A Stable Money Demand: Looking for the Right Monetary Aggregate

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1 A Sable Money Demand: Looking for he Righ Moneary Aggregae Pedro Teles Federal Reserve Bank of Chicago, CEPR. Ruilin Zhou Pennsylvania Sae Universiy January, 2005 Absrac In his paper, we argue ha M1 is no he appropriae measure of money used for ransacions since Banking deregulaion in he 1980s and 1990s and financial innovaion in he 1990s (associaed wih he developmen of elecronic paymens) call for a reconsideraion of he measure of ransacions demand for money. A beer aggregae measure is MZM (Money Zero Mauriy). We derive a money demand relaionship from a simple ransacions echnology model. Using M1 before 1980, and MZM afer 1980 as he measure of ransacion demand for money, we show ha here is a sable long-run relaionship among money, prices, a measure of economic aciviy and a nominal ineres rae. In paricular, he recen movemens in velociy can be accouned for by he movemens in he opporuniy cos of money. We hank Larry Chrisiano, Craig Furfine, Anne Marie Gonczy and Francois Velde for commens and discussions. We would also like o hank David Hwang for excellen research assisance. 1

2 1 Inroducion. The sabiliy of a money demand relaionship has been a major concern in moneary economics in he las 50 years. The reason is clear. A sable relaionship beween money, prices, a measure of economic aciviy and a nominal ineres rae, helps answering imporan quesions such as wha is he average growh rae of money consisen wih price sabiliy, given he average growh of he economy and a sable nominal ineres rae. Knowledge abou he response of he demand of money o changes in he nominal ineres rae may also help quanifying he gains from a low average inflaion rae. In an essay in honor of Allan Melzer, Lucas (1988) reassesses he evidence on he sabiliy of he money demand esimaed by Melzer (1963) and jusifies ha sabiliy no only on empirical grounds bu on heoreical ones. He shows ha here is a heoreical equilibrium relaionship beween hose economic variables, ha can hardly be called a money demand, bu ha is indeed sable in so far as preferences and echnology are srucural. He esimaes ha relaionship using he moneary aggregae M1 as he measure of money, and wih daa up o 1985, and argues ha here is a sable relaionship beween real money, income and he nominal ineres rae, wih a uniary income elasiciy and wih a srong negaive response of real balances o he nominal ineres rae. The relaionship esimaed by Lucas (1988) holds indeed very well unil he mid eighies bu no well a all afer ha. This could lead o he conclusion ha afer all he demand for money is no a sable relaionship as he simple model would sugges. Anoher conclusion, which is he one we subscribe is ha he measure of money is no a sable measure. In paricular we argue ha echnological innovaion and change in regulaory pracices in he las wo decades have made oher moneary aggregaes as liquid as M1, so ha he measure of money should be accordingly adjused. We show ha once a more appropriae measure of money is aken ino consideraion he sabiliy of he money demand is recovered. Banking deregulaion in he 1980s and 1990s and financial innovaion in he 1990s associaed wih he developmen of elecronic paymens indeed call for a reconsideraion of he measure of ransacions demand for money. Unil he end of 1970s he ransacions demand for money was well approximaed by M1. Since hen, however, a series of sweeping regulaory reforms and 2

3 echnological developmens in he banking secor have changed significanly he way banks operae and he way people use banking services and conduc ransacions. Firs, he Deposiory Insiuions Deregulaion and Moneary Conrol Ac of 1980 abolished mos of he ineres-rae ceilings imposed on deposi accouns since he passage of he Banking Ac of 1933, and auhorized naionwide negoiable orders of wihdrawal accouns (NOWs), which are ineres-bearing checking accouns classified in M1. The Garn-S Germain Deposiory Insiuions Ac of 1982 auhorized Money Marke Deposi Accouns (MMDAs), ineres-bearing savings accouns ha can be used for ransacions wih some resricions. MMDAs are classified in M2. These wo major banking reforms blurred he radiional disincion beween he moneary aggregaes M1 and M2 in erms for heir ransacions and savings roles. Second, he rapid developmen of elecronic paymens echnology, in paricular, he growing use of credi cards and he auomaed clearinghouse (ACH) as means of paymens, reinforced he effec of he previous banking reforms in slowing down he growh of M1. Boh credi cards and ACH ransacions can be seled wih MMDAs, and herefore wih M2 raher han M1. Third, he widespread adopion of reail sweep programs by deposiory insiuions since 1994, ha reclassify checking accoun deposis as saving deposis overnigh, drasically reduced he balances ha were classified in M1 by almos half. These fundamenal changes in he regulaory environmen and he ransacions echnology jusify he use of a differen measure of money afer The measure MZM (money zero mauriy) includes balances ha can be used for ransacions immediaely a zero cos, and was iniially proposed by Moley (1988) and Poole (1991) as a more appropriae measure of he ransacions demand for money. We show ha changing he moneary aggregae measure from M1 o MZM from 1980 onward preserves he long run relaionship beween real money, he opporuniy cos of money and economic aciviy up o a consan facor. We proceed as follows: In Secion 2 we show evidence of he difficuly in explaining he behavior of M1 wih he behavior of GDP and he nominal ineres rae. In Secion 3 we discuss why MZM, raher han M1, is an appropriae measure of he ransacions demand for money in he las wo decades. In Secion 4 we esimae a money demand equaion derived from a simple ransacion echnology model, using, as he moneary aggregae, M1 before 1980 and MZM afer 1980, and obain evidence in suppor of he 3

