R. Alton Gilbert

English

Research Papers in Economics

New Seasonal Factors for the
Adjusted Monetary Base
R. Alton Gilbert
..t. HE February 1984 adoptionu of contemuupor-atueous
resenve requirements ICRR(, which cluanuged the tinuu—
it’ig betweenu deposit liahili ties atud mequir-ed reserves,
luas altered the seasonal patten-rus muthe adjusted nuolu-
etary base (AMISI.’ Weekly vam-nability mu tlue AMB has
been substatutially higher sinuce that date, wluiclu sug-
gests that seasotual factors based on past data do nuot
I-elect tlue seasotual patterns in the AMt3 under CRR!
This ar-tide descn’ibes a tuew nuetluod of dem-ivinug sea—
sotual Factors for tlue AMB tluat reflects the timing of
reserve accountinug under CER:’
THE’ CALCULATION OF ‘I’Iff’
AIJJL..JStLI) %‘IONE lAin BASE
‘Flue :~NlBis designed to be a single measure of all
Federal Reserve actionus, itucluding cluanuges mu r-esem-ve
requir-crnetuts, tluat inufluemuce tlue mnotuey stock, It is
equal to tlue source base plus a m’esen’e adiustme nut
nuagtuitude (BAM( tluat accounts for cluanges mu reserve
R. A/ton Gilbert is an assistant vice president at the Federa/ Reserve
Bank ofSt. Louis. Paul B. Christopherprovided research assistance.
‘A general description ofCAR appears in Gilberl and Trebing (1982).
‘The average absolute value of weekly changes in the AMB from
January 1982 through January 1984 was $492 million. This mea-
sure ofweekly variability was $1,723 million for the period February
984 through December1985, more than three times larger than in
the earlier period.
‘An earlier paper by Farley (1984) presents a different method of
deriving seasonal factors that reflectthe timing of reserve account-
ing under CAR.
requirenuents by the Federal Reserve.’
RANt is the diffen’ence hetweemu the n-esemves tluat
would be n-equired given cun-n-ent deposit liabilities( if
the base period’s n-eserve n’equirenuents were in effect
and the n-esetves tlual are actually required givenu cinn-—
renut reserve requiretuuents. Adding RAM to the sour-ce
base pi-oduces a senes tluat shows what tlue sour-ce
base would luave been in eaclu pen-iod if m-esen’e me—
quit-enuent l-alios hail heetu tluose of tlue base permod:
This procedure converts the inupact of reserve require-
ment cluanges inuto equivaletut chanuges mu tlue sour-ce
base, luoldinugreserve, requir-emenuts constant
‘The following articles describe and explain the AMB in greater
detail: Gilbert (1980,1983 and 1984) and Tatom (1980).
‘The source base equals the reserve balances of depository institu-
tions with Federal Reserve Banks, which excludes their required
clearing balances and balances held to compensate for float, plus
total currency in circulation, whether held by depository institutions
orthe public. It is derived from the combined balance sheets ofthe
Federal Reserve Banks and the U.S. Treasury.
‘The base period for calculating RAM is January 1976 through
August 1980. Base period reserve requirements are the average
reserve requirementsover that period fortwo categories of deposit
liabilities: transaction deposits and total time and savings deposits.
For memberbanks, the average required reserve ratio was 12.664
percent on transaction deposits and 3.1964 percent on total time
and savings deposits. For nonmember institutions, base period
reserve requirements were zero, since they were not subject to
reserve requirements of the Federal Reserve in the base period.
Thus, RAM is calculated as the current transaction deposits of
member banks multiplied by 0.12664, plus thecurrent total time and
savings deposits of member banks multiplied by 0.031964, minus
the current required reserves of all depository institutions.
29FEDERAL RESERVE BANK OF ST. LOUtS DECEMBER 1985
tinder the Prior System o/.tagged
Peserre Requirements
Calculation of tlue AMB under lagged reserve re-
quin-ements ILRRI is itlustm-ated in equations 1 tht-ouglu
3, Definitions of the terms in these equatiotus are
presented in table 1, Equation 1 shows how RAM is
calculated fot-each n’esem-ve maintenance pemSocl unden-
LRR.
