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Federal Reserve Bank of Cleveland
series methods (e.g., X-11 ARIMA). Unlike
structural models, time-series models are
based solely on statistical principles and
thus are particularly useful in forecasting
when theoretical knowledge is scarce. Information contained in time-series projections of the money-supply components
can improve seasonal forecasts in the
sense that subsequent revisions of the factor are reduced. When the X-11 is applied
to an extended time series of a given component, which consists of the available
observations
and the projected values of
the unadjusted series, the resulting seasonal forecasts are closer to their final
values, which are determined
only after
the future data are known.i'
Another problem with the X-11 is that it
does not adequately filter calendar effects,
as they do not occur in the same month
each year. Although the X-11 has an
option to estimate the effects of the number
of trading days in a month using a regression model, it has not been useful in
eliminating such calendar effects in money.
Recent studies have indicated that spectral analysis methods may prove useful for
detecting calendar effects; the magnitudes
of calendar effects then can be estimated
using regression methods."
Alternative models also may provide a
framework for constructing
an adequate
filter. A simple statistical test suggests
variations in the irregular componentthe series after X-11 estimates of both
trend-cycle and seasonal components have
been factored out-are
explained by the
day of the week on which the month
3. Judging the quality of a preliminary seasonalfactor estimate by how close it is to its final value
(once all data are available) has been challenged as
being only as accurate as the final estimate allows. In
the absence of a universally accepted set of criteria,
however, it is perhaps the most popular standard.
4. See William S. Cleveland and Susan J. Devlin,
"Calendar Effects in Monthly Time Series: Detection
by Spectrum
Analysis and Graphical
Methods,"
Journal of the American Statistical Association, vol.
75, no. 371 (September
1980), pp. 487-96. See also
William P. Cleveland and Michael R. Grupe, "Modeling Time Series When Calendar Effects Are Present," Special Studies Paper 162 (Board of Governors
of the Federal Reserve System, 1981; processed).
begins.5 A further implication is that estimated coefficients of this model provide
measures of the magnitudes of calendar
effects. Unlike more ambitious efforts to
model the determinants
of seasonality,
research on modifying the X-11 to detect
and measure calendar effects is likely to
produce more immediate improvements in
seasonal adjustment of the money supply.
Improving Seasonal
Adjustment Methods
In early 1978 the Federal Reserve Board
initiated a comprehensive
study to determine appropriate methods for seasonally adjusting financial data, particularly
the money-supply measures. Published in
1981, the study's recommendations
essentially outlined a continuing research
program-one
that subsequently was implcmented." Because possibilities exist for
improvements
in the widely used and accepted X-II program, the Federal Reserve
Board's continuing research effort initially
will focus on developing model-based improvements, including time-series modeling
options and calendar adjustments.
The
Federal Reserve also will experiment with
more general model-based methods that
can incorporate
causal explanations
of
seasonal patterns and measure systematic
effects. The Federal Reserve's research
program thus can be expected to yield
more immediate results from X-II enhance-
ment research while laying the foundation
for fundamental changes-ideally,
a breakthrough leading away from the basic autoadjustment framework.
The study also recommended
that the
Federal Reserve Board consider using
the present seasonal-adjustment
procedure or its recommended
modification on
a concurrent basis to utilize all available
data for estimating seasonal factors. Using
the most current data would produce
smoother initial estimates and reduce the
size of revisions compared with the practice of projecting seasonal factors for the
year ahead. However, concurrent
estimation would entail a number of costly
revisions each month as new data are
used by the procedure.
A reasonable
compromise
might be to estimate the
seasonals semiannually, thus allowing incorporation
of the most current information for mid-year review of the money
targets.
Semiannual
calculations
also
would provide better estimates
of the
April seasonal soon after the raw data for
April become available.
Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland,OH
44101
Conclusion
Ideally, seasonal adjustment should filter all calendar-related
movements,
so
that movements remaining in the seasonally adjusted data cannot be attributed to
difficulties in estimating seasonal factors.
The fact that the April surge in seasonally
adjusted M-l was attributed to seasonal
causes reveals shortcomings in the method
used. As recommended
in the Fed's study
of seasonal adjustment,
an ongoing research program has been organized to
develop better methods of adjustment.
While modifications of the current methods
are likely to lead to improved estimates of
the seasonal factors, fundamental improvements, such as the development of causal
adjustment methods, may not be available
for implementation for some time to come.
John B. Carlson is an economist with the Federal
Reserve Bank of Cleveland.
The views stated herein are those of the author
and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors of
the Federal Reserve System.
BULK RATE
U.S. Postage Paid
C1eveland,OH
Permit No. 385
5. Specifically, the X-ll estimate of the irregular
component
of demand deposits was regressed
on
variables accounting for the day of the week on which
the month begins. The estimation period was January 1976 through December 1979. The F-statistic of
the regression
was 5.19, which indicates that one
cannot reject the hypothesis that movements in the
irregular component
are explained by the monthly
starting day. Indirectly, this evidence supports the
hypothesis that the calendar effects are consequences
of early Social Security payments and extra pay periods, since it is necessary (although not sufficient) that
a month begins on a Thursday or Friday or (in some
months) Wednesday for these events to occur.
6. See Board of Governors of the Federal Reserve
System, Seasonal Adjustment of the Monetary Ag·
gregates, Report of the Committee of Experts on
Seasonal Adjustment
Techniques
(Board of Governors, October 1981).
May 31, 1982
Address Correction Requested: Please send corrected mailing label to the Federal
Reserve Bank of Cleveland, Research Department, P.O. Box 6387, Cleveland, OH 44101.
The Problem of
Seasonally Adjusting Money
by John B. Carlson
When an impending surge in the money
supply filled the financial news in March of
this year, the reports stated that the surge
would result from above-average incometax refunds and early Social Security payments. Consistent with expectations, M-l
(which includes currency plus checkable
deposits) grew 11.8 percent (saar) in April
1982. But personal tax refunds occur
every year. And early Social Security
payments occur whenever the third day of
a month falls on a Saturday, Sunday, or
holiday. The fact that these and other
effects relate to seasonal or recurring
events and can be predicted suggests a
serious question. Why doesn't seasonal
adjustment of the money supply filter all
such movements?
This Economic Commentary examines
the problem of seasonal adjustment, using
April 1982 as an example; this particular
month reflected a number of influences
that can distort
seasonally
adjusted
monthly measures
of money. Although
there is scope for improving the accuracy
of estimated seasonal factors, fundamental improvements
of the current method
of seasonal adjustment will require extensive research. Such a research program
recently was implemented at the Board of
Governors of the Federal Reserve System. 1
l. For a more thorough
discussion
of seasonal
adjustment
and the board's research program, see
David A. Pierce and William P. Cleveland, "Seasonal
Adjustment Methods for the Monetary Aggregates,:'
Federal Reserve Bulletin, vol. 63, no. 12 (December
1981), pp. 875-87.
