Fiat Value in the Theory of Value. Staff Report 530 Revised June 2017

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1 Fia Value in he Theory of Value Edward C. Presco Arizona Sae Universiy, Ausralian Naional Universiy, and Federal Reserve Bank of Minneapolis Ryan Wessel Arizona Sae Universiy Saff Repor 530 Revised June 2017 DOI: hps://doi.org/ /sr.530 Keywords: 100 percen reserve banking; Money in producion funcion; Ineres rae argeing; Inflaion rae argeing; Friedman moneary saiaion JEL classificaion: E0, E4, E5, E6 A preliminary version of his paper circulaed under he ile Moneary Policy wih 100 Percen Reserve Banking: An Exploraion. The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem. Federal Reserve Bank of Minneapolis 90 Hennepin Avenue Minneapolis, MN hps://

2 Fia Value in he Theory of Value Edward C. Presco 1 Ryan Wessel 2 March 17, 2016 Absrac We explore moneary policy in a world wihou currency. In our world, 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 he balanced growh pahs for a se of money ineres rae arge policy regimes. Besides his ineres rae, he only policy variable ha differs across regimes is eiher he labor income ax rae or he inflaion rae. We find ha Friedman moneary saiaion wihou deflaion is possible. We also examine a se of inflaion rae argeing regimes. Here, he only oher policy variable ha differs across policy regimes is he ax rae. There is a sequence of markes wih oucome in each marke being a Debreu valuaion equilibrium, which deermines he vecor of asses and liabiliies households ake ino he subsequen period. Evaluaing a policy regime is an advanced exercise in public finance. Moneary saiaion is no opimal even hough money is cosless o produce. 1 Arizona Sae Universiy; Ausralian Naional Universiy; Federal Reserve Bank of Minneapolis. edward.presco@asu.edu 2 Arizona Sae Universiy. ryan.wessel@asu.edu 1

3 Secion 1: Inroducion Informaion processing echnology is rapidly advancing and is changing he naure of he paymen sysem. Currency is being used less and less o carry ou ransacions and o serve as a sore of value. Indeed, a currency-less moneary sysem has become feasible and may be implemened a some poin. All moneary sysems need a uni of value, and he ransiion o a currency-less sysem would necessiae he creaion of fia value. A quesion is wheher moving o a fia value moneary sysem is socially desirable. This paper is a sep oward addressing his imporan social quesion. The equilibrium concep used in his sudy is Debreu s [1954] valuaion equilibrium. The commodiy space in his framework is resriced only o being a linear opological space. In his sudy, here is a sequence of valuaion equilibria wih households enering a period wih socks of asses and liabiliies. In he accouning period, economic oucomes are a valuaion equilibrium. These oucomes, among oher hings, specify he socks of asses and liabiliies ha households ake ino he subsequen accouning period. This is he way ha he daa are repored. These daa are used o consruc he naional income and produc accouns and balance shees of he household and governmen secors. Large amouns of cash reserves are held by businesses. The amoun relaive o GDP is of he order of 1.3 annual GDP. Businesses hold hese low-reurn asses for a reason namely, for he services hey provide. This leads us o rea he services of he money as a facor of producion, or inpu o he aggregae producion funcions. 3 Our producion funcion is consisen wih he money demand funcion when nominal ineres raes are posiive. I is also consisen wih exended or even permanen periods of zero nominal ineres raes. Wih he fia value moneary sysem considered here, here is no currency, and for some policy regimes, he nominal ineres rae paid on he money sock is negaive and he real naural ineres rae is posiive. A parameric se of neoclassical growh economies is considered. The benchmark economy is seleced o mach seleced facs displayed by he pre-2008 U.S. economy given he values of he policy parameers in ha period. For a se of policy regimes, he seady sae of he benchmark economy is deermined and comparisons made wih he seady sae of a number of policy regimes. These regimes include ineres rae argeing policy regimes and inflaion rae argeing regimes. For he ineres rae regimes, boh he inflaion rae and he ax rae canno be consan across regimes. We consider boh a se of regimes for which he inflaion rae is he same and he ax rae is differen and a se of regimes for which he ax rae is he same and he inflaion rae is differen. 3 Many have suggesed inroducing money ino he producion funcion, including Fischer [1974], Friedman [1969], Sinai and Sokes [1972], and Orphanides and Solow [1990]. 2