4 sabiliy of he money demand. 2 An unsable demand for M1. Figure 1 and Figure 2 reproduce figures 1 and 4 in Lucas (2000) exending he daa hrough Figure 1 suggess ha, over he course of las cenury, movemens in he raio of M1 o nominal GDP are inversely relaed o he movemens in he shor-erm nominal ineres rae. Following Melzer (1963), Lucas (1988) uses daa up o 1985 o esimae a money demand equaion using M1 as he measure of money and a shor-erm nominal ineres rae as he measure for he opporuniy cos of money, and confirms Melzer s resul ha he income elasiciy is abou one and he ineres elasiciy is high. 2 Lucas (1988) repors an ineres rae semi-elasiciy beween 0.05 and 0.1, which for an ineres rae of 4%, corresponds o an ineres elasiciy beween 0.2 and 0.4. Using daa from 1900 hrough 1994, Lucas (2000) repors an ineres elasiciy of 0.5, consisen wih a shopping ime model for he money demand. The money demand equaion derived in Lucas (2000) is M P = αy i γ (1) where M is he moneary aggregae measured by M1, P is he price level, Y denoes he aggregae oupu level, i is he shor-erm nominal ineres rae, and he ineres elasiciy is γ = 0.5, while α is a consan erm. Real money responds o oupu wih a uniary elasiciy and negaively o he nominal ineres rae wih a relaively large elasiciy, so ha in response o a one percen increase in he nominal ineres rae he real money demand declines by 0.5%. Oupu is a measure of ransacions, and people demand more money when he volume of ransacions is higher. The uniary income elasiciy is consisen wih real money growing a he same average rae 1 To be able o make comparisons, we use he same daa as Lucas (2000) for relevan daa analysis and figures. In paricular, M1, real GDP, he price deflaor and he nominal ineres rae are consruced, as in Lucas (2000) from differen daa sources for differen periods. See he Appendix for a deailed descripion of he daa used in his paper. 2 The income and ineres elasiciies measure he percenual increase in real money in response, respecively, o a one per cen increase in real GDP and a one percen decline in he nominal ineres rae. The semi-elasiciy measures he percenual increase in real money induced by a decline in he ineres rae of 100 basis poins. 4

5 as oupu. The negaive response of he demand of money o he nominal ineres rae makes sense because he shor erm nominal ineres rae is he foregone reurn from holding non ineres bearing, bu liquid, money balances. Figure 2 plos he acual and esimaed real balances using he money demand equaion above wih an ineres elasiciy γ = 0.5. Clearly, one would expec a larger reacion of real balances o he lower ineres raes in he 1980s and 1990s. A lower elasiciy of 0.32, insead of 0.5, would sill no ge close o being consisen wih he acual low growh in M1. This is apparen from Figure 3 where we plo he logarihm of he raio of M1 o nominal GDP agains he logarihm of he nominal ineres rae for he period Figure 3 indicaes ha here could be a differen money demand relaionship for each of he hree periods , , The solid line corresponds o he esimaed elasiciy of 0.32 for he enire period. The ineres elasiciy for he hree subperiods would be 0.26, 0.12, 0.07, respecively, so ha he response o he ineres rae movemens would be wih ime less and less pronounced. The consan erm also changes across he hree periods, corresponding o he increased inabiliy o explain he low growh in M1 wih movemens in economic aciviy and he nominal ineres rae. Ball (2001) argues ha he daa afer 1987 is evidence agains a sable money demand. He esimaes a linear relaionship beween he logarihm of real money, he logarihm of oupu and a nominal ineres rae for subperiods of For he period he evidence is consisen wih a sable relaionship wih a uniary income elasiciy and a relaively high ineres elasiciy, as shown by Lucas (1988) and Sock and Wason (1993). However, he need o accoun for he low reacion of M1 o lower ineres raes and higher oupu afer 1980 lowers boh he esimaed ineres elasiciy and income elasiciy. The relaively low income and ineres elasiciy in he pos war period ( ) are significanly differen from he uniary income elasiciy and relaively high ineres elasiciy in he pre war period ( ), herefore leading Ball o conclude agains a sable long run money demand. 3 3 The relaively low income elasiciy is indisinguishable from a ime rend in money demand. 5

