The Multiplier Approach to the Money Supply Process: a Precautionary Note

Home , Money multiplier, Multiplier (economics)

Michelle 11. Garfinkel and I Daniel L. Thornton

Michelle R. Garfinkel, an assistant professor at the University I of California at Irvine, was a senior economist at the Federal Reserve Sank of St. Louis while this paper was written. Daniel L. Thornton is an assistant vice president at the Federal Reserve Sank of St. Louis. Richard L Jako and Scott Leitz pro- I vided research assistance. I I The Multiplier Approach to I the Money Supply Process: I A Precautionary Note I

HE MULTIPLIER MODEL of the money for both checkable deposits and currency are supply, originally developed by Brunner (1961) determined by the same factors, and that indi- and Brunner and Meltzer (1964), has become viduals can quickly and costlessly alter their I the standard paradigm in macroeconomics and holdings of currency and checkable deposits to money and banking textbooks to explain how achieve the desired proposition of the two alter- 1 the policy actions of the Federal Reserve in- native forms of money. Open market purchases, fluence the money stock. It also has been used for example, increase reserves and consequently I in empirical analyses of money stock control checkable deposits; but the public simply shifts and the impact of monetary policy actions on from checkable deposits to currency until the other economic variables. (unchanged) desired ratio of currency relative to I checkable deposits is once again achieved. Be- One important feature of tins model is that it cause policy actions have no impact on the pub- decomposes movements in the money supply in- lic’s holdings of currency relative to checkable I’ to the part that is due directly to Federal Re- deposits, the multiplier does not depend directly serve policy actions (the adjusted monetary base) on the policy actions of the Fed. and the part that is due to changes in technology and the tastes and preferences of depository in- This article investigates the theoretical and I stitutions and the public (the money multiplier). empirical validity of the key feature of the mul- In this decomposition, the multiplier is assumed tiplier approach. In theory, the multiplier is in- to be independent of the policy actions of the dependent of the policy actions of the Federal central bank. The independence is implicitly Reserve only if the demands for currency and I predicated on the assumptions that the demands checkable deposits are determined by identical

1 I The notion that the multiplier is independent of Federal nomic principles. The argument presented here that would Reserve actions—implicit in the work of Brunner and suggest such independence is implicit in works as early as Meltzer (1964, 1968) and, more recently, in Plosser (1991) Fisher (1911). I —has never been demonstrated rigorously with micro-eco- 48

factors and if , conditional on these factors, these cash in the vaults of depository institutions) in demands are strictly proportional. From an em- the banking system, R: pirical perspective, this condition is necessary but not sufficient; the degree to which the mul- (2) MB,= C,+ R,. tiplier is influenced by policy actions also depends on the strength of the relationship be- Currency, supplied by the Federal Reserve on tween policy actions and checkable deposits. demand, reflects the portfolio decisions of the An empirical analysis shows that most of the public rather than monetary policy actions. Re- variability of the observed ratio of currency to serves, in contrast, can be affected directly by checkable deposits is due to variation in check- the Fed’s sales or purchases of government se- able deposits, and thereby suggests that the de- curities in the open market. mand for currency is not strictly proportional For simplicity, assume that the Federal Re- to the demand for checkable deposits. Prior to serve has a simple system of reserve require- the Monetary Control Act of 1980 (MCA), how- ments, with required reserves, RR, given by ever, the link between reserves and checkable deposits was quite loose—so much so, that the (3) RR,= rTClJ,, 0-cr < 1, notion that the multiplier is independent of policy actions was operationally valid. Nevertheless, where r denotes the ratio of reserves that must the empirical relevance of this notion has weak- be held against TCD.2 A change in the reserve ened considerably since the implementation of requirement ratio, r, also would constitute a the MCA in the early 1980s. Since then, the re- monetary policy action by the Fed. lationship between Fed policy actions and checkable deposits and, thus, the multiplier has Furthermore, for simplicity, assume that ac- tightened markedly. tual reserves always equal required reserves so that excess reserves are identically zero. With The evidence presented here, that the multi- this simplifying assumption, equation 3 can be plier is not independent of Federal Reserve ac- rewritten as tions in the post-MCA period, raises some ques- tions about the appropriateness of using the (4) H, = rTCD,. monetary base as an indicator of the effects of policy actions on the money stock. More impor- The model is completed by assuming that cur- tant from a policy perspective, it also suggests a rency is held in some proportion, k, of TCD. modification of the standard approach to money That is, stock control that might yield substantial im- provements in effective monetary aggregate (5) C, = kTCD,, targeting. where the proportion k, hereafter called the k- THE MONEY MULTIPLIER ratio, is the public’s desired ratio of currency to APPROACH: A SIMPLE: EXAMPLE TCD holdings. As a starting point for understanding the de- Combining equations 1, 2, 4 and 5 produces composition of the money supply into the mone- the monetary base-multiplier representation of tary base and the multiplier, note that the nar- the money supply: 11 row money stock, Ml, is defined as

(6) Ml, = m MB,, (1) Ml, = TCD, + C,, where m, the money multiplier, is given by where TCD denotes total checkable deposits and

C denotes the currency held by the nonbank (7) m = (l+k)I(r+k). public. The monetary base (MB), not adjusted for changes in reserve requirements, is simply According to this representation, a policy action the sum of currency and reserves (including that increases R by one dollar, through open 2 5ince the Fed eliminated reserve requirements on all non- position, the discussion to follow abstracts from reserves transaction deposits in December 1990, this representation that depository institutions must hold on government and approximates the current system. For convenience of ex- foreign transactions balances. 49

