Michelle 11. Garfinkel andDaniel L. Thornton

Michelle R. Garfinkel, an assistant professor at the Universityof California at Irvine, was a senior economist at the FederalReserve Sank of St. Louis while this paper was written. DanielL. Thornton is an assistant vice president at the FederalReserve Sank of St. Louis. Richard L Jako and Scott Leitz pro-vided research assistance.

HE MULTIPLIER MODEL of the moneysupply, originally developed by Brunner (1961)and Brunner and Meltzer (1964), has becomethe standard paradigm in macroeconomics andmoney and banking textbooks to explain howthe policy actions of the Federal Reserve in-fluence the money stock. It also has been usedin empirical analyses of money stock controland the impact of monetary policy actions onother economic variables.

One important feature of tins model is that itdecomposes movements in the money supply in-to the part that is due directly to Federal Re-serve policy actions (the adjusted monetary base)and the part that is due to changes in technologyand the tastes and preferences of depository in-stitutions and the public (the money multiplier).In this decomposition, the multiplier is assumedto be independent of the policy actions of thecentral bank. The independence is implicitlypredicated on the assumptions that the demands

for both checkable deposits and currency aredetermined by the same factors, and that indi-viduals can quickly and costlessly alter theirholdings of currency and checkable deposits toachieve the desired proposition of the two alter-native forms of money.1 Open market purchases,for example, increase reserves and consequentlycheckable deposits; but the public simply shiftsfrom checkable deposits to currency until the(unchanged) desired ratio of currency relative tocheckable deposits is once again achieved. Be-cause policy actions have no impact on the pub-lic’s holdings of currency relative to checkabledeposits, the multiplier does not depend directlyon the policy actions of the Fed.

This article investigates the theoretical andempirical validity of the key feature of the mul-tiplier approach. In theory, the multiplier is in-dependent of the policy actions of the FederalReserve only if the demands for currency andcheckable deposits are determined by identical

47

The Multiplier Approach tothe Money Supply Process:A Precautionary Note

IIIIIIII

IIII’IIII

1The notion that the multiplier is independent of FederalReserve actions—implicit in the work of Brunner andMeltzer (1964, 1968) and, more recently, in Plosser (1991)—has never been demonstrated rigorously with micro-eco-

nomic principles. The argument presented here that wouldsuggest such independence is implicit in works as early asFisher (1911).

48

factors and if , conditional on these factors, thesedemands are strictly proportional. From an em-pirical perspective, this condition is necessarybut not sufficient; the degree to which the mul-tiplier is influenced by policy actions also de-pends on the strength of the relationship be-tween policy actions and checkable deposits.

An empirical analysis shows that most of thevariability of the observed ratio of currency tocheckable deposits is due to variation in check-able deposits, and thereby suggests that the de-mand for currency is not strictly proportionalto the demand for checkable deposits. Prior tothe Monetary Control Act of 1980 (MCA), how-ever, the link between reserves and checkabledeposits was quite loose—so much so, that thenotion that the multiplier is independent of pol-icy actions was operationally valid. Nevertheless,the empirical relevance of this notion has weak-ened considerably since the implementation ofthe MCA in the early 1980s. Since then, the re-lationship between Fed policy actions andcheckable deposits and, thus, the multiplier hastightened markedly.

The evidence presented here, that the multi-plier is not independent of Federal Reserve ac-tions in the post-MCA period, raises some ques-tions about the appropriateness of using themonetary base as an indicator of the effects ofpolicy actions on the money stock. More impor-tant from a policy perspective, it also suggests amodification of the standard approach to moneystock control that might yield substantial im-provements in effective monetary aggregate

targeting.

THE MONEY MULTIPLIER

APPROACH: A SIMPLE: EXAMPLE

As a starting point for understanding the de-composition of the money supply into the mone-tary base and the multiplier, note that the nar-row money stock, Ml, is defined as

(1) Ml, = TCD, + C,,

where TCD denotes total checkable deposits andC denotes the currency held by the nonbankpublic. The monetary base (MB), not adjustedfor changes in reserve requirements, is simplythe sum of currency and reserves (including

cash in the vaults of depository institutions) inthe banking system, R:

(2) MB,= C,+ R,.

Currency, supplied by the Federal Reserve ondemand, reflects the portfolio decisions of thepublic rather than monetary policy actions. Re-serves, in contrast, can be affected directly bythe Fed’s sales or purchases of government se-curities in the open market.

For simplicity, assume that the Federal Re-serve has a simple system of reserve require-ments, with required reserves, RR, given by

(3) RR,= rTClJ,, 0 -c r < 1,

where r denotes the ratio of reserves that mustbe held against TCD.2 A change in the reserverequirement ratio, r, also would constitute amonetary policy action by the Fed.

Furthermore, for simplicity, assume that ac-tual reserves always equal required reserves sothat excess reserves are identically zero. Withthis simplifying assumption, equation 3 can berewritten as

(4) H, = rTCD,.

The model is completed by assuming that cur-rency is held in some proportion, k, of TCD.That is,

(5) C, = kTCD,,

where the proportion k, hereafter called the k-ratio, is the public’s desired ratio of currency toTCD holdings.

Combining equations 1, 2, 4 and 5 producesthe monetary base-multiplier representation ofthe money supply:

(6) Ml, = m MB,,

where m, the money multiplier, is given by

(7) m = (l+k)I(r+k).

According to this representation, a policy actionthat increases R by one dollar, through open

25ince the Fed eliminated reserve requirements on all non-transaction deposits in December 1990, this representationapproximates the current system. For convenience of ex-

position, the discussion to follow abstracts from reservesthat depository institutions must hold on government andforeign transactions balances.

11

49

market purchases of government securities, in-creases MB by one dollar and the money stockby m dollars.~

In this representation, policy actions arereflected not only in MB, through changes in H,but in m, through changes in r. With a simpleadjustment to MB, however, the effects of pol-icy actions on the money supply can be isolatedin one measure. This alternative measure of themonetary base, called the adjusted monetarybase, AMB, reflects both changes in H and r. Itis constructed by calculating the hypotheticallevel of reserves that would have been requiredunder the reserve requirements in existence dur-ing a chosen base period for the current (actual)level of reservable deposits. With the chosenbase period, changes in required reserves dueto changes in reserve requirements, r, areadded to the monetary base.~

Specifically, the AMB is given by

(8) AMB, = MB, + RAM,,

where the reserve adjustment magnitude, HAM,is defined as

(9) RAM, = (r*~.~J.)TCD,.

This adjustment measures the reserves releasedor absorbed by changes in r relative to r*, therequired reserve ratio during the base period.In the base period, RAM is zero and AMB = MB.A decrease in r from its base-period level (r*)releases reserves into the banking system andthereby increases RAM and AMB. Conversely,an increase in r reflects the reserve drain byreducing RAM and AMB.

Combining equations 1, 4, 5, 8 and 9 yields

the following decomposition of Ml,

(10) Ml, = m* AMB,,

where

(11) m* = (l+k)I(r*+k).

In this characterization of the money supply pro-cess, all changes in monetary policy, throughchanges in r or H, are reflected in the AMB.Changes in the multiplier reflect only changesin the public’s desire to hold currency relativeto checkable deposits, changes in the k-ratio.~Because, in this model, the k-ratio is not directlyinfluenced by the policy actions of the Fed, themultiplier is independent of policy.