6 3 Measuring money used for ransacions. In his secion we argue ha M1 was a good measure of money used for ransacions before major developmens in banking regulaion and financial innovaion saring in he early 1980 s. Since hen, a measure such as MZM became a more appropriae measure. The curren definiions of he differen moneary aggregaes are as follows. 4 Moneary Aggregaes M1: Currency held by he public + Travelers checks + Demand deposis + Oher checkable deposis, including NOWs (Negoiable Orders of Wihdrawal Accouns), ATS (Auomaic Transfer Services) and share draf accoun balances. M2: M1 + Savings deposis, including MMDAs (Money Marke Deposi Accouns) + Small-denominaion ime deposis + Reail money marke muual funds M3: M2 + Insiuional MMMFs (Money Marke Muual Funds) + Large-denominaion ime deposis + Repurchase agreemens + Eurodollars MZM (Money Zero Mauriy): M2 - Small-denominaion ime deposis + Insiuional MMMFs (end of box) Figure 4 shows he rend growh of all four moneary aggregaes: M1, M2, M3 and MZM since 1959 (daa for MZM are available since 1974). In paricular, since 1980, M1 has grown a a low rae (5.1%), and flaened ou afer In conras, average MZM growh has been 9% since The rapid expansion in MZM is eviden in he figure; is value surpassed ha of M2 in The basic framework for hese definiions was adoped in

7 Before 1980, M1, consising of currency, demand deposis ha were no, and sill aren, ineres bearing, and a very small amoun of ineres bearing checkable deposis (see Figure 5, and discussion in Secion 3.1) was he primary ransacion moneary aggregae. The main componens of M2 oher han M1 were savings deposis which were mosly passbook savings accouns on which checks could no be wrien, and small ime deposis. Neiher could be direcly used for ransacions. The oher componen of M2, reail money marke muual funds (MMMFs), a nonbank financial insrumen (some have resriced check-wriing capaciy) developed in he mid 1970s, and remained very small, as shown in Figure 5. There was herefore a clear disincion beween M1 and he componens of M2 oher han M1, before The former could be used for ransacions a zero cos and did no bear ineres while he laer were ineres bearing insrumens ha could no be direcly used for ransacions. Since hen, his disincion has become less clear-cu. Three major developmens in banking regulaion and financial innovaion are responsible for he change. 3.1 Financial innovaion and regulaory reform since 1980 Banking deregulaion. The banking deregulaion ha ensued in he lae 1970s and early 1980s changed he banking indusry landscape from a highly regulaed one ino a fairly compeiive one. An unavoidable consequence of he deregulaion was he blurring of he various componens of M1 and M2 as ransacion/saving insrumens. The reform sared in he 1970s when many commercial banks and deposiory insiuions were sruggling o survive in he high-inflaion, highineres rae environmen wih heir hands ied by many regulaions, in paricular, Federal Reserve Regulaion Q which prohibied ineres paymen on demand deposis and imposed ineres-rae ceilings on ime and savings deposis. The firs sponaneous iniiaive was he auhorizaion graned, by several norheasern saes, o sae-charered muual saving banks and laer oher deposiory insiuions o offer NOWs, an ineres-bearing ransacion accoun. 5 Oher producs or services designed o provide consumers wih 5 The NOWs were firs inroduced in Massachuses and New Hampshire in 1972, hen Connecicu, Maine, Rhode Island, Vermon in 1976, followed by New York in See 7

