ahead
data are not available
for
the 3 year> at the end of the series to compute
this
7-term
average.
For example,
a 7-term
average
centered
in 1976 needs
data
from
1973 to 1979.
inclusive.
and (as of the end of 1976) data from
lY77 to 1979 are not availaljle.
To compensate
for
this lack of future
data, the X-11 weights
the available S-I ratios
(for 1976 factors,
the ratios for 1973
through
1976) more
heavily
than
if future
data
For example,
in computing
the
xvcrc available.
revised
January
1976 seasonal
factor,
the January
S-I ratio for 1976 is given a weight
of 283, while in
computing
the revised
January
1973 seasonal
factor
the January
1973 S-I ratio is given a weight
of only
,200 [20, p. 611.

6. .-\ nlo\ring
i-year
(60-month)
standard
deviation [a) of these irregular
component
estimates
is
calculated.
and the irregulars
in the central
year of
the j-year
period are tested against
3.5,
Irregulars
greater
than
2.50 are removed,
and the moving
j-year
standard
tlcviation
is again computed
If the
irrcgtilar
for 3 nlonth
in the central
year is:

(I,) less tllan 1.5,
ratio for that month

estimate
revised

11. A weighted
7-term
moving
average
(with
lvcights
1,2,3,3,3,2,1)
of these
S-I ratios
is computed separately
for each month
to oljtain
revised
seasonal
factor estimates.
Thus, the seasonal
factor
for. say, January
1973 is derived
from
the seven
January
S-I ratios
for the years
1970 to 1976. inclusive.

-1. These
factors
arc atljustctl
to hum to 12.000
in ratio form. or 1,200 in index numl)er
form. over
any ll-month
period
so that year-to-year
cllanges
in the series are unaffected
[20. p, 911.
5. The<e
adjusted
first-round
are tlividctl
into the S-I ratios
of the irregular
component.

factor;
a pre-

OF RICHMOND

s,

+

seasonal

factors
for the
the formula

%(S,
factor

-

upcom-

s,-11,
for

year

n.

average
minimizes
the sum
third differences
of a series.
the merits
of the Henderson
especially
Chapter
III.

of the
For a
aver-

23

Moe&zg Scaso~2nl Option
One prol~leni alrend)
alluded to involves the X-1 l’s use of 5 and 7-term
moving averages to separate the seasonal component
Some critics have
from the irregular conil~onent.
argued that the seasonal pattern of the nioney stock
has been quite stable over time, and therefore that
the )(-l l’s use of these relatively short moving averages only serves to smooth the money stock series
excessively.
Poole and Lieberman
[ 17, 1). 327j
argue that the use of the S-l l’s moving senson:J
option to adjust the money stock is justifiable only if
the money stock’s seasonal factors e.\;hibit a recognizable trend. Chart 3 plots M, seasonal factors (unndjusted Ml/adjusted
M,) separately for each month
over the period 1947 to 1976. The chart indicates
that the factors for some months do display a clear
trend. However, it also shows that for periods where
no recognizable trend is present, seasonal factors for
some months still vary significantly
from year to
year. Thus, the evidence suggests both that a niovii~g
seasonal model is warranted,
and that the present
method overly smooths the series. This behavior of
the X-11 seasonal factors reflects the trade-off that
exists between adequately allowing for moving sensonality and preventing nonseasonal movements from
being incorporated
into seasonal factors. The length
of the moving average used reflects the adjuster’s
judgment on this trade-off.
Other evidence
that suggests
that the current
method of seasonal adjustment
is unduly smoothing
the money stock series is given by Kaufman
and
Lombra
[S] . Using spectral analysis, a statistical
technique that decomposes a series into periodic (e.g.,
seasonal)
movements,
they find that the seasonal
adjustment
process flattens out the series at nonseasonal
frequencies,
“which
indicates
excessive
smoothing of the series”
[S, p. 1516J.
SJaifts ipa Seasonal

Yew-Em1 Revisions
Another
shortcoming
involves the year-end
revisions
of the money stock
necessitated by the use of the X-l 1. The X-l 1 uses
data several years before and, when available, after a
given month to determine that nionth’s seasonal fator.
Unfortunately,
sufficient future data are not
available for end years in the series to calculate the
5 and 7-term moving averages of the S-I ratios used
to compute seasonal factors [see Box, steps 3 and
11 J. At the end of each year, the newly availab’ie
data for that year are entered into the X-l 1, and
revised seasonal factors are obtained for these end
years.
These revised factors frequently
differ sig‘/See
the accompanying
article
discussion
of some of the factors
bulge
in MI in 1976 and 1977.