market purchases of government securities, in- (10) Ml, = m* AMB,, creases MB by one dollar and the money stock I by m dollars.~ where In this representation, policy actions are (11) m* = (l+k)I(r*+k). I reflected not only in MB, through changes in H, but in m, through changes in r. With a simple In this characterization of the money supply pro- adjustment to MB, however, the effects of pol- cess, all changes in monetary policy, through I icy actions on the money supply can be isolated changes in r or H, are reflected in the AMB. in one measure. This alternative measure of the Changes in the multiplier reflect only changes monetary base, called the adjusted monetary in the public’s desire to hold currency relative base, AMB, reflects both changes in H and r. It to checkable deposits, changes in the k-ratio.~ is constructed by calculating the hypothetical I Because, in this model, the k-ratio is not directly level of reserves that would have been required influenced by the policy actions of the Fed, the under the reserve requirements in existence dur- multiplier is independent of policy. I ing a chosen base period for the current (actual) level of reservable deposits. With the chosen base period, changes in required reserves due THE DEMAND FOR CURRENCY~ to changes in reserve requirements, r, are CHECKABLE DEPOSITS AND I added to the monetary base.~ NEAR-MONIES: WHAT IS Specifically, the AMB is given by THE k-RATIO? I Interest in the currency-deposit ratio dates (8) AMB, = MB, + RAM,, back to Fisher (1911), who was concerned that the two forms of money had different income I where the reserve adjustment magnitude, HAM, velocities. He realized that these two monies are is defined as imperfect substitutes: currency is especially use- ful for making small, “face-to-face” transactions, (9) RAM, = (r*~.~J.)TCD,. while checkable deposits provide a convenient I means for making large, ‘out-of-town” This adjustment measures the reserves released transactions. or absorbed by changes in r relative to r*, the Fisher reasoned, however, that individuals required reserve ratio during the base period. I achieve an ‘equilibrium” in their holdings of the In the base period, RAM is zero and AMB = MB. two forms of money. The notion of a desired or A decrease in r from its base-period level (r*) releases reserves into the banking system and optimal k-ratio is based on the assumption that individuals decide how much of their money I thereby increases RAM and AMB. Conversely, holdings they will allocate between currency an increase in r reflects the reserve drain by and checkable deposits, based on both the rela- reducing RAM and AMB. tive advantages of each in undertaking an indiv- I Combining equations 1, 4, 5, 8 and 9 yields idual’s planned transactions and their relative the following decomposition of Ml, holding cost. This ratio was assumed to be a

I 3 Note that because r< 1, m >1. If the assumption that ex- ment and foreign transaction balances, m* = (I +k)l cess reserves are not held were replaced by the assump- (r(1 +g+f) + k), where g and f denote the ratios of gov- tion that they are held in a fixed proportion, e, of TCD, ernment and foreign transactions accounts to TCD, re- then the denominator of the multiplier would include e as spectively. If, in addition, excess reserves were held, as I well, so that the multiplier would be smaller than that described in footnote 2, m = (1 .+.k)l(r*(1 +g-i-f)+k÷e). shown in equation 7. These complications can be ignored, however, because 4 See Tatom (1980), for example, who discusses the issue movements in the observed ratio of currency to TCD ex- of choosing the appropriate base period in light of changes plain most of the movements in the multiplier, as will be I in the structure of reserve requirements. This theoretic discussed shortly. discussion focuses on the measure of the adjusted monetary base constructed at the Federal Reserve Bank of St. Louis. See Garfinkel and Thornton (1991) for a more de- I tailed discussion of this measure and a similar one constructed by the Federal Reserve Board. ‘In a slightly more realistic model, which allows for the fact I that depository institutions must hold reserves on govern- 50

function of a number of economic and social ily reflect changes in the optimal k-ratio—that variables.° is, changes in the relative holding cost and ad- Given these variables, the demands for cur- vantages of currency and checkable deposits. rency and checkable deposits were thought to First and perhaps foremost among these is that be strictly proportional to each other. More- the demand for either of these forms of money over, because individuals are free to adjust their might depend on a number of special factors holdings of the two monies quickly and costless- that are unrelated to the demand for the other. ly, it was assumed that the actual currency- i’hus, changes in the relative advantages of deposit ratio would deviate from the desired these two forms of money might not be empiri- ratio for only a short period of time.’ According cally important in explaining changes in the to this line of reasoning, all changes in the ratio of currency to checkable deposits. observed currency-to-deposit ratio, denoted here For example, many believe that currency has by the K-ratio, are to be interpreted as changes no rival for illegal transactions. The same is in the desired ratio caused by one of these fac- true for foreign demand for U.S. currency by tors. While not numerically constant, as it was countries that need “hard currencies” for their assumed to be in the previous analysis, the k- domestic transactions.’ To the extent that cur- ratio was viewed as not being directly affected rency is held for these reasons, independent of by monetary policy actions. factors that determine the demand for check- The following discussion, supported by subse- able deposits, policy actions can induce changes quent empirical analysis, suggests, however, that in TCD without affecting currency demand. Con- the observed ratio of currency to checkable sequently, policy can alter the ratio of currency deposits can be and has been affected directly to ltD and, hence, the multiplier.” by the policy actions of the Federal Reserve.’ This effect can emerge without changing the One might also argue that changes in the rela- relative advantages of currency and checkable tive holding cost of the two monies are not es- deposits or their relative holding cost. pecially relevant for explaining observed changes in the currency-to-deposit ratio. The relative Substitutability, Holding Costs and holding cost of the alternative monies is given the Optimal k-Ratio by the difference between the rates of return on the two forms of money.” The return on There ai-e a number of reasons why one holding currency is zero.” Although non-inter- might question the assumption that changes in est-bearing checking accounts (demand deposits) the observed currency-to-deposit ratio necessar- have an explicit return of zero, they can yield a

‘Fisher assumed that the optimal k-ratio depended on real effect of policy actions on economic variables such as real income or wealth, the degree of development of the income or interest rates. It is argued that such variables business sector, population density, relative holding costs influence the k-ratio or the other ratios that make it up— and custom and habit. (Checkable deposits were thought particularly, the ratio of excess reserves to total checkable to be “superior” to currency, although money in any form deposits. See Mishkin (1989) for a more detailed discus- was a superior good.) Cagan (1958) extends the list of sion of this indirect effect. determinants of the k-ratio considerably. Both he and Hess ‘Because it is difficult to account for a relatively large (1971) attempt to quantify the effects of such factors. amount of the total stock of U.S. currency outstanding, 7 Cagan (1958) recognized that, at times, restrictions might one should not be too surprised to tind that, in the ag- prevent the adjustment of the currency ratio. He explicitly gregate, demand for currency and checkable deposits are considered the case of financial crises where banks sus- not closely related. See, for example, Avery, Elliehausen, pended convertibility. He noted, “At these times individ- Kennickell and Spindt (1986, 1987). uals could not exchange deposits for currency, and the “’This potential influence is illustrated below with an exam- desired currency ratio undoubtedly exceeded the actual ple. To be sure, longer-run movements in the K-ratio might ratio...” Without such restrictions, however, individuals are be attributable to some factors that affect the relative ad- free to adjust their currency holdings to the desired level vantages for the two forms of money. very quickly and at a low cost. “The discussion to follow focuses on the nonbank public’s The assumption that there exists a desired currency-to- perspective. The relative holding costs to depository in- deposit ratio and that individuals adjust their actual hold- stitutions generally will differ. ings of currency to their desired level was made opera- tional for models of the money supply process by Karl “Adjusted for inflation, it is minus the expected rate of infla- Brunner and Allan Meltzer in a series of articles. See tion. Note that currency used for illegal transactions yields Brunner (1961) and Brunner and Meltzer (1964, 1968). a greater return because of the tax avoidance. For foreign- ers, currency can yield a return that diners from zero due ‘It has long been recognized that policy actions can have to the appreciation or depreciation of their home currency an indirect effect on the multiplier through the presumed relative to the U.S. dollar. 1 51