8 more efficien cash managemen ools developed a he same ime. These included auhorizing commercial banks and hrifs o provide prearranged auomaic ransfer services (ATS) from consumers saving accouns o heir checking accouns, allowing cusomers o ransfer heir saving balances o checking remoely, and auhorizing federally charered credi unions o issue share drafs. These innovaions were officially sancioned by he Deposiory Insiuions Deregulaion and Moneary Conrol Ac in More specifically, he Ac eliminaed mos of he ineres rae ceilings on ime deposis and savings accouns, and auhorized he use of, checkable, NOW accouns and oher ineres-bearing accouns (such as ATS and share draf accouns a credi unions) by individuals and non-profi organizaions. The privilege was exended o all levels of governmen agencies in The only excepion is demand deposis of corporaions, on which he 1933 prohibiion of ineres paymen remains in effec oday. 6 These regulaory changes allowed deposiory insiuions o compee more effecively for funds; hey also removed he impedimens for deposiors o earn he marke rae of reurn on heir ransacion balances. The direc consequence of he Ac is he prevalen use of ineres-bearing checking accouns. A second major regulaory banking reform was he Garn-S Germain Deposiory Insiuions Ac of I auhorized he creaion of money marke deposi accouns (MMDAs) o compee wih MMMFs. Classified as an M2 accoun, an MMDA is an ineres-bearing accoun ha carries no reserve requiremens. The accoun offers limied ransacion capaciy: no more han six wihdrawals by check or pre-auhorized ransfer per monh, bu no limi on deposis or number of wihdrawals from an ATM, by mail, or a a branch. As a resul of his Ac, here was a subsanial increase in he use of checkable savings accouns for ransacions. The deregulaory measures of he early 1980s, allowing for ineres paymens on checking accouns and checking privileges on savings accouns, blurred he disincion beween ransacions and savings deposis, consequenly blurring he disincion beween M1 and M2. Anne Marie Lapore (1979). 6 Business cusomers have several ways o minimize he loss of ineres on demand deposis. One way is he sweep programs developed during he 1960s and 1970s ha allow business demand deposis o be swep overnigh ino ineres-bearing accouns such as repurchase agreemens and money marke muual funds. 8

9 Elecronic Paymens. Following he banking deregulaion in he 1980s, he rapid developmen of elecronic paymens in he 1990s has also fosered he use of componens of broader moneary aggregaes for ransacions purposes. Credi cards are paricularly responsible for his. Credi cards are ofen used as a subsiue for cash, check and debi card ransacions. Monhly balances on a credi card can be paid wih an auomaed clearing house (ACH) ransacion or a check wrien on a checking accoun or checkable savings accoun. 7 The fac ha here is a single paymen a a cerain dae reduces he need o mainain high daily balances in checking accouns o mee he uncerain sequence of ransacion and paymen flows. This reducion is reinforced by he fac ha i is possible o use checkable savings accouns o pay for credi card balances. The oal number of credi and debi card ransacions almos ripled in 1990s, from 10.8 billion in 1990 o 30 billion in 2000 (Humphrey, 2002). The ACH is anoher imporan developmen in elecronic paymens. ACH is a naionwide mechanism ha processes elecronically originaed baches of credi and debi ransfers. ACH credi ransfers include direc deposi payroll paymens and paymens o conracors and vendors. ACH debi ransfers include consumer paymens on insurance premiums, morgage loans, and oher kinds of bills. This form of elecronic bill paymen is a subsiue for checks. A share of hese ransacions are from checkable savings accouns, classified in M2, insead of from checking accouns. The naion s larges ACH operaion is a he Federal Reserve banks, ha in 2000 processed more han 80 percen of commercial inerbank ACH ransacions. In 1991, he Federal Reserve processed 1119 million commercial (no including governmen) ACH ransacions ($5549 billion), while in 2003 he number jumped o 5588 million ransacions ( $13952 billion), an annual increase of 14.3% in volume (8% in value). Reail sweep programs A hird imporan developmen leading o he confounding roles of M1 and M2 for ransacions and savings was he adopion of reail sweep programs ha reclassify checking accoun deposis as savings deposis overnigh. Since 1994, commercial banks have sared using 7 The erm checking accoun is used o mean demand deposis and oher checkable accouns, such as Now accouns, classified in M1. Checkable savings accouns are accouns classified in M2 ha have checking privileges. 9

10 deposi-sweeping sofware o dynamically reclassify he balances in checking accouns above a cerain level as MMDAs, and o reclassify hem back when he balances on he checking accouns are oo low. By adoping he pracice, deposiory insiuions avoid reserve requiremens on he reclassified porion of he checking accoun (he reserve requiremen on demand deposis, ATS, NOW, and oher checkable deposis can be as high as 10%, depending on he size of he insiuion). The sofware effecively creaes a shadow MMDA for every checking accoun, based on he cusomer s paymen paerns, subjec o he consrain ha he number of ransfers (reclassificaions) from an MMDA o a checking accoun does no exceed six each monh. The shadow accoun is included in M2, bu no in M1. More and more banks have adoped he reail sweep programs. As indicaed by Figure 6, 8 he oal amoun of sweeps of ransacion deposis ino MMDAs has been rising seadily since 1994, from zero o an amoun nearly equal o ransacions deposis in M1. According o he Board s esimaes, as of December 2003, he sweeps of ransacion deposis ino MMDAs were approximaely $575.5 billions, while oal ransacion deposis in published M1 were $621.3 billions. The widespread use of reail sweep programs subsanially affeced he growh of M1. The nominal value of M1 has been almos fla since MZM as a beer measure of ransacion balances since 1980 As a resul of he financial innovaions and regulaory reforms since 1980, componens of he ransacions aggregae M1 bear ineres, and componens of he savings aggregae M2 are used for ransacions. These changes call for a reconsideraion of he measure of ransacions demand for money, and is opporuniy cos. More specifically, if here is o be a sable, long-run, relaionship beween real money, is opporuniy cos and ransacions, a differen measure of money and is opporuniy cos may be necessary o susain he relaionship. 8 The Federal Reserve Board makes monhly esimaes available on he naionwide change in NOW accouns aribuable o he implemenaion of sweeps during he monh. These are no he curren amouns being swep, and no daa are available regarding he aggregae volume of deposis currenly affeced by sweep programs. Deposiories do no repor o he Federal Reserve he size of heir sweep programs. 10