PRELIMINARY

ECONOMIC

by Cook
believed

and
Broaddus
to have caused

VERSUS REVISED Ml GROWTH

[l]
the

for
a
April

RATIES

1975

(2)

(1)
Preliminary M 1
Growth Rates

Pattcms

Another
problem
occurs when the seasonal pattern of a time series
The X-11 is not designed
to
changes abruptly.
handle sharp, discontinuous
shifts in the seasonal
pattern, and judgmental
changes are seldom able to
correct the X-11 deficiencies perfectly.
Failure to
take such shifts into account can cause computed
seasonally
adjusted
series to exhibit
unexplained
variability.
The recent behavior of the IvI, series may
be an example of a seasonal pattern shift. In April
of both 1976 and 1977, the monthly seasonally adjusted M1 growth rate jumped unexpectedly,
with
the annualized
growth rate being almost 15 percent
in April 1976 and 20 percent in April 1977. Suppose
the seasonal pattern in the demand for M, shifted
abruptly in 1976 in such a way that money demand
24

rose in April relative to the other months. The X-l 1,
with its /^-term moving average of S-I ratios, would
not fully capture this shift until 1979, since the X-1 1
c:Jculatetl
seasonal factors for April in 19TG and
1977 are derived from data hefore this hypothetical
seasonal pattern shift occurs in 1976.
Therefore
these factors will understate
the true seasonal conil)onent for April in 1976 and 1977, causing the reported seasonally adjusted growth rate to overstate
the true seasonally adjusted growth rate.
Whether
these unusually
high April movements
in M1 are
actually the result of a shift in the seasonal pattern
of the demand for money, however, remains to be
seen.L)

January

-11.8

February

-5.1

3.4

March

Revised Ml
Growth Rates*

(2) - (1)
Difference
~6.7

0

-3.4
- 1.7

11.0

9.3

April

3.4

3.4

0

MOY

11.3

11.3

0
-4.6

June

i a.7

14.1

July

2.0

3.7

1.7

August

2.9

5.3

2.4

1.6

- .4

September

2.0

Ociober

-2.4

November

12.2

December

--.8

- 2.8

*Revisions
Source:

made
Federal

REVIEW, NOVEMBER/DECEMBER

9.0
-3.3

in Jonuary
Reserve

1977

1976.

Bulletin.

1.6
-3.2
- .5

nificantly
from the preliminary
factors, and often
affect the previously published MI growth rates. The
accompanying
table lists the 1975 seasonally adjusted
annualized monthly rates of growth of MI published
both before and after the January 1976 year-end revisions.
Absolute differences in the before and after
monthly growth rates vary from 0 to almost 6%
percentage points, with an average absolute deviation
of about 2.2 percentage points.
Most of this clifference can be attributed
to revisions in the seasonal
factors (as opposed to revisions in the underlying
data).
Kaufman and Lombra believe that “the sizable difference between ‘final’ data (employed by the
model-builders)
and the ‘preliminary’
data (viewed
by the policymakers)
introduces
a significant
distortion into estimates of policy impacts”
[S, p. 1525]
Scasoml
Relationships
A~uo~lg Series
Another
problem with seasonal adjustment
involves the way
in which the money stack and other economic variables are seasonally adjusted on a variable-to-variable
llasis, without regard to the relationship
between
seasonal changes in one series and seasonal changes
in other series. Marc Nerlove notes that :
Seasonal
variations
have causes and insofar
as
these causes are measurable
they should be used to
explain
changes
that are normally
regarded
as
seasonal.
Indeed,
seasonality
does not occur in
isolated
economic
series, but seasonal
and other
changes
in one series are related to those in another
[15, p. 2631.

This is especially important because the money stock
is a policy-controlled
variable-i.e.,
the actions of the
monetary
authorities
influence the seasonal pattern
of the money stock. Therefore, if the policy objective
of allowing the money stock to exhibit seasonality is
to affect the seasonal pattern of some other economic
variable, then knowledge of the structural
relationship between seasonal movements
in the two series
would be desirable.
“Unfortunately,
the nature of
ratio-to-moving
average
techniques
and post-war
monetary
tion”

policy
[S,

p.

For example,
its inception

.