positive implicit return—for example, free toast- its are seen as being determined simultaneously I ers for new customers, subsidized accounting with the demand for near-money assets.” and payment services, etc. The return on hold- An important part of the determination of the ing interest-bearing checking accounts is the net ratio of currency to checkable deposits, there- interest paid on these accounts plus free pay- I 3 fore, is the degree of substitutability between mnent services.’ currency and demand deposits on the one hand The relative holding cost of currency and and between each of these money assets and I demand deposits, however, is unresponsive to near-money assets on the other. Although the movements in market interest rates because the explicit rates paid on TCD are relatively unre- explicit returns to both assets are identically sponsive to changes in market interest rates, zero. Surprisingly, the same seems to be true rates paid on near-money assets can vary mark- I for currency and interest-bearing checking ac- edly with variations in other market interest counts, even since the elimination of Regulation rates. The effect of these variations on the pro- Q ceiling rates in 1986. Interest rates paid on portion of Ml held in the form of currency, of I interest-bearing checkable deposits included in course, depends on the degree of substitutabili- TCD have been unresponsive to movements in ty between near-money assets and the two forms short-term interest rates.’4 Despite the fact that of money. If currency is a relatively poor substi- the explicit holding cost of currency relative to tute for such assets while TCD is a relatively I that of checkable deposits has changed little, the good one, the ratio of currency to TCD will observed ratio of currency to checkable depos- change with changes in rates paid on such near- its exhibited sharp swings during the 1980s. money assets because of changes in TCD. Thus, it is unlikely that changes in the public’s I The relevance of this substitutability between holding of currency and checkable deposits are TCD and other near-money assets appears to due primarily to changes in their relative hold- have been heightened by the nationwide intro- ing cost. I duction of interest-bearing checking deposits in January 1981. Since then, the cross-price or interest elasticity of the demand for checkable The Holding qf Currency, deposits has increased. This increase is hardly Checkable Deposits and Other surprising because the payment of interest on Financial Assets checkable deposits has made them closer substitutes for interest-bearing time and savings de- I Thus, it would not appear that individuals posits. Indeed, some evidence suggests that in- simply shift their money holdings between cur- dividuals have shifted a significant portion of rency and checkable deposits in response to their “savings” balances into interest-bearing I variations in their relative advantages or holding checking accounts.” Because these saving bal- cost. This conjecture would be reinforced by ances are substitutes for savings and money the fact that currency and especially checkable market accounts that have higher explicit re- I deposits are substitutes for other “near-money” turns, the interest elasticity of the demand for stores of wealth, for example, money market checkable deposits should have risen, while the mutual funds. From this broader perspective, interest elasticity of currency demand should I the demands for currency and checkable depos- not have changed.” “Net interest is interest net of service charges. For a dis- those that do not. Some evidence suggests that, while cur- cussion of these, see Carraro and Thornton (1986). This rency and demand deposits satisfy this condition for weak explicit return also could be adjusted for inflation. separability, these two assets plus interest-bearing transac- I “Indeed, interest rates on the interest-bearing portion of tion balances do not. See, Fisher (1989), for example. TCD, called other checkable deposits (OCD), have changed Belongia and Chalfant (1989), among others, however, find little during the 1980s. The rate on OCD fluctuated be- that the data are consistent with the notion that the assets tween 5 percent and just over 5.5 percent during our sam- included in Ml and a grouping broader than Ml (currency ple period. and total checkable deposits) satisfy the weak separability I condition. Thus, the empirical results in this line of “This consideration raises a fundamental question—namely, research are not conclusive. what constitutes an appropriate monetary aggregate? In theory, monetary aggregation requires the “monetary” ag- “See Sill (1990). gregate to be “weakly separable.” That is to say, it must “See Thornton and Stone (1991) for a derivation of this I behave as a fundamental commodity with respect to con- result. These results are borne out empirically by simple sumption and other financial assets. There can be linear regressions of the monthly change in both currency substitution between assets that compose the aggregate, and other checkable deposits on a scale measure and the I but not between those that compose the aggregate and three-month T-bill rate. 52

Thus, changes in interest rates, whether pol- fect both the adjusted monetary base and the icy induced or not, can have an asymmetric ef- money multiplier. To see why, consider a policy fect on the demands for currency and checkable action involving the purchase of T-bills in the deposits, with a direct effect on the proportion market by the Fed. This policy action increases in which the alternative monies are heldis Al- the stock of reserves and, assuming zero excess though this asymmetric effect is likely to have reserves, ltD. In the ea,lier formulation of his played a larger role since the introduction of model, the K-ratio was assumed to be unchang- interest-bearing checking accounts in generating ed; the increase in TCD would be accompanied fluctuations in the ratio of currency to TCD, by a proportionate increase in currency, so that policy has induced changes in this ratio more the observed ratio of currency to TCD, K, would directly since the MCA (as discussed below). not change. Thus, the effect of this policy action on the money stock would be isolated in the •IJEPOSIT SUBSTITUTION AND monetary base—the multiplier would be THE MONEY MULTIPLIER unaffected. ln Provided that the demands for currency and the modified model, however, TCD increases while currency is constant. Consequently, the K- checkable deposits are determined by factors ratio falls and the multiplier, m’’, rises. In this that are independent of one another, monetary policy actions can have a direct influence on the instance, the change in monetary policy is reflected both in the adjusted monetary base, be- relative holdings of each and, thus, the multi- cause of a change in R, and in the multiplier plier.’” The channel of influence is most easily because illustrated in the extreme case where the de- of a policy-induced change in K. Al- though this argument is made in terms of a stat- mand for currency is completely independent ic model, the main point, that policy can in- of the demand for checkable deposits. That is, equation 5 is replaced with fluence the multiplier, would carry over into a more realistic dynamic model. ‘I’wo of the more salient features of the longer-run consequences (5’) C, = C, of this analysis are taken up in the shaded in- where C is a constant. Equation I also can be sert on page 54. rewritten as

