NBER WORKING PAPER SERIES MONETARY POLICY WITH 100 PERCENT RESERVE BANKING: AN EXPLORATION. Edward C. Prescott Ryan Wessel

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1 NBER WORKING PAPER SERIES MONETARY POLICY WITH 100 PERCENT RESERVE BANKING: AN EXPLORATION Edward C. Presco Ryan Wessel Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA July 2016 The views expressed herein are hose of he auhor and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peer-reviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Edward C. Presco and Ryan Wessel. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Moneary Policy wih 100 Percen Reserve Banking: An Exploraion Edward C. Presco and Ryan Wessel NBER Working Paper No July 2016 JEL No. E4,E5,E6 ABSTRACT We explore moneary policy in a world wihou fracional reserve banking. In our world, banks are purely ransacion insiuions. Money is a form of governmen deb ha bears ineres, which can be negaive as well as posiive. Services of money are a facor of producion. We show ha he naional accouns mus be revised in his world. Using our baseline economy, we deermine a balanced growh pah for a se of money ineres rae policy regimes. Besides his ineres rae, he only policy variable ha differs across regimes is he labor income ax rae. Wihin his se of policy regimes, here is a balanced growh welfare-maximizing regime. We show ha Friedman moneary saiaion wihou deflaion is possible in his world. We also examine a se of inflaion rae argeing regimes. Here, he only oher policy variable ha differs across regimes is he inflaion rae. Edward C. Presco Arizona Sae Universiy Economics Deparmen P. O. Box Tempe, AZ and NBER edward.presco@asu.edu Ryan Wessel Arizona Sae Universiy Economics Deparmen P. O. Box Tempe, AZ ryan.wessel@asu.edu

3 Secion 1: Inroducion The purpose of his paper is o open a discussion on moneary policy reform in ligh of advancemens in informaion processing echnology. Currenly, here is public discussion abou wheher he ineres rae should be increased and wha he inflaion rae arge should be. Our assessmen is ha exising moneary heory does no provide predicions abou he consequences of hese and oher alernaive moneary policy regimes. We consider a paricular moneary sysem wih (i) ineres-bearing money and (ii) a prohibiion on financial insiuions ha borrow from one group a a low ineres rae and lend o anoher a a higher average ineres rae, hereby realizing posiive ne ineres income. One quesion we will explore is he feasibiliy and desirabiliy of Friedman moneary saiaion. A prior quesion is wheher following he Friedman rule is feasible in our curren fia money sysem. McAndrews [2015] has argued and we hink convincingly ha i is no feasible. He poins ou ha people would no inves in securiies ha bear negaive nominal ineres raes because hey could inves in currency, which bears a zero nominal rae. Wih our alernaive moneary sysem, moneary saiaion is feasible, even wih a non-negaive inflaion rae. In he alernaive moneary sysem considered in his paper, a bank is a business ha issues demand deposis. Commercial banking companies in he Unied Saes and mos oher counries offer a wide range of financial producs in addiion o demand deposis. Only a small par of commercial banks financial aciviies is concerned wih making paymens. Banks in his paymen sysem are pure ransacion/paymen financial insiuions. The key elemens of his alernaive financial sysem are as follows: Limied liabiliy businesses are prohibied from boh borrowing and lending, wih he excepion of lending o he governmen and o ransacion/paymen banks. Only banks can issue demand deposis, and hese deposis mus be 100 percen backed by reserves held a he cenral bank. The cenral bank holds only shor-erm deb on Treasury securiies; herefore, demand deposis are effecively 100 percen backed by money, a form of shor-erm governmen deb. Reserves bear ineres a a rae specified by he governmen. Transacion banks may pay ineres on deposis; however, any ineres hey pay is no subjec o axes. Demand deposis would effecively be ineres-bearing governmen currency. There could no be bank runs wih his sysem. There is no place o run o. Whenever a ransacion akes place 2