11 Moley (1988) and Poole (1991) argue ha he presen classificaion of moneary aggregaes (M1, M2, M3) is inherenly arbirary, in paricular in ligh of he banking indusry developmens discussed above. They believe ha he imporan disincion should be wheher he deposi has a specified erm o mauriy. For example, NOW accouns in M1 and MMDAs in M2 are nonerm deposis, bu small and large denominaion ime deposis in M2 and M3 are erm asses. Nonerm deposis can be readily convered ino ransacion balances, or in oher words, are fully liquid. On he oher hand, erm deposis ha have o be liquidaed before mauriy incur he cos of an early wihdrawal penaly. In an environmen free of governmen regulaion, and wihin he limis of echnology consrains, agens porfolio decisions depend on heir liquidiy preferences and he reurn on he asses. The erm-nonerm disincion of moneary aggregaes is aligned wih privae agens incenives. Moley proposed o classify all nonerm deposis, money ha can be accessed wihou noice and a par, as a new moneary aggregae. Poole coined he name MZM (money zero mauriy) for he measure. Specifically, MZM is defined as MZM = M2 Small denominaion ime deposis + Insiuional MMMFs Insiuional MMMFs, currenly classified in M3, are ineres-bearing checkable accouns ha allow holders o ge around he zero-ineres demand deposis resricion. 4 Moneary Model We consider a simple ransacions echnology moneary model and derive an equilibrium relaionship beween real money, he opporuniy cos of money and oupu ha holds exacly. The economy consiss of an infiniely-lived represenaive household/firm and a governmen. Producion uses labor according o he linear echnology Y = A n where Y is oupu and n is amoun of labor used. A is a sochasic echnological parameer realized in he beginning of period. The hisory of hese 11

12 shocks up o period (or sae a ) is denoed by A. The iniial realizaion A 0 is given. The households have preferences over consumpion c described by he uiliy funcion: E =0 0 β U(c ) (2) U(c ) = c1 σ 1 where β is a discoun facor. The households conduc ransacions according o he Cobb-Douglas ransacions echnology ( ) 1 ν c = ξ (A s ) ν M (3) P where M are money balances, P is he price of he good in unis of money and s is he ime used for ransacions. The oal amoun of ime used for ransacions and for he producion of he good is normalized o one. 1 σ s + n = 1 The governmen issues money M S and makes ransfers o he households T. In he beginning of period, he households ener an asses marke where hey purchase money balances M ha pay ne ineres i m in he following period, as well as nominal bonds B ha pay ineres i and Z +1 unis of sae-coningen nominal securiies, wih price z +1, normalized by he probabiliy of occurrence of sae A +1, in unis of currency a, ha pay one uni of money a he beginning of period + 1 in a paricular sae A +1. Subsequenly, hey ener a goods marke where hey purchase consumpion wih M, according o he ransacions echnology (3). They also receive oal income P A (1 s ), as well as nominal ransfers, ne of axes, T. The period by period budge consrains are M + B + E z +1 Z +1 ( 1 + i m 1) M 1 P 1 c 1 + (1 + i 1 )B 1 +Z + P 1 A 1 (1 s 1 ) + T (4) A compeiive equilibrium is a se of prices and quaniies such ha (i) he households choose {c, s, B, M, Z +1 } =0 o maximize uiliy (2) subjec 12