THE DEMAND FOR CURRENCY~CHECKABLE DEPOSITS ANDNEAR-MONIES: WHAT ISTHE k-RATIO?

Interest in the currency-deposit ratio datesback to Fisher (1911), who was concerned thatthe two forms of money had different incomevelocities. He realized that these two monies areimperfect substitutes: currency is especially use-ful for making small, “face-to-face” transactions,while checkable deposits provide a convenientmeans for making large, ‘out-of-town”transactions.

Fisher reasoned, however, that individualsachieve an ‘equilibrium” in their holdings of thetwo forms of money. The notion of a desired oroptimal k-ratio is based on the assumption thatindividuals decide how much of their moneyholdings they will allocate between currencyand checkable deposits, based on both the rela-tive advantages of each in undertaking an indiv-idual’s planned transactions and their relativeholding cost. This ratio was assumed to be a

IIIIIIIIIIIIIIIII

3Note that because r< 1, m >1. If the assumption that ex-cess reserves are not held were replaced by the assump-tion that they are held in a fixed proportion, e, of TCD,then the denominator of the multiplier would include e aswell, so that the multiplier would be smaller than thatshown in equation 7.

4See Tatom (1980), for example, who discusses the issueof choosing the appropriate base period in light of changesin the structure of reserve requirements. This theoreticdiscussion focuses on the measure of the adjusted mone-tary base constructed at the Federal Reserve Bank of St.Louis. See Garfinkel and Thornton (1991) for a more de-tailed discussion of this measure and a similar one con-structed by the Federal Reserve Board.

‘In a slightly more realistic model, which allows for the factthat depository institutions must hold reserves on govern-

ment and foreign transaction balances, m* = (I +k)l(r(1 +g+f) + k), where g and f denote the ratios of gov-ernment and foreign transactions accounts to TCD, re-spectively. If, in addition, excess reserves were held, asdescribed in footnote 2, m = (1 .+.k)l(r*(1 +g-i-f)+k÷e).These complications can be ignored, however, becausemovements in the observed ratio of currency to TCD ex-plain most of the movements in the multiplier, as will bediscussed shortly.

50

function of a number of economic and socialvariables.°

Given these variables, the demands for cur-rency and checkable deposits were thought tobe strictly proportional to each other. More-over, because individuals are free to adjust theirholdings of the two monies quickly and costless-ly, it was assumed that the actual currency-deposit ratio would deviate from the desiredratio for only a short period of time.’ Accordingto this line of reasoning, all changes in theobserved currency-to-deposit ratio, denoted hereby the K-ratio, are to be interpreted as changesin the desired ratio caused by one of these fac-tors. While not numerically constant, as it wasassumed to be in the previous analysis, the k-ratio was viewed as not being directly affectedby monetary policy actions.

The following discussion, supported by subse-quent empirical analysis, suggests, however, thatthe observed ratio of currency to checkabledeposits can be and has been affected directlyby the policy actions of the Federal Reserve.’This effect can emerge without changing therelative advantages of currency and checkabledeposits or their relative holding cost.

Substitutability, Holding Costs andthe Optimal k-Ratio

There ai-e a number of reasons why onemight question the assumption that changes inthe observed currency-to-deposit ratio necessar-

ily reflect changes in the optimal k-ratio—thatis, changes in the relative holding cost and ad-vantages of currency and checkable deposits.First and perhaps foremost among these is thatthe demand for either of these forms of moneymight depend on a number of special factorsthat are unrelated to the demand for the other.i’hus, changes in the relative advantages ofthese two forms of money might not be empiri-cally important in explaining changes in theratio of currency to checkable deposits.

For example, many believe that currency hasno rival for illegal transactions. The same istrue for foreign demand for U.S. currency bycountries that need “hard currencies” for theirdomestic transactions.’ To the extent that cur-rency is held for these reasons, independent offactors that determine the demand for check-able deposits, policy actions can induce changesin TCD without affecting currency demand. Con-sequently, policy can alter the ratio of currencyto ltD and, hence, the multiplier.”

One might also argue that changes in the rela-tive holding cost of the two monies are not es-pecially relevant for explaining observed changesin the currency-to-deposit ratio. The relativeholding cost of the alternative monies is givenby the difference between the rates of returnon the two forms of money.” The return onholding currency is zero.” Although non-inter-est-bearing checking accounts (demand deposits)have an explicit return of zero, they can yield a

‘Fisher assumed that the optimal k-ratio depended on realincome or wealth, the degree of development of thebusiness sector, population density, relative holding costsand custom and habit. (Checkable deposits were thoughtto be “superior” to currency, although money in any formwas a superior good.) Cagan (1958) extends the list ofdeterminants of the k-ratio considerably. Both he and Hess(1971) attempt to quantify the effects of such factors.

7Cagan (1958) recognized that, at times, restrictions mightprevent the adjustment of the currency ratio. He explicitlyconsidered the case of financial crises where banks sus-pended convertibility. He noted, “At these times individ-uals could not exchange deposits for currency, and thedesired currency ratio undoubtedly exceeded the actualratio...” Without such restrictions, however, individuals arefree to adjust their currency holdings to the desired levelvery quickly and at a low cost.The assumption that there exists a desired currency-to-deposit ratio and that individuals adjust their actual hold-ings of currency to their desired level was made opera-tional for models of the money supply process by KarlBrunner and Allan Meltzer in a series of articles. SeeBrunner (1961) and Brunner and Meltzer (1964, 1968).

effect of policy actions on economic variables such as realincome or interest rates. It is argued that such variablesinfluence the k-ratio or the other ratios that make it up—particularly, the ratio of excess reserves to total checkabledeposits. See Mishkin (1989) for a more detailed discus-sion of this indirect effect.

‘Because it is difficult to account for a relatively largeamount of the total stock of U.S. currency outstanding,one should not be too surprised to tind that, in the ag-gregate, demand for currency and checkable deposits arenot closely related. See, for example, Avery, Elliehausen,Kennickell and Spindt (1986, 1987).

“’This potential influence is illustrated below with an exam-ple. To be sure, longer-run movements in the K-ratio mightbe attributable to some factors that affect the relative ad-vantages for the two forms of money.

“The discussion to follow focuses on the nonbank public’sperspective. The relative holding costs to depository in-stitutions generally will differ.

“Adjusted for inflation, it is minus the expected rate of infla-tion. Note that currency used for illegal transactions yieldsa greater return because of the tax avoidance. For foreign-ers, currency can yield a return that diners from zero dueto the appreciation or depreciation of their home currencyrelative to the U.S. dollar.

‘It has long been recognized that policy actions can havean indirect effect on the multiplier through the presumed

1 51

positive implicit return—for example, free toast-ers for new customers, subsidized accountingand payment services, etc. The return on hold-ing interest-bearing checking accounts is the netinterest paid on these accounts plus free pay-mnent services.’3

The relative holding cost of currency anddemand deposits, however, is unresponsive tomovements in market interest rates because theexplicit returns to both assets are identicallyzero. Surprisingly, the same seems to be truefor currency and interest-bearing checking ac-counts, even since the elimination of RegulationQ ceiling rates in 1986. Interest rates paid oninterest-bearing checkable deposits included inTCD have been unresponsive to movements inshort-term interest rates.’4 Despite the fact thatthe explicit holding cost of currency relative tothat of checkable deposits has changed little, theobserved ratio of currency to checkable depos-its exhibited sharp swings during the 1980s.Thus, it is unlikely that changes in the public’sholding of currency and checkable deposits aredue primarily to changes in their relative hold-ing cost.