(II BAN’t, = BRTB ITR,,,( + BRTS ITS,,,l — RB,
The source base is equal to total curretucy outstand-
ing (that held by the public and in the vaults of deposi-
tory institutionsl plus the reserve balances of deposi-
tony institutions. Under LRR, the items tluat could he
used to nueetrequired reserves mu the current mainte-
nance period were resetve balances held in the cur-
rent period (RB,( plus vault cash held in the week
ending 14 days earlier (V,,,(. This sum is thus equal to
t-equmredreserves IRR,l plus excess reserves (E,L Conse-
quently, thesour-ce base can be expressed as showtu in
equation 2,
121 SB, = CP, ±V ±RB,
=CP,+V,±I1B,±F~—V,,,
Thus, the AMB under LRR is shown in equation 3.
(31 AMB = SB, + RAM,
= CP, ±E, + V — V,.,, ±BR’t’R (TB,)
±BRTS ITS, I
t.~’nder the Current System of
Conteniporaneo.us IUM’erye
.ttequirements (CHIt)
The resenve ruuaintenamuce periods, dun-ing which
ayen’age r’eserves nuust equal ot- exceed r-equin-ed re-
senves, have heen lengthened under CER to two-week
periods ending even’ other Wednesday. ~
setvesontn~)s~Etio9~!22smt~J2n-jhecurn’etuttwo-
wuuk maintenancej~.nod ai bis,~ilacj~
transaction deoosits forthe 14-day neniod ending two
~W
davsbefbr-etheendofthecum-t-entrnaitutenanc~pe-
~
tngs os~sare based on dally ae n-a ~e sits over
a 14 day pun tod cndtng 30 days bufon thu nd of th
citn’entmaintenance permorL The assets 2posttpry
institutions tluat count toward meeting their reserves
in
balances in the current nuatnten ertodj~usaver-
age vault cash ovutthe~4-d~~fl2gendin~0days
Equation 4 illustrates the calculation of the AMB un-
derCRR,
Table 1
Definitions of Terms Used in Specifying
the Adjusted Monetary Base
SB - the source base c-)er Ihc- r’Ia’
1
nlc-nance oe’rod enc’nq
on cay
PAM - reserve ad usmerlt n’,aonrtudp for the ma:ntenor’ce
uonod cndm”g cm— day
BA ER base pcrod reourred reserve ratIo on lie transactroi
oepos-k of me-racer banks
TA -— transacinon cepnsrts of rr’emrhe’ barks mn the wee~
endmr-g 14 oay~ before cay
RATS - base per on ?equren re~eRera’ro on the t-r’ie ano
sav:ugs doposts ni member banks
TS - tIme anc sav:nQs depos.Is 0~ member banks rr- the
weekerid’ng 14 days he’o~e oay
AR — requ’reo mese’ves c’ all deposItory ist tuirons rr the
maIntenance pPrtod endrrg or day I
RB balances c’ deposeory rrstmtLtnm’ns mn tlie-r reserve
acsorrr’ts at redorar Reserve Barks In mhe monte-
nar’ce ceromi enj ng on day I
V - vai.d raslr 0’ deposrory ‘istnjtrons :n tr’e marrte
nancen~rmodenoIrip on day
V -- vaL-:t rash- um oepos:tor’, ns’rmutrons In tie weal’ dm0-ic
t4 days before the ena of the cjmren’ r’-arrienance
oer od
E - - excess reserves rr the rra-ntenance oerrod enenig on
day 1 orror to the rmposrnun of reserve reaurremerts of
the Fedpra Reserve oi a depnsriory rnst’lutro-rs .1
1980 1 ncucos the vault cash o~ ronrlemoer is:rlu-
runs, he dIn the week encrng 14 days earner
GP -— currency held by Inc cubnr In the rr.arntenaice perrod
ondrng on nay:
TA - tr-ancactror r1e;~osrts01 ipmber honks aver the 14
day~ ern-ng two eoy~ before the erd o’ the cjr~emfl
rm;arnltenam’ce Derrod
-- I ac an~ savIngs deoos.ts of member banks cvn~ Inc
14days endrrg 30 days oef~rm-,the end o’ ‘he cjrrent
marntenar.ce perrod
V v~uIi cash Ov’’ the :4o~v~ endinq 30 aays hetorehe
end o’ the cm Term ~arrtenaice oenod
I \\IIt sIt - It Pd
(I’ - I, - ‘
- tIthE H — lIEN-H
IItIim’a,~mmimal ritlirmr’,m,ttm’mmn-,;mi’tin,mitlm-1m,r Is 1mm,
limit,’ mmmcl h.t~mrIgscli’pmmsil— mm,’ mmml m’l1.tmmt4m-ml h~ mit
3~0FEDERAL RESERVE BANK OF SiT LOUIS DEOEMBER 1985
Chart 1
Seasonally Adjusted Monetary Base
Old and Revised Series
Billions of dollars
240
232
224
216
208
200
F MA Mi JASON D J F MA Mi JASON D
1984 1985
NOTE The old series is weekiy; the revised series is biweekly, covering reserve maintenonce periods.