13 o he resricions (3), (4) ogeher wih a no-ponzi games condiion on he holdings of asses, given {P, i, i m, z +1 } =0, and {T } =0 ; (ii) he governmen saisfies M S = ( 1 + i 1) m M S 1 + T and (iii) markes clear, so ha B = 0 (5) Z +1 = 0 (6) M = M S (7) c = A (1 s ) (8) We could derive a money demand equaion using he firs order condiions of he households problem. Tha equaion, however, would be a funcion of all he prices, including he prices on he sae coningen nominal deb, as well as unobservable shocks, and, herefore, could no be direcly esimaed using simple economeric mehods. Insead, he firs order condiions can be used o derive he following relaionship m c = α (i i m ) ν, 0 (9) where m denoes real money balances, m = M P, and α = ( ) ν 1 ν ν ξ 1. As poined ou by Lucas (1988), his equaion is no exacly a money demand, raher i is an equilibrium relaionship beween real money, consumpion and he opporuniy cos of holding money, ha holds exacly in his sochasic environmen. I can be esimaed using OLS. Given ha c = Y, equaion (9) can be rewrien as M P = αy (i i m ) ν, (10) wih ineres elasiciy γ equal o he Cobb-Douglas ransacions echnology parameer ν. Noe ha he derived income elasiciy is one. Lucas (2000) repors he ineres elasiciy o be ν = 1. He jusifies his 2 resul by arguing ha he equaion (9) wih ν = 1 is an approximaion o he 2 13

14 equilibrium relaionship when he ransacions echnology is Baumol-Tobin. In fac, if he ransacions echnology was Baumol-Tobin, ( ) c s = η, m he money demand equaion (9) would be m c = ω ( A c ).5 (i i m ).5, (11) where ω = η.5. The approximaion amouns o ignoring he erm ( ) A.5. c Noe ha he derived income elasiciy is one. The assumpions on he homogeneiy of he ransacions echnology and echnology progress in he wo secors, as well as assumpions on he uiliy funcion, imply ha he long run income elasiciy is one. Alernaive assumpions could imply a rend in money demand. Empirically, his could be capured by a ime rend or by an income elasiciy differen from one, as in Ball (2001). Insead, we argue ha he evidence is consisen wih a sable long run money demand wih a uniary income elasiciy and no ime rend, if he moneary aggregae is appropriaely defined o capure he echnological and regulaory innovaions since The demand for money. In he las secion, we show ha i is possible o derive from a simple general equilibrium moneary model he equilibrium relaionship (10), which is a varian of equaion (1) ha accouns for he fac ha money may earn ineres. This exac relaionship of observable economic variables is no exacly a money demand, bu i does look like he money demand funcions ha are commonly esimaed. As poined ou in Lucas (1988), here is reason o hink ha he empirical analog o ha relaionship, ha will have o accoun for measuremen error, is a sable relaionship. In his secion, we esimae he empirical counerpar of he money demand equaion above using OLS. Firs, as Lucas (1988, 2000), we use M1 as he measure of money and a shor-erm nominal ineres rae as is opporuniy cos. As menioned before, he esimaed ineres elasiciy is 0.32, 14

15 lower han he one repored by Lucas (2000) for he period , which was 0.5. If we were o esimae he elasiciy for hree subperiods, , and , he ineres elasiciies would be lower, respecively, 0.26, 0.12, I would also be apparen ha he curves would be shifed down. Nex, we esimae equaion (10) using M1 as he measure of money for he period and MZM for he period Because componens of M1 bore no ineres before 1980 (mosly cash and demand deposis) and componens of MZM are ineres-bearing afer 1980 (NOWs, MMDAs, MMMFs), we assume ha i m = 0 before 1980 and we se i m o MZM s own rae afer This is compued as a weighed average of he reurns on he differen componens of MZM. 9 We allow differen inerceps for he wo periods, because i is no reasonable o impose he coincidence of he wo series, M1 and MZM, in 1980, bu we do impose a common ineres elasiciy. The esimaed money demand equaion is as follows, ( ) M : ln = ln i P Y ( ) MZM : ln = ln (i i m ) P Y If we allowed for separae ineres elasiciy for he wo periods in he regression, he wo elasiciies would be 0.26 and 0.2, respecively for he firs and second period. 10 Figure 7 plos he logarihm of M1/nominal GDP for he period and ha of MZM/nominal GDP for he subsequen period agains he logarihm of he opporuniy cos of using hese balances, along wih he linear regression line. The roughly common elasiciy across he wo periods suggess ha he response of he money aggregae o changes in is opporuniy cos, in percenage erms, has remained sable over he las cenury, as long as one uses he appropriae definiion of moneary aggregae 9 As he MZM daa, he daa on he rae of reurn on MZM is provided by he Federal Reserve Bank of S. Louis. 10 Our resuls are consisen wih hose of Carlson e al (1999) ha find a sable coinegraing relaionship beween real MZM, an opporuniy cos measure and a measure of economic aciviy, using daa for he period The income elasiciy is no differen from one. 15