The Holding qf Currency,Checkable Deposits and OtherFinancial Assets

Thus, it would not appear that individualssimply shift their money holdings between cur-rency and checkable deposits in response tovariations in their relative advantages or holdingcost. This conjecture would be reinforced bythe fact that currency and especially checkabledeposits are substitutes for other “near-money”stores of wealth, for example, money marketmutual funds. From this broader perspective,the demands for currency and checkable depos-

“Net interest is interest net of service charges. For a dis-cussion of these, see Carraro and Thornton (1986). Thisexplicit return also could be adjusted for inflation.

“Indeed, interest rates on the interest-bearing portion ofTCD,called other checkable deposits (OCD), have changedlittle during the 1980s. The rate on OCD fluctuated be-tween 5 percent and just over 5.5 percent during our sam-ple period.

“This consideration raises a fundamental question—namely,what constitutes an appropriate monetary aggregate? Intheory, monetary aggregation requires the “monetary” ag-gregate to be “weakly separable.” That is to say, it mustbehave as a fundamental commodity with respect to con-sumption and other financial assets. There can besubstitution between assets that compose the aggregate,but not between those that compose the aggregate and

its are seen as being determined simultaneouslywith the demand for near-money assets.”

An important part of the determination of theratio of currency to checkable deposits, there-fore, is the degree of substitutability betweencurrency and demand deposits on the one handand between each of these money assets andnear-money assets on the other. Although theexplicit rates paid on TCD are relatively unre-sponsive to changes in market interest rates,rates paid on near-money assets can vary mark-edly with variations in other market interestrates. The effect of these variations on the pro-portion of Ml held in the form of currency, ofcourse, depends on the degree of substitutabili-ty between near-money assets and the two formsof money. If currency is a relatively poor substi-tute for such assets while TCD is a relativelygood one, the ratio of currency to TCD willchange with changes in rates paid on such near-money assets because of changes in TCD.

The relevance of this substitutability betweenTCD and other near-money assets appears tohave been heightened by the nationwide intro-duction of interest-bearing checking deposits inJanuary 1981. Since then, the cross-price or in-terest elasticity of the demand for checkabledeposits has increased. This increase is hardlysurprising because the payment of interest oncheckable deposits has made them closer substi-tutes for interest-bearing time and savings de-posits. Indeed, some evidence suggests that in-dividuals have shifted a significant portion oftheir “savings” balances into interest-bearingchecking accounts.” Because these saving bal-ances are substitutes for savings and moneymarket accounts that have higher explicit re-turns, the interest elasticity of the demand forcheckable deposits should have risen, while theinterest elasticity of currency demand shouldnot have changed.”

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those that do not. Some evidence suggests that, while cur-rency and demand deposits satisfy this condition for weakseparability, these two assets plus interest-bearing transac-tion balances do not. See, Fisher (1989), for example.Belongia and Chalfant (1989), among others, however, findthat the data are consistent with the notion that the assetsincluded in Ml and a grouping broader than Ml (currencyand total checkable deposits) satisfy the weak separabilitycondition. Thus, the empirical results in this line ofresearch are not conclusive.

“See Sill (1990).“See Thornton and Stone (1991) for a derivation of this

result. These results are borne out empirically by simplelinear regressions of the monthly change in both currencyand other checkable deposits on a scale measure and thethree-month T-bill rate.

52

Thus, changes in interest rates, whether pol-icy induced or not, can have an asymmetric ef-fect on the demands for currency and checkabledeposits, with a direct effect on the proportionin which the alternative monies are heldis Al-though this asymmetric effect is likely to haveplayed a larger role since the introduction ofinterest-bearing checking accounts in generatingfluctuations in the ratio of currency to TCD,policy has induced changes in this ratio moredirectly since the MCA (as discussed below).

•IJEPOSIT SUBSTITUTION ANDTHE MONEY MULTIPLIER

Provided that the demands for currency andcheckable deposits are determined by factorsthat are independent of one another, monetarypolicy actions can have a direct influence on therelative holdings of each and, thus, the multi-plier.’” The channel of influence is most easilyillustrated in the extreme case where the de-mand for currency is completely independentof the demand for checkable deposits. That is,equation 5 is replaced with

(5’) C, = C,

where C is a constant. Equation I also can berewritten as

(1’) Ml, = (1 + K,)TCD,,

where, as defined previously, K, = (C/TCD), isthe observed ratio of currency to TCD.2°

Using equations 1’ and 5’ in place of 1 and 5,the money supply can be written as

(12) Ml, = m~’AMB,,

where m~’= [(1 + K, l/(r* + K,)].

The crucial difference between this expressionand equation 10 is that, here, policy actions at-

fect both the adjusted monetary base and themoney multiplier. To see why, consider a policyaction involving the purchase of T-bills in themarket by the Fed. This policy action increasesthe stock of reserves and, assuming zero excessreserves, ltD. In the ea,lier formulation of hismodel, the K-ratio was assumed to be unchang-ed; the increase in TCD would be accompaniedby a proportionate increase in currency, so thatthe observed ratio of currency to TCD, K, wouldnot change. Thus, the effect of this policy actionon the money stock would be isolated in themonetary base—the multiplier would beunaffected.

ln the modified model, however, TCD increaseswhile currency is constant. Consequently, the K-ratio falls and the multiplier, m’’, rises. In thisinstance, the change in monetary policy is re-flected both in the adjusted monetary base, be-cause of a change in R, and in the multiplierbecause of a policy-induced change in K. Al-though this argument is made in terms of a stat-ic model, the main point, that policy can in-fluence the multiplier, would carry over into amore realistic dynamic model. ‘I’wo of the moresalient features of the longer-run consequencesof this analysis are taken up in the shaded in-sert on page 54.

THE RECENT BEHAVIOROF THE K-RATIO

Figure 1 shows the K-ratio and the observedadjusted monetary base multiplier, Ml/AMB,from January 1970 to November 1990. Note thatthe multiplier is essentially the mirror image ofthe K-ratio; the K-ratio accounts for much ofthe multiplier’s short-run (month-to-month)variability and for the .significant shifts in itslonger-run “trends.” Indeed, as shown in table1, changes in the K-ratio alone explain over 80percent of the month-to-month variahility in

“The same would be expected for changes in the level ofincome. Indeed, Hess (1971) presents estimates indicatingasymmetric effects of both changes in interest rates andincome on the demands for currency and checkabledeposits. It should be emphasized that this effect ofchanges in interest rates on the k-ratio is not the same asthat which was alluded to earlier--i.e., through the relativeholding cost of currency and checkable deposits (see foot-note 8).

‘“Many researchers who have estimated currency demandequations have abstracted from the relationship of curren-cy to TCD. For example, see Hess (1971) and Dotsey(1988).