4 beween privae agens, one pary s demand deposi accoun is credied by he amoun of he ransacion, and he oher pary s demand deposi accoun is debied by he same amoun. This sysem has wo forms of governmen deb: deb held by he cenral bank and deb held by privae agens. The deb held by he cenral bank is money. The sock of money equals he sock of demand deposis or, equivalenly, he sock of reserves. The reurn on hese wo forms of governmen deb can be, and ypically will be, differen. Absen saiaion, he ineres rae on he governmen deb held by he cenral bank will be lower han ha held by he privae secor. The difference in he yields on hese wo forms of deb is equal o he liquidiy services provided by holding demand deposis a ransacion/paymen banks. We assume ha he fiscal auhoriies manage he erm srucure in such a way ha he oal ineres paid on privaely held governmen deb is minimized. This policy resuls in a fla erm srucure. This feaure permis us o absrac from he erm srucure of ineres raes in his sudy. Prohibiing limied liabiliy businesses from boh borrowing from one group and lending o anoher means ha here will be no financial inermediaries wih his sysem. Financial businesses would exis and would consiue a large secor of he economy. These financial businesses would make loans o households and non-financial businesses. The lenders, and no he axpayers, would bear all defaul risk. One quesion is, Will his sysem reduce he funding of businesses? The answer is no. Currenly, mos financing of businesses in he Unied Saes is muual and is no coming from bank deposis. In 2012, checkable and ime/savings deposis were approximaely 0.65 GNP, whereas business borrowing was 2.5 GNP (2012 Flow of Funds, Table L104-5). Nearly all of he res of business borrowing is direcly or indirecly from he household secor. 3 Equiy is a muual arrangemen whereby he owners of he businesses share he disribuions and losses. Anoher par of he sysem is o prohibi non-muual annuiies and non-muual pension funds. Annuiies ha make paymens coningen on he experience of he group are muual arrangemens, which by definiion canno become insolven. Some problems would arise when insurance companies ener ino conracs ha under cerain coningencies canno be honored. Permiing only muual insurance companies would be one mechanism o miigae his problem. Regulaion of insurance companies is less han perfec, and insurance company failures would coninue o occur. Such failures, however, do no give rise o sysemic risk and runs on muual insurance companies. The ime-inconsisency problems would lead o axpayers bailing ou hose wih insured losses ha are defauled upon. 3 There could be some borrowing by business from he governmen. 3

5 In his paper, a simple model is developed and used o explore he consequences of various moneary policy regimes under our alernaive financial sysem. The model reas he services of real money as an inpu o he aggregae producion funcion, resuling in money being incorporaed ino valuaion heory. Ohers have proposed having money as an inpu o he aggregae producion funcion, 4 bu hey have no worked ou he implicaions of using valuaion equilibrium heory, as we do here. I urns ou ha having money services as a facor of producion necessiaes significan revisions o he naional accouns. We begin wih a se of naional accouns and consruc a model economy ha is consisen wih hese accouns. We examine he balanced growh pah for a se of moneary policy regimes. We keep consan he public-consumpion share of oupu and he lump-sum ransfers o households share of oupu. We do his in order o focus on he consequences of alernaive moneary policies and no on he consequences of alernaive fiscal policies. Moneary and fiscal policy canno be oally separaed, as shown by Sargen and Wallace [1981]. The moneary variables we focus on are he inflaion rae, he size of he money sock, and he ineres rae paid on money. As he inflaion rae eners he governmen accouns, differences in he labor income ax rae are associaed wih policies wih differen seady-sae inflaion rae arges. Ineres rae argeing regimes will have differen inflaion raes, which has consequences for he key balancing condiion in he governmen accouns ha expendiures equal receips plus he defici. As we saed previously, i is impossible o compleely separae fiscal and moneary policy because inflaion has ax consequences. We emphasize ha his is an exploraion sudy. I is designed o foser he examinaion of possible moneary sysem reforms. Before any financial reform is implemened, we should be confiden as o how ha moneary/financial sysem will operae. Currenly, esablished heory canno be used o make such predicions. The rial-and-error approach ha characerizes curren moneary policy is fraugh wih danger, leading us o he hesis ha beer heory is needed. 4 Some of he oher papers ha have proposed money being inroduced ino he producion funcion include Sinai and Sokes [1972], Fischer [1974], and Orphanides and Solow [1990]. 4