I

combine

to obfuscate

such

informa-

1523].

the implicit

has been

policy of the Fed since

to reduce

or eliminate

interest

rate seasonality
(arising from a natural seasonal in
the demand for money) by allowing the money supply
to vary seasonally.
However,
the method used to
seasonally adjust the money stock does not take into
account the structural
relationships
among seasonal
movements
in the money stock, interest rates, and
factors affecting the seasonal in money demand.
Indeed, one of the reasons that the present adjustment
is inadequate
in handlin g abrupt seasonal pattern
shifts

is that it fails

to take into account

the relation-

FEDERAL RESERVE BANK OF RICHMOND

25

ship between abrupt changes in those factors affecting the money seasonal and the money seasonal itself.
Sensomlily
irr Polir~~ .ilctio,zs
One final shortcoming discussed here is that since the money stock
is a policy-controlled
variable, any seasonality in the
Fed’s policy actions may affect the seasonal factors
calculated by the X-l 1. For example, if the Fed
increases its money growth targets at the same time
of the year in successive years, then the X-l 1, with
its moving seasonal option, may incorporate
these
policy movements into its seasonal factors in subsequent revisions.
Thus seasonality in policy actions,
whether accidental or otherwise, may cause changes
in computed
money seasonal factors that are not
due to any change in the underlying
seasonal pattern
of the demand for money and credit.
Poole and
Lieberman
[17, p. 2361 believe that the seasonal
behavior of policy actions has been affecting money
seasonal factors.

Seasonality
and Monetary
Policy
As mentioned
in the beginning
of the article, the purpose of seasonal adjustment
is to enable the user of a time series
to differentiate
between
seasonal and nonseasonal
movements.
However, the above discussion suggests
that the present method used to adjust the money
stock sometimes has trouble separating seasonal from
nonseasonal
movements.
For the Fed to be able to
determine what portion of the current movement in
the money stock is due to seasonal forces, the seasonal factors used to adjust the money data should
reflect the true seasonal pattern in the demand for
money and credit. In other words, nonseasonal movements should not influence the seasonal factors, while
shifts in the seasonal pattern of money and credit
demand should be fully reflected.
However,
the
factors used to adjust current money stock data are
probably the least likely to satisfy these criteria, since
they are based solely on past money stock movements.
These seasonal adjustment
problems can affect Federal Reserve policy. To understand
how, it is necessary to have some idea of the Fed’s short-run strategy
of monetary policy.lO
Each month the Federal Open Market Committee
sets a tolerance range for the two-month growth rate
of the seasonally adjusted money stock and a tolerThe seaance range for the Federal funds rate.ll
sonaliy adjusted
money growth rate is allowed to
fluctuate within this tolerance range in order to limit

10 The following
simplified.
For
11 The
Federal
lend each other

26

description
of the
a fuller
discussion
funds
rate
reserves.

is

the

Fed’s
short-run
strategy
see 131 and [Ill.
rate

at

which

commercial

ECONOMIC

is

Holvever, if the two-month
interest rate variability.
money growth rate appears to be moxing outside of
the tolerance range, the Fed may react by changing
its funds rate target so that longer-run
control of the
money stock can be achieved.
The Fed’s money growth tolerance
ranges are
stated in seasonally adjusted terms, and the factors
used to adjust the money stock are calculated by the
method described above. Unfortunately,
these computed factors may not reflect the true seasonal forces
affecting the demand for money and credit in the
current year.
If they do not, then the seasona!lJ,
adjusted money growth rate may exhibit fluctuations
that are due solely to faulty seasonal adjustment.‘:!
These adjustment
problems increase the difficulty of
setting short-run money growth targets that are compatiljle !,oth with some longer-run
money target ant!
Adjustment
problems
with interest rate stability.
also complicate
the Fed’s taslc of deciding how to
react to a given short-run change in money growth.
For example, suppose that the seasonally ndjustec!
M, growth rate in a given month is either very high
or very low, causing the two-month
money growtll
If the
rate to move outsitle of its tolerance range.
change in money growth is due to faulty seasonal adjustment,
then any corrective action by the Fed will
have to be reversed later in the year, producing WInecessary
fluctuations
in short-term
interest rate:;.
However, if the Fed does not react to this change in
money growth by changing its funds rate target, and
the change in money growth is really caused not by
seasonal adjustment
problems, but by, say, a cyclic:-d
shift in the demand for money, then deviations from
target money growth rates may cumulate, and sonle
longer-run
target may be missed.
Thus season,4
adjustment
problems must be added to that long list
of factors complicating
monetary control.
Conclusion
This article has shown that adjusting
the money stock for seasonality is no trivial matter.
Despite its high degree of sophistication,
the X- 11
program employed to seasonally
adjust the money
stock is far from flawless. The Board of Governors’
staff recognizes
that the X-11 is not perfect and
Even the
attempts to correct for its deficiencies.
Board staff, however, cannot always distinguish
between seasonal and nonseasonal
movements
in the
money stock, especially in current money stock movements.
If the estimated
seasonal factors for the
current
year imperfectly
reflect the influence
of
actual seasonal forces, then the seasonally adjusted

over-

banks

REVIEW,

12 For specific
examples
of
affected
reported
seasonally
and Broaddus
[l].

NOVEMBER/DECEMBER

1977

how seasonal
adjustment
adjusted
money growth

problems
have
rates, see Cook

money data will exhibit
some spurious
volatility
caused by the imperfections.
Considering
the Fed’s
dual policy goals of (a) long-run stability in money
growth, and (b) short-run stability in money market

interest rates, these seasonal adjustment
problems
can complicate the task of determining
the proper
policy response to any given short-run
movement
in the seasonally adjusted money stock.