Why Seasonally
Adjust M-l?
The primary reason for seasonal adjustment is to eliminate repetitive movements
from data that obscure movements
of
greater significance to the user. For policymakers and market analysts, the main
current interest in the money supply is its
target property,
i.e., information about
whether the Federal Reserve is supplying
bank reserves too liberally or too sparingly. In practice, the policy of the Federal
Reserve has been to accommodate changes
in money demand that "meet the needs of
the trade" (i.e., seasonal movements) to
the extent that such demands are consistent with achieving longer-term objectives,
particularly the annual growth-rate targets
for M-l and the broader measures
of
money stock. Thus, the Federal Reserve
sets its monetary growth-rate targets in
terms of seasonally adjusted data, accommodating seasonal fluctuations that are
temporary and offsetting. Errors in measurement of seasonality thereby can lead
to difficulties in conducting monetary policy.
Seasonal Movements
in the April Money Measures
In its most limited sense, seasonality
refers to movements in data that occur
precisely at the same time each year with
the same intensity. As it is typically used,
seasonality refers to all repetitive movements that occur on predetermined
dates,
but which need not occur on the same
date nor with the same intensity. In this
broad sense, economic series that display
seasonality exhibit fairly consistent patterns of fluctuation, recurring at predictable but not necessarily uniform intervals.
Historically, the April pattern has been
one of large recurring increases in the raw
data, particularly in the checkable deposit
component. Over the past five years, this
component has increased an average annual rate of 53.4 percent in April (see table
1). This pattern has been attributed largely
to the effects of income-tax flows (both
refunds and receipts) that are concentrated in April, although other factors
probably were also at work. Presumably,
many refunds are deposited in transactions accounts soon after they are received, tending to inflate money balances.
How quickly deposit holders adjust their
balances to "normal levels" is not clear.
Although it sometimes is assumed that
they adjust fairly quickly (i.e., within two
months or so), evidence supporting this is
indirect and ambiguous.
Money-supply increases associated with
federal income-tax receipts, on the other
hand, arise from float due to mailing and
tax processing, as payors' deposit balances remain high until checks clear. Typically, by early May the Treasury has collected over 90 percent of all individual
nonwithheld tax payments due April 15. In
April 1982, the Treasury processed over
$35 billion in such receipts. Decreases in
raw-money numbers in May tended to
offset much of the increase in April.
The M-l surge in April 1982 also may
have reflected specific details of the calendar. Such variations, known as calendar
effects, may result from payment practices affected by non-regularly recurring
holidays (e.g., Easter), the day of the week
on which the month begins, or the number
of Fridays in the month. These effects
generally do not occur at uniform intervals, nor do they always occur in the
month of April.
One calendar effect, which seems to be
growing in importance, is the consequence
of early Social Security payments. These
payments usually are made on the third
day of the month, unless the third falls on a
weekend; then payments are made on the
first business day prior (Friday, unless it is
a holiday). The third day of April 1982 fell
Table 1 Transactions Deposit Growth
in April
Seasonally adju~ed annual rates
Raw
Year
number,
percent
Seasonal
component,
percent
1978
1979
1980
1981
1982
56.4
40.4
42.8
42.9
40.6
43.7
Average
53.4
42.1
57.0
64.7
17.4
71.4
a
a. Seasonality is estimated, using the ratio of the
first published seasonals for April and March.
on Saturday, so that these payments
(amounting to over $13 billion) were made
one day early. Early payments are likely to
be deposited earlier (over one-third are
deposited directly), while expenditures by
Social Security recipients are not likely to
be altered by early payments. Unless the
recipients immediately transfer deposited
funds into nonmoney assets or use balances to purchase goods or services from
those who do, transactions balances would
be higher than they otherwise would have
been. Thus, early payments make the
weekly average money-supply measure
higher than it otherwise would have been.
If one assumes that neither receipts nor
expenditures in the second week are
affected by the early payments, the impact
should wash out completely in that week.
To the extent that balances are temporarily high for one day, average monthly
balances would be higher, but only about
one-fourth the average weekly effect.
Calendar effects in weekly data are fundamentally different from calendar effects
in monthly data. A monthly calendar effect
that could have contributed to the recent
M-l surge relates to the number of Fridays
in April. When a month has five Fridays, a
large percentage of people who are paid
biweekly receive three paychecks instead
of their usual two. Money balances tend to
swell in such a month and the month
immediately following. (Such an effect occurs twice a year in biweekly payment
cycles.) To the extent that households pay
monthly obligations out of the more typical
two-payday income flows, these households would have more discretionary funds
available in the extra-payday months. Since
it is unlikely that all of the extra funds are
immediately transferred into nonmoney
assets or used to purchase goods and services, transactions balances temporarily
rise. Although balances in a five-Friday
month are on average marginally higher, in
the first month following they could be as
much as $1 billion higher. This effect is
essentially zero by the second month.
The influence of an extra pay period on
the money numbers probably has intensified in recent years, as large firms (with
large payrolls) have adopted more sophisticated cash-management techniques. One
such technique-zero
balancing-allows
firms to invest all available cash on a daily
basis. As funds are transferred from firms
(holding money-market assets) to households (holding funds in checkable deposits), the narrow money measures tend
to increase.
Seasonally Adjusting
the Money Measures
When approaching the problem of seasonality, we should have some knowledge
of the underlying behavior generating the
data to choose the appropriate technique
for adjustment. The behavior of deposit
holders suggests reasons for relating
changes in seasonality of money-supply
components to readily measured variables, such as the volumes of tax receipts
and refunds. In principal, all basic determinants of seasonality could be included
as part of a more general model explaining
the behavior of each of the raw-money
components. Assuming their relationships
could be well estimated, seasonal effects
could be forecast and eliminated to obtain
the seasonally adjusted series. (Seasonal
forecasts for the upcoming year would
require that all contemporaneous determinants also be forecast.) Unfortunately,
such a model has not been established,
nor is it evident that a widely accepted
model could be estimated.
In the absence of an established structural model, the money supply-like virtu-
ally all economic time series-is adjusted
using an auto-adjustment method, i.e.,
seasonal variation is based solely on the
past history of the variable being adjusted.