switch fi-om LRR to CR11, seasonal movements in the
AMB will be diffement under CR11. Fon- example, an
itucrease in transaction deposits will lead to a rise in
the AMB about two weeks ear-lien- under CR11 than
urudem LRR. In contrast, a rise in time and savings
deposits will lead to a rise in theAMB about two weeks
laterunder CRR tluaru under LRR.
Thn’ough 1985, seasonal factot-s for the z\MB wet-c
derived by applying tlue X-1I seasonal adjustmenut
pnogranu to past AMB data, tlue bulk ofwhiclu wem-e for
the period prior to Febn-uary 1984.’ Thus, these data
are generally inappropriate in calculating seasotual
factors fot-the per-iod situce Februany 1984.
Alternative seasomual factors for tlue pem-iod since
February 1984, luowevet-, can he derived by a simple
pn-ocedure. The procedure requim-es the calculationu of
a counterfactual AMB series for seven-al yeans ptiot’ to
February 1984 that reflects what the AMB’s seasonual
patter-ns would have been if CRR had been in effect
‘Theweeklyseasonal factors for the AMB are derived from a version
of the X.11 program that has been modified by the staff of the
Federal Reserve Board to derive weekly seasonal factors from
monthly seasonal factors.
during the earlier perod, Tlue counterfactual AMB
series is derived by adding to the AMB (as calculated
belbre February 1984) the adjustments necessary to
conyeit the timing of reserve accounting to tluat utuder
CRR. Eqitation 5 shows how tluis countemfactual AMB
series is derived, Note that equation 5 reduces dmr-ectly
to equation 4 when conupotuents with opposite signs
are cajucelted.
(SI AMtI, = CP, ±F, ±IV,—~’,
±BRTR (TB,,; ±RRTS ITS
±tV,~,— V,~, I ±BBTR ITR, — TB,
± BBTS ITS, —
The counlerfactual AMB seties fon- per-iods prior to
February 1984 is calculated as shown in equation 3,
vvitlu one modification. ‘[he nuodtfication inuvolves an
adjustment for the cluange in the timing of n-eserve
accounting on vault cash IV,,4
— V,_,,,I. The term V,, is
for weeks ending omu Wednesdays, wluereas v, ,,, is fon
weeks ending onu Motudays. The tinue series cun-m-entl~’
maintained on weekly vault cash is for weeks ending
on Mondays, which is available back to 1975. An ap-
proximation to IV, ,, — V~,,Iin equation 5i sderived as
(V,,
6
— V,:,0 t, using data on the vault cash of all commem--
cial banks ft-om 1975. The counterfactual semies onu the
Billions of dollars
240
31FEDERAL RESERVE SANK OF ST. LOUIS DEOEMSER 1985
Chart 2
Ml Multiplier
Old and Revised Series
!
T
~
I
~
7~
~
‘
~ !
F MA M J JASON 0 J F MA M J JASON 0
1984 1985
NOTE, The old series is weekly; the revised series is biweekly, covering reserve meintenance periods,
A1\1B does not include an adjustnuent for the chamuge in
the timing of reserve accounting for- vault cash mu the
year-s 1969 tht-ough 1974. The counterfactual ~MB se-
ries for’ several yeans prior to F’ebruaty 1984 is com-
binedwith tlue AMB as calculated since Febr-uarv 1984.