References

Marris,
Stephen
N.
“A
Technical
Survey
of
Problems
and Methods of Seasonal Adjustment
in
Europe and North America, with Special Reference
to United States Bureau of the Census Method II.”
Seasonal
Adjustment
on Electronic
Computers.
Washington,
D. C.: Organization
for Economic
Development,
1960, pp. 35-78.
-.
in Census
Electronic

15.

Cullison,
William
E.
“A
Seasonally
Adjusted
World-The
Census
Seasonal
Adjustment
Technique.” Monthly
Review,
Federal Reserve Bank of
Richmond,
(August
1970), pp. 2-8.

MacCauley,
Frederick
R. The Smoothing
of Time
Series.
New York:
National
Bureau of Economic
Research,
1931.

13.

Broaddus,
Alfred
and Cook, Timothy
Q.
“Some
Factors
Affecting
Short-Run
Growth Rates of the
Money Supply.”
Economic Review, Federal Reserve
Bank of Richmond,
(November/December
1977).

2.

12.

14.

1.

Analysis of Seasonal AdNerlove, Marc. “Spectral
Econometrica,
(July 1964))
justment
Procedures.”
pp. 241-286.

“Monetary
Objectives
and
Davis,
Richard
G.
Monetary
Policy.”
Quarterly
Review,
Federal Reserve Bank of New York, (Spring
1977), pp. 29-36.
Diller, Stanley.
The Seasonal Variation
of Interest
Rates.
NBER Occasional
Paper 108. New York:
National Bureau of Economic
Research,
1969.
Friedman,
Mi!ton.
A Program
for Monetary
bility. New York: Fordham University
Press,

Sta1960.

and Schwartz,
Anna J.
A Monetary
History
of the United States:
1867-1960.
A National Bureau of Economic Research Study. Princeton : Princeton
University
Press, 1963.
7.

16. Organization
velopment.
Computers.

Seasonal
Adjustment
of MIFry,
Edward.
Czcr)zxtly
Published
and Alternative
Methods.
Staff
Economic
Studies 87.
Washington,
D. C.:
Board of Governors of the Federal Reserve System,
1976.
Herbert
M. and Lombra,
Raymond
E.
“Short-Run
Variations
in the Money Stock.” Southcy?z Economic
Journal,
(February
1977), pp. 15151527.

11.

19.

“Causes
of Seasonal
Variations
in InRates.”
Monthly
Review,
Federal
Reserve
of Kansas City, (February
1974)) pp. 3-12.

Lombra,
Strategy
Federal
October

and DeElectronic

Committee on Monetary Statistics.
Report
18. Advisory
of the Committee.
Improving
the Monetary
Aggregates.
Washington,
D. C.: Board of Governors
of
the Federal
Reserve
System, 1976.

Variations
in Interest
Kohn, Donald L. “Seasonal
Rates.” Monthly
Review, Federal Reserve Bank of
Kansas City, (November
19’73), pp. 3-10.

10. ----.
terest
Bank

for Economic
Cooperation
Seasonal
Adjustment
on
Washington,
D. C.: 1960.

and Lieberman,
Charles.
“Improv17. Poole, William
ing Monetary
Control.”
Brookings
Papers
on
Economic
Activity,
(2nd quarter,
1972), pp. 292342.

8. Kaufman,

9.

“The Treatment
of Moving Seasonality
Method II.”
Seasonal
Adjustment
on
Computers,
pp. 259-309.

Shiskin, Julius and Eisenpress,
Harry.
Adjustment
by
Electronic
Computer
NBER
Technical
Paper 12. New York:
Bureau of Economic
Research,
1958.

Seasonal
Methods.
National

of Commerce.
Bureau of the
20. U. S. Department
Census.
The X-11 Variant
of the Census Method
II Seasonal
Adjustment
Program,
by J. Shiskin,
A. H. Young, and J. C. Musgrave.
Technical Paper
No. 15. Washington,
D. C.: 1967.

Raymond E. and Torto, Raymond G. “The
of Monetary
Policy.”
Economic
Review,
Reserve
Bank of Richmond,
(September/
1975), pp. 3-14.

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