16 and is opporuniy cos. The upward shif of he funcion (smaller inercep) reflecs he fac ha MZM and M1 include differen liquid asses, even if all are zero mauriy. In Figure 8, we plo he acual and esimaed real money demands using M1 for he period and MZM for he period following he deregulaion and financial innovaion. 6 Concluding remarks While real M1 has increased very lile in he las quarer cenury, nominal ineres raes have come down considerably. If he ineres elasiciy was he one repored by Lucas (2000), we would expec a subsanial increase in M1 ha did no occur. This could indicae ha he money demand relaionship esimaed by Melzer (1963) and Lucas (1988), among many ohers, is no a sable equilibrium relaionship. Insead, we argue ha M1 is no he appropriae measure of money following he regulaory reforms and innovaion in elecronic paymens since he early 1980s. If an alernaive, more appropriae measure of money, i.e. MZM or money zero mauriy, is used he long-run relaionship beween money and is opporuniy cos is preserved. We esimae he ineres elasiciy o be 0.24, so ha a one percen increase in he opporuniy cos of holding money induces a quarer of a percen decline in real money balances. Why do we care abou esimaing a sable money demand, a he cos of an unsable measure of money? In addiion o he heoreical ineres of his issue, here is also a pracical aspec of i. I is a worhy objecive of a moneary auhoriy o provide elasic 11 liquidiy a sable prices. A sable esimae of a money demand, whaever he appropriae moneary aggregae migh be, is an imporan ool in performing his ask. 11 Elasic currency is he wording used in he 1913 Federal Reserve Ac ha esablished he Federal Reserve Sysem. 16

17 References [1] Ball, Laurence, 2001, Anoher look a long-run money demand, Journal of Moneary Economics, vol 47, pp [2] Carlson, John B., Dennis L. Hoffman, Benjamin D. Keen, and Rober H. Rasche, 2000, Resuls of a sudy of he sabiliy of coinegraing relaions comprised of broad moneary aggregaes, Journal of Moneary Economics, Vol. 46, 2, pp [3] Friedman, Milon and Schwarz, Anna, 1982, Moneary Trends in he Unied Saes and he Unied Kingdom, , Chicago: Universiy of Chicago Press, for he Naional Bureau of Economic Research. [4] Friedman, Milon and Schwarz, Anna, 1971, A Moneary Hisory of he U.S , Princeon: Princeon Universiy Press. [5] Humphrey, 2002, U.S. Cash and Card paymens over 25 years, mimeo, Florida Sae Universiy. [6] Kendrick, John W.,1961, Produciviy Trends in he Unied Saes, Princeon: Princeon Universiy Press, for he Naional Bureau of Economic Research. [7] Lapore, Anne Marie, 1979, Proposed redefiniion of money sock measures, Federal Reserve Bank of Chicago, Economic Perspecives, March/April, pp [8] Lucas, Rober E., Jr, 1988, Money demand in he Unied Saes: A quaniaive review, Carnegie-Rocheser Conference Series on Public Policy, Vol. 29, pp [9] Lucas, Rober E., Jr, 2000, Inflaion and welfare, Economerica, Vol. 68, 2, pp [10] Melzer, Allen H., 1963, The demand for money: The evidence from he ime series, Journal of Poliical Economy, Vol. 71, pp [11] Moley, Brain, 1988, Should M2 be redefined? Federal Reserve Bank of San Francisco, Review, Winer, pp

18 [12] Poole, William, 1991, Congressional esimony before he subcommiee on Domesic Moneary Policy of he Commiee on Banking, Finance and Urban Affairs. [13] Sock, James H. and Mark W. Wason, 1993, A simple esimaor of coinegraing vecors in higher order inegraed sysems, Economerica, vol 61, pp [14] U.S. Bureau of he Census, 1960, Hisorical Saisics of he Unied Saes, Colonial Times o 1957, Washingon D.C.: Gov. Prining Office. Daa Appendix The following is a lis of daa used in graphs and regression. Unless explicily specified, all moneary aggregaes are in billion of dollars, and are no seasonally adjused annual daa ( we ake December value of each year as he enire year s value). 12 M1 M2 M : Hisorical Saisics of he Unied Saes (1960, Series X- 267) : Friedman and Schwarz (1971, pp , Table A1, Column 7) : Federal Reserve Board hp://www.federalreserve.gov/releases/h6/his/h6his1.x Federal Reserve Board hp://www.federalreserve.gov/releases/h6/his/h6his1.x Federal Reserve Board hp://www.federalreserve.gov/releases/h6/his/h6his1.x 12 We follow Lucas (2000). 18