4 One finding is ha in our currency-less moneary sysem, here can be Friedman saiaion wih posiive inflaion argeing regimes. This is possible because here is no currency ha can be used as a sore of value. Anoher finding is ha moneary and fiscal policy canno be compleely separaed. Wih he inflaion argeing regimes, he ax rae on labor income is endogenous. This is because wih ineres rae argeing, he inflaion rae has ax consequences for he governmen budge ideniy. We find ha evaluaing moneary policy is an advanced exercise in public finance. In our model economies, here is a complee separaion of he paymen/ransacion moneary sysem from he asse-managemen funcion sysem of he financial secor. Effecively, i is a 100 percen reserve sysem. Limied liabiliy financial businesses ha borrow from one group a a low rae and lend o anoher a a higher rae are no allowed. Financial businesses ha pool asses of households and he businesses hey own and manage hese asses are permied. Wih hese businesses, invesors share he reurns. In he Unied Saes, mos business financing is currenly done his way. In our model world, here are no gains from having insiuions ha accep demand deposis and originae loans in order o make mauriy ransformaion. Thus, here are no social gains from having fracional reserves banking. Furher, here is no oo big o fail problem for financial insiuions. The paper is organized as follows. Secion 2 specifies he parameric se of neoclassical growh model economies used in his sudy. In Secion 3, he benchmark economy in his se is specified by he policy parameers as well as he demographic, preference, and echnology parameers. The model economy in our se maches he pre-2008 U.S. economy along seleced dimensions. Secion 4 ransforms he variables in he sandard way so ha here is seady sae in he ransformed variables. The only policies ha are considered are hose for which here is a seady sae. For any such policy, here is a unique seady-sae equilibrium. Secion 5 compares he balanced growh pah for hree ses of policy regimes. A policy is characerized by he values of seven variables. For a policy regime se, one of he seven variables is he arge variable, and one variable is endogenous across regimes. For hree ses of policy regimes, he seady saes are deermined. One has a money ineres rae arge wih he ax rae endogenous. Anoher has a money ineres rae arge wih he inflaion rae endogenous. The hird se has an inflaion rae arge wih he ax rae endogenous. Secion 6 discusses advanages and possible problems wih he currency-less moneary sysem. Secion 7 offers concluding commens. Secion 2: The Parameric Se of Model Economies The analysis is seady sae, and here is no uncerainy in living sandards. Consequenly, i does no maer wheher an overlapping generaions or 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 3

5 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 B. 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 for 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) π = ( P+ 1 P)/ P. 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. Aggregae Producion Funcion 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. Aggregae oupu is y. Variable z is he Cobb-Douglas aggregae of he angible and human capial services inpus: θ 1 θ (4) z = k ((1 + γ ) h). For hese wo socks, one uni of sock provides one uni of services. We herefore use h and k o denoe boh he socks and he service flows. 4

6 Wih consan reurns o scale, one isoquan suffices o define he aggregae producion funcion. The isoquan for y = A is ploed in Figure 1. In he hree regions, he marginal producs of money are y y Region A = (1 f) if m < λ2 z m m y y m/ z λ 1 Region B = (1 f) if λ2z m λ1z m m λ2 λ1 y Region C = 0 if m > λ1 z m In Region A, he elasiciy of subsiuion beween money m and composie inpu z is one. In his range, he normal demand for money relaion holds. In Region C, he marginal produc of money is zero; ha is, here is money saiaion. In Region B, he marginal produc of money declines o zero as m/ z declines from λ 2 o λ 1. 5