(1’) Ml, = (1 + K,)TCD,, THE RECENT BEHAVIOR OF THE K-RATIO where, as defined previously, K, = (C/TCD), is 2 the observed ratio of currency to TCD. ° Figure 1 shows the K-ratio and the observed Using equations 1’ and 5’ in place of 1 and 5, adjusted monetary base multiplier, Ml/AMB, the money supply can be written as from January 1970 to November 1990. Note that the multiplier is essentially the mirror image of

(12) Ml, = m~’AMB,, the K-ratio; the K-ratio accounts for much of the multiplier’s short-run (month-to-month) where m~’= [(1 + K, l/(r* + K,)]. variability and for the .significant shifts in its longer-run “trends.” Indeed, as shown in table The crucial difference between this expression 1, changes in the K-ratio alone explain over 80 and equation 10 is that, here, policy actions at- percent of the month-to-month variahility in

20 “The same would be expected for changes in the level of Because k is meaningless in this formulation, K, will not income. Indeed, Hess (1971) presents estimates indicating equal k. More generally, currency demand can be thought asymmetric effects of both changes in interest rates and of as having two components, one related to TCD as em- income on the demands for currency and checkable bodied in the k-ratio and the other unrelated to TCD, That deposits. It should be emphasized that this effect of is, C, = C + kTCD,. In this more general formulation, the changes in interest rates on the k-ratio is not the same as k-ratio is determined solely by the relative holding cost of that which was alluded to earlier--i.e., through the relative currency and TCD and the substitutability between them holding cost of currency and checkable deposits (see foot- as discussed above. note 8). C -- . ‘“Many researchers who have estimated currency demand In this case, K, = —a— + k. The restriction in (5), equations have abstracted from the relationship of currency to TCD. For example, see Hess (1971) and Dotsey (1988). that k = 0, is imposed only for illustrative purposes. 53

I Figure 1 The K-Ratio and the Ml Multiplier I January 1970-November 1990 Ratio I 3.1

I 3.0

I 400 2.9

I .375 2.8 I 150

2.7 I .325

2.6 ,300 I I V

I 175 2.5 1970 72 74 76 78 80 82 84 86 88 1990 I I Table 1 Regression Estimates of Changes in the Multiplier on Changes I in the K-ratio

Period Constant K-ratio SEE R OW. I 1/1970-’2/1980 000 --4 355’ 007 598 247 (035J f1394~

1/1981-H/1990 001 —3,714’ 005 818 249 1 (184) ~2302) 3!1984-11/1990 001 —3b04 004 854 302 I ‘i 35) (21 66j .no.cales slansucal s’gn’ficance at the 5 pe”cent level Absolute values of t-s~at,st,csare ‘1 parentheses I 54

The Long-Run Multiplier? 1 That the K-ratio does not appear to he sta- °M~ the I OT’(Hgit di ‘iii aiiti gri )WS at a Li in- tionary tin the SCflM, 01’ being mcdli-reverting) tanl Talc’. ii. then 11w log of the denianci I or 5 iaisc’s ci 0 i titerestlng questiofl ol how the cu em ‘ru is givel i by TuagLilt u de of the muI Lipid is deti iiniiwd in

the 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 i~c’riti( al lv- dc’penclel...I on the sped it’ atsons of 1(111 &~jun is IIvWII15 Iil(’d h~’t he Tout n grm~I h tiw demands br cii event v and RD. tales ol I orc’1i411 and tiiinit’SLII’ tientailils lot’ ~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’lv income, while the dtmiaiid for real TCI) is In nominal iticotlie and that notnituil inc utile 1 cli’ term ned both by real Inc. nine arid the not ii- gi’()fl szi( a nil ml out rate cl—al least in t he

ma’ interest iate, wIuiri~‘IfS) is inveu’M!ly lcn ig ‘oil If ci is less than or equal tii h (I - hI related 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 1 other ncar-Ilionht’S. For siniplucut>. these urn the mniiltipliet \\ 311 apptt}&tl’h I r - ~~here cleniancis arc’ assumed It) he linear in natural P is the base-period reset” I’ I et]uii’vTiWiit (see logs, and the Tic-ome elasticities of the Use tc”.t fur more cietailsl. \ole howeL er thai. in Ins exampit’ the den ian Os for t-urrenev and III) an’ assti mc’d to 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(’that rio 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’- . - - . i cuat.’iIlIig I I’ . \ci\\ ;jssti[1iI, lhiat a t-IIOIIW’ ii’ 1 1 eni~tng(lie ric,niiui’al interest rate ~ hirli ~itir\ reduce’ the gr’n\ th rate ub 1(1) atid. thus 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’\ least thii’ h,uhc~change ~ OLilti (~ilLiSt’ 11W iniEttpl~ would at feet the Iung.rtiti niultiphiem .. .1 - To see n h~. assuriiC that a change ii polity It) appi’ucic’Il its Iong-t~uliecjtlilihl’ILim aloe

raises n’servC grm~th permanently. If this iii- niiirc sici” l~. as it di’i~is dolL a 0. tridet’cl if ct-east’ results in a perni&tnc~it increase in the tic’ grm\ th iate of flU ,lon c’d (ci tlic’ poiil actual and anticipatE’d rates of inlt’iticiil. time ~lti’fl’ 0< hI 1-li) the long-i’WI mtiltiplWi nominal Interest rate ~ III rise. ‘l’he pernian- COLIIO ciitiL et’ge to I rather than I i’. 1 rut ’,- higlwr Ie~el nI the noniitiah intel eM rate UI 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. permanent redo’ non in the mttltipllem’. en mu the long -liii the nuiltipitet’ de;ic’t id— Thc’ sec ond evainpie assunies that the cit’ on ranmietary polity and that he exact ~aIue mood 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~lto 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- 1 stones that the domes ic ciettiand ‘or comm-en- less ~ahcl Rt’lOUt’ 0 nieawngltil ‘long rums cv 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~ t thi’ cost is ccjnstalit. .\gain. these elation- both ilir’ cic’mmianc ‘cii cllrn’iit’.\ and the tie- 1 ships are assume’ 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 AMB umal s~ratioretiecttng only the ‘dative advantages and must be cointograted t costs o curuency and TCD I 55