6 Secion 2: The Model Economy The analysis is seady-sae, and here is no uncerainy in living sandards. Consequenly, i does no maer wheher an overlapping generaion or an infiniely-lived family absracion is used. We use he infiniely-lived absracion because i is easier o use. Preference: There is a measure 1 of idenical households wih preferences ordered by (1) β [logc + αlog(1 h)], = 0 where c > 0 is consumpion and h [0,1] is he fracion of he ime endowmen allocaed o he marke. The parameer β = 1/ (1 + ρ) (0,1) is he discoun facor and ρ is he discoun rae. The parameer α deermines he relaive shares of c and he leisure fracion (1 h ). For he balanced growh pah wih balanced growh rae γ, he seady-sae real ineres rae is (2) i = γ+ ρ+ γρ. This fac will be exploied when characerizing he seady sae for policies for which i exiss. Households hold wo socks of asses ha hey ren o he business secor. These socks are non-human capial k and (real) money m. They also hold nominal governmen bonds Therefore, he households sock of real governmen bonds is b = B / P. These hree socks are he households sae variable. Households also supply labor services h o he business secor. Price Level and Inflaion: There is a sequence of values of he composie oupu good in unis of money. This is he definiion of he price level P a dae. We break wih radiion and define he dae inflaion rae o be (3) = ( P 1 P)/ P. π + We do his because i simplifies and unifies noaion. When consrucing he real value of a variable wheher i is a sock, flows, or prices we simply divide is nominal value by P. B. 5

7 Technology Technology advances a rae γ and is labor augmening. Inpus o he business secor are he services of non-human capial k, he services of human capial h, and he services on real money sock m. The srucure of he producion funcion is as follows. Le z be an aggregae of he angible and human capial services where (4) z k h θ 1 θ = ((1 + γ ) ). For hese wo capial socks, one uni of sock provides one uni of services. We use h and k o denoe boh socks and service flows. The aggregae producion funcion is (5) y = Az m if m < λ z f 1 f y = Aλ z if m λz 1 f (saiaion region) The aggregae producion funcion is increasing and concave and displays consan reurns o scale. The marginal produc of m is zero if m λ z. Figure 1 depics an isoquan of he aggregae producion funcion. Figure 1: A Producion Funcion Isoquan 6

8 Budge Consrains Household The asses held by he household are money, governmen deb, and capial. The inflaion rae, possibly negaive, is π ; governmen lump-sum ransfers in cash or in kind are ψ ; r k and r m are he renal price of capial k and real cash balances m ; i and b im are he ineres raes paid on he wo forms of governmen deb. A primed variable is he nex-period value of ha variable. Wih hese noaional convenions, he household real budge consrain is c+ x+ m'(1 + π) + b'(1 + π) where x is capial invesmen given by = (1 τ) wh+ r k+ r m+ i b+ i m+ b+ m+ ψ, k m b m x= k' (1 δ ) k. This saes ha expendiures are for consumpion, invesmen, currency acquisiion, and governmen deb acquisiion and ha he receips are equal o he afer-ax labor income, renal income on (non-human) capial k, renal income on money, ineres paymens on he wo forms of governmen deb, and lump-sum ransfers received from he governmen. We use capial leers o denoe nominal quaniies. In nominal erms, he dae household s budge consrain is C + X + M+ 1+ B+ 1 = (1 ) Wh + rkk + rmm + imm + ibb + M + B +Ψ. Here, X is invesmen, so K 1 K X δ K + = +. Firm Given consan reurns o scale, revenue is equal o coss, so y= wh+ rk+ rm. k m Governmen The governmen s pure public good consumpion is g. The ineres raes on he wo ypes of governmen deb are i m and i b. The governmen s budge consrain (expendiures equal revenue plus defici) is g + ψ + i m+ i b= τ wh+ [ m'(1 + π) m] + [ b'(1 + π) b]. m b 7

9 Equivalenly, he governmen budge consrain, using capial leers o denoe nominal quaniies, is Equilibrium G +Ψ + i M + i B = Wh + ( M M ) + ( B B). m b Prices are { w, rk, rm, ib, im} 0. Equilibrium condiions are = (1) Households choose an opimal sequence of { c, h, k 1, m 1, b 1} 0 budge consrains = given prices and heir (2) Firms choose a each dae he value maximizing { h, k, m }, given period facor renal prices. (3) The governmen selecion of { g, ψ,, m 1, b 1, im, π} 0 is such ha is budge consrains + + = for all, given prices and he households decision variables, are saisfied. Commen 1: The firm faces a sequence of saic problems. Commen 2: The lis of elemens specifying governmen policy includes boh he prices and he quaniies of money i issues. I will no be possible o arge boh he price and he quaniy of money. 8