The specific method, which follows from
the X-II program developed by the Bureau
of the Census, is applied to each of the
components of the money supply (see
box). Each monthly seasonal factor is
essentially a weighted average of the values
of the data for that month over a number
of years once the trend-cycle component
has been factored out. The number of
years averaged and the values of the
weights are options of the user and should
depend on prior knowledge. If the seasonal is known to be changing, for example, the period over which those data are
averaged should be short, and the weights
given to the most recent data should be
relatively larger. The most recent information is given the most weight.
The auto-adjustment approach assumes
that all information about the relevant
magnitudes of seasonality in money is
embodied in the past history of the series
itself. The fact that the financial markets
anticipated the M-l surge in April based on
expectations of tax flows challenges this
assumption. Although the X-ll method
clearly fails to anticipate all systematic
changes in seasonality that result from
changes in underlying determinants, the
X-ll contains an option that allows it to
detect and partly account for trend change
over time.2
There is some evidence indicating that
the X-ll can better anticipate changing
seasonality when augmented with time-
2. This option adds one-half the change from the
previous year to the seasonals of the last available
year. While such a formula may be rigid, it will, on
average, detect and partially account for trend
change, particularly if this change is large relative to
the irregular movements. Furthermore, X·ll results
are sometimes modified judgmentally to incorporate
expected fluctuations resulting from institutional
changes, such as a change in the tax-filing date.
Because it is difficult to perform this practice consistently over time, it is done only under extreme circumstances. Consistent anticipation of all systematic
changes in seasonality requires more complete
knowledge of the underlying determinants.
The x-u Method
The X-II is the method employed to
estimate monthly seasonal factors. 1 The
X-II involves two fundamental steps to
separate any monthly time series into
three distinct series-the trend-cycle,
seasonal, and irregular components.
The first step isolates the trend-cycle
component from the seasonal and irregular components by dividing the original
series by an estimate of the trend-cycle
component. The second step separates
the seasonal and irregular components.
The X-II procedure is iterative in two
senses: (1) it repeats the second step,
using a revised seasonal component in
which extreme irregular values are eliminated or replaced with dampened ones;
(2) it repeats both steps by re-estimating
the trend-cycle component, using alternative averaging methods on a preliminary seasonally adjusted series obtained
in subsequent rounds.
Although the technique is considered
mechanical, it permits the use of judgment to the extent that some parameters
of the X-II program can be varied. This
discretion is best exemplified by the
user's options for choosing both the
length of the period and the weighting
structure of the moving average. The
moving average options are available
when estimating both the trend-cycle
and seasonal components of the series.
Although the X-ll automatically selects
default values for these options, the user
has available alternatives that permit
variations in the degrees of smoothing. 2
When estimating the final trend cycle,
the degree of smoothing (length of moving average) desired would depend on
the relative importance (average percent
1. Estimating weekly seasonals is a complex process in which the weekly results are prorated to be
consistent with the X-ll results on monthly data.
2. Experience has shown that the seasonal cornponent of many economic time series can be adequately estimated by the same choices of Xv l I
options. Consequently, the X-ll program is preset
to these default options, which can be changed as
circumstances warrant.
change) of the irregular variations to the
trend-cycle movements. The greater the
irregular movements relative to the trend
cycle, the longer the moving average
needed to smooth out the short-term
movements and reveal the trend. Conversely, if cyclical movements dominate,
then a short moving average would better reveal the systematic movements of
the series.
Similarly, when estimating the seasonal
components, the degree of smoothing
desired would depend on the relative
importance of {he regular variation. If a
seasonal for a given month is believed to
be stationary, then all the movement in
the seasonal-irregular (S-I) component
for the month must result from irregular
variation. Thus, the user would choose
to average as many years of that month
as possible to average out the noise. For
this reason, the X-ll has an option that
averages seasonal-irregular values of the
same month for all prior years available,
giving equal weight to each year.
If the seasonal factor is believed to be
changing, then movements in the S-I
component reflect movements of both
individual components, and the default
option may be desirable. This option
takes a five-year moving average that
weights most heavily the S-I component
in the year being estimated. The two
years before and the two years after pre
weighted with lesser weights (declining
away from the year). When the seasonal
being estimated is for the most recently
available year, only the two prior years
are included. Although a short moving
average may fail to average out irregular
noise, it enhances the probability that a
seasonal factor would correctly incorporate movements reflecting fundamental
changes in the determinants of seasonality. It also enhances the probability of
removing irregular variations under the
guise of seasonal variations. The tradeoff is clear. Ifa priori evidence exists that
movements in the seasonal are large relative to irregular variation, then a short
averaging period is desired.
broad sense, economic series that display
seasonality exhibit fairly consistent patterns of fluctuation, recurring at predictable but not necessarily uniform intervals.
Historically, the April pattern has been
one of large recurring increases in the raw
data, particularly in the checkable deposit
component. Over the past five years, this
component has increased an average annual rate of 53.4 percent in April (see table
1). This pattern has been attributed largely
to the effects of income-tax flows (both
refunds and receipts) that are concentrated in April, although other factors
probably were also at work. Presumably,
many refunds are deposited in transactions accounts soon after they are received, tending to inflate money balances.
How quickly deposit holders adjust their
balances to "normal levels" is not clear.
Although it sometimes is assumed that
they adjust fairly quickly (i.e., within two
months or so), evidence supporting this is
indirect and ambiguous.
Money-supply increases associated with
federal income-tax receipts, on the other
hand, arise from float due to mailing and
tax processing, as payors' deposit balances remain high until checks clear. Typically, by early May the Treasury has collected over 90 percent of all individual
nonwithheld tax payments due April 15. In
April 1982, the Treasury processed over
$35 billion in such receipts. Decreases in
raw-money numbers in May tended to
offset much of the increase in April.
The M-l surge in April 1982 also may
have reflected specific details of the calendar. Such variations, known as calendar
effects, may result from payment practices affected by non-regularly recurring
holidays (e.g., Easter), the day of the week
on which the month begins, or the number
of Fridays in the month. These effects
generally do not occur at uniform intervals, nor do they always occur in the
month of April.
One calendar effect, which seems to be
growing in importance, is the consequence
of early Social Security payments. These
payments usually are made on the third
day of the month, unless the third falls on a
weekend; then payments are made on the
first business day prior (Friday, unless it is
a holiday). The third day of April 1982 fell
Table 1 Transactions Deposit Growth
in April
Seasonally adju~ed annual rates
Raw
Year
number,
percent
Seasonal
component,
percent
1978
1979
1980
1981
1982
56.4
40.4
42.8
42.9
40.6
43.7
Average
53.4
42.1
57.0
64.7
17.4
71.4
a
a. Seasonality is estimated, using the ratio of the
first published seasonals for April and March.
on Saturday, so that these payments
(amounting to over $13 billion) were made
one day early. Early payments are likely to
be deposited earlier (over one-third are
deposited directly), while expenditures by
Social Security recipients are not likely to
be altered by early payments. Unless the
recipients immediately transfer deposited
funds into nonmoney assets or use balances to purchase goods or services from
those who do, transactions balances would
be higher than they otherwise would have
been. Thus, early payments make the
weekly average money-supply measure
higher than it otherwise would have been.