I Figure 2 I The K-Ratio, Currency and TCD Ratio Billions of Dollars I .450 600 I ,425 500 ,400 I 400 .375 I 300 350 I 200 325

I 100 .300 I ,275 0 I 1970 72 74 ‘76 78 80 82 84 86 88 1990

changes in the multiplier since the implementa- 2 The Relationship Between Total I tion of the MCA ’ The MCA tightened the link Checkable Deposits and the between the K-ratio and the multiplier by reducing or eliminating other sources of varia- K4latio I tion in the multiplier.22 While the MCA was implemented in a series of steps from November Figure 2 shows the K-ratio, currency and 1980 to September 1987, its major features TCIJ. The behavior of these series suggests that I were almost fully implemented by February changes in the trend of the K-ratio are associ- j93423 Since then, changes in the K-ratio alone ated more closely with changes in the trend of explain over 85 percent of changes in the TCD than with changes in the trend of curren- I multiplier. cy growth. For example, the sharp rise in the 21 23 The Durbin-Watson statistic for each of the equations in- The MCA was first implemented in November 1980 and dicates significant, negative first-order serial correlation, was fully phased-in by September 1987. The empirically I Because we are primarily interested in the explanatory significant features of the act were completed with the power of changes in the k-ratio as measured by the ad- Fed’s adoption of contemporaneous reserve requirements justed A-square, however, maximum likelihood estimates in February 1984, so the sample was broken at this point. of the equations adjusted for serial correlation are not See Garfinkel and Thornton (1989) for a discussion of reported here. Nonetheless, there are no substantive dif- these changes and their effect on the multiplier. I ferences between the maximum likelihood estimates and those reported in table 1. 22 I See Garfinkel and Thornton (1989) for details.

JULVIAtJGuST 1991 56

Figure 3 Deviations of the Growth Rates of the K-Ratio and Currency from Their Means January 1970 thru November 1990

K—Ratio Currency 40 40

30 30

20 20

10 10

0 0

~i0 10

-~ 20 20

—30 —30 1970 72 74 76 78 80 82 84 86 88 1990

K-ratio in the early 1970s is associated with a shown in the figures, the month-to-month vari- slowing in the growth of TCD. The decline in ability in the growth of TC]J is considerably the K-ratio in the early 1980s and its subse- larger than that of currency. The variability of quent rise are clearly associated with a sharp TCIIJ more closely matches the variability of the acceleration in the growth of TCD followed by K-ratio than does the variability of currency. a sharp deceleration in its growth. While the growth rates of the K-ratio and TCD That TCD accounts for much of the short- are highly, inversely related, there is little positive association between the growth rate of run variation in the K-ratio also is evidenced by the K-ratio and the growth rate of currency. figures 3 and 4, which show, respectively, deviations of the growth rate of the K-ratio from its This observation is verified in table 2, which mean and deviations of the growth rates of cur- shows the simple correlations between the rency and TCD from their respective means. As monthly annualized growth rates for currency

ccncnM P V~9M’WflFPT loomS 1 57

I Figure 4 Deviations of the Growth Rates of the K-Ratio I and Total Checkable Deposits From Their Means I January 1970 thru November 1990 K—Ratio TCD 40 I 30 I 20 I 10 I 0

I —10

I —20

I —30 1970 72 74 76 78 80 82 84 86 88 1990 I

and the K-ratio and for TCD and the K-ratio for I four periods of roughly equal length between January 1970 and November 1990. tf variation in Table 2 the K-ratio were simply due to shifts between currency and TCD, its variation would be equally Correlations Between the Monthly I attributable to variation in currency and TCD. Growth Rate of the K-Ratio and the Monthly Growth Rates of Currency and This is not the case, however. The growth TCD I rates of currency and the K-ratio were positive- ly correlated during only two of the four peri- K-ratio K-ratio ods. They were negatively correlated in the Period and currency and TCD other two, although the correlations are not sig- I nificantly different from zero. In contrast, there 1/1970-12/1974 368’ - 901’ is a strong, consistent negative correlation be- W975-12/1979 016 911’ 1/1980 12,1984 112 - 955

tween the growth rate of TCIJ and the K-ratio 11985-11,1990 266 — 951’ I during all four of the periods. Figures 3 and 4 and the correlations reported in table 2 clearly - nolcales statistical signi’-cance at the 5 perce-il level I suggest that month-to-month variability in the JULWAUGUST 1991 58

K-ratio is driven largely by movements in TCD. and saving deposits, while non-member banks and other depository institutions were not re- Finally, as shown in figure 4, periods of per- quired to hold reserves against their transaction sistent deviations in the growth rate of TCD deposits in Ml. Because of these factors, the above (below) its mean are associated with per- link between TCD and reserves was not particu- sistent deviations of the growth rate of the K- larly strong. In reducing or eliminating reserve ratio below (above) its mean. Consequently, both requirements on a number of non-transaction the short and long-run movements of the K- accounts and extending reserve requirements to ratio are associated with movements in TCD all depository institutions, however, the MCA rather than currency. The apparent importance significantly strengthened the relationship be- of TCD in influencing the K-ratio suggests that tween TCD and reserves. K-ratio changes have not occurred simply because of variations in the relative advantages The effect of the MCA is illustrated in table 3, and holding cost of currency and TCD. That is which shows the results of simple linear regres- to say, changes in the K-ratio have not been a sions of changes in TCD on changes in total re- simple result of the public’s desire to shift the serves, ‘FR, for several periods between January composition of Ml between currency and 1970 and November 199023 The regression equa- checkable deposits. tions in this table (and in subsequent ones) are intended to be illustrative and should not be interpreted as alternative models for the money supply process. (See the appendix for details.) In The Link Between Total Checkable all cases but the initial phase-in of the MCA, Deposits and Reserves there is a statistically significant relationship between changes in TCD and TR. The strength Movements in the multiplier appear to be deter- of the relationship, as measured by the adjusted mined primarily by movements in the K-ratio, H-square, however, increases after the imple- which, in turn, appear to be determined pri- mentation of the MCA.2°The adjusted H-square marily by changes in TCD. The question that re- increases from .06 before the MCA to .67 after mains is what determines the stock of TCIJ out- the MCA. All of this improvement emerges in standing? The models of the money supply pre- the period after February 1984, when the ad- sented above provide a simple answer: given justed R-square increases further to .83.27 More- the reserve requirement ratio, TCD is deter- over, the reciprocal of the estimated coefficient mined solely by the amount of reserves supplied on TR is .124, very close to the marginal re- by the Federal Reserve. This strong link arises serve requirement of .12 during the latter peri- in this model because reserves are assumed to od. Indeed, the null hypothesis that this coeffi- be held only to support checkable deposits24 cient is equal to 1/12 cannot be rejected at the Prior to the MCA, commercial member banks 5 percent significance level (the t-statistic were required to hold reserves against all time is 0.82).