19 MZM Federal Reserve Bank of S.Louis FRED Daabase hp://research.slouisfed.org/fred2/daa/mzmns.x. Oher Checkable Deposis (quarerly frequency) FRB daa available hrough Haver Analyics (FMOTN in USECON). MMMFs (Money Marke Muual Funds, quarerly frequency) FRB daa available hrough Haver Analyics (FMGMN in USECON). Insiuional Money Marke Muual Funds (quarerly frequency) FRB daa available hrough Haver Analyics (FMIOMN in USECON). Transacion Deposis Swep ino MMDAs (Cumulaive) FRB daa available hrough Haver Analyics (FMSWEEP in USECON). Demand Deposis FRB daa available hrough Haver Analyics (FMDN in USECON). Price Deflaor (1929=100): Hisorical Saisics of he Unied Saes (1960, Series F-5) (2000=100): BEA daa available hrough Haver Analyics (DAGDP in USECON or USNA). ** These wo series overlap in 1929 and using he raio of he wo series s values in 1929, we consruc a new price deflaor ha goes from 1900 o 2003, wih 2000=1.0. Real GDP (millions of 1929 dollars), Kendrick (1961, Table A-III) (in chained 2000 dollars), BEA daa available hrough Haver Analyics (GDPHA in USECON or USNA) **From hese wo series, a new real GDP in 2000 dollars is consruced using he new price deflaor (2000=1.0). 19

20 Nominal Ineres Rae : Friedman and Schwarz (1982, Table 4.8, Column 6), defined as shor erm commercial paper rae : 3 monh commercial paper, FRB daa available hrough Haver Analyics, FFP3 in USECON. Opporuniy Cos : M1 s opporuniy cos is defined as he nominal ineres rae for his period : MZM s opporuniy cos = 3-monh T-bill rae (Secondary Marke) MZM own rae 3-monh T-bill rae: FRB daa available hrough Haver Analyics (FTBS3 in USECON). MZM own rae: Federal Reserve Bank of S.Louis FRED Daabase hp://research.slouisfed.org/fred2/daa/mzmown.x. Figures 1. Figure 1: M1/nominal GDP and he nominal ineres rae, Figure 2: Acual and esimaed real balances, M1/P ( ), ineres elasiciy of.5. ) ( M1 Esimaing ln = α 0.5 ln i P Y, we have α = Then ) ( M1 he esimaed real balances is = 0.05Y P i Figure 3: M1/nominal GDP and he nominal ineres rae, ) ( M1 Esimaed : ln = ln i P Y ) ( M1 Esimaed : ln = ln i P Y ) ( M1 Esimaed : ln = ln i P Y 20

21 ) ( M1 Esimaed : ln = ln i P Y 4. Figure 4: Moneary aggregaes, Figure 5: Oher Checkable Deposis and MMMFs, Daa used o plo his graph are in quarerly frequency. 6. Figure 6: Reail Sweep Programs, Figure 7: M1/nominal GDP ( ), MZM/nominal GDP ( ) and he opporuniy cos. ) ( M1 Esimaed : ln = ln i P Y ( Esimaed : ln MZM P Y ) = ln (i i m ) 8. Figure 8: Acual and esimaed real balances, M1/P ( ) and MZM/P ( ), common ineres elasiciy of.24. ) ( M1 Esimaed : = 0.13Y P i 0.24 ( ) Esimaed : = 0.17Y (i i m ) 0.24 MZM P Y 21

22 M1 / Nominal GDP 0.6 Figure 1: M1/Nominal GDP and he Nominal Ineres Rae, Ineres Rae M1/ Nominal GDP Nominal Ineres Rae Year 0.00

23 Figure 2: Acual and Esimaed Real Balances M1/P ( ) (Ineres Elasiciy of 0.5) Billions of 2000 Dollars Acual (M1/P) Esimaed (M1/P) Year

24 Figure 3: M1/Nominal GDP and Nominal Ineres Rae, Esimaed ln (M1 / Nominal GDP) Esimaed Esimaed Esimaed ln (Nominal Ineres Rae) -2.5

25 Figure 4: Moneary Aggregaes M1 M3 M2 MZM 6000 Billions of Dollars Year

26 Figure 5: Oher Checkable Deposis and MMMFs, Oher Checkable Deposis Reail MMMFs 1000 Insiuional MMMFs Billions of Dollars Year

27 Figure 6: Reail Sweep Programs Demand Deposis & Oher Checkable Deposis Transacion Deposis Swep ino MMDAs, Cumulaive Billions of Dollars Year

28 Figure 7: M1/Nominal GDP ( ), MZM/Nominal GDP ( ) and he Opporuniy Cos M MZM Esimaed M Esimaed MZM ln(m/nominal GDP) ln(opporuniy Cos) -2.0

29 Figure 8: Acual and Esimaed Real Balances, M1/P ( ) and MZM/P ( ) (Common Ineres Elasiciy of 0.24) Acual M1/P ( ), MZM/P ( ) Esimaed M1/P ( ), MZM/P ( ) 5000 Billions of 2000 Dollars Year

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