20Because k is meaningless in this formulation, K, will notequal k. More generally, currency demand can be thoughtof as having two components, one related to TCD as em-bodied in the k-ratio and the other unrelated to TCD, Thatis, C, = C + kTCD,. In this more general formulation, thek-ratio is determined solely by the relative holding cost ofcurrency and TCD and the substitutability between themas discussed above.

C -- .In this case, K, = —a— + k. The restriction in (5),

that k = 0, is imposed only for illustrative purposes.

53

400

.375

150

.325

,300

175

Ratio

I

V

1970 72 74 76 78 80 82 84 86 88 1990

3.1

3.0

2.9

2.8

2.7

2.6

2.5

Figure 1The K-Ratio and the Ml MultiplierJanuary 1970-November 1990

Table 1Regression Estimates of Changes in the Multiplier on Changesin the K-ratio

Period Constant K-ratio SEE R OW.

1/1970-’2/1980 000 --4 355’ 007 598 247(035J f1394~

1/1981-H/1990 001 —3,714’ 005 818 249(184) ~2302)

3!1984-11/1990 001 —3b04 004 854 302

‘i 35) (21 66j

.no.cales slansucal s’gn’ficance at the 5 pe”cent levelAbsolute values of t-s~at,st,csare ‘1 parentheses

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54

The Long-Run Multiplier?That the K-ratio does not appear to he sta- 1°M~ the I OT’(Hgit di ‘iii aiiti gri )WS at a Li in-

tionary tin the SCflM, 01’ being mcdli-reverting) 5tanl Talc’. ii. then 11w log of the denianci I oriaisc’s ci 0 i titerestlng questiofl ol how the cu em ‘ru is givel i byTuagLil t u de of the muI Lipid is deti iiniiwd inthe long run. T\~reAamples are presented to InC — III - h ln1(’l),shIJ\~ that the multiplier is not I nva i ‘iant to

L\ here I denotes a time tivnd 000 h IS a toll-nionet arv pithev and t IW “ bflgrun multiplier, slant.’ t\ hat haiflwfls to the the K.ratlci in tlit’

- . . . 1(111 &~jun is IIvWII15 Iil(’d h~’t he Tout n grm~I hi~c’riti( al lv dc’penclel I on the sped1it’ atsons of

tales ol I orc’1i411 and tiiinit’SLII’ tientailils lot’tiw demands br cii event v and RD.~11in Iir~te.xa iii pie assunics that i he deniai ul en en-i u ‘V. I’ or exaLt I pIe. as’unit’ that t he dc

Inc real currency is determined snlel~iv real mamid (or nominal ‘1(1) i, fi~Iei’r1ilTiedscjli’lvincome, while the dtmiaiid for real TCI) is In nominal iticotlie and that notnituil inc utilecli’ term1ned both by real Inc. nine arid the not ii- gi’()fl szi( a nil ml out rate cl—al least in t hema’ interest iate, wIuiri~‘IfS) is inveu’M!ly lcn ig ‘oil If ci is less than or equal tii h (I - hIrelated lo the hotel’, ibis e~aiiiph’captures the N-ratio ullI rise n flhotil hound •~ndthe

the notion that the cicnnatid t’oi ‘IC!) is di’ter- nudtipliec ~~ill approach unity. ii 0 Ts greatci’mined si molt aiieousiy ~vitIi the cieiiia nO s for thai Ii I I -hI the K- ta Un LUll oppm’oac’h / nit

other ncar-Ilionht’S. For siniplucut>. these urn1 the mniiltipliet \\ 311 apptt}&tl’h I r - ~~herecleniancis arc’ assumed It) he linear in natural P is the base-period reset” I’ I et]uii’vTiWiit (seelogs, and the Tic-ome elasticities of the Use tc”.t fur more cietailsl.

\ole howeL er thai. in Ins exampit’ theden ian Os for t-urrenev and III) an’ assti mc’dto I ic eq u aI. I ‘nOr r these assumption the luuws 011 tinillLpller Is nnl iiidi.pendi’hl ul (flu—

- ic-i ac’hhin’. I or c~aiiiph’.a~stHn(’thatrio I aral log ol the K -ratio, I riK. dt~)vfldMstudy ‘ . -

on the na I w a I to” of the nomi I id~In tel est -

0>1) li-li) so that hit’ ilitultIplici i~up—rate and is pcusitLveI~’related ~o ii. B~ mIlL’- . -- .

1i1cuat.’iIlIig I I’ . \ci\\ ;jssti[1iI, lhiat a t-IIOIIW’ ii’

~itir\ reduce’ the gr’n\ th rate ub 1(1) atid.eni~tng(lie ric,niiui’al interest rate ~ hirlithus flit’ rate at ml ni nun anti tlie’’nu\\ tli

eqtials the meal latc’ plus a pr(’lilitittI (cii- ox- . . -

pected future iii!lationi, niotletal ~‘ politY . .

nitt’ cit tioliiiliid ~ ~t the u’T’\ leastthii’ h,uhc~change ~ OLilti (~ilLiSt’ 11W 1iniEttpl~

would at feet the Iung.rtiti niultiphiem . . . -

To see n h~. assuriiC that a change ii polity It) appi’ucic’Il its Iong-t~uliecjtlilihl’ILim aloeraises n’servC grm~th permanently. If this iii- niiirc sici” l~. as it di’i~is dolL a 0. tridet’cl ifct-east’ results in a perni&tnc~it increase in the tic’ grm\ th iate of flU ,lon c’d (ci tlic’ poiilactual and anticipatE’d rates of inlt’iticiil. time ~lti’fl’ 0< hI 1-li) the long-i’WI mtiltiplWinominal Interest rate ~ III rise. ‘l’he pernian- COLIIO ciitiL et’ge to I rather than I i’.

rut1’,- higlwr Ie~el nI the noniitiah intel eM rateUI rotirsi’. here art’ .1 flhtllllWi iii other in-~ ill inn ease the level at the K ia tio (‘all Si)ig a

ti’resnhmg ~o~silnhties. J hi’ IflaJOi’ points that.en mu the long -liii the nuiltipitet’ de;ic’t id—permanent redo’ non in the mttltipllem’.

Thc’ sec ond evainpie assunies that the cit’ on ranmietary polity and that he exact ~aIuemood for corm’enc’.\’ i~dih cii lat-gely In t’orres of the long-ian nmhipht’r Imt’tt\ eOO I dull 1 I

exti’t’0~l to the domestic ei’oiuoiny, sos. for- clc’pends r-miticahl) tiii tIn’ sj,t’r~Iit’atlt)ilS tiE liii’vigil dttnlanrl br i-S. rurreflt’~ it also as- ch’niand~for rLirreiw.\ and TM) an’ noiit’tlie-stones that the domes1 ic ciettiand ‘or comm-en- less ~ahcl Rt’lOUt’ 0 nieawngltil ‘long rumscv is determtlimied ,olt’lv hs the relative represc’minltion oi the numitipliei c’ahi he oh-holding cost of curretily ~. id) and that tamed il is nt’n’ssai’Y to 4pt’rit~ c’ai’c’full~thi’ cost is ccjnstalit. .\gain. these elation- both ilir’ cic’mmianct ‘cii cllrn’iit’.\ and the tie-ships are assume’1 io lie linear in the natural omnd toe IC ft-

‘The parameler h might be thouqht oi as the ‘og of the op- ~Nornthat. because the multiplier ~5 bounded. Ml and AMBumal s~ratioretiecttng only the ‘dative advantages and must be cointogratedcosts ot curuency and TCD

55

Figure 2The K-Ratio, Currency and TCDRatio.450

,425

,400

.375

350

325

.300

,275

Billions of Dollars600

1970 72 74 ‘76 78 80 82 84 86 88 1990

changes in the multiplier since the implementa-tion of the MCA2’ The MCA tightened the linkbetween the K-ratio and the multiplier byreducing or eliminating other sources of varia-tion in the multiplier.22 While the MCA was im-plemented in a series of steps from November1980 to September 1987, its major featureswere almost fully implemented by Februaryj93423 Since then, changes in the K-ratio aloneexplain over 85 percent of changes in themultiplier.