24 27 1n reality, of course, depository institutions hold excess The switch from lagged to contemporaneous reserve ac- reserves and are required to hold reserves on transaction counting in February 1984 might explain some of this ap- deposits other than those included in Ml. parent improvement. To account for this possibility, the 25 The total reserves measure used here is total reserves ad- change in TCD was regressed on both the contemporaneous and lagged change in TA. In no case was the coeff i- justed for reserve requirement changes, prepared by the cient on lagged TA statistically significant from zero at the Federal Reserve Board. 26 5 percent level. Indeed, the results differed little from The Durbin-Watson statistic for the first time period sug- those reported in table 3. That the switch from lagged to gests that there is significant first-order positive serial cor- contemporaneous reserve requirements is of no significant relation, as would be expected given the likelihood of consequence is consistent with the conjecture of Thornton misspecification (see the appendix). Maximum likelihood (1983) and the empirical evidence presented by Garfinkel estimates of this equation adjusting for first-order serial and Thornton (1989). The relationship between TR and correlation confirm this result. The estimated coefficient of TCD will likely become even stronger given the recent first-order serial correlation is -.314 with a t-statistic in ab- elimination of reserve requirements on all time and sav- solute value of 3.29. Nevertheless, the parameter ings deposits. estimates after adjusting for serial correlation are generally close to those reported in table 3, and they are statistically significant. More important, the adjusted A-square only increases to .147; hence, the dramatic rise in the adjusted R-square in the 1980s is not due to the fact that total reserve captures the autoregressive part of TCD.

FEDERAL RESERVE BANK OF St LOUIS I I Table 3 I Regression of Changes in TCD on Changes in Total Reserves Total -

I 1/1970-12/1980Period Constant.795’ reserves1.870’ 1.418SEE .062A’ OW.1 35 (5.72) (3.10)

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

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

I ‘ indicatesAbsolute values statisticalof t-statistics significanceareatintheparentheses5 percent levet I Table 4 I Regression Estimates of Changes in the Multiplier on Changes in Total Reserves

Total - Period Constant reserves SEE A’ D.W.

1/1970-12/1980 — 003’ — .003 .011 .004 I 70 I 2 86) (0.67) 1/1981-11/1990 — 004’ .016’ 011 275 2.12 (3 28) (6.77)

I 1/1981-2/1984 (0 77)002 (0.42)- 003 .014 — 023 1 82 3’1984-1i/1990 —.006’ 020’ .007 603 231

I ~6.05) ~11 - indicates statistical significance at the 5 percent level Absotute values of t-statmstmcs are in parentheses

liIisits tIl(’ lSStllllF)lit)l1 Illll J)(IIi’\ ;ii’ti iii’, luiti 110 it tt’Ct DII I hi’ nitiltipilii’r \\il.” 1 rl’d,Oll,thIi’ t~(liking ;NsliOlpLiuIl ht’Ioiv tilt’ adoimtion üI thi-

\IL \. lrmdt-ed change . ill he llltlitipIiit ale lull— ht’ aho\ I’ ana!~Sl7. sl_lgg(’St~tilill I)ohlr\’ artmomp~ . 7 I -. ... flil’fl’Idted ~ itli rhalige7. in 114 dining the ii-— rilIki ru-rI a stiouig el feel Dm1 the mnultiplu-m’ ml nod emichmt’’ I )ec-eumihi’r’ I 9IM1.

I I liellmi~e,I ISO’,in I‘IableFt accountI ‘lion’,tOm’that60 pri’c’otthis I—, titi’ol ease.the I lii-’.t’ ii’.tlIls siiggi-—~t thaI there sIlillilci he ill liii’ ullLlhli})Iier —mci’ \lnn El (It I 1)51. a dranmatic change ill liii’ l’eLttiOllShi ) hi-Inti-ii 1

I linkliii- hetul:uIik’ tellil-i, i (“,et’\—.Ilo~\e’, (hathid herau’,i-total clleck~lble@1 the nosede— changes\I I aiitl it)I’ll ‘tIin I theoil i’h~tuigi’sI 11507,. Smniplrmi ‘Ft cegres-~iomt—.amid chiamlge’—.ol H)

(V1~l)SiiST 1001 Table 5 Regression Estimates of the Change in Ml on the Change on Total Reserves and the Change in the Adjusted Monetary Base Adjusted Total 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 level Ab otu e values of t statistics are in parentheses

23 the AMB I epor ted in table 5 beai this out. TR a rather stmple traightfot n aid appi oach to explains a i’d itit cIt small amount of the ~aria money stock control nas tmplied—namc It to tion in changes in Ml before MC \ and ot cc 80 target the let ci of the adjusted monetart h tse percent of the tariation of changes in Mi since consistent tt ith a money stock target conditional early 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 target creased 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 the declined significantly m elatit etothat 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 the monetary 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 that multiplier st as independent of policy actions ret ising the simple empirical models of the 8 Again the Durbin-Watson statistics indicate significant that changes in TA explain much more of the variation in serial correlation, especially when the AMB is used as the changes in Ml in the 1980s than do changes in the AMB independent variable. In no case did an adlustment for 29even allowing for significant first-order serial correlation. seria] correlation using a maximum likelihood technique 5ee Garfinkel and Thornton (1989) for a discussion of this alter any of the substantive results presented in table 5 r~oint That is these results too suggest that there is a marked increase in the explanatory power of TA in the 1980s and 1 61