7 Figure 1: Producion Funcion Isoquan If m= λ2z, he brackeed erm in he second line is one and he marginal produc of money is equal o ha in he consan elasiciy region. Similarly, if m= λ1z, he brackeed erm in he second line is zero and he marginal produc of money is equal o ha in he zero elasiciy region. The consan reurns o scale producion funcion wih hese isoquans is coninuously differeniable. The aggregae producion funcion given he parameers { λ1, λ2, φθ,, A} is f 1 f m if y = Az m < λ z f 1 f m (,, 1, 2, ) if 2 1 y = Az T m z λ λ f λ z m λ z y = Aλ z G( λ, λ, f) if m> λ z 1 f , where he funcions T and G are λ2 (1 φ) (1 φ) m λ ( 2 ) 2z λ λ2 λ1 λ2 λ1 z (,, λλφ 1, 2, ) = ( ) e Tmz m 6

8 λ2 (1 φ) 2 λ2 λ1 φ 1 λ G( λλφ 1, 2, ) = ( ) e. λ 1 The aggregae producion funcion is increasing and concave, displays consan reurns o scale, and is coninuously differeniable. 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 7

9 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 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}. Equilibrium condiions are 0 = (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, i, π } is such ha is budge consrains m = 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 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,, r, i, i, hkmbk,,,, ', m', b', g, ψτπφ,,,, φ, φ ψ }. k m b m g b 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 Variable y is he oupu of he business secor and does no include he governmen producion of money. From he households maximizaion problem: he inraemporal marginal condiion is ha he marginal rae of subsiuion beween consumpion and leisure is equal o he raio of heir afer-ax prices. The ineremporal condiion is ha he marginal rae of subsiuion beween consumpion in his period and consumpion in he nex period equals he raio of heir prices. These condiions are (E6) αc\ (1 h) = (1 τ) w 9

11 (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 The se of policy variables is { im, m/ y, τπ, }. Values for wo of hese four variables are chosen. A 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. Secion 4: Baseline Economy for Balanced Growh Analyses 10

12 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 2 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 Secion 5: Three 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 predic 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. 4 Thus, he lumpsum 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 are small. 4 Sargen and Wallace [1981], in heir dynamic general equilibrium analysis, find ha moneary and fiscal policy canno be compleely separaed. 15

17 Exploraion 1: Money Supply wih Endogenous Tax Rae 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 Ocober These experimens resuled in a large increase in privae secor deposis and herefore a large increase in he money supply. For he se of regimes considered in his exploraion, he following policy variables are held consan a he values shown: { 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. Given he producion funcion and preferences, he real or naural ineres rae is deermined. In addiion, given he inflaion rae, he nominal ineres raes on he wo forms of governmen deb as well as he real renal price of money are deermined. From he producion funcion laid ou in full deail in he Appendix, he m/ y raio is deermined. 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. Exploraion 2: Money Sock Policy wih Inflaion Rae 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 larger money sock regimes have 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 3: Inflaion Rae Targeing wih Endogenous Tax Rae Regimes 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 Secion 6: 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 deposi insiuions, shadow banking migh develop and pose a problem. This poenial shadow banking problem has a possible soluion. 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 deposiors would have no place o run o. 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 accoun 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 and Hellwig [2013] esablish ha bank equiy is no cosly. Wih our moneary sysem, demand deposis are wha households and 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 shor as much as hey wan. There is no need for mauriy ransformaion. We emphasize ha much needs o be done before he heory can be used o predic 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 Secion 7: 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 warraned 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. Wih beer heory, alernaive moneary sysems can be assessed wihou experimenaion. We hope ha his paper fosers fruiful heoreical work on reforming he paymen sysem in response o advances in informaion processing echnology. 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. Previous 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 businesses were nearly equal o annual GNP. This does no include he cash reserves of businesses in he household secor. Households accumulae cash reserves so ha hey can buy a car or make a down paymen on a residence. 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., and Marin F. Hellwig The Bankers New Clohes: Wha s Wrong wih Banking and Wha o Do abou I. Princeon, NJ: Princeon Universiy Press. 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), Debreu, Gerard Valuaion Equilibrium and Pareo Opimum. Proceedings of he Naional Academy of Sciences of he Unied Saes of America, 40 (7), 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, 8 (1), 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. 24

26 Presco, Edward C Ineres on Reserves, Policy Rules and Quaniaive Easing. Journal of Economic Dynamics and Conrol, 49 (December), 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):