10 Secion 3: Balanced Growh Analysis The sae of he household is is holdings a he beginning of he period real money sock, real governmen deb sock, and real capial sock. One imporan poin is ha ineres raes are nominal. Nominal values of socks and flows grow a he rae of inflaion. Prices, wih he excepion of he ineres raes on governmen bonds and money, grow a he inflaion rae. In a balanced growh equilibrium, oupu, consumpion, invesmen, capial sock, money sock, deb sock, governmen expendiure, and ransfers all grow a rae γ. There are 19 variables o be deermined. They are { wr, k, rm, ib, im, hkmbk,,,, ', m', b', g, ψτπφ,,, g, φb, φ ψ }. The following se of equilibrium condiions are necessary and sufficien for a seady sae for a given policy and are used o find he seady sae. From he firm s maximizaion problem: hree marginal condiions are ha he marginal producs (MPs) of he facors of producion are equal o heir renal prices. There is he zero profi condiion given consan reurns o scale. Aggregae feasibiliy is anoher condiion. (E1) MPk = rk (E2) MPh = w (E3) MPm = rm (E4) c + x + g = rkk + rmm + wh (E5) y = c+ x+ g There is an issue as o wha he marginal produc of money is when m/ y = λ as he producion funcion is no differeniable a poins along ha line. The MP of money is bounded away from zero above he line and is zero below he line. The derivaive from below is he value of he MP of money for poins on his line. Variable y is he oupu of he business secor and does no include he governmen producion of money. From he households maximizaion problem: he inra-emporal marginal condiion is ha he marginal rae of subsiuion beween consumpion and leisure is equal o he raio of heir 9

11 afer-ax prices. The iner-emporal condiion is ha he marginal rae of subsiuion beween his and nex period s consumpions equals he raio of heir prices. These condiions are: (E6) αc\ (1 h) = (1 τ) w (E7) 1 + r = (1 + γ)(1 + r) + δ (E8) 1 + i = (1 + ρ)(1 + π)(1 + γ) (E9) ib = im + rm k b (E10) c + [ k ' (1 δ) k] + m'(1 + π) + b'(1 + π) = (1 τ) wh + r k + (1 + i ) b + (1 + i + r ) m + ψ. k b m m E8 and E9 are no-arbirage condiions. Because here is no uncerainy, he household reurn on money and governmen bonds mus be equal, and he reurn on governmen bonds mus be equal o he reurn on invesing in k. Balanced growh requires (E11) b' = (1 + γ ) b (E12) m' = (1 + γ ) m (E13) k' = (1 + γ ) k. The law of moion of capial is (E14) k' = (1 δ ) k + x. In each of he sequence of valuaion equilibria, here are hree governmen policy consrains and a governmen budge consrain (expendiures equal revenue plus defici): (E15) (E16) (E17) g = φ y g y = φ y y b= φ y b (E18) g + ψ + i m+ i b= τ wh+ [ m'(1 + π) m] + [ b'(1 + π) b]. m b 10

12 The se of policy variables is { i, m/ y, τπ, }. Values for wo of hese four variables are chosen. A m resricion is ha variables i m and m/ y are no boh chosen. This adds wo equaions o our se of necessary equaions. Thus, here are 20 equaions in 19 unknowns. By Walras law, one of he budge consrains is redundan. Baseline Economy for Balanced Growh Analyses A parameric se of economies has been specified. For he baseline economy, a parameer vecor is chosen so ha he baseline economy has a balanced growh ha roughly maches he U.S. economy in consumpion and invesmen shares, fracion of ime worked, asse socks o oupu raios, facor income shares, inflaion rae, and afer-ax reurn on capial. Table 1 displays he naional accouns for our chosen baseline economy. 11

13 Table 1 Naional accouns for he baseline economy Produc and Income Accouns Produc 1.08 Household Consumpion 0.68 Governmen Consumpion 0.05 Capial Invesmen 0.27 Money Invesmen 0.08 Income 1.08 Wages 0.64 Depreciaion of Capial 0.15 Capial Renal Income 0.19 Money Renal Income 0.01 Cenral Bank Profis 0.08 Governmen Accouns Receips 0.43 Tax Revenue 0.33 Money Issuance 0.08 Deb Issuance 0.03 Expendiures 0.43 Governmen Consumpion 0.05 Transfers o Household 0.25 Bond Services 0.04 Money Services 0.10 Asse Socks Capial 3.81 Money 1.50 Bonds 0.50 Oher Hours Worked 0.40 Labor Income Share 0.64 The annual growh rae is 3 percen. 12