Seasonal factor-s are det-ived from this ser-ies amud ap-
plied to the AMB, not seasonally adjusted, since t’eh—
r-uary 1984.’
Much of the increase in short—run variability in the
AMB since February 1984 is elimuuinated by usitug sea-
sonal factor-s based on the coumutem-Iacttmal series. Fur-—
thernuore. ~\MB data for the two—week m-eserve mainte-
‘The counterfactual observations for the AMB in periods prior to
February 1984 are calculatedfor weekly periods. For the purposeof
calculating seasonal factors, observations on the AMB since Febru-
ary 1984 are calculated for each week (seven-dayperiods ending
on Wednesdays), by adding the source base for the week to the
biweekly observation for RAM that includes that week. The X-1 1
program is used to derive weekly seasonal factors from this weekly
series. The weekly seasonal factors are used for calculating the
biweekly observations for the AMB, seasonally adjusted, since
February 1984.
Data on the transaction deposits and on time and savings de-
posits ofmember banks are availableforweeks ending on Mondays
since 1979. Data from 1979 through 1985 provide enough weekly
nance periods are less var-iable than in tlue weekly
data, Char-t I shows the difference between weekly
data omu the AMI3 as published tlur-ough 1983 anud thu
biweekly series with ttue new seasotual factom’s based
on tlue counterlactual mettuod. Cham-t 2 pr-esents a
siniilar contrast between the alternative Ml nuultipli-
ers. Table 2 indicates a lower incidence of lar-gu
cluanges wuth the altenuative seasomuals, especially fom
the biweekly sen-ies.
The weekly adjusted monetary base has beeru mom’r
variable since the Federal Reserve adopted cotutempo
raneous reserve requin-ements mu Febriraty 1984. Th
increase mu its weekly var-iahilitv appear-s to r-efle~
problems with estimating the seasonal patter-ns flutlu
i\MB using data prior- to Febr-uary 1984. New seasona
observations for the calculation of the weekly seasonals. b~
monthly data are needed over a longer period to get meaningfi
results from the X-1 1 program. Monthly average observations fc
the counlerfactual series on the AMB for the years 1969 throug
1978 are derived by using data on deposits for weeks ending o
Wednesdays as approximations for observations on deposits fc
weeksending on Mondays,
Ratio
2.68
2.64
2.60
2.56
2.52
A
Ratio
2.68
264
2.60
2.56
2.52
32FEDERAL RESERVE BANKOF ST. LOUIS DECEMBER 1985
Table 2
Incidence of Large Changes in the Adjusted Monetary Base Series with Two Sets of
Seasonal Factors
$ batlon 64 % 48~9% 7&O% 146%
Zbrfken 357 2a.4 25* Vt
abtllton 4,3 1t4 0
factors have been derived from a counterfactual AMB
series designed to reflect the tinning of reserve ac-
counting undet CRR. Shor’t-m-un variability in the AMB
is reduced substantially byaveraging the AMBoverthe
two-week reserve maintenance periods in effect since
February 1984 and by using seasonal factor’s der-ived
from the counter-factual AMB series.
BEEF’ BENCES
Farley, Dennis E. “Alternative Measures of the Monetary Base,”
paper presented at the Federal Reserve System Commiffee on
Financial Analysismeeting, Federal ReserveBank ofKansas City,
October IS, 1984,
Gitbert, R, Alton, “Calculating the Adjusted Monetary Base under
Contemporaneous Reserve Requirements,” this Review (Febru-
ary 1984), pp 27—32.
“Two Measures of Reserves: WhyAre They Different?”
this Review (June/July 1983), pp. 16—25.
“Revision of the St. Louis Federal Reserve’s Adiusted
Monetary Base[ this Review (December1980), pp. 3—10.
and Michael E. Trebing. “The New System of Contem-
poraneous Reserve Requirements,” this Review (December
1982), pp. 3—7.
Tatom, John A, “Issues in Measuring anAdjusted MonetaryBase,”
this Review (December1980), pp. 11—29.
33

New seasonal factors for the adjusted monetary base

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New seasonal factors for the adjusted monetary base

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