21The Durbin-Watson statistic for each of the equations in-dicates significant, negative first-order serial correlation,Because we are primarily interested in the explanatorypower of changes in the k-ratio as measured by the ad-justed A-square, however, maximum likelihood estimatesof the equations adjusted for serial correlation are notreported here. Nonetheless, there are no substantive dif-ferences between the maximum likelihood estimates andthose reported in table 1.

22See Garfinkel and Thornton (1989) for details.

500

400

300

200

100

0

The Relationship Between TotalCheckable Deposits and theK4latio

Figure 2 shows the K-ratio, currency andTCIJ. The behavior of these series suggests thatchanges in the trend of the K-ratio are associ-ated more closely with changes in the trend ofTCD than with changes in the trend of curren-cy growth. For example, the sharp rise in the

23The MCA was first implemented in November 1980 andwas fully phased-in by September 1987. The empiricallysignificant features of the act were completed with theFed’s adoption of contemporaneous reserve requirementsin February 1984, so the sample was broken at this point.See Garfinkel and Thornton (1989) for a discussion ofthese changes and their effect on the multiplier.

IIIIIIIIIIIIIIIIII

JULVIAtJGuST 1991

56

Figure 3Deviations of the Growth Rates of the K-Ratioand Currency from Their MeansJanuary 1970 thru November 1990K—Ratio

40

30

20

10

0

~i0

-~ 20

—30

K-ratio in the early 1970s is associated with aslowing in the growth of TCD. The decline inthe K-ratio in the early 1980s and its subse-quent rise are clearly associated with a sharpacceleration in the growth of TCD followed bya sharp deceleration in its growth.

That TCD accounts for much of the short-run variation in the K-ratio also is evidenced byfigures 3 and 4, which show, respectively, devi-ations of the growth rate of the K-ratio from itsmean and deviations of the growth rates of cur-rency and TCD from their respective means. As

shown in the figures, the month-to-month vari-ability in the growth of TC]J is considerablylarger than that of currency. The variability ofTCIIJ more closely matches the variability of theK-ratio than does the variability of currency.While the growth rates of the K-ratio and TCDare highly, inversely related, there is littlepositive association between the growth rate ofthe K-ratio and the growth rate of currency.

This observation is verified in table 2, whichshows the simple correlations between themonthly annualized growth rates for currency

Currency40

30

20

10

0

10

20

—301970 72 74 76 78 80 82 84 86 88 1990

ccncnM P V~9M’WflFPT loomS

1 57

IIIIIIIIIIIIIIIII

Figure 4Deviations of the Growth Rates of the K-Ratioand Total Checkable Deposits From Their MeansJanuary 1970 thru November 1990K—Ratio TCD

40

and the K-ratio and for TCD and the K-ratio forfour periods of roughly equal length betweenJanuary 1970 and November 1990. tf variation inthe K-ratio were simply due to shifts betweencurrency and TCD, its variation would be equallyattributable to variation in currency and TCD.

This is not the case, however. The growthrates of currency and the K-ratio were positive-ly correlated during only two of the four peri-ods. They were negatively correlated in theother two, although the correlations are not sig-nificantly different from zero. In contrast, thereis a strong, consistent negative correlation be-tween the growth rate of TCIJ and the K-ratioduring all four of the periods. Figures 3 and 4and the correlations reported in table 2 clearlysuggest that month-to-month variability in the

30

20

10

0

—10

—20

—30

Table 2Correlations Between the MonthlyGrowth Rate of the K-Ratio and theMonthly Growth Rates of Currency andTCD

K-ratio K-ratioPeriod and currency and TCD

1/1970-12/1974 368’ - 901’W975-12/1979 016 911’1/1980 12,1984 112 - 95511985-11,1990 266 — 951’

- nolcales statistical signi’-cance at the 5 perce-il level

1970 72 74 76 78 80 82 84 86 88 1990

JULWAUGUST 1991

58

K-ratio is driven largely by movements in TCD.

Finally, as shown in figure 4, periods of per-sistent deviations in the growth rate of TCDabove (below) its mean are associated with per-sistent deviations of the growth rate of the K-ratio below (above) its mean. Consequently, boththe short and long-run movements of the K-ratio are associated with movements in TCDrather than currency. The apparent importanceof TCD in influencing the K-ratio suggests thatK-ratio changes have not occurred simplybecause of variations in the relative advantagesand holding cost of currency and TCD. That isto say, changes in the K-ratio have not been asimple result of the public’s desire to shift thecomposition of Ml between currency andcheckable deposits.

The Link Between Total CheckableDeposits and Reserves

Movements in the multiplier appear to be deter-mined primarily by movements in the K-ratio,which, in turn, appear to be determined pri-marily by changes in TCD. The question that re-mains is what determines the stock of TCIJ out-standing? The models of the money supply pre-sented above provide a simple answer: giventhe reserve requirement ratio, TCD is deter-mined solely by the amount of reserves suppliedby the Federal Reserve. This strong link arisesin this model because reserves are assumed tobe held only to support checkable deposits24

Prior to the MCA, commercial member bankswere required to hold reserves against all time

and saving deposits, while non-member banksand other depository institutions were not re-quired to hold reserves against their transactiondeposits in Ml. Because of these factors, thelink between TCD and reserves was not particu-larly strong. In reducing or eliminating reserverequirements on a number of non-transactionaccounts and extending reserve requirements toall depository institutions, however, the MCAsignificantly strengthened the relationship be-tween TCD and reserves.

The effect of the MCA is illustrated in table 3,which shows the results of simple linear regres-sions of changes in TCD on changes in total re-serves, ‘FR, for several periods between January1970 and November 199023 The regression equa-tions in this table (and in subsequent ones) areintended to be illustrative and should not be in-terpreted as alternative models for the moneysupply process. (See the appendix for details.) Inall cases but the initial phase-in of the MCA,there is a statistically significant relationshipbetween changes in TCD and TR. The strengthof the relationship, as measured by the adjustedH-square, however, increases after the imple-mentation of the MCA.2°The adjusted H-squareincreases from .06 before the MCA to .67 afterthe MCA. All of this improvement emerges inthe period after February 1984, when the ad-justed R-square increases further to .83.27 More-over, the reciprocal of the estimated coefficienton TR is .124, very close to the marginal re-serve requirement of .12 during the latter peri-od. Indeed, the null hypothesis that this coeffi-cient is equal to 1/12 cannot be rejected at the5 percent significance level (the t-statisticis 0.82).