If one assumes that neither receipts nor
expenditures in the second week are
affected by the early payments, the impact
should wash out completely in that week.
To the extent that balances are temporarily high for one day, average monthly
balances would be higher, but only about
one-fourth the average weekly effect.
Calendar effects in weekly data are fundamentally different from calendar effects
in monthly data. A monthly calendar effect
that could have contributed to the recent
M-l surge relates to the number of Fridays
in April. When a month has five Fridays, a
large percentage of people who are paid
biweekly receive three paychecks instead
of their usual two. Money balances tend to
swell in such a month and the month
immediately following. (Such an effect occurs twice a year in biweekly payment
cycles.) To the extent that households pay
monthly obligations out of the more typical
two-payday income flows, these households would have more discretionary funds
available in the extra-payday months. Since
it is unlikely that all of the extra funds are
immediately transferred into nonmoney
assets or used to purchase goods and services, transactions balances temporarily
rise. Although balances in a five-Friday
month are on average marginally higher, in
the first month following they could be as
much as $1 billion higher. This effect is
essentially zero by the second month.
The influence of an extra pay period on
the money numbers probably has intensified in recent years, as large firms (with
large payrolls) have adopted more sophisticated cash-management techniques. One
such technique-zero
balancing-allows
firms to invest all available cash on a daily
basis. As funds are transferred from firms
(holding money-market assets) to households (holding funds in checkable deposits), the narrow money measures tend
to increase.
Seasonally Adjusting
the Money Measures
When approaching the problem of seasonality, we should have some knowledge
of the underlying behavior generating the
data to choose the appropriate technique
for adjustment. The behavior of deposit
holders suggests reasons for relating
changes in seasonality of money-supply
components to readily measured variables, such as the volumes of tax receipts
and refunds. In principal, all basic determinants of seasonality could be included
as part of a more general model explaining
the behavior of each of the raw-money
components. Assuming their relationships
could be well estimated, seasonal effects
could be forecast and eliminated to obtain
the seasonally adjusted series. (Seasonal
forecasts for the upcoming year would
require that all contemporaneous determinants also be forecast.) Unfortunately,
such a model has not been established,
nor is it evident that a widely accepted
model could be estimated.
In the absence of an established structural model, the money supply-like virtu-
ally all economic time series-is adjusted
using an auto-adjustment method, i.e.,
seasonal variation is based solely on the
past history of the variable being adjusted.
The specific method, which follows from
the X-II program developed by the Bureau
of the Census, is applied to each of the
components of the money supply (see
box). Each monthly seasonal factor is
essentially a weighted average of the values
of the data for that month over a number
of years once the trend-cycle component
has been factored out. The number of
years averaged and the values of the
weights are options of the user and should
depend on prior knowledge. If the seasonal is known to be changing, for example, the period over which those data are
averaged should be short, and the weights
given to the most recent data should be
relatively larger. The most recent information is given the most weight.
The auto-adjustment approach assumes
that all information about the relevant
magnitudes of seasonality in money is
embodied in the past history of the series
itself. The fact that the financial markets
anticipated the M-l surge in April based on
expectations of tax flows challenges this
assumption. Although the X-ll method
clearly fails to anticipate all systematic
changes in seasonality that result from
changes in underlying determinants, the
X-ll contains an option that allows it to
detect and partly account for trend change
over time.2
There is some evidence indicating that
the X-ll can better anticipate changing
seasonality when augmented with time-
2. This option adds one-half the change from the
previous year to the seasonals of the last available
year. While such a formula may be rigid, it will, on
average, detect and partially account for trend
change, particularly if this change is large relative to
the irregular movements. Furthermore, X·ll results
are sometimes modified judgmentally to incorporate
expected fluctuations resulting from institutional
changes, such as a change in the tax-filing date.
Because it is difficult to perform this practice consistently over time, it is done only under extreme circumstances. Consistent anticipation of all systematic
changes in seasonality requires more complete
knowledge of the underlying determinants.
The x-u Method
The X-II is the method employed to
estimate monthly seasonal factors. 1 The
X-II involves two fundamental steps to
separate any monthly time series into
three distinct series-the trend-cycle,
seasonal, and irregular components.
The first step isolates the trend-cycle
component from the seasonal and irregular components by dividing the original
series by an estimate of the trend-cycle
component. The second step separates
the seasonal and irregular components.
The X-II procedure is iterative in two
senses: (1) it repeats the second step,
using a revised seasonal component in
which extreme irregular values are eliminated or replaced with dampened ones;
(2) it repeats both steps by re-estimating
the trend-cycle component, using alternative averaging methods on a preliminary seasonally adjusted series obtained
in subsequent rounds.
Although the technique is considered
mechanical, it permits the use of judgment to the extent that some parameters
of the X-II program can be varied. This
discretion is best exemplified by the
user's options for choosing both the
length of the period and the weighting
structure of the moving average. The
moving average options are available
when estimating both the trend-cycle
and seasonal components of the series.
Although the X-ll automatically selects
default values for these options, the user
has available alternatives that permit
variations in the degrees of smoothing. 2
When estimating the final trend cycle,
the degree of smoothing (length of moving average) desired would depend on
the relative importance (average percent
1. Estimating weekly seasonals is a complex process in which the weekly results are prorated to be
consistent with the X-ll results on monthly data.
2. Experience has shown that the seasonal cornponent of many economic time series can be adequately estimated by the same choices of Xv l I
options. Consequently, the X-ll program is preset
to these default options, which can be changed as
circumstances warrant.
change) of the irregular variations to the
trend-cycle movements. The greater the
irregular movements relative to the trend
cycle, the longer the moving average
needed to smooth out the short-term
movements and reveal the trend. Conversely, if cyclical movements dominate,
then a short moving average would better reveal the systematic movements of
the series.
Similarly, when estimating the seasonal
components, the degree of smoothing
desired would depend on the relative
importance of {he regular variation. If a
seasonal for a given month is believed to
be stationary, then all the movement in
the seasonal-irregular (S-I) component
for the month must result from irregular
variation. Thus, the user would choose
to average as many years of that month
as possible to average out the noise. For
this reason, the X-ll has an option that
averages seasonal-irregular values of the
same month for all prior years available,
giving equal weight to each year.