money supply process to account for the effects currency caused the K-ratio to rise and the mul- I of policy actions on the multiplier could result tiplier to fall, so that Mi grew slowly relative to in improved money stock control. These issues the monetary base during the period.” Because ace discussed briefly in this section. there is now a closer link between TB and MI I than between the IAMB and Ml and because TB The Adjusted Monetary Base as an is less likely to give misleading signals, TB is .Indica for of Police Actions on the likely to be a better indicator of both monetary Money Stock policy and the effects of policy changes on the I money stock. The adjusted monetary base continues to reflect all policy actions—changes in both reserves and reserve requirements; however, it The Multiplier .zI.pproach to I does not fully capture the effects of these actions on the money stock. Indeed, changes in Money Stock Control Ml are now more closely linked to changes in That the multiplier is not independent of I TB than to changes in the IAMB. Consequently, policy actions also has important implications it now appears that total reserves, adjusted for for the multiplier approach to money stock con- reserve requirement changes, is a better indica- trol. Taking this approach, the target level of tor of the effects of monetary policy actions on I Ml is achieved by forecasting the multiplier, the money supply than is the adjusted monetary then supplying the amount of the adjusted mon- base. etary base necessary to hit the desired Ml tar- I Furthermore, the quantity of currency out- get-32 lf, however’, the multiplier is a function of standing is demand-determined. Consequently, open market operations, policymakers must also unlike adjusted reserves, the adjusted monetary predict the effect of their actions on the multi- base can give misleading signals of the course of plier. That is to say, the multiplier approach to I monetary policy when there are exogenous shifts money control should be modified to take ac- in the demand for currency. count of the effects of policy actions on the To take a concrete example, currency growth multiplier. Taking account of such effects un- p accelerated markedly beginning about December doubtedly will improve money control over the 1989.~°This acceleration was accompanied by simple approach that assumes independence be- a sharp acceleration in the growth of the ad- tween the multiplier and policy actions. The I justed monetary base from 3.4 percent in 1989 magnitude of this improvement depends on how to 8.4 percent in 1990. Such a sharp rise in accurately the effects of policy actions on the base growth would tend to indicate that mone- multiplier can be forecast. To the extent that tary policy had eased. But the growth of ad- variations in the multiplier ace largely explained I justed reserves and, thus, ‘I’CD indicate a sub- by variations in the k-ratio and these variations stantially weaker easing of policy. TCD increas- are, in turn, largely influenced by policy (espe- ed at a 1.2 percent rate in 1990 compared with cially in the post-MCA period), such a modifica- I a -1.3 percent rate in 1989. Of course, the ap- tion could produce a substantial improvement in parent exogenous increase in the demand for money stock control.”

I lcWhile the exact cause of this acceleration remains un- nonlinear. One alternative approach would be to simply clear, many attribute it (at least in part) to currency exports forecast the level of currency, then supply the reserves to South American and Eastern bloc countries. necessary to hit a target level of TCD. The target level of 31 An equally interesting, but less frequently discussed, epi- TCD would have to be consistent with both the Ml target I sode occurred during 1989 when, after remaining fairly and the forecast level of currency. Whether this or the constant, currency growth slowed abruptly. During this multiplier approach, suitably modified to account for the period, the K-ratio rose rather than fell, as one might ex- effect of policy actions on the multiplier, would provide pect given the apparent shift in the demand for currency. greater monetary control is an empirical issue well beyond I The increase in the K-ratio was driven by negative growth the scope of this paper. Both approaches will produce in reserves and, hence, TCD during this period. forecast errors when there are unexpected shifts in the de- 32 mand for currency. The real issue is whether better esti- 5ee Balbach (1981), Hafer, Hem and Kool (1983), and mates of the K-ratio can be obtained by estimating the Johannes and Rasche (1979, 1987) for a discussion of this numerator and denominators separately than estimating I approach and for alternative methods that have been used them together. This is an empirical issue. Nevertheless, to forecast the money multiplier. this alternative approach could be simpler to implement “Note that the multiplier approach can be more difficult to and might provide superior control if reasonably accurate I implement. Most notably, the control problem becomes forecasts of currency can be made. . 62