241n reality, of course, depository institutions hold excessreserves and are required to hold reserves on transactiondeposits other than those included in Ml.

25The total reserves measure used here is total reserves ad-justed for reserve requirement changes, prepared by theFederal Reserve Board.

26The Durbin-Watson statistic for the first time period sug-gests that there is significant first-order positive serial cor-relation, as would be expected given the likelihood ofmisspecification (see the appendix). Maximum likelihoodestimates of this equation adjusting for first-order serialcorrelation confirm this result. The estimated coefficient offirst-order serial correlation is -.314 with a t-statistic in ab-solute value of 3.29. Nevertheless, the parameterestimates after adjusting for serial correlation are generallyclose to those reported in table 3, and they are statisticallysignificant. More important, the adjusted A-square only in-creases to .147; hence, the dramatic rise in the adjustedR-square in the 1980s is not due to the fact that totalreserve captures the autoregressive part of TCD.

27The switch from lagged to contemporaneous reserve ac-counting in February 1984 might explain some of this ap-parent improvement. To account for this possibility, thechange in TCD was regressed on both the contemporan-eous and lagged change in TA. In no case was the coeff i-cient on lagged TA statistically significant from zero at the5 percent level. Indeed, the results differed little fromthose reported in table 3. That the switch from lagged tocontemporaneous reserve requirements is of no significantconsequence is consistent with the conjecture of Thornton(1983) and the empirical evidence presented by Garfinkeland Thornton (1989). The relationship between TR andTCD will likely become even stronger given the recentelimination of reserve requirements on all time and sav-ings deposits.

FEDERAL RESERVE BANK OF St LOUIS

II

Table 3

I Regression of Changes in TCD on Changes in Total ReservesTotal -

I Period Constant reserves SEE A’ OW.1/1970-12/1980 .795’ 1.870’ 1.418 .062 1 35(5.72) (3.10)

I 1/1981-11/1990 .742’ 7264’ 2.081 .674 223(342) (15.64)1/1981-2/1984 1 765’ 2.704 2.414 067 2.06

I (3.81) (1 92)3/1984-11/1990 .441 • 8.082’ 1 676 .832 1.94(2.09) (19.90)

I ‘ indicates statistical significance at the 5 percent levetAbsolute values of t-statistics are in parentheses

ITable 4

I Regression Estimates of Changes in the Multiplier on Changesin Total Reserves

Total -

Period Constant reserves SEE A’ D.W.

I 1/1970-12/1980 — 003’ — .003 .011 .004 I 702 86) (0.67)

1/1981-11/1990 — 004’ .016’ 011 275 2.12(3 28) (6.77)

I 1/1981-2/1984 002 - 003 .014 — 023 1 82(0 77) (0.42)

3’1984-1i/1990 —.006’ 020’ .007 603 231

I ~6.05) ~11

- indicates statistical significance at the 5 percent levelAbsotute values of t-statmstmcs are in parentheses

liIisits tIl(’ lSStllllF)lit)l1 Illll J)(IIi’\ ;ii’ti iii’, luiti110 it tt’Ct DII I hi’ nitiltipilii’r \\il.” 1 rl’d,Oll,thIi’

It~(liking ;NsliOlpLiuIl ht’Ioiv tilt’ adoimtion üI thi-\IL \. lrmdt-ed change7. ill he llltlitipIiit ale lull—

ht’ aho\ I’ ana!~Sl7. sl_lgg(’St~tilill I)ohlr\’ artmomp~ .- . . . . flil’fl’Idted ~ itli rhalige7. in 114 dining the ii-—

rilIki ru-rI a stiouig el feel Dm1 the mnultiplu-m’ mlnod emichmt’’ I )ec-eumihi’r’ I 9IM1.

I I lie I ISO’, I able I ‘lion’, that this I—, titi’ ease.llmi~e,in ‘I Ft account tOm’ 60 pri’c’ot ol the I lii-’.t’ ii’.tlIls siiggi-—~t thaI there sIlillilci heill liii’ ullLlhli})Iier —mci’ \lnn El (It I 1)51. a dranmatic change ill liii’ l’eLttiOllShi1) hi-Inti-ii

I liii- l:uIik’ il-i, —.Ilo~\, (hat herau’,i- @1 the nose \I I aiitl I’ll in the I 11507,. Smniplr cegres-~iomt—.ollink hetu tell i (“,et’\ e’ hid total clleck~lblede— changes it) ‘tI I oil i’h~tuigi’s mi ‘Ft amid chiamlge’—. H)

(V1~l)SiiST 1001

Table 5Regression Estimates of the Change in Ml on the Change onTotal Reserves and the Change in the Adjusted Monetary Base

AdjustedTotal monetary

Period Constant reserves base S E R 0 W

1I1970-12/1980 1328 2O79~ 1.529 066 128(8 86) (3 20)

185 2.513 1312 312 1.54(0 74) (7 73)

1/1981-11/1990 1888 7251 2 149 659 213(834) (1512)

280 2773 2939 .361 1.39(053) (823)

1/1981-2/1984 2613 2.910 2554 070 200(5 33) (1 95)

1113 1839 2369 .200 186(15) (320)

3/19841 /1990 1696 7995 1746 817 173(7.73) (18.89)

1023 3158 3138 407 133(1 43) (7 48)

indicates statis cat smgntficance at the 5 percent levelAb otu e values of t statistics are in parentheses

the AMB I epor ted in table 5 beai this out.23 TR a rather stmple traightfot n aid appi oach toexplains a i’d itit cIt small amount of the ~aria money stock control n as tmplied—namc It totion in changes in Ml before MC \ and ot cc 80 target the let ci of the adjusted monetart h tsepercent of the tariation of changes in Mi since consistent tt ith a money stock target conditionalearly 1984. ‘the table also shott s that the cx- on a for cc ist of the multiplier, n her e the multi

plar~atory potter of the monetary base has in- plier foreca t itas not conditional on the targetcreased since the 1CA. as n ould be etpected.~ setting for the monetary base. I his notion also\onetheless the explanatort pon er of the IAMB implied that the adjusted monetary base is thedeclined significantly m elatit e to that of I H. be t indicator of the effects of polict actions on

the money stock.

The realization that the multiplier is not in-

I dependent of pohct actions suggests that themonetary ba -e might not be the best indicator

Prior to the MCz\ tthen it appeared that the of policy actions on the monet stock and thatmultiplier st as independent of policy actions ret ising the simple empirical models of the

8Again the Durbin-Watson statistics indicate significant that changes in TA explain much more of the variation inserial correlation, especially when the AMB is used as the changes in Ml in the 1980s than do changes in the AMBindependent variable. In no case did an adlustment for even allowing for significant first-order serial correlation.seria] correlation using a maximum likelihood technique 295ee Garfinkel and Thornton (1989) for a discussion of thisalter any of the substantive results presented in table 5 r~ointThat is these results too suggest that there is a markedincrease in the explanatory power of TA in the 1980s and

1 61

money supply process to account for the effectsof policy actions on the multiplier could resultin improved money stock control. These issuesace discussed briefly in this section.