If the seasonal factor is believed to be
changing, then movements in the S-I
component reflect movements of both
individual components, and the default
option may be desirable. This option
takes a five-year moving average that
weights most heavily the S-I component
in the year being estimated. The two
years before and the two years after pre
weighted with lesser weights (declining
away from the year). When the seasonal
being estimated is for the most recently
available year, only the two prior years
are included. Although a short moving
average may fail to average out irregular
noise, it enhances the probability that a
seasonal factor would correctly incorporate movements reflecting fundamental
changes in the determinants of seasonality. It also enhances the probability of
removing irregular variations under the
guise of seasonal variations. The tradeoff is clear. Ifa priori evidence exists that
movements in the seasonal are large relative to irregular variation, then a short
averaging period is desired.
broad sense, economic series that display
seasonality exhibit fairly consistent patterns of fluctuation, recurring at predictable but not necessarily uniform intervals.
Historically, the April pattern has been
one of large recurring increases in the raw
data, particularly in the checkable deposit
component. Over the past five years, this
component has increased an average annual rate of 53.4 percent in April (see table
1). This pattern has been attributed largely
to the effects of income-tax flows (both
refunds and receipts) that are concentrated in April, although other factors
probably were also at work. Presumably,
many refunds are deposited in transactions accounts soon after they are received, tending to inflate money balances.
How quickly deposit holders adjust their
balances to "normal levels" is not clear.
Although it sometimes is assumed that
they adjust fairly quickly (i.e., within two
months or so), evidence supporting this is
indirect and ambiguous.
Money-supply increases associated with
federal income-tax receipts, on the other
hand, arise from float due to mailing and
tax processing, as payors' deposit balances remain high until checks clear. Typically, by early May the Treasury has collected over 90 percent of all individual
nonwithheld tax payments due April 15. In
April 1982, the Treasury processed over
$35 billion in such receipts. Decreases in
raw-money numbers in May tended to
offset much of the increase in April.
The M-l surge in April 1982 also may
have reflected specific details of the calendar. Such variations, known as calendar
effects, may result from payment practices affected by non-regularly recurring
holidays (e.g., Easter), the day of the week
on which the month begins, or the number
of Fridays in the month. These effects
generally do not occur at uniform intervals, nor do they always occur in the
month of April.
One calendar effect, which seems to be
growing in importance, is the consequence
of early Social Security payments. These
payments usually are made on the third
day of the month, unless the third falls on a
weekend; then payments are made on the
first business day prior (Friday, unless it is
a holiday). The third day of April 1982 fell
Table 1 Transactions Deposit Growth
in April
Seasonally adju~ed annual rates
Raw
Year
number,
percent
Seasonal
component,
percent
1978
1979
1980
1981
1982
56.4
40.4
42.8
42.9
40.6
43.7
Average
53.4
42.1
57.0
64.7
17.4
71.4
a
a. Seasonality is estimated, using the ratio of the
first published seasonals for April and March.
on Saturday, so that these payments
(amounting to over $13 billion) were made
one day early. Early payments are likely to
be deposited earlier (over one-third are
deposited directly), while expenditures by
Social Security recipients are not likely to
be altered by early payments. Unless the
recipients immediately transfer deposited
funds into nonmoney assets or use balances to purchase goods or services from
those who do, transactions balances would
be higher than they otherwise would have
been. Thus, early payments make the
weekly average money-supply measure
higher than it otherwise would have been.
If one assumes that neither receipts nor
expenditures in the second week are
affected by the early payments, the impact
should wash out completely in that week.
To the extent that balances are temporarily high for one day, average monthly
balances would be higher, but only about
one-fourth the average weekly effect.
Calendar effects in weekly data are fundamentally different from calendar effects
in monthly data. A monthly calendar effect
that could have contributed to the recent
M-l surge relates to the number of Fridays
in April. When a month has five Fridays, a
large percentage of people who are paid
biweekly receive three paychecks instead
of their usual two. Money balances tend to
swell in such a month and the month
immediately following. (Such an effect occurs twice a year in biweekly payment
cycles.) To the extent that households pay
monthly obligations out of the more typical
two-payday income flows, these households would have more discretionary funds
available in the extra-payday months. Since
it is unlikely that all of the extra funds are
immediately transferred into nonmoney
assets or used to purchase goods and services, transactions balances temporarily
rise. Although balances in a five-Friday
month are on average marginally higher, in
the first month following they could be as
much as $1 billion higher. This effect is
essentially zero by the second month.
The influence of an extra pay period on
the money numbers probably has intensified in recent years, as large firms (with
large payrolls) have adopted more sophisticated cash-management techniques. One
such technique-zero
balancing-allows
firms to invest all available cash on a daily
basis. As funds are transferred from firms
(holding money-market assets) to households (holding funds in checkable deposits), the narrow money measures tend
to increase.
Seasonally Adjusting
the Money Measures
When approaching the problem of seasonality, we should have some knowledge
of the underlying behavior generating the
data to choose the appropriate technique
for adjustment. The behavior of deposit
holders suggests reasons for relating
changes in seasonality of money-supply
components to readily measured variables, such as the volumes of tax receipts
and refunds. In principal, all basic determinants of seasonality could be included
as part of a more general model explaining
the behavior of each of the raw-money
components. Assuming their relationships
could be well estimated, seasonal effects
could be forecast and eliminated to obtain
the seasonally adjusted series. (Seasonal
forecasts for the upcoming year would
require that all contemporaneous determinants also be forecast.) Unfortunately,
such a model has not been established,
nor is it evident that a widely accepted
model could be estimated.
In the absence of an established structural model, the money supply-like virtu-
ally all economic time series-is adjusted
using an auto-adjustment method, i.e.,
seasonal variation is based solely on the
past history of the variable being adjusted.
The specific method, which follows from
the X-II program developed by the Bureau
of the Census, is applied to each of the
components of the money supply (see
box). Each monthly seasonal factor is
essentially a weighted average of the values
of the data for that month over a number
of years once the trend-cycle component
has been factored out. The number of
years averaged and the values of the
weights are options of the user and should
depend on prior knowledge. If the seasonal is known to be changing, for example, the period over which those data are
averaged should be short, and the weights
given to the most recent data should be
relatively larger. The most recent information is given the most weight.