14 The size of he sock of money may seem large. The 1.5 imes annual GNP sock is much larger han M2, which is abou 0.6. As poined ou by Williamson [2012], wo ypes of money are used for ransacion purposes. Much of he liquid governmen deb is held as cash reserves, and in 2015 he nominal reurn on his deb in he major advanced indusrial counries was near zero. Businesses make large paymens using he shadow banking secor and small paymens using he commercial banking sysem. The proposed arrangemen has only one ype of money. Because money services are a facor of producion, he naional accouns mus be revised so ha hey are consisen wih he heoreical framework being used. Money, like capial, provides services o he business secor; herefore, here mus be a Money Renal Income enry on he income side of he accouns and a Money Invesmen enry on he produc side of he accouns. The governmen coslessly produces money and earns monopoly profis. These profis are enered on he income side of he naional accouns as he enry Cenral Bank Profis. Table 2 displays he se of governmen policy parameers for he baseline economy. Noe ha he oal facor produciviy (TFP) parameer A is chosen for convenience so ha y is one, and hus levels and levels relaive o y are he same in he baseline economy. Also, he value of he saiaion parameer λ is somewha arbirary. I was se high enough so ha he baseline economy is no saiaed wih money. Table 2 Policy parameer values for he baseline economy Policy Parameers g / y governmen public goods share y / y ransfer share m/ y money-oupu raio b/ y privaely held gov. deb o oupu τ labor ax rae i ineres rae on money i m b ineres rae on gov. bonds π inflaion rae (annual %) % 7.21% 2.00% Table 3 liss he calibraed values of he preference and echnology parameers. 13

15 Table 3 Preference and echnology values for baseline economy Preference and Technology Parameers α relaive preference for leisure β discoun rae (annual) δ depreciaion rae (annual) γ echnical growh rae θ capial cos share φ money cos share A TFP λ money saiaion parameer Values

16 Exploraions In his secion, we will explore he consequences of various moneary policy regimes under our alernaive financial sysem. Our assessmen is ha echnology has changed sufficienly so ha exising moneary heory does no provide predicions as o he consequences of moneary policy regimes. Currenly, here is public discussion as o wheher he ineres rae should be increased and wha he inflaion rae arge should be. Exploraion 1 will explore he consequences of various money supply or, equivalenly, money ineres rae policy regimes. Exploraion 2 will explore he consequences of various inflaion rae argeing regimes. For his analysis, we focus only on moneary policy and herefore minimize he role of fiscal policy. This is done by keeping fiscal policy parameers as fixed as possible. Thus, he lump-sum ransfers and he size of public goods consumpion relaive o oupu are held fixed. We also keep he value of non-moneary governmen deb a a fixed fracion of oupu. The inflaion rae has ax consequences; his requires ha he labor ax rae be endogenous when comparing he balanced growh pahs of policies wih differen inflaion raes. The hree remaining policy variables ener he governmen budge consrain and herefore have some fiscal consequences. For our exploraions, he se of governmen policy variables includes he inflaion rae, he ax rae, and he ineres paid on money. In each exploraion, wo of hese policy variables are fixed, and wo are endogenous. Our measure of welfare across policy regimes is consumpion equivalen (CE) welfare. We repor he percenage change in consumpion ha mus be given o an individual o make him indifferen among worlds wih differen policy regimes. We acknowledge ha his measure of welfare is a seady-sae comparison for one ype and does no ake ino accoun ransiional concerns. Bu given ha he raio of non-human capial o oupu is he same for all balanced growh pahs, he consequences of ransiion for he policy regimes comparisons we consider should be small. 15