The Adjusted Monetary Base as an.Indica for of Police Actions on theMoney Stock

The adjusted monetary base continues toreflect all policy actions—changes in both re-serves and reserve requirements; however, itdoes not fully capture the effects of these ac-tions on the money stock. Indeed, changes inMl are now more closely linked to changes inTB than to changes in the IAMB. Consequently,it now appears that total reserves, adjusted forreserve requirement changes, is a better indica-tor of the effects of monetary policy actions onthe money supply than is the adjusted monetarybase.

Furthermore, the quantity of currency out-standing is demand-determined. Consequently,unlike adjusted reserves, the adjusted monetarybase can give misleading signals of the course ofmonetary policy when there are exogenous shiftsin the demand for currency.

To take a concrete example, currency growthaccelerated markedly beginning about December1989.~°This acceleration was accompanied bya sharp acceleration in the growth of the ad-justed monetary base from 3.4 percent in 1989to 8.4 percent in 1990. Such a sharp rise inbase growth would tend to indicate that mone-tary policy had eased. But the growth of ad-justed reserves and, thus, ‘I’CD indicate a sub-stantially weaker easing of policy. TCD increas-ed at a 1.2 percent rate in 1990 compared witha -1.3 percent rate in 1989. Of course, the ap-parent exogenous increase in the demand for

currency caused the K-ratio to rise and the mul-tiplier to fall, so that Mi grew slowly relative tothe monetary base during the period.” Becausethere is now a closer link between TB and MIthan between the IAMB and Ml and because TBis less likely to give misleading signals, TB islikely to be a better indicator of both monetarypolicy and the effects of policy changes on themoney stock.

The Multiplier .zI.pproach toMoney Stock Control

That the multiplier is not independent ofpolicy actions also has important implicationsfor the multiplier approach to money stock con-trol. Taking this approach, the target level ofMl is achieved by forecasting the multiplier,then supplying the amount of the adjusted mon-etary base necessary to hit the desired Ml tar-get-32 lf, however’, the multiplier is a function ofopen market operations, policymakers must alsopredict the effect of their actions on the multi-plier. That is to say, the multiplier approach tomoney control should be modified to take ac-count of the effects of policy actions on themultiplier. Taking account of such effects un-doubtedly will improve money control over thesimple approach that assumes independence be-tween the multiplier and policy actions. Themagnitude of this improvement depends on howaccurately the effects of policy actions on themultiplier can be forecast. To the extent thatvariations in the multiplier ace largely explainedby variations in the k-ratio and these variationsare, in turn, largely influenced by policy (espe-cially in the post-MCA period), such a modifica-tion could produce a substantial improvement inmoney stock control.”

IIIIIIIIpIIIIIIII.

lcWhile the exact cause of this acceleration remains un-clear, many attribute it (at least in part) to currency exportsto South American and Eastern bloc countries.

31An equally interesting, but less frequently discussed, epi-sode occurred during 1989 when, after remaining fairlyconstant, currency growth slowed abruptly. During thisperiod, the K-ratio rose rather than fell, as one might ex-pect given the apparent shift in the demand for currency.The increase in the K-ratio was driven by negative growthin reserves and, hence, TCD during this period.

325ee Balbach (1981), Hafer, Hem and Kool (1983), andJohannes and Rasche (1979, 1987) for a discussion of thisapproach and for alternative methods that have been usedto forecast the money multiplier.

“Note that the multiplier approach can be more difficult toimplement. Most notably, the control problem becomes

nonlinear. One alternative approach would be to simplyforecast the level of currency, then supply the reservesnecessary to hit a target level of TCD. The target level ofTCD would have to be consistent with both the Ml targetand the forecast level of currency. Whether this or themultiplier approach, suitably modified to account for theeffect of policy actions on the multiplier, would providegreater monetary control is an empirical issue well beyondthe scope of this paper. Both approaches will produceforecast errors when there are unexpected shifts in the de-mand for currency. The real issue is whether better esti-mates of the K-ratio can be obtained by estimating thenumerator and denominators separately than estimatingthem together. This is an empirical issue. Nevertheless,this alternative approach could be simpler to implementand might provide superior control if reasonably accurateforecasts of currency can be made.

62

SUMMARY

This article has examined closely the standardmultiplier model of the money supply process,specifically questioning the view that the ad-justed monetary base multiplier is independentof the policy actions of the central bank. Be-cause the demand for currency depends on anumber of factors that are unrelated to the de-mand for checkable deposits (and vice versa) andbecause the stock of checkable deposits hasbeen more closely tied to the quantity of re-serves supplied by the Federal Reserve since theimplementation of the MCA, changes in mone-tary policy result in changes in the ratio of cur-rency to checkable deposits and, consequently,changes in the multiplier. Hence, the FederalReserve’s monetary policy actions are reflectedboth in the adjusted monetary base and themoney multiplier.

Theoretical considerations suggest that themultiplier has never been independent of policy.The elimination of reserve requirements onsome non-transaction accounts and the exten-sion of Federal Reserve reserve requirements toall depository institutions has greatly increasedthe association between checkable deposits andreserves. These changes have increased signifi-cantly the association between changes in mone-tary policy actions and changes in the multiplier.That the multiplier is affected by policy actionssuggests that money stock control using themultiplier model would be enhanced by takingthe effect of policy actions on the multiplier intoaccount. How much improvement can be expec-ted with this modified approach and how effec-tive alternative approaches to monetary controlcan be is left as a topic for further research.

REFERENCES

Avery, Robert B., George E. Elliehausen, Arthur B.Kennickell, and Paul A. Spindt. “The Use of Cash andTransaction Accounts by American Families.” FederalReserve Bulletin (February 1986), pp. 87-108.

______ - “Changes in the Use of Transactions Accounts andCash for 1984 to 1986.” Federal Reserve Bulletin (March1987), pp. 179-96.

Balbach, Anatol B. “How Controllable is Money Growth?,”this Review (April 1981), pp. 3-12.

Belongia, Michael 11, and James A. Chalfant. “The Chang-ing Empirical Definition of Money: Some Estimates from aModel of the Demand for Money Substitutes,” Journal ofPolitical Economy (April 1989), pp. 387-97.

Brunner, Karl. “A Schema for the Supply Theory of Money,”International Economic Review (January 1961), pp. 79-109.

Brunner, Karl, and Allan H. Meltzer. “Some FurtherInvestigations of Demand and Supply Functions forMoney,” Journal of Finance (May 1964), pp. 240-83.

______- “Liquidity Traps for Money, Bank Credit, and InterestRates,” Journal of Political Economy (January/February1968), pp. 1-37.

_____ - “Money Supply?’ in B. M. Friedman and F. H. Hahneds., Handbook of Monetary Economics (Elsevier SciencePublishers, 1990).

Cagan, Phillip. “The Demand for Currency Relative to theTotal Money Supply,” Journal of Political Economy (August1958), pp. 303-28.

Carraro, Kenneth C., and Daniel L. Thornton. “The Cost ofCheckable Deposits in the United States,” this Review(April 1986), pp. 19-27.

Dotsey, Michael. “The Demand for Currency in the UnitedStates?’ Journal of Money Credit and Banking (February1988), pp. 22-40.

Fisher, Douglas. Money Demand and Monetary Policy (TheUniversity of Michigan Press, 1989).