The auto-adjustment approach assumes
that all information about the relevant
magnitudes of seasonality in money is
embodied in the past history of the series
itself. The fact that the financial markets
anticipated the M-l surge in April based on
expectations of tax flows challenges this
assumption. Although the X-ll method
clearly fails to anticipate all systematic
changes in seasonality that result from
changes in underlying determinants, the
X-ll contains an option that allows it to
detect and partly account for trend change
over time.2
There is some evidence indicating that
the X-ll can better anticipate changing
seasonality when augmented with time-
2. This option adds one-half the change from the
previous year to the seasonals of the last available
year. While such a formula may be rigid, it will, on
average, detect and partially account for trend
change, particularly if this change is large relative to
the irregular movements. Furthermore, X·ll results
are sometimes modified judgmentally to incorporate
expected fluctuations resulting from institutional
changes, such as a change in the tax-filing date.
Because it is difficult to perform this practice consistently over time, it is done only under extreme circumstances. Consistent anticipation of all systematic
changes in seasonality requires more complete
knowledge of the underlying determinants.
The x-u Method
The X-II is the method employed to
estimate monthly seasonal factors. 1 The
X-II involves two fundamental steps to
separate any monthly time series into
three distinct series-the trend-cycle,
seasonal, and irregular components.
The first step isolates the trend-cycle
component from the seasonal and irregular components by dividing the original
series by an estimate of the trend-cycle
component. The second step separates
the seasonal and irregular components.
The X-II procedure is iterative in two
senses: (1) it repeats the second step,
using a revised seasonal component in
which extreme irregular values are eliminated or replaced with dampened ones;
(2) it repeats both steps by re-estimating
the trend-cycle component, using alternative averaging methods on a preliminary seasonally adjusted series obtained
in subsequent rounds.
Although the technique is considered
mechanical, it permits the use of judgment to the extent that some parameters
of the X-II program can be varied. This
discretion is best exemplified by the
user's options for choosing both the
length of the period and the weighting
structure of the moving average. The
moving average options are available
when estimating both the trend-cycle
and seasonal components of the series.
Although the X-ll automatically selects
default values for these options, the user
has available alternatives that permit
variations in the degrees of smoothing. 2
When estimating the final trend cycle,
the degree of smoothing (length of moving average) desired would depend on
the relative importance (average percent
1. Estimating weekly seasonals is a complex process in which the weekly results are prorated to be
consistent with the X-ll results on monthly data.
2. Experience has shown that the seasonal cornponent of many economic time series can be adequately estimated by the same choices of Xv l I
options. Consequently, the X-ll program is preset
to these default options, which can be changed as
circumstances warrant.
change) of the irregular variations to the
trend-cycle movements. The greater the
irregular movements relative to the trend
cycle, the longer the moving average
needed to smooth out the short-term
movements and reveal the trend. Conversely, if cyclical movements dominate,
then a short moving average would better reveal the systematic movements of
the series.
Similarly, when estimating the seasonal
components, the degree of smoothing
desired would depend on the relative
importance of {he regular variation. If a
seasonal for a given month is believed to
be stationary, then all the movement in
the seasonal-irregular (S-I) component
for the month must result from irregular
variation. Thus, the user would choose
to average as many years of that month
as possible to average out the noise. For
this reason, the X-ll has an option that
averages seasonal-irregular values of the
same month for all prior years available,
giving equal weight to each year.
If the seasonal factor is believed to be
changing, then movements in the S-I
component reflect movements of both
individual components, and the default
option may be desirable. This option
takes a five-year moving average that
weights most heavily the S-I component
in the year being estimated. The two
years before and the two years after pre
weighted with lesser weights (declining
away from the year). When the seasonal
being estimated is for the most recently
available year, only the two prior years
are included. Although a short moving
average may fail to average out irregular
noise, it enhances the probability that a
seasonal factor would correctly incorporate movements reflecting fundamental
changes in the determinants of seasonality. It also enhances the probability of
removing irregular variations under the
guise of seasonal variations. The tradeoff is clear. Ifa priori evidence exists that
movements in the seasonal are large relative to irregular variation, then a short
averaging period is desired.
Federal Reserve Bank of Cleveland
series methods (e.g., X-11 ARIMA). Unlike
structural models, time-series models are
based solely on statistical principles and
thus are particularly useful in forecasting
when theoretical knowledge is scarce. Information contained in time-series projections of the money-supply components
can improve seasonal forecasts in the
sense that subsequent revisions of the factor are reduced. When the X-11 is applied
to an extended time series of a given component, which consists of the available
observations
and the projected values of
the unadjusted series, the resulting seasonal forecasts are closer to their final
values, which are determined
only after
the future data are known.i'
Another problem with the X-11 is that it
does not adequately filter calendar effects,
as they do not occur in the same month
each year. Although the X-11 has an
option to estimate the effects of the number
of trading days in a month using a regression model, it has not been useful in
eliminating such calendar effects in money.
Recent studies have indicated that spectral analysis methods may prove useful for
detecting calendar effects; the magnitudes
of calendar effects then can be estimated
using regression methods."
Alternative models also may provide a
framework for constructing
an adequate
filter. A simple statistical test suggests
variations in the irregular componentthe series after X-11 estimates of both
trend-cycle and seasonal components have
been factored out-are
explained by the
day of the week on which the month
3. Judging the quality of a preliminary seasonalfactor estimate by how close it is to its final value
(once all data are available) has been challenged as
being only as accurate as the final estimate allows. In
the absence of a universally accepted set of criteria,
however, it is perhaps the most popular standard.
4. See William S. Cleveland and Susan J. Devlin,
"Calendar Effects in Monthly Time Series: Detection
by Spectrum
Analysis and Graphical
Methods,"
Journal of the American Statistical Association, vol.
75, no. 371 (September
1980), pp. 487-96. See also
William P. Cleveland and Michael R. Grupe, "Modeling Time Series When Calendar Effects Are Present," Special Studies Paper 162 (Board of Governors
of the Federal Reserve System, 1981; processed).
begins.5 A further implication is that estimated coefficients of this model provide
measures of the magnitudes of calendar
effects. Unlike more ambitious efforts to
model the determinants
of seasonality,
research on modifying the X-11 to detect
and measure calendar effects is likely to
produce more immediate improvements in
seasonal adjustment of the money supply.
Improving Seasonal
Adjustment Methods
In early 1978 the Federal Reserve Board
initiated a comprehensive
study to determine appropriate methods for seasonally adjusting financial data, particularly
the money-supply measures. Published in
1981, the study's recommendations
essentially outlined a continuing research
program-one
that subsequently was implcmented." Because possibilities exist for
improvements
in the widely used and accepted X-II program, the Federal Reserve
Board's continuing research effort initially
will focus on developing model-based improvements, including time-series modeling
options and calendar adjustments.