Brunner, Karl, and Allan H. Meltzer. “Some Further SUMMARY Investigations of Demand and Supply Functions for Money,” Journal of Finance (May 1964), pp. 240-83. This article has examined closely the standard ______- “Liquidity Traps for Money, Bank Credit, and Interest multiplier model of the money supply process, Rates,” Journal of Political Economy (January/February specifically questioning the view that the ad- 1968), pp. 1-37. justed monetary base multiplier is independent _____ - “Money Supply?’ in B. M. Friedman and F. H. Hahn of the policy actions of the central bank. Be- eds., Handbook of Monetary Economics (Elsevier Science cause the demand for currency depends on a Publishers, 1990). number of factors that are unrelated to the de- Cagan, Phillip. “The Demand for Currency Relative to the Total Money Supply,” Journal of Political Economy (August mand for checkable deposits (and vice versa) and 1958), pp. 303-28. because the stock of checkable deposits has Carraro, Kenneth C., and Daniel L. Thornton. “The Cost of been more closely tied to the quantity of re- Checkable Deposits in the United States,” this Review serves supplied by the Federal Reserve since the (April 1986), pp. 19-27. implementation of the MCA, changes in mone- Dotsey, Michael. “The Demand for Currency in the United tary policy result in changes in the ratio of cur- States?’ Journal of Money Credit and Banking (February 1988), pp. 22-40. rency to checkable deposits and, consequently, Fisher, Douglas. Money Demand and Monetary Policy (The changes in the multiplier. Hence, the Federal University of Michigan Press, 1989). Reserve’s monetary policy actions are reflected Fisher, Irving. The Purchasing Power of Money (Augustus M. both in the adjusted monetary base and the Kelley, 1911). money multiplier. Garfinkel, Michelle R., and Daniel L. Thornton. “The Link Between Ml and the Monetary Base in the 1980s,” this Theoretical considerations suggest that the Review (September/October 1989), pp. 35-52. multiplier has never been independent of policy. “Measuring the Monetary Base?’ mimeo (February The elimination of reserve requirements on 1991). some non-transaction accounts and the exten- Hafer, R. W., Scott E. Hem and Clemens J. M. Kool. “Fore- sion of Federal Reserve reserve requirements to casting the Money Multiplier: Implications for Money Stock all depository institutions has greatly increased Control and Economic Activity?’ this Review (October 1983), pp. 22-33. the association between checkable deposits and Hess, Alan C. “An Explanation of Short-Run Fluctuations reserves. These changes have increased signifi- in the Ratio of Currency to Demand Deposits,” Journal of cantly the association between changes in mone- Money Credit and Banking (August 1971), pp. 666-79. tary policy actions and changes in the multiplier. Johannes, James M., and Robert H. Rasche. “Predicting the That the multiplier is affected by policy actions Money Multiplier?’ Journal of Monetary Economics (July suggests that money stock control using the 1979), pp. 301-25. ______- Controlling the Growth of Monetary Aggregates multiplier model would be enhanced by taking (Kluwer Academic, 1987). the effect of policy actions on the multiplier into Mishkin, Fredric S. The Economics of Money Banking and account. How much improvement can be expec- Financial Markets, 3rd. ed. (Little, Brown and Company, ted with this modified approach and how effec- 1989). tive alternative approaches to monetary control Plosser, Charles I. “Money and Business Cycles: A Real can be is left as a topic for further research. Business Cycle Interpretation?’ in Michael T. Belongia, ed., Monetary Policy on the 75th Anniversary of the Federal Reserve System (Klumer Academic Publishers, 1991). Sill, Keith. “An Empirical Examination of Money Demand in REFERENCES an Intertemporal Optimizing Framework,” unpublished paper (University of Virginia, 1990). Avery, Robert B., George E. Elliehausen, Arthur B. Stone, Courtenay C., and Daniel L. Thornton. “Solving the Kennickell, and Paul A. Spindt. “The Use of Cash and 1980s’ Velocity Puzzle: A Progress Report,” this Review Transaction Accounts by American Families.” Federal (AugustlSeptember 1987), pp. 5-23. Reserve Bulletin (February 1986), pp. 87-108. Tatom, John A. ‘Issues in Measuring An Adiusted Monetary ______- “Changes in the Use of Transactions Accounts and Base?’ this Review (December 1980), pp. 11-29. Cash for 1984 to 1986.” Federal Reserve Bulletin (March Thornton, Daniel L. “Simple Analytics of the Money Supply 1987), pp. 179-96. Process and Monetary Control,” this Review (October Balbach, Anatol B. “How Controllable is Money Growth?,” 1982), pp. 22-39. this Review (April 1981), pp. 3-12. “Lagged and Contemporaneous Reserve Accoun- Belongia, Michael 11, and James A. Chalfant. “The Chang- ting: An Alternative View?’ this Review (November 1983), ing Empirical Definition of Money: Some Estimates from a pp. 26-3a Model of the Demand for Money Substitutes,” Journal of Thornton, Daniel L., and Courtenay C. Stone. “Financial Political Economy (April 1989), pp. 387-97. Innovations: Causes and Consequences,” in Kevin Dowd Brunner, Karl. “A Schema for the Supply Theory of Money,” and Mearyn K. Lewis, eds., Current Issues in Monetary International Economic Review (January 1961), pp. 79-109. Analysis and Policy, (MacMillan Publishers, 1991). 63 I Appendix A Model of the Money Supply Process I

One might be tempted to interpret the regres- (AZ) C, + TCD, = g + hTR1 + jC~+ q~. I sion equations in the text as representing alternative models of the money supply process; how- With the restriction h =j, equation A.Z is iden- ever, the reader is cautioned not to do so, In- tical to equation A.i. The above analysis, how- I deed, as the article suggests, some existing mod- ever, suggests that the coefficient h should els of the money supply process are misspeci- equal 8.33 and the coefficient j should equal i. fied. This appendix illustrates the bias of some If this is the case, imposing the restriction that of the regression equations estimated in the these coefficients are equal will be resoundingly I article. rejected by the data. The discussion in the paper suggests that, since To test this hypothesis, first-difference specifi- the MCA, there is a very simple linear relation- cations of equations A.I and A.2 are estimated I ship between TCIJ and TR of the form using monthly data for the period from March 1984 through November 1990. These estimates TCD1 = a + bTR1 + e,, use Federal Reserve Board data for the adjusted I monetary base and total reserves, adjusted for where the coefficients a and b are constants changes in reserve requirements. These data and eisaresidual error that is assumed to be come close to satisfying the identity that the I white noise. The error term arises because some monetary base is equal to the currency compo- reserves are held against transaction deposits nent of the money supply plus total reserves. not included in TCD and because depository in- These estimates ace presented in table A.i. in stitutions hold excess reserves. The constant the unrestricted version of the equation, neither p term, a, enters the equation because a lower the null hypothesis that h = 8.33 nor the null reserve requirement for a tcanche of checkable hypothesis that j = I can be rejected at the 5 deposits exists and because some of the vari- percent significance level. The t-statistic for the I ables omitted from this equation might have test that h = 8.33 is .59 and the t-statistic for the non-zero means. If TR is correctly adjusted for’ test that j = i is .25. Hence, it is not surprising changes in reserve requirements, including the that the restriction that h = j is soundly rejected annual change in the deposit tranche, then the by the data. I coefficients a and b should be constant, where bisthe reciprocal of the marginal reserve It is interesting to note that imposing this restriction biases the coefficient of the mone- requirement—that is, b = l/.iZ = 8.33. The I discussion and the empirical evidence in the tary base multiplier away from its true value. paper further suggest that currency holdings The estimated multiplier of 4.005 is nearly 50 are independent of TCD, so that ç is simply ex- percent larger than its average value during this ogenous from the perspective of money stock period. This bias emerges because of an omitted I control. variable. If this representation is true, then a regres- To see this, note that equation A.2 could be I sion of Ml on the monetary base is misspeci- rewritten as either fied, because it imposes a restriction that is in- consistent with the process generating the data. (A.3) Mi, = g + hMB, + (j-h)C1 + ‘I’o see this, consider the following regression I specification: or

= (A.4) Mi, = g + jMB~+ (h-j)TR, + q . I (A.i) Mi1 g + sMB1 + q,- 1 Given the definitions of Ml and MB, this equa- Hence, equation A.i can be obtained by omit- I tion can be rewritten as ting C, from equation A.3 or TR, from equation

~lflV!A~’fl’~~r IEW Table Al Estimates 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 2 Estimates 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) t indrcates statistical significance at the 5 percent level. Absolute values oft statistics are in parentheses

A.4. In the former case the estimate of hisbias- 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 is the estimate of j is biased upward (4.005 vs. 1). hardly surprising that cegre sions of changes in Furthermore, the equation exhibits serial cor- Mi on TB and changes in TCD on JR produce relation, 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 the the demand for currency appears to be indepen coefficient is biased downward slightly when dent 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, -