17 Exploraion 1 Money Supply Policy Regimes In response o he recession of 2008, hose who make U.S. moneary policy have experimened wih new moneary policy approaches. One of hese approaches was quaniaive easing, which increased he Federal Reserve s asses and liabiliies fourfold o over 4 rillion USD. The oher approach was paying ineres on excess reserves, which was permied beginning in These experimens resuled in a large increase in privae secor deposis and herefore in he money supply. For he se of regimes considered in his exploraion, he following policy variables are held consan a he following values: {g/ y = 0.05, y = 0.25, b/ y = 0.5}. The governmen spends 5 percen of oupu and ransfers 25 percen of oupu. The sock of governmen deb is 50 percen of oupu. This sysem keeps fiscal policy as fixed as possible. The se of policy variables whose value varies across he regimes considered is { im, m/ y, πτ, }. Two of hese policy variables are held fixed, and wo are endogenous. In he model, money sock and ineres on money are ied ogeher and canno be chosen independenly. 1.a Ineres on Money Regimes Firs, we explore ineres on money policies. The inflaion rae is held fixed a 2 percen. The ax rae varies endogenously in order o have governmen expendiures equal o governmen receips. Figure 2 shows ha a higher ax rae is associaed wih a higher ineres rae on money. Increasing he ineres on money increases he sock of money relaive o oupu. Thus, he oal ineres paid o owners of money is larger. Since he inflaion rae is fixed, a higher labor ax rae is needed for governmen expendiure o be equal o he sum of governmen receips and he defici. Wih hese policy regimes, he defici-o-oupu raio is fixed. 16

18 Figure 2: Labor ax raes for differen ineres rae arges Figure 3 shows ha here is a seady-sae welfare-maximizing ineres rae on money. A regime wih a higher ineres rae on money has a larger money services inpu o aggregae producion. However, a higher ineres rae regime also has a smaller labor inpu o aggregae producion. For low ineres rae regimes, he oupu increases because he larger money service inpu exceeds he oupu reducion arising from lower labor supply. For high ineres rae regimes, oupu decreases because he reducion in oupu from lower labor supply exceeds he increase in oupu from larger money services. Figure 3 shows ha, for our model economy, welfare is highes in a world where he ineres rae on money is approximaely 6 percen. Figure 3: Seady-sae welfare indicaor for various ineres rae arges 17

19 The nominal ineres rae on governmen bonds is 7.2 percen. Why would he welfaremaximizing ineres rae policy regime no compleely eliminae he gap beween he ineres on money and bonds; ha is, why is moneary saiaion no opimal? Because we have fixed inflaion and governmen spending, a labor ax rae change is needed for balance in he governmen accouns. This highlighs he imporance of fiscal response o moneary policy. In a regime ha arges he inflaion rae, fiscal policy mus respond o changes in ineres rae policy. 1.b Money Sock Regimes Nex, we explore money sock policy regimes. We fix he labor ax rae a 52 percen and allow he inflaion rae o vary endogenously o ensure ha governmen expendiures are equal o governmen receips. We consider money sock policies associaed wih boh saiaion and nonsaiaion. Figure 4 shows ha a larger money sock regimes has a higher seady-sae welfare. However, increasing he money sock increases welfare only up o he saiaion poin, beyond which increasing he money sock does no increase welfare. For policy regimes wih saiaion, money and governmen deb are equivalen. In hese regimes, money plus governmen deb is a consan, and consequenly here is an unimporan indeerminacy. Figure 4: Seady-sae welfare indicaor for various money sock regimes Saiaed Economies 18

20 In figure 5, we see ha for saiaed money sock regimes, he renal price of money services is zero. For hese regimes, he marginal produc of money is equal o he marginal cos of producing money (assumed o be zero). Ineres raes on money and bonds are equal, and money and bonds are idenical governmen deb insrumens. In he Unied Saes, policies ha increase he money sock are enaced by he cenral bank purchasing governmen bonds from banks in exchange for money. Since money and bonds are idenical in saiaed economies, he spli of oal governmen deb beween money and bonds is indeerminae. In he saiaed region, he sum of money and bonds is consan. The Friedman rule leads o saiaion in economies in which money is no a facor of producion. The Friedman rule is o deflae a he real ineres rae [Friedman, 1960]. The reurn on currency is hen equal o he reurn on capial. In he moneary sysem considered here, we eliminae he inefficiency no by deflaing a he real ineres rae bu by choosing a money sock regime ha leads o a saiaed economy. We call his sae Friedman saiaion. When money is a facor of producion, Friedman saiaion can occur wih a range of inflaion arges, including posiive inflaion. This feaure allows for Friedman saiaion wihou he difficulies associaed wih negaive inflaion raes [see McAndrews, 2015]. For example, Friedman saiaion occurs when he arge inflaion rae is 2 percen, he ax rae is 53.5 percen, and he raio of money sock o oupu is Figure 5: Marginal produc of money for various money sock regimes Saiaed Economies 19