The
Federal Reserve also will experiment with
more general model-based methods that
can incorporate
causal explanations
of
seasonal patterns and measure systematic
effects. The Federal Reserve's research
program thus can be expected to yield
more immediate results from X-II enhance-
ment research while laying the foundation
for fundamental changes-ideally,
a breakthrough leading away from the basic autoadjustment framework.
The study also recommended
that the
Federal Reserve Board consider using
the present seasonal-adjustment
procedure or its recommended
modification on
a concurrent basis to utilize all available
data for estimating seasonal factors. Using
the most current data would produce
smoother initial estimates and reduce the
size of revisions compared with the practice of projecting seasonal factors for the
year ahead. However, concurrent
estimation would entail a number of costly
revisions each month as new data are
used by the procedure.
A reasonable
compromise
might be to estimate the
seasonals semiannually, thus allowing incorporation
of the most current information for mid-year review of the money
targets.
Semiannual
calculations
also
would provide better estimates
of the
April seasonal soon after the raw data for
April become available.
Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland,OH
44101
Conclusion
Ideally, seasonal adjustment should filter all calendar-related
movements,
so
that movements remaining in the seasonally adjusted data cannot be attributed to
difficulties in estimating seasonal factors.
The fact that the April surge in seasonally
adjusted M-l was attributed to seasonal
causes reveals shortcomings in the method
used. As recommended
in the Fed's study
of seasonal adjustment,
an ongoing research program has been organized to
develop better methods of adjustment.
While modifications of the current methods
are likely to lead to improved estimates of
the seasonal factors, fundamental improvements, such as the development of causal
adjustment methods, may not be available
for implementation for some time to come.
John B. Carlson is an economist with the Federal
Reserve Bank of Cleveland.
The views stated herein are those of the author
and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors of
the Federal Reserve System.
BULK RATE
U.S. Postage Paid
C1eveland,OH
Permit No. 385
5. Specifically, the X-ll estimate of the irregular
component
of demand deposits was regressed
on
variables accounting for the day of the week on which
the month begins. The estimation period was January 1976 through December 1979. The F-statistic of
the regression
was 5.19, which indicates that one
cannot reject the hypothesis that movements in the
irregular component
are explained by the monthly
starting day. Indirectly, this evidence supports the
hypothesis that the calendar effects are consequences
of early Social Security payments and extra pay periods, since it is necessary (although not sufficient) that
a month begins on a Thursday or Friday or (in some
months) Wednesday for these events to occur.
6. See Board of Governors of the Federal Reserve
System, Seasonal Adjustment of the Monetary Ag·
gregates, Report of the Committee of Experts on
Seasonal Adjustment
Techniques
(Board of Governors, October 1981).
May 31, 1982
Address Correction Requested: Please send corrected mailing label to the Federal
Reserve Bank of Cleveland, Research Department, P.O. Box 6387, Cleveland, OH 44101.
The Problem of
Seasonally Adjusting Money
by John B. Carlson
When an impending surge in the money
supply filled the financial news in March of
this year, the reports stated that the surge
would result from above-average incometax refunds and early Social Security payments. Consistent with expectations, M-l
(which includes currency plus checkable
deposits) grew 11.8 percent (saar) in April
1982. But personal tax refunds occur
every year. And early Social Security
payments occur whenever the third day of
a month falls on a Saturday, Sunday, or
holiday. The fact that these and other
effects relate to seasonal or recurring
events and can be predicted suggests a
serious question. Why doesn't seasonal
adjustment of the money supply filter all
such movements?
This Economic Commentary examines
the problem of seasonal adjustment, using
April 1982 as an example; this particular
month reflected a number of influences
that can distort
seasonally
adjusted
monthly measures
of money. Although
there is scope for improving the accuracy
of estimated seasonal factors, fundamental improvements
of the current method
of seasonal adjustment will require extensive research. Such a research program
recently was implemented at the Board of
Governors of the Federal Reserve System. 1
l. For a more thorough
discussion
of seasonal
adjustment
and the board's research program, see
David A. Pierce and William P. Cleveland, "Seasonal
Adjustment Methods for the Monetary Aggregates,:'
Federal Reserve Bulletin, vol. 63, no. 12 (December
1981), pp. 875-87.
Why Seasonally
Adjust M-l?
The primary reason for seasonal adjustment is to eliminate repetitive movements
from data that obscure movements
of
greater significance to the user. For policymakers and market analysts, the main
current interest in the money supply is its
target property,
i.e., information about
whether the Federal Reserve is supplying
bank reserves too liberally or too sparingly. In practice, the policy of the Federal
Reserve has been to accommodate changes
in money demand that "meet the needs of
the trade" (i.e., seasonal movements) to
the extent that such demands are consistent with achieving longer-term objectives,
particularly the annual growth-rate targets
for M-l and the broader measures
of
money stock. Thus, the Federal Reserve
sets its monetary growth-rate targets in
terms of seasonally adjusted data, accommodating seasonal fluctuations that are
temporary and offsetting. Errors in measurement of seasonality thereby can lead
to difficulties in conducting monetary policy.
Seasonal Movements
in the April Money Measures
In its most limited sense, seasonality
refers to movements in data that occur
precisely at the same time each year with
the same intensity. As it is typically used,
seasonality refers to all repetitive movements that occur on predetermined
dates,
but which need not occur on the same
date nor with the same intensity. In this
Federal Reserve Bank of Cleveland
series methods (e.g., X-11 ARIMA). Unlike
structural models, time-series models are
based solely on statistical principles and
thus are particularly useful in forecasting
when theoretical knowledge is scarce. Information contained in time-series projections of the money-supply components
can improve seasonal forecasts in the
sense that subsequent revisions of the factor are reduced. When the X-11 is applied
to an extended time series of a given component, which consists of the available
observations
and the projected values of
the unadjusted series, the resulting seasonal forecasts are closer to their final
values, which are determined
only after
the future data are known.i'
Another problem with the X-11 is that it
does not adequately filter calendar effects,
as they do not occur in the same month
each year. Although the X-11 has an
option to estimate the effects of the number
of trading days in a month using a regression model, it has not been useful in
eliminating such calendar effects in money.
Recent studies have indicated that spectral analysis methods may prove useful for
detecting calendar effects; the magnitudes
of calendar effects then can be estimated
using regression methods."
Alternative models also may provide a
framework for constructing
an adequate
filter. A simple statistical test suggests
variations in the irregular componentthe series after X-11 estimates of both
trend-cycle and seasonal components have
been factored out-are
explained by the
day of the week on which the month
3. Judging the quality of a preliminary seasonalfactor estimate by how close it is to its final value
(once all data are available) has been challenged as
being only as accurate as the final estimate allows. In
the absence of a universally accepted set of criteria,
however, it is perhaps the most popular standard.