Fisher, Irving. The Purchasing Power of Money (Augustus M.Kelley, 1911).

Garfinkel, Michelle R., and Daniel L. Thornton. “The LinkBetween Ml and the Monetary Base in the 1980s,” thisReview (September/October 1989), pp. 35-52.

1991).“Measuring the Monetary Base?’ mimeo (February

Hafer, R. W., Scott E. Hem and Clemens J. M. Kool. “Fore-casting the Money Multiplier: Implications for Money StockControl and Economic Activity?’ this Review (October 1983),pp. 22-33.

Hess, Alan C. “An Explanation of Short-Run Fluctuationsin the Ratio of Currency to Demand Deposits,” Journal ofMoney Credit and Banking (August 1971), pp. 666-79.

Johannes, James M., and Robert H. Rasche. “Predicting theMoney Multiplier?’ Journal of Monetary Economics (July1979), pp. 301-25.

______ - Controlling the Growth of Monetary Aggregates(Kluwer Academic, 1987).

Mishkin, Fredric S. The Economics of Money Banking andFinancial Markets, 3rd. ed. (Little, Brown and Company,1989).

Plosser, Charles I. “Money and Business Cycles: A RealBusiness Cycle Interpretation?’ in Michael T. Belongia, ed.,Monetary Policy on the 75th Anniversary of the FederalReserve System (Klumer Academic Publishers, 1991).

Sill, Keith. “An Empirical Examination of Money Demand inan Intertemporal Optimizing Framework,” unpublishedpaper (University of Virginia, 1990).

Stone, Courtenay C., and Daniel L. Thornton. “Solving the1980s’ Velocity Puzzle: A Progress Report,” this Review(AugustlSeptember 1987), pp. 5-23.

Tatom, John A. ‘Issues in Measuring An Adiusted MonetaryBase?’ this Review (December 1980), pp. 11-29.

Thornton, Daniel L. “Simple Analytics of the Money SupplyProcess and Monetary Control,” this Review (October1982), pp. 22-39.

“Lagged and Contemporaneous Reserve Accoun-ting: An Alternative View?’ this Review (November 1983),pp. 26-3a

Thornton, Daniel L., and Courtenay C. Stone. “FinancialInnovations: Causes and Consequences,” in Kevin Dowdand Mearyn K. Lewis, eds., Current Issues in MonetaryAnalysis and Policy, (MacMillan Publishers, 1991).

63

AppendixA Model of the Money Supply Process

One might be tempted to interpret the regres-sion equations in the text as representing alter-native models of the money supply process; how-ever, the reader is cautioned not to do so, In-deed, as the article suggests, some existing mod-els of the money supply process are misspeci-fied. This appendix illustrates the bias of someof the regression equations estimated in thearticle.

The discussion in the paper suggests that, sincethe MCA, there is a very simple linear relation-ship between TCIJ and TR of the form

TCD1 = a + bTR1 + e,,

where the coefficients a and b are constantsand e is a residual error that is assumed to bewhite noise. The error term arises because somereserves are held against transaction depositsnot included in TCD and because depository in-stitutions hold excess reserves. The constantterm, a, enters the equation because a lowerreserve requirement for a tcanche of checkabledeposits exists and because some of the vari-ables omitted from this equation might havenon-zero means. If TR is correctly adjusted for’changes in reserve requirements, including theannual change in the deposit tranche, then thecoefficients a and b should be constant, whereb is the reciprocal of the marginal reserverequirement—that is, b = l/.iZ = 8.33. Thediscussion and the empirical evidence in thepaper further suggest that currency holdingsare independent of TCD, so that ç is simply ex-ogenous from the perspective of money stockcontrol.

If this representation is true, then a regres-sion of Ml on the monetary base is misspeci-fied, because it imposes a restriction that is in-consistent with the process generating the data.‘I’o see this, consider the following regression

specification:

(A.i) Mi1 = g + sMB1 + q,-

Given the definitions of Ml and MB, this equa-tion can be rewritten as

(AZ) C, + TCD, = g + hTR1 + jC~+ q~.

With the restriction h =j, equation A.Z is iden-tical to equation A.i. The above analysis, how-ever, suggests that the coefficient h shouldequal 8.33 and the coefficient j should equal i.If this is the case, imposing the restriction thatthese coefficients are equal will be resoundinglyrejected by the data.

To test this hypothesis, first-difference specifi-cations of equations A.I and A.2 are estimatedusing monthly data for the period from March1984 through November 1990. These estimatesuse Federal Reserve Board data for the adjustedmonetary base and total reserves, adjusted forchanges in reserve requirements. These datacome close to satisfying the identity that themonetary base is equal to the currency compo-nent of the money supply plus total reserves.These estimates ace presented in table A.i. inthe unrestricted version of the equation, neitherthe null hypothesis that h = 8.33 nor the nullhypothesis that j = I can be rejected at the 5percent significance level. The t-statistic for thetest that h = 8.33 is .59 and the t-statistic for thetest that j = i is .25. Hence, it is not surprisingthat the restriction that h = j is soundly rejectedby the data.

It is interesting to note that imposing thisrestriction biases the coefficient of the mone-tary base multiplier away from its true value.The estimated multiplier of 4.005 is nearly 50percent larger than its average value during thisperiod. This bias emerges because of an omittedvariable.

To see this, note that equation A.2 could berewritten as either

(A.3) Mi, = g + hMB, + (j-h)C1 +

or

(A.4) Mi, = g + jMB~+ (h-j)TR, + q1.

Hence, equation A.i can be obtained by omit-ting C, from equation A.3 or TR, from equation

IIIIIIIIp

IIIIIIII

~lflV!A~’fl’~~r IEW

Table AlEstimates of Equations Al and Al

Constant AAMB ATA ,SC SEE OW

2099 4.005 3138 407 110(249) (748)

.590 8090 908* 1690 828 193

(121) (1967) (251)

*Indl~tesstatistical significance at the 5 percent level

Absolute values of t statistics are tn parentheses

Table A 2Estimates of Regression of ATCO on ATR and AC:March 1984 November 1990

Constant ATR AC SEE 14 OW.

581 8069 =.115 1685 830 193

(119) (19.67) (032)tindrcates statistical significance at the 5 percent level.

Absolute values oft statistics are in parentheses

A.4. In the former case the estimate of h is bias- TCD and currency, but is not significantly dif-ed downward (4.005 vs. 8.33); in the latter case fecent from zero. Given this independence, it isthe estimate of j is biased upward (4.005 vs. 1). hardly surprising that cegre sions of changes inFurthermore, the equation exhibits serial cor- Mi on TB and changes in TCD on JR producerelation, a common indicator of misspecification. nearly identical r’e ults. Comparing the results

These results are not too surprising given that in table A.i with those in table 5 hows that thethe demand for currency appears to be indepen coefficient is biased downward slightly whendent of the demand for TCD, a illustrated in Ml is regressed on TB I his occurs because C’,table AZ, which shows the result of a cegces- is omitted from the right-hand side of the equa-sion of changes in TCD on changes in I B and tion and because of the weak negati~e associa-changes in C. The coefficient on the change in tion between changes in both C,and TCD, and,C is negative, indicating a substitution between hence, changes in TB, -