21 Exploraion 2 Inflaion Rae Targeing The inflaion rae has been of paricular ineres of lae. The U.S. Federal Reserve Board has been vocal abou waning o increase he inflaion rae o he normal rae of 2 percen. Many have been puzzled by he persisenly low inflaion rae, which is currenly near zero and is expeced o say under 2 percen for he nex 30 years. 5 However, is low inflaion a bad hing? Since price sabiliy is par of a Federal Reserve congressional mandae, a heory ha can address inflaion rae argeing regimes is needed. In his secion, he ineres rae on money is held fixed so ha we can focus on he consequences of inflaion rae argeing regimes. Various inflaion rae policies are chosen. We consider only policies for which here is no saiaion. This resrics he inflaion rae arge o be greaer han or equal o 1.9 percen. The ax rae varies endogenously in order o have governmen expendiures equal o governmen receips. Since ineres on money is held fixed, he money sock also varies endogenously across policies. Figure 6 shows ha a higher labor ax rae is associaed wih a lower inflaion rae regime. Inflaion is a form of ax on money. A higher inflaion rae regime has a lower labor income ax rae, higher labor supply, and higher consumpion. This raises he ineresing possibiliy of using a money ax o reduce he labor disorion creaed by financing he governmen hrough labor income ax. Figure 6: Labor ax raes for inflaion rae argeing regimes 5 Subrac he expeced reurn on inflaion-indexed Treasury securiies from he expeced reurn on nominal Treasury securiies o see his. 20

22 Figure 7 shows seady-sae welfare as measured by consumpion equivalens (CEs) for various inflaion rae argeing regimes. Since higher inflaion is associaed wih lower labor income ax, in a higher inflaion rae regime, more labor is supplied and he consumpion level is higher. The higher inflaion increases hours worked (decreasing welfare) bu also increases consumpion (increasing welfare). This exploraion shows ha differen inflaion raes have, in fac, very lile impac on seady-sae welfare. Figure 7: Seady-sae welfare indicaor for various inflaion rae arges 21

23 Possible Problems and Advanages Some problems wih his sysem are apparen. Privacy proecion would need o be considered. We will no deal wih his more general problem here. Also, in an environmen in which banks are purely ransacional insiuions, shadow banking could be an issue. We offer a possible soluion o he shadow banking issue. To effecively eliminae businesses ha borrow low from one group and lend high o anoher, he governmen could ax ne ineres income a a 100 percen rae for limied liabiliy businesses. This approach would remove any incenive o engage in shadow banking. Our proposed reforms also have possible advanages. Firs, bank runs would be prevened because banks would have nowhere o run. 6 Whenever a ransacion akes place beween privae agens, one pary's demand deposi accoun is credied by he amoun of he ransacion, and he oher pary s demand deposi is debied by he same amoun. Second, our reforms would eliminae he need for cosly regulaions, as is associaed wih he U.S. deposi insurance sysem. A 100 percen reserve requiremen would eliminae he need for sress ess and regulaory eniies o ensure ha banks are no aking on excessive risk. These aciviies cos abou one-half percen per year per dollar deposied a commercial banks. This amoun represens a non-negligible cos. One claimed cos of he moneary sysem we explore is ha i would increase he cos of financing because of he higher commercial bank equiy cos. This argumen is ha wih 100 percen reserve banking, bank equiy would be higher and bank equiy is cosly. Admai, DeMarzo, Hellwig, and Pfleiderer [2011] poin ou, however, ha bank equiy is no cosly. Wih our moneary sysem, demand deposis are wha are households and he businesses choose o hold. Anoher claim ofen made is ha fracional reserve banking is valuable in providing mauriy ransformaion, because agens wan o lend shor and borrow long. The agens in our world can hold as much money as hey wan; ha is, hey can lend as much as hey wan o shor. There is no need for mauriy ransformaion. We emphasize ha much needs o be done before he heory can be used o make predicions as o he consequences of alernaive policy. As done in McGraan and Presco [2016] for he consequences of an alernaive ax policy regime, demographic projecions mus be made and inroduced ino he model economy being used. In addiion, he equilibrium ransiion pah o he balanced growh pah for he alernaive policy regime mus be deermined. 6 A number of economiss have proposed a 100 percen reserve for demand deposis as an arrangemen ha is no prone o bank runs. They include Fisher [1936] and Friedman [1960], and more recenly Cochrane [2014], Presco [2014], and Smih [2013]. 22