4. See William S. Cleveland and Susan J. Devlin,
"Calendar Effects in Monthly Time Series: Detection
by Spectrum
Analysis and Graphical
Methods,"
Journal of the American Statistical Association, vol.
75, no. 371 (September
1980), pp. 487-96. See also
William P. Cleveland and Michael R. Grupe, "Modeling Time Series When Calendar Effects Are Present," Special Studies Paper 162 (Board of Governors
of the Federal Reserve System, 1981; processed).
begins.5 A further implication is that estimated coefficients of this model provide
measures of the magnitudes of calendar
effects. Unlike more ambitious efforts to
model the determinants
of seasonality,
research on modifying the X-11 to detect
and measure calendar effects is likely to
produce more immediate improvements in
seasonal adjustment of the money supply.
Improving Seasonal
Adjustment Methods
In early 1978 the Federal Reserve Board
initiated a comprehensive
study to determine appropriate methods for seasonally adjusting financial data, particularly
the money-supply measures. Published in
1981, the study's recommendations
essentially outlined a continuing research
program-one
that subsequently was implcmented." Because possibilities exist for
improvements
in the widely used and accepted X-II program, the Federal Reserve
Board's continuing research effort initially
will focus on developing model-based improvements, including time-series modeling
options and calendar adjustments.
The
Federal Reserve also will experiment with
more general model-based methods that
can incorporate
causal explanations
of
seasonal patterns and measure systematic
effects. The Federal Reserve's research
program thus can be expected to yield
more immediate results from X-II enhance-
ment research while laying the foundation
for fundamental changes-ideally,
a breakthrough leading away from the basic autoadjustment framework.
The study also recommended
that the
Federal Reserve Board consider using
the present seasonal-adjustment
procedure or its recommended
modification on
a concurrent basis to utilize all available
data for estimating seasonal factors. Using
the most current data would produce
smoother initial estimates and reduce the
size of revisions compared with the practice of projecting seasonal factors for the
year ahead. However, concurrent
estimation would entail a number of costly
revisions each month as new data are
used by the procedure.
A reasonable
compromise
might be to estimate the
seasonals semiannually, thus allowing incorporation
of the most current information for mid-year review of the money
targets.
Semiannual
calculations
also
would provide better estimates
of the
April seasonal soon after the raw data for
April become available.
Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland,OH
44101
Conclusion
Ideally, seasonal adjustment should filter all calendar-related
movements,
so
that movements remaining in the seasonally adjusted data cannot be attributed to
difficulties in estimating seasonal factors.
The fact that the April surge in seasonally
adjusted M-l was attributed to seasonal
causes reveals shortcomings in the method
used. As recommended
in the Fed's study
of seasonal adjustment,
an ongoing research program has been organized to
develop better methods of adjustment.
While modifications of the current methods
are likely to lead to improved estimates of
the seasonal factors, fundamental improvements, such as the development of causal
adjustment methods, may not be available
for implementation for some time to come.
John B. Carlson is an economist with the Federal
Reserve Bank of Cleveland.
The views stated herein are those of the author
and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors of
the Federal Reserve System.
BULK RATE
U.S. Postage Paid
C1eveland,OH
Permit No. 385
5. Specifically, the X-ll estimate of the irregular
component
of demand deposits was regressed
on
variables accounting for the day of the week on which
the month begins. The estimation period was January 1976 through December 1979. The F-statistic of
the regression
was 5.19, which indicates that one
cannot reject the hypothesis that movements in the
irregular component
are explained by the monthly
starting day. Indirectly, this evidence supports the
hypothesis that the calendar effects are consequences
of early Social Security payments and extra pay periods, since it is necessary (although not sufficient) that
a month begins on a Thursday or Friday or (in some
months) Wednesday for these events to occur.
6. See Board of Governors of the Federal Reserve
System, Seasonal Adjustment of the Monetary Ag·
gregates, Report of the Committee of Experts on
Seasonal Adjustment
Techniques
(Board of Governors, October 1981).
May 31, 1982
Address Correction Requested: Please send corrected mailing label to the Federal
Reserve Bank of Cleveland, Research Department, P.O. Box 6387, Cleveland, OH 44101.
The Problem of
Seasonally Adjusting Money
by John B. Carlson
When an impending surge in the money
supply filled the financial news in March of
this year, the reports stated that the surge
would result from above-average incometax refunds and early Social Security payments. Consistent with expectations, M-l
(which includes currency plus checkable
deposits) grew 11.8 percent (saar) in April
1982. But personal tax refunds occur
every year. And early Social Security
payments occur whenever the third day of
a month falls on a Saturday, Sunday, or
holiday. The fact that these and other
effects relate to seasonal or recurring
events and can be predicted suggests a
serious question. Why doesn't seasonal
adjustment of the money supply filter all
such movements?
This Economic Commentary examines
the problem of seasonal adjustment, using
April 1982 as an example; this particular
month reflected a number of influences
that can distort
seasonally
adjusted
monthly measures
of money. Although
there is scope for improving the accuracy
of estimated seasonal factors, fundamental improvements
of the current method
of seasonal adjustment will require extensive research. Such a research program
recently was implemented at the Board of
Governors of the Federal Reserve System. 1
l. For a more thorough
discussion
of seasonal
adjustment
and the board's research program, see
David A. Pierce and William P. Cleveland, "Seasonal
Adjustment Methods for the Monetary Aggregates,:'
Federal Reserve Bulletin, vol. 63, no. 12 (December
1981), pp. 875-87.
Why Seasonally
Adjust M-l?
The primary reason for seasonal adjustment is to eliminate repetitive movements
from data that obscure movements
of
greater significance to the user. For policymakers and market analysts, the main
current interest in the money supply is its
target property,
i.e., information about
whether the Federal Reserve is supplying
bank reserves too liberally or too sparingly. In practice, the policy of the Federal
Reserve has been to accommodate changes
in money demand that "meet the needs of
the trade" (i.e., seasonal movements) to
the extent that such demands are consistent with achieving longer-term objectives,
particularly the annual growth-rate targets
for M-l and the broader measures
of
money stock. Thus, the Federal Reserve
sets its monetary growth-rate targets in
terms of seasonally adjusted data, accommodating seasonal fluctuations that are
temporary and offsetting. Errors in measurement of seasonality thereby can lead
to difficulties in conducting monetary policy.
Seasonal Movements
in the April Money Measures
In its most limited sense, seasonality
refers to movements in data that occur
precisely at the same time each year with
the same intensity. As it is typically used,
seasonality refers to all repetitive movements that occur on predetermined
dates,
but which need not occur on the same
date nor with the same intensity. In this
@FedFRASER