24 Concluding Commens We explore an alernaive financial sysem ha is possible given he curren sae of informaion processing echnology. Before his sysem could be implemened, exising law would have o be changed o permi business enerprises o hold ineres-bearing money. This exploraion is necessary because, in our assessmen, exising heory does no provide predicions abou he consequences of alernaive moneary policy regimes. The rial-and-error approach ha characerizes curren moneary policy is fraugh wih danger; herefore, beer heory is needed. We hope ha his paper fosers fruiful heoreical work on reforming he paymen sysem. By inegraing money ino valuaion heory, he ools of aggregae public finance can be and are applied. This is no he firs use of hese ools o quaniaively predic he consequences of alernaive moneary policy regimes. These sudies modeled he households holding of M1, which was held for ransacion purposes. I was moivaed by Melzer s [1963] finding of a reasonably sable M1 velociy depending on he shor-erm ineres rae. Lucas and Sokey [1987] develop a ransacion-based heory of his ransacion demand for money. Cooley and Hansen [1989] inroduced he Lucas-Sokey heory wih cash and credi goods ino he neoclassical growh model and carried ou a quaniaive general equilibrium analysis of he cos of modes inflaion. This ransacion-based heory does no accoun for he large holding of cash reserves by businesses. Hodrick [2013] repors ha in 2013, he cash reserves of American business were nearly equal o annual GNP. This does no include he cash reserves of businesses in he household secor. Households accumulae cash reserves in order o be able o make a down paymen on a residence or a car. One implicaion is ha much of M3 is made up of he cash reserves held by household businesses. Cash reserves are held by businesses because hey are producive asses ha faciliae he operaion of he business secor. 23

25 References Admai, Ana R., Peer M. DeMarzo, Marin F. Hellwig, and Paul Pfleiderer Fallacies, Irrelevan Facs, and Myhs in he Discussion of Capial Regulaion: Why Bank Equiy is No Expensive. Sanford GSB Research Paper No Cochrane, John H., "Moneary Policy wih Ineres on Reserves. Journal of Economic Dynamics and Conrol, 49 (December), Cooley, Thomas F., and Gary D. Hansen The Inflaion Tax in a Real Business Cycle Model. American Economic Review, 79 (4), Fischer, Sanley Money and he Producion Funcion. Economic Inquiry, 12 (4), Fisher, Irving % Money and he Public Deb. Rev. ed. New York: Adelphia. Friedman, Milon A Program for Moneary Sabiliy. New York: Fordham Universiy Press. Friedman, Milon The Opimum Quaniy of Money. In The Opimum Quaniy of Money and Oher Essays. Chicago: Aldine. Hodrick, Laurie Simon Are U.S. Firms Really Holding Too Much Cash? SIEPR Policy Brief, July. Lucas, Rober E., Jr., and Nancy L. Sokey Money and Ineres in a Cash-in-Advance Economy. Economerica 55 (3), McAndrews, James Negaive Nominal Cenral Bank Policy Raes: Where Is he Lower Bound? Speech, Federal Reserve Bank of New York, May 8. McGraan, Ellen R., and Edward C. Presco On Financing Reiremen wih an Aging Populaion. Quaniaive Economics, forhcoming. Melzer, Allen H The Demand for Money: The Evidence from he Time Series. Journal of Poliical Economy, 71 (3), Orphanides, Ahanasios, and Rober Solow Money, Inflaion, and Growh. In Handbook of Moneary Economics, Vol. 1, edied by B. M. Friedman and F. H. Hahn, Amserdam: Elsevier. Presco, Edward C Ineres on Reserves, Policy Rules and Quaniaive Easing. Journal of Economic Dynamics and Conrol, 49 (December),

26 Sargen, Thomas J., and Neil Wallace Some Unpleasan Monearis Arihmeic. Federal Reserve Bank of Minneapolis Quarerly Review, 5 (3), Sinai, Allen, and Houson H. Sokes Real Money Balances: An Omied Variable from he Producion Funcion? Review of Economics and Saisics,54 (3), Smih, Andrew D How o Make a Run-Proof Bank: Achieving Mauriy Transformaion wihou Fracional Reserves. Paper presened a Ausralian Conference on Economics, July 10. Williamson, Sephen D "Liquidiy, Moneary Policy, and he Financial Crisis: A New Monearis Approach." American Economic Review, 102 (6):